Related papers: Periodic Poisson Solver for Particle Tracking
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
This work introduces an approach to compute periodic phase diagram of micromagnetic systems by solving a periodic linearized Landau-Lifshitz-Gilbert (LLG) equation using an eigenvalue solver with the Finite Element Method formalism. The…
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose…
The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a…
In this paper we apply the newly born choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Some people complain that Luh's choice theory, based on harmonic analysis, is…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
We present a method of solving partial differential equations on the $n$-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the…
An improved finite difference method with compact correction term is proposed to solve the Poisson equations. The compact correction term is developed by a coupled high-order compact and low-order classical finite difference formulations.…
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…
We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a…
We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak…
This paper presents a new method for modelling periodic signals having an aperiodic trend, using the method of variable projection. It is a major extension to the IEEE-standard 1057 by permitting the background to be time varying;…
We develop a general theory for one-way optical guiding in magnetized periodic particle arrays. Necessary conditions for a non-even dispersion curves are derived and presented in the context of Frieze symmetry-groups. It is shown, for…
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MPB equations with the self Green's function as the self…
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…