arXiv subjects

R. Rajesh

Publications and source records attributed to R. Rajesh.

At least 19 recordsLinked to original sources

arXiv2026

Probabilities of rare events in product kernel aggregation: An exact formula and phase diagram

We present an exact method for calculating the large deviation function describing rare fluctuations in the number of particles for product-kernel aggregation. Starting from the master equation, we derive an exact integral representation for the probability $P(M,N,t)$ of observing $N$ particles at time $t$ starting from $M$ monomers for any finite $M, N, t$. From this, we obtain an exact expression for the exponential moment $\langle p^N\rangle$ for integer $p$. Employing a replica conjecture -- numerically validated by finite-$M$ scaling -- we extend this result to real $p \geq 0$. The convex envelope of the large deviation function, obtained via a Legendre-Fenchel transform of the exponential moment, shows singular behavior. The singular structure allows us to construct the full phase diagram of product-kernel aggregation, which contains a tricritical point, separating continuous and discontinuous transitions. We also compute the asymptotic form of the LDF for small $N/M$.

cond-mat.stat-mech↗

arXiv2025

Entropy of full covering of the kagome lattice by straight trimers

We consider the number of ways all the sites of a kagome lattice can be covered by non-overlapping linear rigid rods where each rod covers 3 sites. We establish a 2-to-1 correspondence between the configurations of trimers on the kagome lattice to the covering by dimers of a related hexagonal lattice to show that entropy of coverings per trimer $s_{\text{tri,kag}}$ equals the entropy per dimer $ s_{\text{dim,hex}} $, and is given by $ s_{\text{tri,kag}} = s_{\text{dim,hex}} = \frac{1}{2 \pi} \int_0^{ 2 \pi/3} \log( 2 + 2 \cos k) dk \approx 0.323065947\ldots$.

cond-mat.stat-mech↗

arXiv2025

Finite size scaling and edge effects in the Takayasu model of aggregation diffusion with input

We analytically and numerically study the effect of finite spatial boundaries on the Takayasu model of diffusing and aggregating particles with steady monomer input in one dimension. Exact expressions are derived for the steady-state density profile, two-point correlation functions, and mean-squared density under both open and periodic boundary conditions. The single-site mass distribution exhibits a crossover from a bulk power law $P(m)\sim m^{-4/3}$ to an edge power law $P(m)\sim m^{-5/3}$, occurring near the boundaries or the condensate that forms in periodic systems. The equivalence between the two boundary conditions is shown to break down in the case of multipoint probability distributions near the edge. The exact solution identifies a distinct boundary layer and shows that the edge anomaly arises when spatial mass currents, which scale as $\mathcal{O}(L)$, dominate over the $\mathcal{O}(1)$ constant flux in mass space. We further generalize these results to mass-dependent diffusion.

cond-mat.stat-mech↗

arXiv2025

Splash in an inhomogeneous gas in one dimension: Exact analysis and molecular dynamics simulations

We investigate the splash phenomenon resulting from the energy input at the interface between a vacuum and an inhomogeneous gas with density profile $\rho(r) = \rho_0 r^{-\beta}$. The energy input causes the formation of ballistic spatters that propagate into the vacuum, leading to a decay of the total energy in the inhomogeneous medium following a power law, $E(t) \sim t^{-\delta_s}$. We determine exactly the exponents $\delta_s$ by solving the Euler equation using a self-similar solution of second kind for different values of $\beta$. These exponents are further validated through event-driven molecular dynamics simulations. The determination of these exponents also allows us to numerically determine the spatio-temporal dependence of the density, velocity and temperature.

cond-mat.stat-mech↗

arXiv2024

Mpemba effect in the relaxation of an active Brownian particle in a trap without metastable states

We explore the role of activity in the occurrence of the Mpemba effect within a system of an active colloid diffusing in a potential landscape devoid of metastable minimum. The Mpemba effect is characterized by a phenomenon where a hotter system reaches equilibrium quicker than a colder one when both are rapidly cooled to the same low temperature. While a minimal asymmetry in the potential landscape is crucial for observing this effect in passive colloidal systems, the introduction of activity can either amplify or reduce the threshold of this minimal asymmetry, resulting in the activity-induced and suppressed Mpemba effect. We attribute these variations in the Mpemba effect to the effective translational shift in the phase space, which occurs as activity is changed.

