arXiv subjects

R. Rajesh

Publications and source records attributed to R. Rajesh.

At least 55 records · Page 3Linked to original sources

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.

cond-mat.stat-mech↗

arXiv2019

Phase diagram of a system of hard cubes on the cubic lattice

We study the phase diagram of a system of $2\times2\times2$ hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size $2\times L \times L$ where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solid-like sublattice ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size $2\times 2\times L$ where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters, which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the $O(3)$ universality class perturbed by cubic anisotropy as predicted by the Landau theory.

cond-mat.stat-mech↗

arXiv2018

Shock propagation following an intense explosion: comparison between hydrodynamics and simulations

The solution for the radial distribution of pressure, density, temperature and flow velocity fields in a blast wave propagating through a medium at rest, following an intense explosion, starting from hydrodynamic equations, is one of the classic problems in gas dynamics. However, there is very little direct verification of the theory and its assumptions from simulations of microscopic models. In this paper, we compare the results and assumptions of the hydrodynamic theory with results from large scale event driven molecular dynamics simulations of a hard sphere gas in three dimensions. We find that the predictions for the radial distribution of the thermodynamic quantities do not match well with the numerical data. We improve the theory by replacing the ideal gas law with a more realistic virial equation of state for the hard sphere gas. While this improves the theoretical predictions, we show that they still fail to describe the data well. To understand the reasons for this discrepancy, the different assumptions of the hydrodynamic theory are tested within the simulations. A key assumption of the theory is the existence of a local equation of state. We validate this assumption by showing that the local pressure, temperature and density obey the equation of state for a hard sphere gas. However, the probability distribution of the velocity fluctuations has non-gaussian tails, especially away from the shock front, showing that the assumption of local equilibrium is violated. This, along with neglect of heat conduction, could be the possible reasons for the mismatch between theory and simulations.

cond-mat.stat-mech↗

arXiv2018

Stationary mass distribution and nonlocality in models of coalescence and shattering

We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the large and small mass asymptotic behavior of the mass distribution depend on whether the collision kernel is local (the aggregation mass flux is essentially generated by collisions between particles of similar masses), or non-local (collision between particles of widely different masses give the main contribution to the mass flux). We show that the non-local regime is further divided into two sub-regimes corresponding to weak and strong non-locality. We also observe that at the boundaries between the local and non-local regimes, the mass distribution acquires logarithmic corrections to scaling and calculate these corrections. Exact solutions for special kernels and numerical simulations are used to validate some non-rigorous steps used in the analysis. Our results show that for local kernels, the scaling solutions carry a constant flux of mass due to aggregation, whereas for the non-local case there is a correction to the constant flux exponent. Our results suggest that for general scale-invariant kernels, the universality classes of mass distributions are labeled by two parameters: the homogeneity degree of the kernel and one further number measuring the degree of the non-locality of the kernel.

cond-mat.stat-mech↗

arXiv2017

Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice

We study the different phases and the phase transitions in a system of $Y$-shaped particles, examples of which include Immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbours chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implements an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solid-like sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle-symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle-symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particles undergoes a single discontinuous phase transition from a disordered phase to a solid-like sublattice phase with increasing density of particles.

cond-mat.stat-mech↗

arXiv2017

Shock propagation in locally driven granular systems

We study shock propagation in a system of initially stationary hard-spheres that is driven by a continuous injection of particles at the origin. The disturbance created by the injection of energy spreads radially outwards through collision between particles. Using scaling arguments, we determine the exponent characterizing the power law growth of this disturbance in all dimensions. The scaling functions describing the various physical quantities are determined using large scale event driven simulations in two and three dimensions for both the elastic and the inelastic system. The results are shown to describe well the data from two different experiments on granular systems that are similarly driven.

cond-mat.stat-mech↗

arXiv2017

Diffusion dynamics and steady states of systems of hard rods on the square lattice

It is known from grand canonical simulations of a system of hard rods on two dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drives the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.

cond-mat.soft↗

arXiv2017

The columnar-disorder phase boundary in a mixture of hard squares and dimers

A mixture of hard squares, dimers and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes an Kosterliz-Thouless type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2017

On role of matrix behavior in compressive fracture of bovine cortical bone

In compressive fracture of dry plexiform bone, we examine the individual roles of overall mean porosity, the connectivity of the porosity network, and the elastic as well as the failure properties of the non-porous matrix, using a random spring network model. Porosity network structure is shown to reduce the compressive strength by upto 30%. However, the load bearing capacity increases with increase in either of the matrix properties - elastic modulus or failure strain threshold. To validate the porosity-based RSNM model with available experimental data, bone-specific failure strain thresholds for the ideal matrix of similar elastic properties were estimated to be within 60% of each other. Further, we observe the avalanche size exponents to be independent of the bone-dependent parameters as well as the structure of the porosity network.

cond-mat.soft↗

arXiv2017

Different phases of a system of hard rods on three dimensional cubic lattice

We study the different phases of a system of monodispersed hard rods of length $k$ on a cubic lattice using an efficient cluster algorithm which can simulate densities close to the fully-packed limit. For $k\leq 4$, the system is disordered at all densities. For $k=5,6$, we find a single density-driven transition from a disordered phase to high density layered-disordered phase in which the density of rods of one orientation is strongly suppressed, breaking the system into weakly coupled layers. Within a layer, the system is disordered. For $k \geq 7$, three density driven transitions are observed numerically: isotropic to nematic to layered-nematic to layered-disordered. In the layered-nematic phase, the system breaks up into layers, with nematic order in each in each layer, but very weak correlation between the ordering direction between different layers. We argue that the layered-nematic phase is a finite-size effect, and in the thermodynamic limit, the nematic phase will have higher entropy per site.

