Lectures on structural stability in dynamics

Four Lectures on Noncommutative Dynamics

These lectures concern basic aspects of the theory of semigroups of endomorphisms of type I factors that relate to causal dynamics, dilation theory, and the problem of classifying E0-semigroups up to cocycle conjugacy. We give only a few proofs here; full details can be found in the author’s upcoming monograph Noncommutative Dynamics and E-semigroups, to be published in the Springer series Mono...

On the stability and structural dynamics of metal nanowires

This article presents a brief review of the nanoscale free-electron model, which provides a continuum description of metal nanostructures. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of metal nanowires, and that much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two compe...

Manfred Denker Lectures on Probability and Dynamics

Lectures on Dynamics in Models of Coarsening and Coagulation

Contents 1 Introduction 2 2 A hierarchy of domain coarsening models in one space dimension 5 2.1 Domain walls in the Allen-Cahn equation 5 2.2 Domain wall dynamics by restricted gradient flow 7 2.3 Punctuated equilibrium and 1D bubble bath 11 2.4 Mean-field model of domain growth—the Gallay-Mielke transform 13 2.5 Proof of universal self-similar behavior 19 3 Models of domain coarsening in two ...

p-VERSION FINITE ELEMENTS IN STRUCTURAL DYNAMICS AND STABILITY

The performance of the finite element method (FEM) may be improved in three ways. The first is by the h-version to refine the finite element mesh and the second is by the p-version to increase the order of polynomial shape functions for a fixed mesh. The third is simultaneously to refine the mesh and increase the degrees of elements uniformly or selectively, called the h-p version, which is a c...