Related papers: Perturbation and Numerical Methods for Computing t…

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are…

A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…

In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…

In their 2016 article `Meetings with Lambert $\mathcal{W}$ and Other Special Functions in Optimization and Analysis', Borwein and Lindstrom considered the minimization of an entropy functional utilizing the weighted average of the negative…

In this paper we initiate the study of $2$nd order variational problems in $L^\infty$, seeking to minimise the $L^\infty$ norm of a function of the hessian. We also derive and study the respective PDE arising as the analogue of the…

We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases…

We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

We consider the sublinear problem \begin {equation*} \left\{\begin{array}{r c l c} -\Delta u & = &|u|^{q-2}u & \textrm{in }\Omega, \\ u_n & = & 0 & \textrm{on }\partial\Omega,\end{array}\right. \end {equation*} where $\Omega \subset…

Let $A \subset \mathbb{R} ^2 $ be a smooth doubly connected domain. We consider the Dirichlet energy $E(u)=\int_{A} |\nabla u|^2$, where $u:A \rightarrow \mathbb{C}$, and look for critical points of this energy with prescribed modulus…

We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to…

We describe a modification of the inverted perturbation approach method allowing to construct physically sensible potential energy curves for electronic states of diatomic molecules even when some parts of the potential are not adequately…

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition…

Some methods for the convergence acceleration of the M{\o}ller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by…

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where…

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…

This paper studies the Sobolev regularity of weak solution of degenerate elliptic equations in divergence form $\text{div}[\mathbf{A}(X) \nabla u] = \text{div}[\mathbf{F}(X)]$, where $X = (x,y) \in \mathbb{R}^{n} \times \mathbb{R}$ . The…

We classify all finite energy solutions of an equation which arises as the Euler--Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to Beckner. Our proof uses an extension of the method of moving…

We study the uniqueness of non-negative solutions of the equation \begin{align*} \partial_t\left(|u|^{p-2}u\right)\,=\, \operatorname{div}(|\nabla u|^{p-2}\nabla u). \end{align*} Basic estimates are derived with the Galerkin Method.