Dynamics doi: 10.3390/dynamics6030025

Authors: Laira Pinto Borges Júnia Natália Mendes Batista Amarílis Severino e Souza Rodrigo Béttega

The accuracy of CFD-DEM simulations of particulate systems strongly depends on the proper characterization of particle–particle and particle–wall interaction parameters. In this study, the coefficients of restitution, static friction, and rolling friction for ABS–ABS and ABS–acrylic interactions were experimentally determined for acrylonitrile butadiene styrene (ABS) spheres using free-fall, inclined-plane, and launch-ramp tests, respectively. The obtained parameters were subsequently applied in CFD-DEM simulations of a three-dimensional conical spouted bed operating with different solid loads. In parallel, experimental fluid dynamic tests were conducted to obtain characteristic pressure drop curves and determine the minimum spouting velocity. The experimental results exhibited the typical behavior of spouted beds, including hysteresis between the curves obtained by increasing and decreasing the inlet air velocity and higher minimum spouting velocities at greater solid loads. The CFD-DEM simulations successfully reproduced the main hydrodynamic features of the system, yielding deviations of 0.9%, 6.9%, and 20.5% for the minimum spouting velocities corresponding to solid loads of 400 g, 300 g, and 200 g, respectively. A comparison with the interaction parameters reported in the literature showed that the coefficients obtained through direct measurement provided better agreement between the experimental and simulated results. These findings highlight the importance of accurately characterizing interaction parameters to achieve reliable CFD-DEM simulations of spouted bed systems.

Dynamics doi: 10.3390/dynamics6030024

Authors: Yargo P. Souza Felipe S. Loureiro Delfim Soares Walnório G. Ferreira Webe J. Mansur

A new family of fourth-order accurate time integration schemes is developed by introducing two complex time sub-steps into the classical Newmark family of second-order algorithms. These sub-steps consist of a pair of complex conjugate numbers, enabling the triangularization of a complex-valued effective stiffness matrix. The proposed formulation can be easily implemented in existing codes with only minor modifications to the standard Newmark algorithm. The solution is composed of both real (physical) and imaginary components. The real component provides fourth-order accuracy even in the presence of external loads and physical damping, while the imaginary component offers additional insight into the distribution of numerical errors, an original feature not previously reported for implicit formulations. Compared to the classical Newmark method with a time-step size four times smaller, the proposed scheme exhibits significantly lower numerical dissipation and dispersion errors. Furthermore, the sub-step procedure extends the critical time step of conditionally stable members of the Newmark family by a factor of 3. The numerical analysis performed in the proposed time integration method, along with the results obtained for dynamic structural problems, including a complex three-dimensional (3D) application, clearly demonstrate that the method outperforms both Fung’s fourth-order complex scheme and the classical Newmark approach in terms of accuracy.

Dynamics doi: 10.3390/dynamics6020023

Authors: North Yates Fernando Ponta Joshua Reese Alayna Farrell

A fundamental aspect in the design of modern utility-scale wind turbines is predicting the vibrational response of their blades when excited by gust pulses of various amplitudes and frequencies in atmospheric flow. Improved designs based on accurate blade-response predictions can prevent extreme oscillations, reduce fatigue stress, and extend turbine’s operational life. In previously published works, the authors introduced and applied a novel technique that provided an energy-based Reduced-Order Characterization (ROC) for the oscillatory response of wind turbine rotors, when excited by wind gust pulses with different combinations of timespan and amplitude under various operational conditions. Those studies established the universal nature of the ROC by expressing the turbine aeroelastic response as a vibrational Stability Map, plotted in terms of non-dimensional quantities, which could be applied to turbines of any size that share a similar blade construction. In the present paper, the authors will expand the ROC technique beyond the scope of their previously published studies, to analyze the Multi-Modal Response observed in regions located at the external boundaries of the stable zones of the Stability Map. This will provide valuable information about rotor stability behavior in extreme turbine operational conditions which were previously unexplored.

Dynamics doi: 10.3390/dynamics6020022

Authors: Sarp Adali

Variational principles and variationally consistent boundary conditions are presented for double-layer graphene nanoribbons undergoing time-dependent and free vibrations. The van der Waals forces acting in the core region are modelled as shear and tensile–compressive effects. The nonlocal constitutive formulation of the problem is based on the sandwich beam model in order to represent the graphene nanoribbon layers as faces and van der Waals forces acting in the core region. The constitutive equations which govern the vibrations of the nanoribbons are in the form of four coupled partial differential equations involving the in-plane and out-of-plane deflections. The first part of the study involves the derivation of the variational principle for the system undergoing time-dependent vibrations. Hamilton’s principle is formulated based on the kinetic and potential energies of the system. The next section involves the freely vibrating nanoribbon system and the formulation of the variational principle for this case is given. Based on this formulation, the expressions for the Rayleigh quotients are obtained for the longitudinal natural frequency and the transverse natural frequency. The last section involves the derivation of the variationally consistent boundary conditions and the expressions for the shear force and moment at the boundaries.

Dynamics doi: 10.3390/dynamics6020021

Authors: João Pedro Spadão Rui Marcos Grombone Vasconcellos Murilo Sartorato Wilian Miranda dos Santos

Lift-plus-cruise electric vertical takeoff and landing (eVTOL) aircraft exhibit complex stability characteristics during transition flight, when rotor-borne and wing-borne regimes coexist. This work investigates the dynamic stability of a lift-plus-cruise eVTOL using a nonlinear six-degree-of-freedom model incorporating aerodynamic forces, tractor propulsion, and vertical lifter dynamics. Linearization about representative trimmed conditions enables longitudinal and lateral–directional modal analysis. The results identify a critical near-stall region where lift-curve slope reduction markedly decreases short-period damping. Residual lifter authority partially compensates for this degradation, improving stability in the transition regime. To ensure smooth control transfer, an airspeed-dependent blending strategy between hover and fixed-wing controllers is implemented. Comparative analyses show that a sigmoid blending law improves the minimum short-period damping ratio relative to a linear strategy while preserving similar overall damping variation. Closed-loop simulations of a complete mission profile demonstrate the effectiveness of the proposed approach and reveal an asymmetric dynamic response between hover-to-forward and forward-to-hover transitions. These findings provide a physically grounded explanation for stability degradation during transition and establish practical guidelines for control authority blending in lift-plus-cruise eVTOL aircraft.

Dynamics doi: 10.3390/dynamics6020020

Authors: Anna Markhotok

The effect of atom size on the shock-wave structure in a binary monatomic gas mixture with Rydberg atoms has been investigated. The problem was solved numerically using the system of hydrodynamic equations in argon gas for the atom-size ratios between 2 and 100, T = 1500 K, and the density between 1017 and 1020 m−3. It was found that the presence of larger-sized atoms in the mixture results in shock front splitting that is on the order of the mean free path for this component. The results could be of interest in supersonic plasma dynamics and in astrophysics, studying shock waves in the environments where high-n Rydberg states are present.

Dynamics doi: 10.3390/dynamics6020019

Authors: Zhao Ni Xinfeng Zhang Jie Bai Bing Rao Jiawen Dai Bangji Zhang Zheshuo Zhang

In high-rise firefighting scenarios, unmanned aerial vehicles (UAVs) equipped with water-spraying systems are subjected to high-intensity and rapidly time-varying reaction forces induced by high-speed water jets. These forces introduce mismatched uncertainties with unknown bounds and make stable flight control particularly challenging. To address this problem, this paper proposes an adaptive robust constraint-following control (ARCFC) strategy for vector–rotor UAVs (VRUAVs). The controller is developed directly for the strongly nonlinear dynamics of the VRUAV without resorting to model linearization. Within a constraint-following-based nonlinear regulation framework, water-jet effects are explicitly modeled as rapidly time-varying uncertainties with unknown bounds, and an adaptive law is introduced to estimate conservative uncertainty bounds online for robust compensation. Lyapunov-based analysis is conducted to establish the uniform boundedness and uniform ultimate boundedness of the closed-loop system, and simulation results are presented to verify the effectiveness of the proposed approach. Compared with representative conventional control methods, the proposed ARCFC strategy provides improved disturbance-rejection capability and enhanced flight stability under demanding firefighting conditions.

Dynamics doi: 10.3390/dynamics6020018

Authors: Sebastiano Ettore Spoto

A recent two-layer theory for long-runout turbidity currents explains sustained bypass by allowing a dense lower layer to exchange mass with a more dilute upper layer while avoiding rapid over-thickening. Here, a morphodynamic extension is developed that couples suspended load and bed exchange while treating the two-layer hydrodynamics as a prescribed background. A suspended-sediment balance with bed exchange and Exner’s equation are written on that background, the depositional state variable B=Es/(rC) is introduced, and an exact nonlinear evolution equation for B is derived within the prescribed-background setting. In the weak-exchange limit this equation reduces to an algebraic onset criterion, thereby identifying the regime in which the simpler threshold is valid. Applied to an Amazon-like local-normal-flow reconstruction, the model shows that finite exchange shifts depositional onset upstream relative to the weak-exchange estimate. Background-fidelity checks, grid-refinement tests and closure/inlet sensitivities are reported to delimit the quantitative use of the reduced application. The framework is therefore best interpreted as a coupled reduced theory for suspended load and bed exchange on a prescribed two-layer bypass background rather than a fully hydro-morphodynamic closure.

Dynamics doi: 10.3390/dynamics6020017

Authors: Wasaif H. R. Alruwaele Jitesh S. B. Gajjar

First of all thank you for your comments [...]

Dynamics doi: 10.3390/dynamics6020016

Authors: Carlos A. Valentim Sergio A. David

Computational modeling and machine learning have impacted several different areas of science and accelerated advancements in multiple venues. Yet traditional machine learning models have many well-known drawbacks: besides demanding a significant amount of data, they may fail to generalize beyond training data, are often treated as “black boxes”, and may predict physically inconsistent results. In response to these limitations, Physics-Informed Machine Learning (PIML) has emerged as a new area that integrates domain knowledge, such as energy or mass conservation, directly into data-driven algorithms. This review paper examines the foundations and main strategies of PIML, organizing the approaches into three categories: automated discovery and system identification, continuous-time modeling, and operator learning. In addition, Physics-Informed Neural Networks are analyzed in a dedicated section that covers architecture fundamentals, forward and inverse problem formulations, loss function design and implementation challenges. The paper also presents a survey of interdisciplinary applications of PIML in materials science, biomedical engineering, and fractional calculus. In this context, the review also analyzes open challenges and outlines future directions in the field.

Dynamics doi: 10.3390/dynamics6020015

Authors: Asterios Pantokratoras

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Dynamics doi: 10.3390/dynamics6020014

Authors: Noha M. Hafez

The physical characteristics of a heated non-Newtonian Eyring–Powell fluid in a conduit with sinusoidally moving ciliated walls are highlighted in this analytical study. The impact of mass transmission is considered in this model. The dimensional form of the governing equations is simplified using the long-wavelength estimation and suitable transformations to produce a set of dimensionless partial differential equations with pertinent boundary conditions. To solve it, the perturbation technique is utilized applying polynomial solutions. The solutions of temperature, concentrations, and velocity profiles are obtained, and then are further analyzed through graphical results. An accurate mathematical solution for the pressure gradient is achieved by integrating the velocity profile over the elliptic cross-section. The non-Newtonian Eyring–Powell fluid flows quicker through this vertical ciliated elliptic duct than the Newtonian fluid. Moreover, the cilia elliptic movement eccentricity and the wave number for metachronal wave have a dual effect on the velocity profile. Increasing the dimensionless flow rate and occlusion leads to an increase in closed contour size, as seen in the streamline description.

Dynamics doi: 10.3390/dynamics6020013

Authors: Edward Bormashenko

A graph-theoretical approach to the analysis of motion and rest in many-body systems is developed. Point bodies are represented as vertices of a complete bi-colored graph, termed the motion–rest graph (MRG). Two vertices are connected by a rust-colored edge when the corresponding bodies are at rest relative to each other; that is, when their mutual distance remains constant in time, bodies moving relative to each other are connected by a cyan edge. It is shown that the logical structure of the relation “to be at rest relative to each other” determines the combinatorial structure of the graph. For one-dimensional motion in classical mechanics and special relativity, this relation is reflexive, symmetric, and transitive, and therefore defines an equivalence relation. As a result, rust edges form disjoint complete cliques corresponding to rest-clusters, and the MRG becomes a semi-transitive complete bi-colored graph that is completely determined by the partition of the bodies into equivalence classes. It is proven that any such graph on five vertices necessarily contains a monochromatic triangle. For two- and three-dimensional motion, the transitivity of relative rest generally fails because constant mutual distance does not imply an equality of velocities in the presence of rotational degrees of freedom. In this case, the MRG is non-transitive, and the Ramsey threshold becomes the classical value R(3, 3) = 6. The approach is extended to mixed sets containing moving bodies and reference points, including the center of mass of the system. Generalizations to general relativity and quantum mechanics are also discussed. In general relativity, transitivity of relative rest is generically lost because global rigid congruences do not generally exist. In quantum mechanics, exact transitivity survives only at the level of idealized delocalized eigenstates, whereas for physically realizable localized states, the notion of mutual rest becomes only approximate. The results demonstrate that the interplay between kinematics, logical properties of relational motion, and Ramsey-type combinatorial constraints gives rise to unavoidable ordered substructures in many-body systems.

