Related papers: Lane formation by side-stepping
We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence…
We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition probability of a fixed L\'evy process. In analogy to the…
A simulation model for the dynamic behaviour of pedestrian crowds is mathematically formulated in terms of a social force model, that means, pedestrians behave in a way as if they would be subject to an acceleration force and to repulsive…
The emergence and decline of democratic systems worldwide raises fundamental questions about the dynamics of political change. Contrary to the idea of a stable endpoint of liberal democracy, recent backsliding towards less democratic…
A system consisting of two conservative, oppositely driven species of particles with excluded volume interaction alone is studied on a torus. The system undergoes a phase transition between a homogeneous and an inhomogeneous phase, as the…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians…
We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
We deal with a class of second order in time nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in the theory ofnonlinear plates. Our first result states well-posedness in a…
Dynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamics, specifically using Petri nets with priority rules. A…
We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a…
Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behavior consider only interactions among isolated individuals, it turns out that up to 70% of people…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
A binary system of particles that move in opposite directions under an applied field can exhibit disordered states as well as laned states where the particles organize into oppositely moving high-mobility lanes to reduce collisions.…
The relative dynamics in collision avoidance between individual pedestrians and dyads has been recently studied, and it was shown that individuals may intrude dyads that are not socially interacting. Building on this, our current study…
The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two…
Pedestrian trajectory prediction is a challenging task as there are three properties of human movement behaviors which need to be addressed, namely, the social influence from other pedestrians, the scene constraints, and the multimodal…