arXiv subjects

P. K. Mohanty

Publications and source records attributed to P. K. Mohanty.

At least 55 records · Page 3Linked to original sources

arXiv2016

Multi-critical absorbing phase transition in a class of exactly solvable models

We study diffusion of hardcore particles on a one dimensional periodic lattice subjected to a constraint that the separation between any two consecutive particles does not increase beyond a fixed value $(n+1);$ initial separation larger than $(n+1)$ can however decrease. These models undergo an absorbing state phase transition when the conserved particle density of the system falls bellow a critical threshold $ρ_c= 1/(n+1).$ We find that $ϕ_k$s, the density of $0$-clusters ($0$ representing vacancies) of size $0\le k<n,$ vanish at the transition point along with activity density $ρ_a$. The steady state of these models can be written in matrix product form to obtain analytically the static exponents $β_k= n-k,ν=1=η$ corresponding to each $ϕ_k$. We also show from numerical simulations that starting from a natural condition, $ϕ_k(t)$s decay as $t^{-α_k}$ with $α_k= (n-k)/2$ even though other dynamic exponents $ν_t=2=z$ are independent of $k$; this ensures the validity of scaling laws $β= αν_t,$ $ν_t = z ν$.

cond-mat.stat-mech↗

arXiv2016

Phase coexistence and spatial correlations in reconstituting k-mer models

In reconstituting k-mer models, extended objects which occupy several sites on a one dimensional lattice, undergo directed or undirected diffusion, and reconstitute -when in contact- by transferring a single monomer unit from one k-mer to the other; the rates depend on the size of participating k-mers. This polydispersed system has two conserved quantities, the number of k-mers and the packing fraction. We provide a matrix product method to write the steady state of this model and to calculate the spatial correlation functions analytically. We show that for a constant reconstitution rate, the spatial correlation exhibits damped oscillations in some density regions separated, from other regions with exponential decay, by a disorder surface. In a specific limit, this constant-rate reconstitution model is equivalent to a single dimer model and exhibits a phase coexistence similar to the one observed earlier in totally asymmetric simple exclusion process on a ring with a defect.

cond-mat.stat-mech↗

arXiv2016

The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model

We present simulations of the 1-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sandpile model is hyperuniform to reach system of sizes $> 10^7$. Most previous simulations were seriously flawed by important finite size corrections. We find that all critical exponents have values consistent with simple rationals: $ν=4/3$ for the correlation length exponent, $D =9/4$ for the fractal dimension of avalanche clusters, and $z=10/7 $ for the dynamical exponent. In addition we relate the hyperuniformity exponent to the correlation length exponent $ν$. Finally we discuss the relationship with the quenched Edwards-Wilkinson (qEW) model, where we find in particular that the local roughness exponent is $α_{\rm loc} = 1$.

cond-mat.stat-mech↗

arXiv2015

Additivity property and emergence of power laws in nonequilibrium steady states

We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.

cond-mat.stat-mech↗

arXiv2015

Cluster-factorized steady states in finite range processes

We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbours, with a rate that depends on the occupation of all the neighbouring sites within a range R. This finite range process (FRP) for R=0 reduces to the well known zero-range process (ZRP), giving rise to a factorized steady state (FSS) for any arbitrary hop rate. We show that, provided the hop rates satisfy a specific condition, the steady state of FRP can be written as a product of cluster-weight function of (R+1) occupation variables. We show that, for a large class of cluster-weight functions, the cluster-factorized steady state admits a finite dimensional transfer-matrix formulation, which helps in calculating the spatial correlation functions and subsystem mass distributions exactly. We also discuss a criterion for which the FRP undergoes a condensation transition.

cond-mat.stat-mech↗

arXiv2015

Zeroth law of thermodynamics for nonequilibrium steady states in contact

We ask what happens when two systems having a nonequilibrium steady state are kept in contact and allowed to exchange a quantity, say mass, which is conserved in the combined system. Will the systems eventually evolve to a new stationary state where certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that the zeroth law would hold, provided both systems have short-ranged spatial correlations and they {\it interact weakly} to exchange mass with rates satisfying a balance condition - reminiscent of detailed balance in equilibrium. This proposition is proved for driven systems in general in the limit of small exchange rates (i.e., weak interaction) and is demonstrated} in various conserved-mass transport processes having nonzero spatial correlations.

