Related papers: Boltzmann-type models with uncertain binary intera…
We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called $p=2$…
We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
The mean-field dynamics of a collection of stochastic agents with local versus nonlocal interactions is studied via analytically soluble models. The nonlocal interactions result from a barycentric modulation of the observation range of the…
This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling…
In this work we consider the Allen--Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we…
In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…
We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of solutions and provide a natural variational characterisation…
We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
We study a class of nonlinear kinetic Fokker-Planck type equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence of classical solutions in the perturbative…
The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution…
We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…