Related papers: Generalized Soft-and-Hard/DB Boundary
Continuum models are particularly appealing for theoretical studies of bound states, due to simplicity of their bulk Hamiltonians. The main challenge on this path is a systematic description of the boundary, which comes down to determining…
In this paper the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view the consequences of the boundary conditions at such interfaces are…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
The advent of neural and Gaussian-based radiance field methods have achieved great success in the field of novel view synthesis. However, specular reflection remains non-trivial, as the high frequency radiance field is notoriously difficult…
A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown…
We present a foliation-focused critical review of the boundary conditions and dynamics of 4D gravitational theories. A general coordinate transformation introduces a new foliation and changes the hypersurface on which a natural boundary…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
In relation to the BSSN formulation of the Einstein equations, we write down the boundary conditions that result from the vanishing of the projection of the Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up a…
The correct treatment of boundary conditions is a key step in the development of the SPH method. The SPH community has to face several challenges in this regard - in particular, a primordial aspect for any boundary formulation is to ensure…
Unconditional guaranteed lower and upper eigenvalue bounds are mandatory for the understanding of the Schr\"odinger eigenvalue spectrum and its spectral gaps. While upper eigenvalue bounds are naturally induced by conforming…
The structure and energy of grain boundaries (GBs) are essential for predicting the properties of polycrystalline materials. In this work, we use high-throughput density functional theory calculations workflow to construct the Grain…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
An exact expression of the outgoing boundary intensities in the case of a gray semi-transparent medium confined in a plane parallel slab with a refractive index linearly depending on the position is proposed. It is shown that directly using…
The formation of dispersive shock waves in the one-dimensional Bose gas represents a limitation of Generalized Hydrodynamics (GHD) due to the coarse-grained nature of the theory. Nevertheless, GHD accurately captures the long wavelength…
Radiance field methods (e.g. 3D Gaussian Splatting) have emerged as a powerful paradigm for novel view synthesis, yet their appearance modeling often relies on Spherical Harmonics (SH), which impose fundamental limitations. SH struggle with…
The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and…
We develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions (BCs) that are intrinsically consistent…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
Fresnel reflection has been known for centuries to fundamentally impede efficient transmittance across planar interfaces, especially at grazing incidence. Herein, we present the generalized Huygens' condition (GHC) to resolve such…