arXiv subjects

S. S. Manna

Publications and source records attributed to S. S. Manna.

At least 55 records · Page 3Linked to original sources

arXiv2005

Phase transition in a directed traffic flow network

The generic feature of traffic in a network of flowing electronic data packets is a phase transition from a stationary free-flow phase to a continuously growing congested non-stationary phase. In the most simple network of directed oriented square lattice we have been able to observe all crucial features of such flow systems having non-trivial critical behavior near the critical point of transition. The network here is in the shape of a square lattice and data packets are randomly posted with a rate $ρ$ at one side of the lattice. Each packet executes a directed diffusive motion towards the opposite boundary where it is delivered. Packets accumulated at a particular node form a queue and a maximum of $m$ such packets randomly jump out of this node at every time step to its neighbors on a first-in-first-out (FIFO) basis. The phase transition occurs at $ρ_c=m$. The distribution of travel times through the system is found to have a log-normal behavior and the power-spectrum of the load time-series shows $1/f$ like noise similar to the scenario of Internet traffic.

cond-mat.stat-mech↗

arXiv2004

Directed Fixed Energy Sandpile Model

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.

cond-mat.stat-mech↗

arXiv2004

Pareto Law in a Kinetic Model of Market with Random Saving Propensity

We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents ($0 \le λ< 1$). The system remarkably self-organizes to a critical Pareto distribution of money $P(m) \sim m^{-(ν+ 1)}$ with $ν\simeq 1$. We analyse the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines two century-old distributions: Gibbs (1901) and Pareto (1897) distributions.

cond-mat.stat-mech↗

arXiv2003

Money in Gas-Like Markets: Gibbs and Pareto Laws

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity $λ$ of agents, such that each agent saves a fraction $λ$ of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for $λ=0$, has got a non-vanishing most-probable value for $λ\ne 0$ and Pareto-like when $λ$ is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.

cond-mat.stat-mech↗

arXiv2003

Diffusion limited friendship network: A model for six degrees of separation

A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the pairs of mutual friendships. This network exhibits a novel percolation like phase transition in all dimensions. On introducing simultaneous death and birth rates in the population we show that the friendship network shows the six degrees of separation for ever after where the precise value of the network diameter depends on the death/birth rate. A SIS type model of disease spreading shows that this society remains always healthy if the population density is less than certain threshold value.

cond-mat.stat-mech↗

arXiv2003

Scale free networks from a Hamiltonian dynamics

Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as possible. By applying a local rewiring move, the network reaches equilibrium states assuming broad degree distributions, which have a power law form in an intermediate range of the parameters used. Interestingly, in the same range we find non-trivial hierarchical clustering.

cond-mat.stat-mech↗

arXiv2003

Scale-free network on a vertical plane

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which are below it using the attachment probability: $π_i(t) \sim k_i(t)\ell^α$. Our numerical results indicate that the directed scale-free network for $α=0$ belongs to a different universality class compared to the isotropic scale-free network. For $α< α_c$ the degree distribution is stretched exponential in general which takes a pure exponential form in the limit of $α\to -\infty$. The link length distribution is calculated analytically for all values of $α$.

cond-mat.stat-mech↗

arXiv2003

Percolation in deposits for competitive models in (1+1)-dimensions

The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry. These models are based on the combination of ballistic deposition (BD) and random deposition (RD) models or BD and Family deposition (FD) models. Numerically we find, that for pure RD, FD or BD models the mean height of the percolation deposit $\bar h$ grows with the substrate length $L$ according to the generalized logarithmic law $\bar h\propto (\ln (L))^γ$, where $γ=1.0$ (RD), $γ=0.88\pm 0.020$ (FD) and $γ=1.52\pm 0.020$ (BD). For BD model, the scaling law between deposit density $p$ and its mean height $\bar h$ at the point of percolation of type $p-p_\infty \propto \bar h^{-1/ν_h}$ are observed, where $ν_h =1.74\pm0.02$ is a scaling coefficient. For competitive models the crossover, %in $h$ versus $L$ corresponding to the RD or FD -like behaviour at small $L$ and the BD-like behaviour at large $L$ are observed.

cond-mat.stat-mech↗

arXiv2003

Scale-free Network on Euclidean Space Optimized by Rewiring of Links

A Barabási-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring length associated with a such a network defined on a two dimensional plane is optimized. The optimization process consists of random selection of a pair of links and rewiring them to reduce the total length of the pair but with the constraint that the degree as well as the out-degree and in-degree of each node are precisely maintained. The resulting optimized network has a small diameter as well as high clustering and the link length distribution has a stretched exponential tail.

