Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a 1/r law, are discussed in the mean field approximation.

An approach for ­ nding the e¬ective properties of two-dimensional periodic rectangular checkerboard media is presented; it is demonstrated that one can take a relatively simple model problem, an appropriate system of joined quarter planes, and that after appropriate conformal transformation one can use this to solve for either periodic or doubly periodic structures. Illustrative calculations i...

We consider the Navier-Stokes equations on thin 3D domains Qε = Ω×(0, ε), supplemented mainly with purely periodic boundary conditions or with periodic boundary conditions in the thin direction and homogeneous Dirichlet conditions on the lateral boundary. We prove global existence and uniqueness of solutions for initial data and forcing terms, which are larger and less regular than in previous ...

We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for whic...

Near-linear evolution in the Korteweg-de-Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction. Mathematics Subject Classification: 35Q53

An analytic theory of periodically perturbed magneto-inductive waveguides is developed and used to determine the mode spectrum of distorted MI ring resonators. A set of coupled equations is first established from the recurrence equations for an infinite set of coupled elements, and used to determine the dispersion equation. Solutions for ring resonators are then found using periodic boundary co...

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a 2× 2 matrix of pseudo-differential operators with pseudo-homogeneous kernels. The request of invariance...