Related papers: Approximate third integrals for axisymmetric poten…
We consider the scalar sector of a general renormalizable theory and evaluate the effective potential through three loops analytically. We encounter three-loop vacuum bubble diagrams with up to two masses and six lines, which we solve using…
This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…
An integral equation-based numerical method for scattering from multi-dielectric cylinders is presented. Electromagnetic fields are represented via layer potentials in terms of surface densities with physical interpretations. The existence…
We demonstrate how an iterative method for potential inversion from distribution functions developed for simple liquid systems can be generalized to polymer systems. It uses the differences in the potentials of mean force between the…
In this article we consider cloaking for a quasi-linear elliptic partial differential equation of divergence type defined on a bounded domain in $\mathbb{R}^N$ for $N=2,3$. We show that a perfect cloak can be obtained via a singular change…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
We propose a general method for constructing quasi-exactly solvable potentials with three analytic eigenstates. These potentials can be real or complex functions but the spectrum is real. A comparison with other methods is also performed.
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…
Oscillons are long-lived, spatially localized field configurations, which are supported by attractive non-linearities in the scalar potential. We study oscillons comprised of multiple interacting fields, each having an identical potential…
We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by…
Accurate fitting formulae to the synchrotron function, $F(x)$, and its complementary function, $G(x)$, are performed and presented. The corresponding relative errors are less than $0.26\%$ and $0.035\%$ for $F(x) $ and $G(x)$, respectively.…
We investigate the snaking of localised patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, that are not…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system. We present multiple examples where the accuracy of the approximate energy is improved (sometimes greatly) by…
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approximation is attained if a control parameter is zero or…
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major…
Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…
In this paper, the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thin shell represented by a parametrized surface, it is shown how to transform the stored elastic energy for an…