Professor Andrej Cherkaev

(Андрей Всеволодович Черкаев)
Department of Mathematics 
University of Utah, 

 email: cherk@math.utah.edu
URL:
http://www.math.utah.edu/~cherk

New math for new materials

(Новые мат. методы для новых материалов)

 

Preliminary plan

С вопросами обращайтесь по email: cherk@math.utah.edu. Пожалуйста, используйте латиницу.

Introduction

I.                 Compliant, smart, bio-, nano- and other new materials and related mathematical challenges

II.               Use of the Internet to collect and sort information of hot new topics.

Nonconvex variational problems: optimal composites and phase transitions:

III.             Materials with structural instabilities and nonconvex energies

IV.            Microstructures and minimizing sequences.

V.              Relaxation and quasiconvexity. Necessary and sufficient conditions for quasiconvexity.

VI.            Microstructures from linear materials. Coated spheres, ellipsoids and other exact solutions. Mosaic of Laminates.

VII.          Polyconvexity and beyond.

VIII.        Example 1.  Domains of maximal stiffness.

IX.            Example 2. Phase transition. Problem of local minima

Dynamics of unstable and transitional structures.

X.              Problem of dynamic homogenization

XI.            Periodic systems with localized excitation. Waves in a domino train.

XII.          Waves in piecewise linear systems and waiting-link structures

XIII.        Examples

Optimization, Duality, and new Variational Principles in mechanics

XIV.    Optimal design problems. Variational formulations

XV.        Transform of a minimax principle into minimal principle.

XVI.          Minimax approach to design with uncertain conditions.

XVII.        Understanding of Evolutionary “designs” and the aim functionals.



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