نتایج جستجو برای: directional derivative
تعداد نتایج: 98083 فیلتر نتایج به سال:
Efficient numerical methods for analyzing photonic crystals (PhCs) can be developed using the Dirichlet-to-Neumann (DtN) maps of the unit cells. The DtN map is an operator that takes the wave field on the boundary of a unit cell to its normal derivative. In frequency domain calculations for band structures and transmission spectra of finite PhCs, the DtN maps allow us to reduce the computation ...
Keywords: Euler's tallest column Eigenvalue problem under coefficient constraints Nonlocal problem p-Laplacian type operator with a negative exponent Infinite normal derivative a b s t r a c t In 1757, Leonhard Euler started the study of the tallest column, i.e. the shape of a stable column with the symmetry of revolution, such that it attains the maximum height once the total mass is prescribe...
In this paper we prove the differentiability of Lipschitz maps X → V , where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direct...
the Laplacian, ∂/∂ν denotes the directional derivative along the outward normal on ∂Ω, ai, bi, ci, di (i = 1, 2) are given positive constants and α, γ, δ, β are nonnegative constants. In the system (1.1) u and v are non-negative functions which represent population densities of two competing species, d1 and d2 are respectively their diffusion rates. Parameters a1 and a2 are intrinsic growth rat...
A detailed cortex model (15,000 cells) of the adult cat is presented and it is shown that a combination of unspecific inhibitory mechanisms together with input of aligned receptive fields from the LGN with little elongation (1:1.5) is able to reproduce cortical orientation selectivity and other features of cortical cell behavior. We introduce a novel isotropic intracortical connection scheme (“...
In this paper, numerical methods are proposed for some interface problems in polar or Cartesian coordinates. The new methods are based on a formulation that transforms the interface problem with a non-smooth or discontinuous solution to a problem with a smooth solution. The new formulation leads to a simple second order finite difference scheme for the partial differential equation and a new in...
Exceptional domains are domains on which there exists a positive harmonic function, zero on the boundary and such that the normal derivative on the boundary is constant. Recent results classify (under some mild additional assumptions) exceptional domains as belonging to either a certain one-parameter family of simply periodic domains or one of its scaling limits. We introduce quasi-exceptional ...
We calculate the heat-kernel coefficients, up to a 2 , for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary derivatives acting on the field. The results are used to place restrictions on the general forms of the coefficients. In the specific case considered, there can be a ...
In this work, we present an algorithm to the recovery of the conductance of a n–dimensional grid. The algorithm is based in the solution of some overdetermined partial boundary value problems defined on the grid; that is, boundary value problem where the boundary conditions are set only in a part of the boundary (partial), and moreover in a fix subset of the boundary we prescribe both the value...
We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for harmonic functions in a doubly connected domain D in R2 where an unknown free boundary Γ0 is determined by prescribed Cauchy data on Γ0 in addition to a Dirichlet condition on the known boundary Γ1. Our main idea is to involve the conformal mapping method as proposed and analyzed by Akduman, Haddar...
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