Related papers: A kinetic scheme with variable velocities and rela…
A novel continuum model has been developed to address the vehicle size heterogeneity in mixed traffic. By incorporating the principle of vehicle area conservation, a new set of traffic flow variables centered on the concept of vehicle area…
Merging junctions are important network bottlenecks, and a better understanding of merging traffic dynamics has both theoretical and practical implications. In this paper, we present continuous kinematic wave models of merging traffic flow…
This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
We report an experimental study of particle kinematics in a 3-dimensional system of inelastic spheres fluidized by intense vibration. The motion of particles in the interior of the medium is tracked by high speed video imaging, yielding a…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
An implicit Euler finite-volume scheme for an $n$-species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditions is proposed and analyzed. The scheme preserves the formal…
We introduce a new micro-macro decomposition of collisional kinetic equations in the specific case of the diffusion limit, which naturally incorporates the incoming boundary conditions. The idea is to write the distribution function $f$ in…
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are assumed to be in detailed balance and satisfy a weak…
This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations…
The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simulations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jump processes have gained…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
A general adsorption model is developed to describe the interactions between near-wall fluid molecules and solid surface. This model serves as a framework for the theoretical modelling of the boundary slip phenomena. Based on this…
A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the…
An important class of multi-scale flow scenarios deals with an interplay between kinetic and continuum phenomena. While hybrid solvers provide a natural way to cope with these settings, two issues restrict their performance. Foremost, the…