Seminars and Colloquia by Series

Flame-pressure interactions and stretched laminar flame velocities: implicit simulation methods with realistic chemistry

Series
Math Physics Seminar
Time
Monday, March 26, 2012 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nadeem MalikKing Fahd University of Petroleum and Minerals
An implicit method [1, 2], TARDIS (Transient Advection Reaction Diffusion Implicit Simulations), has been developed that successfully couples the compressible flow to the comprehensive chemistry and multi-component transport properties. TARDIS has been demonstrated in application to two fundamental combustion problems of great interest. First, TARDIS was used to investigate stretched laminar flame velocities in eight flame configurations: outwardly and inwardly propagating H2/air and CH4/air in cylindrical and spherical geometries. Fractional power laws are observed between the velocity deficit and the flame curvature Second, the response of transient outwardly propagating premixed H2/air and CH4/air flames subjected to joint pressure and equivalence ratio oscillations were investigated. A fuller version of the abstract can be obtained from http://www.math.gatech.edu/~rll6/malik_abstract-Apr-2012.docx [1] Malik, N.A. and Lindstedt, R.P. The response of transient inhomogeneous flames to pressure fluctuations and stretch: planar and outwardly propagating hydrogen/air flames. Combust. Sci. Tech. 82(9), 2010. [2] Malik, N. A. “Fractional powers laws in stretched flame velocities in finite thickness flames: a numerical study using realistic chemistry”. Under review, (2012). [3] Markstein, G.H. Non-steady Flame Propagation. Pergamon Press, 1964. [4] Weis,M., Zarzalis, N., and Suntz, R. Experimental study of markstein number effects on laminar flamelet velocity in turbulent premixed flames. Combust. Flame, 154:671--691, 2008.

Local circular law for non-Hermitian random matrices

Series
Math Physics Seminar
Time
Thursday, March 22, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Anna MaltsevHausdorff Center, University of Bonn

Please Note: Note nonstandard day and time.

Consider an N by N matrix X of complex entries with iid real and imaginary parts with probability distribution h where h has Gaussian decay. We show that the local density of eigenvalues of X converges to the circular law with probability 1. More precisely, if we let a function f (z) have compact support in C and f_{\delta,z_0} (x) = f ( z-z^0 / \delta ) then the sequence of densities (1/N\delta^2) \int f_\delta d\mu_N converges to the circular law density (1/N\delta^2) \int f_\delta d\mu with probability 1. Here we show this convergence for \delta = N^{-1/8}, which is an improvement on the previously known results with \delta = 1. As a corollary, we also deduce that for square covariance matrices the number of eigenvalues in intervals of size in the intervals [a/N^2 , b/N^2] is smaller than log N with probability tending to 1.

Nodal count of eigenfunctions as index of instability

Series
Math Physics Seminar
Time
Monday, February 27, 2012 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gregory BerkolaikoTexas A&M Univ.
Zeros of vibrational modes have been fascinating physicists for several centuries. Mathematical study of zeros of eigenfunctions goes back at least to Sturm, who showed that, in dimension d=1, the n-th eigenfunction has n-1 zeros. Courant showed that in higher dimensions only half of this is true, namely zero curves of the n-th eigenfunction of the Laplace operator on a compact domain partition the domain into at most n parts (which are called "nodal domains"). It recently transpired that the difference between this "natural" number n of nodal domains and the actual values can be interpreted as an index of instability of a certain energy functional with respect to suitably chosen perturbations. We will discuss two examples of this phenomenon: (1) stability of the nodal partitions of a domain in R^d with respect to a perturbation of the partition boundaries and (2) stability of a graph eigenvalue with respect to a perturbation by magnetic field. In both cases, the "nodal defect" of the eigenfunction coincides with the Morse index of the energy functional at the corresponding critical point. Based on preprints arXiv:1107.3489 (joint with P.Kuchment and U.Smilansky) and arXiv:1110.5373

Positive commutator methods for unitary operators

Series
Math Physics Seminar
Time
Monday, February 6, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rafael Tiedra de AldecoaCatholic University of Chile
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Some applications for Floquet operators and for cocycles over irrational rotations will be presented.

