Home


Research


Publications


CV



Spontaneous Stochasticity

Physicists are used to statistical description of systems with many degrees of freedom. Here the statistical aspect reflects our limited knowledge about the behavior of the system. We learned to cope with this limited knowledge by realizing that most of the information about the system is irrelevant for describing the macroscopic features. This is generally understood in the framework of renormalization group. However, recently, an understanding has crystallized that there is a fundamentally different type of deterministic system that necessitates statistical description. Here the statistical nature emerges not from the lack of an observer's knowledge about the system, but as an intrinsic feature of the near-singular dynamics. This phenomenon has been dubbed spontaneous stochasticity. I work with Gregory Eyink, Alexei Maylibaev and Nigel Goldenfeld to further our understanding of spontaneous stochasticity. It is our hope that renormalization group hides the keys to this exciting phenomenon, and we made the first steps towards implementing renormalization group program by providing the analysis of a toy model.

Eyink, G.L, Bandak, D. Renormalization group approach to spontaneous stochasticity (2020) Phys. Rev. Res., 2, 043161. [link]

Friction Factor

One of the most concise ways to show that we do not have a good grasp on the problem of hydrodynamic turbulence is the following. Imagine you want to transport viscous incompressible fluid using a slightly rough pipe of a certain length and diameter. What is the pressure drop you need to apply to ensure the fluid is transported with a desired rate? Provided the fluid velocity is faster than a certain threshold, we do not have a satisfying answer to that question. The reason why is that such flow is turbulent, and therefore chaotic and unpredictable. Important strides towards answering this question have been made by my advisor Nigel Goldenfeld, who showed that such flows are closely analogous to critical phenomena. We hope to deepen our understanding of such turbulent flows using the methods developed to describe critical phenomena.