Models of animal movement are necessary both as unambiguous descriptions of particular movement patterns and as starting points for the interpretation of observations on location. Radio-tracking, with frequent sampling so that successive observations are dependent, is an important special case to which only a single narrow class of models has been applied. The standard approach uses a bivariate...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

This paper describes a technique for determining a classi cation map or a hypothesis selection map using a system of reaction-di usion equations. The reaction term of the equations is a replicator equation and provides a mutually exclusive solution. The diffusion term exploits the local consistency of the solution. The technique is e cient for problems with a small labeling space compared to an...

Self-di!usion in zeolites is studied using a simple mean-"eld theory and dynamic Monte-Carlo simulations of di!usion on a lattice model of the zeolite pore space. Our method is powerful, because of its simplicity, #exibility and ability to study the in#uence of various factors: the topology of the pore network, the fraction of strong adsorption sites, the relative strengths of weak and strong s...

There is phenomenological evidence that magnetic reconnection operates in the interstellar medium, and magnetic reconnection is also necessary for the operation of a galactic dynamo. The extremely long ohmic di†usion times of magnetic Ðelds in typical interstellar structures suggest that reconnection occurs in two stages, with thin current layers that have relatively short resistive decay times...

The production of modern microchips requires a large number of fabrication steps. One important step is the creation of semiconducting areas, where charged dopants are implanted into a semiconducting material and under the in uence of high temperatures the dopants penetrate into the layer. This redistribution of dopants and point defects can be described in terms of pair di usion mechanisms. Th...

If u(t; x) is a solution of a one{dimensional, parabolic, second{order, linear partial di erential equation (PDE), then it is known that, under suitable conditions, the number of zero{crossings of the function u(t; ) decreases (that is, does not increase) as time t increases. Such theorems have applications to the study of blow{up of solutions of semilinear PDE, time dependent Sturm Liouville t...

In certain polymer penetrant systems the e ects of Fickian di usion are dominated by nonlinear viscoelastic behavior Consequently such systems often exhibit concentration fronts unlike those seen in classical Fickian systems These fronts not only are sharper than in standard systems but also propagate at constant speed The mathematical model presented is a moving boundary value problem where th...

A convection–di$usion system in one space dimension is a partial di"erential equation of the form ut + A(u)ux =(B(u)ux)x: (1.1) Here u∈Rn, and A(u) and B(u) are n×n matrices that we shall assume are C2 functions of u. If we ignore di"usion, we have the convection system ut + A(u)ux =0: (1.2) If A(u)=Df(u) for some 4ux function f : Rn → Rn, then Eq. (1.2) becomes ut + f(u)x =0; (1.3) a system of...