The current work sets forth a practical approach to numerically solve two-dimensional direct acoustic scattering problems from arbitrary shape obstacles that involve severe singularities, such as corners and cusps. First, boundary conforming coordinates are generated. This generation is performed through an elliptic grid generator algorithm, including control of the coordinate lines. The grid c...

We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to con...

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the Green function for second order differential operators valid in the neighbourhood of the boundary and which is obtained from a corresponding expansion of of the associated heat kernel derived earlier for arbitr...

in this paper the optimal control of boundary heat flux in a 2-d solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. the boundary of the body is subdivided into a number of components. on each component a time-dependent heat flux is applied which is independent of the others. since the thermophysical properties are t...

This paper presents a novel, powerful reconstruction algorithm that can recover correct shape geometry as well as its unknown topology from arbitrarily complicated volumetric datasets. The algorithm starts from a simple seed model (of genus zero) that can be initialized automatically without user intervention. The deformable behavior of the model is then governed by a locally defined objective ...

The discussion in this paper focuses on how boundary based smooth shape design can be carried out. For this we treat surface generation as a mathematical boundary-value problem. In particular, we utilize elliptic Partial Differential Equations (PDEs) of arbitrary order. Using the methodology outlined here a designer can therefore generate the geometry of shapes satisfying an arbitrary set of bo...

We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open sets D. This yields a unique representation of such functions as integrals against measures on Dc∪{∞} satisfying an integrability condition. The corresponding Martin boundary of D is a subset of the Euclidean boundary determined by an integral test. 1 Main results and ...

We reformulate bosonic boundary string field theory in terms of boundary state. In our formulation, we can formally perform the integration of target space equations of motion for arbitrary field configurations without assuming decoupling of matter and ghost. Thus, we obtain the general form of the action of bosonic boundary string field theory. This formulation may help us to understand possib...

We present a new kind of subdivision schemes, which we call combined subdivision schemes. Such schemes are used to reene a given control net, taking into consideration boundary conditions on the limit surface. Several schemes are presented that generate limit surfaces interpolating given boundary curves and cross boundary derivatives. The interpolated boundary curves are arbitrary parametric cu...

In this note we present a generalization of the boundary state formalism for the bosonic string that allows us to calculate the overlap of the boundary state with arbitrary closed string states. We show that this generalization exactly reproduces world-sheet sigma model calculations, thus giving the correct overlap with both onand off-shell string states, and that this new boundary state automa...