arXiv subjects

V. V. Prasad

Publications and source records attributed to V. V. Prasad.

14 recordsLinked to original sources

arXiv2025

Diffusion in a wedge geometry: First-Passage Statistics under Stochastic Resetting

We study the diffusion process in the presence of stochastic resetting inside a two-dimensional wedge of top angle $α$, bounded by two infinite absorbing edges. In the absence of resetting, the second moment of the first-passage time diverges for $α>π/4$ while it remains finite for $α<π/4$, resulting in an unbounded or bounded coefficient of variation in the respective angular regimes. Upon introducing stochastic resetting, we analyze the first-passage properties in both cases and identify the geometric configurations in which resetting consistently enhances the rate of absorption or escape through the boundaries. By deriving the expressions for the probability currents and conditional first-passage quantities such as splitting probabilities and conditional mean first-passage times, we demonstrate how resetting can be employed to bias the escape pathway through the favorable boundary. Our theoretical predictions are verified through Langevin-type numerical simulations, showing excellent agreement.

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arXiv2023

Lattice models for ballistic aggregation: cluster-shape dependent exponents

We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the first the aggregates remain point particles, in the second they retain the fractal shape at the time of collision, and in the third they assume a spherical shape. The exponents describing the power law temporal decay of number of particles and energy as well as dependence of velocity correlations on mass are determined using large scale Monte Carlo simulations. It is shown that the exponents are universal only for the point particle model. In the other two cases, the exponents are dependent on the initial number density and correlations vanish at high number densities. The fractal dimension for the second model is close to 1.49.

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arXiv2021

Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth order critical point

The canonical phase diagram of the Blume-Emery-Griffiths (BEG) model with infinite-range interactions is known to exhibit a fourth order critical point at some negative value of the bi-quadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth order critical point is studied in detail revealing some distinct features from the canonical counterpart.

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arXiv2021

Mpemba effect in anisotropically driven inelastic Maxwell gases

Through an exact analysis, we show the existence of Mpemba effect in an anisotropically driven inelastic Maxwell gas, a simplified model for granular gases, in two dimensions. Mpemba effect refers to the couterintuitive phenomenon of a hotter system relaxing to the steady state faster than a cooler system, when both are quenched to the same lower temperature. The Mpemba effect has been illustrated in earlier studies on isotropically driven granular gases, but its existence requires non-stationary initial states, limiting experimental realisation. In this paper, we demonstrate the existence of the Mpemba effect in anisotropically driven granular gases even when the initial states are non-equilibrium steady states. The precise conditions for the Mpemba effect, its inverse, and the stronger version, where the hotter system cools exponentially faster are derived.

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arXiv2021

Mpemba effect in an anisotropically driven granular gas

We demonstrate the existence, as well as determine the conditions, of a Mpemba effect - a counterintuitive phenomenon where a hotter system equilibrates faster than a cooler system when quenched to a cold temperature - in anisotropically driven granular gases. In contrast to earlier studies of Mpemba effect in granular systems, the initial states are stationary, making it a suitable system to experimentally study the effect. Our theoretical predictions for the regular, inverse and strong Mpemba effects agree well with results of event-driven molecular dynamics simulations of hard discs.

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arXiv2020

Asymptotic velocity distribution of a driven one dimensional binary granular Maxwell gas

We consider the steady states of a driven inelastic Maxwell gas consisting of two types of particles with scalar velocities. Motivated by experiments on bilayers where only one layer is driven, we focus on the case when only one of the two types of particles are driven externally, with the other species receiving energy only through inter-particle collision. The velocity $v$ of a particle that is driven is modified to $-r_w v+η$, where $r_w$ parameterises the dissipation upon the driving and the noise $η$ is taken from a fixed distribution. We characterize the statistics for small velocities by computing exactly the mean energies of the two species, based on the simplifying feature that the correlation functions are seen to form a closed set of equations. The asymptotic behaviour of the velocity distribution for large speeds is determined for both components through a combination of exact analysis for a range of parameters or obtained numerically to a high degree of accuracy from an analysis of the large moments of velocity. We show that the tails of the velocity distribution for both types of particles have similar behaviour, even though they are driven differently. For dissipative driving ($r_w<1$), the tails of the steady state velocity distribution show non-universal features and depend strongly on the noise distribution. On the other hand, the tails of the velocity distribution are exponential for diffusive driving ($r_w=1$) when the noise distribution decays faster than exponential.

