AMSC 698V  B. Li
AMSC 698V: Advanced Topics in Applied Mathematics, Fall, 2003
MATHEMATICAL AND COMPUTATIONAL PROBLEMS IN MATERIALS SCIENCE
MWF, 11:0011:50, Math 0405
Instructor: Bo Li (Office: Math 4304,
Email: bli@math.umd.edu)

Course Description
 References
 Homework Assignments
 Lecture Notes (partially distributed to the class)
 Weak convergence methods for variational problems modeling
crystalline solids
 The theory of quasiconvexity: sequential weak lower
semicontinuity; existence; partial regularity;
various notion of convexity and nullLagrangians.
 The theory of compensated compactness: the DivCurl lemma
and its generalizations; necessary conditions; sufficient
conditions; Young measures and gradient Young measures.
 Mechanics of crystalline solids: Bravais
lattices; martensitic phase transformation; the CauchyBorn rule;
twinning; Hadamard compatibility condition; classification of interfaces.
 Mathematical theory of microstructure: simply laminated microstructure;
the twowell problem; reduction of multiwell problems;
kinematics of microstructure; restrictions on microstructure.
 Additional topics: surface energy and scaling; martensitic thin
films; dynamics.
 Epitaxial growth of thin films
 Island dynamics models
 Continuum models: coarsening and dynamic scaling
 Mathematical and numerical aspects of surface diffusion
 The levelset method for interface motion