Directed Percolation and Generalized Friendly Walkers

We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of m directed random walkers with rather general attractive interactions, when suitably continued to m=0. In 1+1 dimensions, this is dual to a model of interacting steps on a vicinal surface. A similar correspondence with interacting self-avoiding walks is constructed for isotropic percolation.Comment: 4 pages, 3 figures, to be published in Phys. Rev. Let

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Dependence of Maximum Trappable Field on Superconducting Nb3Sn Cylinder Wall Thickness

Uniform dipole magnetic fields from 1.9 to 22.4 kOe were permanently trapped, with high fidelity to the original field, transversely to the axes of hollow Nb3Sn superconducting cylinders. These cylinders were constructed by helically wrapping multiple layers of superconducting ribbon around a mandrel. This is the highest field yet trapped, the first time trapping has been reported in such helically wound taped cylinders, and the first time the maximum trappable field has been experimentally determined as a function of cylinder wall thickness.Comment: 8 pages, 4 figures, 1 table. PACS numbers: 74.60.Ge, 74.70.Ps, 41.10.Fs, 85.25.+

Cosmo-dynamics and dark energy with a quadratic EoS: anisotropic models, large-scale perturbations and cosmological singularities

In general relativity, for fluids with a linear equation of state (EoS) or scalar fields, the high isotropy of the universe requires special initial conditions, and singularities are anisotropic in general. In the brane world scenario anisotropy at the singularity is suppressed by an effective quadratic equation of state. There is no reason why the effective EoS of matter should be linear at the highest energies, and a non-linear EoS may describe dark energy or unified dark matter (Paper I, astro-ph/0512224). In view of this, here we study the effects of a quadratic EoS in homogenous and inhomogeneous cosmological models in general relativity, in order to understand if in this context the quadratic EoS can isotropize the universe at early times. With respect to Paper I, here we use the simplified EoS P=alpha rho + rho^2/rho_c, which still allows for an effective cosmological constant and phantom behavior, and is general enough to analyze the dynamics at high energies. We first study anisotropic Bianchi I and V models, focusing on singularities. Using dynamical systems methods, we find the fixed points of the system and study their stability. We find that models with standard non-phantom behavior are in general asymptotic in the past to an isotropic fixed point IS, i.e. in these models even an arbitrarily large anisotropy is suppressed in the past: the singularity is matter dominated. Using covariant and gauge invariant variables, we then study linear perturbations about the homogenous and isotropic spatially flat models with a quadratic EoS. We find that, in the large scale limit, all perturbations decay asymptotically in the past, indicating that the isotropic fixed point IS is the general asymptotic past attractor for non phantom inhomogeneous models with a quadratic EoS. (Abridged)Comment: 16 pages, 6 figure

Low-density series expansions for directed percolation III. Some two-dimensional lattices

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point $p_c$ and various critical exponents. The exponent estimates differ only in the $5^{th}$ digit, thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems. In addition we also study the non-physical singularities of the series.Comment: 20 pages, 8 figure

Direct access to a cAAC-supported dihydrodiborene and its dianion

The two-fold reduction of (cAAC)BHX2 (cAAC = 1-(2,6-diisopropylphenyl)-3,3,5,5-tetramethylpyrrolidin-2-ylidene); X = Cl, Br) provides a facile, high-yielding route to the dihydrodiborene (cAAC)2B2H2. The (chloro)hydroboryl anion reduction intermediate was successfully isolated using a crown ether. Overreduction of the diborene to its dianion [(cAAC)2B2H2]2– causes a decrease in the B-B bond order whereas the B-C bond orders increase

Spatial patterns in the oxygen isotope composition of daily rainfall in the British Isles

Understanding the modern day relationship between climate and the oxygen isotopic composition of precipitation (δ18OP) is crucial for obtaining rigorous palaeoclimate reconstructions from a variety of archives. To date, the majority of empirical studies into the meteorological controls over δ18OP rely upon daily, event scale, or monthly time series from individual locations, resulting in uncertainties concerning the representativeness of statistical models and the mechanisms behind those relationships. Here, we take an alternative approach by analysing daily patterns in δ18OP from multiple stations across the British Isles (n = 10–70 stations). We use these data to examine the spatial and seasonal heterogeneity of regression statistics between δ18OP and common predictors (temperature, precipitation amount and the North Atlantic Oscillation index; NAO). Temperature and NAO are poor predictors of daily δ18OP in the British Isles, exhibiting weak and/or inconsistent effects both spatially and between seasons. By contrast δ18OP and rainfall amount consistently correlate at most locations, and for all months analysed, with spatial and temporal variability in the regression coefficients. The maps also allow comparison with daily synoptic weather types, and suggest characteristic δ18OP patterns, particularly associated with Cylonic Lamb Weather Types. Mapping daily δ18OP across the British Isles therefore provides a more coherent picture of the patterns in δ18OP, which will ultimately lead to a better understanding of the climatic controls. These observations are another step forward towards developing a more detailed, mechanistic framework for interpreting stable isotopes in rainfall as a palaeoclimate and hydrological tracer