My research explores “the nonlinear dynamics of complex systems” and broadly falls into the burgeoning field of nonlinear and statistical physics. In recent years, I have been interested in:
- Intrinsic Localized Modes in Nonlinear Lattices
- Spontaneous Synchronization of Oscillator Arrays
- Pattern Formation, Instability, Bifurcation, Symmetry Breaking, Self-Organization
- Solitons, Skyrmions, Chimera states
I have studied (both experimentally and numerically) systems as varied as:
- nonlinear electrical transmission lines
- chains of coupled pendula
- networks of neuronal oscillators
- spin lattices
- networks of electrical self-oscillators
In all of these systems, nonlinearity and lattice/network geometry play important roles, as they enable and guide processes of patterns formation. Broadly speaking, I aim to experimentally characterize emergent patterns, study their onset and boundaries in parameter space, and to formulate mathematical models which allow a numerical and/or analytical exploration. Ideas from the field of dynamical systems (such as fixed points, stability, bifurcation, hysteresis) are essential in this endeavor.
Other interests include the Calculus of Variations, magnetism and spin resonance, microwave spectroscopy, medical imagining techniques, and issues within the philosophy of science.