Dynamics doi: 10.3390/dynamics6020012

Authors: Ihor Hrytsay Petro Pukach Myroslava Vovk

The results of the development and practical application of a comprehensive system for studying gear cutting processes are presented. The processes are traditional hobbing, modern power skiving, and radial-circular methods. Carrying out these processes is based on the gear teeth continuous generating method using complex kinematics. This complicates the analysis, description and modeling of the processes. The developed system provides for a logical sequence of step-by-step modeling and simulation of interrelated processes and phenomena accompanying gear processing. Reproducing volumetric chips and calculating their parameters provides the basis for determining deformation and contact processes, cutting forces, elastic deformations, machining accuracy and energy costs per operation. After establishing the operation to overcome friction and heat flows, the degree of heating and the temperature of the working surfaces are calculated to predict tool wear and its service life. Based on the parametric non-uniformity of the considered processes, the intensity of oscillations and vibrations of gear cutting machines is predicted, and their impact on the quality of gear surfaces and the accuracy of gears is determined. These approaches enable the study of such processes at the level of individual teeth and blades during cutting. They also allow gear cutting technology and cutting tools to be optimized according to the most important criteria and performance assessments.

Dynamics doi: 10.3390/dynamics6010011

Authors: Pedro A. S. Braga Luis A. Aguirre

The Rössler system is a paradigmatic chaotic oscillator widely used to investigate synchronization phenomena. Existing studies on monovariate coupling almost exclusively rely on the x or y variables, while coupling through z is commonly regarded as ineffective. In this work, we report that complete synchronization through the z variable is indeed possible, provided that specific parameter values are chosen. We further consider a parameter regime in which the Rössler system exhibits multistability and show that synchronization via z-coupling occurs only when the dynamics evolve on a particular attractor. Although synchronization can be achieved, the admissible range of coupling strengths is very narrow as determined by the master stability function. For small networks, full connectivity is required, whereas larger networks can tolerate the removal of a limited number of links without losing synchronization. An analytical expression predicting the fraction of connections that must be preserved as a function of network size is derived and validated, revealing that a very high average degree is necessary. This effectively excludes common topologies such as small-world and scale-free networks. Numerical examples with up to 100 oscillators are presented, and potential challenges that may yield new insights are discussed.

Dynamics doi: 10.3390/dynamics6010010

Authors: Christian R. Huyck

Simulated spiking neural networks have been explored for over a hundred years. Many of these networks are driven by biological considerations and an attempt to simulate brains, but others are used with little biological consideration. This paper gives some history of the development of spiking neural models, their use for modelling biological and cognitive phenomena, and for machine learning. It introduces the current state of the art in computational biological neuron and synapse modelling and plasticity. It introduces and reviews balanced spiking networks and their engineering applications. Spiking networks are also used for machine learning, with the hope that their implementation on neuromorphic hardware will bring energy and time savings. Similarly, neuromorphic hardware can enable massive parallelism, supporting larger spiking networks. The use of spiking nets for machine learning, both with biologically plausible models and without, is discussed, showing that effective models already exist. The paper concludes with some notes about implementing spiking nets and a discussion including open questions and future work.

Dynamics doi: 10.3390/dynamics6010009

Authors: Alaa Shumran Abdul-Basset A. Al-Hussein Viet-Thanh Pham

The growing need to safeguard sensitive data in various fields, including in relation to education, banking over the phone, private voice conferences, and the military, has grown as dependence on technology in daily life has increased. Encryption schemes based on chaotic systems are among the most commonly utilized approaches in the security field due to their high levels of safety and reliability. This study proposes a secure audio encryption framework based on the Chameleon chaotic algorithm implemented on a Xilinx ZedBoard Zynq-7000 FPGA. The system was designed using a fixed-point arithmetic format with 32-bit precision (eight integers; 24 fractional bits) with the Xilinx System Generator in MATLAB Simulink R2021b and verified using Vivado. The Chameleon Chaotic System, characterized by its transition from self-excited to hidden attractors through parameter variation, adds complexity to the system dynamics and strengthens the encryption algorithm. The Adaptive Feedback Control technique was applied to synchronize the signals. These methods enhance the security of audio data by ensuring robust and fast synchronization during transmission. The performance of the proposed system was assessed using correlation analysis, the mean squared error, histogram analysis, and audio spectrogram analysis. The system demonstrated strong encryption capabilities with low correlation values (−0.0033). In decryption, they achieved high fidelity with a correlation exceeding 0.999 in noise-free conditions and above 0.9933 under 20 dB AWGN. Adaptive Feedback Control showed superior decryption precision with lower MSEU and higher PSNR, confirming its effectiveness under noisy environments.

Dynamics doi: 10.3390/dynamics6010008

Authors: Ahmed Sadeq Hunaish Fatma Noori Ayoob Fadhil Rahma Tahir Viet-Thanh Pham

This paper investigates the dynamics of a permanent magnet synchronous motor (PMSM) and controls its chaotic speed behavior using the synergetic control technique (SCT). The model includes electrical dynamics in the dq frame and mechanical speed dynamics, with a scalar parameter γ capturing cross-coupling effects. The equilibrium structure and local stability properties of the PMSM are analyzed. For zero input voltages and zero load torque, the system exhibits a pitchfork-type bifurcation in the electrical–mechanical equilibrium as γ crosses a critical value. Explicit expressions are derived for all equilibria, and their stability is characterized using eigenvalue analysis and the Routh–Hurwitz criterion, and a secondary loss of stability via a Hopf-type mechanism is identified. The case of nonzero input voltages with zero load torque is also discussed. Numerical simulations confirm the analytical results and highlight the parameter regions that admit stable operation. Bifurcation diagrams show the different PMSM behaviors as the parameter γ varies. For a certain interval of γ, the PMSM speed undergoes chaotic oscillations. The SCT is introduced to control the chaos. Macro variables are chosen to design the SCT. The derived SCT is implemented to eliminate the chaotic speed. The controller provides good performance in suppressing the chaos. The controller is tested under sudden reference speed change where the controller gets the new reference speed accurately. It is also evaluated under sudden and sinusoidal load torque variations.

Dynamics doi: 10.3390/dynamics6010007

Authors: Umida Baltaeva Bobur Khasanov Hamrobek Hayitbayev Jamol I. Baltaev Yolqin Alikulov

We study the Cauchy problem for a loaded fractional integro-differential equation with a time-dependent diffusion coefficient. By reducing the problem to an equivalent Volterra integral equation of the second kind, we derive explicit analytical representations of solutions under appropriate regularity assumptions. The construction of the associated resolvent kernel allows us to establish existence and uniqueness results and to investigate the role of the fractional order and the loading term in the solution structure. Two illustrative examples are presented to demonstrate the applicability of the proposed approach.

Dynamics doi: 10.3390/dynamics6010006

Authors: Konstantin Rybakov

This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. This article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them.

Dynamics doi: 10.3390/dynamics6010005

Authors: Bo Zhong Yang Lv

The dynamic behaviour of a column excited at the base, e.g., under an earthquake load, has been extensively studied. However, the column may also experience impact at the tip like a heavy-duty truck braking on a bridge. The caused base shear of the pier is very important. In this work, the dynamic behaviour, particularly the impact load from the tip to the base, was studied on two different composites: double basalt- and double flax fibre-reinforced polymer tube (DBFRP and DFFRP)-confined coconut fibre-reinforced concrete (CFRC). For each composite, two columns with a height of 1 m, an inner diameter of the outer tube of 100 mm, and an inner tube of 30 mm were fabricated. The column was fully fixed at the base and struck at the top with an impulse hammer. The base shear was calculated through an equivalent mass method using the acceleration at the tip. The results show that both DBFRP-CFRC and DFFRP-CFRC can dissipate a portion of the impact force, resulting in a reduction in force at the base of the specimens. The base shear of DFFRP-CFRC columns is larger and dissipates energy faster than that of DBFRP-CFRC columns.

Dynamics doi: 10.3390/dynamics6010004

Authors: Dimitri Volchenkov Nuwanthika Karunathilaka Vichithra Amunugama Walawwe Fahad Mostafa

Empirical debates about a “crisis of trust” highlight long-lived pockets of high trust and deep distrust in institutions, as well as abrupt, shock-induced shifts between the two. We propose a probabilistic model in which such phenomena emerge endogenously from social learning on hierarchical networks. Starting from a discrete model on a directed acyclic graph, where each agent makes a binary adoption decision about a single assertion, we derive an effective influence kernel that maps individual priors to stationary adoption probabilities. A continuum limit along hierarchical depth yields a degenerate, non-conservative logistic–diffusion equation for the adoption probability u(x,t), in which diffusion is modulated by (1−u) and increases the integral of u rather than preserving it. To account for micro-level uncertainty, we perturb these dynamics by multiplicative Stratonovich noise with amplitude proportional to u(1−u), strongest in internally polarised layers and vanishing at consensus. At the level of a single depth layer, Stratonovich–Itô conversion and Fokker–Planck analysis show that the noise induces an effective double-well potential with two robust stochastic phases, u≈0 and u≈1, corresponding to persistent distrust and trust. Coupled along depth, this local bistability and degenerate diffusion generate extended domains of trust and distrust separated by fronts, as well as rare, Kramers-type transitions between them. We also formulate the associated stochastic partial differential equation in Martin–Siggia–Rose–Janssen–De Dominicis form, providing a field-theoretic basis for future large-deviation and data-informed analyses of trust landscapes in hierarchical societies.

Dynamics doi: 10.3390/dynamics6010003

Authors: Mauro Pontani Giulio De Angelis Edoardo Maria Leonardi

Multi-revolution Lambert solvers are intended to find the elliptic transfer orbits that are traveled multiple times and connect two specified positions in prescribed time, under the assumption of considering natural (Keplerian) orbital motion in the presence of a single attracting body. This study proposes and tests a new, effective multi-revolution Lambert solver that employs the initial true anomaly, which identifies the initial position along the transfer ellipse, as the unknown variable. The related search interval is identified through closed-form expressions for upper and lower bounds. A simple numerical algorithm is developed and employed over the entire search interval to detect all Lambert solutions. The new multi-revolution solver proposed in this work is simple to understand and easy to implement and is successfully tested in several challenging scenarios (corresponding to some pathological cases reported in the recent scientific literature), as well as for the study of Earth–Mars interplanetary transfers. Comparison with alternative, up-to-date techniques points out that the new approach at hand is able to detect all the feasible transfer ellipses, in all cases, with very satisfactory accuracy in terms of final position error, even in challenging scenarios that include a huge number of revolutions or near-antipodal terminal positions.

Dynamics doi: 10.3390/dynamics6010002

Authors: Athanasios V. Serafeim Nikolaos Th. Fourniotis Demetris Stergiopoulos Andreas Langousis

The uneven distribution of flow in water distribution networks (WDNs) can cause inefficient flows and pressure imbalances as well as degraded water quality in areas where demand is higher than the networks’ design limit. In this study, two faulty connections within a WDN in Greece that exhibited unusual geometric shapes favoring preferential flow paths were investigated. The three-dimensional computational fluid dynamics simulations were performed in ANSYS Fluent solver (v. 23.1) to study the internal behavior of this network for steady-state flows. The standard k-ε model was employed to calculate turbulence and energy losses in this network. In Connection A, which is a cross-shaped junction with two inlets and two outlets, and in Connection B, which is a complex 4 → 1 → 4 manifold connection, more than 80% of total inflow was found to be directed to a single outlet. The pressure contour plots revealed that this is due to the large total head losses associated with pronounced changes in flow direction. The role of explicit junction losses in network modeling and network improvements to improve hydraulic behavior has thereby gained prominence through this study. The applicability and capability of computational fluid dynamics in characterizing complex flow problems in urban WDNs have thereby proven to be significant.

Dynamics doi: 10.3390/dynamics6010001

Authors: Diego S. de la Vega Lizbeth Vargas-Cabrera Olga G. Félix-Beltrán Jesus M. Munoz-Pacheco

Circuit implementation is a widely accepted method for validating theoretical insights observed in chaotic systems. It also serves as a basis for numerous chaos-based engineering applications, including data encryption, random number generation, secure communication, neuromorphic computing, and so forth. To get feasible, compact, and cost-effective circuit implementations of chaotic systems, the underlying mathematical model may be simplified while preserving all rich nonlinear behaviors. In this framework, this manuscript presents a simplified Hopfield Neural Network (HNN) capable of generating a broad spectrum of complex behaviors using a minimal number of electronic elements. Based on Shil’nikov’s theorem for heteroclinic orbits, the number of non-zero synaptic connections in the matrix weights is reduced, while simultaneously using only one nonlinear activation function. As a result of these simplifications, we obtain the most compact electronic implementation of a tri-neuron HNN with the lowest component count but retaining complex dynamics. Comprehensive theoretical and numerical analyses by equilibrium points, density-colored continuation diagrams, basin of attraction, and Lyapunov exponents, confirm the presence of periodic oscillations, spiking, bursting, and chaos. Such chaotic dynamics range from single-scroll chaotic attractors to double-scroll chaotic attractors, as well as coexisting attractors to transient chaos. A brief security application of an S-Box utilizing the presented HNN is also given. Finally, a physical implementation of the HNN is given to confirm the proposed approach. Experimental observations are in good agreement with numerical results, demonstrating the usefulness of the proposed approach.

