Related papers: Cross diffusion models in complex frameworks From …
This paper deals with the micro-macro derivation of virus models coupled with a reaction diffusion models that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [5, 6] on a…
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…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…
We present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux…
A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow.…
In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation…
In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model…
The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The crossover between dispersion patterns has been frequently observed in various systems. Inspired by the pathway-based kinetic model for E. coli chemotaxis that accounts for the intracellular adaptation process and noise, we propose a…
Neutral particles in the plasma edge of fusion devices based on magnetic confinement are described by a transient kinetic equation incorporating ionization, recombination, and charge-exchange collisions. In charge-exchange dominated…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the…