Search results for "Kinetic theory"
showing 10 items of 26 documents
From the Classical Boltzmann Equation to the Generalized Kinetic models of Biological Systems
2017
This paper deal with the classical Boltzmann Equation generalized to model populations in complex biological system. In particular, the populations refer to the cells of the immune system and to those of an aggressive host (cancer cells) in a human being. We will focus with the study of a spatially homogeneous continuous model, and derivation of the macroscopic model. The paper starts from a simple description of the classical Boltzmann equation and goes to the mathematical approach proposed to model the large systems of interacting entities focusing the competition between immune system and cancer cells.
A Nonlinear Nonviscous Hydrodynamical Model for Change Transport Derived from Kinetic Theory
2002
In the paper, methods of Extended Thermodynamics are used to derive nonlinear closure relations for hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. For the sake of simplicity only the case of single parabolic band approximation is studied. In this work the velocity v i is not considered as a small parameter; therefore, the models obtained can be useful when one wishes to study phenomena in a neighborhood of a stationary non-equilibrium process.
Thermalization in the initial stage of heavy ion collisions
2017
The high density non-abelian matter produced in heavy ion collisions is extremely anisotropic. Prethermal dynamics for the anisotropic and weakly coupled matter is discussed. Thermalization is realized with the effective kinetic theory in the leading order accuracy of the weakly coupled expansion. With the initial condition from color glass condensate, hydrodynamization time for the LHC energies is realized to be about 1 fm/c, while the thermalization happens much later than the hydrodynamization. peerReviewed
Gibbs equation in the nonlinear nonequilibrium thermodynamics of dilute nonviscous gases
2003
AbstractThis paper deals with the derivation of the Gibbs equation for a nonviscous gas in the presence of heat flux. The analysis aims to shed some light on the physical interpretation of thermodynamic potentials far from equilibrium. Two different definitions for the chemical potential and thermodynamic pressure far from equilibrium are introduced: nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant heat flux q and nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant J = Vq, where V is the specific volume.
Weak and strong coupling equilibration in nonabelian gauge theories
2015
We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an out-of-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of t…
Theory overview of Heavy Ion collisions
2016
This presentation discusses some recently active topics in the theoretical interpretation of high energy heavy ion collisions at the LHC and at RHIC. We argue that the standard paradigm for understanding the spacetime evolution of the bulk of the matter produced in the collision is provided by viscous relativistic hydrodynamics, which can be used to systematically extract properties of the QCD medium from experimental results. The initial conditions of this hydrodynamical evolution are increasingly well understood in terms of gluon saturation, and can be quantified using Classical Yang-Mills fields and QCD effective kinetic theory. Hard and electromagnetic probes of the plasma provide addit…
From the kinetic theory of active particles to the modeling of social behaviors and politics
2007
This paper deals with the modeling of complex social systems by methods of the mathematical kinetic theory for active particles. Specifically, a recent model by the last two authors is analyzed from the social sciences point of view. The model shows, despite its simplicity, some interesting features. In particular, this paper investigates the ability of the model to describe how a social politics and the disposable overall wealth may have a relevant influence towards the trend of the wealth distribution. The paper also outlines various research perspectives.
A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids
2019
A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained i…
From Particle Systems to Partial Differential Equations International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019
2021
This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general…
Self-consistent calculation of the flux-flow conductivity in diffusive superconductors
2017
In the framework of Keldysh-Usadel kinetic theory, we study the temperature dependence of flux-flow conductivity (FFC) in diffusive superconductors. By using self-consistent vortex solutions we find the exact values of dimensionless parameters that determine the diffusion-controlled FFC both in the limit of the low temperatures and close to the critical one. Taking into account the electron-phonon scattering, we study the transition between flux-flow regimes controlled by either the diffusion or the inelastic relaxation of nonequilibrium quasiparticles. We demonstrate that the inelastic electron-phonon relaxation leads to the strong suppression of FFC compared to the previous estimates, mak…