Dynamics doi: 10.3390/dynamics4030026

Authors: Gianluca Gorni Mattia Scomparin Gaetano Zampieri

Some characteristics of stationary flows of the Sawada&ndash;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.

]]>Dynamics doi: 10.3390/dynamics4020025

Authors: Parindra Kusriantoko Per Fredrik Daun Kristian Etienne Einarsrud

Fluidized beds are pivotal in the process industry and chemical engineering, with Computational Fluid Dynamics (CFD) playing a crucial role in their design and optimization. Challenges in CFD modeling stem from the scarcity or inconsistency of experimental data for validation, along with the uncertainties introduced by numerous parameters and assumptions across different CFD codes. This study navigates these complexities by comparing simulation results from the open-source MFIX and OpenFOAM, and the commercial ANSYS FLUENT, against experimental data. Utilizing a Eulerian&ndash;Eulerian framework and the kinetic theory of granular flow (KTGF), the investigation focuses on solid-phase properties through the classical drag laws of Gidaspow and Syamlal&ndash;O&rsquo;Brien across varied parameters. Findings indicate that ANSYS Fluent, MFiX, and OpenFOAM can achieve reasonable agreement with experimental benchmarks, each showcasing distinct strengths and weaknesses. The study also emphasizes that both the Syamlal&ndash;O&rsquo;Brien and Gidaspow drag models exhibit reasonable agreement with experimental benchmarks across the examined CFD codes, suggesting a moderated sensitivity to the choice of drag model. Moreover, analyses were also carried out for 2D and 3D simulations, revealing that the dimensional approach impacts the predictive accuracy to a certain extent, with both models adapting well to the complexities of each simulation environment. The study highlights the significant influence of restitution coefficients on bed expansion due to their effect on particle&ndash;particle collisions, with a value of 0.9 deemed optimal for balancing simulation accuracy and computational efficiency. Conversely, the specularity coefficient, impacting particle&ndash;wall interactions, exhibits a more subtle effect on bed dynamics. This finding emphasizes the critical role of carefully choosing these coefficients to effectively simulate the nuanced behaviors of fluidized beds.

]]>Dynamics doi: 10.3390/dynamics4020024

Authors: Md Shazzad Hossain Ibrahim Sultan Truong Phung Apurv Kumar

Organic Rankine Cycle (ORC)&ndash;based small-scale power plants are becoming a promising instrument in the recent drive to utilize renewable sources and reduce carbon emissions. But the effectiveness of such systems is limited by the low efficiency of gas expanders, which are the main part of an ORC system. Lima&ccedil;on-based expansion machines with a fast inlet control valve have great prospects as they could potentially offer efficiencies over 50%. However, the lack of a highly reliable and significantly fast control valve is hindering its possible application. In this paper, a push&ndash;pull solenoid valve is optimized using a stochastic optimization technique to provide a fast response. The optimization yields about 56&ndash;58% improvement in overall valve response. A performance comparison of the initial and optimized valves applied to a lima&ccedil;on expander thermodynamic model is also presented. Additionally, the sensitivity of the valve towards a changing inlet pressure and expander rotor velocity is analyzed to better understand the effectiveness of the valve and provide clues to overall performance improvement.

]]>Dynamics doi: 10.3390/dynamics4020023

Authors: Nithin Mohan Narayan Pierre Max Landgraf Thomas Lampke Udo Fritsching

High-pressure gas quenching is widely used in the metals industry during the heat treatment processing of steel specimens to improve their material properties. In a gas quenching process, a preheated austenised metal specimen is rapidly cooled with a gas such as nitrogen, helium, etc. The resulting microstructure relies on the temporal and spatial thermal history during the quenching. As a result, the corresponding material properties such as hardness are achieved. Challenges reside with the selection of the proper process parameters. This research focuses on the heat treatment of steel sample batches. The gas quenching process is fundamentally investigated in experiments and numerical simulations. Experiments are carried out to determine the heat transfer coefficient and the cooling curves as well as the local flow fields. Quenched samples are analyzed to derive the material hardness. CFD and FEM models numerically determine the conjugate heat transfer, flow behavior, cooling curve, and material hardness. In a novel approach, the experimental and simulation results are adopted to train artificial neural networks (ANNs), which allow us to predict the required process parameters for a targeted material property. The steels 42CrMo4 (1.7225) and 100Cr6 (1.3505) are investigated, nitrogen is the quenching gas, and geometries such as a disc, disc with a hole and ring are considered for batch series production.

]]>Dynamics doi: 10.3390/dynamics4020022

Authors: Matthew A. Morena Kevin M. Short

In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincar&eacute; sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work.

]]>Dynamics doi: 10.3390/dynamics4020021

Authors: Elizabeth P. Tito Vadim I. Pavlov

Thermo-vortices (bright spots, blobs, swirls) in cosmic fluids (planetary atmospheres, or even black hole accretion disks) are sometimes observed as clustered into quasi-symmetrical quasi-stationary groups but conceptualized in models as autonomous items. We demonstrate&mdash;using the (analytical) Sharp Boundaries Evolution Method and a generic model of a thermo-vorticial field in a rotating &ldquo;thin&rdquo; fluid layer in a spacetime that may be curved or flat&mdash;that these thermo-vortices may be not independent but represent interlinked parts of a single, coherent, multi-petal macro-structure. This alternative conceptualization may influence the designs of numerical models and image-reconstruction methods.

]]>Dynamics doi: 10.3390/dynamics4020020

Authors: Georgios Vontzos Vasileios Laitsos Avraam Charakopoulos Dimitrios Bargiotas Theodoros E. Karakasidis

Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson&rsquo;s correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R2), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures.

]]>Dynamics doi: 10.3390/dynamics4020019

Authors: Michael Tsamparlis Aniekan Magnus Ukpong

A semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets: one set containing the Lie derivative of the metric wrt the Lie symmetry generator, and the other set containing the quantities Bi(x,u),F(x,u). From the first set, it follows that the generators of Lie point symmetries are elements of the conformal algebra of the metric Aij, while the second set serves as constraint equations, which select elements from the conformal algebra of Aij. Therefore, it is possible to determine the Lie point symmetries using a geometric approach based on the computation of the conformal Killing vectors of the metric Aij. In the present article, the nonlinear Poisson equation &Delta;gu&minus;f(u)=0 is studied. The metric defined by this equation is 1 + 2 decomposable along the gradient Killing vector &part;t. It is a conformally flat metric, which admits 10 conformal Killing vectors. We determine the conformal Killing vectors of this metric using a general geometric method, which computes the conformal Killing vectors of a general 1+(n&minus;1) decomposable metric in a systematic way. It is found that the nonlinear Poisson equation &Delta;gu&minus;f(u)=0 admits Lie point symmetries only when f(u)=ku, and in this case, only the Killing vectors are admitted. It is shown that the Noether point symmetries coincide with the Lie point symmetries. This approach/method can be used to study the Lie point symmetries of more complex equations and with more degrees of freedom.

]]>Dynamics doi: 10.3390/dynamics4020018

Authors: Yann Marchesse Christophe Changenet Fabrice Ville

The emergence of electric vehicles has brought new issues such as the problem of rolling element bearings (REBs) operating at high speeds. Losses due to these components in mechanical transmissions are a key issue and must therefore be taken into account right from the design stage of these systems. Among these losses, the one induced by the motion of rolling elements, known as drag loss, becomes predominant in high-speed REBs. Although an experimental approach is still possible, it is difficult to isolate this loss in order to study it properly. A numerical approach based on CFD is therefore a possible way forward, even if other issues arise. The aim of this article is to study the ability of such an approach to correctly estimate the drag coefficient associated with the motion of rolling elements. The influence of the numerical domain extension, the mesh refinement, the simplification of the ring shape, and the presence of the cage on the values of the drag coefficient is presented. While it seems possible to compromise on the calculation domain and mesh size, it appears that the other parameters must be taken into account as much as possible to obtain realistic results.

]]>Dynamics doi: 10.3390/dynamics4020017

Authors: Shingo Tomita Joe Yoshikawa Makoto Sugimoto Hisaya Komen Masaya Shigeta

Characteristic dynamics in lava flows, such as the formation processes of lava levees, toe-like tips, and overlapped structures, were reproduced successfully through numerical simulation using the smoothed particle hydrodynamics (SPH) method. Since these specific phenomena have a great influence on the flow direction of lava flows, it is indispensable to elucidate them for accurate predictions of areas where lava strikes. At the first step of this study, lava was expressed using a molten metal with known physical properties. The computational results showed that levees and toe-like tips formed at the fringe of the molten metal flowing down on a slope, which appeared for actual lava flows as well. The dynamics of an overlapped structure formation were also simulated successfully; therein, molten metal flowed down, solidified, and changed the surface shape of the slope, and the second molten metal flowed over the changed surface shape. It was concluded that the computational model developed in this study using the SPH method is applicable for simulating and clarifying lava flow phenomena.

]]>Dynamics doi: 10.3390/dynamics4020016

Authors: Akio Tsuneda

This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and give the theoretical auto-correlation functions of the new binary sequences, which are expressed by the auto-/cross-correlation functions of the two chaotic binary sequences generated by a single binary function. Furthermore, some numerical experiments are performed to confirm the validity of the theoretical auto-correlation functions.

]]>Dynamics doi: 10.3390/dynamics4020015

Authors: Thomas Kletschkowski

For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches, length scale parameters have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modeling, as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established, there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion, system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach, it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically, it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

]]>Dynamics doi: 10.3390/dynamics4020014

Authors: Cihan Ates Rainer Koch Hans-Jörg Bauer

This paper introduces a robust deposition model designed for exploring the growth dynamics of deposits on surfaces under practical conditions. The study addresses the challenge of characterizing the intricate morphology of deposits, exhibiting significant visual variations. A generative approach is deployed to create diverse natural and engineered surface textures, governed by probabilistic principles. The model&rsquo;s formulation addresses key questions related to deposition initiation, nucleation point behaviour, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. A versatile algorithm, relying on six parameters and employing nested loops and Gaussian sampling, is developed. The algorithm&rsquo;s efficacy is examined through extensive simulations, involving variations in nucleation scaling densities, aggregate scaling scenarios, spread factors, and diffusion rates. Surface statistics are computed for simulated deposits and analyzed using Fast Fourier Transform (FFT). The resulting database enables quantitative comparisons of surfaces generated with different parameters, where the database-derived parallel coordinates offer guidance for selecting optimal model parameters to achieve desired surface morphologies. The proposed approach is validated against urea-derived deposits, exhibiting statistical consistency and agreement with experimental observations. Overall, the model&rsquo;s adaptable framework holds promise for understanding and predicting deposit growth on surfaces in diverse practical scenarios.

