Related papers: Finite Volume Effects in Self Coupled Geometries
In this paper, we study the linear wave equations in an asymptotically anti-de Sitter spacetime. We will consider the mixed boundary problem, where the initial data are given on an outgoing null hypersurface and a timelike hypersurface, and…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
Self-energy and vacuum polarization effects in quantum electrodynamics (QED) are calculated for the supercritical Coulomb field, where Dirac energy levels become embedded in the negative-energy continuum. In this regime, the quantum vacuum…
For the attractive interaction, the L\"uscher's finite volume formula gives the phase shift at negative squared moment $k^2<0$ for the ground state in the finite volume, which corresponds to the analytic continuation of the phase shift at…
We consider the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate without external confinement. We first consider the unstable regime, where the nonlocal nonlinearity is neither positive nor radially symmetric and…
A transitional layer matching the asymptotically flat exterior of a charged, massive toroidal body to an interior with spatially cylindrical symmetry is described. The changes in the geometry, which by themselves would require an energy…
For spaces which are not asymptotically anti-de Sitter where the asymptotic behavior is deformed by replacing the cosmological constant by a dilaton scalar potential, we show that it is possible to have well-defined boundary stress-energy…
We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent)…
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold $(M,g,\partial M)$ under the singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions…
Quantities associated with Casimir forces are calculated in a model wave system of one spatial dimension with Dirichlet or Neumann boundary conditions. 1)Due to zero-point fluctuations, a partition is attracted to the walls of a box if the…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
In this paper we consider a mixed Dirichlet-Neumann boundary value problem. lem involving Choquard nonlinearity with upper critical exponent in the sense of Hardy- Littlewood Sobolev inequality. We investigate the effect of the geometry of…
We establish $L^2$-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker-Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their…
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic free energy cost, as the length of the…
This paper concerns the large time asymptotic behavior of solutions to the free boundary problem of the compressible primitive equations in atmospheric dynamics with physical vacuum. Up to second order of the perturbations of an…
The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided…
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with…