A Precision Model Independent Determination of |Vub| from B -> pi e nu

A precision method for determining |Vub| using the full range in q^2 of B-> pi \ell nu data is presented. At large q^2 the form factor is taken from unquenched lattice QCD, at q^2=0 we impose a model independent constraint obtained from B-> pi pi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |Vub| =(3.54\pm 0.17\pm 0.44) x 10^{-3}. With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.Comment: 4 pages, 3 figure

Universality Class of Two-Offspring Branching Annihilating Random Walks

We analyze a two-offspring Branching Annihilating Random Walk ($n=2$ BAW) model, with finite annihilation rate. The finite annihilation rate allows for a dynamical phase transition between a vacuum, absorbing state and a non-empty, active steady state. We find numerically that this transition belongs to the same universality class as BAW's with an even number of offspring, $n\geq 4$, and that of other models whose dynamic rules conserve the parity of the particles locally. The simplicity of the model is exploited in computer simulations to obtain various critical exponents with a high level of accuracy.Comment: 10 pages, tex, 4 figures uuencoded, also available upon reques

Epidemic analysis of the second-order transition in the Ziff-Gulari-Barshad surface-reaction model

We study the dynamic behavior of the Ziff-Gulari-Barshad (ZGB) irreversible surface-reaction model around its kinetic second-order phase transition, using both epidemic and poisoning-time analyses. We find that the critical point is given by p_1 = 0.3873682 \pm 0.0000015, which is lower than the previous value. We also obtain precise values of the dynamical critical exponents z, \delta, and \eta which provide further numerical evidence that this transition is in the same universality class as directed percolation.Comment: REVTEX, 4 pages, 5 figures, Submitted to Physical Review

Energy constrained sandpile models

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy $E$ becomes the only parameter governing the dynamical behavior of the system. Both models show scale free behavior at a critical value $E_c$ of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different universality class than self-organized critical sandpiles. Despite this difference, the activity (avalanche) probability distributions appear to coincide with the one of the standard self-organized critical sandpile.Comment: 4 pages including 3 figure

Heterogeneous Catalysis on a Disordered Surface

We introduce a simple model of heterogeneous catalysis on a disordered surface which consists of two types of randomly distributed sites with different adsorption rates. Disorder can create a reactive steady state in situations where the same model on a homogeneous surface exhibits trivial kinetics with no steady state. A rich variety of kinetic behaviors occur for the adsorbate concentrations and catalytic reaction rate as a function of model parameters.Comment: 4 pages, gzipped PostScript fil

Towards Classification of Phase Transitions in Reaction--Diffusion Models

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the ``coordinate'' to the ``phase'' space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero ``energy''. We identify four families of topologically distinct classes of phase portraits stable upon RG transformations.Comment: 14 pages, 9 figure

Novel Position-Space Renormalization Group for Bond Directed Percolation in Two Dimensions

A new position-space renormalization group approach is investigated for bond directed percolation in two dimensions. The threshold value for the bond occupation probabilities is found to be $p_c=0.6443$. Correlation length exponents on time (parallel) and space (transverse) directions are found to be $\nu_\parallel=1.719$ and $\nu_\perp=1.076$, respectively, which are in very good agreement with the best known series expansion results.Comment: Latex - Revtex, 5 pages with 6 figures, to be appeared in Physica

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

Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.Comment: 18 pages of text, RevTeX, additional 8 figures in 12 PS file

Mean-field behavior of the sandpile model below the upper critical dimension

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in $d=4$ significantly differ from mean-field predictions, thus suggesting an upper critical dimension $d_c\geq 5$. Using the relations among the dissipation rate $\epsilon$ and the finite lattice size $L$, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.Comment: 4 RevTex pages, 2 eps figures embedde