1,074 research outputs found
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
lattices. Analysis of the series yields accurate estimates of the critical
point and various critical exponents. The exponent estimates differ only
in the 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
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