Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two $A$ particles land onto two vacant sites at the extremities of the catalytic segment, or when any $A$ particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another $A$ particle. Non-catalytic segments are inert with respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.Comment: AMSTeX, 27 pages + 4 figure

Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Spectral Reflectance Measurements of Sulfides at the Planetary Emissivity Laboratory — Analogs for Hollow-Forming Material on Mercury?

We present spectral reflectance measurements at visible and near-infrared wavelengths of fresh and heated samples of MnS, CaS, and MgS, as well as elemental sulfur. We infer that sulfides display a diagnostic feature at or near 0.6 µm

Calibrating fecal NIRS equations for predicting botanical composition of diets

The objectives of this study were to investigate the use of near infrared spectroscopy (NIRS) of fecal samples for predicting the percentage of mountain big sagebrush (Artemisia tridentata Nutt. ssvaseyana (Rydb) Beetle) in sheep diets and to quantify the limitations of using NIRS of fecal samples to predict diet composition. Fecal material from a sheep feeding trial with known levels of sagebrush and several background forages was used to develop fecal NIRS calibration equations validated with fecal material from 2 other sheep feeding trials with known levels of sagebrush in the diets. The 1996 calibration trial varied the level of sagebrush, alfalfa, and grass hay in the diets. The 1998 trial compared frozen to air-dried sagebrush. The Wyoming trial was a metabolism study using frozen sagebrush. Trials used different levels of sagebrush varying from 0 to 30% of the diet in increments of 4 to 10 percentage points. Internal validation of the 1996 trial with a subset of the samples not used for calibration showed that when predicted samples are from the same population as the calibration samples, this procedure can accurately predict percent sagebrush (R2=0.96, SEP=1.6). However, when predicted samples were from a different population than calibration samples, accuracy was much less, but precision was not affected greatly. Low accuracy was caused by a compression of the range of data in the predicted values compared to the reference values, and the predicted sagebrush levels in the diet should be considered to represent an interval scale of measurement. Modified partial least squares regression resulted in better calibration than stepwise regression, and calibration data sets with only high, low, and no sagebrush resulted in calibrations almost as good as data sets with several intermediate levels of sagebrush. High values of the H statistic were related to low precision but did not affect the accuracy of predictions. We believe the interval scale of measurement will contain sufficient information for the purpose of addressing many questions on rangelands

Assessing sleepiness in the rat: a multiple sleep latencies test compared to polysomnographic measures of sleepiness

Sleepiness following 6 h of sleep deprivation (SD) was evaluated with a rat multiple sleep latencies test (rMSLT), and the findings were compared to conventional polysomnographic measures of sleepiness. The 6 h of SD was produced by automated activity wheels, and was terminated at either the end of the light period or at the beginning of the dark period. The rMSLT consisted of 5 min wakefulness induced by sensory stimulation followed by 25 min of freedom to sleep. This procedure was repeated every 30 min for 3 h and was designed to minimize the amount of sleep lost due to the testing procedure. In separate rats, 6 h SD was followed by undisturbed recovery, allowing evaluation of conventional polysomnographic measures of sleepiness. Sleep onset latencies were reduced following SD, with recovery in the light (baseline = 8 min, 3 s versus post-SD = 1 min, 17 s) and dark period (baseline = 14 min, 17 s versus 7 min, 7 s). Sleep onset latencies were not altered by varying the duration criterion for the first sleep bout (i.e., sleep bout length criteria of 10, 20, 30, or 60 s were compared). Polysomnographic variables (non-rapid eye movement sleep episode duration, delta power, and number of awakenings) also provided reliable indirect measures of sleepiness, regardless of whether the recovery sleep occurred in the light or dark period. Evaluation of effect size indicated that the rMSLT was a strong measure of sleepiness, and was influenced by homeostatic, circadian, and illumination factors. The rMSLT provided a simple, objective, robust and direct measure of sleepiness that was as effective as conventional polysomnographic measures of sleepiness

Long-Distance Dispersal and the Reef-Building Corals of the Eastern Pacific

It is currently widely accepted that the hermatypic coral fauna in the Eastern Pacific Ocean underwent massive extinction during the mid-Tertiary, with subsequent transoceanic colonization by planulae from the Indo-West Pacific region during periods of favorable conditions. We suggest that the available evidence does not strongly support this biogeographic hypothesis; moreover, we contend that it is untestable in its present form. In its place we propose an alternative hypothesis based upon modification of a previously widespread, pan-Tethyan coral biota which has since been modified by tectonic events, speciations, and extinctions