Local limit theorems for multiplicative free convolutions

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random variables implies superconvergence of their probability densities to the density of the limit law. Superconvergence to the marginal law of free multiplicative Brownian motion at a specified time is also studied. In the unitary case, the superconvergence to free Brownian motion and that to the Haar measure are shown to be uniform over the entire unit circle, implying further a free entropic limit theorem and a universality result for unitary free Lévy processes. Finally, the method of proofs on the positive half-line gives rise to a new multiplicative Boolean to free Bercovici–Pata bijection.     

Quantum chemical studies of semiconductor surface chemistry using cluster models

Modern quantum chemical methods can be used to investigate many properties of novel molecules and materials with predictive power. We have carried out accurate quantum chemical calculations with cluster models to investigate chemical reactions on semiconductor surfaces. The structure–property relationships that emerge from these studies are illustrated with particular emphasis on silicon as well as indium phosphide surface chemistry. Some new strategies that we have developed to provide a proper balance between covalent and dative bonding in compound semiconductors are discussed. Embedded cluster models have been used in some cases to include the effects of the surroundings on the active region. The structural and mechanistic understanding that emerges from our studies is illustrated by selected results on atomic layer deposition of Al₂O₃ on silicon and hydrogenation of P-rich and In-rich indium phosphide surfaces.     

Infra-red spectrum,structure and properties of the N2-Ar van der Waals molecule

The first spectroscopic observation of bound N₂-Ar van der Waals molecules has been achieved with a cryogenic long path cell maintained at 87 K. The infra-red spectrum exhibits prominent fine structure near the N₂ stretching frequency which is assigned to hindered internal rotation of N₂ within the weakly bound complex. An analysis of this fine structure yields a T-shaped equilibrium geometry in which the N₂ bond axis is perpendicular to the N₂-Ar van der Waals bond axis. The observed spectrum is shown to be consistent with an internal rotational barrier of 20 cm^-1 (57 cal/mole). Approximately 20 per cent of the bound species are trapped by this rotational barrier and acquire a locked semi-rigid structure. The remaining 80 per cent have ill-defined geometry and undergo hindered internal rotation. The rotational envelope of an infra-red fundamental is analysed to give an estimate of the N₂-Ar bond length as 3·9 Å.     

Monotone factors of I.I.D. processes

LetB(p) andB(q) be Bernoulli shifts on {0, 1,...,d - 1}^ℤ. Ifh(p)>h(q), it is a classical theorem of Sinai that there is a factor map takingB(p) toB(q). If, in addition,p stochastically dominatesq, we can ask whether there is such a factor map ϕ which is monotone: ϕ(x) _i≤x_i for each coordinatei of almost every pointx. Here we show that there is a monotone finitary code fromB(p) toB(q) in the case whereB(q) is a shift on two symbols.     

Calorimetry

Methods for determining the heat content E ^*/A of hot nuclei formed in energetic nuclear reactions are discussed. The primary factors involved in converting raw data into thermal physics distributions include: 1) design of the detector array, 2) constraints imposed by the physics of the reaction mechanism, and 3) assumptions involved in converting the filtered data into E ^*/A. The two primary sources of uncertainty in the calorimetry are the elimination of nonequilibrium emissions from the event components and accounting for the contribution of neutron emission to the excitation energy sum.     

Detection

This review on second- and third-generation multidetectors devoted to heavy-ion collisions aims to cover the last twenty years. The presented list of devices is not exhaustive but regroups most of the techniques used during this period for nuclear reactions at intermediate energy (≃ 10A MeV to 1A GeV), both for charged-particle and neutron detection. The main part will be devoted to 4π multidetectors, projectile decay fragmentation, high-resolution magnetic spectrometers, auxiliary detectors and neutron detection. The last part will present the progress in electronics and detection in view of the construction of future-generation detectors.     

Charged particle multiplicity distributions ine + e − annihilation at 29 GeV: a comparison with hadronic data

The charged particle multiplicity distributions for two-jet events ine ⁺ e ^? annihilation at 29 GeV have been measured using the High Resolution Spectrometer at PEP. A Poisson distribution describes the data for both the complete event and for the single jets. In addition, no correlation is observed between the multiplicities in the two jets of an event. For fixed values of the prong number of the complete event, the multiplicity sharing between the two jets is in good agreement with a binomial distribution. The rapidity gap distribution is exponential with a slope equal to the mean rapidity density. These observations, which are consistent with a picture of independent emission of single particles, are contrasted to the results from soft hadronic collisions and conclusions are drawn about the nature of clusters.     

Explicit dimension estimates of attractors for the MHD equations in three-dimensional space

In this article we estimate the dimension of functional invariant sets that arise from the MHD equations, in terms of some physically relevant parameters. We follow the analysis of Constantin, Foias and Temam for 3D Navier-Stokes equations and derive comparable estimates.