cond-mat.stat-mech↗

arXiv2017

Universality properties of steady driven coagulation with collisional evaporation

Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small probability is the sink. Using exact and heuristic analyses, we find a universal regime and two distinct non-universal regimes distinguished by the relative importance of mergers between small and large particles. At the boundary between the regimes we find an analogue of the logarithmic correction conjectured by Kraichnan for two-dimensional turbulence.

cond-mat.stat-mech↗

arXiv2017

Estimating the Critical Parameters of the Hard Square Lattice Gas Model

The hard square lattice gas model on a square lattice is known to undergo a continuous phase transition from a low density fluid-like phase to high density phase with columnar or smectic order. We estimate the critical activity $z_c$ by calculating, within an approximation scheme, the interfacial tension between two differently ordered columnar phases, and then setting it to zero. The approximation scheme allows for the ordered phases to have multiple defects and the interface between the ordered phases to have overhangs. We estimate $z_c=105.35$, which is in good agreement with existing Monte Carlo simulation results of $z_c \approx 97.5$, and is an improvement over earlier best estimates of $z_c=54.87$ and $z_c=135.63$.

cond-mat.stat-mech↗

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.

cond-mat.stat-mech↗

arXiv2016

Non-equilibrium phase diagram for a model with coalescence, evaporation and deposition

We study a d-dimensional lattice model of diffusing coalescing massive particles, with two parameters controlling deposition and evaporation of monomers. The unique stationary distribution for the system exhibits a phase transition in all dimensions d greater or equal to one between a growing phase, in which the expected mass is infinite at each site, and an exponential phase in which the expected mass is finite. We establish rigorous upper and lower bounds on the critical curve describing the phase transition for this system, and some asymptotics for large or small deposition rates.

math.PR↗

arXiv2016

Mechanism of chain collapse of strongly charged polyelectrolytes

We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius $R_g $ on the reduced Bjerrum length $\ell_B$ and find two different regimes. In the first one, called as a weak electrostatic regime, $R_g \sim \ell_B^{-1/2}$, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find $R_g \sim \ell_B^{-1/5}$. To explain the novel regime we modify the counterion-fluctuation theory.

cond-mat.soft↗

arXiv2016

The High Density Phase of the $k$-NN Hard Core Lattice Gas Model

The $k$-NN hard core lattice gas model on a square lattice, in which the first $k$ next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two dimensional continuum. It has been conjectured that the lattice model, like its continuum counterpart, will show multiple entropy-driven transitions with increasing density if the high density phase has columnar or striped order. Here, we determine the nature of the phase at full packing for $k$ up to $820302$. We show that there are only eighteen values of $k$, all less than $k=4134$, that show columnar order, while the others show solid-like sublattice order.

cond-mat.stat-mech↗

arXiv2016

Stability of columnar order in assemblies of hard rectangles or squares

A system of $2\times d$ hard rectangles on square lattice is known to show four different phases for $d \geq 14$. As the covered area fraction $ρ$ is increased from $0$ to $1$, the system goes from low-density disordered phase, to orientationally-ordered nematic phase, to a columnar phase with orientational order and also broken translational invariance, to a high density phase in which orientational order is lost. For large d, the threshold density for the first transition $ρ_1^*$ tends to $0$, and the critical density for the third transition $ρ_3^*$ tends to $1$. Interestingly, simulations have shown that the critical density for the second transition $ρ_2^*$ tends to a non-trivial finite value $\approx 0.73$, as $d \rightarrow \infty$, and $ρ_2^* \approx 0.93$ for $d=2$. We provide a theoretical explanation of this interesting result. We develop an approximation scheme to calculate the surface tension between two differently ordered columnar phases. The density at which the surface tension vanishes gives an estimate $ρ_2^* = 0.746$, for $d\to \infty$, and $ρ_2^*=0.923$ for $d=2$. For all values of $d$, these estimates are in good agreement with Monte Carlo data.

cond-mat.stat-mech↗

arXiv2015

Phase diagram of a bidispersed hard rod lattice gas in two dimensions

We obtain, using extensive Monte Carlo simulations, virial expansion and a high-density perturbation expansion about the fully packed monodispersed phase, the phase diagram of a system of bidispersed hard rods on a square lattice. We show numerically that when the length of the longer rods is $7$, two continuous transitions may exist as the density of the longer rods in increased, keeping the density of shorter rods fixed: first from a low-density isotropic phase to a nematic phase, and second from the nematic to a high-density isotropic phase. The difference between the critical densities of the two transitions decreases to zero at a critical density of the shorter rods such that the fully packed phase is disordered for any composition. When both the rod lengths are larger than $6$, we observe the existence of two transitions along the fully packed line as the composition is varied. Low-density virial expansion, truncated at second virial coefficient, reproduces features of the first transition. By developing a high-density perturbation expansion, we show that when one of the rods is long enough, there will be at least two isotropic-nematic transitions along the fully packed line as the composition is varied.

cond-mat.stat-mech↗