We study the dynamical properties of a particle in a nonplanar square billiard. The plane of the billiard has a sinusoidal shape. We consider both the static and time-dependent plane. We study the affect of different parameters that control the geometry of the billiard in this model. We consider variations of different parameters of the model and describe how the particle trajectory is affected by these parameters. We also investigate the dynamical behavior of the system in the static condition using its reduced phase plot and show that the dynamics of the particle inside the billiard may be regular, mixed, or chaotic. Finally, the problem of the particle energy growth is studied in the billiard with the time-dependent plane. We show that when in the static case, the billiard is chaotic, then the particle energy in the time-dependent billiard grows for a small number of collisions, and then it starts to saturate. But when the dynamics of the static case is regular, then the particle average energy in the time-dependent situation stays constant.

In the present paper, the avoidance behavior of pedestrians was characterized by controlled experiments. Several conflict situations were studied considering different flow rates and group sizes in crossing and head-on configurations. Pedestrians were recorded from above, and individual two-dimensional trajectories of their displacement were recovered after image processing. Lateral swaying amplitude and step lengths were measured for free pedestrians, obtaining similar values to the ones reported in the literature. Minimum avoidance distances were computed in two-pedestrian experiments. In the case of one pedestrian dodging an arrested one, the avoidance distance did not depend on the relative orientation of the still pedestrian with respect to the direction of motion of the first. When both pedestrians were moving, the avoidance distance in a perpendicular encounter was longer than the one obtained during a head-on approach. It was found that the mean curvature of the trajectories was linearly anticorrelated with the mean speed. Furthermore, two common avoidance maneuvers, stopping and steering, were defined from the analysis of the acceleration and curvature in single trajectories. Interestingly, it was more probable to observe steering events than stopping ones, also the probability of simultaneous steering and stopping occurrences was negligible. The results obtained in this paper can be used to validate and calibrate pedestrian dynamics models.

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model's fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions.

Analyzing the physical and chemical properties of single DNA-based molecular machines such as polymerases and helicases requires to track stepping motion on the length scale of base pairs. Although high-resolution instruments have been developed that are capable of reaching that limit, individual steps are oftentimes hidden by experimental noise which complicates data processing. Here we present an effective two-step algorithm which detects steps in a high-bandwidth signal by minimizing an energy-based model (energy-based step finder, EBS). First, an efficient convex denoising scheme is applied which allows compression to tuples of amplitudes and plateau lengths. Second, a combinatorial clustering algorithm formulated on a graph is used to assign steps to the tuple data while accounting for prior information. Performance of the algorithm was tested on Poissonian stepping data simulated based on published kinetics data of RNA polymerase II (pol II). Comparison to existing step-finding methods shows that EBS is superior in speed while providing competitive step-detection results, especially in challenging situations. Moreover, the capability to detect backtracked intervals in experimental data of pol II as well as to detect stepping behavior of the Phi29 DNA packaging motor is demonstrated.

We simulate selective $A1BA2\text{−}A$ and $A1BA2\text{−}B$ triblock solutions (that is, mixtures of the $A1BA2$ triblock with a solvent of either type $A$ or type $B$) using a lattice Monte Carlo method. Although the simulated triblock chains are compositionally symmetric in terms of the $A$ to $B$ volume ratio, the $A1$ block is significantly shorter than the $A2$ block. For the pure $A1BA2$ melt the phase behavior is relatively well known, including the existence and stability of the recently discovered interstitial micelles which were found at the very strong segregation limit. In this paper, we investigate the stability of the interstitial micelles as a function of triblock volume fraction in a selective solvent of either type $A$ or type $B$. The main finding of this paper is that adding a selective solvent of type $A$ shifts the stability of the interstitial micelles into significantly higher temperatures which may provide a pathway towards experimental studies of interstitial micelles in real triblock solutions. We also find that adding selective solvents to the $A1BA2$ melt gives rise to a variety of nonlamellar nanostructures for temperatures and compositions at which the interstitial micelles are stable.

The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such types of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution, but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is “unphysical”) of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem, but all nonlinear processes, both the Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time $\tau$. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples.

