We study a nematic crystal model appearing in [Liu et al.,2007] modeling stretching effects depending on the different shape of microscopic molecules of the material, under periodic boundary conditions. The aim of the present article is twofold: to extend the results given in [Sun & Liu, 2009], to a model with more complete stretching terms and to obtain some stability and asymptotic stability ...

We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure loss coefficient enables us to establish a relation on the pressure and to thus formulate an equivalent problem.

Fast Algorithms with Applications to PDEs

*Correspondence: [email protected] Department of Applied Mechanics, Chalmers University of Technology, Hörsalsvägen 7, 412 96 Göteborg, Sweden Abstract Background: Seepage in porous media is modeled as a Stokes flow in an open pore system contained in a rigid, impermeable and spatially periodic matrix. By homogenization, the problem is turned into a two-scale problem consisting of a Da...

i dAj dt + γ|Aj |Aj + ε(Aj+1 + Aj−1) = 0, (1) where i = √−1, the index j ranges over the 1D lattice. The lattice may be infinite (j = 0,±1,±2, . . .) or finite (j = 1, 2, . . . , f). In the latter case one usually assumes periodic boundary conditions, Aj+f = Aj . The quantity Aj = Aj(t) is the complex mode amplitude of the oscillator at site j, and γ is a anharmonic parameter. The connection wi...

– We study in d = 3 dimensions the short-range Ising spin glass with Jij = ±1 couplings and periodic boundary conditions at T = 0. We show that the overlap distribution is non-trivial in the limit of large system size. Introduction. – There has been an upsurge of interest in the Edwards-Anderson model [1] of the short-range Ising spin glass with binary couplings,

We discuss solutions of the one-dimensional telegrapher’s equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green’s function. Furthermore, we formulate a backreaction boundary condition, which has been widely used in the context of diffusion-controlled reversible reactions, for a one-...

In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

We present conjectured exact expressions for two types of correlations in the dense O(n = 1) loop model on L×∞ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by m loops and the probability that k consecutive points on a row are on the same or on different loops. The dense O(n = 1) loop model is equivalent to the bond percolation model at ...

We implement the new transform method for solving boundary value problems developed by Fokas for periodic boundary conditions. The approach presented here is not a replacement for classical methods nor is it necessarily an improvement. However, in addition to establishing that periodic problems can indeed be solve by the new transform method (which enhances further its scope and applicability),...