Applied Mathematics Seminar, Spring 2015

## Mondays 3:55 PM - 5:00 PM, LCB 219

• This seminar can be taken for credit: Students can get 1-3 credits by registering to the Applied Math Seminar class Math 7875 Section 010 for Spring 2015. Grading is based on attendance and giving at least one talk presenting an applied-mathematics paper (not necessarily your own). Student talks will be appropriately labeled to distinguish them from visitor talks. The seminar organizer is available to review your slides, for dry-runs etc.
• Please direct questions or comments about the seminar (or its class) to Yekaterina Epshteyn (epshteyn (at) math.utah.edu)
• Talks are announced through the applied-math mailing list. Please ask the seminar organizer for information about how to subscribe to this list.

January 23. Note: 3:55pm - 5:00pm, Room LCB 225
Speaker: Alexander Mamonov, Schlumberger
Title: Reduced order models for seismic full waveform inversion.
Abstract:We present a framework for the numerical solution of the seismic full waveform inversion (FWI) problem using the reduced order models (ROMs). In FWI one determines the spatial distribution of the acoustic or elastic properties of the subsurface from the surface or well-bore measurements of the seismic data induced by sources. In our approach the ROM is a projection of the acoustic or elastic PDE operator on the subspace spanned by the snapshots of the solutions to the forward problem. The ROM can be found directly from the measured time domain seismic data. The use of the ROM in inversion is twofold. First, after the transformation to the block tridiagonal (finite difference) form the ROM misfit can be used as an objective functional for optimization. Such functional is more convex than the conventional data misfit and thus is less prone to common issues like abundant local minima (cycle skipping), multiple reflection artifacts, etc. Second, if a background kinematic model is available the projected PDE operator can be backprojected to obtain a seismic image directly. This leads to a non-linear migration algorithm that recovers not only the locations of discontinuities (reflectors) but also their relative strength, the process known as the true amplitude migration.

Joint work with V. Druskin and M. Zaslavsky.

January 26 (Student Talk)
Speaker: Predrag Krtolica, Department of Mathematics, University of Utah
Title: Compatibility Conditions in Discrete Structures
Abstract:The talk will be about the analysis of compatibility conditions of 2-dimensional hexagonal frameworks, which, in the limit, lead to the continuum compatibility condition, suggesting the equivalence. This fact has many applications, as it is much easier to study brittleness of materials on a discrete model than on a continuum.

In addition, I will briefly talk about the statics of hexagonal grids, assuming infinitesimal deformation, and their possible applications.

February 2
Speaker: Ching-Shan Chou, Department of Mathematics, Ohio State University
Title: Computer Simulations of Yeast Mating Reveal Robustness Strategies for Cell-Cell Interactions
Abstract: Cell-to-cell communication is fundamental to biological processes which require cells to coordinate their functions. A simple strategy adopted by many biological systems to achieve this communication is through cell signaling, in which extracellular signaling molecules released by one cell are detected by other cells via specific mechanisms. These signal molecules activate intracellular pathways to induce cellular responses such as cell motility or cell morphological changes. Proper communication thus relies on precise control and coordination of all these actions.

The budding yeast Saccharomyces cerevisiae, a unicellular fungi, has been a model system for studying cell-to-cell communication during mating because of its genetic tractability. In this work, we performed for the first time computer simulations of the yeast mating process. Our computational framework encompassed a moving boundary method for modeling cell shape changes, the extracellular diffusion of mating pheromones, a generic reaction-diffusion model of yeast cell polarization, and both external and internal noise. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the alpha-factor protease Bar1, and the regulation of sensing sensitivity; all were consistent with data in the literature. In summary, we constructed a framework for simulating yeast mating and cell-cell interactions more generally, and we used this framework to reproduce yeast mating behaviors qualitatively and to identify strategies for robust mating.

February 9
Speaker: Hyeonbae Kang, Department of Mathematics, Inha University
Title: Spectral theory of Neumann-Poincare operator and applications
Abstract:The Neumann-Poincare (NP) operator is a boundary integral operator which arises naturally when solving boundary value problems using layer potentials. It is not self-adjoint with the usual inner product. But it can symmetrized by introducing a new inner product on $H^{-1/2}$ spaces using Plemelj's symmetrization principle. Recently many interesting properties of the NP operator have been discovered. I will discuss about this development and various applications including solvability of PDEs with complex coefficients and plasmonic resonance.

February 23
Speaker: Lajos Horvath, Department of Mathematics, University of Utah
Title: Functional Data Analysis with Some Applications
Abstract:TBA

February 27, Special Joint Time Series/Stochastics/Applied Math Seminar

Note: Time 3pm, Room LCB 219

Speaker: Alexander Aue, Department of Statistics, University of California, Davis
Title: TBA
Abstract:TBA

March 9
Speaker: Jay Gopalakrishnan, Department of Mathematics, Portland State University
Title: TBA
Abstract:TBA

March 13
Title: Reduced order models for large scale wave problems
Abstract:Reduced order models approximate transfer functions of large-scale linear dynamical systems by small equivalent ones. Their matrices can be geometrically interpreted as finite-difference operators discretized on so-called optimal grids, a. k. a. spectrally matched grids or finite-difference Gaussian quadrature rules. In this talk we discuss some recent applications of this powerful approach to numerical solution of hyperbolic problems in the time and frequency domains. They include optimal discretization of perfectly matched layers and multi-scale elastic wave propagation. Time permitting, I will discuss another recent model reduction approach for wave propagation in unbounded domains, based on scattering resonance representation.

Contributors: Mikhail Zaslavsky; Alex Mamonov; Leonid Knizhnerman; Stefan Güttel and Rob Remis.

March 23
Speaker: Becca Thomases, Department of Mathematics, University of California, Davis
Title: TBA
Abstract:TBA

March 30
Speaker: Maxence Cassier, Department of Mathematics, University of Utah
Title: The limiting amplitude principle in a medium composed of a dielectric and a metamaterial
Abstract:TBA

April 13 (Student Talk)
Speaker: Ornella Mattei, Visiting Department of Mathematics, University of Utah
Title: Variational formulations for the linear viscoelastic problem in the time domain
Abstract:TBA

April 20 (reserved)
Speaker: TBA
Title: TBA
Abstract:TBA

Seminar organizer: Yekaterina Epshteyn (epshteyn (at) math.utah.edu).

155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, T:+1 801 581 6851, F:+1 801 581 4148