]]>Dynamics doi: 10.3390/dynamics4020013

Authors: Vassil M. Vassilev Galin S. Valchev

The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli&ndash;Euler beam theory. Several additional terms are included in the basic equations in order to take into account the influence of the conveyed fluid, the impact of the surrounding medium and the effect of the van der Waals interaction between the inner and outer single-walled carbon nanotubes constituting a double-walled one. In the present work, the flow-induced vibrations of the considered nano-pipes are studied for different values of the length of the pipe, its inner radius, the characteristics of the ambient medium and the velocity of the fluid flow, which is assumed to be constant. The critical fluid flow velocities are obtained at which such a cantilevered double-walled carbon nanotube embedded in an elastic medium loses stability.

]]>Dynamics doi: 10.3390/dynamics4020012

Authors: Alessandro Di Pretoro Ludovic Montastruc Stéphane Negny

Given the exponential rise in the amount of data requiring processing in all engineering fields, phenomenological models have become computationally cumbersome. For this reason, more efficient data-driven models have been recently used with the purpose of substantially reducing simulation computational times. However, especially in process engineering, the majority of the proposed surrogate models address steady-state problems, while poor studies refer to dynamic simulation modeling. For this reason, using a response function-based approach, a crystallization unit case study was set up in order to derive a dynamic data-driven model for crystal growth whose characteristic differential parameters are derived via Response Surface Methodology. In particular, multiple independent variables were considered, and a well-established sampling technique was exploited for sample generation. Then, different sample sizes were tested and compared in terms of accuracy indicators. Finally, the domain partition strategy was exploited in order to show its relevant impact on the final model accuracy. In conclusion, the outcome of this study proved that the proposed procedure is a suitable methodology for dynamic system metamodeling, as it shows good compliance and relevant improvement in terms of computational time. In terms of future research perspectives, testing the proposed procedure on different systems and in other research fields would allow for greater improvement and would, eventually, extend its validity.

]]>Dynamics doi: 10.3390/dynamics4010011

Authors: Jinjie Liu Samuel Appiah-Adjei Moysey Brio

In this paper, we explore the iterated Crank&ndash;Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics, we apply the ICN algorithm for temporal discretization and the midpoint quadrature method for spatial integration. Several numerical tests are carried out to evaluate the performance of the ICN method. In general, the ICN method demonstrates second-order accuracy, consistent with the St&ouml;rmer&ndash;Verlet (SV) method. When the weight is 1/3, the ICN method behaves as a third-order Runge&ndash;Kutta method and maintains strong stability-preserving (SSP) properties for linear problems. Regarding energy conservation, the ICN algorithm maintains at least second-order accuracy, making it superior to the SV method, which converges linearly. Furthermore, selecting a weight of 0.25 results in fourth-order superconvergent energy variation for the ICN method. In this case, the ICN method exhibits energy variation similar to that of the fourth-order Runge&ndash;Kutta method but operates approximately 20% faster. Higher-order convergence for energy can also be achieved by increasing the number of iterations in the ICN method.

]]>Dynamics doi: 10.3390/dynamics4010010

Authors: Peristera Karananou Theodore Andronikos

This paper presents an innovative entanglement-based protocol to address the Dining Cryptographers problem, utilizing maximally entangled |GHZn&#10217; tuples as its core. This protocol aims to provide scalability in terms of both the number of cryptographers n and the amount of anonymous information conveyed, represented by the number of qubits m within each quantum register. The protocol supports an arbitrary number of cryptographers n, enabling scalability in both participant count and the volume of anonymous information transmitted. While the original Dining Cryptographers problem focused on a single bit of information&mdash;whether a cryptographer paid for dinner&mdash;the proposed protocol allows m, the number of qubits in each register, to be any arbitrarily large positive integer. This flexibility allows the transmission of additional information, such as the cost of the dinner or the timing of the arrangement. Another noteworthy aspect of the introduced protocol is its versatility in accommodating both localized and distributed versions of the Dining Cryptographers problem. The localized scenario involves all cryptographers gathering physically at the same location, such as a local restaurant, simultaneously. In contrast, the distributed scenario accommodates cryptographers situated in different places, engaging in a virtual dinner at the same time. Finally, in terms of implementation, the protocol accomplishes uniformity by requiring that all cryptographers utilize identical private quantum circuits. This design establishes a completely modular quantum system where all modules are identical. Furthermore, each private quantum circuit exclusively employs the widely used Hadamard and CNOT quantum gates, facilitating straightforward implementation on contemporary quantum computers.

]]>Dynamics doi: 10.3390/dynamics4010009

Authors: Jorge A. Muñoz Jorge A. López

Two neural networks were trained to predict, respectively, the Euler characteristic and the curvature of nuclear pastas in neutron star crust conditions generated by molecular dynamics simulations of neutron star matter with 0.1 &lt; x &lt; 0.5, 0.040 fm&minus;3 &lt; &rho; &lt; 0.085 fm&minus;3 (0.68 &times; 1014 g/cm3 &lt; &rho; &lt; 1.43 &times; 1014 g/cm3), and 0.2 MeV &lt; T &lt; 4.0 MeV, where x is proton content, the density is &rho;, and the temperature is T. The predictions of the two networks were combined to determine the nuclear pasta phase that is thermodynamically stable at a given x, &rho;, and T, and a three-dimensional phase diagram that extrapolated slightly the regions of existing molecular dynamics data was computed. The jungle gym and anti-jungle gym structures are prevalent at high temperature and low density, while the anti-jungle gym and anti-gnocchi structures dominate at high temperature and high density. A diversity of structures exist at low temperatures and intermediate density and proton content. The trained models used in this work are open access and available at a public repository to promote comparison to pastas obtained with other models.

]]>Dynamics doi: 10.3390/dynamics4010008

Authors: Anvar Gilmanov Ponnuthurai Gokulakrishnan Michael S. Klassen

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence&ndash;combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence&ndash;chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damk&ouml;hler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damk&ouml;hler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damk&ouml;hler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications.

]]>Dynamics doi: 10.3390/dynamics4010007

Authors: Ivan S. Maksymov

Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more-efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper, we experimentally validated a physical RC system that substitutes the effect of randomness that underpins the operation of the traditional RC algorithm for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the &lsquo;next-generation&rsquo; improvement of the traditional RC algorithm.

]]>Dynamics doi: 10.3390/dynamics4010006

Authors: Apurva Baruah Fernando Ponta

The development and deployment of the next generation of wind energy systems calls for simulation tools that model the entire wind farm while balancing accuracy and computational cost. A full-system wind farm simulation must consider the atmospheric inflow, the wakes and consequent response of the multiple turbines, and the implementation of the appropriate farm-collective control strategies that optimize the entire wind farm&rsquo;s output. In this article, we present a novel vortex lattice model that enables the effective representation of the complex vortex wake dynamics of the turbines in a farm subject to transient inflow conditions. This work extends the capabilities of our multi-physics suite, CODEF, to include the capability to simulate the wakes and the high-fidelity aeroelastic response of multiple turbines in a wind farm. Herein, we compare the results of our GVLM technique with the LiDAR measurements obtained at Sandia National Laboratories&rsquo; SWiFT facility. The comparison shows remarkable similarities between the simulation and field measurements of the wake velocity. These similarities demonstrate our model&rsquo;s capabilities in capturing the entire wake of a wind turbine at a significantly reduced computational cost as compared to other techniques.

]]>Dynamics doi: 10.3390/dynamics4010005

Authors: Aleksander Aleksiev Stefanov

We derive a new system of integrable derivative non-linear Schr&ouml;dinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac&ndash;Moody algebra A2(1). The construction of the fundamental analytic solutions of L is outlined and they are used to introduce the scattering data, thus formulating the scattering problem for the Lax pair L,M.

]]>Dynamics doi: 10.3390/dynamics4010004

Authors: Anna Markhotok

The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to the specific mechanism of recovery other than simply its compensation. Even though the full restoration of the hypersonic flow state does not occur in a strict sense of it, clear reverse changes toward the initial shape of the shock front eventually take place, thus creating an appearance of a full recovery seen in experiments. From analysis of different interface symmetries, the factors determining the recovery dynamics are identified. The results are directly applicable to the problem of energy deposition into a hypersonic flow; however, it can be useful anywhere else where the flow modifications following the interaction are important. The dimensionless form of the equations allows applications on any scale other than that demonstrated for the optical discharges.

]]>Dynamics doi: 10.3390/dynamics4010003

Authors: Dimitri Volchenkov

The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.

]]>Dynamics doi: 10.3390/dynamics4010002

Authors: Yangyang Liu Ziying Zhang Hua Zhang Yaguang Liu

In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems.

]]>Dynamics doi: 10.3390/dynamics4010001

Authors: Michel Planat David Chester Klee Irwin

The symmetries of a Riemann surface &Sigma;&#8726;{ai} with n punctures ai are encoded in its fundamental group &pi;1(&Sigma;). Further structure may be described through representations (homomorphisms) of &pi;1 over a Lie group G as globalized by the character variety C=Hom(&pi;1,G)/G. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere &Sigma;=S2(4) and the &lsquo;space-time-spin&rsquo; group G=SL2(C). In such a situation, C possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface Va,b,c,d(x,y,z) with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlev&eacute; VI equation (or PVI); and (iii) there exists a finite set of 1 (Cayley&ndash;Picard)+3 (continuous platonic)+45 (icosahedral) solutions of PVI. In this paper, we feature the parametric representation of some solutions of PVI: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups fp encountered in TQC or DNA/RNA sequences are proposed.

]]>Dynamics doi: 10.3390/dynamics3040046

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

We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable &lambda; governs the kinetic energy that is non-local in &lambda;. The interaction between the particle&rsquo;s charge and the electromagnetic four-potential is non-local in &lambda;, while the interaction between the particle&rsquo;s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential.

]]>Dynamics doi: 10.3390/dynamics3040045

Authors: Amin Ghorbanpour

Robot manipulators possess the capability to autonomously execute complex sequences of actions. Their proficiency in handling challenging and hazardous tasks has led to their widespread adoption across diverse sectors, including industry, business, household appliances, rehabilitation, and many more. However, certain tasks prove to be challenging for individual robots, primarily due to constraints in their structure and limited degrees of freedom. Cooperative robot manipulators (CRMs) emerge as a compelling solution when dealing with large, heavy, or flexible payloads. The utilization of CRMs offers a host of benefits, including enhanced manipulation performance achieved through the synergy of sensing and actuation capabilities or by tapping into increased redundancy. Numerous techniques have been devised for the control and dynamical modeling of CRMs. Nevertheless, the field continues to present technical challenges and scientific inquiries. To inspire and facilitate further research and development in this realm, this review aims to consolidate the current body of knowledge pertaining to CRMs kinematics, dynamics modeling, and various control methodologies used for payload manipulation via CRMs.

