In the first part of this paper the moment method is employed to solve the nonlinear Boltzmann equation. An expansion about a local Maxwellian distribution is used with the basis functions introduced by Waldmann [in Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1958), Vol. 12, p. 295]. Earlier approaches are extended by the inclusion of more expansion functions (Sonine polynomials) in order to obtain an approximation for the velocity distribution function. General relations for the coupling of the moments are derived and the resulting transport relaxation equations are solved for the special Couette geometry. The influence of the higher moments on the viscosity coefficients is small, but the higher moments are essential for the distribution function itself. The inclusion of the quadratic collision matrix elements leads to minor modifications only. In another part of the paper the velocity distribution function is obtained from nonequilibrium molecular dynamics. Excellent agreement with the predictions of the moment method is found provided that the constant temperature constraint of the simulation is taken into account by incorporating a nonconservative external force term into the Boltzmann equation. The effect of this modification is discussed in detail for the viscosity coefficients. The non-Newtonian flow behavior of gases is studied on the microscopic level of the velocity distribution function. In addition an isotropic distortion of the Maxwellian distribution is observed.

We use the homogenization method to obtain an expression for the effective diffusion coefficient $D^{\mathrm{*}}$ for convective flows. We evaluate this expression numerically by a finite-mode truncation for two-dimensional laminar flows with arbitrary Péclet numbers. Our results allow us to establish the range of validity of the small- and large-Péclet-number asymptotic evaluations of $D^{\mathrm{*}}$. In particular, we find that for the case of rigid boundary conditions corrections to the asymptotic scaling decay only very slowly for large Péclet numbers and are still about 5% for Péclet numbers as high as ${10}^6$.

The complete set of Lyapunov exponents for a two-dimensional two-body shearing system is calculated using an extension of the method of Hoover and Posch. The Lyapunov dimension is found to be a decreasing function of the shear rate. This implies that the nonequilibrium distribution function is a fractal attractor whose dimension is less than that of the equilibrium phase space.

The technique of photon-correlation spectroscopy was exploited to study turbulent pipe flow behind a grid. We measure the correlation function g(t) of the light intensity scattered by small particles suspended in the turbulent fluid. The results imply that the probability distribution function for the small relative velocity fluctuations in the turbulent grid flow is Lorentzian-like. The statistical properties of the small velocity fluctuations over varying length scales possess a self-similar feature. This self-similarity was seen only when the Reynolds number becomes larger than a specific value ${\mathrm{scrR}}_c$. All the measurements suggest that the flow changes its character at this point.

Investigation of Hopfield’s model of associative-memory implementation by a neural network led to an associative-memory model based on a generalized potential surface. In this model, there are no spurious memories, and any set of desired points can be stored with unlimited capacity (in the continuous-time real-space version of the model). There are no limit cycles in this system, and the size of all basins of attraction can reach up to half the distance between stored points by proper choice of the design parameters. A discrete-time version with its state-space being the unit hypercube is also derived, and admits a worst-case capacity (under any fixed desired size of basins of attractions) which grows exponentially with the number of neurons at a rate that is asymptotically optimal in the information theory sense. The computational complexity of this model is similar to that of the Hopfield memory. The results are derived under an axiomatic approach which determines the desired properties and shows that the above-mentioned model is the only one to achieve them.

The dynamics of a multidimensional kicked rotor or standard map are investigated in the chaotic regime. A general perturbative expression for the diffusion coefficient D in momentum space is developed in d dimensions. Explicit values are found for two and three dimensions. The covariance between the motion in different directions is calculated and found to vanish, and the diffusion in momentum space is completely isotropic. The calculated values of D are found to be in good agreement with results of numerical simulations that are presented as well.

We have investigated the linear–electric-field effect (LEFE) in cupric ions situated in ligand fields of low symmetry. General properties of LEFE signals resulting from various low-symmetry models are described. Treating g values, we show how hybrid-orbital ‘‘united-atom’’ models can be used for direct calculation of the LEFE signal expected from cupric sites of specific low-symmetry geometries. This hybrid–atomic-orbital approach is shown to give a straightforward method for interpreting LEFE data in terms of cupric electronic states that directly reflect the ligand environment. Results are presented which demonstrate the potential of calculations with this model to account quantitatively for the LEFE data from blue cupric proteins.

A variational approach based on the path-integral formulation of the statistical mechanics is applied for calculating the partition function of the sine-Gordon field. This is done by determining an effective potential which includes, in a complete quantum way, the linear modes of the field, while treating variationally the nonlinear excitations. Using this effective potential the temperature renormalization is separately studied both for the vacuum and the one-soliton sector, recovering the total one-loop self-consistent (Hartree-Fock) renormalized approximation. A high-temperature expansion is calculated whose range of applicability is found to be much wider with respect to previous expansions of the same kind. Finally, a comparison with a Monte Carlo simulation is presented, obtaining a very good agreement with the numerical data.

Experiments have been performed to detect the existence of 1/f fluctuations in the γ decay of the radioactive source ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$. No evidence for such fluctuations has been found.

