Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar-Parisi-Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.

Department of Physics

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Journal of Statistical Physics

Phase Separation Driven by a Fluctuating Two-Dimensional Self-Affine Potential Field

We study the distribution of persistent sites (sites unvisited by particles A) in the one-dimensional A+A → ∅ reaction-diffusion model. We define the empty intervals as the separations between adjacent persistent sites, and study their size distribution n(k, t) as a function of interval length k and time t. The decay of persistence is the process of irreversible coalescence of these empty intervals, which we study analytically under the independent interval approximation (IIA). Physical considerations suggest that the asymptotic solution is given by the dynamic scaling form n(k, t) = s-2 f (k/s) with the average interval size s ∼ t1/2. We show under the IIA that the scaling function f(x) ∼ x-τ as x → 0 and decays exponentially at large x. The exponent τ is related to the persistence exponent θ through the scaling relation τ = 2(1-θ). We compare these predictions with the results of numerical simulations. We determine the two-point correlation function C(r, t) under the IIA. We find that for r ≪ s, C(r, t) ∼ r-α where α = 2 - τ, in agreement with our earlier numerical results.

Fulltext

Journal of Physics A: Mathematical and General

Spatial distribution of persistent sites

We show that the persistence probability [Formula Presented] in a coarsening system of linear size L at a time t, has the finite-size scaling form [Formula Presented] where θ is the persistence exponent and z is the coarsening exponent. The scaling function [Formula Presented] for [Formula Presented] and is constant for large x. The scaling form implies a fractal distribution of persistent sites with power-law spatial correlations. We study the scaling numerically for the Glauber-Ising model at dimension [Formula Presented] to 4 and extend the study to the diffusion problem. Our finite-size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent [Formula Presented]. © 2000 The American Physical Society.

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Persistence in higher dimensions: A finite size scaling study

The spatial distribution of unvisited/persistent sites in ID A+A→0 model is studied numerically. Over length scales smaller than a cut-off ξ (t) ∼ tz, the set of unvisited sites is found to be a fractal. The fractal dimension d f, dynamical exponent z and persistence exponent θ are related through z(1 - d f) = θ. The observed values of d f and z are found to be sensitive to the initial density of particles. We argue that this may be due to the existence of two competing length scales, and discuss the possibility of a crossover at late times.