]]>Dynamics doi: 10.3390/dynamics3040044

Authors: Constantin Fetecau Shehraz Akhtar Costică Moroşanu

In this paper, exact analytical expressions are derived for dimensionless steady-state solutions corresponding to the modified Stokes&rsquo; problems for incompressible generalized Burgers&rsquo; fluids, considering the influence of porous and magnetic effects. Actually, these are the first exact solutions for such motions of these fluids. They can easily be particularized to give similar solutions for Newtonian, second-grade, Maxwell, Oldroyd-B and Burgers&rsquo; fluids. It is also proven that MHD motion problems of such fluids between infinite parallel plates can be investigated when shear stress is applied at the boundary. To validate the obtained results, the velocity fields are presented in two distinct forms, and their equivalence is proven through graphical representations. The obtained outcomes are utilized to determine the time required to reach a steady state and to elucidate the impacts of porous and magnetic parameters on the fluid motion. This investigation reveals that the attainment of a steady state occurs later when a porous medium or magnetic field is present. Additionally, the fluid&rsquo;s flow resistance is augmented in the presence of a magnetic field or through a porous medium. Thus, as was expected, the fluid moves slower through porous media or in the presence of a magnetic field.

]]>Dynamics doi: 10.3390/dynamics3040043

Authors: Daniel Strömbom Catherine Futterman

Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general.

]]>Dynamics doi: 10.3390/dynamics3040042

Authors: Roberto da Silva Sandra Denise Prado

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapted and applied it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance overlap criterion for the chaos boundary at K&asymp;2.43, reinforcing its effectiveness. Additionally, we verified our findings by employing a combined approach that incorporates Lyapunov exponents and bifurcation diagrams. Lastly, we demonstrate the adaptability of our technique to other maps, establishing its capability to capture the transition to chaos, as evidenced in the logistic map.

]]>Dynamics doi: 10.3390/dynamics3040041

Authors: Marija Mitrović Dankulov Bosiljka Tadić Roderick Melnik

The essence of the stochastic processes behind the empirical data on infection and fatality during pandemics is the complex interdependence between biological and social factors. Their balance can be checked on the data of new virus outbreaks, where the population is unprepared to fight the viral biology and social measures and healthcare systems adjust with a delay. Using a complex systems perspective, we combine network mapping with K-means clustering and multifractal detrended fluctuations analysis to identify typical trends in fatality rate data. We analyse global data of (normalised) fatality time series recorded during the first two years of the recent pandemic caused by the severe acute respiratory syndrome coronavirus 2 as an appropriate example. Our results reveal six clusters with robust patterns of mortality progression that represent specific adaptations to prevailing biological factors. They make up two significant groups that coincide with the topological communities of the correlation network, with stabilising (group g1) and continuously increasing rates (group g2). Strong cyclic trends and multifractal small-scale fluctuations around them characterise these patterns. The rigorous analysis and the proposed methodology shed more light on the complex nonlinear shapes of the pandemic&rsquo;s main characteristic curves, which have been discussed extensively in the literature regarding the global infectious diseases that have affected humanity throughout its history. In addition to better pandemic preparedness in the future, the presented methodology can also help to differentiate and predict other trends in pandemics, such as fatality rates, caused simultaneously by different viruses in particular geographic locations.

]]>Dynamics doi: 10.3390/dynamics3040040

Authors: Benjamin S. Novak Andrés Aragoneses

Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is fundamental for chaos control, chaos classification, and behavior-transition forecasting, among others. It is a complicated task that becomes increasingly difficult as systems involve more dimensions and parameters. Here, we extend methods inspired in ordinal patterns to analyze 2D iterative maps to unveil underlying approximate symmetries of their dynamics. We distinguish different families of chaos within the systems, find similarities among chaotic maps, identify approximate temporal and dynamical symmetries, and anticipate sharp transitions in dynamics. We show how this methodology displays the evolution of the spatial correlations in a dynamical system as the control parameter varies. We prove the power of these techniques, which involve simple quantifiers as well as combinations of them, in extracting relevant information from the complex dynamics of 2D systems, where other techniques are less informative or more computationally demanding.

]]>Dynamics doi: 10.3390/dynamics3040039

Authors: Alon Davidy

Olefins are crucial building blocks for petrochemical industry, serving as raw materials for the production of various products such as plastics, synthetic fibers, detergents, solvents, and other chemicals. In FCC, heavy petroleum feedstocks are injected into a catalytic cracking unit, where they are mixed with a catalyst. The catalyst aids in breaking down the large hydrocarbon molecules into smaller fragments, including olefins like Propylene and Ethylene. These polymerization reactions occur at high temperatures. They demand that heat removal occurs as quickly as possible in order to control the reactor temperature and to avoid &ldquo;hot spots&rdquo; in the Regenerator or localized oxidation reactions (and to avoid creep rupture of the regenerator steel cladding). The cooling of the regenerator cladding surface can be achieved by impinging water droplets (spray), ejected from a spray nozzle. Spray cooling can provide uniform cooling and handle high heat fluxes in both a single phase and two phases. This research provides a thermal hydraulic design of regenerator spray cooling systems. In the framework of this research, Fire Dynamics Simulator (FDS) software was applied in order to simulate the temperature field and the water vapor mass fraction. A COMSOL Multiphysics finite element code was used in order to calculate the temperature field inside the regenerator cladding. The calculated surface temperatures and heat transfer convective coefficient, obtained using FDS software, were validated successfully against COMSOL numerical results and previous results in the literature. The numerical simulations were carried out for two cases. The first case was carried out at a distance of 0.5 m, and the second case was carried out at a distance of 0.2 m. A grid sensitivity study was carried out on the FDS model. Numerical integrations were carried out over time in order to calculate the average temperatures. The difference between these four average temperatures, calculated by applying different grids, is less than 7.4%. The calculated surface temperatures and heat transfer convective coefficient were validated successfully against COMSOL numerical results and previous research. It was shown that the calculated temperatures decrease in the second case. The water spray system managed to cool the steel wall more effectively as the water spray system approaches the steel cladding.

]]>Dynamics doi: 10.3390/dynamics3040038

Authors: John G. Rosser Tyamo Okosun Orlando J. Ugarte Chenn Q. Zhou

A continuous iron ore pellet feed system for a direct reduction ironmaking furnace is reportedly jamming in a hopper above the furnace, where a counterflowing gas seals off the furnace flue gas. The conditions that result in jamming are not well understood. The system is computationally modeled utilizing the coupled discrete element method (DEM) and computational fluid dynamics (CFD) technique. The technique is computationally expensive; therefore, the pellet sizing is modified while preserving the key metrics important in jamming. The model is used to study the impact of pellet moisture, heating, and ice formation between pellets in relation to the jamming event. The results indicate that the influence of moisture alone on the bulk shear rate is unlikely to jam the system and that insufficient heat is supplied by the counterflowing gas to raise the temperature of the pellets, which suggests freezing conditions can exist within the hopper. Particle bonding is implemented to replicate wet and icy pellets freezing and breaking up. The results indicate that the system jams in winter conditions when the hopper is charged with a minimum of 15% icy pellets, or 10% icy with 5% wet pellets. These results agree with industry reports of jamming during winter operations.

]]>Dynamics doi: 10.3390/dynamics3040037

Authors: Charis Anastopoulos Maria-Electra Plakitsi

We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime.

]]>Dynamics doi: 10.3390/dynamics3040036

Authors: Francisco Gonzalez Montoya

In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space. The different behaviours of the trajectories around important geometrical objects like normally hyperbolic invariant manifolds, their stable and unstable manifolds, and KAM structures generate characteristic patterns in the scalar field generated by the action. Also, we present a simple argument based on the conservation of energy and the behaviour of the trajectories to understand the origin of the patterns in this scalar field. As examples, we study the phase space of open Hamiltonian systems with two and three degrees of freedom.

]]>Dynamics doi: 10.3390/dynamics3040035

Authors: Hiep Dai Le Tamara Nestorović

This article aims to develop a new Adaptive Proportional Integral Derivative (PID) Nonsingular Dual Terminal Sliding Mode Control, designed for tracking the position of robot manipulators under disturbances and uncertainties. Compared with existing PID Nonsingular Fast Terminal Sliding Mode (PIDNFTSM) controllers, this work effectively avoids singularity problems in control while significantly enhancing the convergence speed of errors. An adaptive reaching law is proposed to estimate the bound information of the first derivative of lumped disturbance by regulating itself based on sliding variables. The overall system stability is proven by using the Lyapunov approach. Subsequent simulation results verify the effectiveness of the proposed controller regarding tracking error reduction, energy efficiency enhancements, and singularity avoidance.

]]>Dynamics doi: 10.3390/dynamics3040034

Authors: Ricardo A. Calix Orlando Ugarte Tyamo Okosun Hong Wang

Computational fluid dynamics (CFD)-based simulation has been the traditional way to model complex industrial systems and processes. One very large and complex industrial system that has benefited from CFD-based simulations is the steel blast furnace system. The problem with the CFD-based simulation approach is that it tends to be very slow for generating data. The CFD-only approach may not be fast enough for use in real-time decisionmaking. To address this issue, in this work, the authors propose the use of machine learning techniques to train and test models based on data generated via CFD simulation. Regression models based on neural networks are compared with tree-boosting models. In particular, several areas (tuyere, raceway, and shaft) of the blast furnace are modeled using these approaches. The results of the model training and testing are presented and discussed. The obtained R2 metrics are, in general, very high. The results appear promising and may help to improve the efficiency of operator and process engineer decisionmaking when running a blast furnace.

]]>Dynamics doi: 10.3390/dynamics3030033

Authors: Domenico Pomarico

Computational complexity reduction is at the basis of a new formulation of many-body quantum states according to tensor network ansatz, originally framed in one-dimensional lattices. In order to include long-range entanglement characterizing phase transitions, the multiscale entanglement renormalization ansatz (MERA) defines a sequence of coarse-grained lattices, obtained by targeting the map of a scale-invariant system into an identical coarse-grained one. The quantum circuit associated with this hierarchical structure includes the definition of causal relations and unitary extensions, leading to the definition of ground subspaces as stabilizer codes. The emerging error correcting codes are referred to logical indices located at the highest hierarchical level and to physical indices yielded by redundancy, framed in the AdS-CFT correspondence as holographic quantum codes with bulk and boundary indices, respectively. In a use-case scenario based on errors consisting of spin erasure, the correction is implemented as the reconstruction of a bulk local operator.

]]>Dynamics doi: 10.3390/dynamics3030032

Authors: Lidia Jiménez-Lara Jaume Llibre

We review from a different perspective the approach and solution to the torque-free Euler equations, also called the free asymmetric top equations. We aim to simplify and broaden the study of the asymmetric free rigid body. This is an old but important integrable problem that has two first integrals: the energy and the angular momentum. We reduce this problem by eliminating the time as the independent variable in the three autonomous Euler equations written in cylindrical dimensionless variables, which allows a geometric study of the solution as a function of the cylindrical angle variable &psi;, by means of continuous deformations dependent on the two independent parameters &kappa; and e0. The parameter space is divided into six disjoint regions, whose boundaries are the separatices and degenerated cases. The solutions are given in terms of trigonometric functions of the independent cylindric angle &psi;.

