arXiv subjects

S. B. Santra

Publications and source records attributed to S. B. Santra.

At least 19 recordsLinked to original sources

arXiv2023

Collective dynamics and phase transition of active matter in presence of orientation adapters

In this work, the orientation adapter, a species of active particles that adapt their direction of motion from the other active particles, is introduced. The orientation adapters exist besides the usual Vicsek-like particles; both are self-driven, however, follow different interaction rules. We have studied the dynamics in high speed of the particles keeping dissimilar speeds for these different species. The effect of orientation adapters on the collective behaviour of the system is explored in this model. The orientational order-disorder phase transition is mainly studied in such systems. First, for equal density of both species, when the adapter speed $v_a=1.2v_0$ and usual particles speed $v_0=1.0$, both adapters and the usual particles form dense travelling bands and move in the same direction. Near the transition point, such bands appear and disappear over time, giving rise to the co-existence of two phases. The adapters and the usual particles both undergo a discontinuous transition. The nature of the transition is further confirmed by the existence of hysteresis in the order parameter under a continuously varying noise field. However, when the adapter velocity becomes much higher than the usual SPPs $v_a \approx 7v_0$, the formation of travelling bands disappears from the system, and the transition becomes continuous. The density ratio is also varied, keeping the velocities constant, and the phase transition is studied. For a high adapter velocity with $v_a=10v_0$, the continuous transition is found with low-density values of the adapters. The critical exponents related to the continuous transition are also determined.

cond-mat.soft↗

arXiv2022

Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles

The collective behavior of a binary mixture of polar self-propelled particles (SPPs) with different motile properties is studied. The binary mixture consists of slow-moving SPPs (sSPPs) of fixed velocity $v_s$ and fast-moving SPPs (fSPPs) of fixed velocity $v_f$. These SPPs interact via a short-range interaction irrespective of their types. They move following certain position and velocity update rules similar to the Vicsek model (VM) under the influence of an external noise $η$. The system is studied at different values of $v_f$ keeping $v_s=0.01$ constant for a fixed density $ρ=0.5$. Different phase-separated collective patterns that appear in the system over a wide range of noise $η$ are characterized. The fSPPs and the sSPPs are found to be orientationally phase-synchronized at the steady-state. We studied an orientational order-disorder transition varying the angular noise $η$ and identified the critical noise $η_c$ for different $v_f$. Interestingly, both the species exhibit continuous transition for $v_f<100v_s$, and discontinuous transition for $v_f>100v_s$. A new set of critical exponents is determined for the continuous transitions. However, the binary model is found to be non-universal as the values of the critical exponents depend on the velocity. The effect of interaction radius on the system behavior is also studied.

cond-mat.soft↗

arXiv2019

Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone

Both the deterministic and stochastic sandpile models are studied on the percolation backbone, a random fractal, generated on a square lattice in $2$-dimensions. In spite of the underline random structure of the backbone, the deterministic Bak Tang Wiesenfeld (BTW) model preserves its positive time auto-correlation and multifractal behaviour due to its complete toppling balance, whereas the critical properties of the stochastic sandpile model (SSM) still exhibits finite size scaling (FSS) as it exhibits on the regular lattices. Analysing the topography of the avalanches, various scaling relations are developed. While for the SSM, the extended set of critical exponents obtained is found to obey various the scaling relation in terms of the fractal dimension $d_f^B$ of the backbone, whereas the deterministic BTW model, on the other hand, does not. As the critical exponents of the SSM defined on the backbone are related to $d_f^B$, the backbone fractal dimension, they are found to be entirely different from those of the SSM defined on the regular lattice as well as on other deterministic fractals. The SSM on the percolation backbone is found to obey FSS but belongs to a new stochastic universality class.

cond-mat.stat-mech↗

arXiv2017

Stochastic sandpile model on small-world networks: scaling and crossover

A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $ϕ$ where $ϕ=0$ and $1$ represent a regular lattice and a random network respectively. In the small-world regime ($2^{-12} \le ϕ\le 0.1$), the critical behaviour of the model is explored studying different geometrical properties of the avalanches as a function of avalanche size $s$. For both the dimensions, three regions of $s$, separated by two crossover sizes $s_1$ and $s_2$ ($s_1 s_1$ are sparse as they are on network and follow mean-field scaling. Coexistence of different scaling forms in the small-world regime leads to violation of usual finite-size scaling, in contrary to the fact that the model follows the same on the regular lattice as well as on the random network independently. Simultaneous appearance of multiple scaling forms are characterized by developing a coexistence scaling theory. As SWN evolves from regular lattice to random network, a crossover from diffusive to super-diffusive nature of sand transport is observed and scaling forms of such crossover is developed and verified.

cond-mat.stat-mech↗

arXiv2017

Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition

A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and the clusters are grown from these nucleation centers with a tunable growth probability g. As the growth probability g is varied from 0 to 1 two distinct regimes are found to occur. For g\le 0.5, the model exhibits continuous percolation transitions as ordinary percolation whereas for g\ge 0.8 the model exhibits discontinuous percolation transitions. The discontinuous transition is characterized by discontinuous jump in the order parameter, compact spanning cluster and absence of power law scaling of cluster size distribution. Instead of a sharp tricritical point, a tricritical region is found to occur for 0.5 < g < 0.8 within which the values of the critical exponents change continuously till the crossover from continuous to discontinuous transition is completed.