Dynamics doi: 10.3390/dynamics5040054

Authors: Carlos Alejandro Velázquez-Morales Luis Hernández-Martínez Esteban Tlelo-Cuautle Luis Gerardo de la Fraga

The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the gm/ID method to find the initial width (W) and length (L) sizes of the transistors. These size values are used to run the non-dominated sorting genetic algorithm (NSGA-II) to perform a multi-objective optimization of three OTA topologies. The gm/ID method begins with transistor characterization using MATLAB R2024a generated look-up tables (LUTs), which map normalized transconductance of the transistor channel dimensions, and key performance metrics of a complementary metal–oxide–semiconductor (CMOS) technology. The LUTs guide the initial population generation within NSGA-II during the optimization of OTAs to achieve not only a desired transconductance but also accuracy alongside linearity, high DC gain, low power consumption, and stability. The feasible W/L size solutions provided by NSGA-II are used to enhance the CMOS design of a memristor emulator, where the OTA with the desired transconductance is adapted to tune the behavior of the memristor, demonstrating improved pinched hysteresis loop characteristics. In addition, process, voltage and temperature (PVT) variations are performed by using TSMC 180 nm CMOS technology. The memristor-based on optimized OTAs is used to design a Leaky Integrate-and-Fire (LIF) neuron, which produces identical spike counts (seven spikes) under the same input conditions, though the time period varied with a CMOS inverter scaling. It is shown that increasing transistor widths by 100 in the inverter stage, the spike quantity is altered while changing the spiking period. This highlights the role of device sizing in modulating LIF neuron dynamics, and in addition, these findings provide valuable insights for energy-efficient neuromorphic hardware design.

Dynamics doi: 10.3390/dynamics5040053

Authors: Guillermo Chacón-Acosta Adrian Perez-Rodriguez

Diffusion on curved surfaces deviates from the flat case due to geometrical corrections in the evolution of its moments, such as the geodesic mean square displacement. Moreover, anomalous diffusion is widely used to model transport in disordered, confined, or crowded environments and can be described by a temporal subordination scheme, leading to a time-fractional diffusion equation. In this work, we analyze the dynamics of time subordinated anomalous diffusion on curved surfaces. By using a generalized Taylor expansion with fractional derivatives in the Caputo sense, we express the moments as a temporal power series and show that the anomalous exponent couples with curvature terms, leading to a competition between geometric and anomalous effects. This coupling indicates a mechanism through which curvature modulates anomalous transport.

Dynamics doi: 10.3390/dynamics5040052

Authors: Sunder Lal Meena Radhey Shyam Jangid

This research investigates the seismic behavior of continuous-span base-isolated bridges integrated with fluid inerter damper (FID) through a linear analytical framework under recorded earthquake excitations. The resisting mechanism of the FID is modelled as a combination of inertial and viscous forces, which are functions of the relative acceleration and velocity between connected nodes. Linear time-history simulations and a series of parametric analyses are conducted to examine how variations in inertance, damping ratio, and installation location affect key seismic response parameters, including deck acceleration, bearing displacement, and substructure base shear. Comparative analyses with conventional viscous dampers and isolation alone establish the relative effectiveness of FID. Analysis indicates that FID effectively reduces deck accelerations through apparent mass amplification, suppresses bearing displacements via viscous damping, and redistributes seismic forces depending on placement strategies. An optimum inertance range is identified that minimizes accelerations without amplifying base shear, with abutment-level placement proving most effective for pier shear control, while intermediate placement provides balanced reductions. Overall, FID consistently outperforms viscous dampers and conventional isolation, underscoring their potential as an advanced inerter-based solution for both new bridge design and retrofit applications.

Dynamics doi: 10.3390/dynamics5040050

Authors: Illiani Carro-Pérez Juan Gonzalo Barajas-Ramírez

In this study, we explore the emergence of generalized synchronization (GS) in arrays of Hindmarsh–Rose (HR) neurons that are coupled through memristive synapses. We design coupling functions utilizing active memristors to facilitate GS in a bidirectionally coupled two-neuron memristive neural network (MNN). Our analysis employs a nearest neighbor (NN) approach. Our findings indicate that there is a threshold coupling strength for the active memristive synapses required to achieve GS. Additionally, we investigate how memristor parameters affect the temporal characteristics of synchronized neuronal firing patterns. Specifically, we discover that the interburst interval (IBI) is directly proportional to the coupling strength of the memristive synapses, while the interspike interval (ISI) is inversely proportional to this strength.

Dynamics doi: 10.3390/dynamics5040051

Authors: Marco A. Tapia-Valerdi Irán Ramos-Prieto Francisco Soto-Eguibar Héctor M. Moya-Cessa

We provide an analytical framework for describing the propagation of light in waveguide arrays, considering both infinite and semi-infinite cases. The interaction up to second neighbors is taken into account, which provides a more realistic setup. We show that these solutions follow a distinctive structural pattern. This pattern reflects a transition from conventional Bessel functions to the lesser-known one-parameter generalized Bessel functions, offering new insights into the propagation dynamics in these systems.

Dynamics doi: 10.3390/dynamics5040049

Authors: Matthaios Katsanikas Stephen Wiggins

In this paper, we study the different types of trajectories that correspond to a particular orbital behavior of caldera-type Hamiltonian systems. This particular orbital behavior is dynamical matching. Dynamical matching is an important chemical phenomenon that is encountered in many caldera-type organic chemical reactions. In this paper we will distinguish the different types of trajectories that correspond to this phenomenon using periodic orbit dividing surfaces.

Dynamics doi: 10.3390/dynamics5040048

Authors: Gui-Lin She Lei-Lei Gan

This study investigates the combined resonance phenomenon in magneto-electro-elastic (MEE) cylindrical shells under longitudinal and lateral excitations with thermal factors, addressing the complex interaction between mechanical, electrical, and magnetic fields in smart structures. The research aims to establish a theoretical framework for predicting resonance behaviors in energy harvesting and sensing applications. Using Maxwell’s equations and Hamilton’s principle, the governing equations for combined resonance are derived. The method of varying amplitude (MVA) is employed to acquire the combined resonance response across varying parameters. Furthermore, the Runge–Kutta method is applied to investigate the bifurcation and chaotic motion characteristics under different longitudinal and lateral excitation conditions. Key findings reveal the coupling effects of multi-physical fields on resonance frequencies, demonstrating quantitative agreement with prior studies. The results provide fundamental insights into the dynamic characteristics of MEE materials, offering theoretical support for optimizing their performance in adaptive engineering systems.

Dynamics doi: 10.3390/dynamics5040047

Authors: Chamalka Dharmasiri Upeksha Perera

We develop a four-dimensional nonlinear model of a reflexive financial system by extending the Xin–Zhang system with a self-reinforcing sentiment channel. The model comprises four interacting variables—interest rate, investment demand, price index, and market confidence—and incorporates reflexivity to capture feedback between economic fundamentals and investor sentiment. A Lyapunov function shows that the system is well-posed and dissipative, ensuring bounded trajectories. We then analyse the dynamics using standard nonlinear-dynamics tools. Reflexive confidence sustains chaotic motion, inhibits convergence to equilibria, and produces irregular, aperiodic bifurcation patterns; sentiment-driven feedback destabilises a dissipative macroeconomic model and sustains volatility, as evidenced by a positive largest Lyapunov exponent and Kolmogorov–Sinai entropy greater than zero. Using U.S. monthly consumer sentiment and the S&P 500, we observe co-movement, a medium-horizon lead of sentiment, and a nonlinear persistence map wt+1=f(wt)—stylised facts consistent with the model’s self-reinforcing confidence channel.

Dynamics doi: 10.3390/dynamics5040046

Authors: Edward Bormashenko Ramita Sarkar Mark Frenkel Shraga Shoval

We propose a Ramsey approach to the dimensional analysis of physical systems, which complements the seminal Buckingham theorem. Dimensionless constants describing a given physical system are represented as vertices of a graph, referred to as a dimensions graph. Two vertices are connected by an aqua-colored edge if they share at least one common dimensional physical quantity and by a brown edge if they do not. In this way, a bi-colored complete Ramsey graph is obtained. The relations introduced between the vertices of the dimensions graph are non-transitive. According to the Ramsey theorem, a monochromatic triangle must necessarily appear in a dimensions graph constructed from six vertices, regardless of the order of the vertices. Mantel–Turán analysis is applied to study these graphs. The proposed Ramsey approach is extended to graphs constructed from fundamental physical constants. A physical interpretation of the Ramsey analysis of dimensions graphs is suggested. A generalization of the proposed Ramsey scheme to multi-colored Ramsey graphs is also discussed, along with an extension to infinite sets of dimensionless constants. The introduced dimensions graphs are invariant under rotations of reference frames, but they are sensitive to Galilean and Lorentz transformations. The coloring of the dimensions graph is independent of the chosen system of units. The number of vertices in a dimensions graph is relativistically invariant and independent of the system of units.

Dynamics doi: 10.3390/dynamics5040045

Authors: Andrii Slipchuk Petro Pukach Myroslava Vovk

The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov–Mitropolsky). Using this methods, differential equations were obtained in a standard form, determining the law of variation in amplitude and frequency as functions of kinematic, force, and physico-mechanical parameters in both resonant and non-resonant regimes. The fourth-order Runge–Kutta method was applied for the oscillatory system numerical analysis. The computation of complex mathematical expressions and graphical representation of the results were implemented in the mathematical software Maple 15. The results obtained can be applied for engineering calculations of structures containing moving beams subjected to compressive or tensile forces.

Dynamics doi: 10.3390/dynamics5040044

Authors: Umida Baltaeva Bobur Khasanov Omongul Egamberganova Hamrobek Hayitbayev

We investigate the Cauchy problem for a heat equation incorporating variable diffusion coefficients and fractional memory effects modeled by a separable convolution kernel. By employing the fundamental solution of the associated parabolic equation, the problem is reformulated as a Volterra-type integral equation. Under appropriate regularity assumptions, we establish existence and uniqueness of classical solutions. Furthermore, we address an inverse problem aimed at simultaneously recovering the memory kernel and the solution. Using a differentiability-based approach, we derive a stable and well-posed formulation that enables the identification of memory effects in fractional heat models.

Dynamics doi: 10.3390/dynamics5040043

Authors: Luis Manuel Lopez-Jimenez Esteban Tlelo-Cuautle Luis Fortino Cisneros-Sinencio Alejandro Diaz-Sanchez

This paper presents two classic analog oscillators: a relaxation oscillator and a Wien bridge one, where a memristor replaces a resistor. The circuits are simulated in TopSPICE 7.12 using a memristor emulation circuit and commercially available components to evaluate the memristor’s impact. In the case of the relaxation oscillator, which includes the memristor, a notable increase in oscillation frequency was observed compared to the classical circuit, with a nearly 10-fold increase from 790 Hz to 7.78 kHz while maintaining a constant amplitude. This confirms the influence of the memristor’s dynamic resistance on the circuit time constant. On the other hand, the Wien-bridge oscillator exhibits variations in specific parameters, such as peak voltage, amplitude, and frequency. In this case, the oscillation frequency decreased from 405 Hz to 146 Hz with the addition of the memristor, a characteristic introduced by the proposed memristive element’s nonlinear interactions. Experimental results confirm the feasibility of incorporating memristors into classical oscillator circuits, enabling frequency changes while maintaining stable oscillations, allowing reconfigurable and adaptable analog designs that leverage the properties of memristive devices.

Dynamics doi: 10.3390/dynamics5040042

Authors: Oleksiy Kuznyetsov

The dynamics of port-Hamiltonian systems is based on energy balance principles (the first law of thermodynamics) embedded in the structure of the model. However, when dealing with thermodynamic subsystems, the second law (entropy production) should also be explicitly taken into account. Several frameworks were developed as extensions to the thermodynamic domain of port-Hamiltonian systems. In our work, we study three of them, namely irreversible port-Hamiltonian systems, entropy-based generalized Hamiltonian systems, and entropy-production-metric-based port-Hamiltonian systems, which represent alternative approaches of selecting the state variables, the storage function, simplicity of physical interpretation, etc. On the example of a simplified lumped-parameter model of a heat exchanger, we study the frameworks in terms of their implementability for an IDA-PBC-like control and the simplicity of using these frameworks for practitioners already familiar with the port-Hamiltonian systems. The comparative study demonstrated the possibility of using each of these approaches to derive IDA-PBC-like thermodynamically consistent control and provided insight into the applicability of each framework for the modeling and control of multiphysics systems with thermodynamic subsystems.

