Mathematical Physics Seminar
Rutgers University
Hill Center, Room 705

April Schedule

Organized by: Joel L. Lebowitz
lebowitz@math.rutgers.edu



Please join us for coffee and cookies in the kitchen of Hill 705 at 11:45am before seminars



Speaker: M. Alber, University of Notre Dame

Date/Time/Place: Thursday, April 2, 2009, 12:00pm, Hill 705

Title: Connection between discrete stochastic and continuous models in biology

Abstract: Swarming, a collective motion of many thousands of cells, produces colonies that rapidly spread over surfaces. A detailed cell- and behavior-based computational model of M. xanthus swarming [1] will be used in this talk to show that reversals of gliding direction are essential for swarming and that the reversal period predicted to maximize the swarming rate is the same as the period observed in experiments. This suggests that the circuit regulating reversals evolved to its current sensitivity under selection for growth achieved by swarming. Also, an orientation correlation function will be used to show that microscopic social interactions help to form the ordered collective motion observed in swarms [2].
Then a continuous limit will be described of a two-dimensional stochastic discrete model describing cells moving in a medium and reacting to each other through direct contact, cell-cell adhesion, and long range chemotaxis [3]. Contrary to classical Keller- Segel model, solutions of the obtained nonlinear diffusion equation do not collapse in finite time and can be used even when relative volume occupied by cells is ruther large. A very good agreement was demonstrated between Monte Carlo simulations and numerical solutions of the obtained macroscopic nonlinear diffusion equation. Combination of microscopic and macroscopic models was used to simulate growth of structures similar to early vascular networks.
  1. Wu, Y., Jiang, Y., Kaiser, D., and M. Alber [2007], Social Interactions in Myxobacterial Swarming, PLoS Computational Biology 3 12, e253.
  2. Wu, Y., Jiang, Y., Kaiser, D., and M. Alber [2009], Periodic reversal of direction allows Myxobacteria to swarm, Proc. Natl. Acad. Sci. USA 106 4 1222-1227 (featured in the Nature News, January 20th, 2009, doi:10.1038/news.2009.43).
  3. Lushnikov, P.P., Chen, N., and M.S. Alber [2008], Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, Phys. Rev. E. 78, 061904.


THURSDAY, APRIL 9TH: NO SEMINAR - PASSOVER HOLIDAY



Speaker: E. Presutti, University of Rome

Date/Time/Place:April 16, 2009, 12:00pm, Hill 705

Title: Microscopic models for heat conduction

Abstract: Fourier's law describes the heat current in a body whose sides are kept at different temperatures by connections to thermal reservoirs. The microscopic nature of the reservoirs is the main issue in my talk where I compare the case of infinite reservoirs and finite reservoirs with additional thermostatic forces (which keep the temperature of the reservoir constant). I shall first describe a stochastic model, stirring process with an additional birth-death generator, (work in preparation with A. De Masi and D. Tsagkarojoannis) and then a hamiltonian model (work in collaboration with G. Gallavotti).


Speaker: C. Radin, University of Texas

Date/Time/Place: April 23, 2009, 12:00pm, Hill 705

Title: Modelling sand Abstract: We discuss probability distributions on packings of spheres and other shapes, as a function of the volume fraction of the packings. We then introduce a simple model of static sand piles and use Monte Carlo simulation to analyze the phenomenon of random loose packing. This is joint work with D. Aristoff.

THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM. PLEASE JOIN US


Speaker: Alexandre Morozov, Rutgers University

Date/Time/Place: April 23, 2009, 2:00pm, Hill 705

Title: Evolution induces pairwise and higher-order correlations among amino acid mutations in proteins

Abstract: Protein structure and function are determined by its amino acid sequence. As proteins evolve, patterns of amino acid mutations reveal those positions that contribute most to the protein stability and function. In particular, pairwise and higher-order correlations between amino acid mutations are ubiquitous in protein families. Here we demonstrate that modeling such correlations is crucial for understanding the emergence of complex mutational patterns that confer drug resistance to the HIV-1 subtype B protease. The observed correlations may arise through physical proximity of mutated residues, or may appear due to the non-linear dependence of protein stability on the folding free energy. In the latter case, a destabilizing mutation is compensated for by a stabilizing one, which restores protein function to the wild-type levels even if mutated sites are not in close spatial proximity. The proposed compensatory mechanism may explain why attempts to identify amino acid contacts in the structure from mutational data have only met with limited success so far. Understanding the correlations in terms of both physical and compensatory interactions will guide design of future algorithms that identify amino acid contacts from protein sequence alignments.


SPECIAL SEMINAR
Speaker:J. Froehlich, Swiss Federal Inst. of Tech. Zurich/IAS
Date/Time/Place: April 29, 2009
Title:Are there any mysteries about quantum mechanics?
Abstract: After some introductory remarks about quantum theory and the atomistic structure of matter, questions concerning the nature of quantum mechanics will be addressed. It will first be recalled in what sense quantum mechanics is fundamentally non-deterministic. Subsequently, the notions of "events" and "causal sequences of events" (or "histories") will be introduced, and the good, old calculus of "frequencies of histories" will be recalled. Then it will be explained what "(nearly) consistent histories" are. The role of decoherence in rendering histories nearly consistent will be explained. If time permits some mechanisms of decoherence will be sketched. This is an old man's attempt to get around "wave function collapse" and eliminate this and other misleading concepts from the jargon we use when talking about quantum mechanics.


Speaker: D. Ruelle, IHES, France

Date/Time/Place: April 30, 2009, 12:00pm, Hill 705

Title: Characterization of Lee-Yang Polynomials

Abstract: We define Lee-Yang polynomials P(z_1,...,z_n) as those multi-affine polynomials in n variables which do not vanish when the |z_j| are all <1 or all >1 (including no zero at infinity). Polynomials of this type where used by Lee and Yang in the proof of their well-known circle theorem. We find a useful characterization of such polynomials, and obtain in particular non-classical examples where the circle theorem holds. We also show that physical situations where the circle theorem holds at all temperatures are covered by the classical two-body interactions considered by Lee and Yang.

THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM. PLEASE JOIN US


Speaker: A. Giuliani, University of Rome

Date/Time/Place: April 30, 2009, 2:00pm, Hill 705

Title: The 2D Hubbard model on the honeycomb lattice

Abstract: We consider the 2D Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analiticity is proved by making use of constructive fermionic renormalization group methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the ground state. We also prove that the correlations verify a Ward Identity similar to the one for massless Dirac fermions, up to asymptotically negligible corrections and an asymmetric renormalization of the charge velocity.