cond-mat.stat-mech↗

arXiv2003

Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^β_i \ell^α$. For $α> -0.5$, the network is scale free at $β= 1$ with the degree distribution $P(k) \propto k^{-γ}$ and $γ= 3.0$ as in the Barabási-Albert model ($α=0, β=1$). We find a phase boundary in the $α-β$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $β> 1$ for $α< -0.5$ where the existence of a new universality class is indicated from the behaviour of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behaviour of most real networks for increasing negative values of $α$ on the phase boundary.

cond-mat.stat-mech↗

arXiv2002

Small-world properties of the Indian Railway network

Structural properties of the Indian Railway network is studied in the light of recent investigations of the scaling properties of different complex networks. Stations are considered as `nodes' and an arbitrary pair of stations is said to be connected by a `link' when at least one train stops at both stations. Rigorous analysis of the existing data shows that the Indian Railway network displays small-world properties. We define and estimate several other quantities associated with this network.

cond-mat.soft↗

arXiv2002

Quasistatic Scale-free Networks

A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node, the other end being connected to any other node with degree $k$ randomly selected with an attachment probability proportional to $k^α$. Tuning the control parameter $α$ we observe a transition where the average degree of the largest node $ $ changes its variation from $N^0$ to $N$ at a specific transition point of $α_c$. The network is scale-free i.e., the nodal degree distribution has a power law decay for $α\ge α_c$.

cond-mat.stat-mech↗

arXiv2002

Modulated Scale-free Network in the Euclidean Space

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability proportional to $k_i \ell^α$. Our numerical study indicates that the network is Scale-free for all values of $α> α_c $ and the degree distribution decays stretched exponentially for the other values of $α$. The link length distribution follows a power law: $D(\ell) \sim \ell^δ$ where $δ$ is calculated exactly for the whole range of values of $α$.

cond-mat.stat-mech↗

arXiv2002

Percolation in Models of Thin Film Depositions

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and ballistic (BD) deposition rules. In the mixed one-component models with deposition of only conducting particles, the mean height of the percolation layer (measured in monolayers) grows continuously from 0.89832 for the pure RD model to 2.605 for the pure RD model, but the percolation transition belong to the same universality class, as in the 2- dimensional random percolation problem. In two- component models with deposition of conducting and isolating particles, the percolation layer height approaches infinity as concentration of the isolating particles becomes higher than some critical value. The crossover from 2d to 3d percolation was observed with increase of the percolation layer height.

cond-mat.soft↗

arXiv2002

Self-organized random walks and stochastic sandpile: From linear to branched avalanches

In a model of self-organized criticality unstable sites discharge to just one of their neighbors. For constant discharge ratio $α$ and for a certain range of values of the input energy, avalanches are simple branchless Pólya random walks, and their scaling properties can be derived exactly. If $α$ fluctuates widely enough, avalanches become branched, due to multiple discharges, and behave like those of the stochastic sandpile. At the threshold for branched behaviour, peculiar scaling and anomalous diffusive transport are observed.

cond-mat.stat-mech↗

arXiv2001

A Percolation Model of Diagenesis

The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in dense environments. Starting from sub-critical states of ordinary percolation the system evolves under the diagenetic rules to critical percolation configurations. Our numerical simulation results in two dimensions indicate that the stable configuration has the same critical behaviour as the ordinary percolation.

cond-mat.soft↗

arXiv2000

Self-Organization in a Granular Medium by Internal Avalanches

Internal avalanches of grain displacements can be created inside a granular material kept in a bin in two ways: (i) By removing a radomly selected grain at the bottom of the bin (ii) By breaking a stable arch of grains clogging a hole at the bottom of the bin. Repeated generations of such avalanches lead the system to a steady state. The question asked, is this state a critical state as that in Self-Organized Criticality? We review here some of the recent studies on this problem using cellular automata as well as hard disc models.

cond-mat.soft↗

arXiv1999

Intermittent Granular Flow and Clogging with Internal Avalanches

The dynamics of intermittent granular flow through an orifice in a granular bin and the associated clogging due to formation of arches blocking the outlet, is studied numerically in two-dimensions. Our numerical results indicate that for small hole sizes, the system self-organizes to a steady state and the distribution of the grain displacements decays as power laws. On the other hand, for large holes, the outflow distributions are also observed to follow power law distributions.

cond-mat.soft↗