My research explores “the nonlinear dynamics of complex systems” and broadly falls into the burgeoning field of nonlinear and statistical physics.
Most recently, I am investigating two research questions:
Can networks of nonlinear electrical oscillators be used to build an Ising machine that can function as an unconventional computing platform for combinatorial optimization problems? A proof-of-principle was established in a recent paper. Also, can we use networks of electronic self-oscillators in a similar manner?
Can we construct electrical lattices in one- and two dimensions that exhibit flat bands, and can we excite compact localized modes in them?
In recent years, I have also worked on:
Intrinsic Localized Modes (ILMs) and impurity modes in nonlinear lattices
Spontaneous synchronization of oscillator networks - both electrical and mechanical
Solitons in left-handed materials
Edge states in topologically nontrivial lattices
Pattern Formation, modulational instability, bifurcation, symmetry breaking, self-organization
I have studied - both experimentally and numerically - systems as varied as:
Nonlinear electrical transmission lines
Chains of coupled pendula
Networks of neuronal oscillators
Antiferromagnetic Spin lattices, and electronic analogs of Ising spins
Networks of electrical self-oscillators
Synchronization dynamics of coupled metronomes
In all of these systems, nonlinearity and lattice/network geometry play important roles, as they enable and guide processes of patterns formation. In some systems, frustration and ground-state degeneracy also becomes important considerations.
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.