Francis Jack Smith

TRANSPORT COEFFICIENTS OF IONIZED GASES.

The repulsive and attractive screened Coulomb potentials may be used to represent interactions among charged particles in a gas. The classical Chapman‐Enskog collision integrals are calculated for these potentials over a wide range of reduced temperatures, equivalent to a wide range of electron densities and temperatures. At high temperatures the repulsive and attractive collision integrals are equal and agree with the earlier calculations of Kihara and Liboff. At lower temperatures the attractive collision integrals grow larger than the repulsive collision integrals as the temperature falls, and both grow apart from the previous results. It is shown that quantum effects are large in high‐density plasmas at all temperatures and in low‐density plasmas at very high temperatures.

The efficient calculation of the transport properties of a dilute gas to a prescribed accuracy

Abstract We study in detail the numerical techniques needed to minimize the computation time in calculations of the transport properties of a dilute gas. We iterate all numerical processes until the results are uniformly correct to the accuracy prescribed by the user. Thus in 1 min. we may calculate a set of transport properties to an accuracy of 1 in 100, but 10 min. may be needed for an accuracy of 1 in 10,000. The principal numerical difficulties encountered are centered around the evaluation of some singular definite integrals. We eliminate the singularities by changes of variable and evaluate the resulting well behaved integrals using the Clenshaw-Curtis method. We found this to be the most efficient quadrature method, mainly because of its accuracy and its error estimates. For the same reasons, we adopted the Chebyshev polynomial curve fitting techniques for interpolation rather than the Lagrangian or Spline method.

Extension of Zipf's law to words and phrases

Zipfs law states that the frequency of word tokens in a large corpus of natural language is inversely proportional to the rank. The law is investigated for two languages English and Mandarin and for n-gram word phrases as well as for single words. The law for single words is shown to be valid only for high frequency words. However, when single word and n-gram phrases are combined together in one list and put in order of frequency the combined list follows Zipfs law accurately for all words and phrases, down to the lowest frequencies in both languages. The Zipf curves for the two languages are then almost identical.

Quantum Transport Cross Sections for Ionized Gases

Transport cross sections and collision integrals are calculated over a wide range of energies and temperatures for the attractive and repulsive screened Coulomb potentials. Results accurate to 1% over the whole range from classical to quantum‐mechanical behavior are given in the form of numerical tables. Results of lower accuracy are given as analytical expressions.

Robust speech recognition using probabilistic union models

This paper introduces a new statistical approach, namely the probabilistic union model, for speech recognition involving partial, unknown frequency-band corruption. Partial frequency-band corruption accounts for the effect of a family of real-world noises. Previous methods based on the missing feature theory usually require the identity of the noisy bands. This identification can be difficult for unexpected noise with unknown, time-varying band characteristics. The new model combines the local frequency-band information based on the union of random events, to reduce the dependence of the model on information about the noise. This model partially accomplishes the target: offering robustness to partial frequency-band corruption, while requiring no information about the noise. This paper introduces the theory and implementation of the union model, and is focused on several important advances. These new developments include a new algorithm for automatic order selection, a generalization of the modeling principle to accommodate partial feature stream corruption, and a combination of the union model with conventional noise reduction techniques to deal with a mixture of stationary noise and unknown, nonstationary noise. For the evaluation, we used the TIDIGITS database for speaker-independent connected digit recognition. The utterances were corrupted by various types of additive noise, stationary or time-varying, assuming no knowledge about the noise characteristics. The results indicate that the new model offers significantly improved robustness in comparison to other models.

Transport Properties of Quadrupolar Gases

Collision integrals for quadrupolar gases are computed on the assumption of fixed relative orientation per collision, with a 12–6−5 potential model, for a range of reduced temperatures and reduced quadrupole moments. The quadrupole effects on diffusion and viscosity are small, but not completely negligible if one wants accurate values for the parameters of the spherically symmetric component of the potential. These values are needed to obtain quadrupole moments from properties like second virial coefficients, which are more sensitive to quadrupole effects. Thermal‐diffusion factors are the most strongly affected of the transport coefficients; the presence of quadrupolar intermolecular forces can wipe out the thermal‐diffusion inversion temperatures.

Hydrogen atom spin-change collisions

Abstract Spin-change cross-sections and rate coefficients are calculated for collisions between two hydrogen atoms and for collisions between hydrogen atoms and protons taking account of nuclear symmetry. It is shown that the effect of the identity of the two nuclei is to reduce the rate at which the populations of the hydrogen spin-states is changed by HH collisions by a factor of 1 4 . It is also shown that the rate coefficients for spin-change by e − −H collisions is 5 or 6 times larger than the rate coefficients for H + -H collisions above about 100°K. To calculate the rate coefficients for H + −H collisions the electron capture cross-sections were calculated down to very low energies using the exact JWKB approximation for the phase shifts. Above about 10 −2 eV these cross sections agree within a few per cent with previous calculations by Bates and Boyd.

A weighted average n-gram model of natural language

A new n-gram model of natural language designed to aid speech recognition is presented in which the probabilities are calculated as a weighted average of maximum likelihood probabilities obtained from a training corpus. This simple approach produces a model that can be constructed quickly and is easily adapted either by changing the weights or by changing the training corpus. The model is compared with two other models; the first is based on Turing-Good estimates and uses Katzs back-off approach. The second model is a deleted estimate model which combines different probability distributions in approximately optimal proportions. We introduce a new measure for language models based on their performance when predicting words removed randomly from samples of unseen text. The performance of all three models using both this new measure and the existing measure of perplexity have been compared. Results indicate that the performance of the new model is close to the performance of the deleted estimate model, while both are superior to the Turing-Good model.

A Bayesian approach for building triphone models for continuous speech recognition

This paper introduces a new statistical framework for constructing triphonic models from models of less context-dependency. This composition reduces the number of models to be estimated by higher than an order of magnitude and is therefore of great significance in relieving the data sparsity problem in triphone-based continuous speech recognition. The new framework is derived from Bayesian statistics, and represents an alternative to other triphone-by-composition techniques, particularly to the model-interpolation and quasitriphone approaches. The potential power of this new framework is explored by an implementation based on the hidden Markov modeling technique. It is shown that the new model structure includes the quasitriphone model as a special case, and leads to more efficient parameter estimation than the model-interpolation method. Phone recognition experiments show an increase in the accuracy over that obtained by comparable models.

Molecular Rainbows for the 12–6 Potential in the Airy Approximation

Numerical values are given for those quantities needed to describe molecular rainbow scattering in the Airy approximation, for the 12–6 potential. These are the value of the rainbow angle and the curvature of the deflection function at the rainbow angle; some values of the third derivative are also presented. An example is given of the determination of the potential parameters e and σ from just the measured angular positions of the first maximum and minimum in the differential cross section.