cond-mat.stat-mech↗

arXiv2015

A microscopic model of ballistic-diffusive crossover

Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomena in the coarse grained level, a microscopic picture that consistently describes both the ballistic and the diffusive transport regimes has been lacking. In this work we derive a scaling from for the thermal current in a class of one dimensional systems attached to heat baths at boundaries, and show rigorously that the crossover occurs when the characteristic length scale of the system competes with the system size.

cond-mat.stat-mech↗

arXiv2015

Phase separation transition of reconstituting k-mers in one dimension

We introduce a driven diffusive model involving poly-dispersed hard k-mers on a one dimensional periodic ring and investigate the possibility of phase separation transition in such systems. The dynamics consists of a size dependent directional drive and reconstitution of k-mers. The reconstitution dynamics constrained to occur among consecutive immobile k-mers allows them to change their size while keeping the total number of k-mers and the volume occupied by them conserved. We show by mapping the model to a two species misanthrope process that its steady state has a factorized form. Along with a fluid phase, the interplay of drift and reconstitution can generate a macroscopic k-mer, or a slow moving k-mer with a macroscopic void in front of it, or both. We demonstrate this phenomenon for some specific choice of drift and reconstitution rates and provide exact phase boundaries which separate the four phases.

cond-mat.stat-mech↗

arXiv2015

Self-organised criticality in stochastic sandpiles: Connection to directed percolation

We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive and dissipation limit, i.e. the so-called self-organised critical (SOC) regime and show that the system exhibits a crossover from ordinary DP scaling to a dissipation-controlled scaling which is independent of the underlying dynamics or spatial dimension. The new scaling regime continues all the way to the zero bulk drive limit suggesting that the corresponding SOC behaviour is only DP, modified by the dissipation-controlled scaling. We demonstrate this for the continuous and discrete Manna model driven by noise and bulk dissipation.

cond-mat.stat-mech↗

arXiv2015

How are Forbush decreases related to interplanetary magnetic field enhancements ?

Aims. Forbush decrease (FD) is a transient decrease followed by a gradual recovery in the observed galactic cosmic ray intensity. We seek to understand the relationship between the FDs and near-Earth interplanetary magnetic field (IMF) enhancements associated with solar coronal mass ejections (CMEs). Methods. We use muon data at cutoff rigidities ranging from 14 to 24 GV from the GRAPES-3 tracking muon telescope to identify FD events. We select those FD events that have a reasonably clean profile, and magnitude > 0.25%. We use IMF data from ACE/WIND spacecrafts. We look for correlations between the FD profile and that of the one hour averaged IMF. We ask if the diffusion of high energy protons into the large scale magnetic field is the cause of the lag observed between the FD and the IMF. Results. The enhancement of the IMF associated with FDs occurs mainly in the shock-sheath region, and the turbulence level in the magnetic field is also enhanced in this region. The observed FD profiles look remarkably similar to the IMF enhancement profiles. The FDs typically lag the IMF enhancement by a few hours. The lag corresponds to the time taken by high energy protons to diffuse into the magnetic field enhancement via cross-field diffusion. Conclusions. Our findings show that high rigidity FDs associated with CMEs are caused primarily by the cumulative diffusion of protons across the magnetic field enhancement in the turbulent sheath region between the shock and the CME.

astro-ph.SR↗

arXiv2014

Gammalike mass distributions and mass fluctuations in conserved-mass transport processes

We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that joint mass distribution of subsystems is factorized in the thermodynamic limit. The factorization condition is not too restrictive as it would hold in systems with short-ranged spatial correlations. To demonstrate the result, we revisit a broad class of mass transport models and its generic variants, and show that the variance of subsystem mass in these models is proportional to square of its mean. This particular functional form of the variance constrains the subsystem mass distribution to be a gamma distribution irrespective of the dynamical rules.

