Related papers: The boundary element approach to Van der Waals int…
We present an explicit finite difference method to simulate the non-ideal multi-phase fluid flow. The local density and the momentum transport are modeled by the Navier-Stokes (N-S) equations and the pressure is computed by the Van der…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
We study the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value problem of a fractional Laplace equation.
This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…
Adhesion is a key issue for researchers of various fields, it is therefore of uppermost importance to understand the parameters that are involved. Commonly, only surface parameters are employed to determine the adhesive forces between…
We study the discretization of an elliptic partial differential equation, posed on a two- or three-dimensional domain with smooth boundary, endowed with a generalized Robin boundary condition which involves the Laplace-Beltrami operator on…
In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\Sigma)$, where $\Sigma := \partial \Omega \times…
We analyze a family of singular Schr\"odinger operators with local singular interactions supported by a hypersurface $\Sigma \subset \mathbb{R}^n, n \ge 2$, being the boundary of a Lipschitz domain, bounded or unbounded, not necessarily…
The van der Waals (vdW) interaction plays a prominent role between neutral objects at separations where short ranged chemical forces are negligible. This type of dispersive coupling is determined by the interplay between geometry and…
We introduce a class of variational wavefunctions that capture the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
We review the screening nature and many-body physics foundation of the van der Waals density functional (vdW-DF) method, a systematic approach to construct truly nonlocal exchange-correlation energy density functionals. To that end we…
Proper inclusion of van der Waals (vdW) interactions in theoretical simulations based on standard density functional theory (DFT) is crucial to describe the physics and chemistry of systems such as organic and layered materials. Many…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
In this paper, we study the existence of nontrivial solutions of the Dirichlet boundary value problem for the following elliptic system: \begin{equation} \left\{ \begin{aligned} -\Delta u & = au + bv + f(x,u,v); &\quad\mbox{ for…
Intensity distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations for both time dependent and…
We analyze the phase diagram of a quantum mean spherical model in terms of the temperature $T$, a quantum parameter $g$, and the ratio $p=-J_{2}/J_{1}$, where $J_{1}>0$ refers to ferromagnetic interactions between first-neighbor sites along…
We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method,…
This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value…
In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in…