Statistical Thermodynamics and Differential Geometry of Microstructured Materials

1. Front Matter

   Pages i-xv

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2. The Geometric Calculus of Variations and Modelling Natural Phenomena

   • Fred Almgren

   Pages 1-5

3. Hyperbolic Statistical Analysis

   • Jerry Donato

   Pages 7-13

4. A Crystallographic Approach to 3-Periodic Minimal Surfaces

   • Elke Koch, Werner Fischer

   Pages 15-48

5. The Conformation of Fluid Vesicles

   • D. M. Kroll, G. Gompper

   Pages 49-55

6. Harmonic Maps for Bumpy Metrics

   • Libin Mou

   Pages 57-68

7. Periodic Surfaces That are Extremal for Energy Functionals Containing Curvature Functions

   • Johannes C. C. Nitsche

   Pages 69-98

8. The Least Gradient Method for Computing Area-Minimizing Hypersurfaces

   • Harold R. Parks

   Pages 99-116

9. Modelling of Homogeneous Sinters and Some Generalizations of Plateau’s Problem

   • J. Christian Schön, Peter Salamon

   Pages 117-121

10. A Generalization of a Theorem of Delaunay on Constant Mean Curvature Surfaces

    • Brian Smyth

    Pages 123-130

11. Willmore Surfaces and Computers

    • Ivan Sterling

    Pages 131-136

12. Difference Versus Gaussian Curvature Energies; Monolayer Versus Bilayer Curvature Energies; Applications to Vesicle Stability

    • Håkan Wennerström, David M. Anderson

    Pages 137-152

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.

• Gaussian curvature
• Mean curvature
• Minimal surface
• crystallography
• curvature
• differential geometry
• geometric calculus
• statistical thermodynamics
• thermodynamics

• Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, USA

  H. Ted Davis

• School of Mathematics, University of Minnesota, Minneapolis, USA

  Johannes C. C. Nitsche

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