We consider an arbitrary translationally invariant chain model, with nearest neighbors interaction and satisfying periodic boundary condition. The approach developed here allows a thermodynamic description of the chain model directly in terms of grand potential per site. This thermodynamic function is derived from an auxiliary function constructed only from open connected sub-chains. To exempli...

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We consider a stochastic optimal control problem for an heat equation with boundary noise and boundary controls. Under suitable assumptions on the coefficients, we prove existence of optimal controls in strong sense by solving the stochastic hamiltonian system related.

Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution of the anisotropic discrete Dirichlet boundary value problem. Our results generalize and improve those of [16]. Math Subject Classifications: 39A10, 34B18, 58E30.

The theory of infinite tube magnetization reversal, formulated by Lee and Chang, has been reconsidered. For this purpose, a standard micromagnetic simulation package OOMMF was used. To account for elongated geometry of ferromagnetic nanotubes grown nowadays, an extension module has been written allowing application of periodic boundary conditions in one dimension. The results of the modelling e...

We prove short time existence and uniqueness of smooth solutions ( in C with k ≥ 2) to the 2-D semi-geostrophic system and semi-geostrophic shallow water system with variable Coriolis parameter f and periodic boundary conditions, under the natural convexity condition on the initial data. The dual space used in analysis of the semi-geostrophic system with constant f does not exist for the variab...

In this paper, we illustrated one scenario to modify the Ivanenko-LandauKähler equation. Since Ivanenko and Landau introduced the equation in 1928, the equation has been regarded as having a certain role as a fermion in particular in the discrete Lattice. Also, although it correctly is formulated as an alternative classical field equation by the Ideal projection for the Dirac equation in the Mi...

In this paper we present an existence result for a first order impulsive differential inclusion with periodic boundary conditions and impulses at the fixed times under the convex condition of multi-functions.

The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that...

In this paper we address the error growth in time for hyperbolic problems on first order form. The energy method is used to study when an error growth or a fixed error bound is obtained. It is shown that the choice of boundary procedure is a crucial point. Numerical experiments corroborate the theoretical findings. 1. Introduction. Stable approximations of hyperbolic problems on first order for...