cond-mat.stat-mech↗

arXiv2024

Exact calculation of the large deviation function for $k$-nary coalescence

We study probabilities of rare events in the general coalescence process, $kA\rightarrow \ell A$, where $k>\ell$. For arbitrary $k, \ell$, by rewriting these probabilities in terms of an effective action, we derive the large deviation function describing the probability of finding $N$ particles at time $t$, when starting with $M$ particles initially. Additionally, the most probable trajectory corresponding to a fixed rare event is derived.

cond-mat.stat-mech↗

arXiv2024

Shock propagation following an intense explosion in an inhomogeneous gas: core scaling and hydrodynamics

We study the shock propagation in a spatially inhomogeneous gas following an intense explosion. We generalize the exact solution of the Euler equation for the spatio-temporal variation of density, velocity, and temperature to arbitrary dimensions. From the asymptotic behavior of the solution near the shock center, we argue that only for a critical dimension dependent initial density distribution will the Euler equation provide a correct description of the problem. For general initial density distributions, we use event-driven molecular dynamics simulations in one dimension to demonstrate that the Euler equation fails to capture the behavior near the shock center. However, the Navier-Stokes equation successfully resolves this issue. The crossover length scale below which the dissipation terms are relevant and the core scaling for the data near the shock center are derived and confirmed in EDMD simulations.

cond-mat.stat-mech↗

arXiv2024

Shock propagation in a driven hard sphere gas: molecular dynamics simulations and hydrodynamics

The continuous injection of energy in a stationary gas creates a shock wave that propagates radially outwards. We study the hydrodynamics of this disturbance using event driven molecular dynamics of a hard sphere gas in two and three dimensions, the numerical solution of the Euler equation with a virial equation of state for the gas, and the numerical solution of the Navier-Stokes equation, for the cases when the driving is localised in space and when it is uniform throughout the shock. We show that the results from the Euler equation do not agree with the data from hard sphere simulations when the driving is uniform and has singularities when the driving is localised. Including dissipative terms through the Navier-Stokes equation results in reasonably good description of the data, when the coefficients of dissipation are chose parametrically.

cond-mat.stat-mech↗

arXiv2024

Exact calculation of the probabilities of rare events in cluster-cluster aggregation

We develop an action formalism to calculate probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels and establish a pathwise large deviation principle with total mass being the rate. As an application, the rate function for the number of surviving particles as well as the optimal evolution trajectory are calculated exactly for the constant, sum and product kernels. For the product kernel, we argue that the second derivative of the rate function has a discontinuity. The theoretical results agree with simulations tailored to the calculation of rare events.

cond-mat.stat-mech↗

arXiv2023

Acoustic emission data based modelling of fracture of glassy polymer

Acoustic emission (AE) activity data resulting from the fracture processes of brittle materials is valuable real time information regarding the evolving state of damage in the material. Here, through a combined experimental and computational study we explore the possibility of utilising the statistical signatures of AE activity data for characterisation of disorder parameter in simulation of tensile fracture of epoxy based polymer. For simulations we use a square random spring network model with quasi-brittle spring behaviour and a normally distributed failure strain threshold. We show that the disorder characteristics while have marginal effect on the power law exponent of the avalanche size distribution, are strongly correlated with the waiting time interval between consecutive record breaking avalanches as well as the total number of records. This sensitivity to disorder is exploited in estimating the disorder parameter suitable for the experiments on tensile failure of epoxy based polymer. The disorder parameter is estimated assuming equivalence between the amplitude distribution of AE data and avalanche size distribution of the simulations. The chosen disorder parameter is shown to well reproduce the failure characteristics in terms of the peak load of the macroscopic response, the power-law behaviour with avalanche dominated fracture type as well as realistic fracture paths.

cond-mat.stat-mech↗

arXiv2023

Record statistics based prediction of fracture in the random spring network model

