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 Ca 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 Schr&ouml;dinger) equation or for Klein&ndash;Gordon and Dirac wavefunctions defined in the Foldy&ndash;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.

]]>Dynamics doi: 10.3390/dynamics1020012

Authors: Fernando Vadillo

In this short paper, we compare the deterministic model for the nuclear reactor dynamic (Hetrick, 1993) with the stochastic model (Kinard and Allen, 2004). Our numerical results show coincidences between the deterministic model and the mean of the stochastic paths, although, as already observed by other authors, there is alarge amount of dispersion between the individual paths. Notably, we always observe that the neutron density approaches zero within a short time. In this paper, we investigate this question; more concretely, we study the mean-extinction of the neutron density. The technique used here first builds the backward Kolmogorov differential equation and then solves it numerically using the finite-element method with FreeFem++. Our results confirm that in a very short time the neutrons disappear although later they recover probably due to the external source.

]]>Dynamics doi: 10.3390/dynamics1020011

Authors: Bosiljka Tadić Roderick Melnik

Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. Subject to the external and endogenous driving forces, these collective states with long-range spatial and temporal correlations often arise from the intrinsic dynamics with the threshold nonlinearity and geometry-conditioned interactions. The self-similarity of critical fluctuations enables us to describe the system using fewer parameters and universal functions that, on the other hand, can simplify the computational and information complexity. Currently, the cutting-edge research on self-organised critical systems across the scales strives to formulate a unifying mathematical framework, utilise the critical universal properties in information theory, and decipher the role of hidden geometry. As a prominent example, we study the field-driven spin dynamics on the hysteresis loop in a network with higher-order structures described by simplicial complexes, which provides a geometric-frustration environment. While providing motivational illustrations from physical, biological, and social systems, along with their networks, we also demonstrate how the self-organised criticality occurs at the interplay of the complex topology and driving mode. This study opens up new promising routes with powerful tools to address a long-standing challenge in the theory and applications of complexity science ingrained in the efficient analysis of self-organised critical states under the competing higher-order interactions embedded in complex geometries.

]]>Dynamics doi: 10.3390/dynamics1020010

Authors: Salvador Castillo-Rivera Maria Tomas-Rodriguez

In this work, a tail rotor is modelled with the aid of a multibody software to provide an alternative tool in the field of helicopter research. This advanced application captures the complex behaviour of tail rotor dynamics. The model has been built by using VehicleSim software (Version 1.0, Mechanical Simulation Corporation, Ann Arbor, MI, USA) specialized in modelling mechanical systems composed of rigid bodies. The dynamic behaviour and the control action are embedded in the code. Thereby, VehicleSim does not need an external link to another software package. The rotors are articulated, the tail rotor considers flap and feather degrees of freedom for each of the equispaced blades and their dynamic couplings. Details on the model’s implementation are derived, emphasising the modelling aspects that contribute to the coupled dynamics. The obtained results are contrasted with theoretical approaches and these have displayed to agree with the expected behaviour. This rotorcraft model helps to study the performance of a tail rotor under certain dynamic conditions.

]]>Dynamics doi: 10.3390/dynamics1020009

Authors: Moise Bonilla-Licea Dieter Schuch

For time dependent Hamiltonians like the parametric oscillator with time-dependent frequency, the energy is no longer a constant of motion. Nevertheless, in 1880, Ermakov found a dynamical invariant for this system using the corresponding Newtonian equation of motion and an auxiliary equation. In this paper it is shown that the same invariant can be obtained from Bohmian mechanics using complex Hamiltonian equations of motion in position and momentum space and corresponding complex Riccati equations. It is pointed out that this invariant is equivalent to the conservation of angular momentum for the motion in the complex plane. Furthermore, the effect of a linear potential on the Ermakov invariant is analysed.

]]>Dynamics doi: 10.3390/dynamics1010008

Authors: Gheorghe Maria Ioana Mirela Peptănaru

Multi-enzymatic reactions can successfully replace complex chemical syntheses, using milder reaction conditions, and generating less waste. The present model-based analysis compares the performances of several optimally operated Batch Reactors (BR) with those of an optimally operated serial Sequence of BRs (SeqBR). In multi-enzymatic systems, SeqBR could be more advantageous and flexible, allowing the optimization of costly enzymes amounts used in each BR in the series. Exemplification was made for the bi-enzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and the 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 coupled enzymatic systems, the model-based engineering evaluations are difficult tasks, because they must account for the common species’ initial levels, their interaction, and their dynamics. The determination of optimal operating modes of sole BR or of a SeqBR turns into a multi-objective optimization problem with multiple constraints to be solved for every particular system. The study presents multiple elements of novelty: (i) the proof of higher performances of an optimal SeqBR (including N-BRs) compared to a sole optimal BR operated for N-number of runs and (ii) the effect of using a multi-objective optimization criteria on SeqBR adjustable dynamics.

