Modeling mesoscopic phenomena in extended dynamical systems Page: 3 of 11
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Modeling Mesoscopic Phenomena in Extended Dynamical Systems
Alan Bishop,* Peter Lomdahl, Niels Gronbech Jensen, and David Cai
Los Alamos National Laboratory
Franz Mertenz
University of Bayreuth, Germany
Hidetoshi Konno
University of Tsukuba, Japan
Markku Salkola
Stanford University
Abstract
This is the final report of a three-year, Laboratory-Directed Research and
Development project at the Los Alamos National Labortory (LANL). We have
obtained classes of nonlinear solutions on curved geometries that demonstrate a
novel interplay between topology and geometric frustration relevant for
nanoscale systems. We have analyzed the nature and stability of localized
oscillatory nonlinear excitations (multi-phonon bound states) on discrete
nonlinear chains, including demonstrations of successful perturbation theories,
existence of quasiperiodic excitations, response to external statistical time-
dependent fields and point impurities, robustness in the presence of quantum
fluctuations, and effects of boundary conditions. We have demonstrated multi-
timescale effects for nonlinear Schroedinger descriptions and shown the success
of memory function approaches for going beyond these approximations. In
addition we have developed a generalized rate-equation framework that allows
analysis of the important creation/annihilation processes in driven nonlinear,
nonequilibrium systems.
1. Background and Research Objectives
Two of the important lines along which complexity in nonlinear condensed matter has
evolved over the last decade are complex dynamics of coherent structures in problems with
competing length and/or time scales and partial differential equations (PDEs) with length and
time scales controlled by additive or parametric forcing and damping. We are now at last able
to also tackle the fundamental concern of combining nonlinearity with disorder and noise. This
opportunity raises major issues for applications of mathematics-particularly stochastic
nonlinear PDEs-and a new role for the synergistic combination of analysis and scientific
computing. Our intent was to develop the necessary analytical and numerical technology base
for several emerging themes in nonlinear condensed matter and materials science. Our
principal concern was to address aspects of coherence and chaos as they appear in PDEs and* Principal Investigator, E-mail: bishopalan@ltnl.gov
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Bishop, A.; Lomdahl, P.; Jensen, N.G.; Cai, D.S.; Mertenz, F.; Konno, Hidetoshi et al. Modeling mesoscopic phenomena in extended dynamical systems, report, August 1, 1997; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc698662/m1/3/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.