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arXiv2019

Asymptotic behavior of the velocity distribution of driven inelastic gas with scalar velocities: analytical results

We determine the asymptotic behavior of the tails of the steady state velocity distribution of a homogeneously driven granular gas comprising of particles having a scalar velocity. A pair of particles undergo binary inelastic collisions at a rate that is proportional to a power of their relative velocity. At constant rate, each particle is driven by multiplying its velocity by a factor $-r_w$ and adding a stochastic noise. When $r_w <1$, we show analytically that the tails of the velocity distribution are primarily determined by the noise statistics, and determine analytically all the parameters characterizing the velocity distribution in terms of the parameters characterizing the stochastic noise. Surprisingly, we find logarithmic corrections to the leading stretched exponential behavior. When $r_w=1$, we show that for a range of distributions of the noise, inter-particle collisions lead to a universal tail for the velocity distribution.

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arXiv2019

Velocity distribution of driven granular gases

The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of the velocity distribution of a driven granular gas is a stretched exponential that, counterintuitively, decays slower than that of the corresponding elastic gas in equilibrium. However, a derivation of this result starting from a microscopic model is lacking. Here, we obtain analytical results for a microscopic model for a granular gas where particles with two-dimensional velocities are driven homogeneously and isotropically by reducing the velocities by a factor and adding a stochastic noise. We find two universal regimes. For generic physically relevant driving, we find that the tail of the velocity distribution is a Gaussian with additional logarithmic corrections. Thus, the velocity distribution decays faster than the corresponding equilibrium gas. The second universal regime is less generic and corresponds to the scenario described by kinetic theory. Here, the velocity distribution is shown to decay as an exponential with additional logarithmic corrections, in contradiction to the predictions of the phenomenological kinetic theory, necessitating a re-examination of its basic assumptions.

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arXiv2019

Landau theory of restart transitions

We develop a Landau like theory to characterize the phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two phases is characterized by the behavioral change in the order parameter of the system namely the optimal restart rate. Like in the original theory of Landau, the optimal restart rate can undergo a first or second order transition depending on the details of the system. Nonetheless, there exists no unified framework which can capture the onset of such novel phenomena. We unravel this in a comprehensive manner and show how the transition can be understood by analyzing the first passage time moments. Power of our approach is demonstrated in two canonical paradigm setup namely the Michaelis Menten chemical reaction and diffusion under restart.

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arXiv2019

First passage under stochastic resetting in an interval

We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive study of the first passage properties of this trapping phenomena. We compute the mean first passage time and derive the criterion upon which restart always expedites the underlying completion. We show how this set-up is a manifestation of a success-failure problem. We obtain the success and failure rates and relate them with the splitting probabilities, namely, the probability that the particle will eventually be trapped on either of the boundaries without hitting the other one. Numerical studies are presented to support our analytic results.

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arXiv2017

Driven inelastic Maxwell gas in one dimension

A lattice version of the driven inelastic Maxwell gas is studied in one dimension with periodic boundary conditions. Each site $i$ of the lattice is assigned with a scalar `velocity', $v_i$. Nearest neighbors on the lattice interact, with a rate $τ_c^{-1}$, according to an inelastic collision rule. External driving, occurring with a rate $τ_w^{-1}$, sustains a steady state in the system. A set of closed coupled equations for the evolution of the variance and the two-point correlation is found. Steady state values of the variance, as well as spatial correlation functions, are calculated. It is shown exactly that the correlation function decays exponentially with distance, and the correlation length for a large system is determined. Furthermore, the spatio-temporal correlation $C(x,t)=\langle v_i(0) v_{i+x} (t)\rangle$ can also be obtained. We find that there is an interior region $-x^* < x < x^*$, where $C(x,t)$ has a time-dependent form, whereas in the exterior region $|x| > x^*$, the correlation function remains the same as the initial form. $C(x,t)$ exhibits second order discontinuity at the transition points $x=\pm x^*$ and these transition points move away from the $x=0$ with a constant speed.

