Related papers: A particle method for continuous Hegselmann-Krause…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…
In this paper, the fractional order Hegselmann-Krause type model with leadership is studied.We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics.…
We consider a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an eikonal equation. Hydrodynamic multi-group models are derived from the…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
The Clausius Virial theorem of Classical Kinetic Theory is used to evaluate the pressure of a suspension of small particles at equilibrium in an isotropic homogeneous and stationary turbulent flow. It then follows a similar approach to the…
Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total…
Starting with a microscopic (individual-based) Brownian dynamics model of charged particles (ions), its macroscopic description is derived as a system of partial differential equations that govern the evolution of ion concentrations in…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration…
In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a…
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the…
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
We introduce a ``two-particle factorization'' condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy inequality. This formulation yields an H-Theorem. We provide…
We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative…
Motivated by a recent method for approximate solution of Fredholm equations of the first kind, we develop a corresponding method for a class of Fredholm equations of the \emph{second kind}. In particular, we consider the class of equations…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…