Chennai Mathematical Institute

Lecture Series


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SCHEDULE FOR THE WEEKLY SEMINAR ON FLUID DYNAMICS
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08/01/09:
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Time: 2.30pm

Speaker: S.G. Rajeev (University of Rochester, U.S.A)

Title: Geometrical Aspects of Fluid Dynamics.

15/01/09:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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.






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