Anna Vainchtein

  • Professor, PhD

Education & Training

  • Ph.D. 1998, Cornell University

Representative Publications

(please see my personal website for a complete list of publications)

A. Vainchtein. Solitary waves in FPU-type lattices. Physica D, 434: 133252, 2022 (review article).

A. Vainchtein, J. Cuevas-Maraver, P. Kevrekidis and H. Xu. Stability of traveling waves in a driven Frenkel-Kontorova model. Communications in Nonlinear Science and Numerical Simulation, 85: 105236, 2020.

L. Truskinovsky and A. Vainchtein. Strictly supersonic solitary waves in lattices with second-neighbor interactions. Physica D, 389:24-50, 2019.

A. Vainchtein, Y. Starosvetsky,  J. D. Wright and R. Perline. Solitary waves in diatomic chains. Physical Review E, 93, 042210, 2016.

L. Truskinovsky and A. Vainchtein. Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain. Physical Review E, 90, 042903, 2014.

P. G. Kevrekidis, A. Vainchtein, M. Serra Garcia and C. Daraio. Interaction of traveling waves with mass-with-mass defects within a Hertzian chain. Physical Review E, 87, 042911, 2013.

A. Vainchtein. The role of spinodal region in the kinetics of lattice phase transitions. Journal of the Mechanics and Physics of Solids, 58(2): 227-240, 2010.

L. Truskinovsky and A. Vainchtein. Kinetics of martensitic phase transitions: Lattice model. SIAM Journal on Applied Mathematics, 66(2): 533-553, 2005.

A. Vainchtein. Non-isothermal kinetics of a moving phase boundary. Continuum Mechanics and Thermodynamics,15(1): 1-19, 2003.

A. Vainchtein and P. Rosakis. Hysteresis and stick-slip motion of phase boundaries in dynamic models of phase transitions. Journal of Nonlinear Science, 9: 697-719, 1999.


Research Area

Research Interests

I am generally interested in mathematical modeling and analysis of nonlinear phenomena in materials science, physics and biology. Examples include traveling waves and discrete breathers in nonlinear lattices, dynamics of phase boundaries, cracks and dislocations in crystals and hysteresis in phase-transforming materials. The resulting mathematical problems typically involve minimization of nonconvex functionals, nonlinear PDEs that change type, dynamical systems with many degrees of freedom and functional differential equations. Thus nonstandard analytical and numerical techniques are required.

Research Grants

National Science Foundation, DMS-2204880, 2022-2025
National Science Foundation, DMS-1808956, 2018-2022
National Science Foundation, DMS-1506904, 2015-2019
National Science Foundation, DMS-1007908, 2010-2014
CAREER Award, National Science Foundation, DMS-0443928, 2005-2011
ADVANCE Fellow Award, National Science Foundation, DMS-0137634, 2002-2006