Dynamics, Volume 2, Issue 4 (December 2022) – 10 articles

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’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. Full article

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. Full article

This paper is concerned with inconsistent results that can be obtained when modeling rigid body collisions via algebraic equations. Newton’s approach is kinematic and fails in several cases. Poisson’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. Full article

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 $(\mathcal{H},\rho )$-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. Full article

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’ 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. Full article

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. Full article

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–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. Full article

Aging and Alzheimer’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 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–alpha attenuation and delta 2 and beta 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 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. Full article

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–Co cutting tool surface. Full article

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. Full article