We present a three-dimensional probabilistic model of particle transport in a medium where the particles suffer quasielastic collisions. The model accounts for bulk and surface scattering, as well as partial reflections at the boundaries of the medium. We give analytical and numerical methods for the evaluation of the particle transmission probability in the case of a medium with a plane-parallel geometry. The influence of the various parameters of the model on this probability is also discussed.

The probabilistic description of quasielastic particle transport given in a previous paper is used to analyze the results of low-energy electron transmission experiments on thin solid xenon and molecular nitrogen films deposited on a metal substrate. Values of the entrance probabilities of the incident electrons at the vacuum-film interface and of the electron scattering mean free paths in the films are extracted in the electron energy range 1.6–7.9 eV for xenon, and 2.4–7.4 eV for molecular nitrogen. The effects of anisotropy in the surface scattering and in the reflections at the two interfaces of the films are also discussed.

The existence of thermal conductivity is examined for a one-dimensional chain of Lennard-Jones particles, using techniques of equilibrium and nonequilibrium molecular dynamics. The transport of energy by soundlike pulses is related to the anomalous fluctuations of the heat flux in this model. Equilibrium time properties are governed by two time scales which can be measured. The effects of modifications to the original model are also examined: particles having different masses, eventually with different interaction potentials or under the influence of an external sinusoidal field.

We study a new critical point which terminates a first-order transition line along which two smectic-A (SmA) liquid-crystal phases (or more generally any layered phases with uniaxial symmetry) with different layer spacing coexist. We call this new critical point C the SmA-SmA’ critical point. We develop a model nonlinear elastic Hamiltonian to describe physical properties in the vicinity of C. We study this model using mean-field theory, one-loop-order perturbation theory, and the ε expansion. In mean-field theory, the SmA-SmA’ transition is identical to the mean-field liquid-gas transition. In one-loop perturbation theory, critical corrections to the compressibility become important below an upper critical dimension of 6. In addition, there are important critical corrections to third-order vertex function between 6 and 8 dimensions indicating deviations from mean-field behavior below 8 dimensions. We determine a fixed point in 6-ε dimensions describing C and calculate critical exponents to the first order in ε. This fixed point exhibits anisotropic scaling with different correlation length exponents ${\nu }_{?}$ and ${\nu }_{\perp }$ parallel and perpendicular to the director. Scaling properties and x-ray scattering patterns in the vicinity of the SmA-SmA’ critical point are also considered.

By implementing the algorithm of classical perturbation theory on the Schrödinger equation for a large class of periodically driven rotators, it is shown that the classical resonance overlapping criterion for the onset of chaotic motion implies the existence of avoided crossings among an arbitrarily large number of quantum quasienergy levels at the classical limit ħ small, nħ=A close to a classically resonant torus.

A generalized Fermi-Segrè-Goudsmit formula is derived for a Rydberg electron’s interaction with an open shell atomic ion via nuclear hyperfine interactions, in conjunction with eigenchannel quantum-defect theory. This formula predicts the splitting of ionization potentials by hyperfine interactions, which includes both magnetic dipole and electrostatic quadrupole moments of the nucleus and the autoionizing structures in the continuum. The results are applied to analyze the hyperfine structure of the 5sns Rydberg series of the Sr atom with n>100.

Phase variations during a phase-conjugation process are considered in detail, following our own method of analytical solution of the degenerate four-wave mixing including pump depletion and arbitrary phase mismatch between the light interference and the refractive-index gratings. Closed-form expressions are obtained for the phase transfer, and some apparent misconceptions concerning phase changes in optical phase conjugation are discussed.

Numerical calculations of laser-irradiated ${\mathrm{EuF}}_2$ targets predict gain coefficients of 0.3–1.6 ${\mathrm{cm}}^{\mathrm{-}1}$ on several 4d-4p Ni-like Eu lines from 66 to 104.5 Å. Dielectronic recombination is important both in determining the ionization balance and in populating the J=1,2 4d excited states. Targets which are optimized for 0-1 gain show significantly less effect due to trapping on the 0-1 line than on the 2-1 line.

The frequency dependence of the deviation from Kleinman symmetry for the electronic part of the third-order nonlinear susceptibility tensor ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ has been experimentally determined for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. The electronic contribution is extracted from the measured Kleinman symmetry deviation, obtained by means of an electric-field-induced second-harmonic-generation experiment, by making a correction for the vibrational and rotational contributions. The deviation measured at λ=1064 nm where the vibrational contribution is dominant provides a test of the adequacy of the calculated corrections.

The spectrum of scaling exponents of multifractal, hyperbolic strange attractors is quantitatively understood by realizing that each unstable periodic point contributes one scaling exponent to the spectrum. The calculation of the f(α) function can thus be reduced to counting periodic orbits.

Expressions for photoionization channel amplitudes are derived applying the Dill and Fano angular-momentum–transfer formalism to the j-l coupling scheme. This expression will be useful in understanding excited-state photoeffects of rare-gas atoms. The situation in which the present formula reduces to that of the Cooper-Zare model is also discussed.