cond-mat.stat-mech↗

arXiv2017

Sandpile model on Scale Free Networks with preferential sand distribution: a new universality class

A two state sandpile model with preferential sand distribution is developed and studied numerically on scale free networks with power-law degree ($k$) distribution, {\em i.e.}: $P_k\sim k^{-α}$. In this model, upon toppling of a critical node sand grains are given one to each of the neighbouring nodes with highest and lowest degrees instead of two randomly selected neighbouring nodes as in a stochastic sandpile model. The critical behaviour of the model is determined by characterizing various avalanche properties at the steady state varying the network structure from scale free to random, tuning $α$ from $2$ to $5$. The model exhibits mean field scaling on the random networks, $α>4$. However, in the scale free regime, $2<α<4$, the scaling behaviour of the model not only deviates from the mean-field scaling but also the exponents describing the scaling behaviour are found to decrease continuously as $α$ decreases. In this regime, the critical exponents of the present model are found to be different from those of the two state stochastic sandpile model on similar networks. The preferential sand distribution thus has non-trivial effects on the sandpile dynamics which leads the model to a new universality class.

cond-mat.stat-mech↗

arXiv2016

Dissipative stochastic sandpile model on small world network : properties of non-dissipative and dissipative avalanches

A dissipative stochastic sandpile model is constructed and studied on small world networks in one and two dimensions with different shortcut densities $ϕ$, where $ϕ=0$ represents regular lattice and $ϕ=1$ represents random network. The effect of dimension, network topology and specific dissipation mode (bulk or boundary) on the the steady state critical properties of non-dissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and non-dissipative avalanches display stochastic scaling at $ϕ=0$ and mean-field scaling at $ϕ=1$, the dissipative avalanches display non trivial critical properties at $ϕ=0$ and $1$ in both one and two dimensions. In the small world regime ($2^{-12} \le ϕ\le 0.1$), the size distributions of different types of avalanches are found to exhibit more than one power law scaling with different scaling exponents around a crossover toppling size $s_c$. Stochastic scaling is found to occur for $s s_c$. As different scaling forms are found to coexist in a single probability distribution, a coexistence scaling theory on small world network is developed and numerically verified.

cond-mat.stat-mech↗

arXiv2016

Finite size scaling study of a two parameter percolation model

A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration ρand a growth parameter g as two tunable parameters. Percolation transition is determined by the final static configuration of spanning clusters. A finite size scaling theory for such transition is developed and numerically verified. The scaling functions are found to depend on both g and ρ. The singularities at the critical growth probability gc of a given ρare described by appropriate critical exponents. The values of the critical exponents are found to be same as that of the original percolation at all values of ρat the respective gc . The model then belongs to the same universality class of percolation for the whole range of ρ.

cond-mat.stat-mech↗

arXiv2016

Discontinuous transition in an equilibrium percolation model with suppression

Discontinuous transition is observed in the equilibrium cluster properties of a percolation model with suppressed cluster growth as the growth parameter g0 is tuned to the critical threshold at sufficiently low initial seed concentration rho in contrast to the previously reported results on non- equilibrium growth models. In the present model, the growth process follows all the criteria of the original percolation model except continuously updated occupation probability of the lattice sites that suppresses the growth of a cluster according to its size. As rho varied from higher values to smaller values, a line of continuous transition points encounters a coexistence region of spanning and non- spanning large clusters. At sufficiently small values of rho (less equal 0.05), the growth parameter g0 exceeds the usual percolation threshold and generates compact spanning clusters leading to discontinuous transitions.

cond-mat.stat-mech↗

arXiv2015

Crossover from rotational to stochastic sandpile universality in the random rotational sandpile model

In the rotational sandpile model, either the clockwise or the anti-clockwise toppling rule is assigned to all the lattice sites. It has all the features of a stochastic sandpile model but belongs to a different universality class than the Manna class. A crossover from rotational to Manna universality class is studied by constructing a random rotational sandpile model and assigning randomly clockwise and anti-clockwise rotational toppling rules to the lattice sites. The steady state and the respective critical behaviour of the present model are found to have a strong and continuous dependence on the fraction of the lattice sites having the anti-clockwise (or clockwise) rotational toppling rule. As the anti-clockwise and clockwise toppling rules exist in equal proportions, it is found that the model reproduces critical behaviour of the Manna model. It is then further evidence of the existence of the Manna class, in contradiction with some recent observations of the non-existence of the Manna class.