]]>Dynamics doi: 10.3390/dynamics3030031

Authors: Fernando C. Pérez-Cárdenas

Boltzmann&rsquo;s H-theorem is considered a great triumph of science. Though some modifications are necessary to adapt it to modern dynamical theories, it is well established that one of its main tenets remains widely accepted: the introduction of probability is a key element in achieving a transition from time-reversible, deterministic dynamical laws at the microscopic level to irreversible laws describing the approach to equilibrium of isolated macroscopic systems. Thus, it is somehow surprising that we still find instances where this subject is labeled as paradoxical and elusive. More remarkable is the fact that this often happens in texts that succeed in presenting Boltzmann&rsquo;s ideas with clarity. In order to shed light on how probability allows us to go form microscopic reversibility to macroscopic irreversibility, we use numerical results from a two-dimensional lattice gas composed of distinguishable particles. We discuss the roles played by noise, coarse graining, and probability. The simplicity of our model might help the newcomer to this area in better grasping Boltzmann&rsquo;s fundamental breakthrough.

]]>Dynamics doi: 10.3390/dynamics3030030

Authors: Christos Volos

We are thrilled to introduce the new scope of the Dynamics, a platform that will unravel the captivating world of diverse dynamics and their multifaceted applications [...]

]]>Dynamics doi: 10.3390/dynamics3030029

Authors: Angelo Morro

This paper investigates the modelling of Korteweg-type fluids and hence the dependence of the stress tensor on gradients of mass density. This topic, originating from the need for describing capillarity effects, is mainly of interest in connection with nanosystems where the mean free path may be comparable with the geometric dimensions of the system. In addition to the Korteweg fluid model, the paper gives a review of the stress tensor function arising in quantum fluid hydrodynamics. Next, thermodynamic consistency is established for a fluid involving first- and second-order density gradients. The modelling investigated is a generalization of the classical Korteweg fluid and allows a better understanding of previous thermodynamic restrictions. The restrictions determined for the general scheme with second-order gradients are applied to the particular cases of the Korteweg fluid and the quantum fluid. Further, to allow for discontinuity wave solutions with finite speed of propagation, a model is established which involves higher-order derivatives and reduces to the Korteweg fluid in stationary conditions.

]]>Dynamics doi: 10.3390/dynamics3030028

Authors: Felix Sadyrbaev

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

]]>Dynamics doi: 10.3390/dynamics3030027

Authors: Ralf F. A. Cox

Two experiments and a dynamic model forhuman limb selection are reported. In Experiment 1, left-handed and right-handed participants (N = 36) repeatedly used one hand for grasping a small cube. After a clear switch in the cube&rsquo;s location, perseverative limb selection was revealed in both handedness groups. In Experiment 2, the cubes were presented in a clockwise and counter-clockwise sequence to right-handed participants (N = 15). A spatial shift in the switch point between right-hand use and left-hand use was observed. The model simulates the experiments by implementing the nonlinear multiple-timescale dynamics of the action-selection process underlying limb selection. It integrates two mechanisms that were earlier proposed to underlie this selection aspect of manual activity: limb dominance and attentional information. Finally, the model is used to simulate an influential earlier experiment, by establishing a conceptual link between cross-lateral inhibition asymmetry and the direction and strength of handedness.

]]>Dynamics doi: 10.3390/dynamics3030026

Authors: Stefano Zaghi Cristiano Andolfi

This manuscript relates to the exploiting of the abstract calculus pattern (ACP) for the (numerical) solution of ordinary differential equation (ODEs) systems, which are ubiquitous mathematical formulations of many physical (dynamical) phenomena. We present FOODIE, a software suite aimed to numerically solve ODE problems by means of a clear, concise, and efficient abstract interface. The results presented prove manifold findings, in particular that our ACP approach enables ease of code development, clearness and robustness, maximization of code re-usability, and conciseness comparable with computer algebra system (CAS) programming (interpreted) but with the computational performance of compiled programming. The proposed programming model is also proven to be agnostic with respect to the parallel paradigm of the computational architecture: the results show that FOODIE applications have good speedup with both shared (OpenMP) and distributed (MPI, CAF) memory architectures. The present paper is the first announcement of the FOODIE project: the current implementation is extensively discussed, and its capabilities are proved by means of tests and examples.

]]>Dynamics doi: 10.3390/dynamics3030025

Authors: Yanfang Zhang Miaozi Zheng Li Zhang Chaofei Zhang Jian Tan Yulong Zhang Menglan Duan

Ocean Thermal Energy Conversion (OTEC) is a process that can produce electricity by utilizing the temperature difference between deep cold water and surface warm water. The cold-water pipe (CWP) is a key component of OTEC systems, which transports deep cold water to the floating platform. The CWP is subjected to various environmental and operational loads, such as waves, currents, internal flow, and platform motion, which can affect its dynamic response and stability. In this paper, we establish a computational model of the mechanical performance of the CWP based on the Euler&ndash;Bernoulli beam theory and the Morrison equation, considering the effects of internal flow, sea current, and wave excitation. We use the differential quadrature method (DQM) to obtain a semi-analytical solution of the lateral displacement and bending moment of the CWP. We verify the correctness and validity of our model by comparing it with the finite element simulation results using OrcaFlex software. We also analyze the effects of operating conditions&mdash;such as wave intensity, clump weight at the bottom, and internal flow velocity&mdash;on the dynamic response of the CWP using numerical simulation and the orthogonal experimental method. The results show that changing the wave strength and internal flow velocity has little effect on the lateral displacement of the CWP but increasing the current velocity can significantly increase the lateral displacement of the CWP, which can lead to instability. The effects of waves, clump weight, internal flow, and sea current on the maximum bending moment of the CWP are similar; all of them increase sharply at first and then decrease gradually until they level off. The differences in the effects are mainly reflected in the different locations of the pipe sections. This paper suggests some design guidance for CWP in terms of dynamic responses depending on the operating conditions. This paper contributes to the journal&rsquo;s scope by providing a novel and efficient method for analyzing the mechanical performance of CWP for OTEC systems, which is an important ocean energy resource.

]]>Dynamics doi: 10.3390/dynamics3030024

Authors: Murillo V. B. Santana

Many physical processes can be described via nonlinear second-order ordinary differential equations and so, exact solutions to these equations are of interest as, aside from their accuracy, they may reveal beforehand key properties of the system&rsquo;s response. This work presents a method for computing exact solutions of second-order nonlinear autonomous undamped ordinary differential equations. The solutions are divided into nine cases, each depending on the initial conditions and the system&rsquo;s first integral. The exact solutions are constructed via a suitable parametrization of the unknown function into a class of functions capable of representing its behavior. The solution is shown to exist and be well-defined in all cases for a general nonlinear form of the differential equation. Practical properties of the solution, such as its period, time to reach an extreme value or long-term behavior, are obtained without the need of computing the solution in advance. Illustrative examples considering different types of nonlinearity present in classical physical systems are used to further validate the obtained exact solutions.

]]>Dynamics doi: 10.3390/dynamics3030023

Authors: Lauren A. Moseley Enrique Peacock-López

To further explore the origins of Life, we consider three self-replicating chemical models. In general, models of the origin of Life include molecular components that can self-replicate and achieve exponential growth. Therefore, chemical self-replication is an essential chemical property of any model. The simplest self-replication mechanisms use the molecular product as a template for its synthesis. This mechanism is the so-called First-Order self-replication. Its regulatory limitations make it challenging to develop chemical networks, which are essential in the models of the origins of Life. In Second-Order self-replication, the molecular product forms a catalytic dimer capable of synthesis of the principal molecular product. In contrast with a simple template, the dimers show more flexibility in forming complex chemical networks since the chemical activity of the dimers can be activated or inhibited by the molecular components of the network. Here, we consider three minimal models: the First-Order Model (FOM), the Second-Order Model (SOM), and an Extended Second-Order Model (ESOM). We construct and analyze the mechanistic dimensionless ordinary differential equations (ODEs) associated with the models. The numerical integration of the set of ODEs gives us a visualization of these systems&rsquo; oscillatory behavior and compares their capacities for sustained autocatalytic behavior. The FOM model displays more complex oscillatory behavior than the ESOM model.

]]>Dynamics doi: 10.3390/dynamics3030022

Authors: David K. Belashchenko

The phenomena of electrical conductivity and electromigration in metallic systems are related, since in both cases the basic physical process is the scattering of conduction electrons by metal ions. Numerous searches have been made for equations connecting the conductivity with electromigration. In the case of a liquid metal, when using the Drude&ndash;Sommerfeld (DS) conductivity equation, it was not possible to obtain a quantitative relationship between these phenomena, which would be correct. Attempts to find such a relationship when taking into account the N. Mott correction (g-factor) in the DS equation were unsuccessful. This article proposes a different correction (b-factor) to the DS equation, which takes into account the possibility of varying the momentum transferred by the conduction electron to a metal ion during the scattering. This correction allows to establish a quantitative relationship between conductivity and electromigration as well as between electromigration in various binary systems with common components, in agreement with the experiment. The proposed theory describes well, in particular, two- and multi-component metal systems of any concentration (the consistency rule for triangles A&ndash;B, B&ndash;C, C&ndash;A). The value of the b-factor smoothly changes depending on the heat of vaporization of the metal, per unit volume.

]]>Dynamics doi: 10.3390/dynamics3030021

Authors: Franz Konstantin Fuss

This study attempts to shed new light on the dynamics of a turning ship using the principles of free body diagrams (FBDs). Unexpectedly, the literature gap is defined by incomplete and flawed FBDs. The method behind this new approach involves the FBD of a turning ship, with all the essential forces included, namely propulsive force, sideward thruster force (producing the initial turning moment), drag force, lift force, centrifugal force, inertial force, and hydrodynamic force couple. From these forces, the force and moment equations are derived. The accelerations are calculated from the force and moment equilibria to simulate the dynamics from input parameters such as mass m, length L, draught D, and fluid density &rho;. The turning dynamics are explained in terms of velocities, accelerations, forces, and moments, based on two conditions: flat and steep angles of attack (AoA) and long and short turning radii R. A critical result is the proportionality of lift and centrifugal forces, leading to the proposal of a pleometric index (m&middot;L&ndash;2&middot;D&ndash;1&middot;&rho;&ndash;1), which is nonlinearly proportional to the product of AoA and R/L, characterising the dynamics of a turning ship. The FBD approach of this study also identified missing databases required for accurate simulation of turning dynamics, such as drag and lift coefficients of different hull geometries.

]]>Dynamics doi: 10.3390/dynamics3020020

Authors: Ramon F. Álvarez-Estrada

Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn&rsquo;s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov&ndash;Born&ndash;Green&ndash;Kirkwood&ndash;Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn&rsquo;s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical &#981;4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum &#981;4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum &#981;4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical &#981;4 one, yielding an approach to equilibrium.

