Geometry and analysis in physical systems; papers presented in honour of Darryl D Holm's 60th birthday

Abstract

This special issue of Journal of Physics A: Mathematical and Theoretical is dedicated to Darryl Holm on the occasion of his 60th birthday. The papers were largely drawn from the lectures at a meeting held in his honour at the Bernoulli Center at the EPFL in Lausanne, Switzerland, 22–28 July, 2007.The papers cover, as much as it is possible, the tremendous range and depth of work done by Darryl over the years. These topics include theCamassa–Holm equation and waves, geometric mechanics, symmetry and integrable systems, fluid and plasma dynamics, including stabilityproblems, regularized incompressible fluid models (such as the α- or LANS models), including turbulence and multiscale methods, ocean dynamics,the EPDiff equation (a higher dimensional version of the CH equation) and computational anatomy. Perhaps a little less well known is Darryl'sinfluential work in adiabatic fluids in general relativity, liquid crystals and other topics. But underlying all of Darryl's work is the geometric viewof mechanics and physics, which was already kindled in his 1976 PhD thesis at Michigan.One of Darryl's and our favorite accomplishments is the development of the Camassa–Holm equation, a remarkable integrable PDE with, amazingly,spatially non-smooth, peaked, solitions. This is understandable—the equation caught on like wildfire because of its fascinating properties andthe ideas in that paper proved to be a gold mine of research. It is his most cited paper with nearly a thousand citations, according to GoogleScholar. We are pleased that our joint 1985 paper on fluid and plasma stability comes in second and the paper that was a precursor to the alphamodel series of papers, namely our Euler–Poincaré paper, comes in third.Of course having an equation named after you is a very nice bonus. Congratulations Darryl on a brilliant career that shows no signs of slowingdown!