Biomedical subjects

Mustansir Barma

Publications and source records attributed to Mustansir Barma.

6 recordsLinked to original sources

PubMed2006

Strong clustering of noninteracting, sliding passive scalars driven by fluctuating surfaces.

We study the clustering of passive, noninteracting particles moving under the influence of a fluctuating field and random noise, in one and two dimensions. The fluctuating field in our case is provided by surfaces governed by the Kardar-Parisi-Zhang (KPZ) and the Edwards-Wilkinson (EW) equations, and the sliding particles follow the local surface slope. As the KPZ equation can be mapped to the noisy Burgers equation, the problem translates to that of passive scalars in a Burgers fluid. Monte Carlo simulations on discrete lattice models reveal very strong clustering of the passive particles for all sorts of dynamics under consideration. The resulting strong clustering state is defined using the scaling properties of the two point density-density correlation function. Our simulations show that the state is robust against changing the ratio of update speeds of the surface and particles. We also solve the related equilibrium problem of a stationary surface and finite noise, well known as the Sinai model for random walkers on a random landscape. For this problem, we obtain analytic results which allow closed form expressions to be found for the quantities of interest. Surprisingly, these results for the equilibrium problem show good agreement with the nonequilibrium KPZ problem.

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PubMed2006

Dynamics of fluctuation-dominated phase ordering: hard-core passive sliders on a fluctuating surface.

We study the dynamics of a system of hard-core particles sliding downwards on a one-dimensional fluctuating interface, which in a special case can be mapped to the problem of a passive scalar advected by a Burgers fluid. Driven by the surface fluctuations, the particles show a tendency to cluster, but the hard-core interaction prevents collapse. We use numerical simulations to measure the autocorrelation function in steady state and in the aging regime, and space-time correlation functions in steady state. We have also calculated these quantities analytically in a related surface model. The steady-state autocorrelation is a scaling function of t/L(z), where L is the system size and z is the dynamic exponent. Starting from a finite intercept, the scaling function decays with a cusp, in the small argument limit. The finite value of the intercept indicates the existence of long-range order in the system. The space-time correlation, which is a function of r/L and t/L(z), is nonmonotonic in t for fixed r. The aging autocorrelation is a scaling function of t(1) and t(2) where t(1) is the waiting time and t(2) is the time difference. This scaling function decays as a power law for t(2)>>t(1); for t(1)>>t(2), it decays with a cusp as in steady state. To reconcile the occurrence of strong fluctuations in the steady state with the fact of an ordered state, we measured the distribution function of the length of the largest cluster. This shows that fluctuations never destroy ordering, but rather the system meanders from one ordered configuration to another on a relatively rapid time scale.

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PubMed2005

Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in two dimensions: a study using deposition-evaporation kinetics.

Deposition and evaporation of infinitely thin hard rods (needles) is studied in two dimensions using Monte Carlo simulations. The ratio of deposition to evaporation rates controls the equilibrium density of rods, and increasing it leads to an entropy-driven transition to a nematic phase in which both static and dynamical orientational correlation functions decay as power laws, with exponents varying continuously with deposition-evaporation rate ratio. Our results for the onset of the power-law phase agree with those for a conserved number of rods. At a coarse-grained level, the dynamics of the nonconserved angle field is described by the Edwards-Wilkinson equation. Predicted relations between the exponents of the quadrupolar and octupolar correlation functions are borne out by our numerical results. We explore the effects of spatial inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based arguments, and a study of the additional terms introduced in the free energy. The primary effect is that needles tend to align along the local spatial gradient of the ratio. A uniform gradient thus induces a uniformly aligned state, as does a gradient which varies randomly in magnitude and sign, but acts only in one direction. Random variations of deposition-evaporation rates in both directions induce frustration, resulting in a state with glassy characteristics.

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PubMed2003

Dynamics of a disordered, driven zero-range process in one dimension.

We study a disordered, driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterize the dynamical properties of the mass fluctuations in the steady state in one dimension both analytically and numerically and show that there is a dynamic phase transition in the density-disorder plane. We also determine the form of the scaling function which describes the growth of the condensate as a function of time, starting from a uniform density distribution.

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PubMed2003

Asymptotic distributions of periodically driven stochastic systems.

We study the large-time behavior of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where these driving forces are rapidly oscillating with an amplitude that is not necessarily small. We develop a perturbative method for the high-frequency regime to find the large-time behavior of periodically driven stochastic systems. The asymptotic distribution of Brownian particles is then determined to second order. To first order, these particles are found to execute small-amplitude oscillations around an effective static potential that can have interesting forms.

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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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