Related papers: Solution to the modified Helmholtz equation for ar…
The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number $\kappa$ in bounded domains in $\mathbb{R}^d$. The discrete trial and test spaces are generated from…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
The longitudinal charge density of an electron beam in its equilibrium state is given by the solution of the Ha\"issinski equation, which provides a stationary solution of the Vlasov-Fokker-Planck equation. The physical input is the…
Explicit analytical expressions for Helmholtz free energy, chemical potential, entropy and pressure of the multi-component dimerizing Yukawa hard-sphere fluid are presented. These expressions are written in terms of the Blum's scaling…
We develop a modified Poisson-Nernst-Planck model which includes both the long-range Coulomb and short-range hard-sphere correlations in its free energy functional such that the model can accurately describe the ion transport in complex…
From a multiple scale analysis, we find an analytic solution of spherical and cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent co-ions, divalent counter-ions) and a 2:1 (reversed situation) electrolyte. Our approach consists…
The electron-screening acceleration of laboratory fusion reactions at astrophysical energies is an unsolved problem of great importance to astrophysics. That effect is modeled here by considering the fusion of hydrogen-like atoms whose…
We study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin $hp$-finite element method. Well-posedness of the discrete equations is typically investigated by applying a…
The two dimensional Hasegawa-Mima (HM) equation $$ -\Delta u_t+u_t = \{u,\Delta u\} + ku_y$$ describes the time evolution of drift waves in magnetically-confined plasma. Several authors have treated the HM equation theoretically and…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
It has been shown that in investigating the electromagnetic and meson fields of elementary particles, the effects of gravitational interaction cannot be neglected. The present note is an attempt to find solutions to the equations of the…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
The deconvolution algorithm for measuring distribution of space charge under dc by the pressure wave propagation (PWP) method is studied in this paper. A new Fredholm integral equation of first kind, including a space charge distribution…
In the calculation of hot-plasma atomic structure, the continuum wavefunctions are characterized by phase shifts, which therefore determine the scattering cross-sections. In this short paper, we propose a recurrence relation for the phase…
Motivated by a number of realizations of long-range interacting systems, including ultra-cold atomic and molecular gases, we study a neutral plasma with power-law interactions longer-ranged than Coulombic. We find that beyond a crossover…
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or…
We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and…