arXiv subjects

P. K. Mohanty

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

At least 73 records · Page 4Linked to original sources

arXiv2012

Restricted Exclusion Processes without Particle Conservation Flows to Directed Percolation

Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken suitably. The same transition, when studied using the average density as the controlling parameter, yields critical exponents quite different from DP; we argue that these exponents are actually related to DP by a scaling factor $1/β_{DP}.$ These conclusions also apply to conserved lattice gas in one dimension.

cond-mat.stat-mech↗

arXiv2012

Absorbing State Phase Transition in presence of Conserved Continuous Local Field

We study absorbing state phase transition in one dimension in presence of a conserved continuous local field (CCLF) called energy. A pair of sites on a lattice is said to be active if one or both sites posses more energy than a pre-defined threshold. The active pair of sites are allowed to redistribute their energy following a stochastic rule. We show that, the CCLF model undergo a continuous absorbing state transition when energy per site is decreased below a critical value. The critical exponents are found to be different from those of DP.

cond-mat.stat-mech↗

arXiv2011

Driven k-mers: Correlations in space and time

Steady state properties of hard objects with exclusion interaction and a driven motion along a one-dimensional periodic lattice are investigated. The process is a generalization of the asymmetric simple exclusion process (ASEP) to particles of length k, and is called the k-ASEP. Here, we analyze both static and dynamic properties of the k-ASEP. Density correlations are found to display interesting features, such as pronounced oscillations in both space and time, as a consequence of the extended length of the particles. At long times, the density autocorrelation decays exponentially in time, except at a special k-dependent density when it decays as a power law. In the limit of large k at a finite density of occupied sites, the appropriately scaled system reduces to a nonequilibrium generalization of the Tonks gas describing the motion of hard rods along a continuous line. This allows us to obtain in a simple way the known two-particle distribution for the Tonks gas. For large but finite k, we also obtain the leading-order correction to the Tonks result.

cond-mat.stat-mech↗

arXiv2011

Comments on "Critical Study on the Absorbing Phase Transition in a Four-State Predator-Prey Model in One Dimension"

In a recent article [arXiv:1108.5127] Park has shown that the four-state predator-prey model studied earlier in [J. Stat. Mech, L05001 (2011)] belongs to Directed Percolation (DP) universality class. It was claimed that predator density is not a reasonable order parameter, as there are many absorbing states; a suitably chosen order parameter shows DP critical behavior. In this article, we argue that the configuration that does not have any predator is the only dynamically accessible absorbing configuration, and the predator density too settles to DP critical exponents after a long transient.

cond-mat.stat-mech↗

arXiv2011

Phase Transition in an Exactly Solvable Extinction Model

We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective stress level is greater than their individual fitness. The model exhibits a phase transition to a completely extinct phase as the environmental stress or the mutation rate is varied. We discuss the generic conditions for which this transition is continuous. The model is exactly solvable and the critical behavior is characterized by an unusual dynamic exponent z=1/3. Apart from predicting large scale evolution, the model can be applied to understand the trends in the available fossil data.

cond-mat.stat-mech↗

arXiv2011

Asymmetric Simple Exclusion Process on a Cayley Tree

We study the asymmetric exclusion process on a regular Cayley tree with arbitrary co-ordination number. In this model particles can enter the system only at the parent site and exit from one of the sites at the last level. In the bulk they move from the occupied sites to one of their unoccupied downward neighbours, chosen randomly. We show that the steady state current that flow from one level to the next is independent of the exit rate, and increase monotonically with the entry rate and the co-ordination number. Unlike TASEP, the model has only one phase and the density profile show no boundary layers. We argue that in blood, air or water circulations systems branching is essential to maintain a free flow within the system which is independent of exit rates.

cond-mat.stat-mech↗

arXiv2011

Modules of human micro-RNA co-target network

Human micro RNAs (miRNAs) target about 90% of the coding genes and form a complex regulatory network. We study the community structure of the miRNA co-target network considering miRNAs as the nodes which are connected by weighted links. The weight of link that connects a pair of miRNAs denote the total number of common transcripts targeted by that pair. We argue that the network consists of about 74 modules, quite similar to the components (or clusters) obtained earlier [Online J Bioinformatics, 10,280 ], indicating that the components of the miRNA co-target network are self organized in a way to maximize the modularity.

q-bio.MN↗

arXiv2011

Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator, or occupied by a single prey, or by both. Along with the pairwise death of predators and growth of preys, we introduce an interaction where the predators can eat one of the neighboring prey and reproduce a new predator there instantly. The model shows a non-equilibrium phase transition into a unusual absorbing state where predators are absent and the lattice is fully occupied by preys. The critical exponents of the system are found to be different from that of the Directed Percolation universality class and they are robust against addition of explicit diffusion.

cond-mat.stat-mech↗

arXiv2011

A Novel Approach to Discontinuous Bond Percolation Transition

We introduce a bond percolation procedure on a $D$-dimensional lattice where two neighbouring sites are connected by $N$ channels, each operated by valves at both ends. Out of a total of $N$, randomly chosen $n$ valves are open at every site. A bond is said to connect two sites if there is at least one channel between them, which has open valves at both ends. We show analytically that in all spatial dimensions, this system undergoes a discontinuous percolation transition in the $N\to \infty$ limit when $γ=\frac{\ln n}{\ln N}$ crosses a threshold. It must be emphasized that, in contrast to the ordinary percolation models, here the transition occurs even in one dimensional systems, albeit discontinuously. We also show that a special kind of discontinuous percolation occurs only in one dimension when $N$ depends on the system size.

