Related papers: Modeling Crowd Dynamics through Hyperbolic - Ellip…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
This article concerns an optimal crowd motion control problem in which the crowd features a structure given by its organization into N groups (participants) each one spatially confined in a set. The overall optimal control problem consists…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
We consider self-similar potential flow for compressible gas with polytropic pressure law. Self-similar solutions arise as large-time asymptotes of general solutions, and as exact solutions of many important special cases like Mach…
We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be…
We consider a crowd of N persons trying to exit some area trough a small exit. The probability is calculated that an individual is able to withdraw from the crowd under one's own steam. The problem is simulated within the generalized force…
It is very important to understand urban mobility patterns because most trips are concentrated in urban areas. In the paper, a new model is proposed to model collective human mobility in urban areas. The model can be applied to predict…
Assessing quantitatively the state and dynamics of a social system is a very difficult problem. It is of great importance for both practical and theoretical reasons such as establishing the efficiency of social action programs, detecting…
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…
In finite-size population models, one can derive Fokker-Planck equations to describe the fluctuations of the species numbers about the deterministic behaviour. In the steady state of populations comprising two or more species, it is…
Hydrodynamics provides a successful framework to effectively describe the dynamics of complex many-body systems ranging from subnuclear to cosmological scales by introducing macroscopic quantities such as particle densities and fluid…
Collective behavior of people in large groups and emergent crowd dynamics can have dangerous and disastrous results when panic is introduced. These events can be caused by emergency situations such as fires in a large building or a…
In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is…
We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…