1,169 research outputs found
O(N) and RP^{N-1} Models in Two Dimensions
I provide evidence that the 2D model for is equivalent
to the -invariant non-linear -model in the continuum limit. To
this end, I mainly study particular versions of the models, to be called
constraint models. I prove that the constraint and models are
equivalent for sufficiently weak coupling. Numerical results for their
step-scaling function of the running coupling are
presented. The data confirm that the constraint model is in the samei
universality class as the model with standard action. I show that the
differences in the finite size scaling curves of i and models
observed by Caracciolo et al. can be explained as a boundary effect. It is
concluded, in contrast to Caracciolo et al., that and models
share a unique universality class.Comment: 14 pages (latex) + 1 figure (Postscript) ,uuencode
Memory Effects and Scaling Laws in Slowly Driven Systems
This article deals with dynamical systems depending on a slowly varying
parameter. We present several physical examples illustrating memory effects,
such as metastability and hysteresis, which frequently appear in these systems.
A mathematical theory is outlined, which allows to show existence of hysteresis
cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure
Measuring the dark side (with weak lensing)
We introduce a convenient parametrization of dark energy models that is
general enough to include several modified gravity models and generalized forms
of dark energy. In particular we take into account the linear perturbation
growth factor, the anisotropic stress and the modified Poisson equation. We
discuss the sensitivity of large scale weak lensing surveys like the proposed
DUNE satellite to these parameters. We find that a large-scale weak-lensing
tomographic survey is able to easily distinguish the Dvali-Gabadadze-Porrati
model from LCDM and to determine the perturbation growth index to an absolute
error of 0.02-0.03.Comment: 19 pages, 11 figure
A new interaction potential for swarming models
We consider a self-propelled particle system which has been used to describe
certain types of collective motion of animals, such as fish schools and bird
flocks. Interactions between particles are specified by means of a pairwise
potential, repulsive at short ranges and attractive at longer ranges. The
exponentially decaying Morse potential is a typical choice, and is known to
reproduce certain types of collective motion observed in nature, particularly
aligned flocks and rotating mills. We introduce a class of interaction
potentials, that we call Quasi-Morse, for which flock and rotating mills states
are also observed numerically, however in that case the corresponding
macroscopic equations allow for explicit solutions in terms of special
functions, with coefficients that can be obtained numerically without solving
the particle evolution. We compare thus obtained solutions with long-time
dynamics of the particle systems and find a close agreement for several types
of flock and mill solutions.Comment: 23 pages, 8 figure
Cosmic string parameter constraints and model analysis using small scale Cosmic Microwave Background data
We present a significant update of the constraints on the Abelian Higgs
cosmic string tension by cosmic microwave background (CMB) data, enabled both
by the use of new high-resolution CMB data from suborbital experiments as well
as the latest results of the WMAP satellite, and by improved predictions for
the impact of Abelian Higgs cosmic strings on the CMB power spectra. The new
cosmic string spectra (presented in a previous work) were improved especially
for small angular scales, through the use of larger Abelian Higgs string
simulations and careful extrapolation. If Abelian Higgs strings are present
then we find improved bounds on their contribution to the CMB anisotropies,
f10< 0.095, and on their tension, G\mu< 0.57 x 10^-6, both at 95% confidence
level using WMAP7 data; and f10 < 0.048 and G\mu < 0.42 x 10^-6 using all the
CMB data. We also find that using all the CMB data, a scale invariant initial
perturbation spectrum, ns=1, is now disfavoured at 2.4\sigma\ even if strings
are present. A Bayesian model selection analysis no longer indicates a
preference for strings.Comment: 8 pages, 3 figures; Minor corrections, matches published versio
The extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary models
In (Hansen et al. 2002) we presented a new approach for measuring
non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern,
based on the multivariate empirical distribution function of the spherical
harmonics a_lm of a CMB map. The present paper builds upon the same ideas and
proposes several improvements and extensions. More precisely, we exploit the
additional information on the random phases of the a_lm to provide further
tests based on the empirical distribution function. Also we take advantage of
the effect of rotations in improving the power of our procedures. The suggested
tests are implemented on physically motivated models of non-Gaussian fields;
Monte-Carlo simulations suggest that this approach may be very promising in the
analysis of non-Gaussianity generated by non-standard models of inflation. We
address also some experimentally meaningful situations, such as the presence of
instrumental noise and a galactic cut in the map.Comment: 15 pages, 6 figures, submitted to Phys. Rev.