]]>Dynamics doi: 10.3390/dynamics1010007

Authors: Sudath C. Siriwardane Nirosha D. Adasooriya Dimitrios Pavlou

Offshore structures are subjected to dynamic environmental loads (wave and wind loads). A stress-life fatigue strength curve is proposed for tubular joints which are in the splash zone area of offshore jacket structures. The Det Norske Veritas (DNV) offshore structures standards given design T-curve in the air is modified with the environment-dependent parameters to obtain this fatigue strength curve. Validity of the curve is done by comparing fatigue lives given by the proposed curve with experimental fatigue lives of tubular joints tested in seawater under different loading conditions. The fatigue assessment of a case study tubular joint is performed using the proposed curve. Nominal stress ranges of the members, which are connected to the joint, are obtained by dynamic analysis of the jacket structure. Stress concentration factors are utilized with the nominal stresses to obtain the hot spot stress ranges. Fatigue lives are calculated and compared with the conventional approach. Hence the applicability and significance of the proposed fatigue strength curve are discussed.

]]>Dynamics doi: 10.3390/dynamics1010006

Authors: Eugene Oks

Analytical solutions to a variety of simplified versions of the restricted three-body problem in celestial mechanics possess long running history that encompasses several centuries. Most of the successes were limited either to the planar configuration of the three bodies, to the motion around the Lagrange points, or to the Kozai–Lidov effect. We review some analytical advances obtained by separating rapid and slow subsystems as presented in recently published papers concerning the non-planar motion of the three bodies unrelated to the Lagrange points and to the Kozai–Lidov effect. Most (but not all) of the discussed advances correspond to the bound motion in the considered celestial systems.

]]>Dynamics doi: 10.3390/dynamics1010005

Authors: Stylianos Markolefas Dimitrios Fafalis

In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).

]]>Dynamics doi: 10.3390/dynamics1010004

Authors: Stavros S. A. Lykakos Protesilaos K. Kostazos Odysseas-Vasilios Venetsanos Dimitrios E. Manolakos

Offshore structures are exposed to risks of vessel collisions and impacts from dropped objects. Tubular members are extensively used in offshore construction, and thus, there is scope to investigate their crashworthiness behaviour. Aluminium, glass fibre reinforced polymer (GFRP) and hybrid aluminium/GFRP circular tube specimens were fabricated and then tested under quasi-static and dynamic axial loading conditions. Two hybrid configurations were examined: external and internal layers from respectively aluminium and GFRP, and vice versa. The material impregnated with epoxy resin woven glass fabric was allowed to cure attached to the aluminium layer to ensure interlayer bonding. The quasi-static and dynamic tests were conducted using respectively a universal testing machine at a prescribed crosshead speed of 10 mm/min, and a 78 kg drop hammer released from 2.5 m. The non-hybrid configurations (aluminium and GFRP specimens) outperformed their hybrid counterparts in terms of crashworthiness characteristics.

]]>Dynamics doi: 10.3390/dynamics1010003

Authors: Christos Volos

Nowadays, the subject of studying system dynamics behavior has become very important in many branches of technology [...]

]]>Dynamics doi: 10.3390/dynamics1010002

Authors: Andrea Natale Impiombato Giorgio La Civita Francesco Orlandi Flavia Schwarz Franceschini Zinani Luiz Alberto Oliveira Rocha Cesare Biserni

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.

]]>Dynamics doi: 10.3390/dynamics1010001

Authors: Eugene Oks

According to the existing paradigm, helium atoms and helium-like ions (hereafter, heliumic systems) in a relatively weak external static electric field do not exhibit the linear Stark effect—in distinction to hydrogen atoms and hydrogen-like ions. In the present paper we consider the classical dynamics of a muonic-electronic heliumic system in Rydberg states–starting from the concept from our previous paper. We show that there are two states of the system where the averaged electric dipole moment is non-zero. Consequently, in these states the heliumic system should exhibit the linear Stark effect even in a vanishingly small electric field, which is a counter-intuitive result. We also demonstrate the possibility of controlling the overall precession of the electronic orbit by an external electric field. In particular, we show the existence of a critical value of the external electric field that would “kill” the precession and make the electronic orbit stationary. This is another counter-intuitive result. We calculate analytically the value of the critical field and show that it is typically smaller or even much smaller than 1 V/cm.

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