CAM Colloquium: Anna Vainchtein (University of Pittsburgh) - Traveling waves in lattices


Frank H. T. Rhodes Hall 655


Abstract: The interplay of spatial discreteness and nonlinearity in many physical and biological systems often results in formation of traveling waves. Such solutions of lattice dynamical systems can be used to describe the motion of dislocations and phase boundaries in crystalline materials, energy transport in muscle proteins, signal transmission in mechanical and electrical networks and many other phenomena. Despite much progress over the last sixty years in understanding traveling wave solutions, particularly in integrable Hamiltonian systems, many open questions remain. In this talk I will consider examples of traveling waves in non-integrable lattices and discuss some recent work addressing their existence, properties and stability. Bio: Professor Anna Vainchtein received Ph.D. in Theoretical and Applied Mechanics from Cornell University in 1998. After a postdoctoral appointment at Stanford University, she became a faculty member at the University of Pittsburgh, where she is now a Professor of Mathematics. Her research focuses on mathematical modeling and analysis of nonlinear phenomena such as dynamics of phase boundaries and dislocations in crystals, energy transport in granular metamaterials and hysteresis in shape-memory alloys.