Biomedical subjects

Supriya Krishnamurthy

Publications and source records attributed to Supriya Krishnamurthy.

5 recordsLinked to original sources

PubMed2003

Persistence properties of a system of coagulating and annihilating random walkers.

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In one dimension, the system models the zero-temperature Glauber dynamics of domain walls in the q-state Potts model. We calculate P(m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m-1) coagulations. Using perturbative renormalization group analysis for d<2, we show that, if the number of coagulations m is much less than the typical number M(t), then P(m,t) approximately m(zeta/d)t(-theta), with theta=dQ+Q(Q-1/2)epsilon+O(epsilon(2)), zeta=(2Q-1)epsilon+(2Q-1)(Q-1)(1/2+AQ)epsilon(2)+O(epsilon(3)), where Q=(q-1)/q, epsilon=2-d and A=-0.006....M(t) is shown to scale as M(t) approximately t(d/2-delta), where delta=d(1-Q)+(Q-1)(Q-1/2)epsilon+O(epsilon(2)). In two dimensions, we show that P(m,t) approximately ln(t)(Q(3-2Q))ln(m)((2Q-1)(2))t(-2Q) for m<<t(2Q-1). We also derive an exact nonperturbative relation between the exponents: namely delta(Q)=theta(1-Q). The one-dimensional results corresponding to epsilon=1 are compared with results from Monte Carlo simulations.

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PubMed2003

Shearing of loose granular materials: a statistical mesoscopic model.

A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized along a single shear band which is a spanning path on the lattice chosen through an extremum condition. The dynamics consists of randomly changing the "density" of the sites only along the shear band, and then repeating the procedure of locating the extremal path and changing it. Starting from an initially uncorrelated density field, it is found that this dynamics leads to a slow compaction along with a nontrivial patterning of the system, with high-density regions forming which shelter long-lived low-density valleys. Further, as a result of these large density fluctuations, the shear band, which was initially equally likely to be found anywhere on the lattice, gets progressively trapped for longer and longer periods of time. This state is, however, metastable, and the system continues to evolve slowly in a manner reminiscent of glassy dynamics. Several quantities have been studied numerically which support this picture and elucidate the unusual system-size effects involved.

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PubMed2003

Slow relaxation due to optimization and restructuring: solution on a hierarchical lattice.

Motivated by the large strain shear of loose granular materials, we introduced a model that consists of consecutive optimization and restructuring steps leading to a self-organization of a density field. The extensive connections to other models of statistical physics are discussed. We investigate our model on a hierarchical lattice that allows an exact asymptotic renormalization treatment. A surprisingly close analogy is observed between the simulation results on the regular and the hierarchical lattices. The dynamics is characterized by the breakdown of ergodicity, by unusual system size effects in the development of the average density, as well as by the age distribution, the latter showing multifractal properties.

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PubMed2002

Kang-Redner small-mass anomaly in cluster-cluster aggregation.

The large-time small-mass asymptotic behavior of the average mass distribution P(m,t) is studied in a d-dimensional system of diffusing aggregating particles for 1< or =d< or =2. By means of both a renormalization group computation as well as a direct resummation of leading terms in the small-reaction-rate expansion of the average mass distribution, it is shown that P(m,t) approximately (1/t(d))(m(1/d)/sqrt[t])(e(KR)) for m<<t(d/2), where e(KR)=epsilon+O(epsilon(2)) and epsilon=2-d. In two dimensions, it is shown that P(m,t) approximately ln(m)ln(t)/t(2) for m<<t/ln(t). Numerical simulations in two dimensions supporting the analytical results are also presented.

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PubMed2002

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles.

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation, and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady state, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite-size system, however, continues to show a signature of the original transition, and we characterize the finite-size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.

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