Schedule-at-a-Glance

29 PRIMA 2013 Abstractssolid substrate and the wetting transition of a droplet ona rough surface will be presented.Multiscale methods for wave propagationproblemsOlof RunborgKTH Royal Institute of Technology, Swedenolofr@nada.kth.seMultiscale wave propagation problems are computationallycostly to solve by traditional techniques because thesmallest scales must be represented over a domain determinedby the largest scales of the problem. We considernumerical methods for multiscale wave propagation inthe framework of the heterogeneous multiscale method.These methods couple simulations on macro- and microscalesfor problems with rapidly oscillating coefficients.The complexity is significantly lower than that of traditionaltechniques with a computational cost that is essentiallyindependent of the microscale. In this talk weshow analysis of how the method works in the long timecase, where the macroscale solution show dispersive behavior,and how the method, although designed for waveproblems, can be beneficial for solving multiscale ellipticproblems.Modeling and simulation of three-componentflows on solid surfaceXiao-Ping WangHong Kong University of Science and Technology, HongKong, Chinaxpwhk63@gmail.comWe propose a phase field model for the study of threecomponentimmiscible flows with boundary. The modelis a generalization of the two-component model. We firststudy certain consistency conditions for the forms of thebulk free energy and surface energy. We then developan adaptive mesh refinement(AMR) technique to solvethe system in order to improve the efficiency of the problem.Several numerical results are given, including theliquid lens spreads between two phases, the buoyancydrivendroplet through a fluid-fluid interface, spreadingof a compound droplet on a stationary substrate, andshear flows of a compound droplet on a channel.A path way based mean field model for E. colichemotaxisXu YangUniversity of California, SantaBarbara, USAxuyang@math.ucsb.eduIn this talk, we give a mathematical derivation of apathway- based mean-field model for E. coli chemotaxisbased on the moment closure in kinetic theory. The pathwaybased model incorporate the most recent intracellularchemical dynamics. The derived moment system,under some assumptions, gets to the chemotaxis modelproposed in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys.Rev. Lett., 109 (2012), 048101], especially an importantphysical assumption made in which can be understoodexplicitly in this new moment system. We obtain theKeller-Segal limit by considering the moment system inthe regime of long time and strong tumbling rate. Numericalexperiments are presented to show the agreementof the moment system with (individual based) signalingpathway- based E. coli chemotaxis simulator ([L. Jiang,Q. Ouyang and Y. Tu, PLoS Comput. Biol., 6 (2010),e1000735]).Generalized Irving-Kirkwood formula for thecalculation of continuum quantities in moleculardynamics modelsZhijian YangWuhan University, Chinazjyang.math@whu.edu.cnContinuum mechanics quantities can be computed frommolecular dynamics (MD) models based on the classicalIrving-Kirkwood (IK) formalism. Practical implementationsof IK formulas involve a spatial averaging usinga smooth kernel function. The obtained results usuallyneed to be further processed to reduce the fluctuation,e.g., by ensemble or time averaging. In this talk the IKformalism is extended to systematically incorporate bothspatial and temporal averaging into the expression of continuumquantities. We will present the results both inLagrangian and Eulerian coordinates.Special Session 15Number Theory and Representation TheoryOn a classification of irreducible modulo p representationsof p-adic groupsNoriyuki AbeHokkaido University, Japanabenori@math.sci.hokudai.ac.jpBarthel-Livné introduced the notion of modulo p supersingularrepresentations of GL 2 . It is generalized to splitgroups by Herzig and to connected reductive groups byHenniart and Vignéras. In this talk, we discuss about aclassification of irreducible modulo p representations interms of supersingular representations.This is joint work with G. Henniart, F. Herzig and M.-F.Vignéras.Parity sheaves on the affine Grassmannianand the Mirković–Vilonen conjecturePramod N. AcharLouisiana State University, USApramod@math.lsu.eduThe geometric Satake equivalence gives a realization ofthe category of representations of a split reductive algebraicgroup over any field in terms of perverse sheaves onthe affine Grassmannian for the dual group. In this setting,Mirković and Vilonen conjectured that the perversesheaves corresponding to Weyl modules should enjoy aparity-vanishing property, similar to that of l-adic intersectioncohomology complexes. This conjecture has nowbeen proved (with a few exceptions in small characteristics)in joint work with Laura Rider. I will discuss theingredients in the proof, along with potential applicationsof our techniques to questions in modular representationtheory.Rectifiers and the local Langlands correspondenceMoshe AdrianUniversity of Utah, USAmadrian@math.utah.eduAbstract: In this talk, I will recall the notion of a rectifieras in the work of Bushnell/Henniart in the localLanglands correpsondence for GL(n). I will then proposea definition for rectifier for general unramified groups G.I will describe rectifiers in this setting, and show that ourdefinition agrees with Bushnell/Henniart’s in the depthzero case. This is joint work with David Roe.Uniform in p estimates for orbital integralsJulia GordonUniversity of British Columbia, Canadagor@math.ubc.ca