Associate Professor of
Room 104, 182 George Street
Phone: +1 401 863 3793
Ph.D, Brown University, 2001
I work on dynamical systems and partial differential equations arising in fluid mechanics, materials science and physical chemistry. My recent has been on scaling laws that appear in many guises in these areas. Our goal is to rigorously pin down these deceptively simple laws with methods from analysis and probability theory.
My formal education is in applied mathematics (Ph.D, Brown University, 2001), theoretical and applied mechanics (MS, Cornell University, 1996), and mechanical engineering (B.Tech, IIT Kharagpur, 1994). This was followed by temporary appointments at the Max Planck Institute for Mathematics in the Sciences, Leipzig (2000-2001), and the University of Wisconsin, Madison (Van Vleck Assistant Professor, 2001-2004). I returned to Brown as an Assistant Professor in July, 2004. I have also spent short stints at the University of Bonn, the University of Crete, and the IMA at the University of Minnesota.
The ideas of scaling and self-similarity are central organizing principles in applied mathematics and condensed matter physics. Famous examples are the central limit theorem in probability, the Kolmogorov spectrum in fully developed turbulence, coarsening of domains in the spinodal decomposition of alloys and polymer melts, and the roughening of growing interfaces. Yet, these apparently simple`laws' can defy rigorous understanding, and are often macroscopic manifestations of deeper microscopic mechanisms. My goal is a rigorous understanding of `dynamic scaling laws' in a few carefully chosen examples in fluid mechanics, materials science and physical chemistry. The emphasis is on applied analysis-- to prove theorems (motivated by experiments and numerics) that explain scaling behavior universality.
My work in the past five years was focused on two projects: (a) the long time behavior of free surface instabilities (for example, the Rayleigh-Taylor instability observed at the launch of a rocket, or in the supernova in the Crab Nebula), (b) models of coalescence, describing for instance the formation of smoke, dust and haze. A striking result has been the discovery of the fundamental utility of classical methods in probability for the description of such scaling dynamical systems. This has led to a basic framework that underlies a class of apparently unrelated problems. Current work is focused on rigorous models of turbulence and free boundary problems in fluid mechanics, models of domain coarsening in materials science, and models of conformation changes in polymer chemistry.
Clay Mathematics Institute Emissary, Aug. 2000,
Stella Dafermos Prize, Brown University, May 2000,
Wonderlic Fellowship, Brown University, 1998-1999
NSF Career Award, 2008
American Mathematical Society (AMS)
Society for Industrial and Applied Mathematics (SIAM)
Ordinary and Partial Differential Equations, Methods of Applied Mathematics.