Dynamics doi: 10.3390/dynamics5040041

Authors: Adriana Sofia Rodríguez-Pérez Héctor Eduardo Gilardi-Velázquez Stephanie Esmeralda Velázquez-Pérez

Burns represent a significant medical challenge, and the development of theoretical models has the potential to contribute to the advancement of new diagnostic tools. This study aimed to perform numerical simulations of the Pennes bioheat transfer equation, incorporating heat generation terms due to the body’s immunological response to thermal injury, as well as changes in skin thermal parameters and blood perfusion for each burn type. We propose the incorporation of specific parameters and boundary conditions related to multilayer perfusion into the Pennes bioheat model. Using the proposed layered skin model, we evaluate temperature differences to establish correlations for determining burn depth. In this investigation, 1D and 3D algorithms based on the finite volume method were applied to capture transient and spatial thermal variations, with the resulting temperature distributions demonstrating the ability of the proposed models to describe the expected thermal variations in healthy and burned tissue. This work demonstrates the potential of the finite volume method to approximate the solution of the Pennes biothermal equation. Overall, this study provides a computational framework for analyzing heat transfer in burn injuries and highlights the relevance of mathematical simulations as a tool for future research on infrared thermography in medicine.

Dynamics doi: 10.3390/dynamics5040040

Authors: Abdul-Basset A. Al-Hussein Fadhil Rahma Tahir Hamzah Abdulkareem Abbood Mazin Majid Abdulnabi Viet-Thanh Pham

This paper investigates the nonlinear dynamics behavior and practical realization of a V/Heart-shape chaotic system. Nonlinear analysis contemporary tools, including bifurcation diagram, Lyapunov exponents, phase portraits, power spectral density (PSD) bicoherence, and spectral entropy (SE), are employed to investigate the system’s complex dynamical behaviors. To discover the system’s versatility, two case studies are presented by varying key system parameters, revealing various strange attractors. The system is modeled and implemented using an industrial-grade programmable logic controller (PLC) with structured text (ST) language, enabling robust hardware execution. The dynamics of the chaotic system are simulated, and the results are rigorously compared with experimental data from laboratory hardware implementations, demonstrating excellent agreement. The results indicate the potential usage of the proposed chaotic system for advanced industrial applications, secure communication, and dynamic system analysis. The findings confirm the successful realization of the V-shape and Heart-shape Chaotic Systems on PLC hardware, demonstrating consistent chaotic behavior across varying parameters. This practical implementation bridges the gap between theoretical chaos research and real-world industrial applications.

Dynamics doi: 10.3390/dynamics5030039

Authors: Juanjuan Ma Limei Qi Hongqiang Dong Ting Liu Mei Zeng

Chemical synaptic coupling is crucial in the nervous system. This paper establishes a chemical synaptic Chay neuronal coupling system using the Heaviside function and analyzes the equilibrium point’s type and stability based on the Jacobian matrix. Matcont simulation found that the Hopf bifurcation point transformed into a Bogdanov–Takens bifurcation point under the influence of chemical coupling strength, and a series of saddle-node bifurcation points are generated. The discharge time history of the system and the evolution of single-parameter bifurcation behavior were numerically simulated through a language and Matlab. The parameter matching results indicated that the chemical synaptic reversible potentials and synaptic thresholds were −15 mV and −35 mV, respectively. The bifurcation behavior and its changes under multi-parameter conditions were studied by using various numerical methods such as time series diagrams, bifurcation diagrams, and two-parameter diagrams. The similarity function identified key factors affecting synchrony in a chemical synaptic coupling system. Results indicate that synchrony primarily depends on chemical coupling strength, with other factors providing positive feedback to enhance it. The simulation of the spatiotemporal dynamics in a chemically synaptic coupled network of 2000 ring neurons revealed that altering the maximum conductance at local positions within the network can induce the generation of traveling waves. Strong coupling strengths ensure that the induced traveling waves propagate at greater velocities and can excite and awaken a larger number of neurons in a shorter time frame. The nonlinear properties of chemical synaptic neuronal system offer essential tools and foundations for studying neurobiology and brain dynamics.

Dynamics doi: 10.3390/dynamics5030038

Authors: Fernando C. Pérez-Cárdenas

The Fluctuation Theorem establishes a relationship between microscopic reversibility and macroscopic irreversible phenomena, such as dissipation. In this short paper, we present an elementary derivation of this theorem within the framework of stochastic thermodynamics. Beginning with a brief examination of the time-reversible laws of motion that rule at the microscopic level, we discuss how through coarse-graining we arrive at the principle of detailed balance. This principle, which was originally proved for equilibrium processes, is extended to out-of-equilibrium situations in order to arrive at the Fluctuation Theorem. Though this extension is theoretically sound, one of the main purposes of this paper is to show that the origin of the practical limitations encountered, when applying this theorem to processes lasting longer than a certain duration, can be explained by the paucity of unlikely events that arise in out-of-equilibrium processes. The numerical results from the one-dimensional, one-particle stochastic model that is introduced here agree very well with the Fluctuation Theorem and, at the same time, bring to light the limits of its applicability in relation to the number of simulations or experiments and the duration of the process under study.

Dynamics doi: 10.3390/dynamics5030037

Authors: Vhahangwele Colleen Sigonde Desejo Filipeson Sozinando Bernard Xavier Tchomeni Alfayo Anyika Alugongo

Gear transmission error (GTE) is a critical factor influencing the performance and service life of gear systems, as it directly contributes to vibration, noise generation, and premature wear. The present study introduces a combined theoretical and experimental approach to characterizing GTE in a single-stage spur gear system. A six-degree-of-freedom nonlinear dynamic model was formulated to capture coupled lateral–torsional vibrations, accounting for gear mesh stiffness, bearing and coupling characteristics, and a harmonic transmission error component representing manufacturing and assembly imperfections. Simulations and experiments were conducted under healthy and eccentricity-faulted conditions, where a controlled 890 g eccentric mass induced misalignment. Frequency domain inspection of faulty gear data showed pronounced sidebands flanking the gear mesh frequency near 200 Hz, as well as harmonics extending from 500 Hz up to 1200 Hz, in contrast with the healthy case dominated by peaks confined to 50–100 Hz. STFT analysis revealed dispersed spectral energy and localized high-intensity regions, reinforcing its role as an effective fault diagnostic tool. Experimental findings aligned with theoretical predictions, demonstrating that the integrated modelling and time–frequency framework is effective for early fault detection and performance evaluation of spur gear systems.

Dynamics doi: 10.3390/dynamics5030036

Authors: Maria Eduarda F. Capponero Giovani D. Telli Elizaldo D. dos Santos Liércio A. Isoldi Mateus das Neves Gomes Cesare Biserni Luiz Alberto O. Rocha

The energy potential of sea waves has gained relevance, leading to extensive research on converters. The present work analyzes the contribution of Constructal Design to the development of wave energy converters. Constructal Design utilizes performance indicators to enhance system efficiency by varying the degrees of freedom where flow occurs. Thus, the systematic literature review methodology was applied to gather a collection of documents focused on the research topic. This study identified articles published between 2014 and 2024 by 40 authors affiliated with institutions in Brazil, Italy, and Portugal. The oscillating water column (OWC) converter received the most research attention, followed by the overtopping converter. Analyzing the documents collected for this study, the performance indicators revealed improvements ranging from 1.19 to 839 times, indicating the lowest and highest enhancements observed, respectively. The Constructal Design method has proven highly effective in identifying specific architectures or geometric arrangements that enhance flow configuration and improve the performance of wave energy converters. However, relatively few studies have applied the Constructal Design method to wave energy converters in comparison to other methodologies, presenting a significant opportunity for future research.

Dynamics doi: 10.3390/dynamics5030035

Authors: Gheorghe Maria Daniela Gheorghe Crina Muscalu Andreea Scoban

Currently, D-fructose (DF) is produced through enzymatic isomerization of beta-D-glucose (DG) under disadvantageous conditions (equilibrium conversion of 50%, costly separation, etc.). Alternatively, the two-step Cetus enzymatic process became a promising approach for producing high-purity DF. First, DG is oxidized to keto-glucose (kDG) using commercial pyranose 2-oxidase (P2Ox). To avoid the fast P2Ox inactivation by the in situ produced hydrogen peroxide, catalase is added to decompose this byproduct. The DG oxidation occurs with high conversion and selectivity, leading to kDG free of allergenic aldose compounds. Then, kDG is reduced to DF by using the NADPH cofactor and aldose reductase (ALR). This study aims to evaluate the continuous in situ regeneration of NADPH at the expense of formate decomposition in the presence of formate dehydrogenase (FDH). By adopting a kinetic model from literature, this in silico analysis determines the optimal operation of a batch reactor (BR) used in the Cetus second step to maximize the DF production and minimize the consumption of costly NADPH. Compared to its simple operation, the optimized BR with cofactor regeneration reported a 25% lower NADPH consumption, though the amount of the processed substrate is ca. 3× higher. Also, the costly enzymes (ALR, FDH) consumption is 2× smaller.

Dynamics doi: 10.3390/dynamics5030034

Authors: Maximilian T. Meyer Arno Schindlmayr

Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller’s rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset.

Dynamics doi: 10.3390/dynamics5030033

Authors: Thibaut Torres Yasser Diab Christophe Changenet Thomas Touret Bérengère Guilbert

This study aims to develop a new model for windage losses, building upon existing formulation, complemented by dedicated experimental campaigns and a specific methodology designed to isolate and quantify windage losses. The model relies on an analytical approach to flow characterization, incorporating a correction factor accounting for air density reduction. The experimental investigation was carried out on a dedicated test bench and includes both spur and helical gears. The results demonstrate good agreement between the proposed model and the experimental data, with and without the presence of nearby obstacles, such as side flanges, highlighting the model’s robustness across different configurations. The proposed windage loss model reproduces the experimental results with significantly greater accuracy than the original one, yielding relative deviations below 5% compared to almost 20% for spur gears, and below 9% compared to over 21%, and in some cases up to 50%, for helical gears.

Dynamics doi: 10.3390/dynamics5030032

Authors: Shigetoshi Nara Naoya Miyahara Yutaka Yamaguti Ichiro Tsuda

The high-dimensional chaos generated in a neural network consisting of pseudo-neuron devices invented by one of the authors (S.N.) has been successfully applied to control the complex motion of a roving robot, e.g., to solve a maze, as reported in the previous papers. On the basis of successful works and the concept that chaos plays important functional roles in biological systems, in the present paper, we report new experiments to show the functional aspects of chaos via behavioral interactions in an ill-posed context and solve problems with chaotic neural networks. Explicitly, experiments on two roving robots in a maze (labyrinth) are reported, in which both seek to catch each other or one chases and the other flees, mimicking the survival activities of insects in natural environments. The two-dimensional robot motion is controlled with motion control systems, each of which is equipped with a chaotic neural network to generate autonomous and adaptive actions depending on sensor inputs of obstacles and/or target detection information including uncertainty. We report both computer experiments and practical hardware implementations, where for the latter, only the chaotic neural network is run on a desktop computer, the motion signals are coded into two-dimensional space, and sensor signals are transferred via Bluetooth device between robots and computers.

Dynamics doi: 10.3390/dynamics5030031

Authors: Aleksander Stefanov Stanislav Varbev

We derive a new exactly solvable multi-component system of non-linear evolution equations (NLEEs). The system consists of three 1+1-dimensional evolution equations—one first-order and two second-order in the spatial variable. We review their Lax representation, formulate the scattering problem, and derive the soliton-like solutions of the system.

Dynamics doi: 10.3390/dynamics5030030

Authors: Qing Gu Zeqi Wu Yongquan Li Huo Tao Boyu Li Wen Li

This work systematically addresses the dual challenges of non-inertial dynamic coupling and kinematic constraint redundancy encountered in dynamic modeling of serial–parallel–serial hybrid robotic mechanisms, and proposes an improved Newton–Euler modeling method with constraint compensation. Taking the Skiing Simulation Platform with 6-DOF as the research mechanism, the inverse kinematic model of the closed-chain mechanism is established through GF set theory, with explicit analytical expressions derived for the motion parameters of limb mass centers. Introducing a principal inertial coordinate system into the dynamics equations, a recursive algorithm incorporating force/moment coupling terms is developed. Numerical simulations reveal a 9.25% periodic deviation in joint moments using conventional methods. Through analysis of the mechanism’s intrinsic properties, it is identified that the lack of angular momentum conservation constraints on the end-effector in non-inertial frames leads to system controllability degradation. Accordingly, a constraint compensation strategy is proposed: establishing linearly independent differential algebraic equations supplemented with momentum/angular momentum balance equations for the end platform. Co-Simulation results demonstrate that the optimized model reduces the maximum relative error of actuator joint moments to 0.98%, and maintains numerical stability across the entire configuration space. The constraint compensation framework provides a universal solution for dynamics modeling of complex closed-chain mechanisms, validated through applications in flight simulators and automotive driving simulators.

Dynamics doi: 10.3390/dynamics5030029

Authors: Italo Guarneri

Schmidt entropy is used as a common denotation for all Hilbert space entropies that can be defined via the Schmidt decomposition theorem; they include quantum entanglement entropies and classical separability entropies. Exact results about the asymptotic growth in time of such entropies (in the form of Renyi entropies of any order ≥1) are directly derived from the Schmidt decompositions. Such results include a proof that pure point spectra entail boundedness in time of all entropies of order larger than 1; and that slower than exponential transport forbids faster than logarithmic asymptotic growth. Applications to coupled Quantum Kicked Rotors and to Floquet systems are presented.

