Andrej Cherkaev Research Page

Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.

An engineer thinks that his equations are an approximation to reality.
A physicist thinks that reality is an approximation to his equations.
A mathematician doesn't care.

A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.

Quotes from our Mathjokes site.

• Progress in methods for nonconvex variational problems Nonconvex problems: Equilibrium

• Progress in dynamics of chains and lattices from bistable links. Nonconvex problems: Dynamics

• The currently built site MathMat explains mathematical methods in material research and optimal design.

• The site Mystery of the spiral trees discusses an inverse optimization problem:
  Why are the natural "designs" the way they are?

My research areas are:
Structural Optimization	Optimal Composites	Nonconvex Variational Problems
New areas:
Dynamics of unstable materials and the phase transition	Optimality of bio-materials: search for functionals.	Dynamics of damageable matherials.
You can find here an informal description of some unsolved problems in these areas.

List of publications

Recent preprints

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Links

My references to papers and books in Calculus of variation, Structural optimization, micro-inhomogeneous media, etc. A large bibtex file
An optimization source  NEOS Guide Optimization Tree
An organized directory of papers in Structural Optimization
Ole Sigmund homepage with the amazing interactive structural optimization software.
How Things Break  by Michael Marder and Jay Fineberg

 CHAOGRAPHY!!! Animation using chaos, by Elizabeth Bradley
 Visualization in Mathematics: Gallery by Richard Palais
 A Chronology of Game Theory by Paul Walker

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Description of my related graduate courses:

M-675-2 - Modern Problems in Calculus of Variations.
M-7710 - Optimization and Homogenization.

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