cond-mat.stat-mech↗

arXiv2013

Critical properties of a dissipative sandpile model on small world networks

A dissipative sandpile model (DSM) is constructed and studied on small world networks (SWN). SWNs are generated adding extra links between two arbitrary sites of a two dimensional square lattice with different shortcut densities $ϕ$. Three different regimes are identified as regular lattice (RL) for $ϕ\lesssim 2^{-12}$, SWN for $2^{-12}<ϕ< 0.1$ and random network (RN) for $ϕ\ge 0.1$. In the RL regime, the sandpile dynamics is characterized by usual Bak, Tang, Weisenfeld (BTW) type correlated scaling whereas in the RN regime it is characterized by the mean field (MF) scaling. On SWN, both the scaling behaviors are found to coexist. Small compact avalanches below certain characteristic size $s_c$ are found to belong to the BTW universality class whereas large, sparse avalanches above $s_c$ are found to belong to the MF universality class. A scaling theory for the coexistence of two scaling forms on SWN is developed and numerically verified. Though finite size scaling (FSS) is not valid for DSM on RL as well as on SWN, it is found to be valid on RN for the same model. FSS on RN is appeared to be an outcome of super diffusive sand transport and uncorrelated toppling waves.

cond-mat.stat-mech↗

arXiv2008

Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction

The cytoplasm of a living cell is crowded with several macromolecules of different shapes and sizes. Molecular diffusion in such a medium becomes anomalous due to the presence of macromolecules and diffusivity is expected to decrease with increase in macromolecular crowding. Moreover, many cellular processes are dependent on molecular diffusion in the cell cytosol. The enzymatic reaction rate has been shown to be affected by the presence of such macromolecules. A simple numerical model is proposed here based on percolation and diffusion in disordered systems to study the effect of macromolecular crowding on the enzymatic reaction rates. The model explains qualitatively some of the experimental observations.

cond-mat.stat-mech↗

arXiv2008

Finite-Size Scaling for Directed Percolation Models

A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed scaling theory has been verified numerically on two different anisotropic percolation models.

cond-mat.soft↗

arXiv2008

Multifractality in Rotational Percolation Models

In rotationally constrained percolation models, a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint. A state variable $s_i$ is assigned to each lattice site whose value corresponds to the number times it has been visited during the growth of a cluster. It is proposed here that the percolation transition and the multifractal aspects of infinite percolation clusters under rotational constraint can be studied defining suitable measures in terms of the state variable $s_i$. This method does not require to introduce any external agency like an electric current or a random walker in order to explore multifractality as in the case of ordinary percolation. The state variable representation also describes the universality class of the percolation models appropriately.

cond-mat.soft↗

arXiv2008

Characteristics of Deterministic and Stochastic Sandpile Models in a Rotational Sandpile Model

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of equilibrium situation like self-organized criticality, a new two state ``quasi-deterministic'' rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains. An extended set of new critical exponents are found to characterize the avalanche properties at the non-equilibrium steady state of the model. The probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves. The model exhibits characteristics of both deterministic and stochastic sandpile models.

cond-mat.soft↗

arXiv2005

Multifractal Collision Spectrum of Ballistic Particles with Fractal Surfaces

Ballistic particles interacting with irregular surfaces are representative of many physical problems in the Knudsen diffusion regime. In this paper, the collisions of ballistic particles interacting with an irregular surface modeled by a quadratic Koch curve, are studied numerically. The $q$ moments of the source spatial distribution of collision numbers $μ(x)$ are characterized by a sequence of ``collision exponent'' $τ(q)$. The measure $μ(x)$ is found to be multifractal even when a random micro-roughness (or random re-emission) of the surface exists. The dimensions $f(α)$, obtained by a Legendre transformation from $τ(q)$, consist of two parabolas corresponding to a trinomial multifractal. This is demonstrated for a particular case by obtaining an exact $f(α)$ for a multiplicative trinomial mass distribution. The trinomial nature of the multifractality is related to the type of surface macro-irregularity considered here and is independent of the micro-roughness of the surface which however influence the values of $α_{min}$ and $α_{max}$. The information dimension $D_I$ increases significantly with the micro-roughness of the surface. Interestingly, in contrast with this point of view, the surface seems to work uniformly. This correspond to an absence of screening effects in Knudsen diffusion.

cond-mat.dis-nn↗

arXiv2005

Effect of Field Direction and Field Intensity on Directed Spiral Percolation

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field ($E$) and a field of rotational nature ($B$) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of $E$ field and intensities of both $E$ and $B$ fields in 2 dimensions. The system shows interesting and unusual critical behaviour at the percolation threshold. Not only the universality class of DSP model is found to belong in a new universality class than that of other percolation models but also the universality class remains invariant under the variation of $E$ field direction. Varying the intensities of the $E$ and $B$ fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields $E$ and $B$.

cond-mat.dis-nn↗

arXiv2005

Self-Organized Dynamical Equilibrium in the Corrosion of Random Solids

Self-organized criticality is characterized by power law correlations in the non-equilibrium steady state of externally driven systems. A dynamical system proposed here self-organizes itself to a critical state with no characteristic size at ``dynamical equilibrium''. The system is a random solid in contact with an aqueous solution and the dynamics is the chemical reaction of corrosion or dissolution of the solid in the solution. The initial difference in chemical potential at the solid-liquid interface provides the driving force. During time evolution, the system undergoes two transitions, roughening and anti-percolation. Finally, the system evolves to a dynamical equilibrium state characterized by constant chemical potential and average cluster size. The cluster size distribution exhibits power law at the final equilibrium state.

cond-mat.soft↗