Dynamics doi: 10.3390/dynamics5030028

Authors: Aslam Abdullah Mohd Fadhli Zulkafli Muhammad Akmal Abdul Halim Ramanathan Ashwin Thanneermalai Bambang Basuno

Mid-altitude sounding rockets are essential for atmospheric research and suborbital experimentation, where aerodynamic optimization and structural integrity are crucial for achieving targeted apogees. This study uses OpenRocket v23.09 for preliminary flight performance prediction and SolidWorks 2024 to integrate aerodynamic and structural analyses through Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA). SolidWorks Flow Simulation and SolidWorks Simulation are used to assess how nose cone and fin geometries, as well as thermal deformation, influence flight performance. Among nine tested configurations, the ogive nose cone with trapezoidal fins achieved the highest simulated apogee of 2639 m, with drag coefficients of 0.480 (OpenRocket) and 0.401 (SolidWorks Flow Simulation). Thermal–structural analysis revealed a maximum nose tip displacement of 0.7249 mm for the rocket with the ogive nose cone, leading to an increasing drag coefficient of 0.404. However, thermal deformation of the ellipsoid nose cone led to a reduction in the drag coefficient from 0.419 to 0.399, even though it exhibited a slightly higher maximum displacement of 0.7443 mm. Mesh independence was confirmed with outlet velocity deviations below 1% across refinements. These results highlight the importance of integrated CFD–FEA approaches, geometric optimization, and material resilience for enhancing the aerodynamic performance of subsonic sounding rockets.

Dynamics doi: 10.3390/dynamics5030027

Authors: Dimitri Volchenkov

We advance a mathematical framework for collective conviction by deriving a continuum theory from the network-based model introduced by us recently. The resulting equation governs the evolution of belief through a degenerate anisotropic logistic–diffusion process, where diffusion slows as conviction saturates. In one spatial dimension, we prove global well-posedness, demonstrate spectral front pinning that arrests the spread of influence at finite depth, and construct explicit traveling-wave solutions. In two dimensions, we uncover a geometric mechanism of curvature–induced quenching, where belief propagation halts along regions of low effective mobility and curvature. Building on this insight, we formulate a variational principle for optimal control under resource constraints. The derived feedback law prescribes how to spatially allocate repression effort to maximize inhibition of front motion, concentrating resources along high-curvature, low-mobility arcs. Numerical simulations validate the theory, illustrating how localized suppression dramatically reduces transverse spread without affecting fast axes. These results bridge analytical modeling with societal phenomena such as protest diffusion, misinformation spread, and institutional resistance, offering a principled foundation for selective intervention policies in structured populations.

Dynamics doi: 10.3390/dynamics5030026

Authors: Cresus Fonseca de Lima Godinho Claudio Maia Porto Marcos Cardoso Rodriguez Ion Vasile Vancea

The recently proposed conformable deformation of quantum mechanics by a fractional parameter α∈(0,1] has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at α=1. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the xα-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the α=1 limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator.

Dynamics doi: 10.3390/dynamics5030025

Authors: Marco A. Tapia-Valerdi Irán Ramos-Prieto Francisco Soto-Eguibar Héctor M. Moya-Cessa

We present an analytical framework for describing light propagation in infinite waveguide arrays, incorporating a generalized long-range coupling to achieve a more realistic model. We demonstrate that the resulting solution can be expressed in terms of generalized Bessel-like functions. Additionally, by applying the concept of eigenstates, we borrow from quantum mechanics a basis given in terms of phase states that allows the analysis of the transition from the discrete to the continuum limit, obtaining a relationship between the field amplitudes and the Fourier series coefficients of a given function. We apply our findings to different coupling functions, providing new insights into the propagation dynamics of these systems.

Dynamics doi: 10.3390/dynamics5030024

Authors: Gabriel Antonio Felipe Carlos Alberto Valentim Sergio Adriani David

Fractional modeling has emerged as an important resource for describing complex phenomena and systems exhibiting non-local behavior or memory effects, finding increasing application in several areas in physics and engineering. This study presents the analytical derivation of equations pertinent to the modeling of different systems, with a focus on heat conduction. Two specific boundary value problems are addressed: a Helmholtz equation modified with a fractional derivative term, and a fractional formulation of the Laplace equation applied to steady-state heat conduction in circular geometry. The methodology combines the separation of variables technique with fractional power series expansions, primarily utilizing the Caputo fractional derivative. An important aspect of this paper is its instructional emphasis, wherein the mathematical derivations are presented with detail and clarity. This didactic approach is intended to make the analytical methodology transparent and more understandable, thereby facilitating greater comprehension of the application of these established methods to non-integer-order systems. The final goal is not only to provide a different approach of solving these physical models analytically, but to provide a clear, guided pathway for those engaging in the treatment of fractional differential equations.

Dynamics doi: 10.3390/dynamics5030023

Authors: Getu Abyu Girum Urgessa Ameen Topa

This research explores how RC columns respond to blast-induced dynamic effects, with a novel focus on partially submerged scenarios, bridging a gap between air blast and underwater explosion (UNDEX) research. Using advanced finite element modeling in LS-DYNA, the study captures the unique behavior of RC columns under mixed-media conditions, where shockwaves propagate through water and air interfaces. Comprehensive parametric analyses explore the influence of charge size, blast stand-off, and depth of water, revealing distinct dampening mechanisms and structural responses. Key findings include a measurable reduction in peak displacement of partially submerged explosions compared to fully submerged explosions, attributed to the moderating effects of the water–air interface. A total of 60 simulation cases were conducted to systematically analyze partially submerged scenarios, providing robust insights into energy transmission and damage mechanisms. The numerical models, validated against published experimental data by others, demonstrate the accuracy of computational modeling in simulating damage profiles, displacement histories, and energy dissipation trends. This research offers practical implications for designing resilient RC structures in coastal and maritime environments. The results contribute significantly to the field of blast mechanics, advancing our understanding of mixed-media shockwave dynamics and their impact on critical infrastructure.

Dynamics doi: 10.3390/dynamics5020022

Authors: Karel Vokurka

The buoyancy of radially oscillating spark-generated bubbles is studied experimentally. Bubble sizes, defined as the maximum bubble radius, range from 26.6 to 52.1 mm, and the bubbles oscillate at a hydrostatic pressure of 127 kPa in a large expanse of liquid. We found that the position of these bubbles is relatively stable during the first two oscillations. They move upwards only in short time intervals when their size is, due to contraction, close to the minimum volume. The vertical movement, therefore, takes place in the form of steps. The relative heights of these steps, defined as the ratio of step heights to bubble size, increase with bubble size and range from 0.15 to 0.29. No significant deformations in the spherical shape of bubbles are observed during the first two oscillations.

Dynamics doi: 10.3390/dynamics5020021

Authors: Sarp Adali

A variational formulation and variationally consistent boundary conditions were derived for a coupled system of two boron nitride nanotubes (BNNTs), with the piezoelectric and surface effects taken into account in the formulation. The coupling between the nanotubes was defined in terms of Winkler and Pasternak interlayers. The equations governing the vibrations of the coupled system were expressed as a system of four partial differential equations based on nonlocal elastic theory. After deriving the variational principle for the double BNNT system, Hamilton’s principle was expressed in terms of potential and kinetic energies. Next, the differential equations for the free vibration case were presented and the variational form for this case was derived. The Rayleigh quotient was formulated for the vibration frequency, which indicated that piezoelectric and surface effects led to higher vibration frequencies. Next, the variationally consistent boundary conditions were formulated in terms of moment and shear force expressions. It was observed that the presence of the Pasternak interlayer between the nanotubes led to coupled boundary conditions when a shear force and/or a moment was specified at the boundaries.

Dynamics doi: 10.3390/dynamics5020020

Authors: Hong Wang Sunil Subedi Wenbo Jia

To address grid variability caused by renewable energy integration and to maintain grid reliability and resilience, hydropower must quickly adjust its power generation over short time periods. This changing energy generation landscape requires advance technology integration and adaptive parameter optimization for hydropower systems via digital twin effort. However, this is difficult owing to the lack of characterization and modeling for the nonlinear nature of hydroturbines. To solve this issue, this paper first formulates a six-coefficient Kaplan hydroturbine model and then proposes a parametric optimization tuning framework based on the Nelder–Mead algorithm for adaptive dynamic learning of the six-coefficients so as to build models that describe the turbine. To assess the performance of the proposed optimal parametric tuning technique, operational data from a real-world Kaplan hydroturbine unit are collected and used to model the relationship between the gate opening and the generated power production. The findings show that the proposed technique can effectively and adaptively learn the unknown dynamics of the Kaplan hydroturbine while optimally tune the unknown coefficients to match the generated power output from the real hydroturbine unit with an inaccuracy of less than 5%. The method can be used to provides optimal tuning of parameters critical for controller design, operational optimization and daily maintenance for hydroturbines in general.

Dynamics doi: 10.3390/dynamics5020019

Authors: Carmine Maria Pappalardo Giuseppe Isola Angela Donadio Rosario La Regina Valentino Paolo Berardi Domenico Guida

This research work aims to design and develop a dynamic vibration absorber that effectively reduces the vibrations of a flexible structure subjected to external loads. The analysis presented in this paper initially focuses on identifying the resonance frequencies of a typical structural system, which serves as the case study, since these frequencies are critical to dampening due to their potential to cause excessively large vibration amplitudes. Following this, the optimal parameters of the vibration absorber, including the mass, stiffness, and damping characteristics of the proposed design, were determined. Additionally, this paper proposes and examines the use of viscous-type damping, which is achieved through piston–cylinder systems connected to the structural components of the analyzed frame structure. Thus, the main contributions of this work include the analytical dimensioning, the technical design, and the virtual prototyping of a dynamic absorber constructed using a guyed mast structure capable of significantly reducing mechanical vibrations. This design solution ultimately enhances the strength and durability of the frame structure represented in the case study under external excitation, particularly in the worst-case scenario of seismic action. Furthermore, a key aspect of this study is implementing a new numerical procedure for identifying the system equivalent stiffness coefficient based on its mass and modal parameters, which is particularly useful in engineering applications. The numerical experiments conducted in this work support the effectiveness of the proposed design solution, devised specifically for the dynamic vibration absorber developed in this paper.

Dynamics doi: 10.3390/dynamics5020018

Authors: Boutros Azizi Habib Eslami Kais Jribi

An analytical study of the nonlinear response of imperfect stiffened doubly curved shells made of functionally graded material (FGM) is presented. The formulation of the problem is based on the first-order shear deformation shell theory in conjunction with the von Kármán geometrical nonlinear strain–displacement relationships. The nonlinear equations of the motion of stiffened double-curved shells based on the extended Sanders’s theory were derived using Galerkin’s method. The material properties vary in the direction of thickness according to the linear rule of mixture. The effect of both longitudinal and transverse stiffeners was considered using Lekhnitsky’s technique. The fundamental frequencies of the stiffened shell are compared with the FE solutions obtained by using the ABAQUS 6.14 software. A stepwise approximation technique is applied to model the functionally graded shell. The resulting nonlinear ordinary differential equations were solved numerically by using the fourth-order Runge–Kutta method. Closed-form solutions for nonlinear frequency–amplitude responses were obtained using He’s energy method. The effect of power index, functionally graded stiffeners, geometrical parameters, and initial imperfection on the nonlinear response of the stiffened shell are considered and discussed.

Dynamics doi: 10.3390/dynamics5020017

Authors: Dario Handrick Mattie Eckenrode Junsoo Lee

This paper presents a comprehensive review of tethered unmanned aerial vehicles (UAVs), focusing on their challenges and potential applications across various domains. We analyze the dynamic characteristics of tethered UAV systems and address the unique challenges they present, including complex tether dynamics, impulsive forces, and entanglement risks. Additionally, we explore application-specific challenges in areas such as payload transportation and ground-connected systems. The review also examines existing tethered UAV testbed designs, highlighting their strengths and limitations in both simulation and experimental settings. We discuss advancements in multi-UAV cooperation, ground–air collaboration through tethers, and the integration of retractable tether systems. Moreover, we identify critical future challenges in developing tethered UAV systems, emphasizing the need for robust control strategies and innovative solutions for dynamic and cluttered environments. Finally, the paper provides insights into the future potential of variable-length tethered UAV systems, exploring how these systems can enhance versatility, improve operational safety, and expand the range of feasible applications in industries such as logistics, emergency response, and environmental monitoring.

Dynamics doi: 10.3390/dynamics5020016

Authors: Christina Durón Hannah Kravitz Moysey Brio

In this work, we introduce an edge centrality measure for the Helmholtz equation on metric graphs, a particular flow network, based on spectral edge energy density. This measure identifies influential edges whose removal significantly changes the energy flow on the network, as indicated by statistically significant p-values from the two-sample Kolmogorov–Smirnov test comparing edge energy densities in the original network to those with a single edge removed. We compare the proposed measure with eight vertex centrality measures applied to a line graph representation of each metric graph, as well as with two edge centrality measures applied directly to each metric graph. Both methods are evaluated on two undirected and weighted metric graphs—a power grid network adapted from the IEEE 14-bus system and an approximation of Poland’s road network—both of which are multigraphs. Two experiments evaluate how each measure’s edge ranking impacts the energy flow on the network. The results demonstrate that the proposed measure effectively identifies influential edges in metric graphs that significantly change the energy distribution.