Symmetry results for Caffarelli-Kohn-Nirenberg inequalities

Series
Math Physics Seminar
Time
Monday, January 30, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael LossSchool of Mathematics, Georgia Tech
This talk is concerned with new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities in a range of parameters for which no explicit results of symmetry have previously been known. The method proceeds via spectral estimates. This is joint work with Jean Dolbeault and Maria Esteban.

Parallel heat transport in reverse shear magnetic fields

Series
Math Physics Seminar
Time
Monday, January 23, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel BlazevskiUniversity of Texas
I will discuss local and nonlocal anisotropic heat transport along magnetic field lines in a tokamak, a device used to confine plasma undergoing fusion. I will give computational results that relate certain dynamical features of the magnetic field, e.g. resonance islands, chaotic regions, transport barriers, etc. to the asymptotic temperature profiles for heat transport along the magnetic field lines.

On the behavior at infinity of solutions to difference equations in Schroedinger form

Series
Math Physics Seminar
Time
Tuesday, December 6, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Lilian WongSoM, Georgia Tech
We offer several perspectives on the behavior at infinity of solutions of discrete Schroedinger equations. First we study pairs of discrete Schroedinger equations whose potential functions differ by a quantity that can be considered small in a suitable sense as the index n \rightarrow \infty. With simple assumptions on the growth rate of the solutions of the original system, we show that the perturbed system has a fundamental set of solutions with the same behavior at infinity, employing a variation-of-constants scheme to produce a convergent iteration for the solutions of the second equation in terms of those of the original one. We use the relations between the solution sets to derive exponential dichotomy of solutions and elucidate the structure of transfer matrices.Later, we present a sharp discrete analogue of the Liouville-Green (WKB) transformation, making it possible to derive exponential behavior at infinity of a single difference equation, by explicitly constructing a comparison equation to which our perturbation results apply. In addition, we point out an exact relationship connecting the diagonal part of the Green matrix to the asymptotic behavior of solutions. With both of these tools it is possible to identify an Agmon metric, in terms of which, in some situations, any decreasing solution must decrease exponentially. This is joint work with Evans Harrell.

A microscopic derivation of Ginzburg-Landau theory

Series
Math Physics Seminar
Time
Tuesday, November 1, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rupert FrankDept. of Math, Princeton University
We describe the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. The talk is based on joint work with C. Hainzl, R. Seiringer and J. P. Solovej.

The analityicity transition in Frenkel-Kontorova models and XY models in 1-D

Series
Math Physics Seminar
Time
Tuesday, October 25, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rafael De la LlaveSoM Georgia Tech
We consider several models from solid state Physics and consider the problem offinding quasi-periodic solutions. We present a KAM theorem that showsthat given an approximate solution with good condition numbers, onecan find a true solution close by. The method of proof leads tovery efficient algorithms. Also it provides a criterion for breakdown.We will present the proof, the algorithms and some conjectures obtainedby computing in some cases. Much of the work was done with R. Calleja and X. Su.

New Exciting Approaches to Particle Scattering Amplitudes

Series
Math Physics Seminar
Time
Wednesday, September 28, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Marcus Nanotech Conference
Speaker
Henriette ElvangPhysics Department, University of Michigan

Please Note: Hosted by Predrag Cvitanovic, School of Physics

Particle scattering processes at experiments such as the Large Hadron Collider at CERN are described by scattering amplitudes. In quantum field theory classes, students learn to calculate amplitudes using Feynman diagram methods. This is a wonderful method for a process like electron + positron -> muon^- + muon^+, but it is a highly challenging for a process like gluon+gluon -> 5 gluons, which requires 149 diagrams even at the leading order in perturbation theory. It turns out, however, that the result for such gluon scattering processes is remarkably simple, in some cases it is just a single term! This has lead to new methods for calculating scattering amplitudes, and it has revealed that amplitudes have a surprisingly rich mathematical structure. The applications of these new methods range from calculation of processes relevant for LHC physics to theoretical explorations of quantum gravity. I will give a pedagogical introduction to these new approaches to scattering theory and their applications, not assuming any prior knowledge of quantum field theory or Feynman rules.

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