Ion and polymer dynamics in polymer electrolytes PPO-LiClO4: II. 2H and 7Li NMR stimulated-echo experiment

We use 2H NMR stimulated-echo spectroscopy to measure two-time correlation functions characterizing the polymer segmental motion in polymer electrolytes PPO-LiClO4 near the glass transition temperature Tg. To investigate effects of the salt on the polymer dynamics, we compare results for different ether oxygen to lithium ratios, namely, 6:1, 15:1, 30:1 and infinity. For all compositions, we find nonexponential correlation functions, which can be described by a Kohlrausch function. The mean correlation times show quantitatively that an increase of the salt concentration results in a strong slowing down of the segmental motion. Consistently, for the high 6:1 salt concentration, a high apparent activation energy E_a=4.1eV characterizes the temperature dependence of the mean correlation times at Tg < T< 1.1T_g, while smaller values E_a=2.5eV are observed for moderate salt contents. The correlation functions are most nonexponential for 15:1 PPO-LiClO4, whereas the stretching is reduced for higher and lower salt concentrations. A similar dependence of the correlation functions on the evolution time in the presence and in the absence of ions indicates that addition of salt hardly affects the reorientational mechanism. For all compositions, mean jump angles of about 15 degree characterize the segmental reorientation. In addition, comparison of results from 2H and 7Li NMR stimulated-echo experiments suggests a coupling of ion and polymer dynamics in 15:1 PPO-LiClO4.Comment: 14 pages, 12 figure

Classical Loop Actions of Gauge Theories

Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.Comment: LaTeX 14 page

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16

Fluctuations of Fluctuation-Induced "Casimir" Forces

The force experienced by objects embedded in a correlated medium undergoing thermal fluctuations--the so-called fluctuation--induced force--is actually itself a fluctuating quantity. We compute the corresponding probability distribution and show that it is a Gaussian centered on the well-known Casimir force, with a non-universal standard deviation that can be typically as large as the mean force itself. The relevance of these results to the experimental measurement of fluctuation-induced forces is discussed, as well as the influence of the finite temporal resolution of the measuring apparatus.Comment: 4 pages, 2 figure

Stochastic Comparison Results for Non-Blocking Switches with Output Queueing

We propose a systematic approach to quantify the impact of nonuniform traffic on the performance of non-blocking switches with output queueing. We do so in the context of a simple queueing model where cells arrive to input ports according to independent Bernoulli processes, and are switched to an output port under a random routing mechanism. We give conditions on pairs of input rate vectors and switching matrices which ensure various stochastic comparisons for performance measures of interest. These conditions are formulated in terms of the majorization ordering while the comparison results are expressed in the strong and convex increasing orderings. <BR

Cell Loss Probabilities in Input Queueing Crossbar Switches Via Light Traffic

Under most system assumptions, closed form solutions of performance measures for input queueing crossbar switches are not available. In this paper, we present expressions and bounds for the derivatives of cell loss probabilities with respect to the arrival rate evaluated at a zero arrival rate. These bounds are used to give an approximation by Taylor expansion, thereby providing an economical way to estimate cell loss probabilities in light traffic

Large Size Asymptotics for Crossbar Switches with Input Queueing

With the advent of high-speed networks, various switch architectures have been proposed to meet the increasingly stringent performance requirements being placed on the underlying switching systems. In general, the performance analysis of such a switch architecture is a difficult task mainly due to the fact that a switch consists of a large number of queues which interact with each other in a fairly complicated manner. In this paper, we analyze a crossbar switch with input queueing in terms of maximum throughput, and formalize the phenomenon that virtual queues formed by the head-of-line cells become decoupled as the switch size grows unboundedly large. We also establish various properties of the limiting queue size processes so obtained

The First Detections of the Extragalactic Background Light at 3000, 5500, and 8000A (III): Cosmological Implications

(Abridged) We have used HST WFPC2 and ground-based spectroscopy to measure the integrated extragalactic background light (EBL) at optical wavelengths. We have also computed the integrated light from individual galaxy counts in the images used to measure the EBL and in the Hubble Deep Field. We find that the flux in galaxies as measured by standard galaxy photometry methods has generally been underestimated by about 50%. Further, we find that the total flux in individually detected galaxies is a factor of 2 to 3 less than the EBL at 3000--8000A. We show that a significant fraction of the EBL may come from normal galaxies at z<4, which are simply undetectable as a result of K-corrections and cosmological surface brightness dimming. This is consistent with recent redshift surveys at z<4. In the context of some simple models, we discuss the constraints placed by the EBL on the evolution of the luminosity density at z>1. Based on our optical EBL and published UV and IR EBL measurements, we estimate that the total EBL from 0.1--1000 microns is 100+/-20 nW/m^2/sr. If the total EBL were produced entirely by stellar nucleosynthesis, then we estimate that the total baryonic mass processed through stars is Omega_* = 0.0062 (+/- 0.0022) h^{-2}, which corresponds to 0.33+/-0.12 Omega_B for currently favored values of the baryon density. This estimate is smaller by roughly 7% if 7 h_{0.7} nW/m^2/sr of the total EBL comes from accretion onto central black holes. This estimate of Omega_* suggests that the universe has been enriched to a total metal mass of 0.21(+/-0.13) Z_sun Omega_B. Our estimate is consistent with other measurements of the cumulative metal mass fraction of stars, stellar remnants, and the intracluster medium of galaxy clusters in the local universe.Comment: Accepted for publication in ApJ, 20 pages using emulateapj.sty, version with higher resolution figures available at http://www.astro.lsa.umich.edu/~rab/publications.html or at http://nedwww.ipac.caltech.edu/level5/Sept01/Bernstein3/frames.htm