Talks & presentations

This talk explores how body forces alter the canonical picture of the laminar–turbulent transition in pipe flow. By extending the standard framework of directed percolation to include external forcing, we identify a tricritical regime that interpolates between continuous and discontinuous transitions. The resulting phase diagram reveals how sufficiently strong body forces induce metastability, coexistence, and relaminarization—features observed in curved and centrifugal pipes. The analysis provides a unifying theoretical basis for diverse experimental and numerical observations of forced transitional turbulence.

The laminar-turbulent transition in straight pipes is believed to occur through a continuous non-equilibrium phase transition in the directed percolation universality class. However, in curved pipes or in the presence of body forces it is possible to observe a discontinuous transition and other phenomenology which seem inconsistent with the emerging consensus. Here, we consider the perturbing effects of body forces and incorporate them into a minimal Landau theory of the transition. We calculate the phase diagram as a function of Reynolds number and body force strength, and show that above a threshold strength of the latter, there is a tricritical point which accounts for the observed discontinuity behavior, including spatially heterogeneous states. Our results are consistent with recent experiments in centrifugal pipes and direct numerical simulations of heated flows.

A talk on the low-rank hypothesis of complex systems: how high-dimensional complex systems — ecosystems, neural networks, social structures — exhibit effective low-rank behavior, enabling dimension reduction and interpretable dynamics.

Classification of order parameters within a generalized BCS theory, and the nature of physical observables for different pairing symmetries.

A two-part seminar. The first session derived the bosonization identities; the second presented a physical and heuristic view of the technique. Applications included calculating conductance in an impurity-ridden Luttinger wire via the renormalization group, illustrating the new physics that emerges from reduced dimensions, interactions, and the mesoscopic nature of transport.

Invited by the course instructor to present to the non-linear dynamics class: the notion of fractional dimension, methods to characterize the dimension of a fractal, and the relevance of fractals to stochastic processes.