Applied Mathematics Seminar, Fall 2014

## Mondays 3:55 PM - 5:00 PM, LCB 222

• 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 Fall 2014. 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.

September 19, Joint Stochastics/Applied Math/Math Biology Seminar, Note Time 3:00 - 4:00 pm, Room LCB 219
Speaker: Peter Bossaerts, Finance Department, University of Utah
Title: Human reaction to extreme events and its biological foundations
Abstract:The talk will discuss recent work on how humans react to extreme events. A deeper understanding of human reactions requires proper definition of an extreme event (linking it to the concept of an outlier in statistical analysis) and its nature (distinguishing between leptokurtic and platykurtic settings, and whether the outlier is transient or reflects more persistent changes). Evidently, the noradrenergic system in the human brain provides crucial support for tracking outliers, while signals in the anterior insula allow humans to distinguish between transient and fundamental outliers. Overall, human reaction to outliers that signal fundamental changes is better adapted than reaction to transient outliers. The latter type of outlier is ubiquitous in modern large-scale social institutions, however, such as financial markets, internet and air traffic.

September 22
Speaker: Tatyana Sorokina, Department of Mathematics, Towson University
Title: Dimension of splines and intrinsic supersmoothness
Abstract:The phenomenon, known assupersmoothness" was first observed for bivariate splines and attributed to the polynomial nature of splines. Using only standard tools from multivatiate calculus it is easy to show that if we continuously glue two smooth functions along a curve with a corner", the resulting continuous function must be differentiable at the corner, as if to compensate for the singularity of the curve. Moreover, locally, this property characterizes non-smooth curves. We generalize this phenomenon to higher order derivatives. Additionally, we show how supersmoothness helps to find dimension of multivariate splines.
This talk is a part of the special session of CMDS13.

September 29
Speaker: Graeme Milton, Department of Mathematics, University of Utah
Title: The searchlight effect in hyperbolic media
Abstract:Hyperbolic media in which the dielectric tensor has both positive and negative eigenvalues have been shown to defeat the diff raction limit, and allow features at very small wavelengths to be resolved as demonstrated through hyperlenses. Even in quasistatics the underlying equation resembles a wave equation. Whereas a circular hole in a dielectric media has a simple dipolar field around it, we will see that a circular hole in an almost lossless hyperbolic media, has surrounding quasistatic fields which diverge along characteristic lines tangent to the hole, and which have finite total energy absorption along these lines, even as the loss in the media tends to zero. In a hyperbolic medium a dipole with small polarizability can dramatically influence the dipole moment of a distant polarizable dipole, if it is appropriately placed. We call this the searchlight e ffect, as the enhancement depends on the orientation of the line joining the polarizable dipoles and can be varied by changing the frequency. For some particular polarizabilities the enhancement can actually increase the further the polarizable dipoles are apart, like the way quarks interact more strongly the further they are apart.
Graeme Milton, R.C.McPhedran, A. Sihvola

October 6
Speaker: Maxence Cassier, Department of Mathematics, University of Utah
Title: Analysis of two time-dependent wave propagation phenomena: 1) Space-time focusing on unknown scatterers; 2) Limiting amplitude principle in a medium composed of a dielectric and a metamaterial.
Abstract:This talk consists of two independent parts related to my Ph.D research thema. In the first one, we are motivated by this challenging question: in a propagative medium which contains several unknown scatterers, how can one generate a wave that focuses selectively on one scatterer not only in space, but also in time? In other words, we look for a wave that "hits hard at the right spot". The technique proposed here is based on DORT method (French acronym for Decomposition of the Time Reversal Operator) which leads to space focusing properties in the frequency domain. The second part is devoted to a transmission problem between a dielectric and a metamaterial. The question we consider here is the following : does the limiting amplitude principle hold in such a medium? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of an infinite two-layered medium composed of a dielectric and a particular metamaterial (Drude model).

October 20
Speaker: Andrejs Treibergs, Department of Mathematics, University of Utah
Title: Which Electric Fields are Realizable in Conducting Materials?
Abstract:The usual problem is that we are given the conductivity $\sigma$ and seek the electric field in the material, $\nabla u$, by solving the conductivity equation for the potential $$\operatorname{div}(\sigma\nabla u) = 0.$$ We ask instead, given a field $\nabla u$, is it possible to find a conductivity scalar or matrix $\sigma$ to satisfy the conductivity equation? In other words, is the field is realizable? We show periodic fields are isotropically realizable by solving a first order PDE, although the conductivity may not be periodic. We can characterize fields that are isotropically realizable by a periodic conductivity. We also give conditions for periodic realizability by matrix conductivities.

This is joint work with Marc Briane and Graeme Milton.

October 27
Speaker: Elena Cherkaev, Department of Mathematics, University of Utah
Title: TBA
Abstract:TBA

November 3
Speaker: Braxton Osting, Department of Mathematics, University of Utah
Title: TBA
Abstract:TBA

November 17
Speaker: Benjamin Webb, Department of Mathematics, Brigham Young University
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