Related papers: Natural Boundary Conditions for Smoothing in Geome…
A novel methodology to efficiently approximate the Hessian for numerical shape optimization is considered. The method enhances operator symbol approximations by including body fitted coordinates and spatially changing symbols in a semi…
A vast array of phenomena, ranging from chemical reactions to phase transformations, are analysed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used,…
We propose a method to determine the smoothness of sufficiently flat solutions of one phase Hele-Shaw problems. The novelty is the observation that under a flatness assumption the free boundary --represented by the hodograph transform of…
The energy functional, the governing partial differential equation(s) (PDE), and the boundary conditions need to be consistent with each other in a modeling system. In electrolyte solution study, people usually use a free energy form of an…
In this study, we explore the precise physical quantities in the thermodynamic limit of the one-dimensional Hubbard model with nonparallel boundary magnetic fields based on the off-diagonal Bethe ansatz solution. A particular emphasis is…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We investigate the universal property of curvatures in surface models which display a flat phase and a rough phase whose criticality is described by the Gaussian model. Earlier we derived a relation between the Hessian of the free energy…
The flow properties at the leading edge of a flat plate represent a singularity to the Blasius laminar boundary layer equations; by applying the Lagrangian approach the leading edge velocity profiles of the laminar boundary layer over a…
The surface Hamiltonian for a spin zero particle that is pinned to a surface by letting the thickness of a layer surrounding the surface go to zero -- assuming a strong normal force -- is constructed. The new approach we follow to achieve…
The dependence of the smoothness of variational solutions to the first boundary value problems for second order elliptic operators are studied. The results use Sobolev-Slobodetskii and Nikolskii-Besov spaces and their properties. Methods…
We consider the three-dimensional incompressible free-boundary Euler equations in a bounded domain and with surface tension. Using Lagrangian coordinates, we establish a priori estimates for solutions with minimal regularity assumptions on…
We study free boundary problems for incompressible inhomogeneous flows governed by the Navier--Stokes equations, focusing on the regularity and global-in-time well-posedness of solutions in critical functional frameworks for small initial…
This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for…
We consider a relaxed notion of energy of non-parametric codimension one surfaces that takes account of area, mean curvature, and Gauss curvature. It is given by the best value obtained by approximation with inscribed polyhedral surfaces.…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…
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…
Models of grain boundary energy are essential for predicting the behavior of polycrystalline materials. Typical models represent the minimum boundary energy as a function of macroscopic boundary parameters. An energy model may allow for…
This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…