
RESEARCH INTERESTS: nonequilibrium statistical physics
biophysics (population genetics) physics of algorithms (statistical physics approach to computer science)
soft condensed matter physics (glassy systems) fluid dynamics (especially turbulence) mathematical physics
My current research is on the interfaces of biology, physics and computer science. One of my main scientific goals is to understand systems far from equilibrium in their diversity and unity. I use a variety of analytical and numerical tools to study stochastic and dynamical systems driven out of equilibrium.
I worked on several problems of nonequilibrium statistical physics and theory of turbulence. Such as clustering of particles due to compressibility and inertia, fluctuation theorems, developing faster Monte Carlo algorithms etc. I focus on problems of in the realm of nonequilibrium statistical physics. These include disordered systems (glasses), population dynamics, physics of algorithms (interface of statistical physics and computer science), theory of turbulence and population genetics. Currently I am working on: glassy systems (with Matthieu Wyart), advancing parallel tempering algorithms (with Jon Machta), inference from geneological trees (with Boris Shraiman).

Some of the topics that I have worked on

Emergence of Clones in Sexual Populations
In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection, populations consist of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, which is realized for example in the facultatively sexual populations that outcross in only a fraction of reproductive cycles, selection can amplify individual genotypes into large clones. Such clones emerge, when the fitness advantage of some of the genotypes is large enough that they grow to a significant fraction of the population, despite being broken down by recombination. The occurrence of this "clonal condensation" depends, in addition to the outcrossing rate, on the heritability of fitness. Clonal condensation leads to a strong genetic heterogeneity of the population which is not adequately described by traditional population genetics measures, such as Linkage Disequilibrium. Here we point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy we explicitly calculate as a function of the key parameters in a simple model of sexual populations, the probability, Y, that two individuals are genetically identical. While Y is the analog of the spinglass order parameter, it is also closely related to rate of coalescence in population genetics: Two individuals that are part of the same clone have a recent common ancestor. We suggest that the "clonal condensation" phenomenon is relevant not only to the facultatively sexual populations, but also for the quantitative understanding of the distribution of haplotypes in obligatory sexual populations. 

Fractal isocontours of passive scalar in 2D smooth random flows
We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new effective semianalytic algorithm to model the scalar turbulence. We then carry massive numerics of passive scalar turbulence with the focus on the statistics of nodal lines. The distribution of contours over sizes and perimeters is shown to depend neither on the flow realization nor on the resolution (diffusion) scale for scales exceeding it. The scalar isolines are found fractal/smooth at the scales larger/smaller than the pumping scale L. We characterize the statistics of bending of a long isoline by the driving function of the Loewner map, show that it behaves like diffusion with the diffusivity independent of resolution yet, most surprisingly, dependent on the velocity realization and the time of scalar evolution. 

Nonequilibrium mixing accelerates Monte Carlo
A guiding principle of the development of MC sampling techniques is that equilibrium systems evolve according to detailed balance. It is known that detailed balance is a sufficient but not a necessary condition, for MC to converge to a steady state. If so, a question naturally arrises: Can one utilize nonequilibrium mixing to reach a given steady state faster? The answer to this question happens to be affirmative in many cases. Indeed, our recent work shows how to build an irreversible deformation of a reversible algorithm, after which the sampling procedure is substantially improved.
The further development of similar ideas might be useful in studies of phase transitions, soft matter dynamics, protein structures, granular media and etc. 



Clustering of Matter and Mixing in Turbulent Flows
We interested in the statistics of particles suspended in turbulent flows. These particles can be water droplets in clouds, dust in air, planetesimals in the early Solar system, concentration of plankton or an oil slick on the ocean surface etc. Spontaneous formation of clusters of particles suspended in chaotic flows may originate from two different physical processes: compressibility of the fluid flow and particle inertia. In the first case particles are trapped in regions of ongoing compression, while in the second case inertia causes their ejection from vortical regions. The underlying link between these phenomena is manifested in the limit of weak inertia, in which the particle dynamics in incompressible flows can be approximated by that of tracers in a weakly compressible velocity field. We are interested in describing different scenarios of clustering of particles due to compressibility and inertia, respectively. 

 Coauthors and collaborators
 Michael Chertkov, Physics of Condensed Matter and Complex Systems, Los Alamos National Laboratory
 Barak Dayan, Department of Chemical Physics, Weizmann Institute of Science
 Adel Dayarian, Kavli Institute of Theoretical Physics, UCSB
 Gustavo Düring, Department of Physics, New York University
 Gregory Falkovich, Department of Physics of Complex Systems, Weizmann Institute of Science
 Itzhak Fouxon, Tel Aviv University
 Asher Freesem, Department of Physics of Complex Systems, Weizmann Institute of Science
 Edo Kussell, Department of Biology and Department of Physics, New York University
 Jon Machta, University of Massachusetts Amherst
 Marc Mezard, Laboratoire de Physique Théorique et Modeles Statistiques, Paris
 Stefano Musacchio, Universite' de Nice SophiaAntipolis
 Richard Neher, Max Planck Institute for Developmental Biology,Tübingen
 Avi Pe'er, Bar Ilan Institute of Nanotechnology and Advanced Materials, Bar Ilan University
 Leonid Piterbarg, Department of Mathematics, UCS Dornsife
 Yaron Silberberg, Department of Physics of Complex Systems, Weizmann Institute of Science
 Boris Shraiman, Kavli Institute of Theoretical Physics, Department of Physics, UCSB
 Mikhail Stepanov, Department of Mathematics, University of Arizona
 Konstantin S. Turitsyn, Department of Mechanical Engineering, MIT
 Matthieu Wyart, Department of Physics, New York University