cond-mat.stat-mech↗

arXiv2010

Bimodal response in periodically driven diffusive systems

We study the response of one dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system can be characterized in terms of the structure factor. We find an interesting frequency dependent response -- the current carrying majority excitons cyclically crosses over from a short wavelength mode to a long wavelength mode with an intermediate regime of coexistence. This effect being boundary driven, decays inversely with system size. Analytic calculations show that this behavior is common to diffusive systems, both in absence and presence of correlations.

cond-mat.stat-mech↗

arXiv2010

Discontinuous Absorbing State Transition in $(1+1)$ Dimension

A $(1+1)$ dimensional model of directed percolation is introduced where sites on a tilted square lattice are connected to their neighbours by $N$ channels, operated at both ends by valves which are either open or closed. The spreading fluid is assumed to propagate from any site to the neighbours in a specified direction only through those channels which have open valves at both sites. We show that the system undergoes a discontinuous absorbing state transition in the large $N$ limit when the number of open valves at each site $n$ crosses a threshold value $n_c=\sqrt N.$ Remarkable dynamical properties of discontinuous transitions, like hysteresis and existence of two well separated fluctuating phases near the critical point are also observed. The transition is found to be discontinuous in all $(d+1)$ dimensions.

cond-mat.stat-mech↗

arXiv2010

Particle Ordering in Zero Range Process : Exact spatial correlations of the corresponding exclusion models

A one dimensional exclusion process is introduced where particles hop to a neighbouring vacant site with a rate that depends on the size of the block they belong to. This model is equivalent to a zero range process (ZRP) and shares the same steady state distribution. However positional ordering is lost in this mapping and spatial correlations which depend on position indices can not be calculated directly from the ZRP equivalence. We devise a method to calculate these correlations and illustrate it by reproducing certain known results. Unexplored correlations in some other model systems are also investigated. This method can be generically used to find exact correlations of one dimensional exclusion processes which has ZRP correspondence.

cond-mat.stat-mech↗

arXiv2010

Phase separation transition in anti-ferromagnetically interacting particle systems

One dimensional non-equilibrium systems with short-range interaction can undergo phase transitions from homogeneous states to phase separated states as interaction ($ε$) among particles is increased. One of the model systems where such transition has been observed is the extended Katz-Lebowitz-Spohn (KLS) model with ferro-magnetically interacting particles at $ε=4/5$. Here, the system remains homogeneous for small interaction strength ($ε<4/5$), and for anti-feromagnetic interactions ($ε<0$). We show that the phase separation transitions can also occur in anti-ferromagnetic systems if interaction among particles depends explicitly on the size of the block ($n$) they belong to. We study this transition in detail for a specific case $ε= δ/n$, where phase separation occurs for $δ< -1$.

cond-mat.stat-mech↗

arXiv2010

TASEP on a ring with internal degrees of freedom

A totally asymmetric exclusion process on a ring with $ν$ non-conserved internal degrees of freedom, where particles hop forward with a rate that depends on their internal state, has been studied. We show, using a mapping of the model to a zero range process with $ν$ different kinds of boxes, that steady state weights can be written in a matrix product form and calculate the spatial correlations exactly. A comparison of the model with an equivalent conserved system reveals that unequal hopping rates of particles belonging to different internal states is responsible for the non-trivial correlations.

cond-mat.stat-mech↗

arXiv2010

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.

cond-mat.stat-mech↗

arXiv2009

Phase diagram of the ABC model on an interval

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a one-dimensional lattice of N sites with closed (zero flux) boundaries. In this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical Gibbs measure with long range asymmetric pair interactions. This generalizes results for the ring case, where detailed balance holds, and in fact the steady state measure is known only for the case of equal densities of the different species: in the latter case the stationary states of the system on a ring and on an interval are the same. We prove that in the N to infinity limit the scaled density profiles are given by (pieces of) the periodic trajectory of a particle moving in a quartic confining potential. We further prove uniqueness of the profiles, i.e., the existence of a single phase, in all regions of the parameter space (of average densities and temperature) except at low temperature with all densities equal; in this case a continuum of phases, differing by translation, coexist. The results for the equal density case apply also to the system on the ring, and there extend results of Clincy et al.

cond-mat.stat-mech↗

arXiv2009

Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models

We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left neighbour is occupied and the right neighbour is vacant. Particles from such active sites hop stochastically to their right. We show that, both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these non-equilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely directed percolation.

cond-mat.stat-mech↗

arXiv2009

Modeling wealth distribution in growing markets

We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on how much they invest, and stochastically on how much they gain from the noisy market. The average wealth of the market could be fixed or growing. We show that in a market where investment capacity of agents differ, average wealth of agents generically follow the Pareto-law. In few cases, the individual distribution of wealth of every agent could also be obtained exactly. We also show that the underlying dynamics of other well studied kinetic models of markets can be mapped to the dynamics of our auto-regressive model.

q-fin.GN↗