Constraints on Brane Inflation and Cosmic Strings
By considering simple, but representative, models of brane inflation from a
single brane-antibrane pair in the slow roll regime, we provide constraints on
the parameters of the theory imposed by measurements of the CMB anisotropies by
WMAP including a cosmic string component. We find that inclusion of the string
component is critical in constraining parameters. In the most general model
studied, which includes an inflaton mass term, as well as the brane-antibrane
attraction, values n_s < 1.02 are compatible with the data at 95 % confidence
level. We are also able to constrain the volume of internal manifold (modulo
factors dependent on the warp factor) and the value of the inflaton field to be
less than 0.66M_P at horizon exit. We also investigate models with a mass term.
These observational considerations suggest that such models have r < 2*10^-5,
which can only be circumvented in the fast roll regime, or by increasing the
number of antibranes. Such a value of r would not be detectable in CMB
polarization experiment likely in the near future, but the B-mode signal from
the cosmic strings could be detectable. We present forecasts of what a similar
analysis using PLANCK data would yield and find that it should be possible to
rule out G\mu > 6.5*10^-8 using just the TT, TE and EE power spectra.Comment: 11 pages, 3 figures, revtex4, typos corrected, references adde
The role of point-like topological excitations at criticality: from vortices to global monopoles
We determine the detailed thermodynamic behavior of vortices in the O(2)
scalar model in 2D and of global monopoles in the O(3) model in 3D. We
construct new numerical techniques, based on cluster decomposition algorithms,
to analyze the point defect configurations. We find that these criteria produce
results for the Kosterlitz-Thouless temperature in agreement with a topological
transition between a polarizable insulator and a conductor, at which free
topological charges appear in the system. For global monopoles we find no pair
unbinding transition. Instead a transition to a dense state where pairs are no
longer distinguishable occurs at T<Tc, without leading to long range disorder.
We produce both extensive numerical evidence of this behavior as well as a
semi-analytic treatment of the partition function for defects. General
expectations for N=D>3 are drawn, based on the observed behavior.Comment: 14 pages, REVTEX, 13 eps figure
Entropic effects on the Size Evolution of Cluster Structure
We show that the vibrational entropy can play a crucial role in determining
the equilibrium structure of clusters by constructing structural phase diagrams
showing how the structure depends upon both size and temperature. These phase
diagrams are obtained for example rare gas and metal clusters.Comment: 5 pages, 3 figure
Zircon ages in granulite facies rocks: decoupling from geochemistry above 850 °C?
Granulite facies rocks frequently show a large spread in their zircon ages, the interpretation of which raises questions: Has the isotopic system been disturbed? By what process(es) and conditions did the alteration occur? Can the dates be regarded as real ages, reflecting several growth episodes? Furthermore, under some circumstances of (ultra-)high-temperature metamorphism, decoupling of zircon U–Pb dates from their trace element geochemistry has been reported. Understanding these processes is crucial to help interpret such dates in the context of the P–T history. Our study presents evidence for decoupling in zircon from the highest grade metapelites (> 850 °C) taken along a continuous high-temperature metamorphic field gradient in the Ivrea Zone (NW Italy). These rocks represent a well-characterised segment of Permian lower continental crust with a protracted high-temperature history. Cathodoluminescence images reveal that zircons in the mid-amphibolite facies preserve mainly detrital cores with narrow overgrowths. In the upper amphibolite and granulite facies, preserved detrital cores decrease and metamorphic zircon increases in quantity. Across all samples we document a sequence of four rim generations based on textures. U–Pb dates, Th/U ratios and Ti-in-zircon concentrations show an essentially continuous evolution with increasing metamorphic grade, except in the samples from the granulite facies, which display significant scatter in age and chemistry. We associate the observed decoupling of zircon systematics in high-grade non-metamict zircon with disturbance processes related to differences in behaviour of non-formula elements (i.e. Pb, Th, U, Ti) at high-temperature conditions, notably differences in compatibility within the crystal structure
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