In this paper, we study the Casimir effect of a scalar field with Dirichlet boundary condition in some certain topologies. By numerical analysis we show that Casimir energy is a shape-dependent quantity. We also obtain the phase transition in different topologies in which the Casimir force changes from attractive to repulsive or vice versa.  eararqr

Geometric morphometric method was used to examine body shape variations among all the seven valid species of the genus Alburnus in Iran. In total 409 specimens of A. chalcoides, A. filippii, A. atropatenae, A. caeruleus, A. mossulensis, A. hohenackeri and A. zagrosensis were collected from Babolrud, Baleqlu-Chai, Miriseh, Sarabeleh, Gamasiyab, Mahabad-Chai Rivers and the Gandoman lagoon, respec...

The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter " > 0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order O(" 2) are derived for smooth evolutions, that is before singularities develop. Key ingredients are the cons...

Grazing incidence x-ray diffraction study of Fe epitaxial ultrathin films (1.5-13 nm) on GaAs (001) reveals an anisotropy of both domain shape and strain, with [110] and [1-10] as the principal directions. It is shown that the observed thickness-dependent strain anisotropy, together with a uniaxial interface term, can provide an unambiguous explanation to the usual in-plane magnetic anisotropy ...

This paper presents a new approach to the problem of modelling daily rainfall using neural networks. We first model the conditional distributions of rainfall amounts, in such a way that the model itself determines the order of the process, and the time-dependent shape and scale of the conditional distributions. After integrating over particular weather patterns, we are able to extract seasonal ...

We prove local a posteriori error estimates for pointwise gradient errors in finite element methods for a second-order linear elliptic model problem. First we split the local gradient error into a computable local residual term and a weaker global norm of the finite element error (the “pollution term”). Using a mesh-dependent weight, the residual term is bounded in a sharply localized fashion. ...

We prove the existence of a volume preserving crystalline mean curvature at ow starting from a compact convex set C ⊂ R and its convergence, modulo a time-dependent translation, to a Wul shape with the corresponding volume. We also prove that if C satis es an interior ball condition (the ball being the Wul shape), then the evolving convex set satis es a similar condition for some time. To prove...