Dynamics doi: 10.3390/dynamics5020015

Authors: Gianluca Megna Luciano Cantone Andrea Bracciali

Buffer stops have always been installed on blind tracks to mitigate the hazards associated with overruns due to insufficient or wrong braking. Conventional buffer stops fixed to the rails may absorb only limited energy while Energy-Absorbing Buffers Stops (EABS) dissipate higher energy hydraulically and/or by friction from sliding blocks clamped to the rail head. The assessment of EABS performances in terms of maximum stopping distance and maximum allowed deceleration is usually performed by using the common kinematic rules of motion and considering the overrunning train as a single mass hitting the buffer stop. This paper studies the dynamic characteristics of the collision of entire trains with a friction EABS applying a Longitudinal Train Dynamics (LTD) approach. Several realistic scenarios using the UIC approved TrainDy software were simulated considering various train compositions, with different types of vehicles (locomotives, freight wagons and passenger coaches) and different kinds of buffers. The results show that high dynamic loads are exerted on the vehicles within the train, while the average deceleration and the stopping distance are not greatly influenced when compared with a simpler Finite Element Method (FEM) approach that does not consider the train composition. The progressive application of the EABS braking force increases the stopping distance but can reduce the peak deceleration of about 50%. The results may be used to tune the design parameters of friction EABS according to the currently available specifications and standards for rolling stock structural assessment considering that no international standards for EABS exist currently.

Dynamics doi: 10.3390/dynamics5020014

Authors: Rui Zhang Qingyuan Yang Hui Li Dazheng Zhang Siyu Zheng Shengyou Yang

As high-speed train operations increase, the aerodynamic pressure generated by these trains can jeopardize the structural integrity of sound barriers, potentially compromising train safety and the stability of nearby facilities. This paper investigates the unique aerodynamic pressures and load distribution of various types of sound barriers. We analyze the aerodynamic pressure distribution on sound barriers in relation to high-speed trains by utilizing Computational Fluid Dynamics (CFDs) analysis. We explore the theoretical foundations, design of the computational domain, and settings for boundary conditions. The findings indicate that high-speed trains generate both overpressure from compression waves and under pressure from expansion waves. As the barriers become more open, peak aerodynamic pressure and fluctuations decrease. Notably, the highest pressure occurs at the entrance of the barriers. The accuracy of the model is validated with data from a CRH series train traveling at 350 km/h. This paper offers valuable insights to enhance our understanding and improve sound barrier design for a quieter future.

Dynamics doi: 10.3390/dynamics5020013

Authors: Majid Aleyaasin

This paper uses the flexural vibration of cantilever beams as a benchmark problem to test mesh-free and finite element methods in structural dynamics. First, a symbolic analysis of the “kernel collocation” type mesh-free method is carried out, in which the collocation function satisfies the boundary conditions. This enables both Finite Element (FE) and mesh-free results to be compared with exact analytical ones. Thereafter, the natural frequencies and Frequency Response Function (FRF), in terms of the beam parameters, are determined and compared with the analytical results, that exist in the literature. It is shown that by adjusting the parameters of the kernel function, we can find identical peaks to those of the analytical method. The finite element method is also employed to solve this problem, and the first three natural frequencies were computed in terms of the beam parameters. When comparing the two methods, we see that by increasing the number of elements in the FEM we can always achieve better accuracy, but we will obtain twice the number of modal frequencies. However, the mesh-free method with the same number of nodes does not provide these extra frequencies. From this benchmark problem, it is concluded that the accuracy of the mesh-free methods always depends on the adjustment of the kernel function. However, the FEM is advantageous because it does not require such adjustments.

Dynamics doi: 10.3390/dynamics5020012

Authors: North Yates Fernando Ponta Alayna Farrell

One concern in the field of Horizontal Axis Wind Turbines (HAWTs) is what control strategies are needed to handle gust pulses in the wind to prevent extreme oscillations of the blades to reduce fatigue stress, prevent blade rupture, and extend the turbine’s operational life. In order to design innovative control strategies to modify the blade’s oscillatory response, it is crucial to establish the fundamental vibrational behavior of the blades when excited by gust pulses of different frequencies and amplitudes present in the fluctuating wind inflow. In a series of previous works, the authors presented a novel Reduced-Order Characterization (ROC) technique that provided an energy-based characterization of the fundamental modes of oscillation of wind turbine rotors when excited by combinations of wind gust pulses of different frequencies and amplitudes. The main focus of the present work is to extend these original notions of energy-based ROC to a universal technique expressed in terms of non-dimensional quantities that could be applied to turbines of any size, operating in any set of wind conditions, as long as they share geometrical and material similarity. The ROC technique provides a simple formula that is capable of predicting the dominant vibrational modes of a blade with sufficient precision to be useful in the determination of a control decision that can be computed in real time, an aspect of fundamental importance in dealing with rapid fluctuations in wind conditions.

Dynamics doi: 10.3390/dynamics5020011

Authors: Edward Bormashenko

The Ramsey approach is applied to analyses of the kinematics of systems built of non-relativistic, motile point masses/particles. This approach is based on colored graph theory. Point masses/particles serve as the vertices of the graph. The time dependence of the distance between the particles determines the coloring of the links. The vertices/particles are connected with orange links when particles move away from each other or remain at the same distance. The vertices/particles are linked with violet edges when particles converge. The sign of the time derivative of the distance between the particles dictates the color of the edge. Thus, a complete, bi-colored Ramsey temporal graph emerges. The suggested coloring procedure is not transitive. The coloring of the links is time-dependent. The proposed coloring procedure is frame-independent and insensitive to Galilean transformations. At least one monochromatic triangle will inevitably appear in the graph emerging from the motion of six particles due to the fact that the Ramsey number R3,3=6. This approach is extended to the analysis of systems containing an infinite number of moving point masses. An infinite monochromatic (violet or orange) clique will necessarily appear in the graph. Applications of the introduced approach are discussed. The suggested Ramsey approach may be useful for the analysis of turbulence seen within the Lagrangian paradigm.

Dynamics doi: 10.3390/dynamics5010010

Authors: Daniela Gheorghe Gheorghe Maria Laura Renea Crina Muscalu

In recent years, inulin enzymatic hydrolysis has become a very promising alternative for producing fructose on a large scale. Genetically modified chicory was used to extract inulin of industrial quality. By using an adequate kinetic model from the literature, this study aimed to determine the optimal operating alternatives of a batch (BR) or fed-batch (FBR) reactor used for the hydrolysis of inulin to fructose. The operation of the FBR with a constant or variable/dynamic feeding was compared to that of the BR to determine which best maximizes reactor production while minimizing enzyme consumption. Multi-objective optimal solutions were also investigated by using the Pareto-optimal front technique. Our in-silico analysis reveals that, for this enzymatic process, the best alternative is the FBR operated with a constant control variable but using the set-point given by the (breakpoint) of the Pareto optimal front under the imposed technological constraints. This set point reported the best performances, regarding all the considered opposite economic objectives. Also, the FBR with a constant, but NLP optimal feeding, reported fairly good performances.

Dynamics doi: 10.3390/dynamics5010009

Authors: Stylianos Vasileios Kontomaris Gamal M. Ismail Vassilis Alimisis Christos Dimas Anna Malamou

Solving nonlinear oscillations is challenging, as solutions to the corresponding differential equations do not exist in most cases. Therefore, numerical methods are usually employed to calculate the precise oscillation frequency. In addition, many interesting mathematical approaches leading to approximate solutions have also been developed. This paper focuses on a classic case of a nonlinear oscillator: the oscillator with an odd-power polynomial restoring force. This case encompasses nearly all scenarios of undamped nonlinear oscillations. The idea is to combine two well-known strategies from the literature: He’s approximation, which is simple to apply and valid for small amplitudes, and the analytical solutions for oscillations with power-law restoring forces. It is shown that by combining these approaches, a universal equation accurate for any amplitude is derived. Many tests of the proposed method’s accuracy are presented using polynomials of various degrees and classic examples, such as the rotating pendulum, cubic–quintic Duffing oscillators, and oscillators with cubic and harmonic restoring forces. In addition, a novel ‘electrical analogue’ of the oscillation with a polynomial-type restoring force is introduced to demonstrate that the methods presented in this paper can be applied in real industrial applications.

Dynamics doi: 10.3390/dynamics5010008

Authors: Edward B. Ang Jaime P. Honra

Global climate change has renewed interest in wind energy adoption and integration for on-grid and off-grid applications. Savonius wind turbines offer substantial advantages for small-scale energy generation in low-wind speed conditions, like urban environments, but suffer from low efficiency. This study focused on the numerical characterization of a novel compact three-blade Savonius rotor design with modified pointed deflectors to promote better flow attachment and enhance airflow guidance directionality. Computational Fluid Dynamics (CFD) was employed to identify the flow characteristics and optimal tip speed ratios for maximum power and torque coefficients under two different uniform low-wind-speed conditions. A Finite Element Analysis-Computational Fluid Dynamics (FEA-CFD) coupled analysis method was also utilized to determine the aerodynamic and structural characteristics of the design in ABS plastic. Flow visualization and FEA-CFD coupled analysis highlighted the novel tip deflectors’ exceptional performance in directing wind flow and pressure toward the concave side of the approaching blades, enhancing drag differential and rotor efficiency. Modest power and low torque coefficients and the optimal TSR values under different uniform low-wind-speed conditions were also identified. The work provided valuable insights on the turbine performance of the novel design and guidance on potential future improvements.

Dynamics doi: 10.3390/dynamics5010007

Authors: Akihiro Nishiyama Shigenori Tanaka Jack Adam Tuszynski

In this paper, we introduce waveguide Quantum Electrodynamics (wQED) for the description of tryptophans in microtubules representing data qubits for information storage and, possibly, information processing. We propose a Hamiltonian in wQED and derive Heisenberg equations for qubits and photons. Using the Heisenberg equations, we derive time-evolution equations for the probability of qubits and the distribution of photons both at zero and finite temperature. We then demonstrate the resultant sub-radiance with small decay rates, which is required to achieve robust data qubits for information storage by coupling tryptophan residues containing data qubits with water molecules as Josephson quantum filters (JQFs). We also describe an oscillation processes of qubits in a tubulin dimer through the propagation of excitations with changing decay rates of JQFs. Data qubits are found to retain initial values by adopting sub-radiant states involving entanglement with water degrees of freedom.

Dynamics doi: 10.3390/dynamics5010006

Authors: Egor S. Rodionov Andrey Ya. Cherepanov Alfiya G. Fazlitdinova Timur T. Sultanov Victor G. Lupanov Polina N. Mayer Alexander E. Mayer

A novel method to measure dynamic flow stress and corresponding strain rates obtained from Taylor tests using profiled samples with a reduced cylindrical head part was applied to study the dynamic characteristics of similar commercial 7075 and V95T1 aluminum alloys. The measured dynamic flow stress is verified using a classical Taylor’s approach with uniform cylinders and compared with the literature data. Our study shows that the dynamic flow stress of 7075 alloy, which is 786 MPa at strain rates of (4–8) × 103 s−1, exceeds the value of 624 MPa for V95T1 alloy at strain rates of (2–6) × 103 s−1 by 25%. The threshold impact velocity resulting in fracture of the 4 mm head part of the profiled samples is 116–130 m/s for 7075 alloy and only 108 m/s for V95T1 alloy. The fracture pattern is also different between the alloys with characteristic shear-induced cracks oriented at 45° to the impact direction in the case of V95T1 alloy and perpendicular to the breaking off head part in the case of 7075 alloy. On the other hand, the compressive fracture strain of V95T1 alloy, which is 0.29–0.36, exceeds that of 7075 alloy, which is 0.27–0.33, by approximately 8%. Thus, V95T1 aluminum alloy exhibits less strength but is more ductile, while 7075 aluminum alloy exhibits more strength but is simultaneously more brittle.

Dynamics doi: 10.3390/dynamics5010005

Authors: Sören Bieler Kerstin Weinberg

The Split-Hopkinson pressure bar (SHPB) test is a commonly accepted experiment to investigate the material behavior under high strain rates. Due to the low impedance of soft materials, here, the test has to be performed with plastic bars instead of metal bars. Such plastic bars have a certain viscosity and require a correction of the measured signals to account for the attenuation and dispersion of the transmitted waves. This paper presents a signal correction method based on a spectral decomposition of the strain-wave signals using Fast Fourier Transform and additional applied strain gauges in the experimental setup. The concept can be used to adapt the pulses and to concurrently validate the measurement method, which supports the evaluation of the experiment. Our investigation is carried out with a Split-Hopkinson pressure bar setup of PMMA bars and silicon-like specimens produced by the 3D printing process of digital light processing.

