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91.
Yuri V. Kozitsky 《Journal of statistical physics》1997,87(3-4):799-820
The hierarchical ferromagneticN-dimensional vector spin model as a sequence of probability measures onR
N
is considered. The starting element of this sequence is chosen to belong to the Lee-Yang class of measures that is defined in the paper and includes most known examples (4 measures, Gaussian measures, and so on). For this model, we probe two thermodynamic limit theorems. One of them is just the classical central limit theorem for weakly dependent random vectors. It describes the convergence of classically normed sums of spins when temperature is sufficiently high. The other theorem describes the convergence of more than normally normed sums that holds for some fixed temperature. It corresponds to the strong dependence of spins, which appears at the critical point of the model. 相似文献
92.
Wang Yaguang 《偏微分方程(英文版)》1990,3(1)
We give an example to show that there will be anomalous singularities on the forward half light cone issuing from the reflection point after the reflection at the boundary of two progressing waves carrying singularities. It perfects the results of [1]. 相似文献
93.
Wang Weike 《偏微分方程(英文版)》1991,4(4)
We consider a solution of the semi-linear partial differential equations in higher space dimensions. We show that if there exist two characteristic hypersurface bearing different weak singularities intersect transversally, and another one characteristic hypersurface issues from above intersection, then the solution would be conormal with respect to the union of these surfaces, and satisfy the so-called “sum law”. 相似文献
94.
Z. Yosibash M. Arad A. Yakhot G. Ben-Dor 《Numerical Methods for Partial Differential Equations》1998,14(3):281-296
A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281–296, 1998 相似文献
95.
F. Assous P. Ciarlet P.‐A. Raviart E. Sonnendrücker 《Mathematical Methods in the Applied Sciences》1999,22(6):485-499
The solution of Maxwell's equations in a non‐convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
96.
The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic
hierarchy , where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding
of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying
the ellipticity of the principal edge symbol which includes the (in general not explicitly known) number of additional conditions of trace and potential type on the edge.
We focus here on these questions and give explicit answers for a wide class of elliptic operators that are connected with
the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation
and ellipticity for Dirichlet–Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues
of the Agranovich–Dynin formula for edge boundary value problems.
Nicoleta Dines and Bert-Wolfgang Schulze were supported by Chinese-German Cooperation Program “Partial Differential Equations”,
NNSF of China and DFG of Germany. Xiaochun Liu was supported by NNSF of China through Grant No. 10501034, and Chinese-German
Cooperation Program “Partial Differential Equations”, NNSF of China and DFG of Germany. 相似文献
97.
G. I. Shishkin 《Computational Mathematics and Mathematical Physics》2009,49(8):1348-1368
The Dirichlet problem for a singularly perturbed parabolic reaction-diffusion equation with a piecewise continuous initial condition in a rectangular domain is considered. The higher order derivative in the equation is multiplied by a parameter ?2, where ? ∈ (0, 1]. When ? is small, a boundary and an interior layer (with the characteristic width ?) appear, respectively, in a neighborhood of the lateral part of the boundary and in a neighborhood of the characteristic of the reduced equation passing through the discontinuity point of the initial function; for fixed ?, these layers have limited smoothness. Using the method of additive splitting of singularities (induced by the discontinuities of the initial function and its low-order derivatives) and the condensing grid method (piecewise uniform grids that condense in a neighborhood of the boundary layers), a finite difference scheme is constructed that converges ?-uniformly at a rate of O(N ?2ln2 N + n 0 ?1 ), where N + 1 and N 0 + 1 are the numbers of the mesh points in x and t, respectively. Based on the Richardson technique, a scheme that converges ?-uniformly at a rate of O(N ?3 + N 0 ?2 ) is constructed. It is proved that the Richardson technique cannot construct a scheme that converges in ?-uniformly in x with an order greater than three. 相似文献
98.
We prove two related results. The first is an “earthquake theorem” for closed hyperbolic surfaces with cone singularities
where the total angle is less than π: any two such metrics in are connected by a unique left earthquake. The second result
is that the space of “globally hyperbolic” AdS manifolds with “particles” – cone singularities (of given angle) along time-like
lines – is parametrized by the product of two copies of the Teichmüller space with some marked points (corresponding to the
cone singularities). The two statements are proved together.
F.B. was partially supported by the A.N.R. project GEODYCOS. J.-M.S. was partially supported by the A.N.R. programs RepSurf,
2006-09, ANR-06-BLAN-0311, GeomEinstein, 2006-09, 06-BLAN-0154, and FOG, 2007-10, ANR-07-BLAN-0251-01. 相似文献
99.
Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s–d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior. 相似文献
100.
N. Kleemann 《Mathematical Methods in the Applied Sciences》2012,35(12):1365-1391
This paper studies conical diffraction problems with non‐smooth grating structures. We prove the existence, uniqueness and regularity results for solutions in weighted Sobolev spaces of Kondratiev type. An a priori estimate that follows from these results is then used to prove shape differentiability of solutions. Finally, a characterization of the shape derivative as a solution of a modified transmission problem is given. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献