]]>Dynamics doi: 10.3390/dynamics3020019

Authors: René Lozi

Since its original publication in 1978, Lozi&rsquo;s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure or applied its properties in many fields (electronic devices such as memristors, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial two-dimensional map into a multidimensional one. However, they do not respect the original constraint that allows this map to be one of the few strictly hyperbolic: a constant Jacobian. In this paper, we introduce a three-dimensional piece-wise linear extension respecting this constraint and we explore a special property never highlighted for chaotic mappings: the coexistence of thread chaotic attractors (i.e., attractors that are formed by a collection of lines) and sheet chaotic attractors (i.e., attractors that are formed by a collection of planes). This new three-dimensional mapping can generate a large variety of chaotic and hyperchaotic attractors. We give five examples of such behavior in this article. In the first three examples, there is the coexistence of thread and sheet chaotic attractors. However, their shapes are different and they are constituted by a different number of pieces. In the last two examples, the blow up of the attractors with respect to parameter a and b is highlighted.

]]>Dynamics doi: 10.3390/dynamics3020018

Authors: Jesús Fuentes

Quantum squeezing, an intriguing phenomenon that amplifies the uncertainty of one variable while diminishing that of its conjugate, may be studied as a time-dependent process, with exact solutions frequently derived from frameworks grounded in adiabatic invariants. Remarkably, we reveal that exact solutions can be ascertained in the presence of time-variant elastic forces, eschewing dependence on invariants or frozen eigenstate formalism. Delving into these solutions as an inverse problem unveils their direct connection to the design of elastic fields, responsible for inducing squeezing transformations onto canonical variables. Of particular note is that the dynamic transformations under investigation belong to a class of gentle quantum operations, distinguished by their delicate manipulation of particles, thereby circumventing the abrupt energy surges commonplace in conventional control protocols.

]]>Dynamics doi: 10.3390/dynamics3020017

Authors: John E. Parker Kevin M. Short

Recent work has highlighted the vast array of dynamics possible within both neuronal networks and individual neural models. In this work, we demonstrate the capability of interacting chaotic Hindmarsh&ndash;Rose neurons to communicate and transition into periodic dynamics through specific interactions which we call mutual stabilization, despite individual units existing in chaotic parameter regimes. Mutual stabilization has been seen before in other chaotic systems but has yet to be reported in interacting neural models. The process of chaotic stabilization is similar to related previous work, where a control scheme which provides small perturbations on carefully chosen Poincar&eacute; surfaces that act as control planes stabilized a chaotic trajectory onto a cupolet. For mutual stabilization to occur, the symbolic dynamics of a cupolet are passed through an interaction function such that the output acts as a control on a second chaotic system. If chosen correctly, the second system stabilizes onto another cupolet. This process can send feedback to the first system, replacing the original control, so that in some cases the two systems are locked into persistent periodic behavior as long as the interaction continues. Here, we demonstrate how this process works in a two-cell network and then extend the results to four cells with potential generalizations to larger networks. We conclude that stabilization of different states may be linked to a type of information storage or memory.

]]>Dynamics doi: 10.3390/dynamics3020016

Authors: Nir Shvalb Mark Frenkel Shraga Shoval Edward Bormashenko

Ramsey theory constitutes the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected by two kinds of ideal Hookean springs. The suggested system mechanically corresponds to cyclic molecules, in which functional groups are interconnected by two kinds of chemical bonds, represented mechanically with two springs k1 and k2. In this paper, we consider a cyclic system (molecule) built of six equal masses m and two kinds of springs. We pose the following question: what is the minimal number of masses in such a system in which three masses are constrained to be connected cyclically with spring k1 or three masses are constrained to be connected cyclically with spring k2? The answer to this question is supplied by the Ramsey theory, formally stated as follows: what is the minimal number&nbsp;R(3,3)? The result emerging from the Ramsey theory is R(3,3)=6. Thus, in the aforementioned interconnected mechanical system at least one triangle, built of masses and springs, must be present. This prediction constitutes the vibrational spectrum of the system. Thus, the Ramsey theory and symmetry considerations supply the selection rules for the vibrational spectra of the cyclic molecules. A symmetrical system built of six vibrating entities is addressed. The Ramsey approach works for 2D and 3D molecules, which may be described as abstract complete graphs. The extension of the proposed Ramsey approach to the systems, partially connected by ideal springs, viscoelastic systems and systems in which elasticity is of an entropic nature is discussed. &ldquo;Multi-color systems&rdquo; built of three kinds of ideal springs are addressed. The notion of the inverse Ramsey network is introduced and analyzed.

]]>Dynamics doi: 10.3390/dynamics3020015

Authors: José J. Gil

Dual-rotating retarder polarimeters constitute a family of well-known instruments that are used today in a great variety of scientific and industrial contexts. In this work, the periodic intensity signal containing the information of all sixteen Mueller elements of depolarizing or nondepolarizing samples is determined for different ratios of angular velocities and non-ideal retarders, which are mathematically modeled with arbitrary retardances and take into account the possible diattenuating effect exhibited by both retarders. The alternative choices for generating a sufficient number of Fourier harmonics as well as their discriminating power are discussed. A general self-calibration procedure, which provides the effective values of the retardances and diattenuations of the retarders, the relative angles of the retarders and the analyzer, and the overall scale coefficient introduced by the detection and processing device are also described, leading to the absolute measurement of the Mueller matrix of the sample.

]]>Dynamics doi: 10.3390/dynamics3020014

Authors: Ximei Li Guang Jin Mingcong Deng

This paper presents a nonlinear fault-tolerant vibration control system for a flexible arm, considering partial actuator fault. A lightweight flexible arm with lower stiffness will inevitably cause vibration which will impair the performance of the high-precision control system. Therefore, an operator-based robust nonlinear vibration control system is integrated by a double-sided interactive controller actuated by the Shape Memory Alloy (SMA) actuators for the flexible arm. Furthermore, to improve the safety and reliability of the safety-critical application, fault-tolerant dynamics for partial actuator fault are considered as an essential part of the proposed control system. The experimental cases are set to the partial actuator as faulty conditions, and the proposed vibration control scheme has fault-tolerant dynamics which can still effectively stabilize the vibration displacement. The reconfigurable controller improves the fault-tolerant performance by shortening the vibration time and reducing the vibration displacement of the flexible arm. In addition, compared with a PD controller, the proposed nonlinear vibration control has better performance than the traditional controller. The experimental results show that the effectiveness of the proposed method is confirmed. That is, the safety and reliability of the proposed fault-tolerant vibration control are verified even if in the presence of an actuator fault.

]]>Dynamics doi: 10.3390/dynamics3020013

Authors: Nooshin Bahador Milad Lankarany

The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, so far, has shown excellent performance in combining the dynamics of individual nodes and the coupling strengths between them within a network. Despite the undoubted impact of the attention mechanism, it is not yet clear why some nodes of a network obtain higher attention weights. To come up with more explainable solutions, we tried to look at the problem from a stability perspective. Based on stability theory, negative connections in a network can create feedback loops or other complex structures by allowing information to flow in the opposite direction. These structures play a critical role in the dynamics of a complex system and can contribute to abnormal synchronization, amplification, or suppression. We hypothesized that those nodes that are involved in organizing such structures could push the entire network into instability modes and therefore need more attention during analysis. To test this hypothesis, the attention mechanism, along with spectral and topological stability analyses, was performed on a real-world numerical problem, i.e., a linear Multi-Input Multi-Output state-space model of a piezoelectric tube actuator. The findings of our study suggest that the attention should be directed toward the collective behavior of imbalanced structures and polarity-driven structural instabilities within the network. The results demonstrated that the nodes receiving more attention cause more instability in the system. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics.

]]>Dynamics doi: 10.3390/dynamics3010012

Authors: Lauren Ribordy Timothy Sands

The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the van der Pol oscillator. Deterministic artificial intelligence is a feedforward and feedback control method that leverages the known physics of the van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of deterministic artificial intelligence employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error between the target trajectory and the response oscillator trajectory over time. Two algorithms performed better than the benchmark with necessary discussion of the conditions under which they perform best. Recursive least squares with exponential forgetting had the lowest mean absolute error overall, with a 2.46% reduction in error compared to the baseline, feedforward without deterministic artificial intelligence. While least mean squares with normalized gradient adaptation had worse initial error in the first 10% of the simulation, after that point it exhibited consistently lower error. Over the last 90% of the simulation, deterministic artificial intelligence with least mean squares with normalized gradient adaptation achieved a 48.7% reduction in mean absolute error compared to baseline.

]]>Dynamics doi: 10.3390/dynamics3010011

Authors: André de Oliveira Gomes Pedro Catuogno

This work studies a two-time-scale functional system given by two jump diffusions under the scale separation by a small parameter &epsilon;&rarr;0. The coefficients of the equations that govern the dynamics of the system depend on the segment process of the slow variable (responsible for capturing delay effects on the slow component) and on the state of the fast variable. We derive a moderate deviation principle for the slow component of the system in the small noise limit using the weak convergence approach. The rate function is written in terms of the averaged dynamics associated with the multi-scale system. The core of the proof of the moderate deviation principle is the establishment of an averaging principle for the auxiliary controlled processes associated with the slow variable in the framework of the weak convergence approach. The controlled version of the averaging principle for the jump multi-scale diffusion relies on a discretization method inspired by the classical Khasminkii&rsquo;s averaging principle.

]]>Dynamics doi: 10.3390/dynamics3010010

Authors: Ravi Agarwal Gabriela Mihaylova Petio Kelevedjiev

The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y&prime;,y&Prime;,y&#8244;), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.

]]>Dynamics doi: 10.3390/dynamics3010009

Authors: Erik Bartoš Stanislav Dubnička Anna Zuzana Dubničková

The damped oscillating structures recently revealed by a three parametric formula from the proton &ldquo;effective&rdquo; form factor data extracted of the measured total cross section &sigma;totbare(e+e&minus;&rarr;pp&macr;) still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one&rsquo;s own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process e+e&minus;&rarr;&pi;+&pi;&minus; are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of &chi;2/ndf, while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the &ldquo;effective&rdquo; proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision.

]]>Dynamics doi: 10.3390/dynamics3010008

Authors: Luis H. Favela Mary Jean Amon

In the cognitive and neural sciences, Bayesianism refers to a collection of concepts and methods stemming from various implementations of Bayes&rsquo; theorem, which is a formal way to calculate the conditional probability of a hypothesis being true based on prior expectations and updating priors in the face of errors. Bayes&rsquo; theorem has been fruitfully applied to describe and explain a wide range of cognitive and neural phenomena (e.g., visual perception and neural population activity) and is at the core of various theories (e.g., predictive processing). Despite these successes, we claim that Bayesianism has two interrelated shortcomings: its calculations and models are predominantly linear and noise is assumed to be random and unstructured versus deterministic. We outline ways that Bayesianism can address those shortcomings: first, by making more central the nonlinearities characteristic of biological cognitive systems, and second, by treating noise not as random and unstructured dynamics, but as the kind of structured nonlinearities of complex dynamical systems (e.g., chaos and fractals). We provide bistable visual percepts as an example of a real-world phenomenon that demonstrates the fruitfulness of integrating complex dynamical systems theory in Bayesian treatments of perception. Doing so facilitates a Bayesianism that is more capable of explaining a number of currently out-of-reach natural phenomena on their own, biologically realistic terms.

