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| Saturday, January 6 — Session 11: Statistical and Computational Physics |
| 11:40 am-noon |
Stephen Wolfram
In the early 1980s I gave a talk at a Dynamics Days, predicting that there would be interesting things to discover in simple programs like cellular automata. Here I'll give a very brief follow-up about some of the science, mathematics, and technology that I've found or created over the past twenty-five years by exploring the broader computational universe of possible programs. There'll probably be glimpses of the new Mathematica that's been under development for the past decade, and with luck I'll be able to show a live computer experiment directly relevant to nonlinear dynamics, and I'll talk a bit about what I expect to see over the next twenty or so years.
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| 1-1:40 pm |
Karin Dahmen
University of Illinois at Urbana Champaign
authors: Karin A. Dahmen and Yang Liu
Disorder Induced Critical Scaling In and Out of Equilibrium: are they the same ?
The zero-temperature random-field Ising model (a model for disordered magnets that is applicable to a much larger class of disordered systems) shows surprisingly similar universal scaling behavior near a critical disorder both in equilibrium and far from equilibrium! We compare the no-passing rule, critical exponents and universal scaling functions in mean field theory and in 3D (avalanche exponents, fractal dimensions and anisotropy measures) for the equilibrium and non equilibrium phase transition and show compelling evidence that these two transitions belong to the same universality class, which may even be shared by the demagnetization curve of the same system and by a related a history induced phase transition. Related experimental systems are also discussed, as well as an interesting connection to the statistics of earthquakes. |
| 1:40-2 pm |
Derek Moulton
University of Delaware
Email: moulton@math.udel.edu
authors: Derek Moulton, University of Delaware; John Pelesko, University of Delaware
Catenoid in an Electric Field
In the 1960's, G.I. Taylor launched the field of electrohydrodynamics with his seminal study of drops, films, and liquid jets subjected to an electric field. This work led, for one thing, to the discovery of Taylor cones, which play a significant role in many industrial applications. In this talk, we extend the work begun by Taylor to the case of an axially symmetric liquid bridge soap bubble subjected to an external electric field. We apply a potential difference between the membrane and an
outer cylinder, and study equilibrium shapes of the membrane. A model is formulated from variational principles, and the resulting non-linear ODE is analyzed. Perturbation techniques are utilized for special cases of small voltage and small deviation from a cylindrical bridge. The general solution set is analyzed in a dynamical framework by considering the nature of trajectories in the phase plane, and stability is characterized in terms of the dimensionless parameters describing the applied voltage and the length ratios of the device. Such surfaces may be classified as Field Driven Mean Curvature (F.D.M.C.) surfaces, and have potential application in liquid handling strategies in reduced gravity environments as well as in switches, pumps, and other actuators for MEMS purposes. |
| 2-2:40 pm |
Yves Pomeau
University of Arizona
An equilibrium that is not thermal
Abstract In our Galaxy as in others, some stars aggregate in large self gravitating clumps, called the globular clusters. The apparent stability of these objects remains somewhat mysterious, because no thermal equilibrium exists with Newtonian interactions. This problem can be (and has been) analysed by expansion in a small parameter, the inverse of the number of stars in the cluster. The leading order is the mean field Newton-Vlasov limit, with many stable equilibria. Collisions (more specifically irreversible effects) are included at next order and make it a very hard problem, because they destroy the stability of the cluster in the long term. I shall explain how to escape this paradox.
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