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.
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.
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 pi
cture 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.
We introduce the spatial correlation function $C_Q(r)$ and temporal autocorrelation function $C_Q(t)$ of the local tetrahedral order parameter $Qequiv Q(r,t)$. Using computer simulations of the TIP5P model of water, we investigate $C_Q(r)$ in a broad
region of the phase diagram. First we show that $C_Q(r)$ displays anticorrelation at $rapprox 0.32$nm at high temperatures $T>T_Wapprox 250$ K, which changes to positive correlation below the Widom line $T_W$. Further we find that at low temperatures $C_Q(t)$ exhibits a two-step temporal decay similar to the self intermediate scattering function, and that the corresponding correlation time $tau_Q$ displays a dynamic crossover from non-Arrhenius behavior for $T>T_W$ to Arrhenius behavior for $T<T_W$. Finally, we define an orientational entropy $S_Q$ associated with the {it local} orientational order of water molecules, and show that $tau_Q$ can be extracted from $S_Q$ using an analog of the Adam-Gibbs relation.
We introduce a stochastic model of growing networks where both, the number of new nodes which joins the network and the number of connections, vary stochastically. We provide an exact mapping between this model and zero range process, and use this ma
pping to derive an analytical solution of degree distribution for any given evolution rule. One can also use this mapping to infer about a possible evolution rule for a given network. We demonstrate this for protein-protein interaction (PPI) network for Saccharomyces Cerevisiae.
We revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class. Our earlier theoretical arguments in favor, supported by evidence from numerical simulations [ Phys. Rev. L
ett., {bf 89} (2002) 104303], have been disputed by Bonachela et al. [Phys. Rev. E {bf 74} (2004) 050102] for sandpiles with no preferred direction. We discuss possible reasons for the discrepancy. Our new results of longer simulations of the one-dimensional undirected model fully support our earlier conclusions.
In many professons employees are rewarded according to their relative performance. Corresponding economy can be modeled by taking $N$ independent agents who gain from the market with a rate which depends on their current gain. We argue that this simp
le realistic rate generates a scale free distribution even though intrinsic ability of agents are marginally different from each other. As an evidence we provide distribution of scores for two different systems (a) the global stock game where players invest in real stock market and (b) the international cricket.