]]>Dynamics doi: 10.3390/dynamics3010007

Authors: Chun-Lin Yang Nandan Shettigar C. Steve Suh

The human brain is a complex network of connected neurons whose dynamics are difficult to describe. Brain dynamics are the global manifestation of individual neuron dynamics and the synaptic coupling between neurons. Membrane potential is a function of synaptic dynamics and electrophysiological coupling, with the parameters of postsynaptic potential, action potential, and ion pump dynamics. By modelling synaptic dynamics using physical laws and the time evolution of membrane potential using energy, neuron dynamics can be described. This local depiction can be scaled up to describe mesoscopic and macroscopic hierarchical complexity in the brain. Modelling results are favorably compared with physiological observation and physically acquired action potential profiles as reported in the literature.

]]>Dynamics doi: 10.3390/dynamics3010006

Authors: Kostas Kleidis Nikolaos K. Spyrou

A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter&ndash;energy content is represented by a perfect fluid whose volume elements perform polytropic flows. When the (thermodynamic) energy of the associated internal motions is taken into account as an additional source of the universal gravitational field, it compensates the DE needed to compromise spatial flatness in an accelerating universe. The unified model which is driven by a polytropic fluid not only interprets the observations associated with universe expansion but successfully confronts all the current issues of cosmological significance, thus arising as a viable alternative to the &Lambda;CDM model.

]]>Dynamics doi: 10.3390/dynamics3010005

Authors: Xabier Gutierrez de la Cal Alex Matzkin

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schrödinger) equation or for Klein–Gordon and Dirac wavefunctions defined in the Foldy–Wouthuysen representation. In this work, we quantitatively investigate the degree of non-causality for free propagation for different types of wavepackets that all initially have a compact spatial support. In the studied examples, we find that non-causality appears as a small transient effect that can in most cases be neglected. We display several numerical results and discuss the fundamental and practical consequences of our findings concerning this peculiar dynamical feature.

]]>Dynamics doi: 10.3390/dynamics3010004

Authors: Arnold Kiv Arkady Bryukhanov Vladimir Soloviev Andrii Bielinskyi Taras Kavetskyy Dmytro Dyachok Ivan Donchev Viktor Lukashin

Plastic deformation of DC04 steel is regarded as a nonlinear, complex, irreversible, and self-organized process. The stress&ndash;strain time series analysis provided the possibility to identify areas of (quasi-)elastic deformation, plastic deformation, and necking. The latter two regions are the most informative. The area of inelastic deformation is reflected by collective, self-organized processes that lead to the formation of pores, and finally, the development of microcracks and a general crack as the cause of sample failure. Network measures for the quantitative assessment of the structural deformations in metals are proposed. Both spectral and topological measures of network complexity were found to be especially informative. According to our results, they can be used not only to classify the stages of plastic deformation, but also, they can be applied as a precursor of the material destruction process.

]]>Dynamics doi: 10.3390/dynamics3010003

Authors: Dynamics Editorial Office Dynamics Editorial Office

High-quality academic publishing is built on rigorous peer review [...]

]]>Dynamics doi: 10.3390/dynamics3010002

Authors: Dieter Schuch Moise Bonilla-Licea

For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency &omega;(t), still, a dynamical invariant can be found that now has the dimension of action. The question, if such an invariant still exists after the addition of a dissipative friction force is analyzed for the classical as well as for the quantum mechanical case from different perspectives, particularly from that of a complex hydrodynamic formulation of quantum mechanics.

]]>Dynamics doi: 10.3390/dynamics3010001

Authors: Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski

We describe non-equilibrium &#981;4 theory in a hierarchical manner to develop a method for manipulating coherent fields as a toy model of introducing control into Quantum Field Theory (QFT) of the brain, which is called Quantum Brain Dynamics (QBD). We begin with the Lagrangian density of &#981;4 model, where we adopt 2-Particle-Irreducible (2PI) effective action, and derive the Klein&ndash;Gordon equation of coherent fields with a damping term as an input&ndash;output equation proposed in areas of morphological computation or reservoir computing. Our analysis is extended to QFT in a hierarchy representing multiple layers covering cortex in a brain. We find that the desired target function is achieved via time-evolution in the Klein&ndash;Gordon equations in a hierarchy of numerical simulations when a signal in both the input and output prevails over noise in the intermediate layers. Our approach will be applied to control coherent fields in the systems (in a hierarchy) described in the QFT framework, with potential applications allowing the manipulation of quantum fields, especially holograms in QBD. We could then provide realistic physical degrees of freedom of a light&ndash;matter system in the contexts of quantum cognition and the associated free-energy principle.

]]>Dynamics doi: 10.3390/dynamics2040027

Authors: Daniel Strömbom Grace Tulevech Rachel Giunta Zachary Cullen

Moving animal groups often spontaneously change their group structure and dynamics, but standard models used to explain collective motion in animal groups are typically unable to generate changes of this type. Recently, a model based on attraction, repulsion and asymmetric interactions designed for specific fish experiments was shown capable of producing such changes. However, the origin of the model&rsquo;s ability to generate them, and the range of this capacity, remains unknown. Here we modify and extend this model to address these questions. We establish that its ability to generate groups exhibiting changes depends on the size of the blind zone parameter &beta;. Specifically, we show that for small &beta; swarms and mills are generated, for larger &beta; polarized groups forms, and for a region of intermediate &beta; values there is a bistability region where continuous switching between milling and polarized groups occurs. We also show that the location of the bistability region depends on group size and the relative strength of velocity alignment when this interaction is added to the model. These findings may contribute to advance the use of self-propelled particle models to explain a range of disruptive phenomena previously thought to be beyond the capabilities of such models.

]]>Dynamics doi: 10.3390/dynamics2040026

Authors: Bosiljka Tadić

The transport of information packets in complex networks is a prototype system for the study of traffic jamming, a nonlinear dynamic phenomenon that arises with increased traffic load and limited network capacity. The underlying mathematical framework helps to reveal how the macroscopic jams build-up from microscopic dynamics, depending on the posting rate, navigation rules, and network structure. We investigate the time series of traffic loads before congestion occurs on two networks with structures that support efficient transport at low traffic or higher traffic density, respectively. Each node has a fixed finite queue length and uses next-nearest-neighbour search to navigate the packets toward their destination nodes and the LIFO queueing rule. We find that when approaching the respective congestion thresholds in these networks, the traffic load fluctuations show a similar temporal pattern; it is described by dominant cyclical trends with multifractal features and the broadening of the singularity spectrum regarding small-scale fluctuations. The long-range correlations captured by the power spectra show a power-law decay with network-dependent exponents. Meanwhile, the short-range correlations dominate at the onset of congestion. These findings reveal inherent characteristics of traffic jams inferred from traffic load time series as warning signs of congestion, complementing statistical indicators such as increased travel time and prolonged queuing in different transportation networks.

]]>Dynamics doi: 10.3390/dynamics2040025

Authors: Haim Baruh

This paper is concerned with inconsistent results that can be obtained when modeling rigid body collisions via algebraic equations. Newton&rsquo;s approach is kinematic and fails in several cases. Poisson&rsquo;s formulation has been shown lead to energetic inconsistencies, particularly in work done by the impulsive forces. This paper shows that the energetic formulation may lead to unexpected results in the magnitudes of the impulsive forces. These inconsistencies are due to the simplifying assumptions made to model collisions as occurring instantaneously. The inconsistencies increase as friction in the system becomes higher. We propose an optimization procedure for solving the algebraic equations of impact so that inconsistencies are minimized. Using experimental results, we present a discussion about the coefficients of restitution and friction.

]]>Dynamics doi: 10.3390/dynamics2040024

Authors: Guglielmo Inferrera Francesco Oliveri

This paper deals with the application of the mathematical apparatus of quantum mechanics for the formulation of an operatorial model of a couple of populations spatially distributed over a one-dimensional region. The two populations interact with a competitive mechanism and are able to diffuse over the region. A nonlocal competition effect is also included. In more detail, we consider a one-dimensional region divided in N cells where the actors, represented by annihilation, creation, and a number fermionic operators, interact. The dynamics is governed by a self-adjoint and time-independent Hamiltonian operator describing the various interactions. The results of some numerical simulations are presented and discussed. The recently introduced variant of the standard Heisenberg approach, named (H,&rho;)-induced dynamics, is also used in order to take into account some changes in time of the attitudes of the two populations, and obtain more realistic dynamical outcomes.

]]>Dynamics doi: 10.3390/dynamics2040023

Authors: Damodaran Santhamani Shibu Soman Latha Nitin Christophe Chesneau Muhammed Rasheed Irshad Sobhanam Padmini Shibin Radhakumari Maya

The hybrid normal (HN) distribution is a new generalization of the normal distribution that we introduce and study in this article. Its mathematical foundation is based on the logarithmically transformed version of the famous hybrid log-normal (HLN) distribution, which is an unexplored direction in the literature. We emphasize the applicability of the HN distribution with the aim of fitting versatile data, such as, in this paper, fiber data on the strength of glass. In particular, the unknown parameters are estimated using both Bayesian and maximum likelihood estimation approaches, with Bayesian estimation carried out using the MCMC approach. A thorough simulation study is performed to determine the flexibility of the estimates&rsquo; performance. The glass fiber data are then analyzed, with an assessment of several existing distributions from the literature used to demonstrate how the HN distribution is relevant in this regard.

]]>Dynamics doi: 10.3390/dynamics2040022

Authors: Vasileios-Martin Nikiforidis Dimitrios G. Tsalikis Pavlos S. Stephanou

Since its introduction in the late 1970s, the non-affine or slip parameter, &xi;, has been routinely employed by numerous constitutive models as a constant parameter. However, the evidence seems to imply that it should be a function of polymer deformation. In the present work, we phenomenologically modify a constitutive model for the rheology of unentangled polymer melts [P. S. Stephanou et al. J. Rheol. 53, 309 (2009)] to account for a non-constant slip parameter. The revised model predictions are compared against newly accumulated rheological data for a C48 polyethylene melt obtained via direct non-equilibrium molecular dynamics simulations in shear. We find that the conformation tensor data are very well predicted; however, the predictions of the material functions are noted to deviate from the NEMD data, especially at large shear rates.

]]>Dynamics doi: 10.3390/dynamics2040021

Authors: Natalya V. Burmasheva Evgeniy Yu. Prosviryakov

The article considers thermal diffusion shear flows of a viscous incompressible fluid with spatial acceleration. The simulation uses a system of thermal diffusion equations (in the Boussinesq approximation), taking into account the Dufour effect. This system makes it possible to describe incompressible gases, for which this effect prevails, from a unified standpoint. It is shown that for shear flows, the system of equations under study is nonlinear and overdetermined. In view of the absence of a theorem on the existence and smoothness of the solution of the Navier&ndash;Stokes equation, the integration of the existing system seems to be an extremely difficult task. The article studies the question of the existence of a solution in the class of functions represented as complete linear forms in two Cartesian coordinates with non-linear (with respect to the third Cartesian coordinate) coefficients. It is shown that the system is non-trivially solvable under a certain condition (compatibility condition) constructed by the authors. The corresponding theorem is formulated and proven. These conclusions are illustrated by a comparison with the previously obtained results.

