Current Research
 

Research Interest

Critical Phenomena

 Over the last few decades a lot of effort has been expended in comparing theoretical prediction and observations near a second order phase transition point. An interesting example is the case of the divergence of the viscosity at the transition point. In the late sixties and early seventies, it was established that the diverges is weak. In the beginning the theorists and experimentalists were happy with a logarithmic divergence. As the efficiency in both calculation and experimentation grew, both sides agreed that it was a small power low divergence. The shear viscosity divergence as the temperature approaches the critical temperature with an index which is somewhere between 0.04 and 0.05. The dust has almost settled now and along the way small but significant efforts like viscoelastic effects and shear thinning have been predicted and subjected to experimental tests.

Dynamic scaling for the critical viscosity of a classical fluid (with R.A. Ferrell) Phys Lett. 78A 465 (1980)

Frequency dependent critical viscosity of a classical fluid (with R.A. Ferrell) Phys. Rev. A27 1544 (1983)

Frequency dependent viscosity near the critical point: the scale to two loop order (with P.Das) Phys. Rev. E 63 020202 (2001)

Critical viscosity exponent for fluids: effect of higher loops (with P.Das) Phys. Rev. E 71 021201 (2005)

Shear thinning of a critical viscoelastic fluid (with P.Das) Phys. Rev. E71 036145 (2005)

Instabilities, Pattern formation, chaos, turbulence

A fluid heated from below can become unstable either due to buoyancy forces or surface tension. The hotter bottom layers rise to the top and the colder upper layers fall to the bottom setting up a convective flow which has a cellular pattern. This is the effect which causes the hexagonal dust pattern to appear on hot roads after a cooling shower. The dust particles are carried by the convective flow and are distributed according to the convective pattern after the water has evaporated. Is the convection driven by buoyancy or surface tension? The answer depends on the thickness of the fluid. For a thick layer the convection is buoyancy dominated while it is surface tension dominated for a thin layer. If the fluids is near its critical point then the correlation length is a yet another length scale in the problem. The competition between the thickness of the fluid layer and the correlation length sets the stage for interesting crossover phenomena.

Rayleigh-Marangoni convection in a critical fluid: A tale of two crossovers (with K.S.Das) Phys. Rev. 016311 (2001)

Ouset of convection in a binary mixture near the plant point (with K.S.Das) Phys. Rev. E61 (2000) 5191

Stationary convection in dilute rotating 3He-4He superfluid mixture: a linear stability analysis (with M.Thurlow, M.LJ.Lee and P.G.J.Lucas) Physica B329 (2003) 172

A logistic map with memory shows phenomena which had not been observed in one dimensional maps. Unusual intermittency, period adding bifurcations etc. are among the various possibilities.

The phase modulated logistic map (with A.Nandy, D.Datta and R.Ramaswam,y) Chaos 023107 (2005)

Astrophysical flows usually have high Reynolds numbers and as such are ideal for studying turbulence. In the context of accretion flows, turbulence plays a dominant role in the two-dimensional geometry and what it is interesting, a not so negligible role in the spherically symmetric case.

Large scale properties in turbulent spherically symmetric accretion (with A.K.Ray), Astrophys. J. 627 (2005) 368

Topics of general interest

The Poincare-Lindstedt technique is the standard method of handling nonlinear classical oscillators. What is its quantum generalization ? How does one set up a scaling argument for the eigenvalues in the case of a singular potential ? Questions such as these along with variational approaches to problems of a two electron quantum dot, the ground state of a particle confined in a super ellipse, setting up of perturbation theory for a class of time dependent problems in electromagnetism have been of interest to us in the last few years.

Ultraviolet divergence and scaling is a class of singular potentials (with S.Bhattacharyya), J. Phys. A36 (2003) L223

Time dependent perturbation theory with a classical limit (with Shanik Banerjee), Phys. Rev. Lett. 93 (2004) 120403

How do supersingular perturbations generate non-Taylor series (with S.Bandopadhyay and K.Bhattacharyya), J. Phys. A38 (2005) L331
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