Related papers: Lane formation by side-stepping
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
Nonlinear PDE's having {\bf given} conditional symmetries are constructed. They are obtained starting from the invariants of the "conditional symmetry" generator and imposing the extra condition given by the characteristic of the symmetry.…
We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under…
We study a lattice model of two perpendicular intersecting flows of pedestrians represented by hard core particles of two types, eastbound (`$\pE$') and northbound (`$\pN$'). Each flow takes place on a strip of width $M$ so that the…
We consider a finite number of particles that move in $\mathbb Z$ as independent random walks. The particles are of two species that we call $a$ and $b$. The rightmost $a$ particle becomes a $b$ particle at constant rate, while the leftmost…
To explore the pedestrian motion navigation and conflict reaction mechanisms in practice, we organized a series of circle antipode experiments. In the experiments, pedestrians are uniformly initialized on the circle and required to leave…
We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the…
A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is…
Classical second order models of pedestrian dynamics, like the social-force model, suffer from various unrealistic behaviors in the dynamics, e.g. backward motion, oscillations and overlapping of pedestrians. These effects are not related…
We numerically examine the dynamic phases and pattern formation of two-dimensional monodisperse repulsive disks driven over random quenched disorder. We show that there is a series of distinct dynamic regimes as a function of increasing…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Interaction between vehicles and pedestrians is seen in many areas such as crosswalks and intersections. In this paper, we study a totally asymmetric simple exclusion process with a bottleneck at a boundary caused by an interaction. Due to…
An extended social force model with a dynamic navigation field is proposed to study bidirectional pedestrian movement. The dynamic navigation field is introduced to describe the desired direction of pedestrian motion resulting from the…
This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically,…