Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

Teflon FEP Analyzed After Retrieval From the Hubble Space Telescope

During the Hubble Space Telescope (HST) Second Servicing Mission, 6.8 years after the telescope was deployed in low Earth orbit, degradation of unsupported Teflon FEP (DuPont; fluorinated ethylene propylene), used as the outer layer of the multilayer insulation (MLI) blankets, was evident as large cracks on the telescope light shield. A sample of the degraded outer layer (see the photograph) was retrieved during the second servicing mission and returned to Earth for ground testing and evaluation. Also retrieved was a Teflon FEP radiator surface from a cryogen vent cover that was exposed to the space environment on the aft bulkhead of the HST. NASA Goddard Space Flight Center directed the efforts of the Hubble Space Telescope MLI Failure Review Board, whose goals included determining the FEP degradation mechanisms. As part of the investigations into the degradation mechanisms, specimens retrieved from the first and second HST servicing missions, 3.6 and 6.8 years after launch, respectively, were characterized through exhaustive mechanical, optical, and chemical testing. Testing led by Goddard included scanning electron microscopy, optical microscopy, tensile testing, solar absorptance measurements, time-of-flight secondary ion mass spectroscopy (TOF-SIMS), Fourier transform infrared microscopy (m-FTIR), attenuated total reflectance infrared microscopy (ATR/FTIR), and x-ray diffraction (XRD). The NASA Lewis Research Center contributed significantly to the analysis of the retrieved HST materials by leading efforts and providing results of bend testing, surface microhardness measurements, x-ray photoelectron spectroscopy, solid-state nuclear magnetic resonance spectroscopy, and density measurements. Other testing was conducted by Nano Instruments, Inc., and the University of Akron

A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0

We present a formalism for computing the complexity of metastable states and the zero-temperature magnetic hysteresis loop in the soft-spin random-field model in finite dimensions. The complexity is obtained as the Legendre transform of the free-energy associated to a certain action in replica space and the hysteresis loop above the critical disorder is defined as the curve in the field-magnetization plane where the complexity vanishes; the nonequilibrium magnetization is therefore obtained without having to follow the dynamical evolution. We use approximations borrowed from condensed-matter theory and based on assumptions on the structure of the direct correlation functions (or proper vertices), such as a local approximation for the self-energies, to calculate the hysteresis loop in three dimensions, the correlation functions along the loop, and the second moment of the avalanche-size distribution.Comment: 28 pages, 12 figure

A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. VI. Binary collision approximations for the memory function for self correlation functions

We use computer simulation results for a dense Lennard-Jones fluid for a range of temperatures to test the accuracy of various binary collision approximations for the memory function for density fluctuations in liquids. The approximations tested include the moderate density approximation of the generalized Boltzmann-Enskog memory function (MGBE) of Mazenko and Yip, the binary collision approximation (BCA) and the short time approximation (STA) of Ranganathan and Andersen, and various other approximations derived by us using diagrammatic methods. The tests are of twotypes. The first is a comparison of the correlation functions predicted by each approximate memory function with the simulation results, especially for the self longitudinal current correlation function (SLCC). The second is a direct comparison of each approximate memory function with a memory function numerically extracted from the correlation function data. The MGBE memory function is accurate at short times but decays to zero too slowly and gives a poor description of the correlation function at intermediate times. The BCA is exact at zero time, but it predicts a correlation function that diverges at long times. The STA gives a reasonable description of the SLCC but does not predict the correct temperature dependence of the negative dip in the function that is associated with caging at low temperatures. None of the other binary collision approximations is a systematic improvement upon the STA. The extracted memory functions have a rapidly decaying short time part, much like the STA, and a much smaller, more slowly decaying part of the type predicted by mode coupling theory. Theories that use mode coupling commonly include a binary collision term in the memory function but do not discuss in detail the nature of that term. ...Comment: 18 pages, 10 figure

Requirements on collider data to match the precision of WMAP on supersymmetric dark matter

If future colliders discover supersymmetric particles and probe their properties, one could predict the dark matter density of the Universe and would constrain cosmology with the help of precision data provided by WMAP and PLANCK. We investigate how well the relic density can be predicted in minimal supergravity (mSUGRA), with and without the assumption of mSUGRA when analysing data. We determine the parameters to which the relic density is most sensitive, and quantify the collider accuracy needed. Theoretical errors in the prediction are investigated in some detail.Comment: 42 pages, 16 figures. v2 incorporates referee's comments: minor corrections/clarifications with additional figures to show regions of m12-m0 plane considere

Charge and Density Fluctuations Lock Horns : Ionic Criticality with Power-Law Forces

How do charge and density fluctuations compete in ionic fluids near gas-liquid criticality when quantum mechanical effects play a role ? To gain some insight, long-range $\Phi^{{\mathcal{L}}}_{\pm \pm} / r^{d+\sigma}$ interactions (with $\sigma>0$), that encompass van der Waals forces (when $\sigma = d = 3$), have been incorporated in exactly soluble, $d$-dimensional 1:1 ionic spherical models with charges $\pm q_0$ and hard-core repulsions. In accord with previous work, when $d>\min \{\sigma, 2\}$ (and $q_0$ is not too large), the Coulomb interactions do not alter the ($q_0 = 0$) critical universality class that is characterized by density correlations at criticality decaying as $1/r^{d-2+\eta}$ with $\eta = \max \{0, 2-\sigma\}$. But screening is now algebraic, the charge-charge correlations decaying, in general, only as $1/r^{d+\sigma+4}$; thus $\sigma = 3$ faithfully mimics known \textit{non}critical $d=3$ quantal effects. But in the \textit{absence} of full ($+, -$) ion symmetry, density and charge fluctuations mix via a transparent mechanism: then the screening \textit{at criticality} is \textit{weaker} by a factor $r^{4-2\eta}$. Furthermore, the otherwise valid Stillinger-Lovett sum rule fails \textit{at} criticality whenever $\eta =0$ (as, e.g., when $\sigma>2$) although it remains valid if $\eta >0$ (as for $\sigma<2$ or in real $d \leq 3$ Ising-type systems).Comment: 8 pages, in press in J. Phys. A, Letters to the Edito

On-Orbit Teflon(trademark) FEP Degradation

During the Hubble Space Telescope (HST) Second Servicing Mission (SM2), degradation of unsupported Teflon(trademark) FEP (fluorinated ethylene propylene), used as the outer layer of the multi-layer insulation (MLI) blankets, was evident as large cracks on the telescope light shield. A sample of the degraded outer layer was retrieved during the mission and returned to Earth for ground testing and evaluation. The results of the Teflon(trademark) FEP sample evaluation and additional testing of pristine Teflon FEP led the investigative team to theorize that the HST damage was caused by thermal cycling with deep-layer damage from electron and proton radiation which allowed the propagation of cracks along stress concentrations, and that the damage increased with the combined total dose of electrons, protons, UV and x-rays along with thermal cycling. This paper discusses the testing and evaluation of the Teflon(trademark) FEP

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result