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arXiv2017

Velocity Distribution of Driven Inelastic One-component Maxwell gas

The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and if universal what it is. We determine the tails of the steady state velocity distribution of a driven inelastic Maxwell gas, which is a simple model of a granular gas where the rate of collision between particles is independent of the separation as well as the relative velocity. We show that the steady state velocity distribution is non-universal and depends strongly on the nature of driving. The asymptotic behavior of the velocity distribution are shown to be identical to that of a non-interacting model where the collisions between particles are ignored. For diffusive driving, where collisions with the wall are modelled by an additive noise, the tails of the velocity distribution is universal only if the noise distribution decays faster than exponential.

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arXiv2015

Driven inelastic Maxwell gases

We consider the inelastic Maxwell model, which consists of a collection of particles that are characterized by only their velocities, and evolving through binary collisions and external driving. At any instant, a particle is equally likely to collide with any of the remaining particles. The system evolves in continuous time with mutual collisions and driving taken to be point processes with rates $τ_c^-{1}$ and $τ_w^{-1}$ respectively. The mutual collisions conserve momentum and are inelastic, with a coefficient of restitution $r$. The velocity change of a particle with velocity $v$, due to driving, is taken to be $Δv=-(1+r_w) v+η$, mimicking the collision with a vibrating wall, where $r_w$ the coefficient of restitution of the particle with the "wall" and $η$ is Gaussian white noise. The Ornstein-Uhlenbeck driving mechanism given by $\frac{dv}{dt}=-Γv+η$ is found to be a special case of the driving modeled as a point process. Using both the continuum and discrete versions we show that while the equations for the one-particle and the two-particle velocity distribution functions do not close, the joint evolution equations of the variance and the two-particle velocity correlation functions close. With the exact formula for the variance we find that, for $r_w\ne-1$, the system goes to a steady state. On the other hand, for $r_w=-1$, the system does not have a steady state. Similarly, the system goes to a steady state for the Ornstein-Uhlenbeck driving with $Γ\not=0$, whereas for the purely diffusive driving ($Γ=0$), the system does not have a steady state.

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arXiv2014

High-Energy Tail of the Velocity Distribution of Driven Inelastic Maxwell Gases

A model of homogeneously driven dissipative system, consisting of a collection of $N$ particles that are characterized by only their velocities, is considered. Adopting a discrete time dynamics, at each time step, a pair of velocities is randomly selected. They undergo inelastic collision with probability $p$. With probability $(1-p)$, energy of the system is changed by changing the velocities of both the particles independently according to $v\rightarrow -r_w v +η$, where $η$ is a Gaussian noise drawn independently for each particle as well as at each time steps. For the case $r_w=- 1$, although the energy of the system seems to saturate (indicating a steady state) after time steps of $O(N)$, it grows linearly with time after time steps of $O(N^2)$, indicating the absence of a eventual steady state. For $ -1 <r_w \leq 1$, the system reaches a steady state, where the average energy per particle and the correlation of velocities are obtained exactly. In the thermodynamic limit of large $N$, an exact equation is obtained for the moment generating function. In the limit of nearly elastic collisions and weak energy injection, the velocity distribution is shown to be a Gaussian. Otherwise, for $|r_w| < 1$, the high-energy tail of the velocity distribution is Gaussian, with a different variance, while for $r_w=+1$ the velocity distribution has an exponential tail.

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