Shock fluctuations in the asymmetric simple exclusion process

Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv _, , a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionX _t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim _t t ^–1(E(X _t )²–(EX _t )²) and findD=(p–q)(–)^–1((1–)+(1–)) as conjectured by Spohn (1991). We show that in the scale the position ofX _t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

An exact numerical analysis of coupled planar electron waveguides with asymmetric rectangular potential profiles

An exact numerical analysis is given of electron waves in a pair of coupled semiconductor heterojunction electron waveguides modelled by a rectangular potential distribution. The waveguide lengths required for electron current transfer between the guides agree asymptotically with estimates from Yariv's coupled mode theory and are usefully more accurate. Moreover the electron wave coupling due to an ideal launcher can be worked out, leading to estimates of the off/on current ratio occurring in the waveguides when regarded as an ultrafast switch. For a Poisson probability distribution of the number of electrons N making up a bit-pulse, we have calculated the minimum average N, dependent upon , which would be required to keep the switching bit-error rate below prescribed limits. Pulse rise times and switching delays are derived from the explicit forms for the longitudinal electron wave group velocity. Combining the bit-error and switching-time calculations leads to estimates of the waveguide current densities which would be required in practice. Some normalized sets of curves relating to our analysis are given and used to predict the performance of particular examples of recently proposed AlGaAs/GaAs heterojunction electron waveguide switch/couplers.     

New routes to beta-cycloalkylalanine derivatives using serine-derived organozinc reagents

Two distinct routes to beta-cycloalkylalanine derivatives have been developed. The first route employs the reaction of the iodoalanine-derived zinc-copper reagent 2 with cycloalk-1-en-3-yl phosphates, and the second uses the palladium-catalysed coupling of the iodoalanine-derived zinc reagent 1 with cycloalkenyl triflates; in each case, catalytic hydrogenation of the unsaturated product leads to the protected beta-cycloalkylalanine. The latter route allows access to a range of cycloalkyl derivatives, with ring sizes of 5-8. beta-(1-Methyl-1-cyclohexyl)alanine may be prepared using reaction of the zinc-copper reagent 2 with 3-methyl-2-cyclohexenyl chloride, followed by hydrogenation. The corresponding cyclopentyl derivative may be prepared by reaction of the same zinc-copper reagent 2 with diethyl geranylphosphate, followed by ring-closing metathesis and hydrogenation.     

The reactions of some halogenated pyridines with methoxide and methanethiolate ions in dimethylformamide

The reactions of 2,6- and 2,5-dibromopyridines and of 2,3- and 3,5-dichloropyridines with sodium isopropanethiolate and methanethiolate afforded the products of mono- or of bis-substitution depending on the experimental conditions. The same pyridines reacted with sodium methoxide to give good yields of the mono-substituted products; bis-substitution occurred easily only in the case of the 2,6-dibromo- and of the 3,5-dichloropyridine. The syntheses of some methoxy thiomethoxypyridine, starting from the halogeno methoxypyridines or from the halogeno thiomethoxypyhdines are also described. The bis-(alkylthio)pyridines can be fragmented by sodium in HMPA to give the bis(mercapto)pyridines.     

Air monitoring of volatile aromatic compounds by means of long-term exposure diffusive samplers

Results obtained by using "Analyst", a long-term diffusive sampler, in some monitoring campaigns, performed for the determination of benzene and the volatile aromatic pollutants, in five cities of the Italian Umbria Region and at the city of Forlì, are presented and discussed. First results of an inter comparison between the "Analyst" and "radial-type" diffusive samplers, carried out by the Regional Agency for the Ambient Protection (ARPA) of Forlì, point out substantial advantages with the long-time sampling devices.     

Adsorption and thermal condensation mechanisms of amino acids on oxide supports. 1. Glycine on silica

Glycine was adsorbed on the surface of a well-defined silica from aqueous solutions of variable concentrations and pHs. The adsorbed molecules were characterized using middle-IR and UV-vis-NIR spectroscopies. Except at the lowest pH (2.0), they were predominantly present on the surface as zwitterions. Two successive deposition mechanisms were evidenced with increasing glycine concentration. At low concentrations, glycine is specifically adsorbed on silica surface sites, probably through its NH3+ moiety. The pH dependence suggests that these sites may be silanolate groups (approximately equal to Si-O-). At higher concentrations, specific adsorption sites are saturated and surface-induced precipitation of beta-glycine is observed. The thermal reactivity of adsorbed/deposited glycine was then investigated by thermogravimetric analysis, in situ diffuse reflectance IR spectroscopy, and thermoprogrammed desorption coupled with mass spectrometry. Adsorbed glycine molecules react to form peptide bonds at a temperature considerably lower than that for bulk crystalline alpha-glycine. The main reaction product is the cyclic dimer diketopiperazine, with no evidence of the linear dimer. The activation mechanism is not diffusionally limited; the formation of "surface acyls", previously proposed for related systems, has not been evidenced here. These findings are of relevance for the evaluation of prebiotic peptide synthesis scenarios.