Publications
Research
Published work, preprints, and projects-in-progress on statistical mechanics, turbulence, and complexity-stability.
- Tricritical Directed Percolation Controls the Laminar-Turbulent Transition in Pipes with Body ForcesTransition to turbulence in shear flows has been established to be a non-equilibrium phase transition. Body forces can make the transition discontinuous. Observed phenomenology can be explained by a new tricritical point near transition, enriching the phase diagram of transitional turbulence.
- Superconductor–topological insulator heterostructures are a leading route to engineered topological superconductivity, but the back-action of the topological insulator on the superconductor is far less understood than the forward proximity effect. This work asks how topological bound states at the interface modify superconducting order in the quasi-one-dimensional limit.
- In geophysical shear flows, ocean thermoclines, atmospheric boundary layers, stable density stratification suppresses vertical motion and competes with shear-driven turbulence, controlling whether turbulence is sustained or collapses to a laminar state. The laminar-turbulent transition in unstratified shear flow is now understood as a directed percolation (DP) phase transition: the turbulent fraction vanishes continuously at a critical Reynolds number with universal scaling exponents. Whether stratification shifts this critical point, modifies the exponents, or drives the transition into a different universality class entirely is an open question with both fundamental and geophysical significance.
- May’s 1972 theorem establishes that sufficiently complex random systems are generically unstable, yet evolved ecosystems systematically violate this prediction through structural mechanisms that natural selection has had billions of years to build. This project investigates whether neural networks, as another class of optimized systems, develop analogous stabilizing structure, or remain in the random-matrix regime, and what properties of the optimization process determine the difference.
For collaboration or reprint requests, email gjayasingh@ucsd.edu.