Biomedical subjects

SN Majumdar

Publications and source records attributed to SN Majumdar.

At least 19 recordsLinked to original sources

PubMed2000

Analytical results for random walk persistence

In this paper, we present a detailed calculation of the persistence exponent straight theta for a nearly Markovian Gaussian process X(t), a problem initially introduced elsewhere in [Phys. Rev. Lett. 77, 1420 (1996)], describing the probability that the walker never crosses the origin. Resummed perturbative and nonperturbative expressions for straight theta are derived, which suggest a connection with the result of the alternative independent interval approximation. The perturbation theory is extended to the calculation of straight theta for non-Gaussian processes, by making a strong connection between the problem of persistence and the calculation of the energy eigenfunctions of a quantum mechanical problem. Finally, we give perturbative and nonperturbative expressions for the persistence exponent straight theta(X0), describing the probability that the process remains larger than X(0)sqrt[ ].

Journal Article↗

PubMed2000

Phase transition in the takayasu model with desorption

We study a lattice model where particles carrying different masses diffuse and coalesce upon contact, and also unit masses adsorb to a site with rate q or desorb from a site with nonzero mass with rate p. In the limit p=0 (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power-law tail P(m) approximately m(-tau) for large mass. We show that varying the desorption rate p induces a nonequilibrium phase transition in all dimensions. For fixed q, there is a critical p(c)(q) such that if p p(c)(q), P(m) approximately exp(-m/m(*)) for large m. The model is studied analytically within a mean-field theory and numerically in one dimension.

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PubMed2000

Exact calculation of the spatiotemporal correlations in the takayasu model and in the q model of force fluctuations in bead packs

We calculate exactly the two point mass-mass correlations in arbitrary spatial dimensions in the aggregation model of Takayasu. In this model, masses diffuse on a lattice, coalesce upon contact, and adsorb unit mass from outside at a constant rate. Our exact calculation of the variance of mass at a given site proves explicitly, without making any assumption of scaling, that the upper critical dimension of the model is 2. We also extend our method to calculate the spatiotemporal correlations in a generalized class of models with aggregation, fragmentation, and injection, which include, in particular, the q model of force fluctuations in bead packs. We present explicit expressions for the spatiotemporal force-force correlation function in the q model. These can be used to test the applicability of the q model in experiments.

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PubMed2000

Extremal paths on a random cayley tree

We investigate the statistics of extremal path(s) (both the shortest and the longest) from the root to the bottom of a Cayley tree. The lengths of the edges are assumed to be independent identically distributed random variables drawn from a distribution rho(l). Besides, the number of branches from any node is also random. Exact results are derived for arbitrary distribution rho(l). In particular, for the binary 0,1 distribution rho(l)=pdelta(l,1)+(1-p)delta(l, 0), we show that as p increases, the minimal length undergoes an unbinding transition from a "localized" phase to a "moving" phase at the critical value, p=p(c)=1-b(-1), where b is the average branch number of the tree. As the height n of the tree increases, the minimal length saturates to a finite constant in the localized phase (p p(c)) where the velocity v(min)(p) is determined via a front selection mechanism. At p=p(c), the minimal length grows with n in an extremely slow double-logarithmic fashion. The length of the maximal path, on the other hand, increases linearly as v(max)(p)n for all p. The maximal and minimal velocities satisfy a general duality relation, v(min)(p)+v(max)(1-p)=1, which is also valid for directed paths on finite-dimensional lattices.

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PubMed1996