arXiv subjects

Mustansir Barma

Publications and source records attributed to Mustansir Barma.

At least 73 records · Page 4Linked to original sources

arXiv2004

Clustering of advected passive sliders on a fluctuating surface

We study the clustering properties of advected, non-interacting,passive scalar particles in a Burgers fluid with noise, a problem which maps to that of passive sliding particles moving under gravity on a surface evolving through the Kardar-Parisi-Zhang equation. Numerical simulations show that both the density-density correlation function and the single-site mass distribution scale with system size. The scaling functions diverge at small argument, indicating strong clustering of particles. We analytically evaluate the scaling functions for the two-point correlation and mass distribution of noninteracting particles in thermal equilibrium in a random landscape, and find that the results are remarkably similar to those for nonequilibrium advection.

cond-mat.stat-mech↗

arXiv2003

Asymptotic distributions of Periodically Driven Stochastic Systems

We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where these driving forces are rapidly oscillating with an amplitude that is not necessarily small. We develop a perturbative method for the high-frequency regime to find the large-time behavior of periodically driven stochastic systems. The asymptotic distribution of Brownian particles is then determined to second order. To first order, these particles are found to execute small-amplitude oscillations around an effective static potential which can have interesting forms.

cond-mat.stat-mech↗

arXiv2003

Dynamics of a disordered, driven zero range process in one dimension

We study a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical properties of the mass fluctuations in the steady state in one dimension both analytically and numerically and show that the transport properties are anomalous in certain regions of the density-disorder plane. We also determine the form of the scaling function which describes the growth of the condensate as a function of time, starting from a uniform density distribution.

cond-mat.stat-mech↗

arXiv2002

Phase separation driven by a fluctuating two-dimensional self-affine potential field

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 symmetery 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.

cond-mat.stat-mech↗

arXiv2002

Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates

The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all alpha > 0 in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite size scaling implications of this are characterized. The exponents characterizing the steady state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean field approximation and found to compare well with the results from numerical simulations in one dimension.

cond-mat.stat-mech↗

arXiv2001

Locating the minimum : Approach to equilibrium in a disordered, symmetric zero range process

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the probability distribution $f(w) \sim (w-c)^{n}$, where $c$ is the lower cutoff. For $n > 0$, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the latter case, it is interesting to ask how the system locates the site with globally minimum rate. We use an argument based on local equilibrium, supported by Monte Carlo simulations, to describe the approach to the steady state. We find that at large enough time, the mass transport in the regions with a smooth density profile is described by a diffusion equation with site-dependent rates, while the isolated points where the mass distribution is singular act as the boundaries of these regions. Our argument implies that the relaxation time scales with the system size $L$ as $L^{z}$ with $z=2+1/(n+1)$ for $n > 1$ and suggests a different behaviour for $n < 1$.

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arXiv2001

Phase Diagram of a Two-Species Lattice Model with a Linear Instability

We review recent progress in understanding the full phase diagram of a one-dimensional, driven, two-species lattice model [Lahiri and Ramaswamy, PRL 79 (1997) 1150] in which the mobility of each species depends on the density of the other. The model shows three phases. The first is characterised by phase separation of an exceptionally robust sort, termed Strong Phase Separation, which survives at all temperature. The second phase has trivial static correlations, but density fluctuations are transported by a pair of kinematic waves involving both species. In the most interesting case, the two linearised eigenmodes, although nonlinearly coupled, have different dynamic exponents. The third ``phase'' arises at the phase boundary between the first two. Here, the first species evolves autonomously, but its fluctuations influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, with density fluctuations persisting even in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law.

