Related papers: Local Structure-Preserving Relaxation Method for C…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external…
We study theoretically and numerically how hard frictionless particles in random packings can rearrange. We demonstrate the existence of two distinct unstable non-linear modes of rearrangement, both associated with the opening and the…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov…
This article is a review of results on the nonlinear Schroedinger / Gross-Pitaevskii equation (NLS / GP). Nonlinear bound states and aspects of their stability theory are discussed from variational and bifurcation perspectives. Nonlinear…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
We present a geometric Particle-in-Cell (PIC) algorithm on two-dimensional (2D) unstructured meshes for studying electrostatic perturbations in magnetized plasmas. In this method, ions are treated as fully kinetic particles, and electrons…
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…
We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special…
In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on…
We study the stationary state of a Poisson problem for a system of N perfectly conducting metal balls driven by electric forces to move within a medium of very low electrical conductivity onto which charges are sprayed from outside. When…
Nonequilibrium steady states in an open system connecting two reservoirs of platelike colloidal particles are investigated by means of a recently proposed phenomenological dynamic density functional theory [M. Bier and R. van Roij, Phys.…
The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single…
We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
Dense granular and suspension flows under inhomogeneous shear exhibit persistent particle motion in regions where the local yield criterion is subcritical, an apparent breakdown of locality that has motivated the development of a generation…
In this paper we propose a new high order accurate space-time DG finite element scheme for the solution of the linear elastic wave equations in first order velocity-stress formulation in two and three-space dimensions on staggered…