## Undergraduate Research Opportunities

Design and analysis and numerical simulations of self-synchronizing sets of mechanical auto-oscillators, eccentric DC motors on plates, with a view towards emulation of lasing.

Large scale numerical simulations of stochastic seismic wave propagation.

## Research Statement

**Ultrasonic Analog for a Random Laser** (with colleagues Oleg Lobkis, UIUC, and Alexey Yamilov, U Missouri) — We report measurements on ultrasonic systems analogous to random lasers. An auto-oscillating, and spontaneously emitting, piezoelectric device is found to emit more energetically when stimulated by an incident wave field. The emission is at the same frequency as the stimulating field, and with a phase relation corresponding to super radiance. Over a wide range of parameters we observe narrow single emission lines, sensitivity to linear cavity properties, complex multi-mode emissions, and line narrowing. Line widths are more narrow than we can measure. Theory suggests they have Schawlow–Townes widths as low as 10^{-9} Hz. Systems of several such oscillators are observed to self-organize into a coherent state with power emission that rises faster than the first power of the number of oscillators.

**Statistical Elastodynamics of Large Structures and Quantum Chaos** (with Oleg Lobkis, UIUC, and Thomas Seligman, Centro de Ciencias Fisicas, UNAM) — Numerical simulations, analytic theory and laboratory measurements are used to study the statistics of linear waves in complex systems. Particular attention is paid to wave energy density (or probability for quantum waves), and its mean flow and fluctuations. We seek methods to predict mean flow and fluctuations over long times, based on information in ray optics or direct numerical simulations over short times.

**Seismic Noise Correlations** (with M Campillo, B van Tiggelen and E Larose, U Joseph Fourier, and O Lobkis UIUC and X Song UIUC Geology) — Recent attention to diffuse fields in seismology, inspired in part by laboratory experiments done at UIUC, is leading to new methods for probing the interior of the earth. We observe and exploit mesoscopic residual correlations in nominally incoherent multiply scattered elastic wave fields, on the moon, in the seismic coda, in local geophone noise, and in long period world-wide background seismicity.

**Determination of Thin-Film Interfacial Properties by Laser Generated Stress Waves** (with N Sottos UIUC MatSE) — We investigate, both theoretically and experimentally, the generation of high-amplitude compression waves due to the sudden deposition of heat from a YAG laser pulse in a thin metallic film between two solids. The resulting pulse, with a duration of 10 nsec and a strain amplitude of the order of 1%, is measured using laser interferometry. Particular issues of concern include the effects of nonlinearity in the wave propagation and the corresponding development of shocks, and mode conversion at oblique interfaces with consequent generation of high-amplitude shear waves. Each of these effects is critical in ultimate application to the testing, by high-speed stress loading, of thin-film coatings.

## Graduate Research Opportunities

Theory and large scale numerical simulations of stochastic wave propagation with a view towards applications in seismology, in particular the retrieval of information on the earth's structure and its changes from analysis of seismic noise correlations.