Description:
The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics, and the macroscopic behavior of such materials often depends critically on their substructures. This work, written by leading mathematicians and engineers, features a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories within the context of modeling material substructures. Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from the work and may find suggestions for further research in its rich collection of open problems.
Review Quotes:
"As an outgrowth of a symposium held in Taormina, Italy, in 2001, ten invited papers on multifield theories for continua with substructure are presented here. Multifield theories aim to bridge the area between materials science and continuum mechanics. From the standpoint of material constituents, the simplest model is considered in the contribution of I. Müller: a monatomic gas.... Other contributions deal with the interaction of polymer chains and the turbulent state of a fluid...with topological properties of defects, of shape memory and others. The perhaps most theoretical article is by Cendra, Marsden and Ratiu on...extended...Poisson brackets with cocycles. The articles, though dealing with nontrivial matters, are quite readable and informative even for the nonspecialist."
--Monatshefte für Mathematik
"...This compendium is extremely diverse ...The individual contributions in this compendium are certainly quite interesting and worth reading."
--Rezensionen