Dynamics doi: 10.3390/dynamics5010004

Authors: Leonardi Hernández-Sánchez Irán Ramos-Prieto Francisco Soto-Eguibar Héctor M. Moya-Cessa

In this study, we present an exact solution to the Lindblad master equation describing the interaction of two quantized electromagnetic fields in a decaying cavity coupled to a thermal reservoir at a finite temperature. The solution is obtained using the superoperator technique, leveraging commutation relations to factorize the exponential of the Lindblad superoperators into a product of exponentials. To demonstrate the applicability of this approach, we analyze the dynamics of the system both analytically and numerically for two initial conditions: nonentangled and entangled coherent states, exploring their temporal evolution. Additionally, we employ entropy and quantum discord analysis to characterize quantum correlations and analyze the behavior of entanglement (or lack thereof) during the evolution. This comprehensive analysis provides valuable insights into the behavior of open quantum systems and their interaction with the environment.

Dynamics doi: 10.3390/dynamics5010003

Authors: João Marcos P. Vieira José Pedro G. Carvalho Dênis E. C. Vargas Érica C. R. Carvalho Patrícia H. Hallak Afonso C. C. Lemonge

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss).

Dynamics doi: 10.3390/dynamics5010002

Authors: Nayema Islam Nima Mohammed Abdul Hannan

This study investigates mixed convection flow over a vertical thin needle with variable surface heat, mass, and microbial flux, incorporating the influence of gyrotactic microorganisms. The governing partial differential equations are transformed into ordinary differential equations using appropriate similarity transformations and then solved numerically by employing MATLAB’s Bvp4c solver. The primary focus lies in examining the influence of various dimensionless parameters, including the mixed convection parameter, power-law index, buoyancy parameters, bioconvection parameters, and needle size parameters, on the velocity, temperature, concentration, and microbe profiles. The results indicate that these parameters significantly affect the surface (wall) temperature, fluid concentration, and motile microbe concentration, as well as the corresponding velocity, temperature, concentration, and microorganism profiles. The findings provide insights into the intricate dynamics of mixed convection flow with bioconvection and have potential applications in diverse fields such as biomedicine and engineering.

Dynamics doi: 10.3390/dynamics5010001

Authors: Chao Wang Xingyou Yi Jinlei Lv Qiang Peng

A static pressure probe is a crucial tool for measuring static pressure fluctuations, and its internal cavity structure can significantly affect the accuracy of the data obtained. This study investigates the impact of the static pressure probe cavity on the frequency response characteristics of fluctuating pressure using both experimental and numerical simulations. The results are validated by comparing them with the behavior of a second-order system. Our findings indicate that the internal cavity of the static pressure probe acts as a second-order underdamped system. This system amplifies fluctuating pressure signals at frequencies below the characteristic frequency while attenuating those above it. The frequency response characteristics of the probe’s cavity are similar to those of a Helmholtz resonator. Among various factors, the diameter of the pressure tap within the cavity has the most significant effect on the system’s characteristic frequency and amplification ratio. By optimizing the design of the static pressure probe’s cavity dimensions, the precision of fluctuating pressure data below the system’s characteristic frequency can be improved. In the research, based on the Helmholtz resonance equation, we provide a semi-empirical formula for predicting the characteristic frequency of fluctuating pressure in a static pressure probe. Furthermore, by leveraging the mechanism of the static pressure probe’s cavity as a second-order underdamped system, we propose a method for rapid and accurate calibration of the static pressure probe’s fluctuating pressure measurements.

Dynamics doi: 10.3390/dynamics4040046

Authors: Moussa Tembely

In this paper, an analytical technique is proposed to obtain the forced response of a cantilevered tube conveying fluid. By considering the pipe subjected to an arbitrary harmonic force, either distributed or concentrated, an analytical solution is found using Green’s function method. The closed-form solution obtained satisfies the differential equations governing the vibrating tube conveying fluid. The proposed method, which provides exact solutions, is more accurate than the classical eigenfunction expansion or Galerkin’s method and eliminates the need for eigenfunctions, eigenvalues, or infinite series.

Dynamics doi: 10.3390/dynamics4040045

Authors: Alexandra G. Aspioti Nikolaos Th. Fourniotis

In this paper, a brief review regarding the hydrodynamic circulation of the Mediterranean gulfs is presented. Studies concerning the hydrodynamics of the Mediterranean gulfs with significant environmental and commercial importance were gathered as an initial insight of studies in the Mediterranean microtidal environment. Numerical models, field measurements, and satellite images are the methods used by the investigators for the description and prediction of the circulation in the gulfs. The basic hydrodynamic characteristics of the gulfs are mainly defined by the wind action and less by tide and baroclinicity. Most of the gulfs are characterized by a cyclonic wind-driven circulation, since the tidal effect remains weak in the Mediterranean basin. However, tidal resonance and strong currents are evident in the shallow coastal areas as well as in the wider area of straits. Basic gulfs’ characteristics are summarized in a table that gives an overview of the main Mediterranean gulfs, which can be especially useful for young researchers or new hydroenvironmental studies in the Mediterranean marine and coastal environment.

Dynamics doi: 10.3390/dynamics4040044

Authors: Anna Markhotok

The specifics of a shock wave propagation down a positive column of a DC discharge in molecular chemically inert gases has been investigated. It was shown that axial gradients caused by the imbalance in the charged particle momentum transfer to the gas molecules can be a reason for the shock velocity dependence on the electric field direction. In pure nitrogen gas, the calculated shock velocity difference of up to 13.5% is in good agreement with the 12% value obtained in the experiment. A returning gas flow organizing in the discharge as a possible mechanism for an extended shock structure and a number of kinetical factors capable of affecting the shock motion are discussed.

Dynamics doi: 10.3390/dynamics4040043

Authors: Edward Bormashenko Nir Shvalb

We propose a Ramsey-theory-based approach for the analysis of the behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero. The mechanical system is described by a Ramsey-theory-based, bi-colored, complete graph. Vectors of momenta of the particles p→i  serve as the vertices of the graph. We start from the graph representing the system in the frame of the center of masses, where the momenta of the particles in this system are p→cmi. If (p→cmi(t)·p→cmj(t))≥0 is true, the vectors of momenta of the particles numbered i and j are connected with a red link; if (p→cmi(t)·p→cmj(t))<0 takes place, the vectors of momenta are connected with a green link. Thus, the complete, bi-colored graph emerges. Considering an isolated system built of six interacting particles, according to the Ramsey theorem, the graph inevitably comprises at least one monochromatic triangle. The coloring procedure is invariant relative to the rotations/translations of frames; thus, the graph representing the system contains at least one monochromatic triangle in any of the frames emerging from the rotation/translation of the original frame. This gives rise to a novel kind of mechanical invariant. Similar coloring is introduced for the angular momenta of the particles. However, the coloring procedure is sensitive to Galilean/Lorenz transformations. Extensions of the suggested approach are discussed.

Dynamics doi: 10.3390/dynamics4040042

Authors: Ihor Shchur Marek Lis Rostyslav-Ivan Kuzyk

Wind–solar power generating and hybrid battery-supercapacitor energy storage complex is used for autonomous power supply of consumers in remote areas. This work uses passivity-based control (PBC) for this complex in accordance with the accepted energy management strategy (EMS). Structural and parametric synthesis of the overall PBC system was carried out, which was accompanied by a significant amount of research. In order to simplify this synthesis, a structural decomposition of the overall dynamic system of the object presented in the form of a port-Hamiltonian system, which was described by a system of differential equations of the seventh order, into three subsystems was applied. These subsystems are a wind turbine, a PV plant, and a hybrid battery-supercapacitor system. For each of the subsystems, it is quite simple to synthesize the control influence formers according to the interconnections and damping assignment (IDA) method of PBC, which locally performs the tasks set by the EMS. The results obtained by computer simulation of the overall and decomposed systems demonstrate the effectiveness of this approach in simplifying synthesis and debugging procedures of complex multi-physical systems.

Dynamics doi: 10.3390/dynamics4040041

Authors: Erik Bartoš Stanislav Dubnička Anna Zuzana Dubničková Lukáš Holka Andrej Liptaj

Regular damped oscillatory structures from the “effective” electromagnetic form factors of the hadrons h=π±,K±,K0,p,n were investigated. The “effective” electromagnetic form factor behaviors were calculated from the experimental data on the total cross-sections σtot(e+e−→hh¯) with errors. The apparent oscillations were observed for the first time for the proton, and we show, also taking other hadrons into consideration, that they are an arbitrary artifact resulting from a very simplistic theoretical description based on an elementary three-parameter model. If the data are described by a more appropriate and physically well-founded Unitary and Analytic model, then the oscillations disappear. In spite of this, if the three-parameter model is used to describe the “effective” electromagnetic form factor data, an interesting phenomenon is observed. The oscillations are opposite for particles which form an isospin doublet. By using the physically well-founded Unitary and Analytic model, it is demonstrated that this feature originates from the special transformation properties of the electromagnetic current of the corresponding particles in the isotopic space.

Dynamics doi: 10.3390/dynamics4040040

Authors: Andreas Kardoulias Alexandros Arailopoulos Panagiotis Seventekidis

Structural Health Monitoring (SHM) plays a vital role in ensuring the health status of a wide range of structures, such as bridges, buildings, and large infrastructure in general. The advantages of this process can be further enhanced by incorporating more numerical and statistical approaches into traditional methods, such as finite element analysis and Machine Learning. In this study, a truss bridge structure is examined, and neural networks are trained with data derived from finite element analyses under static loads and dynamic excitations. The contributions of this work are based on comparing neural networks trained with static and dynamic analyses, as well as deriving important insights into the key parameters that impact their performance in SHM. Initially, a binary classification problem is addressed, where numerically trained classifiers are tasked with identifying whether the structure is in a healthy state or not. This category is further divided into two subcategories, depending on the extent of the damage present in the structure. Subsequently, a multi-class classification problem is defined, where three different damage classes of the same extent are considered, and the trained network is required to distinguish between them. Although the training of all neural networks was highly satisfactory, the prediction results varied, with success rates ranging from 55% to 90%. Finally, conclusions are drawn from the results of the study regarding the model error influence, the impact of the damage size, and the types of neural networks and training data used.

Dynamics doi: 10.3390/dynamics4040039

Authors: Le Hong Thai Huynh Dinh Tu Tran Dac Dung Truong

Marine propeller design requirements have risen in quantity and quality in recent decades. Reduced propeller cavitation is targeted to ensure that comfort requirements and environmental regulations are met. This paper presents the development of a mesh refinement process for the numerical prediction of tip vortex cavitation (TVC) using the commercial CFD package STAR-CCM+. Given the strong dependence on the mesh resolution within the areas of interest, mesh refinement and the use of field functions for adaptive meshing were demonstrated. The developed numerical model was substantiated against relevant published test data. Subsequently, the validated mesh refinement process was extended to scaled-up models representing medium- and full-scale propellers. The results showed that this process can be applied to CFD simulations to capture the minimum pressure within a tip vortex core. This process is also applicable to different types of hydrodynamic propulsors at both model scale and full scale. Additionally, the cavitation inception scaling law was evaluated for all small-scale and full-scale models, and it was found that the scaling parameter obtained using the developed refinement process was somewhat close to that obtained using existing methods. It is expected that the mesh refinement process developed in this study can be used to investigate the effect of scaling on tip vortex cavitation inception.

Dynamics doi: 10.3390/dynamics4040038

Authors: Niclas Strömberg

In this study, a novel non-cooperative two-player game for minimizing static (Player 1) and dynamic (Player 2) compliances is introduced, implemented, and demonstrated using a multi-scale topology optimization framework for triply periodic minimal surface (TPMS)-based lattice structures. Player 1 determines the optimal macro-layout by minimizing the static compliance based on a micro-layout provided by Player 2. Conversely, player 2 identifies the optimal micro-layout (grading of the TPMS-based lattice structure) by minimizing the dynamic compliance given a macro-layout from Player 1. The multi-scale topology optimization formulations are derived using two density variables in each finite element. The first variable is the standard density, which dictates whether the finite element is void or contains the graded lattice structure and is governed by the rational approximation of material properties (RAMP) model. The second density variable represents the local relative density of the TPMS-based lattice structure, determining the effective orthotropic elastic properties of the finite element. The multi-scale game is implemented for three-dimensional problems, and solved using a Gauss–Seidel algorithm with sequential linear programming. It is numerically demonstrated for several benchmarks that the proposed multi-scale game generates equilibrium designs with strong performance for both static and harmonic load cases, effectively avoiding resonance at harmonic load frequencies. Validation is achieved through modal analyses of finite element models of the optimal designs.

