A hopping model described by Katz, Lebowitz, and Spohn [J. Stat. Phys. 34, 497 (1983)] and by Valles and Marro [J. Stat. Phys. 43, 441 (1986)] is studied analytically for small lattice systems. The dependence of the nonequilibrium steady state on various parameters and transition rate functions is obtained exactly. The results are compared with simulations on large systems.

We examine the falloff of power spectra at high frequencies as a possible means of distinguishing systems exhibiting deterministic chaos from systems subject to noise. To this end, we derive the asymptotic series describing the high-frequency falloff of the power spectrum for systems subject to noise. Our analysis applies to systems with an arbitrary finite number of degrees of freedom and includes the cases of additive and multiplicative white noise and the case of continuous nonwhite noise appearing with a general parametric dependence. In the case of colored noise, we show that the frequency at which crossover to the asymptotic behavior occurs is the effective bandwidth of the noise, i.e., the inverse of the correlation time. This result should be particularly useful in cases where the noise is not directly observable.

Synchrotron x-ray diffraction methods employing a position-sensitive detector were used to study smectic-C (SmC) and smectic-I (SmI) phases in thin (2–6 molecular layers) liquid-crystal films of 4-(n-heptyloxy)benzylidene-4-(n-heptyl)aniline (7O.7). Above ∼78 °C, the entire film is SmC and below ∼69 °C, the entire film is SmI, a stacked tilted hexatic. Between 69?deC and 78?deC, the surface layers of the films are hexatic SmI and the interior layers are SmC. There is a pretransitional broadening of the surface hexatic peaks as the surface layers melt into the SmC phase.

We analyze the shape z(x) of two-dimensional needle crystals far away from the tip and find that in general the deviation Δz away from the Ivantsov solution has an asymptotic behavior of the form Δz∼$x^{\mathrm{-}\alpha }$, with α a noninteger exponent. For the asymptotic behavior, the regime where the Péclet number p is less than (1/2) and the one where p is larger than (1/2) are distinct. For p>(1/2), the exponent is calculated explicitly, while for p<(1/2), we present numerical evidence for the existence of the exponent α. These results differ from those used in earlier numerical and analytical studies of two-dimensional dendritic growth.

The Hopfield model of a neural network is extended to allow for the storage and retrieval of biased patterns, {${\xi }_i^{\mu }$}, where $N^{\mathrm{-}1}$${\mathcal{J}}_i^N$${\xi }_i^{\mu }$=a is arbitrary. Such patterns represent levels of activity (i.e., percentage of firing neurons) equal to (1/2)(1+a), -1<a<1. If the coupling constants (synaptic efficacies) are constructed as in the original Hopfield model, the system can retrieve at most a very small number of patterns (p<1+$a^{\mathrm{-}2}$). This is due to the finite correlations (overlaps) between the patterns. The model is modified by subtracting the bias a from each pattern as it enters into the couplings. This modification restores the ability of the model to store a macroscopic number of patterns. Yet spurious states are found to plague the dynamics. It is then argued that the dynamics of the network should be consistent with the levels of activity of the stored patterns. This is implemented by adding a global constraint, which restricts the configuration space to states whose mean activity is in the neighborhood of (1/2)(1+a). The consequences of the restricted dynamics are analyzed in the replica symmetric mean-field theory. The global constraint suppresses spurious states and leads to the unexpected result that the storage capacity is higher than that of the unbiased network, up to very high values of the bias (‖a‖≃0.99). However, the information content of such networks is shown to be a monotonically decreasing function of a.

Dynamical aspects of the entropy are discussed within the information-theory context. General invariants of the motion are formulated and related both to the entropy and to the number of accessible states. Examples on finite systems (Schottky anomaly, echo spins) are presented. The entropy evolution through nonequilibrium states is also discussed.

Invariants for quantal or classical Hamiltonians are derived via the information-theory form of the statistical operator ρ^ which satisfy the maximum-entropy principle. The invariants can be constructed even for nonlinear time-dependent Hamiltonians, and recourse to the statistical operator allows for the possibility of ascribing a thermodynamical meaning to our invariants.

