74,985 research outputs found

    On rational boundary conditions for higher-order long-wave models

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    Higher-order corrections to classical long-wave theories enable simple and efficient modelling of the onset of wave dispersion and size effects produced by underlying micro-structure. Since such models feature higher spatial derivatives, one needs to formulate additional boundary conditions when confined to bounded domains. There is a certain controversy associated with these boundary conditions, because it does not seem possible to justify their choice by purely physical considerations. In this paper an asymptotic model for onedimensional chain of particles is chosen as an exemplary higher-order theory. We demonstrate how the presence of higher-order derivative terms results in the existence of non-physical “extraneous” boundary layer-type solutions and argue that the additional boundary conditions should generally be formulated to eliminate the contribution of these boundary layers into the averaged solution. Several new methods of deriving additional boundary conditions are presented for essential boundary. The results are illustrated by numerical examples featuring comparisons with an exact solution for the finite chain

    DISTRIBUTION OF INTEGER LATTICE POINTS IN A BALL CENTRED AT A DIOPHANTINE POINT

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    We study the variance of the fluctuations in the number of lattice points in a ball and in a thin spherical shell of large radius centred at a Diophantine point

    Cocliques of maximal size in the prime graph of a finite simple group

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    In this paper we continue our investgation of the prime graph of a finite simple group started in http://arxiv.org/abs/math/0506294 (the printed version appeared in [1]). We describe all cocliques of maximal size for all finite simple groups and also we correct mistakes and misprints from our previous paper. The list of correction is given in Appendix of the present paper.Comment: published version with correction

    Multigrid for propagators of staggered fermions in four-dimensional SU(2)SU(2) gauge fields

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    Multigrid (MG) methods for the computation of propagators of staggered fermions in non-Abelian gauge fields are discussed. MG could work in principle in arbitrarily disordered systems. The practical variational MG methods tested so far with a ``Laplacian choice'' for the restriction operator are not competitive with the conjugate gradient algorithm on lattices up to 18418^4. Numerical results are presented for propagators in SU(2)SU(2) gauge fields.Comment: 4 pages, 3 figures (one LaTeX-figure, two figures appended as encapsulated ps files); Contribution to LATTICE '92, requires espcrc2.st
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