Mathematical Physics
Seminar
October Schedule

Organizer: Joel L. Lebowitz
lebowitz@math.rutgers.edu

• Speaker- S. Fishman, Technion
• Title-Trapping of Particles by Lasers: The Quantum Kapitza Pendulum
• Time/place-Thursday 10/2/03, 11:30am in Hill 423
• Abstract- It is demonstrated that a bound rapidly oscillating potential typically traps particles even if its time average vanishes. The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency. The work is an extension of the classical result for the Kapitza pendulum. This work may be relevant for the manipulation of cold atoms. Work done in collaboration with Nimrod Moiseyev, Saar Rahav and Ido Gilary.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker-S. Chanillo, Rutgers University
• Title- Nonlinear Eigenvalues and Analytic Hypo-ellipticity
• Time/place-Thursday 10/2/03, 1:30pm in Hill 423
• Abstract- We consider a non-linear eigenvalue problem that arises in the study of analytic hypoellipticity. The core of the problem is a non-self adjoint , compact linear operator. We prove that the point spectrum is not empty.
  
  

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• Speaker-H. Brezis, University of Paris/Rutgers University
• Title-Thomas-Fermi Revisited
• Time/place-Thursday 10/9/03, 11:30am in Hill 705**PLEASE NOTE ROOM CHANGE**
• Abstract- Please click here for abstract.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker-Thierry Bodineau, Universite Paris, France
• Title-Slab Percolation for Ising Model
• Time/place-Thursday 10/9/03, 1:30pm in Hill 705**PLEASE NOTE ROOM CHANGE**
• Abstract-In this talk we are going to discuss the problem of implementing rigorous renormalization schemes for the FK measures which are are a representation of the q-Potts models in terms of dependent percolation models.
  Under the assumption that percolation occurs in a slab, Pisztora introduced a coarse graining procedure which provides a very good description of the typical configurations in the phase transition regime of the FK measures. It is conjectured that the slab percolation assumption is valid in the whole phase transition regime. This was proven in the case of Bernoulli percolation (q=1) by Grimmett and Marstrand. We will present a proof of this conjecture for the Ising model (q=2). This result implies that Pisztora's coarse graining is valid up to the critical temperature.
  
  

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• Speaker- J.-P. Eckmann, University of Geneva
• Title-The Use of Geometry and Entropy in Analyzing Large Networks (WWW, e-mail traffic,...)
• Time/place-Thursday 10/16/03, 11:30am in Hill 423
• Abstract-Elisha Moses, Danilo Sergi, and I have been studying large networks using the "clustering coefficient" (a ratio of triangles and links) to extract relevant information from the local geometry of large networks. I will try to explain the geometric ideas, and will illustrate how they are being applied in a variety of networks we have studied: WWW, Protein Networks, Citations. In addition, we use notions of (Kullback-Leibler) relative entropy to analyze e-mail traffic as a function of time, discovering interest groups in a set of communicating agents.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker- C. Newman, Courant Institute
• Title-Continuum Nonsimple Loops and 2D Critical Percolation
• Time/place-Thursday 10/16/03, 1:30pm in Hill 423
• Abstract-Substantial progress has been made in recent years on the 2D critical percolation scaling limit and its conformal invariance properties. In particular, chordal SLE_6 (the Stochastic Loewner Evolution with parameter 6) was, in the work of Schramm and of Smirnov, identified as the scaling limit of the critical percolation "exploration process." In joint work with Federico Camia, we use that and other results to construct what we argue is the full scaling limit of the collection of all closed contours surrounding the critical percolation clusters on the 2D triangular lattice. This random process or gas of continuum nonsimple loops in the plane is constructed inductively by repeated use of chordal SLE_6. These loops do not cross but do touch each other --- indeed, any two loops are connected by a finite "path" of touching loops.
  
  

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• Speaker- M. Alber, University of Notre Dame
• Title- Multiscale Approaches to Modelling Morphogenesis
• Time/place-Thursday 10/23/03, 11:30am in Hill 423
• Abstract-In this talk we discuss different applications of the lattice-gas-based cellular automata (LGCA) and the extended cellular Potts model (CPM) to modelling biological pattern formation. In particular, we describe several extensions of the classical LGCA model to groups of self-driven biological cells including recent models for rippling, aggregation of cells and fruiting body formation in myxobacteria, as well as to limb chondrogenesis in micromass culture.
  The CPM is a more sophisticated model which describes individual cells as extended objects of variable shape. We discuss various new extensions to the original Potts model from statistical mechanics and describe their application to morphogenesis, the development of a complex spatial structure by a collection of cells including cell sorting in aggregates of embryonic chicken cells. These models include intercellular and extracellular interactions, as well as cell growth.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  This is a joint seminar with Dimacs.
• Speaker- I. Kanter, Bar-Ilan University
• Title- Statistical Mechanical Aspects of Joint Source-channel Coding
• Time/place-Thursday 10/23/03, 1:30pm in Hill 423
• Abstract-An efficient joint source-channel (S/C) decoder based on the side information of the source and on the MN-Gallager Code over Galois fields, $q$, is presented. The dynamical posterior probabilities are derived either from the statistical mechanical approach for calculation of the entropy for the correlated sequences, or by the Markovian joint S/C algorithm. The Markovian joint S/C decoder has many advantages over the statistical mechanical approach, among them: (a) there is no need for the construction and the diagonalization of a $q \timesq$ matrix and for a solution to saddle point equations in $q$ dimensions; (b) a generalization to a joint S/C coding of an array of two-dimensional bits (or higher dimensions) is achievable; (c) using parametric estimation, an efficient joint S/C decoder with the lack of side information is discussed. Besides the variant joint S/C decoders presented, we also show that the available sets of autocorrelations consist of a convex volume, and its structure can be found using the Simplex algorithm.
  

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• Speaker- D. Ruelle, IHES/Rutgers
• Title- First and Second Order Perturbation Calculations in Smooth Ergodic Theory
• Time/place-Thursday 10/30/03, 11:30am in Hill 423
• Abstract-Quantities associated with a differentiable map $f$: $M \to M$ often depend very discontinuously on $f$. But sometimes (with some hyperbolicity present) one can prove differentiability. It is then interesting to COMPUTE derivatives or (in other language) do PERTURBATION THEORY, at least to first nontrivial order (first or second).
  We describe three examples of this situation.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker- J. Wilkening, New York University
• Title- Grain Boundary Diffusion Due to Stress and Electromigration
• Time/place-Thursday 10/30/03, 1:30pm in Hill 423
• Abstract- The stress driven grain boundary diffusion problem is a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries. The model involves coupling many different equations and phenomena, and difficulties such as non-locality, stiffness, complex geometry, and singularities in the stress tensor near corners and junctions make the problem difficult to analyze rigorously and simulate numerically. We present a new approach to this problem using techniques from semigroup theory to represent the solution, and study the problem numerically using a singularity capturing least squares finite element method.