Theory, experiments, and numerical simulations of stochastic wave propagation, with a view towards applications in material science, quantum chaos, and seismology.
Experiments in Slow Dynamic Nonlinear Elasticity. -- with J Y Yoritomo, J Popovics and K Dahmen (UIUC). We use reverberant ultrasound to probe a universal but perplexingly peculiar non-equilibrium phenomenon originating at the internal surfaces of heterogeneous solids and manifesting in large scale behavior. These structures will exhibit an apparent loss of stiffness after even modest applied strains, as if the strain did damage. Yet the stiffness is seen to then recover, like log(t), quickly at first and then steadily slower, on times from msec to years. The phenomenon is observed widely, from natural rocks to cements to cracked glass, and from the laboratory scale to the seismic. Neither the loss of stiffness nor the universal recovery is understood. In a search for the microphysical basis, we employ MHz reverberant ultrasound to monitor the changing stiffness while controlling external parameters.
Mechanical Analog for a Random Laser with J P Coleman (UIUC) Numerical simulations of phase transitions among nonlinear auto-oscillators coupled through a wave bearing substrate show most of the features of optical lasing, including spectral purity and greatly enhanced luminescence.
Statistical Elastodynamics of Large Structures and Quantum Chaos 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.
Seismic Noise Correlations (with M Campillo, University Grenoble-Alpes, and X Song UIUC Geology) Recent attention to diffuse fields in seismology, inspired by (scaled by a factor of 10^-6) laboratory experiments done here is leading to new methods for probing the interior of the earth in which the seismic Green function is retrieved from noise. We observe and exploit mesoscopic residual correlations in nominally incoherent multiply scattered elastic wave fields, on the moon, in the seismic coda after earthquakes, in local geophone noise, and in long period world-wide background seismicity.
Graduate Research Opportunities
We have an opening for a student in an experimental/theoretical PhD research project funded by the DOE. The new student would build on previous work in the group using novel methods with reverberant ultrasound to probe a universal but perplexingly peculiar phenomenon originating at the internal surfaces of heterogeneous solids. The project is mostly experimental, but includes theory for the modeling of the multiply scattered ultrasound, and theory for the phenomenon itself. Laboratory techniques include design of the experiments and digital RF signal processing.
Students with interest in complex classical waves and/or nonlinear material properties, are encouraged to contact Prof. Weaver for more information.