Google Scholar profile

My Present and Past Research Interests

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• Large fluctuations in non-equilibrium stochastic systems 
• Clustering, pattern formation and phase separation in granular flows 
• Phase transition kinetics, Ostwald ripening
• Self-similarity and dynamic scaling in physics 
• Fluid dynamics and plasma theory 
• Nonlinear oscillations and waves, chaos 

We currently have openings for graduate students.

Highlights

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We have recently determined, using the Inverse Scattering Method, the full statistics of nonstationary heat or mass transfer in some lattice gas models:

1. Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
2. Full statistics of nonstationary heat transfer in the Kipnis–Marchioro–Presutti model
3. Complete integrability of the problem of full statistics of nonstationary mass transfer in the simple inclusion process
4. Full statistics of regularized local energy density in a freely expanding Kipnis–Marchioro–Presutti gas

 

We have published a series of papers on large deviations of the surface height in the Kardar-Parisi-Zhang equation:

1. Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation
2. Short-time height distribution in the one-dimensional Kardar-Parisi-Zhang equation: Starting from a parabola
3. Dynamical phase transition in large-deviation statistics of the Kardar-Parisi-Zhang equation
4. Large deviations of surface height in the 1+1-dimensional Kardar–Parisi–Zhang equation: exact long-time results for λH<0
5. Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions
6. Nonequilibrium steady state of a weakly-driven Kardar–Parisi–Zhang equation
7. Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface
8. Exact short-time height distribution for the flat Kardar-Parisi-Zhang interface
9. Large fluctuations of a Kardar-Parisi-Zhang interface on a half line
10. Large fluctuations of a Kardar-Parisi-Zhang interface on a half line: The height statistics at a shifted point
11. Time-averaged height distribution of the Kardar–Parisi–Zhang interface
12. Optimal paths of nonequilibrium stochastic fields: The Kardar-Parisi-Zhang interface as a test case
13. Observing symmetry-broken optimal paths of the stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
14. Short-time large deviations of the spatially averaged height of a Kardar–Parisi–Zhang interface on a ring

In some cases, large deviations of Brownian motion and fractional Brownian motion can be described using concepts from geometrical optics:

1. Geometrical optics of constrained Brownian excursion: from the KPZ scaling to dynamical phase transitions
2. Geometrical optics of constrained Brownian motion: three short stories
3. Large fluctuations of the area under a constrained Brownian excursion
4. Statistics of first-passage Brownian functionals
5. Geometrical optics of large deviations of fractional Brownian motion
6. Geometrical optics of first-passage functionals of random acceleration
7. Geometrical optics of large deviations of Brownian motion in inhomogeneous media
8. First-passage area distribution and optimal fluctuations of fractional Brownian motion

We have studied extinction of long-lived isolated populations in a series of papers and reviews:

1. Spectral Theory of Metastability and Extinction in Birth-Death Systems
2. Noise Enhanced Persistence in a Biochemical Regulatory Network with Feedback Control
3. How Colored Environmental Noise Affects Population Extinction
4. Extinction rates of established spatial populations
5. Minimizing the Population Extinction Risk by Migration
6. Stochastic models of population extinction (a non-technical review)
7. WKB theory of large deviations in stochastic populations (a more comprehensive review)

More Papers:

• Suppose that a gas of interacting diffusing particles is trapped inside a cavity with a small hole. What is the average exit time of the first particle from the cavity? Narrow Escape of Interacting Diffusing Particles
• Why so many sperm cells? Mortality, Redundancy, and Diversity in Stochastic Search
• We have developed a theoretical and computational framework for understanding granular levitation — a phenomenon in which a dense granular cluster is supported from below by a dilute granular gas: Close-Packed Floating Clusters: Granular Hydrodynamics Beyond the Freezing Point?

• We explored an intriguing analogy between a collection of marbles and an expanding universe by studying clustering in a freely cooling granular gas: Hydrodynamic Singularities and Clustering in a Freely Cooling Inelastic Gas

• We developed a theoretical framework describing nonequilibrium Ostwald ripening in granular clusters in electrostatically driven metallic powders: Phase Separation and Coarsening in Electrostatically Driven Granular Media

• Fractal coarsening is the shape relaxation of fractal objects driven by surface tension or other "fractality spoilers." We explored this phenomenon through numerical simulations of diffusion-controlled coarsening in DLA clusters. Our work also addresses why these and related systems may not exhibit simple dynamic scaling behaviors: 
  • Enjoy a small animation or a larger-scale movie.
  • Scaling and Self-Similarity in an Unforced Flow of Inviscid Fluid Trapped Inside a Viscous Fluid in a Hele-Shaw Cell

• What is autoresonance? We explored this phenomenon in several papers, including theoretical and experimental studies:

  • Strong autoresonance exitation of Rydberg atoms: The Rydberg accelerator

  • Experimental Study of Parametric Autoresonance in Faraday Waves

• I also worked in plasma physics. I wrote a review on the nonlinear dynamics of thermal instability in plasmas cooled by their own radiation: Nonlinear dynamics of radiative condensations in optically thin plasmas