Fast Algorithms with Applications to PDEs

The purpose of Steps 1-3 is to establish that zero-order relationships among the variables exist. If one or more of these relationships are nonsignificant, researchers usually conclude that mediation is not possible or likely (although this is not always true; see MacKinnon, Fairchild, & Fritz, 2007). Assuming there are significant relationships from Steps 1 through 3, one proceeds to Step 4. I...

The classical methods for solving initial-boundary-value problems for linear partial differential equations with constant coefficients rely on separation of variables, and specific integral transforms. As such, they are limited to specific equations, with special boundary conditions. Here we review a method introduced by Fokas, which contains the classical methods as special cases. However, thi...

*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,

BACKGROUND Symptoms other than pain are a heavy burden for patients with either malignant or progressive nonmalignant disease and significantly reduce quality of life. OBJECTIVE This article discusses the management of symptoms of malignant or progressive nonmalignant disease in the general practice setting. DISCUSSION The approach to management of the symptoms of malignant or progressive n...

We extend the trace formula recently proven for general one-dimensional Schrödinger operators which obtains the potential V (x) from a function ξ(x,λ) by deriving trace relations computing moments of ξ(x,λ)dλ in terms of polynomials in the derivatives of V at x. We describe the relation of those polynomials to KdV invariants. We also discuss trace formulae for analogs of ξ associated with bound...

This paper presents a parameterized family of equilibrium strategy profiles for three-player Kuhn poker. This family illustrates an important feature of three-player equilibrium profiles that is not present in two-player equilibrium profiles the ability of one player to transfer utility to a second player at the expense of the third player, while playing a strategy in the profile family. This f...

2014 We study the influence of boundary conditions on the existence and coexistence of distortions (textures, defects) in ordered media. The standard topological classification is based on mappings from spheres into the manifold of internal states (characterizing the order). For periodic, or partly periodic boundary conditions, the spheres have to be replaced by tori, or quasitori. The modifica...