Universal scaling behavior of directed percolation around the upper critical dimension

In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field. Additionally to the universal scaling functions, several universal amplitude combinations are considered. We compare our results with those of a renormalization group approach.Comment: 19 pages, 8 figures, accepted for publication in J. Stat. Phy

Continuously varying exponents in a sandpile model with dissipation near surface

We consider the directed Abelian sandpile model in the presence of sink sites whose density f_t at depth t below the top surface varies as c~1/t^chi. For chi>1 the disorder is irrelevant. For chi<1, it is relevant and the model is no longer critical for any nonzero c. For chi=1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this dependence exactly, and verify the results with simulations.Comment: 13 pages, 4 figures, accepted for publication in J. Stat. Phy

A deterministic sandpile automaton revisited

The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice.Comment: 7 pages, 8 figures, EPJ style, accepted for publication in European Physical Journal

Density Fluctuations and Phase Transition in the Nagel-Schreckenberg Traffic Flow Model

We consider the transition of the Nagel-Schreckenberg traffic flow model from the free flow regime to the jammed regime. We examine the inhomogeneous character of the system by introducing a new method of analysis which is based on the local density distribution. We investigated the characteristic fluctuations in the steady state and present the phase diagram of the system.Comment: 4 pages, 7 figures, accepted for publication in Phys. Rev.

Density fluctuations and phase separation in a traffic flow model

Within the Nagel-Schreckenberg traffic flow model we consider the transition from the free flow regime to the jammed regime. We introduce a method of analyzing the data which is based on the local density distribution. This analyzes allows us to determine the phase diagram and to examine the separation of the system into a coexisting free flow phase and a jammed phase above the transition. The investigation of the steady state structure factor yields that the decomposition in this phase coexistence regime is driven by density fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M. Schreckenberg, Springer, Singapore (1998

Interface Motion in Disordered Ferromagnets

We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by logarithmic corrections. This suggests that d=5 is the upper critical dimension of the depinning transition in the random-field Ising model. Furthermore, we investigate the so-called creep regime (small driving fields and temperatures) where the interface velocity is given by an Arrhenius law.Comment: some misprints correcte

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Dense transcript profiling in single cells by image correlation decoding

Sequential barcoded fluorescent in situ hybridization (seqFISH) allows large numbers of molecular species to be accurately detected in single cells, but multiplexing is limited by the density of barcoded objects. We present correlation FISH (corrFISH), a method to resolve dense temporal barcodes in sequential hybridization experiments. Using corrFISH, we quantified highly expressed ribosomal protein genes in single cultured cells and mouse thymus sections, revealing cell-type-specific gene expression

Meson-Baryon Form Factors in Chiral Colour Dielectric Model

The renormalised form factors for pseudoscalar meson-baryon coupling are computed in chiral colour dielectric model. This has been done by rearranging the Lippmann-Schwinger series for the meson baryon scattering matrix so that it can be expressed as a baryon pole term with renormalized form factors and baryon masses and the rest of the terms which arise from the crossed diagrams. Thus we are able to obtain an integral equation for the renormalized meson-baryon form factors in terms of the bare form factors as well as an expression for the meson self energy. This integral equation is solved and renormalized meson baryon form factors and renormalized baryon masses are computed. The parameters of the model are adjusted to obtain a best fit to the physical baryon masses. The calculations show that the renormalized form factors are energy-dependent and differ from the bare form factors primarily at momentum transfers smaller than 1 GeV. At nucleon mass, the change in the form factors is about 10% at zero momentum transfer. The computed form factors are soft with the equivalent monopole cut-off mass of about 500 MeV. The renormalized coupling constants are obtained by comparing the chiral colour dielectric model interaction Hamiltonian with the standard form of meson-nucleon interaction Hamiltonian. The ratio of $\Delta N\pi$ and $NN\pi$ coupling constants is found to be about 2.15. This value is very close to the experimental value.Comment: 16 pages, 7 postscript figure