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arXiv2001

Fluctuation-Dominated Phase Ordering Driven by Stochastically Evolving Surfaces

We study a new kind of phase ordering phenomenon in coarse-grained depth (CD) models of the hill-valley profile of fluctuating surfaces with zero overall tilt, and for hard-core particles sliding on such surfaces under gravity. For Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surfaces, our analytic and numerical results show that CD models exhibit coarsening to an ordered steady state in which the order parameter has a broad distribution even in the thermodynamic limit. Moreover, the distribution of particle cluster sizes decays as a power-law (with an exponent $θ$), and the scaled 2-point spatial correlation function has a cusp (with an exponent $α= 1/2$) at small values of the argument. The latter feature indicates a deviation from the Porod law. For linear CD models with dynamical exponent $z$, we show that $α= (z - 1)/2$ for $z < 3$, while $α= 1$ for $z > 3$, and there are logarithmic corrections for $z = 3$. This implies $α= 1/2$ for the EW surface and 1 for the Golubovic-Bruinsma-Das Sarma-Tamborenea (GBDT) surface. Within the independent interval approximation we show that $α+ θ= 2$. The scaled density-density correlation function of the sliding particle model shows a cusp with exponent $α\simeq 0.5$, and 0.25 for the EW and KPZ surfaces. The particles on the GBDT surface show conventional coarsening (Porod) behavior with $α\simeq 1$.

cond-mat.stat-mech↗

arXiv2001

Phases of a conserved mass model of aggregation with fragmentation at fixed sites

To study the effect of quenched disorder in a class of reaction-diffusion systems, we introduce a conserved mass model of diffusion and aggregation in which the mass moves as a whole to a nearest neighbour on most sites while it fragments off as a single monomer (i.e. chips off) from certain fixed sites. Once the mass leaves any site, it coalesces with the mass present on its neighbour. We study in detail the effect of a \emph{single} chipping site on the steady state in arbitrary dimensions, with and without bias. In the thermodynamic limit, the system can exist in one of the following phases -- (a) Pinned Aggregate (PA) phase in which an infinite aggregate (with mass proportional to the volume of the system) appears with probability one at the chipping site but not in the bulk. (b) Unpinned Aggregate (UA) phase in which $\emph{both}$ the chipping site and the bulk can support an infinite aggregate simultaneously. (c) Non Aggregate (NA) phase in which there is no infinite cluster. Our analytical and numerical studies show that the system exists in the UA phase in all cases except in 1d with bias. In the latter case, there is a phase transition from the NA phase to the PA phase as density is increased. A variant of the above aggregation model is also considered in which total particle number is conserved and chipping occurs at a fixed site, but the particles do not interact with each other at other sites. This model is solved exactly by mapping it to a Zero Range Process. With increasing density, it exhibits a phase transition from the NA phase to the PA phase in all dimensions, irrespective of bias. Finally, we discuss the likely behaviour of the system in the presence of extensive disorder.

cond-mat.stat-mech↗

arXiv2000

Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves

We study the coupled dynamics of the displacement fields in a one dimensional coupled-field model for drifting crystals, first proposed by R.Lahiri and S.Ramaswamy [{\em Phys. Rev. Lett.} {\bf 79}, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model, for a special subspace in the parameter space, within the region where the model displays kinematic waves. We use these to construct the effective continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the long-time, large-distance properties of the correlation functions of the eigenmodes by using symmetry arguments, Monte Carlo simulations and self-consistent mode coupling methods. For most parameter values, the scaling exponents of the Kardar-Parisi-Zhang equation are obtained. However, for certain symmetry-determined values of the coupling constants the two eigenmodes, although nonlinearly coupled, are characterized by two distinct dynamic exponents. We discuss the possible application of the dynamic renormalization group in this context.

cond-mat↗

arXiv2000

Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws

We study a system of hard-core particles sliding downwards on a fluctuating one-dimensional surface which is characterized by a dynamical exponent $z$. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale $\sim t^{1/z}$. The structure factor deviates from the Porod law in some cases. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provides insight into the origin of this behaviour.

