Related papers: Pad\'e-based arbitrary wavelength polarization clo…
In this article we present a system of coupled non-linear PDEs modeling an anisotropic electrokinetic flow. We show the existence of suitable weak solutions in three spatial dimensions, that is weak solutions which fulfill an energy…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…
Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
This work presents a polyelectrolyte (PE) model based on a freely jointed chain (FJC) in which the beads are ionizable and the bonds are rigid. Electrostatic interactions considered are of the short range type up to next-nearest neighbours…
We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained…
We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly…
A method for solving the half-space Sommerfeld problem is proposed, which allows us to obtain exact solutions in the form of Sommerfeld integrals, as well as their short-wave asymptotics. The first carried out by reducing the Sommerfeld…
We present a theoretical treatment of overdamped Brownian motion on a multidimensional tilted periodic potential that is analogous to the tight-binding model of quantum mechanics. In our approach we expand the continuous Smoluchowski…
The present paper is concerned with large-time behavior of solutions to an outflow problem for an ideal polytropic model of compressible viscous gases in one-dimensional half space, and with a convergence rate of solutions toward a…
We study the nearly critical behaviour of holographic superfluids at finite temperature and chemical potential in their probe limit. This allows us to examine the coupled dynamics of the full complex order parameter with the charge density…
We derive exact solutions of a linear form of the Grad-Shafranov (GS) equation, including incompressible equilibrium flow, using ansatz-based similarity reduction methods. The linearity of the equilibrium equation allows linear combinations…
In this paper, a mixed high order finite difference scheme-Pad\'{e} approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference…
We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single…
This work is concerned with a simple model for a polar fluid, a Gaussian field model based on the excess density and on the polarization. It is a convenient framework to implement the dielectric properties of correlated liquids that stem…
We develop a comprehensive continuum model capable of treating both electrostatic and structural interactions in liquid dielectrics. Starting from a two-order parameter description in terms of charge density and polarization, we derive a…
We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
The Dupree-Weinstock renormalization is used to prove that a reactive closure exists for drift wave turbulence in magnetized plasmas. The result is used to explain recent results in gyrokinetic simulations and is also related to the…