Related papers: Kinetic models with randomly perturbed binary coll…
A kinetic model is proposed for rarefied flows of molecular gas with rotational and temperature-dependent vibrational degrees of freedom. The model reduces to the Boltzmann equation for monatomic gas when the energy exchange between the…
We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kinetic Boltzmann equations and the kinetic wave equations, in…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…
We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac-Born-Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
We discuss a possibility of deriving an H-theorem for nonlinear discrete time evolution equation that describes random wealth exchanges. In such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a…
This paper considers ideal gas-like models of trading markets, where each agent is identified as a gas molecule that interacts with others trading in elastic or money-conservative collisions. Traditionally, these models introduce different…
In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
We introduce a new class of billiard systems in the plane, with boundaries formed by finitely many arcs of confocal conics such that they contain some reflex angles. Fundamental dynamical, topological, geometric, and arithmetic properties…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
The Kramers problem for quantum fermi-gases with specular - diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers problem the new generalised method of a source of the decision of the boundary problems…
We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to the description of the evolution of systems whose dynamics is…
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic on networks. These conditions are based on the consideration of the free space on the respective roads. The macroscopic limit of the kinetic…