Lecture Series

 ************************************************************ SCHEDULE FOR THE WEEKLY SEMINAR ON FLUID DYNAMICS ************************************************************ 08/01/09: -------- Time: 2.30pm Speaker: S.G. Rajeev (University of Rochester, U.S.A) Title: Geometrical Aspects of Fluid Dynamics. 15/01/09: -------- Time: 11am Speaker: G. Baskaran (IMSC, Chennai) Title: Quantum Fluids: Superfluidity and Superconductivity Abstract: Fluid is a dominant state of matter on earth. Phenomena on this planet at all length scales are governed by some kind of fluid flow or other. Our understanding of fluid mechanics has grown over decades and continues along with growth of mathematics. Most of the fluids we come across are classical fluids. There are certain fluids called quantum fluids that occur under extreme conditions such as low temperatures or ultra-strong magnetic fields. Two well-known cases are1) liquid Helium IV containing identical quantum mechanical He^4 atoms and 2) conduction electrons in some solids. Liquid He^4 supports a remarkable superfluid state at very low temperatures. This state is characterised by zero viscosity and a certain resistance to macroscopic rotation. It is a consequence of quantum mechanics and indistinguishable and boson character of He^4 atoms. Similarly metallic electrons in certain solids exhibit a property called superconductivity: it is a state of zero electrical resistance and spontaneous expulsion of any external magnetic field from inside the superconductor (Meissner effect). It is also a consequence of quantum mechanics of indistinguishable and boson character of electron pairs. At the heart of these phenomena is a macroscopic coherence phenomenon called Bose-Einstein condensation. In a Bose-Einstein condensed state, a finite fraction of particles enter into one quantum state described by a macroscopic wave function $\psi (\vec r, t)$. In describing quantum fluids, one has to go beyond Newton's laws and use new emergent fields and variables. Dynamics and flow properties of the above quantum fluids are determined by the time evolution of the wave function. Gross-Pitaevskii (for neutral fluids) and Ginzburg-Landau equations (for superconductors) determine the time evolutions of $\psi (\vec r, t)$. Superfluids and superconductors combine the richness of classical fluids with some unique flow properties and phenomena arising from quantum mechanics. We get a glimpse of the world of quantum fluids in these two lectures. and Time: 2.30pm Speaker: S.R.S Varadhan (Courant Institute, New York) Title Part 1: Derivation of Euler Equations Abstract: We will discuss how Euler Equations of compressible gas dynamics are formally derived from Hamilton motion of large number of particles with a suitable binary interaction potential. We explore how the formal derivation can be made rigorous. Title Part 2: A class of examples of interacting particle systems and their scaling limits Abstract: Simple exclusion processes provide a class of examples where similar scaling limits can be proven mathematically. We shall describe some of these results. 20/01/09: -------- Time: 2.30pm Speaker: K.R. Sreenivasan (ASICTP, Trieste, Italy) Title: Cryogenic Turbulence Abstract: This talk will describe the speaker's recent work on the subject and put it in historical perspective. 22/01/09: -------- Time: 11am Speaker: Siddhartha Sen (University College, Dublin) Title: Quantum Weak Turbulence Abstract: Turbulence is regarded by some researchers (notably Zakharov) as a nonlinear, dissipative, far from equilibrium phenomenon. Such a framework can be used to model Kolmogorov scaling for fluids and can be adopted to study several non-fluid systems as well. The approach uses Hamiltonian methods. In this talk, the basic ideas of this approach as well as a way of extending the approach to quantum systems will be described. and Time: 2.30pm Speaker: A. Thyagaraja (Culham Labs, U.K. Atomic Energy Agency) Title: Introduction to Plasma Turbulence and its Transport Consequences in Fusion Plasmas 29/01/09: -------- Time: 11am Speaker: Shiraz Minwalla (TIFR, Mumbai) Title: String Theory and Fluid Dynamics and Time: 2.30pm Speaker: Rajaram Nityananda (NCRA, Pune) Title: Stellar Dynamics: the gravitational N-body problem in the fluid limit Abstract: The subject of stellar dynamics traditionally deals with a statistical description of N gravitating particles via a phase space distribution function and its time evolution. Astronomically, the three regimes of interest are star clusters, galaxies, and the universe, each with its own special features and interesting phenomena. A broad overview of what is known/believed from general arguments and simulations, and possible future directions will be given. 05/02/09: -------- Time: 11am Speaker: S. Sridhar (RRI, Bangalore) Tentative Title: Astrophysical Fluid Dynamics and Time: 2.30pm Speaker: K. Subramanian (IUCAA, Pune) Title: Topological Aspects in Magnetohydrodynamics and Dynamo Theory 12/02/09: -------- Time: 11am Speaker: R. Narasimha (JNCASR, Bangalore) Title: Clouds as a Problem in Fluid Dynamics and Time: 2.30pm Speaker: Gautam Menon (IMSc, Chennai) Title Part 1: Random Organization and the Reversible-Irreversible Transition Title Part 2: Two problems in the hydrodynamic description of active systems 19/02/09: -------- Time: 11am Speaker: A. M. Srivastava (IOP, Bhubaneswar) Title: Quark-Gluon Plasma and Time: 2.30pm Speaker: R. Shankar (IMSc, Chennai) Title: Quantum Hall Fluids 26/02/09: -------- Time: 11am Speaker: Madan Rao (RRI, Bangalore) Title: Active Hydrodynamics in the Cellular Context and Time: 2.30pm Speaker: R. Rajesh (IMSc, Chennai) Title: Constant Flux Relation for Turbulent Systems 05/03/09: -------- Time: 11 am Speaker: M. Vanninathan (TFIR, Bangalore) Tentative Title: The Navier-Stokes Millenium Problem and Time: 2.30pm Speaker: V. V. Sreedhar (CMI, Chennai) Tentative Title: Symmetries and Conservation Laws in Fluid Dynamics.