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Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J.…
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J.…
It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport…
The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor…
We study the derivation of second order macroscopic traffic models from kinetic descriptions. In particular, we recover the celebrated Aw-Rascle model as the hydrodynamic limit of an Enskog-type kinetic equation out of a precise…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a…
The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models…
Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform directed motion. Extending the paradigm of active matter to a quantum framework…
Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…