We study the role of record statistics of damage avalanches in predicting the fracture of a heterogeneous material under tensile loading. The material is modeled using a two-dimensional random spring network where disorder is introduced through randomness in the breakage threshold strains of the springs. It is shown that the waiting time between successive records of avalanches has a maximum for moderate disorder, thus showing an acceleration of records with impending fracture. Such a signature is absent for low disorder strength when the fracture is nucleation-dominated, and high disorder strength when the fracture is percolation type. We examine the correlation between the record with the maximum waiting time and the crossover record at which the avalanche statistics change from off-critical to critical. Compared to the avalanche based predictor for failure, we show that the record statistics have the advantage of both being real-time as well as able to predict final fracture at much smaller strains. We also show that in the avalanche-dominated regime, the failure strain is shown to have a linear relation with the strain at the maximum waiting time, making possible a quantitative prediction.

cond-mat.stat-mech↗

arXiv2023

The conformational phase diagram of charged polymers in the presence of attractive bridging crowders

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions ($CE$), (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation ($CCI$), and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or crosslinks ($CCB$). Importantly, the simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the $CCI$ and $CE$ phases to the $CCB$ phase.

cond-mat.soft↗

arXiv2023

Dissipation and recovery in collagen fibrils under cyclic loading: a molecular dynamics study

The hysteretic behavior exhibited by collagen fibrils, when subjected to cyclic loading, is known to result in both dissipation as well as accumulation of residual strain. On subsequent relaxation, partial recovery has also been reported. Cross-links have been considered to play a key role in overall mechanical properties. Here, we modify an existing coarse grained molecular dynamics model for collagen fibril with initially cross-linked collagen molecules, which is known to reproduce the response to uniaxial strain, by incorporating reformation of cross-links to allow for possible recovery of the fibril. Using molecular dynamics simulations, we show that our model successfully replicates the key features observed in experimental data, including the movement of hysteresis loops, the time evolution of residual strains and energy dissipation, as well as the recovery observed during relaxation. We also show that the characteristic cycle number, describing the approach towards steady state, has a value similar to that in experiments. We also emphasize the vital role of the degree of cross-linking on the key features of the macroscopic response to cyclic loading.

cond-mat.soft↗

arXiv2023

Phase transitions in systems of particles with only hard-core interactions

This article contains our comments and views on the status of the current understanding of phase transitions in systems with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in $d$-dimensions is discussed. The universal repulsive Lee-Yang singularities in the complex activity plane, and its relation to the directed and undirected polymer models are outlined. We also discuss orientationally disordered crystalline mesophases, and some of their models.

cond-mat.stat-mech↗

arXiv2023

Mpemba effect for a Brownian particle trapped in a single well potential

Mpemba effect refers to the counterintuitive phenomenon of a hotter system equilibrating faster than a colder system when both are quenched to the same low temperature. For a Brownian particle trapped in a piece-wise linear single well potential that is devoid of any other metastable minima we show the existence of Mpemba effect for a wide range of parameters through an exact solution. This result challenges the prevalent explanation of the Mpemba effect that requires the energy landscape to be rugged with multiple minima. We also demonstrate the existence of inverse and strong Mpemba effects.

cond-mat.stat-mech↗

arXiv2023

Mpemba effect in a Langevin system: population statistics, metastability and other exact results

The Mpemba effect is a fingerprint of the anomalous relaxation phenomenon wherein an initially hotter system equilibrates faster than an initially colder system when both are quenched to the same low temperature. Experiments on a single colloidal particle trapped in a carefully shaped double well potential have demonstrated this effect recently [Nature 584, 64 (2020)]. In a similar vein, here, we consider a piece-wise linear double well potential that allows us to demonstrate the Mpemba effect using an exact analysis based on the spectral decomposition of the corresponding Fokker-Planck equation. We elucidate the role of the metastable states in the energy landscape as well as the initial population statistics of the particles in showcasing the Mpemba effect. Crucially, our findings indicate that neither the metastability nor the asymmetry in the potential is a necessary or a sufficient condition for the Mpemba effect to be observed.

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arXiv2023

Mpemba effect in driven granular gases: role of distance measures

Mpemba effect refers to the counterintuitive effect where a system which is initially further from the final steady state equilibrates faster than an identical system that is initially closer. The closeness to the final state is defined in terms of a distance measure. For driven granular systems, the Mpemba effect has been illustrated in terms of an ad-hoc measure of mean kinetic energy as the distance function. In this paper, by studying four different distance measures based on the mean kinetic energies as well as velocity distribution, we show that the Mpemba effect depends on the definition of the measures.

cond-mat.stat-mech↗

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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