Thursday, January 29, 2015, 3:30 - 4:30 PM EST
Quenched Invariance Principle for Random Walks in Time-Dependent Random EnvironmentAbstract: In this talk we discuss random walks in a time-dependent zero-drift random environment in Z^d. We prove a quenched invariance principle under an appropriate moment condition. The proof is based on the use of a maximum principle for parabolic difference operators.
Thursday, January 29, 2015, 3:30 - 4:30 PM EST
Array Imaging Using Sparse Optimization in Discrete and Continuous SettingsAbstract: Recently there have been works where the ideas from compressive sensing are applied to the sparse imaging problem where the sources or scatterers are assumed to be sparse. In this talk we present some of these sparse optimization methods and how they are applied to the array imaging problem. We discuss the relation between the sparsity of the unknown localized sources and unique recoverability of the image in the discrete setting. Then our goal is to apply these ideas to the imaging problem in the continuous setting, where we discuss discretization error, the conditions of unique recoverability, and also the reconstruction when the uniqueness and exact reconstruction condition doesn't hold. We also present some of the related numerical simulations. This talk is based on a current work with Liliana Borcea.
Thursday, January 29, 2015, 4:00 - 5:00 PM EST
Permutohedra, Configuration Spaces and Spineless CactiAbstract: The cellular chain operad of the spineless cacti $Cact$, which is a model of the little 2-disks operad $D_2$, acts on the Hochschild cochain complex of an associative algeba, giving the associated Hochschild cohomology a Gerstenhaber algebra structure. There is a zig-zag of operadic equivalences between $D_2$ and $Cact$, but a direct morphism from one to the other is desirable.\\ In this talk, I will explain how to build a direct $S_n$-equivariant homotopy equivalence from $D_2(n)$ to $Cact(n)$ for each $n$. Though not collectively being an operadic morphism, these maps do give a partial geometric interpretation of why $D_2$ and $Cact$ are equivalent. Assuming we don't know how, I will first prove by homological and complex analytical methods that why the $3n$ dimensional $D_2(n)$ can be deformation retracted to a CW complex of the small (but not smaller) dimension $n-1$, which is the dimension of the normalized spinelss cacti $Cact^1(n)$. In fact, the above deformation retract of $D_2(n)$ is obtained by gluing $n!$ copies of permutohedra along their proper faces. If we glue more, we will get $Cact^1(n)$, which is a deformation retract of $Cact(n)$. This quotient map is a homotopy equivalence.\\ I will start by giving an accessible introduction to the configuration spaces of ordered distinct points in the complex plane and how one might start to think about their homotopy types.
Friday, January 30, 2015, 11:30 - 12:30 PM EST
Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations from Bose-Einstein CondensationAbstract: Since 1995, Gross-Pitaevskii equation (GPE) has regained considerable research interests due to the experimental success of Bose-Einstein condensates (BEC), which can be well described by GPE at ultra-cold temperature. In this talk, we will mainly focus on the dipolar GPE modeling degenerate dipolar quantum gas. The two important issues in the study of BEC, the ground states and the dynamics, will be discussed. Then we will talk about dipolar BEC in lower dimensions. In the end of the talk, I will talk about some interesting and important future research topics.
Computational & Applied Mathematics Seminar, Professor Zhangli Peng, University of Notre Dame, REC 108
Monday, February 2, 2015, 3:30 - 4:30 PM EST
Computational & Applied Mathematics Seminar, Professor Robert Lipton, Louisiana State University, REC 108
Monday, February 23, 2015, 3:30 - 4:30 PM EST
Monday, March 2, 2015, 3:30 - 4:30 PM EST
Friday, March 6, 2015, 11:30 - 12:30 PM EST
Modeling and Simulation of Porous Lithium-Ion BatteriesAbstract: In modern high energy density lithium-ion battery electrodes, the underlying topology controls the macroscopic charge, total delivered energy, and instantaneous power of the cell, particularly at high electronic current and power densities. In this presentation, we report on progress towards the development of a combined numerical+analytical framework to describe the effect of spatial distributions and morphologies of battery particle materials on the processing-induced macroscopic and position dependent performance. The state-of-the-art, theoretical and numerical limits of the field are described. Here, by proposing variational principles and spatially resolving the electrochemical fields, the effect of particle size polydispersity on the voltage behavior is analyzed. We detail such effects in structures of controlled processing and materials parameters on the macroscopic response for existing and emerging energy storage devices. The framework presented herein enables to establish relations that combine geometrical parameters such as tortuosity and reactivity of the individual (starting) components.
Monday, March 9, 2015, 3:30 - 4:30 PM EDT
Computational & Applied Mathematics Seminar, Professor John Lowengrub, University of California at Irvine, REC 108
Monday, March 23, 2015, 3:30 - 4:30 PM EDT
Computational & Applied Mathematics Seminar, Professor Oliver Goubet, University of Picardie Jules Verne, REC 108
Monday, March 30, 2015, 3:30 - 4:30 PM EDT
Computational & Applied Mathematics Seminar, Professor Zhiliang Xu, University of Notre Dame, REC 108
Monday, April 6, 2015, 3:30 - 4:30 PM EDT
Monday, April 13, 2015, 3:30 - 4:30 AM EDT
Monday, April 27, 2015, 3:30 - 4:30 PM EDT