For the purpose of these lectures, a microstructure is any structure on a scale between the
macroscopic scale (on which we usually make observations) and the atomic scale. Such …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus
of Variations | SpringerLink Skip to main content Advertisement Springer Nature Link Account …

Hysteresis is an exciting and mathematically challenging phenomenon that oc curs in rather
different situations: jt, can be a byproduct offundamental physical mechanisms (such as …

A general framework is given for the phenomenological kinetics of phase transitions in
which not only the order parameter but also the temperature may vary in time and space …

We study the limiting behavior of solutions to appropriately rescaled versions of the Allen‐
Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish …

We construct local minimisers to certain variational problems. The method is quite general
and relies on the theory of Γ-convergence. The approach is demonstrated through the model …

..." What do you call work?"" Why ain't that work?" Tom resumed his whitewashing, and
answered carelessly:" Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom …

This paper presents a novel reaction-diffusion (RD) method for implicit active contours that is
completely free of the costly reinitialization procedure in level set evolution (LSE). A diffusion …

In this paper we extend the Van der Waals-Cahn-Hilliard theory of phase transitions to the
case of a mixture of n non-interacting fluids. By describing the state of the mixture as given …