**Research Interests:**

Research publications (published during April 2010 - October 2011) where affiliation of the Centre is shown or is acknowledged.

- Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives - P. Perlekar, D. Mitra, and R. Pandit, Phys. Rev. E, 82, 066313 (2010), (also available at http://arxiv.org/abs/1008.0051)
- Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence - G. Sahoo, P. Perlekar and R. Pandit, New J. Phys. 13,0130363 (2011); doi:10.1088/1367-2630/13/1/013036.
- The Persistence Problem in Two-Dimensional Fluid Turbulence - P. Perlekar, S. S. Ray, D. Mitra, and R. Pandit, Phys. Rev. Lett. 106, 054501 (2011), (also available at http://arxiv.org/abs/1009.1494)
- Scroll-wave dynamics in human cardiac tissue: lesson from a mathematical model with inhomogeneties and fiber architecture- R. Majumder, A. R. Nayak, and R. Pandit, PLoS ONE,6(4): e18052. doi:10.1371/journal.pone.0018052.
- An Overview of Spiral- and Scroll-Wave Dynamics In Mathematical Models for Cardiac Tissue - R. Majumder, A. R. Nayak, and R. Pandit, invited book chapter, in O.N. Tripathi, U. Ravens, and M.C. Sanguinetti (eds.), Heart Rate and Rhythm, DOI 10.1007/978-3-642-17575-6 14, (Springer-Verlag, Berlin, Heidelberg 2011) Chapter 14, pp 269-282.
- Dynamic Multiscaling in Two-dimensional Fluid Turbulence- S.S. Ray, D. Mitra, P. Perlekar, and R. Pandit, accepted for publication in Phys. Rev. Lett. (2011); available at http://arxiv.org/abs/1105.5160.

**Recent Awards:**

- Utrecht-Asia Visiting Professorship, July 2010.
- Distinguished Alumini Award, IIT Delhi, August 2010.
- UGC-BSR one-time research grant (given to science-department faculty members, who have supervised the theses of many PhD students) - December 2010.

**A short paragraph on research highlights (April 2010 - November 2011)**

The work in my group has systematized the studies of five classes of problems in the area of turbulence, namely, (I) the dynamic multiscaling of time-dependent structure functions in fluid and passive-scalar turbulence, (II) dissipation reduction by polymer additives in fluid turbulence, (III) the statistical properties of turbulence in two-dimensional fluid films, (IV) the effects of hyperviscosity in hydrodynamical equations, (V) the magnetic-Prandtl-number depedence of the dynamo boundary and the statistical properties of magnetohydrodynamic (MHD) turbulence, and

(VI) the persistence problem in turbulence. Furthermore, we have studied spiral- and scroll-wave dynamics in a variety of mathematical models for cardiac tissue ranging from simple, two-variable models, which account for the transmembrane potential V and a slow, recovery variable, to state-of-the-art models, which include V and several ionic currents, gating variables for the associated voltage-gated ion channels, ion pumps, and ion exchangers.

**A short paragraph on research plans for the coming year**

Over the next year we will extend our studies of turbulence to (a) the persistence problem for three-dimensional fluid turbulence, (b) real-space manifestations of bottlenecks in energy-spectra bottlenecks in turbulent flows, (c) fluid turbulence with polymer additives in two dimensions. We will extend our studies of mathematical models of cardiac tissue to anatomically realistic simulation domains. We will also study phases and transitions in Bose-Hubbard and extended-Bose-Hubbard models by using the entanglement entropy and an inhomogeneous mean-field theory.