Long-term power-law fluctuation in Internet traffic

Power-law fluctuation in observed Internet packet flow are discussed. The data is obtained by a multi router traffic grapher (MRTG) system for 9 months. The internet packet flow is analyzed using the detrended fluctuation analysis. By extracting the average daily trend, the data shows clear power-law fluctuations. The exponents of the fluctuation for the incoming and outgoing flow are almost unity. Internet traffic can be understood as a daily periodic flow with power-law fluctuations.Comment: 10 pages, 8 figure

Reentrant phase diagram of branching annihilating random walks with one and two offsprings

We investigate the phase diagram of branching annihilating random walks with one and two offsprings in one dimension. A walker can hop to a nearest neighbor site or branch with one or two offsprings with relative ratio. Two walkers annihilate immediately when they meet. In general, this model exhibits a continuous phase transition from an active state into the absorbing state (vacuum) at a finite hopping probability. We map out the phase diagram by Monte Carlo simulations which shows a reentrant phase transition from vacuum to an active state and finally into vacuum again as the relative rate of the two-offspring branching process increases. This reentrant property apparently contradicts the conventional wisdom that increasing the number of offsprings will tend to make the system more active. We show that the reentrant property is due to the static reflection symmetry of two-offspring branching processes and the conventional wisdom is recovered when the dynamic reflection symmetry is introduced instead of the static one.Comment: 14 pages, Revtex, 4 figures (one PS figure file upon request) (submitted to Phy. Rev. E

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady states, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite size system, however, continues to show a signature of the original transition, and we characterize the finite size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte

Coupled-Map Modeling of One-Dimensional Traffic Flow

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle properly, and the maps are coupled to each other through the headway distance. By simulating the model, we obtain a plot of the flow against the concentration similar to the observed data in real traffic flows. Realistic traffic jam regions are observed in space-time trajectories.Comment: 5 postscript figures available upon reques

Critical phenomena of nonequilibrium dynamical systems with two absorbing states

We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase which belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain wall language, the parity conservation is not affected by the presence of the symmetry-breaking field. So the symmetry between the absorbing states rather than the conservation laws plays an essential role in determining the universality class. We also perform Monte Carlo simulations for the various interface dynamics between different absorbing states, which yield new universal dynamic exponents. With the symmetry-breaking field, the interface moves, in average, with a constant velocity in the direction of the unpreferred absorbing state and the dynamic scaling exponents apparently assume trivial values. However, we find that the hyperscaling relation for the directed percolation universality class is restored if one focuses on the dynamics of the interface on the side of the preferred absorbing state only.Comment: 11 pages, 21 figures, Revtex, submitted to Phy. Rev.

Directed Ising type dynamic preroughening transition in one dimensional interfaces

We present a realization of directed Ising (DI) type dynamic absorbing state phase transitions in the context of one-dimensional interfaces, such as the relaxation of a step on a vicinal surface. Under the restriction that particle deposition and evaporation can only take place near existing kinks, the interface relaxes into one of three steady states: rough, perfectly ordered flat (OF) without kinks, or disordered flat (DOF) with randomly placed kinks but in perfect up-down alternating order. A DI type dynamic preroughening transition takes place between the OF and DOF phases. At this critical point the asymptotic time evolution is controlled not only by the DI exponents but also by the initial condition. Information about the correlations in the initial state persists and changes the critical exponents.Comment: 12 pages, 10 figure

Dimensional reduction in a model with infinitely many absorbing states

Using Monte Carlo method we study a two-dimensional model with infinitely many absorbing states. Our estimation of the critical exponent beta=0.273(5) suggests that the model belongs to the (1+1) rather than (2+1) directed-percolation universality class. We also show that for a large class of absorbing states the dynamic Monte Carlo method leads to spurious dynamical transitions.Comment: 6 pages, 4 figures, Phys.Rev. E, Dec. 199

Nonuniversal Critical Spreading in Two Dimensions

Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary continuously with the density phi in the surrounding region. The exponent delta changes by more than an order of magnitude, and eta changes sign. The location of the critical point also depends on phi, which has important implications for scaling. As expected on the basis of universality, the static critical behavior belongs to the directed percolation class.Comment: 21 pages, REVTeX, figures available upon reques

Pair contact process with diffusion - A new type of nonequilibrium critical behavior?

Recently Carlon et. al. investigated the critical behavior of the pair contact process with diffusion [cond-mat/9912347]. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that the transition might belong to the same universality class as branching annihilating random walks with even numbers of offspring. This is surprising since the model does not have an explicit parity-conserving symmetry. In order to understand this contradiction, we estimate the critical exponents by Monte Carlo simulations. The results suggest that the transition might belong to a different universality class that has not been investigated before.Comment: RevTeX, 3 pages, 2 eps figures, adapted to final version of cond-mat/991234

Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous dynamics. Asymptotic large-time results for particle densities are derived and discussed in the framework of universality.Comment: 13 pages in plain Te