Statistical Thermodynamics and Differential Geometry of Microstructured Materials

✍ Scribed by Fred Almgren (auth.), H. Ted Davis, Johannes C. C. Nitsche (eds.)

• Publisher: Springer-Verlag New York
• Year: 1993
• Tongue: English
• Leaves: 160
• Series: The IMA Volumes in Mathematics and its Applications 51
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
The Geometric Calculus of Variations and Modelling Natural Phenomena....Pages 1-5
Hyperbolic Statistical Analysis....Pages 7-13
A Crystallographic Approach to 3-Periodic Minimal Surfaces....Pages 15-48
The Conformation of Fluid Vesicles....Pages 49-55
Harmonic Maps for Bumpy Metrics....Pages 57-68
Periodic Surfaces That are Extremal for Energy Functionals Containing Curvature Functions....Pages 69-98
The Least Gradient Method for Computing Area-Minimizing Hypersurfaces....Pages 99-116
Modelling of Homogeneous Sinters and Some Generalizations of Plateau’s Problem....Pages 117-121
A Generalization of a Theorem of Delaunay on Constant Mean Curvature Surfaces....Pages 123-130
Willmore Surfaces and Computers....Pages 131-136
Difference Versus Gaussian Curvature Energies; Monolayer Versus Bilayer Curvature Energies; Applications to Vesicle Stability....Pages 137-152

✦ Subjects

Statistical Physics, Dynamical Systems and Complexity;Differential Geometry;Thermodynamics