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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