Dynamics doi: 10.3390/dynamics4030037

Authors: Huy Tran Pooria Pirdavari Min Y. Pack

The Tea Leaf Paradox (TLP) describes unsteady fluid motions which help entrain and deposit suspended particles at the center of rotation. Various applications depend on the TLP for particle separations—spanning orders of magnitude in length scales—making it an important problem in fluid mechanics. Despite papers describing the phenomenon, the efficacy of particle separation using the TLP remains unclear as to the relative importance of, for example, hydrostatics, particle-fluid density ratio, wall friction, liquid bath aspect ratio and the rotation speed. The dynamics involved are notably complex and require a careful tuning of each variable. In this study, we have investigated the role of the limit of the aggregation dynamics in rotational flows within 3D-printed vessels of various sizes in tandem with particle imaging to probe the dissipation effects on the particle motions. We have found that the liquid bath aspect ratio limits how much aggregation may occur for a particle-fluid density ratio greater than unity (e.g., ρp/ρf>1), where ρp is the density of the particle and ρf is the ambient fluid density.

Dynamics doi: 10.3390/dynamics4030036

Authors: Qingcheng Yu Wenjun Gao Ping Gong Yuanhao Li Can Li

The distribution of oil and gas phases around ball–raceway local regions is an important basis and foundation for determining whether a bearing is sufficiently lubricated. To obtain the oil phase distribution law in the inner raceway–ball contact local region (IBCR) and outer raceway–ball contact local region (OBCR) of the ball bearing with under-race lubrication, the numerical simulation method is used. The effects of bearing rotation speed, oil flow rate, oil viscosity, and oil density on these two regions are studied. The results indicate that the oil phase exhibited significant periodic changes in both time and space. Compared with that in the IBCR, the oil phase distribution in the OBCR is more uniform. Increasing the bearing rotation speed and reducing the oil flow rate made the IBCR and OBCR more uniform. Changing the oil viscosity only alters the distribution pattern of the OBCR. The oil density may not affect the fluid flow state or the oil phase distribution in the bearing.

Dynamics doi: 10.3390/dynamics4030035

Authors: Gabriel J. Williams

Tropical cyclones (TCs) can be characterized as a 3D annular structure of elevated potential vorticity (PV). However, strong mature TCs often develop a secondary eyewall, leading to a 3D annular vortex with a double-eyewall structure. Using 2D linear stability analysis, it is shown that three types of barotropic instability (BI) are present for annular vortices with a double-eyewall structure: Type-1 BI across the secondary eyewall, Type-2 BI across the moat of the vortex, and Type-3 BI across the primary eyewall. The overall stability of these vortices (and the type of BI that develops) depends principally upon five vortex parameters: the thickness of the primary eyewall, the thickness of the secondary eyewall, the moat width, the vorticity ratio between the eye and the primary eyewall, and the vorticity ratio between the primary and secondary eyewall. The adiabatic evolution of 3D annular vortices with a double-eyewall structure is examined using a primitive equation model in normalized isobaric coordinates. It is shown that Type-2 BI is the most common type of BI for 3D annular vortices whose vortex parameters mimic TCs with a double-eyewall structure. During the onset of Type-2 BI, eddy kinetic energy budget analysis indicates that barotropic energy conversion from the mean azimuthal flow is the dominant energy source of the eddies, which produces a radial velocity field with a quadrupole structure. Absolute angular momentum budget analysis indicates that Type-2 BI generates azimuthally averaged radial outflow across the moat, and the eddies transport absolute angular momentum radially outward towards the secondary eyewall. The combination of these processes leads to the dissipation of the primary eyewall and the maintenance of the secondary eyewall for the vortex.

Dynamics doi: 10.3390/dynamics4030034

Authors: Wasaif H. R. Alruwaele Jitesh S. B. Gajjar

In this paper, we consider the flow of a nanofluid in an enclosed lid-driven cavity using a single-phase model. Two cases are considered: one in which the top and bottom walls are kept at adiabatic conditions, and a second case in which the left- and right-side walls are kept in adiabatic conditions. The impact of different viscosity models on the mixed convection heat transfer is examined, and numerical methods are used to obtain solutions for the Navier–Stokes equations for various parameter ranges. Using our robust methods, we are able to obtain novel solutions for large Reynolds numbers and very small Richardson numbers. Using water as the base fluid and aluminium oxide nanoparticles, our results suggest that heat transfer enhancement occurs with increasing particle concentration and decreasing Richardson numbers. There are also significant differences depending on the viscosity model used in terms of the impact of reducing corner recirculation regions in the cavity.

Dynamics doi: 10.3390/dynamics4030033

Authors: A. H. Abbas Hend Abdel-Ghani Ivan S. Maksymov

Artificial intelligence (AI) systems of autonomous systems such as drones, robots and self-driving cars may consume up to 50% of the total power available onboard, thereby limiting the vehicle’s range of functions and considerably reducing the distance the vehicle can travel on a single charge. Next-generation onboard AI systems need an even higher power since they collect and process even larger amounts of data in real time. This problem cannot be solved using traditional computing devices since they become more and more power-consuming. In this review article, we discuss the perspectives on the development of onboard neuromorphic computers that mimic the operation of a biological brain using the nonlinear–dynamical properties of natural physical environments surrounding autonomous vehicles. Previous research also demonstrated that quantum neuromorphic processors (QNPs) can conduct computations with the efficiency of a standard computer while consuming less than 1% of the onboard battery power. Since QNPs are a semi-classical technology, their technical simplicity and low cost compared to quantum computers make them ideally suited for applications in autonomous AI systems. Providing a perspective on the future progress in unconventional physical reservoir computing and surveying the outcomes of more than 200 interdisciplinary research works, this article will be of interest to a broad readership, including both students and experts in the fields of physics, engineering, quantum technologies and computing.

Dynamics doi: 10.3390/dynamics4030032

Authors: Dario Sanna David Paolo Madonna Mauro Pontani Paolo Gasbarri

The NASA’s Artemis project intends to bring humans back to the Moon in the next decade. A key element of the project will be the Lunar Gateway, a space station placed in a peculiar, near rectilinear Halo orbit in the vicinity of a collinear libration point in the Earth–Moon system. This study focuses on the high-fidelity description of the relative orbit dynamics of a chaser spacecraft with respect to the Gateway, as well as on the design of a proper orbit control strategy for rendezvous maneuvers. A novel formulation of the Battin–Giorgi approach is introduced, in which the reference orbit is that traveled by the Gateway, i.e., it is a highly non-Keplerian, perturbed orbit. The modified Battin–Giorgi approach allows for the description of a relative orbit motion with no restrictive assumption, while including all the relevant orbit perturbations on both the chaser and the Gateway. Moreover, nonlinear hybrid predictive control is introduced as a feedback guidance strategy. This new technique is shown to outperform the classical, well-established feedback linearization in terms of success rate and accuracy on the final conditions. Moreover, a Monte Carlo analysis confirms that hybrid predictive control is also effective in the presence of the temporary unavailability of propulsion or thrust misalignment.

Dynamics doi: 10.3390/dynamics4030031

Authors: Jason Knight Jay Patel Harry Prouse-Edwards Simon Fels Diogo Montalvao Andrew Lewis

The dynamic behaviour of a spring-mounted symmetrical NACA0012 wing in a freestream flow of air is studied in the pre-stall region, over 0° to 12° angles of incidence. The primary aim of this work is for use within the automotive sector to reduce drag and fuel emissions. However, this work will also be of interest in the motorsport sector to improve performance, and also have some applications within the aerospace and renewable energy sectors. The general operation of the concept has previously been verified at these low angles in the pre-stall region with that of a theoretical estimation using finite and infinite wings. This paper provides a numerical solution of the same problem and is compared with the previous experimentation. At these low angles, the computations yield a dynamic response settling into a static equilibrium. The stable solutions match the start of a steady regime well, when compared with the experiment. The trends are also comparable with the experiment, but the velocities at which they occur are underestimated in the computation. The computations demonstrate a drag reduction of 59% when compared to a fixed wing, whereas the lift remains stable at a near constant value with increasing wind speed. Thence, downforce is maintained whilst drag is reduced, which will facilitate higher speeds on the straight whilst maintaining vehicle direction stability. Limitations to this proof-of-concept work are highlighted and future development work is suggested to achieve even further increases in performance.

Dynamics doi: 10.3390/dynamics4030030

Authors: Kaleem Iqbal Eugenia Rossi di Schio Muhammad Adnan Anwar Mudassar Razzaq Hasan Shahzad Paolo Valdiserri Giampietro Fabbri Cesare Biserni

A finite element method is employed to examine the impact of a magnetic field on the development of plaque in an artery with stenotic bifurcation. Consistent with existing literature, blood flow is characterized as a Newtonian fluid that is stable, incompressible, biomagnetic, and laminar. Additionally, it is assumed that the arterial wall is linearly elastic throughout. The hemodynamic flow within a bifurcated artery, influenced by an asymmetric magnetic field, is described using the arbitrary Lagrangian–Eulerian (ALE) method. This technique incorporates the fluid–structure interaction coupling. The nonlinear system of partial differential equations is discretized using a stable P2P1 finite element pair. To solve the resulting nonlinear algebraic equation system, the Newton-Raphson method is employed. Magnetic fields are numerically modeled, and the resulting displacement, velocity magnitude, pressure, and wall shear stresses are analyzed across a range of Reynolds numbers (Re = 500, 1000, 1500, and 2000). The numerical analysis reveals that the presence of a magnetic field significantly impacts both the displacement magnitude and the flow velocity. In fact, introducing a magnetic field leads to reduced flow separation, an expanded recirculation area near the stenosis, as well as an increase in wall shear stress.

Dynamics doi: 10.3390/dynamics4030029

Authors: Gianluca Megna

Freight wagons in Europe have used Y25 bogies since the 1960s. Although very cost-effective, Y25 suffers from intrinsic limitations due to its architecture and running behaviour. This study introduces an innovative lightweight bogie, named 4L bogie, aimed at removing those limitations as well as improving running dynamics and track friendliness. This task was particularly challenging as the high ratio between laden and tare weight (up to 5:1) forced us to use a non-conventional suspension system and an innovative architecture of frame, reducing the mass by about 15% and the yaw moment of inertia by about 30% with respect to the Y25 bogie. Maintenance issues were addressed by reducing the number of components and easing overhaul, while the new design was validated from both the structural and the running dynamics point of view, assessing its interaction with the track in terms of stability, curving behaviour and the vertical response of the 4L bogie. Stability was improved by about 20% even in empty conditions and high conicity at the wheel/rail contact. Vertical dynamic force on a straight track, evaluated according to the Ride Force Count metric, and wear behaviour on sharp and mild curves were considerably reduced, leading to an improved track friendliness of the bogie.

Dynamics doi: 10.3390/dynamics4030028

Authors: Natalya Grachyova Eugenii Fomin Alexander Mayer

The development of dynamic plasticity models with accounting of interplay between several plasticity mechanisms is an urgent problem for the theoretical description of the complex dynamic loading of materials. Here, we consider dynamic plastic relaxation by means of the combined action of dislocations and phase transitions using Al-Cu solid solutions as the model materials and uniaxial compression as the model loading. We propose a simple and robust theoretical model combining molecular dynamics (MD) data, theoretical framework and machine learning (ML) methods. MD simulations of uniaxial compression of Al, Cu and Al-Cu solid solutions reveal a relaxation of shear stresses due to a combination of dislocation plasticity and phase transformations with a complete suppression of the dislocation activity for Cu concentrations in the range of 30–80%. In particular, pure Al reveals an almost complete phase transition from the FCC (face-centered cubic) to the BCC (body-centered cubic) structure at a pressure of about 36 GPa, while pure copper does not reveal it at least till 110 GPa. A theoretical model of stress relaxation is developed, taking into account the dislocation activity and phase transformations, and is applied for the description of the MD results of an Al-Cu solid solution. Arrhenius-type equations are employed to describe the rates of phase transformation. The Bayesian method is applied to identify the model parameters with fitting to MD results as the reference data. Two forward-propagation artificial neural networks (ANNs) trained by MD data for uniaxial compression and tension are used to approximate the single-valued functions being parts of constitutive relation, such as the equation of state (EOS), elastic (shear and bulk) moduli and the nucleation strain distance function describing dislocation nucleation. The developed theoretical model with machine learning can be further used for the simulation of a shock-wave structure in metastable Al-Cu solid solutions, and the developed method can be applied to other metallic systems, including high-entropy alloys.

Dynamics doi: 10.3390/dynamics4030027

Authors: Driss Lahboub Rodolphe Heyd Mohamed Lotfi Abderrahim Bakak Abdelaziz Koumina

This paper focuses on the numerical study of spherical particle sedimentation, taking into account hydrodynamic interactions. Infinite impulse response (IIR) digital filters, specially tailored to solve the sedimentation dynamics, were used in the present study to numerically solve the coupled ordinary differential equations with the time-dependent coefficients of the problem. Hydrodynamic interactions are modeled using the Rotne–Prager–Yamakawa (RPY) approximation, to which a correction is made to better account for short-range interactions. In order to validate both the proposed numerical resolution method and the RPY correction, this paper begins with the study of two interacting spherical particle sedimentation methods. Comparisons with previously published analytical or numerical results confirm the relevance of the present approach.

Dynamics doi: 10.3390/dynamics4030026

Authors: Gianluca Gorni Mattia Scomparin Gaetano Zampieri

Some characteristics of stationary flows of the Sawada–Kotera system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom. All of these systems come in couples that have the same equations of motion, although they are not related by a gauge transform. Some nonpolynomial examples are provided.