arXiv subjects

Purusattam Ray

Publications and source records attributed to Purusattam Ray.

At least 19 recordsLinked to original sources

arXiv2026

Diffusive-to-Ballistic transition in a Persistent Random Walk

We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim t^{-\alpha}$ and show that the system undergoes a transition at $\alpha=1$, separating a super-diffusive regime for $\alpha<1$ from ballistic regime for $\alpha \geq 1$. Using the results for velocity correlations and persistence statistics, together with finite time scaling of the Binder cumulant and displacement fluctuations, we characterize the transition and its properties in detail. We further argue that the transition is not limited to the power law form, but can also arise for several other time dependent reversal probabilities satisfying the same criterion. The transition persists in arbitrary spatial dimensions provided isotropy of the velocity space is preserved.

cond-mat.stat-mech↗

arXiv2022

Modeling crack propagation in heterogeneous materials: Griffith's law, intrinsic crack resistance and avalanches

Various kinds of heterogeneity in solids including atomistic discreteness affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in heterogeneous materials, known as the fiber bundle model. We find three distinct regimes for fracture dynamics depending on the initial crack size. If the initial crack is smaller than a certain value, it does not affect the rupture dynamics and the critical stress. While for a larger initial crack, the growth of the crack leads to a breakdown of the entire system, and the critical stress depends on the crack size in a power-law manner with a nontrivial exponent. The exponent, as well as the limiting crack size, depend on the strength of heterogeneity and the range of stress relaxation in the system.

cond-mat.stat-mech↗

arXiv2020

$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

A one dimensional $A+A \to \emptyset$ system where the direction of motion of the particles is determined by the position of the nearest neighours is studied. The particles move with a probability $0.5 + \epsi$ towards their nearest neighbours with $-0.5 \leq \epsi \leq 0.5$. This implies a stochastic motion towards the nearest neighbour or away from it for positive and negative values of $\epsi$ respectively, with $\epsi = \pm ~0.5$ the two deterministic limits. The position of the particles are updated in parallel. The macroscopic as well as tagged particle dynamics are studied which show drastic changes from the diffusive case $\epsi=0$. The decay of particle density shows departure from the usual power law behaviour as found in $\epsi =0$, on both sides of $\epsi =0$ and a scaling regime is obtained for $\epsi > 0$. The $\epsi =0.5$ point is characterized by the presence of dimers, which are isolated pairs of particles in adjacent sites that are never annihilated. The persistence probability is also calculated that decays in a stretched exponential manner for $\epsi < 0$ and switches over to power law behaviour for $\epsi \geq 0$, with different exponents for $\epsi =0$ and $\epsi > 0$. For the tagged particle, the probability distribution $\Pi(x,t)$ that it is at position $x$ at time $t$ shows the existence of a scaling variable $x/t^\nu$ where $\nu = 0.55 \pm 0.05$ for $\epsi > 0$ and varies with $\epsi$ for $\epsi < 0$. Finally, a comparative analysis for the behaviour of all the relevant quantities for the system using parallel and asynchronous dynamics (studied recently) shows that there are significant differences for $\epsi > 0$ while the results are qualitatively similar for $\epsi < 0$.

cond-mat.stat-mech↗

arXiv2019

Tagged particle dynamics in one dimensional $A+ A \to kA$ models with the particles biased to diffuse towards their nearest neighbour

Dynamical features of tagged particles are studied in a one dimensional $A+A \rightarrow kA$ system for $k=0$ and 1, where the particles $A$ have a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ to hop one step in the direction of their nearest neighboring particle. $\epsilon=0$ represents purely diffusive motion and $\epsilon=0.5$ represents purely deterministic motion of the particles. We show that for any $\epsilon$, there is a time scale $t^*$ which demarcates the dynamics of the particles. Below $t^*$, the dynamics are governed by the annihilation of the particles, and the particle motions are highly correlated, while for $t \gg t^*$, the particles move as independent biased walkers. $t^*$ diverges as $(\epsilon_c-\epsilon)^{-\gamma}$, where $\gamma=1$ and $\epsilon_c =0.5$. $\epsilon_c$ is a critical point of the dynamics. At $\epsilon_c$, the probability $S(t)$, that a walker changes direction of its path at time $t$, decays as $S(t) \sim t^{-1}$ and the distribution $D(\tau)$ of the time interval $\tau$ between consecutive changes in the direction of a typical walker decays with a power law as $D(\tau) \sim \tau^{-2}$.