]]>Dynamics doi: 10.3390/dynamics2040020

Authors: Vasily Vorobyov Alexander Deev Zoya Oganesyan Frank Sengpiel Aleksey A. Ustyugov

Aging and Alzheimer&rsquo;s disease (AD) are characterized by common pathological features associated with alterations in neuronal connections. These inevitably affect the functioning of specific brain areas and their interrelations, leading to questions about neuronal plasticity and the compensatory mechanisms associated with dopaminergic (DA) mediation. In this study on twelve-month-old freely moving 5XFAD-transgenic mice, serving as a model of AD, and their wild-type (WT) littermates, we analyze electroencephalograms (EEGs) from the motor cortex (MC), putamen (Pt) and the DA-producing ventral tegmental area (VTA) and substantia nigra (SN). Baseline EEGs in the transgenic mice were characterized by delta&nbsp;2 activity enhancements in VTA and alpha attenuation in VTA and SN. In contrast to WT mice, which lack differences in EEG from these brain areas, 5XFAD mice showed theta&ndash;alpha attenuation and delta&nbsp;2 and beta&nbsp;2 enhancements in EEG from both VTA and SN vs. MC. In 5XFAD mice, a DA mimetic, apomorphine, lowered (vs. saline) the theta oscillations in Pt, VTA and SN and enhanced alpha in MC, Pt, VTA and beta&nbsp;1 in all brain areas. These results and those obtained earlier in younger (six-month-old) mice suggest that the age-related characteristics of cerebral adaptive mechanisms affected by AD might be associated with modification of dopaminergic mediation in the mechanisms of intracerebral dynamic interrelations between different brain areas.

]]>Dynamics doi: 10.3390/dynamics2040019

Authors: Michael Craig Jay Raval Bruce Tai Albert Patterson Wayne Hung

This research studied the effect of channel roughness on micro-droplet distributions in internal minimum quantity lubrication for effective machining. Mixtures of different oils and air were flown though internal channels with simulated different roughness: as fabricated, partially threaded, and fully threaded. The airborne droplets were collected, analyzed, and compared with simulated results by computational fluid dynamics. For low-viscous lubricant, the rough channel surface helped to break large droplets in the boundary layer into smaller droplets and reintroduce them into the main downstream flow. The opposite trend was found for the higher viscous lubricant. The study also performed chemical etching to roughen selected surfaces of carbide cutting tools. The synergy of hand and ultrasonic agitation successfully roughened a carbide surface within twelve minutes. Scanning electron microscopy examination showed deep etching that removed all grinding marks on a WC&ndash;Co cutting tool surface.

]]>Dynamics doi: 10.3390/dynamics2040018

Authors: Fabien Beaumont Fabien Bogard Sebastien Murer Guillaume Polidori

This study is based on the hypothesis that the bubbles-induced vortex flows could enhance the release of carbon dioxide (CO2) from a glass of effervescent wine. To provide tangible evidence, we conducted a series of experiments, the first of which aimed to correlate the filling height and the bubble-induced flow dynamics with the CO2 volume flux released from the vessel during a tasting. The results obtained through micro-weighing and PIV experiments showed a correlation between the filling height, the mixing flow dynamics, and the amount of CO2 released at the air/wine interface by several mechanisms (bubble burst, diffusion). In order to hide the role of bubbles, we proposed a simple experimental device that consisted in stirring the wine (supersaturated in dissolved gas) mechanically, while avoiding the phenomenon of nucleation. This mechanical stirring system allowed for controlling the intensity of convective movements of the liquid phase by varying the rotation frequency of a glass rod. The results of this experiment have provided irrefutable evidence of a close link between the stirring dynamics of a wine supersaturated in dissolved gases and the release of CO2 by a mass convection-diffusion phenomenon.

]]>Dynamics doi: 10.3390/dynamics2030017

Authors: Germano D’Abramo

We investigate in detail an apparently unnoticed consequence of special relativity. It consists in time dilation/contraction and frequency shift for emitted light affecting accelerated reference frames at astronomical distances from an inertial observer. The frequency shift is non-cosmological and non-Doppler in nature. We derive the main formulae and compare their predictions with the astronomical data available for Proxima Centauri. We found no correspondence with observations. Since the implications of the new time dilation/contraction and frequency shift are blatantly paradoxical, we do not expect to find one. By all indications, we are dealing with a genuine, and not a merely apparent, relativity paradox.

]]>Dynamics doi: 10.3390/dynamics2030016

Authors: Jason Andrew Colwell

The setting is a system containing achiral reactants which form a chiral compound. In 1983, Kondepudi and Nelson proposed a model for the breaking of chiral symmetry. The present article reduces the conditions for bifurcation to a single condition which is shown to be both necessary and sufficient. A number of other papers on this topic also propose models for the breaking of chiral symmetry. These are shown to be essentially special cases of the model of Kondepudi and Nelson, with the same necessary and sufficient condition. The central question of this line of research is: in a racemic mixture of a chiral compound, could an excess of one enantiomer over the other develop on its own? Our answer is yes, if and only if a certain simple condition is satisfied. This answer should prove useful in further research, both theoretical and experimental, into the origin of life.

]]>Dynamics doi: 10.3390/dynamics2030015

Authors: Mohammad-Hassan Naddaf Bożena Czerny Michal Zajaček

We perform non-hydrodynamical 2.5D simulations to study the dynamics of material above accretion disk based on the disk radiation pressure acting on dust. We assume a super-accreting underlying disk with the accretion rate of 10 times the Eddington rate with central black hole mass ranging from 107 up to 109M&#8857;. Such high accretion rates are characteristic for extreme sources. We show that for high accretors the radiatively dust-driving mechanism based on the FRADO model always leads to a massive outflow from the disk surface, and the failed wind develops only at larger radii. The outflow rate strongly depends on the black hole mass, and an optically thick energy-driven solution can exceed the accretion rate for masses larger than 108M&#8857; but momentum-driven outflow does not exceed the accretion rate even for super-Eddington accretion, therefore not violating the adopted stationarity of the disk. However, even in this case the outflow from the disk implies a strong mechanical feedback.

]]>Dynamics doi: 10.3390/dynamics2030014

Authors: Gheorghe Maria Laura Renea Cristina Maria

Enzymatic reactions can successfully replace complex chemical syntheses using milder reaction conditions and generating less waste. The developed model-based numerical analysis turned out to be a beneficial tool to determine the optimal operating policies of complex multienzymatic reactors. As proved, for such cases, the determination of a Fed-Batch Reactor (FBR) optimal operating policy results in a difficult multiobjective optimization problem. Exemplification is made for the bienzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and nicotinamide adenine dinucleotide (NADH) cofactor with the in situ continuous regeneration of NADH at the expense of formate degradation in the presence of FDH (formate dehydrogenase). For such a coupled system, the model-based engineering evaluations must account for multiple competing (opposable) optimization objectives. Among the multiple novelty elements: i) an optimally operated FBR with a tightly controlled variable feeding (of the time stepwise type) during the batch can lead to higher performance; ii) the optimally operated FBR reported better performance compared to an optimally single or cyclic BR, or to optimally serial batch-to-batch reactors (SeqBR), when considering a multiobjective optimization; iii) the concomitant variable feeding with substrate, enzymes, and cofactor during the FBR &ldquo;time-arcs&rdquo; is an option seldom approached in the literature but which is proved here, leading to consistent economic benefits.

]]>Dynamics doi: 10.3390/dynamics2030013

Authors: Dimitri Volchenkov C. Steve Suh

We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi&ndash;Dirac distribution of node&rsquo;s fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as the unique stationary solution of a discrete Fokker&ndash;Planck equation describing the time evolution of probability distribution of stochastic processes in networks. Nodes of inferior centrality are the most likely candidates for the future structural changes in the network.

]]>Dynamics doi: 10.3390/dynamics2030012

Authors: Sarah Gebai Gwendal Cumunel Mohammad Hammoud Gilles Foret Emmanuel Roze Elodie Hainque

The current work promotes the use of non-invasive devices for reducing involuntary tremor of human upper limb. It concentrates on building up an upper limb model used to reflect the measured tremor signal and is suitable for the design of a passive vibration controller. A dynamic model of the upper limb is excited by the measured electromyography signal scaled to reach the wrist joint angular displacement measured by an inertial measurement unit for a patient with postural tremor. A passive tuned-mass-damper (TMD) placed on the hand is designed as a stainless-steel beam with a length of 91 mm and a cross-sectional diameter of 0.79 mm, holding a mass of 14.13 g. The damping ratio and mass position of the TMD are optimized numerically. The fundamental frequency of the TMD is derived and validated experimentally through measurements for different mass positions, with a relative error of 0.65%. The modal damping ratio of the beam is identified experimentally as 0.14% and increases to 0.26&ndash;0.46% after adding the mass at different positions. The optimized three TMDs reduce 97.4% of the critical amplitude of the power spectral density at the wrist joint.

]]>Dynamics doi: 10.3390/dynamics2030011

Authors: Larisa Morozyuk Boris Kosoy Viktoriia Sokolovska-Yefymenko Volodymyr Ierin

The present study is an analysis of the processes in the components of the LPG (propane/butane) reliquefaction plant under the conditions of co-mingling in tanks when transporting by sea. For the analysis, the monitoring data of an LPG cargo operation have been used. An energy analysis of the mixture-based reliquefaction plant has been performed. The characteristics of the mixture in the tanks, the operating conditions of the reliquefaction plant, and the performance of the system have been considered. The method of equivalence has been applied for thermodynamic analysis. The result of the substitution of actual processes with equivalent ones allows for the accomplishment of the parameters control of each working fluid within the mixture as a pure working fluid. It is shown that the low-boiling component determines the operating parameters of the entire reliquefaction plant. The method of equivalence and visualization of the processes within the LPG as a mixture using the thermodynamic diagrams of pure working fluids is recommended to shorten the path to set up the appropriate reliquefaction plant management strategy. The energy analysis performed using the method of equivalent cycles has been validated with the existing reliquefaction plant characteristics. The inaccuracies are in the limit of 4%.

]]>Dynamics doi: 10.3390/dynamics2020010

Authors: Akihiro Nishiyama Shigenori Tanaka Jack Adam Tuszynski

We describe non-equilibrium quantum brain dynamics (QBD) for the breakdown of symmetry and propose the possibility of hologram memory based on QBD. We begin with the Lagrangian density of QBD with water rotational dipole fields and photon fields in 3+1 dimensions, and derive time evolution equations of coherent fields. We show a solution for super-radiance derived from the Lagrangian of QBD and propose a scenario of holography by the interference of two incident super-radiant waves. We investigate the time evolution of coherent dipole fields and photon fields in the presence of quantum fluctuations in numerical simulations. We find that the breakdown of the rotational symmetry of dipoles occurs in inverted populations for incoherent dipoles. We show how the waveforms of holograms with interference patterns evolve over time in an inverted population for incoherent dipoles. The optical information of hologram memory can be transferred to the whole brain during information processing. The integration of holography and QBD will provide us with a prospective approach in memory formation.