We demonstrate a nonlinear, nonequilibrium field-driven ion flux phenomenon, which unlike Teorell's nonlinear multiple field theory, requires only the application of one field: robust autonomous current-mass flux oscillations across a porous monolith coupled to a capillary with a long air bubble, which mimics a hydrophobic protein in an ion channel. The oscillations are driven by the hysteretic wetting dynamics of the meniscus when electro-osmotic flow and pressure driven backflow, due to bubble expansion, compete to approach zero mass flux within the monolith. Delayed rupture of the film around the advancing bubble cuts off the electric field and switches the monolith mass flow from the former to the latter. The meniscus then recedes and repairs the rupture to sustain an oscillation for a range of applied fields. This generic mechanism shares many analogs with current oscillations in cell membrane ion channel. At sufficiently high voltage, the system undergoes a state transition characterized by appearance of the ubiquitous $1/f$ power spectrum.

Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems.

We apply the matrix-product ansatz to study the totally asymmetric simple exclusion process on a ring with a generalized discrete-time dynamics depending on two hopping probabilities, $p$ and $\tilde{p}$. The model contains as special cases the TASEP with parallel update, when $\tilde{p}=0$, and with sequential backward-ordered update, when $\tilde{p}=p$. We construct a quadratic algebra and its two-dimensional matrix-product representation to obtain exact finite-size expressions for the partition function, the current of particles, and the two-point correlation function. Our main new result is the derivation of the finite-size pair correlation function. Its behavior is analyzed in different regimes of effective attraction and repulsion between the particles, depending on whether $\tilde{p}>p$ or $\tilde{p}<p$. In particular, we explicitly obtain an analytic expression for the pair correlation function in the limit of irreversible aggregation $\tilde{p}\to 1$, when the stationary configurations contain just one cluster.

It is known that amplitude death can occur in networks of coupled identical oscillators if they interact via diffusive time-delayed coupling links. Here we consider networks of oscillators that interact via direct time-delayed coupling links. It is shown analytically that amplitude death is impossible for directly coupled Stuart-Landau oscillators, in contradistinction to the case of diffusive coupling. We demonstrate that amplitude death in the strict sense does become possible in directly coupled networks if the node dynamics is governed by second-order delay differential equations. Finally, we analyze in detail directly coupled nodes whose dynamics are described by first-order delay differential equations and find that, while amplitude death in the strict sense is impossible, other interesting oscillation quenching scenarios exist.

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple mechanism gives rise to an effective maximal degree within communities. This observation is related to the anthropological theory known as Dunbar's number, i.e., the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. The second mechanism is based on a recently proposed generalization of preferential attachment to community structure, appropriately called structural preferential attachment (SPA). The combination of these two mechanisms into a single model (SPA+) allows us to reproduce a number of the global statistics of real networks: The distribution of community sizes, of node memberships, and of degrees. The SPA+ model also predicts (a) three qualitative regimes for the degree distribution within overlapping communities and (b) strong correlations between the number of communities to which a node belongs and its number of connections within each community. We present empirical evidence that support our findings in real complex networks.

We investigate the driven polymer translocation through a nanometer-scale pore in the presence and absence of hydrodynamics both in good and bad solvent. We present our results on tension propagating along the polymer segment on the cis side that is measured for the first time using our method that works also in the presence of hydrodynamics. For simulations we use stochastic rotation dynamics, also called multiparticle collision dynamics. We find that in the good solvent the tension propagates very similarly whether hydrodynamics is included or not. Only the tensed segment is by a constant factor shorter in the presence of hydrodynamics. The shorter tensed segment and the hydrodynamic interactions contribute to a smaller friction for the translocating polymer when hydrodynamics is included, which shows as smaller waiting times and a smaller exponent in the scaling of the translocation time with the polymer length. In the bad solvent hydrodynamics has a minimal effect on polymer translocation, in contrast to the good solvent, where it speeds up translocation. We find that under bad-solvent conditions tension does not spread appreciably along the polymer. Consequently, translocation time does not scale with the polymer length. By measuring the effective friction in a setup where a polymer in free solvent is pulled by a constant force at the end, we find that hydrodynamics does speed up collective polymer motion in the bad solvent even more effectively than in the good solvent. However, hydrodynamics has a negligible effect on the motion of individual monomers within the highly correlated globular conformation on the cis side and hence on the entire driven translocation under bad-solvent conditions.

