Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett. style files included; slightly expanded reincarnatio

Finite-size scaling of directed percolation above the upper critical dimension

We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.Comment: 4 pages, one figur

On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion

It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the coupling constant of these models renormalizes nontrivially. This implies that the widely accepted supposedly exact scaling exponents are to be corrected. A two-loop calculation shows that the corrections are small and these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let

Transport on Directed Percolation Clusters

We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.Comment: 4 page

Tearing Out the Income Tax by the (Grass)Roots

Landscapes are increasingly fragmented, and conservation programs have started to look at network approaches for maintaining populations at a larger scale. We present an agent-based model of predator–prey dynamics where the agents (i.e. the individuals of either the predator or prey population) are able to move between different patches in a landscaped network. We then analyze population level and coexistence probability given node-centrality measures that characterize specific patches. We show that both predator and prey species benefit from living in globally well-connected patches (i.e. with high closeness centrality). However, the maximum number of prey species is reached, on average, at lower closeness centrality levels than for predator species. Hence, prey species benefit from constraints imposed on species movement in fragmented landscapes since they can reproduce with a lesser risk of predation, and their need for using anti-predatory strategies decreases.authorCount :

Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process

A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well known exponents of Reggeon field theory. In addition this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte

Driven diffusive system with non-local perturbations

We investigate the impact of non-local perturbations on driven diffusive systems. Two different problems are considered here. In one case, we introduce a non-local particle conservation along the direction of the drive and in another case, we incorporate a long-range temporal correlation in the noise present in the equation of motion. The effect of these perturbations on the anisotropy exponent or on the scaling of the two-point correlation function is studied using renormalization group analysis.Comment: 11 pages, 2 figure

Finite-size scaling of directed percolation in the steady state

Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in non-equilibrium systems at the instance of directed percolation (DP), which has become the paradigm of non-equilibrium phase transitions into absorbing states, above, at and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a new signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.Comment: 21 pages, 6 figure

Spreading with immunization in high dimensions

We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, $p_0$, and reinfections, $p$. When the two probabilities are equal, the model reduces to directed percolation, while for perfect immunization one obtains the general epidemic process belonging to the universality class of dynamical percolation. We focus on the critical behavior in the vicinity of the directed percolation point, especially in high dimensions $d>2$. It is argued that the clusters of immune sites are compact for $d\leq 4$. This observation implies that a recently introduced scaling argument, suggesting a stretched exponential decay of the survival probability for $p=p_c$, $p_0\ll p_c$ in one spatial dimension, where $p_c$ denotes the critical threshold for directed percolation, should apply in any dimension $d \leq 3$ and maybe for $d=4$ as well. Moreover, we show that the phase transition line, connecting the critical points of directed percolation and of dynamical percolation, terminates in the critical point of directed percolation with vanishing slope for $d<4$ and with finite slope for $d\geq 4$. Furthermore, an exponent is identified for the temporal correlation length for the case of $p=p_c$ and $p_0=p_c-\epsilon$, $\epsilon\ll 1$, which is different from the exponent $\nu_\parallel$ of directed percolation. We also improve numerical estimates of several critical parameters and exponents, especially for dynamical percolation in $d=4,5$.Comment: LaTeX, IOP-style, 18 pages, 9 eps figures, minor changes, additional reference

Single pulse and profile variability study of PSR J1022+1001

Millisecond pulsars (MSPs) are known as highly stable celestial clocks. Nevertheless, recent studies have revealed the unstable nature of their integrated pulse profiles, which may limit the achievable pulsar timing precision. In this paper, we present a case study on the pulse profile variability of PSR J1022+1001. We have detected approximately 14,000 sub-pulses (components of single pulses) in 35-hr long observations, mostly located at the trailing component of the integrated profile. Their flux densities and fractional polarisation suggest that they represent the bright end of the energy distribution in ordinary emission mode and are not giant pulses. The occurrence of sub-pulses from the leading and trailing components of the integrated profile is shown to be correlated. For sub-pulses from the latter, a preferred pulse width of approximately 0.25 ms has been found. Using simultaneous observations from the Effelsberg 100-m telescope and the Westerbork Synthesis Radio Telescope, we have found that the integrated profile varies on a timescale of a few tens of minutes. We show that improper polarisation calibration and diffractive scintillation cannot be the sole reason for the observed instability. In addition, we demonstrate that timing residuals generated from averages of the detected sub-pulses are dominated by phase jitter, and place an upper limit of ~700 ns for jitter noise based on continuous 1-min integrations.Comment: 13 pages, 20 figures, 3 tables, accepted for publication in MNRA