Statistical Thermodynamics and Differential Geometry of Microstructured Materials

ISBN-13: 9781461383260 / Angielski / Miękka / 2011 / 172 str.

H. Ted Davis; Johannes C. C. Nitsche

Opis

Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful. Examples of such substances include liquid crystals, microemulsions, biological matter, polymer mixtures and composites, vycor glasses, and zeolites. In this volume, an interdisciplinary group of researchers report their developments in this field. Topics include statistical mechanical free energy theories which predict the appearance of various microstructures, the topological and geometrical methods needed for a mathematical description of the subparts and dividing surfaces of heterogeneous materials, and modern computer-aided mathematical models and graphics for effective exposition of the salient features of microstructured materials.

Spis treści

The geometric calculus of variations and modelling natural phenomena.- Hyperbolic statistical analysis.- A crystallographic approach to 3-periodic minimal surfaces.- The conformation of fluid vesicles.- Harmonic maps for bumpy metrics.- Periodic surfaces that are extremal for energy functionals containing curvature functions.- The least gradient method for computing area-minimizing hypersurfaces.- Modelling of homogeneous sinters and some generalizations of plateau’s problem.- A generalization of a theorem of Delaunay on constant mean curvature surfaces.- Willmore surfaces and computers.- Difference versus Gaussian curvature energies; monolayer versus bilayer curvature energies; applications to vesicle stability.

O autorze

In this volume, an interdisciplinary group of researchers report their developments. Topics include statistical mechanical free energy theories which predict the appearance of various microstructures, the topological and geometrical methods needed for a mathematical description of the subparts and dividing surfaces of heterogeneous materials, and modern computer-aided mathematical models and graphics for effective exposition of the salient features of microstructured materials.