96 DS13 Abstracts IP1 ity of earthquakes may be dynamically triggered. Our work Tire Tracks, the Stationary Schr¨odinger’s Equation indicates that the granular physics of the fault core, fault and Forced Vibrations gouge, plays a key role in triggering. Because direct access to the fault is not possible, we are characterizing the granu- I will describe a newly discovered equivalence between the lar physics of triggering at laboratory scales using physical first two objects mentioned in the title. The stationary experiments and numerical simulations. Schr¨odinger’s equation, a.k.a. Hills equation, is ubiqui- tous in mathematics, physics, engineering and chemistry. Paul Johnson Just to mention one application, the main idea of the Paul Los Alamos National Laboratory, USA trap (for which W. Paul earned the 1989 Nobel Prize in
[email protected] physics) amounts to a certain property of Hill’s equation. Surprisingly, Hill’s equation is equivalent to a seemingly completely unrelated problem of “tire tracks”. As a fur- IP5 ther surprise, there is a yet another connection between Pattern Recognition with Weakly Coupled Oscilla- the “tire tracks” problem and the high frequency forced tory Networks vibrations. Traditional neural networks consist of many interconnected Mark Levi units and are thus inherently difficult to construct. In the Department of Mathematics lecture, we focus on neural network models of weakly cou- Pennsylvania State University pled oscillators with time-dependent coupling. In these
[email protected] models, each oscillator has only one connection to a com- mon support, which makes them predestinated for hard- ware implementation. Two coupling strategies are consid- IP2 ered.