627 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

### 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

### 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

### 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

### Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

The response of pipe flow to physically realistic, temporally and spatially continuous(periodic) forcing is investigated by decomposing the resolvent into orthogonal forcing and response pairs ranked according to their contribution to the resolvent 2-norm. Modelling the non-linear terms normally neglected by linearisation as unstructured forcing permits qualitative extrapolation of the resolvent norm results beyond infinitesimally small perturbations to the turbulent case. The concepts arising have a close relationship to input output transfer function analysis methods known in the control systems literature. The body forcings that yield highest disturbance energy gain are identified and ranked by the decomposition and a worst-case bound put on the energy gain integrated across the pipe cross-section. Analysis of the spectral variation of the corresponding response modes reveals interesting comparisons with recent observations of the behavior of the streamwise velocity in high Reynolds number (turbulent) pipe flow, including the importance of very long scales of the order of ten pipe radii, in the extraction of turbulent energy from the mean flow by the action of turbulent shear stress against the velocity gradient

### Devil's Staircase in Magnetoresistance of a Periodic Array of Scatterers

The nonlinear response to an external electric field is studied for classical
non-interacting charged particles under the influence of a uniform magnetic
field, a periodic potential, and an effective friction force. We find numerical
and analytical evidence that the ratio of transversal to longitudinal
resistance forms a Devil's staircase. The staircase is attributed to the
dynamical phenomenon of mode-locking.Comment: two-column 4 pages, 5 figure

### ASYMPTOTIC BEHAVIOR OF COMPLEX SCALAR FIELDS IN A FRIEDMAN-LEMAITRE UNIVERSE

We study the coupled Einstein-Klein-Gordon equations for a complex scalar
field with and without a quartic self-interaction in a curvatureless
Friedman-Lema\^{\i}\-tre Universe. The equations can be written as a set of
four coupled first order non-linear differential equations, for which we
establish the phase portrait for the time evolution of the scalar field. To
that purpose we find the singular points of the differential equations lying in
the finite region and at infinity of the phase space and study the
corresponding asymptotic behavior of the solutions. This knowledge is of
relevance, since it provides the initial conditions which are needed to solve
numerically the differential equations. For some singular points lying at
infinity we recover the expected emergence of an inflationary stage.Comment: uuencoded, compressed tarfile containing a 15 pages Latex file and 2
postscipt figures. Accepted for publication on Phys. Rev.

### Low-density series expansions for directed percolation IV. Temporal disorder

We introduce a model for temporally disordered directed percolation in which
the probability of spreading from a vertex $(t,x)$, where $t$ is the time and
$x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using
a very efficient algorithm we calculate low-density series for bond percolation
on the directed square lattice. Analysis of the series yields estimates for the
critical point $p_c$ and various critical exponents which are consistent with a
continuous change of the critical parameters as the strength of the disorder is
increased.Comment: 11 pages, 3 figure

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