Related papers: Kinetic models for systems of interacting agents w…
We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence…
As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the…
In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology…
We propose a stochastic map model of economic dynamics. In the last decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of…
Motivated by the development of dynamics in probability spaces, we propose a novel multi-agent dynamic of consensus type where each agent is a probability measure. The agents move instantaneously towards a weighted barycenter of the…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…
We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations…
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…
A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution…
In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime…
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…
Von Neuman's work on universal machines and the hardware development have allowed the simulation of dynamical systems through a large set of interacting agents. This is a bottom-up approach which tries to derive global properties of a…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our…
We present examples of agent-based and stochastic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
A version of the Schelling model on $\mathbb{Z}$ is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then…
The purpose of the present effort is threefold. Firstly, it is shown that there exists a principle, that we call Kinetical Interaction Principle (KIP), underlying the non linear kinetics in particle systems, independently on the picture…