Nonlinear and Statistical Physics

California Institute of Technology

1. Basic theory of the synchronization of oscillators with disparate frequencies, and the application to arrays of nanomechanical devices (funded by NSF)
2. Theory of phase noise in oscillators, and how to exploit nonlinearity to reduce phase noise (funded by DARPA)
3. Dynamics of nonlinear, disordered, composite materials, with applications to energy harvesting and vibration isolation (funded by Boeing)
4. Noise driven rare events in driven, nonequilibrium systems
5. General theory of systems far from equilibrium

I am currently seeking a graduate student to work on each of projects 1 and 2.

In the not-too-distant past I have also worked on

• Nonlinear dynamics of nanomechanical systems
• Nanoscale cantilevers as biomolecular probes
• General theory of systems far from equilibrium
• Pattern Formation
• Spatiotemporal chaos in models of experimental systems
• Coarsening in systems far from equilibrium
• Numerical simulations of experimentally realistic fluid dynamics systems showing pattern formation.
• Coupled map lattices
• Chemical instabilities
• Statistical mechanics of ideal two dimensional fluids
• Quantum limit of thermal transport, including the universal phonon conductance at low temperatures, and the effect of scattering by geometry and roughness
• Magnetic resonance force microscopy
• Spin transport

Recent Publications.