Biomedical subjects

Dibyendu Das

Publications and source records attributed to Dibyendu Das.

5 recordsLinked to original sources

PubMed2006

Motion of a random walker in a quenched power law correlated velocity field.

We study the motion of a random walker in one longitudinal and transverse dimensions with a quenched power law correlated velocity field in the longitudinal direction. The model is a modification of the Matheron-de Marsily model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse coordinates as , we analytically calculate the two-time correlation function of the coordinate. We find that the motion of the coordinate is a fractional Brownian motion (FBM), with a Hurst exponent . From this and known properties of FBM, we calculate the disorder averaged persistence probability of up to time . We also find the lines in the parameter space of and along which there is marginal behavior. We present results of simulations which support our analytical calculation.

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PubMed2005

Critical dynamics of dimers: implications for the glass transition.

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.

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PubMed2005

Persistence of randomly coupled fluctuating interfaces.

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h(1) and h(2) , respectively, each growing over a d -dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h(2) , however, is coupled to h(1) via a quenched random velocity field. In the limit d-->0 , our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t(0) -->infinity , the stochastic process h(2) , at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H2 =1- beta(1) /2 , where beta(1) is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be theta(2)(s) =1- H2 = beta(1) /2 . These analytical results are verified by numerical simulations.

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PubMed2004

Landau-like theory of glassy dynamics.

An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topology of the order parameter space in which the number of energy lowering trajectories rapidly diminishes as the ordered ground state is approached. This leads to an asymmetry in the effective transition rates which results in a nonexponential relaxation of the order-parameter fluctuations and a Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass transition. We argue that the Landau model provides a general framework for studying glassy dynamics in a variety of systems.

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PubMed2002

Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates.

The effect of introducing a mass-dependent diffusion rate approximately m(-alpha) in a model of coagulation with single-particle breakup is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all alpha>0 in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite-size scaling implications of this are characterized. The exponents characterizing the steady-state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean-field approximation and found to compare well with the results from numerical simulations in one dimension.

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