Center for Nonlinear Studies

Nonlinear Behavior in Complex Systems (2005-2007)

The emergence and appreciation of universal approaches to complex systems are based on notions of nonlinearity, especially low-dimensional dynamical systems, pattern formation, and coherent/localized states, i.e., solitons. From this rich but rather restricted sense of nonlinearity, there has emerged a broader viewpoint often referred to as the study of complex systems. We use the tools of nonlinear science combined with other techniques from statistical physics, mathematical physics and applied mathematics to study traditional problems in pattern formation and solitons as well as complex states of real world significance. Examples include global climate, the characterization of systems beyond experimental testing, design and manufacture of complex micro- and nano-scale devices and systems, the understanding of materials with complicated structure arising from meso-scale features, and non-equilibrium statistical mechanics of material failure under high strain rate conditions. Of particular emphasis:

Solitons, patterns and nonlinear dynamics
Excitations in condensed matter materials
Nature of mathematical equations

Highlight Publications:

Amoruso, C., A. K. Hartmann, M. B. Hastings, and M. A. Moore. Conformal invariance and stochastic Loewner evolution processes in two-dimensional Ising spin glasses. 2006. Physical Review Letters. 97 (26): 267202.
Araujo, P.T., S. K. Doorn, S. Kilina, S. Tretiak, E. Einarsson, S. Maruyama, H. Chacham, M. A. Pimenta, and A. Jorio. Third and fourth optical transitions in semiconducting carbon nanotubes. 2007. Physical Review Letters. 98 (6): 067401.
Bender, C.M., and E. Ben-Naim. Nonlinear integral-equation formulation of orthogonal polynomials. 2007. Journal of Physics A-Mathematical and Theoretical. 40 (1): F9.
Gambetta, A., C. Manzoni, E. Menna, M. Meneghetti, G. Cerullo, G. Lanzani, S. Tretiak, A. Piryatinski, A. Saxena, R. L. Martin, and A. R. Bishop. Real-time observation of nonlinear coherent phonon dynamics in single-walled carbon nanotubes. 2006. Nature Physics. 2 (8): 515.
Peters, O., and J. D. Neelin. Critical phenomena in atmospheric precipitation. 2006. Nature Physics. 2 (6): 393.
Piryatinski, A., M. Stepanov, S. Tretiak, and V. Chernyak. Semiclassical scattering on conical intersections. 2005. Physical Review Letters. 95 (22): 223001.
Shreve, A., E. Haroz, S. Bachilo, R. Weisman, S. Tretiak, S. Kilina, and S. Doorn. Determination of exciton-phonon coupling elements in singe-walled carbon nano-tubes by Raman overtone analysis. 2007. Physical Review Letters. 98 (3): 037405.
Tretiak, S., S. Kilina, A. Piryatinski, A. Saxena, R. Martin, and A. Bishop. Excitons and Peierls distortion in conjugated carbon nanotubes. 2007. Nanoletters. 7 (1): 86.
1.Wu, C., S. Tretiak, and V. Y. Chernyak. Excited states and optical response of a donor-acceptor substituted polyene: A TD-DFT study. 2007. Chemical Physics Letters. 433 (4-6): 305.
1.Wu, C., S. V. Malinin, S. Tretiak, and V. Y. Chernyak. Exciton scattering and localization in branched dendrimeric structures. 2006. Nature Physics. 2 (9): 631.