cond-mat.stat-mech↗

arXiv2000

Phase Transition in the Takayasu Model with Desorption

We study a lattice model where particles carrying different masses diffuse, coalesce upon contact, and also unit masses adsorb to a site with rate $q$ or desorb from a site with nonzero mass with rate $p$. In the limit $p=0$ (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power law tail $P(m)\sim m^{-τ}$ for large mass. We show that varying the desorption rate $p$ induces a nonequilibrium phase transition in all dimensions. For fixed $q$, there is a critical $p_c(q)$ such that if $p p_c(q)$, $P(m)\sim \exp(-m/m^*)$ for large $m$. The model is studied analytically within a mean field theory and numerically in one dimension.

cond-mat.stat-mech↗

arXiv1999

Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation

We study nonequilibrium phase transitions in a mass-aggregation model which allows for diffusion, aggregation on contact, dissociation, adsorption and desorption of unit masses. We analyse two limits explicitly. In the first case mass is locally conserved whereas in the second case local conservation is violated. In both cases the system undergoes a dynamical phase transition in all dimensions. In the first case, the steady state mass distribution decays exponentially for large mass in one phase, and develops an infinite aggregate in addition to a power-law mass decay in the other phase. In the second case, the transition is similar except that the infinite aggregate is missing.

cond-mat.stat-mech↗

arXiv1999

Strong Phase Separation in a Model of Sedimenting Lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a 1-d lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels--- hence the term Strong Phase Separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.

cond-mat.stat-mech↗

arXiv1999

Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation and Fragmentation

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass distribution decays exponentially for large mass in one phase. On the contrary, in the other phase it has a power law tail and in addition an infinite aggregate. The model is solved exactly within a mean field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent $χ$ and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.

cond-mat.stat-mech↗

arXiv1999

Polytype Kinetics and Quenching of Spin Chains with Competing Interactions using Trimer-flip Dynamics

We consider the effects of a quench to T = 0 on a spin system with axial next-next nearest neighbour Ising interactions, evolving under a conserved 3-spin flip dynamics. Such a model is motivated by the kinetics of stacking layers in polytypes near the 3C-6H transition. We find that the system generically gets arrested in interesting metastable states which have inhomogeneously distributed quiescent and active regions. In such arrested states, the autocorrelation function decays as a stretched exponential $\sim \exp(-(t/τ_{o})^{1 \over 3})$. The latter feature can be understood in terms of a mapping of the dynamics within active stretches to the well known simple exclusion process of particles on a line, and bounds can be put on $τ_o$.

cond-mat.stat-mech↗

arXiv1999

Arrested States formed on Quenching Spin Chains with Competing Interactions and Conserved Dynamics

We study the effects of rapidly cooling to T = 0 a spin chain with conserved dynamics and competing interactions. Depending on the degree of competition, the system is found to get arrested in different kinds of metastable states. The most interesting of these has an inhomogeneous mixture of interspersed active and quiescent regions. In this state, the steady-state autocorrelation function decays as a stretched exponential $\sim \exp(-{(t/τ_{o})}^{{1}\over{3}})$, and there is a two-step relaxation to equilibrium when the temperature is raised slightly.

cond-mat.stat-mech↗

arXiv1998

Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures

We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the morphology of the interface. We find evidence for the formation of a structure which moves along with the growth site. The time average of the structure, which is defined with respect to the active spot of growth, defines an activity-centered pattern. Extensive Monte Carlo simulations show that the pattern has a tail which decays slowly, as a power law. To understand this sort of pattern formation, we write down an approximate integral equation involving the local interface dynamics and long-ranged jumps of the growth spot. We clarify the nature of the approximation by considering a model for which the integral equation is exactly derivable from an extended master equation. Improvements to the equation are considered by adding a second coupled equation which provides a self-consistent description. The pattern, which defines a one-point correlation function, is shown to have a strong effect on ordinary space-fixed two-point correlation functions. Finally we present evidence that this sort of pattern formation is not confined to the interface problem, but is generic to situations in which the activity at succesive time steps is correlated, as for instance in several other extremal models. We present numerical results for activity-centered patterns in the Bak-Sneppen model of evolution and the Zaitsev model of low-temperature creep.

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