cond-mat.stat-mech↗

arXiv2018

Universality classes of absorbing phase transitions in generic branching-annihilating particle systems

We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one dimensional ring, where the walkers hop to their nearest neighbor with a bias $\epsilon$. For $\epsilon=0$, three universality classes: directed percolation (DP), parity conserving (PC) and pair contact process with diffusion (PCPD) are typically observed in such systems. We find that the introduction of $\epsilon$ does not change the DP universality class but alters the other two universality classes. For non-zero $\epsilon$, the PCPD class crosses over to DP and the PC class changes to a new universality class.

cond-mat.stat-mech↗

arXiv2018

A Renormalization Group Procedure for Fiber Bundle Models

We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is the work performed on the fiber bundle to produce a given damage. The renormalization group conserves this work. In the first version of the renormalization group, we take advantage of ordering the strength of the individual fibers. This procedure, which is the simpler one, gives EXACT results -but cannot be generalized to other fiber bundle models such as the local load sharing one. The second renormalization group scheme based on the physical location of the individual fibers may be generalized to other fiber bundle models.

cond-mat.soft↗

arXiv2016

Modes of failures in disordered solids

The two principal ingredients determining the failure modes of disordered solids are the level of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage, the two extreme failure modes. In this study, using the random fiber bundle model as a prototype for disorder solids, we classify every failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes.

cond-mat.dis-nn↗

arXiv2016

Partial Breaking of Three-Fold Symmetry via Percolation of a Domain Wall

We show that suppression of vortex strings splits the order-disorder transition in the three-state Potts ferromagnet on a simple cubic lattice and opens up an intermediate phase characterized by partial breaking of the three-fold symmetry and long-range order. In contrast, suppression of vortices in the same model on a square lattice results in an intermediate phase with enhanced U(1) symmetry and quasi-long-range order. We show that the difference between the two phases originates from distinct patterns of domain wall proliferation. A domain wall, separating the two most populous spin states, percolates on its own in the former phase but remains at a percolation threshold in the latter.

cond-mat.stat-mech↗

arXiv2016

Failure time in heterogeneous systems

We show that the failure time $\tau_f$ in fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $\delta$ and the stress release range $R$ in the system. For $R$ beyond a critical value $R_c$ the distribution of $\tau_f$ follows Weibull form. In this region, the average $\tau_f$ shows the variation $\tau_f \sim L^{\alpha}$ where $L$ is the system size. For $R<R_c$, $\tau_f\sim L/R$. We find that the crossover length scale has the scaling form $R_c \sim L^{1-\alpha}$. This scaling has been found to be valid for various disorder distributions. For $\delta<\delta_c$, $\alpha$ is an increasing function of $\delta$. For all $\delta \ge \delta_c$, $\alpha$=1/3.

cond-mat.dis-nn↗

arXiv2015

Quasi Long Range Order and Vortex Lattice in the Three State Potts Model

We show that the order-disorder phase transition in the three state Potts ferromagnet on a square lattice is driven by a coupled proliferation of vortices and domain walls. Raising the vortex core energy above a certain value decouples the proliferation and splits the transition into two. The phase between the two transitions exhibits an emergent U(1) symmetry and quasi long range order. Lowering the core energy also splits the order-disorder transition but the proliferation does not decouple and a vortex lattice appears as the intermediate phase.

