31,256 research outputs found
Anomalous scaling of passive scalar in turbulence and in equilibrium
We analyze multi-point correlation functions of a tracer in an incompressible
flow at scales far exceeding the scale at which fluctuations are generated
(quasi-equilibrium domain) and compare them with the correlation functions at
scales smaller than (turbulence domain). We demonstrate that the scale
invariance can be broken in the equilibrium domain and trace this breakdown to
the statistical integrals of motion (zero modes) as has been done before for
turbulence. Employing Kraichnan model of short-correlated velocity we identify
the new type of zero modes, which break scale invariance and determine an
anomalously slow decay of correlations at large scales
Scaling studies of QCD with the dynamical HISQ action
We study the lattice spacing dependence, or scaling, of physical quantities
using the highly improved staggered quark (HISQ) action introduced by the
HPQCD/UKQCD collaboration, comparing our results to similar simulations with
the asqtad fermion action. Results are based on calculations with lattice
spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical
HISQ quarks. The strange and charm quark masses are near their physical values,
and the light-quark mass is set to 0.2 times the strange-quark mass. We look at
the lattice spacing dependence of hadron masses, pseudoscalar meson decay
constants, and the topological susceptibility. In addition to the commonly used
determination of the lattice spacing through the static quark potential, we
examine a determination proposed by the HPQCD collaboration that uses the decay
constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the
lattice artifacts in the HISQ simulations are much smaller than those in the
asqtad simulations at the same lattice spacings and quark masses.Comment: 36 pages, 11 figures, revised version to be published. Revisions
include discussion of autocorrelations and several clarification
Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion
Nonlocal QFT of one-component scalar field in -dimensional
Euclidean spacetime is considered. The generating functional (GF) of complete
Green functions as a functional of external source , coupling
constant , and spatial measure is studied. An expression for GF
in terms of the abstract integral over the primary field
is given. An expression for GF in terms of integrals
over the primary field and separable Hilbert space (HS) is obtained by means of
a separable expansion of the free theory inverse propagator over the
separable HS basis. The classification of functional integration measures
is formulated, according to which trivial and
two nontrivial versions of GF are obtained. Nontrivial versions
of GF are expressed in terms of -norm and -norm,
respectively. The definition of the -norm generator is suggested.
Simple cases of sharp and smooth generators are considered. Expressions for GF
in terms of integrals over the separable HS with new integrands
are obtained. For polynomial theories and for
the nonpolynomial theory , integrals over the separable HS in
terms of a power series over the inverse coupling constant for
both norms (-norm and -norm) are calculated. Critical values of model
parameters when a phase transition occurs are found numerically. A
generalization of the theory to the case of the uncountable integral over HS is
formulated. A comparison of two GFs , one in the case of
uncountable HS integral and one obtained using the Parseval-Plancherel
identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared
for the special issue "QCD and Hadron Structure" of the journal Particles;
v3: minimal corrections; v4: paragraphs added related to Reviewer comment
Approximate Killing Vectors on S^2
We present a new method for computing the best approximation to a Killing
vector on closed 2-surfaces that are topologically S^2. When solutions of
Killing's equation do not exist, this method is shown to yield results superior
to those produced by existing methods. In addition, this method appears to
provide a new tool for studying the horizon geometry of distorted black holes.Comment: 4 pages, 3 figures, submitted to Physical Review D, revtex
-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions
Nonlocal quantum theory of one-component scalar field in -dimensional
Euclidean spacetime is studied in representations of -matrix
theory for both polynomial and nonpolynomial interaction Lagrangians. The
theory is formulated on coupling constant in the form of an infrared smooth
function of argument for space without boundary. Nonlocality is given by
evolution of Gaussian propagator for the local free theory with ultraviolet
form factors depending on ultraviolet length parameter . By representation
of the -matrix in terms of abstract functional integral over
primary scalar field, the form of a grand canonical partition
function is found. And, by expression of -matrix in terms of the
partition function, the representation for in terms of basis
functions is obtained. Derivations are given for discrete case where basis
functions are Hermite functions, and for continuous case where basis functions
are trigonometric functions. The obtained expressions for the
-matrix are investigated within the framework of variational
principle based on Jensen inequality. Equations with separable kernels
satisfied by variational function are found and solved, yielding results
for both the polynomial theory and the nonpolynomial sine-Gordon
