260 research outputs found
Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation
We study the asymptotic behaviour of positive solutions of the Cauchy problem
for the fast diffusion equation near the extinction time. We find a continuum
of rates of convergence to a self-similar profile. These rates depend
explicitly on the spatial decay rates of initial data
Solving Large-Scale Optimization Problems Related to Bell's Theorem
Impossibility of finding local realistic models for quantum correlations due
to entanglement is an important fact in foundations of quantum physics, gaining
now new applications in quantum information theory. We present an in-depth
description of a method of testing the existence of such models, which involves
two levels of optimization: a higher-level non-linear task and a lower-level
linear programming (LP) task. The article compares the performances of the
existing implementation of the method, where the LPs are solved with the
simplex method, and our new implementation, where the LPs are solved with a
matrix-free interior point method. We describe in detail how the latter can be
applied to our problem, discuss the basic scenario and possible improvements
and how they impact on overall performance. Significant performance advantage
of the matrix-free interior point method over the simplex method is confirmed
by extensive computational results. The new method is able to solve problems
which are orders of magnitude larger. Consequently, the noise resistance of the
non-classicality of correlations of several types of quantum states, which has
never been computed before, can now be efficiently determined. An extensive set
of data in the form of tables and graphics is presented and discussed. The
article is intended for all audiences, no quantum-mechanical background is
necessary.Comment: 19 pages, 7 tables, 1 figur
A note on bound entanglement and local realism
We show using a numerical approach that gives necessary and sufficient
conditions for the existence of local realism, that the bound entangled state
presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local
and realistic description. We also find the lowest possible amount of some
appropriate entangled state that must be ad-mixed to the bound entangled state
so that the resulting density operator has no local and realistic description
and as such can be useful in quantum communication and quantum computation.Comment: 5 page
Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
We report the details and revised analysis of an experiment to measure the
specific heat of helium with subnanokelvin temperature resolution near the
lambda point. The measurements were made at the vapor pressure spanning the
region from 22 mK below the superfluid transition to 4 uK above. The experiment
was performed in earth orbit to reduce the rounding of the transition caused by
gravitationally induced pressure gradients on earth. Specific heat measurements
were made deep in the asymptotic region to within 2 nK of the transition. No
evidence of rounding was found to this resolution. The optimum value of the
critical exponent describing the specific heat singularity was found to be a =
-0.0127+ - 0.0003. This is bracketed by two recent estimates based on
renormalization group techniques, but is slightly outside the range of the
error of the most recent result. The ratio of the coefficients of the leading
order singularity on the two sides of the transition is A+/A- =1.053+ - 0.002,
which agrees well with a recent estimate. By combining the specific heat and
superfluid density exponents a test of the Josephson scaling relation can be
made. Excellent agreement is found based on high precision measurements of the
superfluid density made elsewhere. These results represent the most precise
tests of theoretical predictions for critical phenomena to date.Comment: 27 Pages, 20 Figure
Reheating Temperature and Gauge Mediation Models of Supersymmetry Breaking
For supersymmetric theories with gravitino dark matter, the maximal reheating
temperature consistent with big bang nucleosynthesis bounds arises when the
physical gaugino masses are degenerate. We consider the cases of a stau or
sneutrino next-to-lightest superpartner, which have relatively less constraint
from big bang nucleosynthesis. The resulting parameter space is consistent with
leptogenesis requirements, and can be reached in generalized gauge mediation
models. Such models illustrate a class of theories that overcome the well-known
tension between big bang nucleosynthesis and leptogenesis.Comment: 30 pages, 4 figures; v2: refs adde
High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion
We determine the critical exponents for the XY universality class in three
dimensions, which is expected to describe the -transition in He.
They are obtained from the analysis of high-temperature series computed for a
two-component model. The parameter is fixed such that
the leading corrections to scaling vanish. We obtain ,
, . These estimates improve previous
theoretical determinations and agree with the more precise experimental results
for liquid Helium.Comment: 8 pages, revte
Equation of state for Universe from similarity symmetries
In this paper we proposed to use the group of analysis of symmetries of the
dynamical system to describe the evolution of the Universe. This methods is
used in searching for the unknown equation of state. It is shown that group of
symmetries enforce the form of the equation of state for noninteracting scaling
multifluids. We showed that symmetries give rise the equation of state in the
form and energy density
, which
is commonly used in cosmology. The FRW model filled with scaling fluid (called
homological) is confronted with the observations of distant type Ia supernovae.
We found the class of model parameters admissible by the statistical analysis
of SNIa data. We showed that the model with scaling fluid fits well to
supernovae data. We found that and (), which can correspond to (hyper) phantom fluid, and to a
high density universe. However if we assume prior that
then the favoured model is close to concordance
CDM model. Our results predict that in the considered model with
scaling fluids distant type Ia supernovae should be brighter than in
CDM model, while intermediate distant SNIa should be fainter than in
CDM model. We also investigate whether the model with scaling fluid is
actually preferred by data over CDM model. As a result we find from
the Akaike model selection criterion prefers the model with noninteracting
scaling fluid.Comment: accepted for publication versio
Search for Global Dipole Enhancements in the HiRes-I Monocular Data above 10^{18.5} eV
Several proposed source models for Ultra-High Energy Cosmic Rays (UHECRs)
consist of dipole distributions oriented towards major astrophysical landmarks
such as the galactic center, M87, or Centaurus A. We use a comparison between
real data and simulated data to show that the HiRes-I monocular data for
energies above 10^{18.5} eV is, in fact, consistent with an isotropic source
model. We then explore methods to quantify our sensitivity to dipole source
models oriented towards the Galactic Center, M87, and Centaurus A.Comment: 17 pages, 31 figure
Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum
We have measured the cosmic ray spectrum at energies above eV using
the two air fluorescence detectors of the High Resolution Fly's Eye experiment
operating in monocular mode. We describe the detector, PMT and atmospheric
calibrations, and the analysis techniques for the two detectors. We fit the
spectrum to models describing galactic and extragalactic sources. Our measured
spectrum gives an observation of a feature known as the ``ankle'' near eV, and strong evidence for a suppression near eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio
The Effect of Convection on Disorder in Primary Cellular and Dendritic Arrays
Directional solidification studies have been carried out to characterize the spatial disorder in the arrays of cells and dendrites. Different factors that cause array disorder are investigated experimentally and analyzed numerically. In addition to the disorder resulting from the fundamental selection of a range of primary spacings under given experimental conditions, a significant variation in primary spacings is shown to occur in bulk samples due to convection effects, especially at low growth velocities. The effect of convection on array disorder is examined through directional solidification studies in two different alloy systems, Pb-Sn and Al-Cu. A detailed analysis of the spacing distribution is carried out, which shows that the disorder in the spacing distribution is greater in the Al-Cu system than in Pb-Sn system. Numerical models are developed which show that fluid motion can occur in both these systems due to the negative axial density gradient or due the radial temperature gradient which is always present in Bridgman growth. The modes of convection have been found to be significantly different in these systems, due to the solute being heavier than the solvent in the Al-Cu system and lighter than it in the Pb-Sn system. The results of the model have been shown to explain experimental observations of higher disorder and greater solute segregation in a weakly convective Al-Cu system than those in a highly convective Pb-Sn system
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