cond-mat.stat-mech↗

arXiv2014

Criticality in Fiber Bundle Model

We report a novel critical behavior in the breakdown of an equal load sharing fiber bundle model at a dispersion $\delta_c$ of the breaking threshold of the fibers. For $\delta < \delta_c$, there is a finite probability $P_b$, that rupturing of the weakest fiber leads to the failure of the entire system. For $\delta \geq \delta_c$, $P_b = 0$. At $\delta_c, P_b \sim L^{-\eta}$, with $\eta \approx 1/3$, where $L$ is the size of the system. As $\delta \rightarrow \delta_c$, the relaxation time $\tau$ diverges obeying the finite size scaling law: $\tau \sim L^{\beta}(|\delta-\delta_c| L^{\alpha})$ with $\alpha, \beta = 0.33 \pm 0.05$. At $\delta_c$, the system fails, at the critical load, in avalanches (of rupturing fibers) of all sizes $s$ following the distribution $P(s) \sim s^{-\kappa}$, with $\kappa = 0.50 \pm 0.01$. We relate this critical behavior to brittle to quasi-brittle transition.

cond-mat.stat-mech↗

arXiv2014

Nucleation versus percolation: Scaling criterion for failure in disordered solids

One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as $R$ scales slower than $L^{\zeta}$, with $\zeta=2/3$. For a faster increase in $R$, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.

cond-mat.stat-mech↗

arXiv2014

$A+A \rightarrow \emptyset $ model with a bias towards nearest neighbor

We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $\epsilon=0$ to the mean-field value of unity for any non-zero $\epsilon$. We study the problem analytically using independent interval approximation and compare the scaling results with that obtained from simulation. The distribution $P(k,t)$ of the spacing $k$ between two walkers (per site) is given by $t^{-2/z} f(k/t^{1/z})$ as expected; however, the scaling function shows different behaviour in the two approaches.

cond-mat.stat-mech↗

arXiv2013

Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface

A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model.

cond-mat.stat-mech↗

arXiv2012

Shock Propagation in Granular Flow Subjected to an External Impact

We analyze a recent experiment [Phys. Rev. Lett., {\bf103}, 224501 (2009)] in which the shock, created by the impact of a steel ball on a flowing monolayer of glass beads, is quantitatively studied. We argue that radial momentum is conserved in the process, and hence show that in two dimensions the shock radius increases in time $t$ as a power law $t^{1/3}$. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction, and is shown to compare well at intermediate times. At late times, the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to accumulation of particles at the shock front, and propose a simple hard sphere model which incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.

cond-mat.soft↗

arXiv2011

Opinion dynamics model with domain size dependent dynamics: novel features and new universality class

A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening dynamics of the equivalent Ising model shows power law behavior and has been found to belong to a new universality class with the dynamic exponent $z=1.0 \pm 0.01$ and persistence exponent $\theta \simeq 0.235$ in one dimension. The critical behavior has been found to be robust for a large variety of annealed disorder that has been studied. Further, by mapping Model I to a system of random walkers in one dimension with a tendency to walk towards their nearest neighbour with probability $\epsilon$, we find that for any $\epsilon > 0.5$, the Model I dynamical behaviour is prevalent at long times.

physics.soc-ph↗

arXiv2009

Universal scaling dynamics in a perturbed granular gas

We study the response of a granular system at rest to an instantaneous input of energy in a localised region. We present scaling arguments that show that, in $d$ dimensions, the radius of the resulting disturbance increases with time $t$ as $t^{\alpha}$, and the energy decreases as $t^{-\alpha d}$, where the exponent $\alpha=1/(d+1)$ is independent of the coefficient of restitution. We support our arguments with an exact calculation in one dimension and event driven molecular dynamic simulations of hard sphere particles in two and three dimensions.

cond-mat.soft↗

arXiv2008

Classical and quantum breakdown in disordered materials

We have discussed the classical failure of the fuse system, the dielectric breakdown and the quantum breakdown in the Anderson insulators. We have discussed how the extreme value statistics and the resulting Gumbel distribution arises in breakdown and failure processes, especially when the disorder concentration is low. At high concentration of disorder near the percolation threshold, we have discussed how the cross-over might take place from extreme value to percolation statistics. We have discussed the system size dependence that arises at the distribution of the failure current at low disordered regime. Finally, the extension of Zener breakdown phenomenon for band insulators to the disordered-induced Anderson insulators has been discussed.

cond-mat.stat-mech↗