theory. A new definition of the -matrix is proposed to solve
additional divergences which arise in application of Jensen inequality for the
continuous case. Analytical results are illustrated numerically. For simplicity
of numerical calculation: the case is considered, and propagator for the
free theory is in the form of Gaussian function typically in the
Virton-Quark model. The formulation for nonlocal QFT in momentum space of
extra dimensions with subsequent compactification into physical spacetime is
discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and
plots edited, references and acknowledgments added; prepared for the special
issue of the journal Particles in memory of G.V. Efimo
Predictions for Polarized-Beam/Vector-Polarized-Target Observables in Elastic Compton Scattering on the Deuteron
Motivated by developments at HIGS at TUNL that include increased photon flux
and the ability to circularly polarize photons, we calculate several
beam-polarization/target-spin dependent observables for elastic Compton
scattering on the deuteron. This is done at energies of the order of the pion
mass within the framework of Heavy Baryon Chiral Perturbation Theory. Our
calculation is complete to O(Q^3) and at this order there are no free
parameters. Consequently, the results reported here are predictions of the
theory. We discuss paths that may lead to the extraction of neutron
polarizabilities. We find that the photon/beam polarization asymmetry is not a
good observable for the purpose of extracting \alpha_n and \beta_n. However,
one of the double polarization asymmetries, \Sigma_x, shows appreciable
sensitivity to \gamma_{1n} and could be instrumental in pinning down the
neutron spin polarizabilities.Comment: 26 pages, 13 figures, revised version to be published in PR
A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems
In this paper we introduce a new kind of Lax-Oleinik type operator with
parameters associated with positive definite Lagrangian systems for both the
time-periodic case and the time-independent case. On one hand, the new family
of Lax-Oleinik type operators with an arbitrary as
initial condition converges to a backward weak KAM solution in the
time-periodic case, while it was shown by Fathi and Mather that there is no
such convergence of the Lax-Oleinik semigroup. On the other hand, the new
family of Lax-Oleinik type operators with an arbitrary
as initial condition converges to a backward weak KAM solution faster than the
Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some
reference
On the number of Mather measures of Lagrangian systems
In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact
the minimizers of a "universal" infinite dimensional linear programming
problem. This fundamental result has many applications, one of the most
important is to the estimates of the generic number of Mather measures.
Ma\~n\'e obtained the first estimation of that sort by using finite dimensional
approximations. Recently, we were able with Gonzalo Contreras to use this
method of finite dimensional approximation in order to solve a conjecture of
John Mather concerning the generic number of Mather measures for families of
Lagrangian systems. In the present paper we obtain finer results in that
direction by applying directly some classical tools of convex analysis to the
infinite dimensional problem. We use a notion of countably rectifiable sets of
finite codimension in Banach (and Frechet) spaces which may deserve independent
interest
IRIS: A new generation of IRAS maps
The Infrared Astronomical Satellite (IRAS) had a tremendous impact on many
areas of modern astrophysics. In particular it revealed the ubiquity of
infrared cirrus that are a spectacular manifestation of the interstellar medium
complexity but also an important foreground for observational cosmology. With
the forthcoming Planck satellite there is a need for all-sky complementary data
sets with arcminute resolution that can bring informations on specific
foreground emissions that contaminate the Cosmic Microwave Background
radiation. With its 4 arcmin resolution matching perfectly the high-frequency
bands of Planck, IRAS is a natural data set to study the variations of dust
properties at all scales. But the latest version of the images delivered by the
IRAS team (the ISSA plates) suffer from calibration, zero level and striping
problems that can preclude its use, especially at 12 and 25 micron. In this
paper we present how we proceeded to solve each of these problems and enhance
significantly the general quality of the ISSA plates in the four bands (12, 25,
60 and 100 micron). This new generation of IRAS images, called IRIS, benefits
from a better zodiacal light subtraction, from a calibration and zero level
compatible with DIRBE, and from a better destriping. At 100 micron the IRIS
product is also a significant improvement from the Schlegel et al. (1998) maps.
IRIS keeps the full ISSA resolution, it includes well calibrated point sources
and the diffuse emission calibration at scales smaller than 1 degree was
corrected for the variation of the IRAS detector responsivity with scale and
brightness. The uncertainty on the IRIS calibration and zero level are
dominated by the uncertainty on the DIRBE calibration and on the accuracy of
the zodiacal light model.Comment: 16 pages, 17 figures, accepted for publication in ApJ (Suppl). Higher
resolution version available at
http://www.cita.utoronto.ca/~mamd/IRIS/IrisTechnical.htm
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