Brown Bag Seminar
The brown bag seminar is a weekly meeting organized by and for graduate students. The goal of the brown bag is to encourage students to practice presenting their work by giving talks to each other in a casual setting.
SIAM Research Communication, Competitions, and Conversations Roundtable
AbstractFeel free to come to socialize, eat, and share/develop ideas about publicizing/promoting research as well as the in-and-outs of finding an advisor and getting into research (for you first- and second-years). We will brainstorm and talk with each other about • communicating research to a general audience and competing in the Elevating Mathematics Video Competition or the UA Grad Slam, • how to find an advisor to work with for RTG and beyond, • or anything that's on your mind about research, quals, courses, etc.
What's new in conductivity imaging
DateFriday, February 8, 2019 - 12:00pm
AbstractSince the 1980s, significant attention has been given in biomedical imaging towards mapping the electrical conductivity of tissue. The conductivity map must be mathematically reconstructed from some set measurements by solving an inverse problem. Recent work has focused on so-called hybrid methods, which take advantage of the interactions between different types of physical fields. In this talk, I will give a cursory introduction to some of the mathematical models seen in hybrid methods for conductivity imaging as well as their associated inverse problems. If time permits, I will also present the results of some numerical simulations from work I completed on one such modality known as magneto-acousto-electrical tomography.
Resonance States and Non-Hermittian Quantum Mechanics: An Application to Nano-Tips
DateFriday, February 15, 2019 - 12:00pm
AbstractThe resonance states or quasi stationary states have been known from scattering theory of quantum systems. These states are like stationary states but with a finite life time after which they will not remain localized. They arise in various problems and we can consider them as the eigen functions of a non-Hermittian Hamiltonian. Using these states to describe the time evolution of the system can be of great advantage over the standard Hermittian formalism in some classes of problems. In addition to providing us with a better understanding of physics of the system in consideration, it is sometimes the only possible way to computationally model the system. In my research, I am solving a simplified model for metallic nano-tips using these resonance states. In this talk, I will show the power of this formalism in attacking some problems including our simplified model, and then I briefly talk about the current state of my research.
Drive-Based Motivation for Coordination of Limit Cycle Behaviors
DateFriday, February 22, 2019 - 12:00pm
AbstractNavigation is often be considered a prototypical behavior for a robotic system. Constructing robots capable of complex behaviors requires developing a method for switching among possible behaviors, for example using a hybrid automaton. Recent work has developed an alternative approach using continuous dynamical systems that use an internal drive state to select the desired behavior. In one particular result, authors developed drive dynamics that result in trajectories where the robot repeatedly flows to one point attractor and then another, yielding a limit cycle where the robot patrols between two points. A further level of complexity arises when one seeks to create a system that switches between these basic limit cycles instead of the original point attractors. This work outlines the problem using the recently-developed drive-based dynamical framework. As a proof-of-concept we demonstrate the existence of an attracting set consisting of orbits that repeatedly flow between two canonical limit cycles (e.g., Hopf oscillators). This attracting set connecting limit cycle behaviors arises from a bifurcation depending on a family of parameters which is analogous to the bifurcation that produces the limit cycle connecting two point-attractor behaviors in previously-published system. Implications and next-steps in the case of arbitrary limit cycles are discussed.