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...

Visual tasks often require a hierarchical representation of shapes and images in scales ranging from coarse to ne. A variety of linear and nonlinear smoothing techniques, such as Gaussian smoothing, anisotropic di usion, regularization, etc. , have been proposed, leading to scalespace representations. We propose a geometric smoothing method based on local curvature in shapes and images. This de...

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...

In a number of disciplines, directional data provides a fundamental source of information. A novel framework for isotropic and anisotropic di usion of directions is presented in this paper. The framework can be applied both to regularize directional data and to obtain multiscale representations of it. The basic idea is to apply and extend results from the theory of harmonic maps in liquid cryst...

We consider a nonconforming streamline-diiusion nite element method for solving convection-diiusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not a suucient stabilization. Additional parameter dependent jump terms have been proposed which preserve...

A molecular dynamics study of atomic self-diiusion in Frank-Kasper type do-decagonal quasicrystals is presented. It is found that the quasicrystal-speciic ip mechanism for atomic diiusion, predicted by Kalugin and Katz, indeed occurs in this system. However, in order to be eeective, this mechanism needs to be catalyzed by other defects, such as half-vacancies. For this reason, it is diicult to ...

The behaviour of a system comprising two competitive autocatalytic processes, A ] B] 2B, and A] C] 2C, rate \ k1a6 b 6 where and represent the concentrations of the various species, is considered. In a well-stirred batch reactor, the rate \ 2 a6 c6 , a6 , b 6 c6 Ðnal equilibrium composition always corresponds to a mixture of the two product species B and C, with their respective equilibrium con...

The helium-atmosphere (DB) white dwarfs are commonly thought to be the descendants of the hotter PG 1159 stars, which initially have uniform He/C/O atmospheres. In this evolutionary scenario, diffusion builds a pure He surface layer which gradually thickens as the star cools. In the temperature range of the pulsating DB white dwarfs (Teff ∼ 25, 000 K) this transformation is still taking place, ...