Biomedical subjects

Jayanta K Bhattacharjee

Publications and source records attributed to Jayanta K Bhattacharjee.

5 recordsLinked to original sources

PubMed2005

Shear thinning of a critical viscoelastic fluid.

The frequency and shear dependent critical viscosity at a correlation length xi= kappa(-1) has the form eta= eta(0) kappa(- x(eta) ) G ( z(1) , z(2) ) , where z(1) and z(2) are the independent dimensionless numbers in the problem defined as z(1) =-iomega/2 Gamma(0) kappa(3) and z(2) =-iomega/2 Gamma(0) kappa(3)(c) . The decay rate of critical fluctuations of correlation length kappa(-1) is Gamma(0) kappa(3) and k(c) is the effective wave number for which Gamma(0) k(3)(c) =S , the shear rate. The function G ( z(1) , z(2) ) is calculated in a one-loop self-consistent theory.

Journal Article↗

PubMed2005

Critical viscosity exponent for classical fluids.

A self-consistent mode-coupling calculation of the critical viscosity exponent z(eta) for classical fluids is performed by including the memory effect and the vertex corrections. The incorporation of the memory effect is through a self-consistency procedure that evaluates the order parameter and shear momentum relaxation rates at nonzero frequencies, thereby taking their frequency dependence into account. This approach offers considerable simplification and efficiency in the calculation. The vertex corrections are also demonstrated to have significant effects on the numerical value for the critical viscosity exponent, in contrast to some previous theoretical work which indicated that the vertex corrections tend to cancel out from the final result. By carrying out all of the integrations analytically, we have succeeded in tracing the origin of this discrepancy to an error in earlier work. We provide a thorough treatment of the two-term epsilon expansion, as well as a complete three-dimensional analysis of the fluctuating order-parameter and transverse hydrodynamic modes. The study of the interactions of these modes is carried out to high order so as to arrive at z(eta) = 0.0679+/-0.0007 for comparison with the experimentally observed value, 0.0690+/-0.0006 .

Journal Article↗

PubMed2005

The phase-modulated logistic map.

We study the logistic mapping with the nonlinearity parameter varied through a delayed feedback mechanism. This history dependent modulation through a phaselike variable offers an enhanced possibility for stabilization of periodic dynamics. Study of the system as a function of nonlinearity and modulation parameters reveals new phenomena: In addition to period-doubling and tangent bifurcations, there can be bifurcations where the period increases by unity. These are extensions of crises that arise in nonlinear dynamical systems. Periodic orbits in this system can be systematized via the kneading theory, which in the present case extends the analysis of Metropolis, Stein, and Stein for unimodal maps.

Logistic Models↗

PubMed2004

Scaling function for the critical diffusion coefficient of a critical fluid in a finite geometry.

The long-wavelength diffusion coefficient of a critical fluid confined between two parallel plates, separated by a distance L, is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion coefficient as xi(-1) for xi< >L. We show that this is not strictly true. There is a logarithmic scaling violation. We construct a Kawasaki-like scaling function that connects the thermodynamic regime to the extreme critical (xi>>L) regime.

Journal Article↗

PubMed2003

Critical viscosity exponent for fluids: effect of the higher loops.

We arrange the loopwise perturbation theory for the critical viscosity exponent x(eta), which happens to be very small, as a power series in x(eta) itself, and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by x(eta)=(8/15pi(2))(1+8/3pi(2)) approximately 0.0685.

Journal Article↗