AMSC 698V - B. Li
AMSC 698V: Advanced Topics in Applied Mathematics, Fall, 2003
MATHEMATICAL AND COMPUTATIONAL PROBLEMS IN MATERIALS SCIENCE
MWF, 11:00-11:50, Math 0405
Instructor: Bo Li (Office: Math 4304,
- Homework Assignments
- Lecture Notes (partially distributed to the class)
- Weak convergence methods for variational problems modeling
- The theory of quasi-convexity: sequential weak lower
semi-continuity; existence; partial regularity;
various notion of convexity and null-Lagrangians.
- The theory of compensated compactness: the Div-Curl lemma
and its generalizations; necessary conditions; sufficient
conditions; Young measures and gradient Young measures.
- Mechanics of crystalline solids: Bravais
lattices; martensitic phase transformation; the Cauchy-Born rule;
twinning; Hadamard compatibility condition; classification of interfaces.
- Mathematical theory of microstructure: simply laminated microstructure;
the two-well problem; reduction of multi-well problems;
kinematics of microstructure; restrictions on microstructure.
- Additional topics: surface energy and scaling; martensitic thin
- Epitaxial growth of thin films
- Island dynamics models
- Continuum models: coarsening and dynamic scaling
- Mathematical and numerical aspects of surface diffusion
- The level-set method for interface motion