cond-mat.stat-mech↗

arXiv2014

Universality splitting in distribution of number of miRNA co-targets

In a recent work [arXiv:1307.1382] it was pointed out that the link-weight distribution of microRNA (miRNA) co-target network of a wide class of species are universal up to scaling. The number cell types, widely accepted as a measure of complexity, turns out to be proportional to these scale-factor. In this article we discuss additional universal features of these networks and show that, this universality splits if one considers distribution of number of common targets of three or more number of miRNAs. These distributions for different species can be collapsed onto two distinct set of universal functions, revealing the fact that the species which appeared in early evolution have different complexity measure compared to those appeared late.

q-bio.GN↗

arXiv2013

Revisiting Absorbing Phase Transition in Energy Exchange Models

A recent study of conserved Manna model, with both discrete and continuous variable, indicates that absorbing phase transitions therein belong to the directed percolation (DP) universality class. In this context we revisit critical behaviour in energy exchange models with a threshold. Contrary to the previous claims [PRE 83, 061130 (2011), arXiv:1102.1631], our results indicate that both the maximal and minimal versions of this model belong to the DP class.

cond-mat.stat-mech↗

arXiv2013

Link-weight distribution of microRNA co-target networks exhibit universality

MicroRNAs (miRNAs) are small non-coding RNAs which regulate gene expression by binding to the 3' UTR of the corresponding messenger RNAs. We construct miRNA co-target networks for 22 different species using a target prediction database, MicroCosm Tagets. The miRNA pairs of individual species having one or more common target genes are connected and the number of co-targets are assigned as the weight of these links. We show that the link-weight distributions of all the species collapse remarkably onto each other when scaled suitably. It turns out that the scale-factor is a measure of complexity of the species. A simple model, where targets are chosen randomly by miRNAs, could provide the correct scaling function and explain the universality.

q-bio.MN↗

arXiv2013

High rigidity Forbush decreases: due to CMEs or shocks?

We seek to identify the primary agents causing Forbush decreases (FDs) observed at the Earth in high rigidity cosmic rays. In particular, we ask if such FDs are caused mainly by coronal mass ejections (CMEs) from the Sun that are directed towards the Earth, or by their associated shocks. We use the muon data at cutoff rigidities ranging from 14 to 24 GV from the GRAPES-3 tracking muon telescope to identify FD events. We select those FD events that have a reasonably clean profile, and can be reasonably well associated with an Earth-directed CME and its associated shock. We employ two models: one that considers the CME as the sole cause of the FD (the CME-only model) and one that considers the shock as the only agent causing the FD (the shock-only model). We use an extensive set of observationally determined parameters for both these models. The only free parameter in these models is the level of MHD turbulence in the sheath region, which mediates cosmic ray diffusion (into the CME, for the CME-only model and across the shock sheath, for the shock-only model). We find that good fits to the GRAPES-3 multi-rigidity data using the CME-only model require turbulence levels in the CME sheath region that are only slightly higher than those estimated for the quiet solar wind. On the other hand, reasonable model fits with the shock-only model require turbulence levels in the sheath region that are an order of magnitude higher than those in the quiet solar wind. This observation naturally leads to the conclusion that the Earth-directed CMEs are the primary contributors to FDs observed in high rigidity cosmic rays.

astro-ph.SR↗

arXiv2012

Thermally driven classical Heisenberg model in one dimension

We study thermal transport in a classical one-dimensional Heisenberg model employing a discrete time odd even precessional update scheme. This dynamics equilibrates a spin chain for any arbitrary temperature and finite value of the integration time step $Δt$. We rigorously show that in presence of driving the system attains local thermal equilibrium which is a strict requirement of Fourier law. In the thermodynamic limit heat current for such a system obeys Fourier law for all temperatures, as has been recently shown [A. V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)]. Finite systems, however, show an apparent ballistic transport which crosses over to a diffusive one as the system size is increased. We provide exact results for current and energy profiles in zero- and infinite-temperature limits.

cond-mat.stat-mech↗

arXiv2012

Conserved mass models with stickiness and chipping

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass sticks to the site. In the asymmetric version, the chipped off mass is distributed among the site and the right neighbour, whereas in the symmetric version the redistribution occurs among the two neighbours. The steady state mass distribution of the model is obtained using a perturbation method for both parallel and random sequential updates. In most cases, this perturbation theory provides a steady state distribution with reasonable accuracy.

cond-mat.stat-mech↗

arXiv2012

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.

cond-mat.stat-mech↗