Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session S5: Solitons in Physics: 50 Years Since Fermi, Pasta & Ulam |
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Sponsoring Units: GSNP Chair: Charlie Doering, University of Michigan Room: LACC 502B |
Wednesday, March 23, 2005 2:30PM - 3:06PM |
S5.00001: From FPU to Intrinsic Localized Modes Invited Speaker: Intrinsic localized modes (ILMs), also known as ``discrete breathers,'' have been appealing theoretical possibilities for more than a decade. Roughly speaking, they represent the extension of the continuum concept of ``solitons'' to spatially extended discrete (lattice) systems. Importantly, theory suggests that ILMs are far more ubiquitous than solitons, in that they can occur in discrete systems in any number of spatial dimensions and with a wide range of nonlinear interactions. In the past several years, ILMs have been observed experimentally in physical systems as distinct as charge-transfer solids, Josephson junction arrays, photonic structures, and micromechanical oscillator arrays. Beginning with a brief historical overview of the origin of the concept of ILMs, we focus on their current theoretical and experimental and discuss some exciting possible future directions and applications of these novel nonlinear excitations. [Preview Abstract] |
Wednesday, March 23, 2005 3:06PM - 3:42PM |
S5.00002: The FPU problem and statistical mechanics Invited Speaker: Most of the investigations of the FPU model have led to the discovery of new, very interesting properties of this seminal model such as solitons, breathers, etc., creating the field of non-linear dynamics. However, the original question FPU posed was a statistical mechanical one, namely to verify the approach of a very simple system initially not in equilibrium to equilibrium. To their and most physicists’ consternation their model did not show this, throwing one of the basic tenets of statistical mechanics into doubt. The reasons why FPU did not find an approach to equilibrium will be discussed here as related to stochasticity thresholds in Hamiltonian dynamics and a connection with the phase space geometry of this model will be mentioned. [Preview Abstract] |
Wednesday, March 23, 2005 3:42PM - 4:18PM |
S5.00003: Solitons and Coherent Structures in Bose-Einstein Condensates Invited Speaker: The Fermi-Pasta-Ulam (FPU) model was formulated fifty years ago in an attempt to explain heat conduction in non-metallic lattices and develop ``experimental'' (computational) methods for research on nonlinear dynamical systems. Further studies of the FPU problem ten years later led to the first analytical description of solitons, which occur ubiquitously in diverse physical situations ranging from water waves to plasmas, optical fibers, and more. More recently, the study of solitons and coherent structures in Bose-Einstein condensates (BECs) has come to the forefront of experimental and theoretical efforts, drawing attention from both atomic and nonlinear physicists. In this talk, I will discuss localized (soliton) and spatially extended solutions of the Gross-Pitaevskii (GP) equation describing the macroscopic behavior of BECs near zero temperature. As a key example, I will discuss BECs loaded into deep, spatially periodic optical potentials, which effectively splits the condensate into a chain of linearly-interacting, nonlinear droplets, the dynamics of which is characterized by nonlinear lattice models. This talk will highlight some of the dynamical structures in BECs reminiscent of the discoveries that originated from the FPU model. [Preview Abstract] |
Wednesday, March 23, 2005 4:18PM - 4:54PM |
S5.00004: Heat Conduction in Low Dimensions Invited Speaker: The Fourier law describing heat conduction is almost two hundred years old and yet a first-principle derivation of this simple law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions and the necessary and sufficient conditions for its validity are also far from clear. In this talk I’ll give a review of work done in this area and I’ll report our recent work on heat conduction in the Frenkel- Kontorova model. Application of knowledge gained in the study of heat conduction in one dimension to the design of a thermal diode will also be discussed. [Preview Abstract] |
Wednesday, March 23, 2005 4:54PM - 5:30PM |
S5.00005: FPU, Solitons and Nonlinear Science: History, Visiometrics and Art \& Science Invited Speaker: I review how the discipline of ``nonlinear'' physics arose from the '54-`55 Fermi-Pasta-Ulam (FPU) digital computer simulations of the nonlinear one-dimensional alpha-lattice and the discovery of the soliton (1965) and ``n-curve'' states (1967). Recently, applications to accelerated inhomogeneous (Richtmyer-Meshkov) flows have been made and evolving vortex bilayers and ``vortex projectiles'' discovered in the emerging turbulence. Underlying these innovations is the cogent visiometrics approach, whose representations can provide peak insights that lead to pathways for discovery and can stimulate artistic expression. See (http://www.mechanical.rutgers.edu/scart4/ especially ''Links''); also, `` FPU, solitons {\&} the fabric of nonlinear science: History, synergetics and visiometrics'' in CHAOS (to be published in `05).- [Preview Abstract] |
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