Department of Mathematics
Applied Mathematics Seminar, Spring 2015

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

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

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

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

March 13
Speaker: Vladimir Druskin, Schlumberger
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 GŁttel and Rob Remis.

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

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

April 20 (reserved)
Speaker: TBA
Title: TBA

Seminar organizer: Yekaterina Epshteyn (epshteyn (at)

Past lectures: Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.

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