The impact of the volumetric charged density of the dielectric rigid core on the electrophoresis of a soft particle is analyzed numerically. The volume charge density of the inner core of a soft particle can arise for a dendrimer structure or bacteriophage MS2. We consider the electrokinetic model based on the conservation principles, thus no conditions for Debye length or applied electric field is imposed. The fluid flow equations are coupled with the ion transport equations and the equation for the electric field. The occurrence of the induced nonuniform surface charge density on the outer surface of the inner core leads to a situation different from the existing analysis of a soft particle electrophoresis. The impact of this induced surface charge density together with the double-layer polarization and relaxation due to ion convection and electromigration is analyzed. The dielectric permittivity and the charge density of the core have a significant impact on the particle electrophoresis when the Debye length is in the order of the particle size. We find that by varying the ionic concentration of the electrolyte, the particle can exhibit reversal in its electrophoretic velocity. The role of the polymer layer softness parameter is addressed in the present analysis.

Large collections of autonomously moving agents, such as animals or micro-organisms, are able to flock coherently in space even in the absence of a central control mechanism. While the direction of the flock resulting from this critical behavior is random, this can be controlled by a small subset of informed individuals acting as leaders of the group. In this article we use the Vicsek model to investigate how flocks respond to leadership and make decisions. Using a combination of numerical simulations and continuous modeling we demonstrate that flocks display a linear response to leadership that can be cast in the framework of the fluctuation-dissipation theorem, identifying an effective temperature reflecting how promptly the flock reacts to the initiative of the leaders. The linear response to leadership also holds in the presence of two groups of informed individuals with competing interests, indicating that the flock's behavioral decision is determined by both the number of leaders and their degree of influence.

We present a numerical implementation of an active inclusion in a granular material submitted to a biaxial test. We discuss the dependence of the response to this perturbation on two parameters: the intragranular friction coefficient on one hand, and the degree of the loading on the other hand. We compare the numerical results to theoretical predictions taking into account the change of volume of the inclusion as well as the anisotropy of the elastic matrix.

In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)] and Zadehgol [Phys. Rev. E 91, 063311 (2015)]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual “branes” which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the “branes,” in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the “apparent jumps” in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others.

We use small-angle neutron scattering (SANS) to study labeled short chains with and without the influence of an entangled and highly stretched surrounding environment of longer chains. We find unequivocal evidence of nematic effects as the blend chains in steady state flow are stretched a factor $\sim 1.5$ more from the presence of the long chain nematic field. In the pure melt we confirm that the nonaffine mean-field result $\nu =0.5$ for the strain coupling is still valid for very fast flows, while in the nematic system our analysis predicts an increased coupling constant. We provide a structural explanation for the two first regimes of the nonlinear relaxation, particularly a transition regime where the long chains are relaxing in a sea of reptating short chains.

Recent developments have cemented the realization that many concepts and quantities in thermodynamics and information theory are shared. In this paper, we consider a highly relevant quantity in information theory and complex systems, the transfer entropy, and explore its thermodynamic role by considering the implications of time reversal upon it. By doing so we highlight the role of information dynamics on the nuanced question of observer perspective within thermodynamics by relating the temporal irreversibility in the information dynamics to the configurational (or spatial) resolution of the thermodynamics. We then highlight its role in perhaps the most enduring paradox in modern physics, the manifestation of a (thermodynamic) arrow of time. We find that for systems that process information such as those undergoing feedback, a robust arrow of time can be formulated by considering both the apparent physical behavior which leads to conventional entropy production and the information dynamics which leads to a quantity we call the information theoretic arrow of time. We also offer an interpretation in terms of optimal encoding of observed physical behavior.