Related papers: Lane formation by side-stepping
Pedestrians in crowds frequently move as part of small groups, constituting up to 70% of individuals. Dyads (groups of two) are the most frequent. Understanding quantitatively the dynamics of dyads walking in crowds is therefore an…
We consider a kinetic theory approach to model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools…
The main directions in the development of the nonholonomic dynamics are briefly considered in this paper. The first direction is connected with the general formalizm of the equations of dynamics that differs from the Lagrangian and…
Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these…
Depending on how the dynamical activity of a particle in a random environment is influenced by an external field $E$, its differential mobility at intermediate $E$ can turn negative. We discuss the case where for slowly changing random…
We study the periodical solutions of a Poisson-gradient PDEs system with bounded nonlinearity. Section 1 introduces the basic spaces and functionals. Section 2 studies the weak differential of a function and establishes an inequality.…
Decisions to pursue higher education are not fully explained by economic incentives, with social influence and peer effects playing a crucial, yet dynamically understudied, role. This paper develops a theoretical non-linear dynamics model…
Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\"odinger equations. To relate N^2…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
Collective human movement is a hallmark of complex systems, exhibiting emergent order across diverse settings, from pedestrian flows to biological collectives. In high-speed scenarios, alignment interactions ensure efficient flow and…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
The behavior of pedestrians shows certain regularities, which can be described by quantitative (partly stochastic) models. The models are based on the behavior of individual pedestrians, which depends on the pedestrian intentions and on the…
Real-life, out-of-laboratory, measurements of pedestrian movements allow extensive and fully-resolved statistical analyses. However, data acquisition in real-life is subjected to the wide heterogeneity that characterizes crowd flows over…
This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Z^d. We assume that once walks meet, they…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first one is deduced from a balance law for entropy and…
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…