]]>Dynamics doi: 10.3390/dynamics2020009

Authors: Natalya Burmasheva Evgeniy Prosviryakov

The paper announces a family of exact solutions to Navier&ndash;Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). The structure of the fluid motion equations is such that the incompressibility equation enables us to establish the velocity defect law for nonuniform Poiseuille flow. In this case, the velocity field is dependent on two coordinates and time, and it is an arbitrary-degree polynomial relative to the horizontal (longitudinal) coordinate. The polynomial coefficients depend on the vertical (transverse) coordinate and time. The exact solution under consideration was built using the method of indefinite coefficients and the use of such algebraic operations was for addition and multiplication. As a result, to determine the polynomial coefficients, we derived a system of simplest homogeneous and inhomogeneous parabolic partial equations. The order of integration of the resulting system of equations was recurrent. For a special case of steady flows of a viscous fluid, these equations are ordinary differential equations. The article presents an algorithm for their integration. In this case, all components of the velocity field, vorticity vector, and shear stress field are polynomial functions. In addition, it has been noted that even without taking into account the thermohaline convection (creeping current) all these fields have a rather complex structure.

]]>Dynamics doi: 10.3390/dynamics2020008

Authors: Dionysios Sourailidis Christos Volos Lazaros Moysis Efthymia Meletlidou Ioannis Stouboulos

In the present study, the simulation of an immunotherapy effect for a known dynamical system, that describes the process for avascular, vascular, and metastasis tumor growth based on a chemical network model, has been presented. To this end, square signals of various amplitudes have been used, to model the effect of external therapy control, in order to affect the population of immune cells. The results of the simulations show that for certain values of the amplitude of the square signal, the populations of the proliferating tumor cells in the vascular and metastasis stages have been reduced.

]]>Dynamics doi: 10.3390/dynamics2020007

Authors: Marc Lizana Joan R. Casas

One of the objectives of structural health monitoring (SHM) is to maximize the information while keeping the number of sensors, and consequently the cost of the sensor system, to a minimum. Besides, the sensor configurations must be robust in the sense that the feasibility of small errors inherent to the process must not lead to large variations in the final results. This paper presents novelties regarding the robustness evaluation to model and measurement errors of four of the most influential optimal sensor placement (OSP) methods: the modal kinetic energy (MKE) method; the effective independence (EFI) method; the information entropy index (IEI) method; and the MinMAC method. The four OSP methods were implemented on the Streicker Bridge, a footbridge located on the Princeton University Campus, to identify five mode shapes of the bridge. The mode shapes, obtained in a FE model&rsquo;s modal analysis, were used as input data for the OSP analyses. The study indicates that the MKE method seems to be the most suitable method to estimate the optimal sensor positions: it provides a relatively large amount of information with the lowest computational time, and it outperforms the other three methods in terms of robustness in the usual range of number of sensors.

]]>Dynamics doi: 10.3390/dynamics2020006

Authors: Nandan Shettigar Chun-Lin Yang Kuang-Chung Tu C. Steve Suh

The human brain is a complex network whose ensemble time evolution is directed by the cumulative interactions of its cellular components, such as neurons and glia cells. Coupled through chemical neurotransmission and receptor activation, these individuals interact with one another to varying degrees by triggering a variety of cellular activity from internal biological reconfigurations to external interactions with other network agents. Consequently, such local dynamic connections mediating the magnitude and direction of influence cells have on one another are highly nonlinear and facilitate, respectively, nonlinear and potentially chaotic multicellular higher-order collaborations. Thus, as a statistical physical system, the nonlinear culmination of local interactions produces complex global emergent network behaviors, enabling the highly dynamical, adaptive, and efficient response of a macroscopic brain network. Microstate reconfigurations are typically facilitated through synaptic and structural plasticity mechanisms that alter the degree of coupling (magnitude of influence) neurons have upon each other, dictating the type of coordinated macrostate emergence in populations of neural cells. These can emerge in the form of local regions of synchronized clusters about a center frequency composed of individual neural cell collaborations as a fundamental form of collective organization. A single mode of synchronization is insufficient for the computational needs of the brain. Thus, as neural components influence one another (cellular components, multiple clusters of synchronous populations, brain nuclei, and even brain regions), different patterns of neural behavior interact with one another to produce an emergent spatiotemporal spectral bandwidth of neural activity corresponding to the dynamical state of the brain network. Furthermore, hierarchical and self-similar structures support these network properties to operate effectively and efficiently. Neuroscience has come a long way since its inception; however, a comprehensive and intuitive understanding of how the brain works is still amiss. It is becoming evident that any singular perspective upon the grandiose biophysical complexity within the brain is inadequate. It is the purpose of this paper to provide an outlook through a multitude of perspectives, including the fundamental biological mechanisms and how these operate within the physical constraints of nature. Upon assessing the state of prior research efforts, in this paper, we identify the path future research effort should pursue to inspire progress in neuroscience.

]]>Dynamics doi: 10.3390/dynamics2020005

Authors: Nikolay Kryukov Eugene Oks

The review covers the dynamics of different kinds of one electron Rydberg quasimolecules in various environments, such as being subjected to electric and/or magnetic fields or to a plasma environment. The higher than geometrical symmetry of these systems is due to the existence of an additional conserved quantity: the projection of the supergeneralized Runge&ndash;Lenz vector on the internuclear axis. The review emphasizes the fundamental and practical importance of the results concerning the dynamics of these systems.

]]>Dynamics doi: 10.3390/dynamics2020004

Authors: Amélie Ferran Sofía Angriman Pablo D. Mininni Martín Obligado

It has been shown that, for dense, sub-Kolmogorov particles advected in a turbulent flow, carrier phase properties can be reconstructed from the particles&rsquo; velocity field. For that, the instantaneous particles&rsquo; velocity field can be used to detect the stagnation points of the carrier phase. The Rice theorem can therefore be used, implying that the Taylor length is proportional to the mean distance between such stagnation points. As this model has been only tested for one-dimensional time signals, this work discusses if it can be applied to two-phase, three-dimensional flows. We use direct numerical simulations with turbulent Reynolds numbers Re&lambda; between 40 and 520 and study particle-laden flows with a Stokes number of St=0.5. We confirm that for the carrier phase, the Taylor length is proportional to the mean distance between stagnation points with a proportionality coefficient that depends weakly on Re&lambda;. Then, we propose an interpolation scheme to reconstruct the stagnation points of the particles&rsquo; velocity field. The results indicate that the Rice theorem cannot be applied in practice to two-phase three-dimensional turbulent flows, as the clustering of stagnation points forms very dense structures that require a very large number of particles to accurately sample the flow stagnation points.

]]>Dynamics doi: 10.3390/dynamics2020003

Authors: Faisal Alobaid Saied Taheri

Obtaining the modal parameters of a tire with ground contact and rolling conditions represents a challenge due to the complex vibration characteristic behaviors that cause the distortion of the tire&rsquo;s symmetry and the bifurcation phenomena of the natural frequencies. An in-plane rigid&ndash;elastic-coupled tire model was used to examine the 200 DOF finite difference method (FDM) modal analysis accuracy under non-ground contact and non-rotating conditions. The discrete in-plane rigid&ndash;elastic-coupled tire model was modified to include the contact patch restriction, centrifugal force and Coriolis effect, covering a range from 0 to 300 Hz. As a result, the influence of the contact patch and the rotating tire conditions on the natural frequencies and modes were obtained through modal analysis.

]]>Dynamics doi: 10.3390/dynamics2010002

Authors: John Dzielski Mark Blackburn

This paper presents an explanation of why a spinning football rotates so that the spin axis remains nearly aligned with the velocity vector, and approximately parallel to the tangent to the trajectory. The paper derives the values of the characteristic frequencies associated with the football&rsquo;s precession and nutation. The paper presents a graphical way of visualizing how the motions associated with these frequencies result in the observed &ldquo;wobble&rdquo; of the football. A solution for the linearized dynamics shows that there is a minimum amount of spin required for the motion to be stable and for the football not to tumble. This paper notes the similarity of this problem to that of spun projectiles. The results show that the tendency of a football to align itself with and rotate with the velocity vector is associated with an equilibrium condition with a non-zero aerodynamic torque. The torque is precisely the value required for the football to rotate at the same angular rate as the velocity vector. An implication of this is that a release with the football spin axis and velocity vector aligned (zero aerodynamic torque) is not the condition that results in minimum motion after release. Minimum &ldquo;wobble&rdquo; occurs when the ball is released with its symmetry axis slightly to the right or left of the velocity vector, depending on the direction of the spin. There are additional forces and moments acting on the football that affect its trajectory and its stability, but it is not necessary to consider these to explain the tendency of the ball to align with the velocity vector and to &rdquo;wobble.&rdquo; The results of this paper are equally applicable to the spiral pass in American football and the screw kick in rugby.

]]>Dynamics doi: 10.3390/dynamics2010001

Authors: Han Sun Haim Baruh

This paper is concerned with the modeling and simulation of two- and three-dimensional impact in the presence of friction. Single impacts are considered, and the impact equations are solved algebraically. Impact generates impulsive normal and frictional forces and the direction of sliding can change during impact. A procedure is developed to estimate the change in direction of sliding during three-dimensional impact. The modes of impact, such as sliding, sticking, or change in direction of sliding, are classified for both two- and three-dimensional impact. Simulations are conducted to analyze the energy lost, change in impact direction, and stick-slip conditions, where different models for restitution are compared. A closed-form solution is developed to analyze the modes of sliding for two-dimensional impact.

]]>Dynamics doi: 10.3390/dynamics1020013

Authors: Fabien Beaumont Fabien Bogard Hassen Hakim Sébastien Murer Bastien Bouchet Guillaume Polidori

Partial body cryotherapy cabins most often use liquid nitrogen as their cryogenic fluid, which raises safety concerns during operation. In this study, an innovative cryotherapy cabin design is presented, featuring an electric cooling system suitable for producing cold air at &minus;30 &deg;C. The geometry of the designed cryotherapy cabin is evaluated by a thermodynamic modeling which aims at optimizing the circulation of cold air flows inside the cabin. The numerical study is carried out in two successive phases, the first one being necessary to model the pre-cooling phase and to estimate the time required to reach an average temperature close to the set temperature of &minus;30 &deg;C. The second one aims at modeling a 3-min cryotherapy session by taking into account the thermal transfers between the human body and its environment. Results demonstrate the potential benefits of the cold air injection device which has been designed to optimize the thermal transfers and homogenize the temperatures within the therapeutic enclosure. The main innovation of this study is the ability to customize cryotherapy protocols by injecting cold air at different levels through targeting of specific body areas. Further calculations would be required to determine the precise impact of zone-targeted injection on skin cooling.

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