A tunable, pulsed dye laser has been used to observe photodetachment from negative sulfur ions near the S(3 ${}_{}{}^1{}_{}{}^{}s$ channel threshold at 384.7 nm. The measured cross section is compatible with Wigner-law behavior over a range of 300 ${\mathrm{cm}}^{\mathrm{-}1}$. No resonance structure was observed. The ratio of the cross section for the ${}_{}{}^1{}_{}{}^{}\mathrm{D}$ channel to the cross section for the ${}_{}{}^3{}_{}{}^{}\mathrm{P}$ channel was measured to be 0.19(3) at an energy of 300 ${\mathrm{cm}}^{\mathrm{-}1}$ above the ${}_{}{}^1{}_{}{}^{}\mathrm{D}$ threshold.

The ground-state wave function for a system with nonsingular potentials is free from zero except at the boundaries and hence its logarithm is regular. We show that the first-order perturbation iteration method, when applied to the logarithm of the wave function in ground-state problems, provides a systematic method in arriving at improved trial wave functions resulting in a decreasing sequence for the variational energy. In situations where the ground state truly exists, this sequence is bounded from below by the true energy and hence the decreasing sequence would converge to the true energy with the corresponding trial wave function (the logarithm of which is regular) converging to the correct wave function.

We report the first measurement of the 1s2s ${}^3$$S_1$–1s2p ${\mathrm{}}^3$$P_2$ transition in heliumlike krypton produced by beam-foil interaction at 34.31 MeV/amu. Measurement is sensitive to higher-order relativistic contributions and to quantum electrodynamic effects. The accuracy corresponds to about 5% of the Lamb shift.

Fast superelastic electron heating by collision quenching of one- and two-photon laser pumped states has been demonstrated in a relatively cold strontium plasma created by two-photon ionization of strontium vapor contained within a crossed heat-pipe oven.

We show that when a system of coupled ordinary nonlinear differential equations undergoes a symmetry-breaking transition before period doubling, the threshold of the symmetry-breaking transition can be found from harmonic balance.

Intense two-electron radiative transitions from core-excited levels in Cs and K have been observed. Calculations show the large two-electron transition strengths are due to a strong relaxation effect—the induced uncollapse of spectator d-electron wave functions.

Na excitation and ionization cross sections in ${\mathrm{H}}^{+}$+Na collisions are determined at impact energies 0.7–50 keV within the semiclassical close-coupling method with atomic-orbital basis sets including pseudostates. Calculated Na(3s→3p) excitation cross sections and the 3p alignment show structures which agree very well with available experimental data. While a structure at 3 keV is predominantly caused by interaction between capture and excitation channels, interaction between excitation and ionization channels leads to a shoulder in the calculated 3p excitation cross section at higher energies and a correlated distinct dip in the predicted ionization cross section.

Bound ${\mathrm{Li}}_2$ states of principal quantum number n=12–14 converging to v=2 and 3 levels of the ground state of ${\mathrm{Li}}_2$${\mathrm{}}^{+}$ can be ionized by fields of ∼200 V/cm, 2 orders of magnitude less than expected for direct field ionization of these levels. The result is shown to be due to forced autoionization. The field depresses the ionization limit of the series converging to the lowest rotational-vibrational ${\mathrm{Li}}_2$${\mathrm{}}^{+}$ levels, and the n=12–14 levels in question autoionize to the Stark-induced continuum.

The effect of colloidal interactions on the structure of aggregates formed by irreversible diffusion-controlled aggregation is studied by Brownian dynamics simulation. Three-dimensional systems of spherical particles with Derjaguin-Landau-Verwey-Overbeek (DLVO) pair potentials are simulated at various volume fractions. We find that the form of DLVO potential affects short-range structure as measured by the particle-particle correlation function, but not long-range structure as measured by the fractal dimension.

We study viscous fingering in the radial Hele-Shaw cell with a set of parallel grooves on one of the plates in order to obtain the morphological phase diagram of a system with imposed uniaxial anisotropy. Varying the pressure of air injected into glycerin and the distance between the plates, a rich variety of phases can be obtained corresponding to all of the possible combinations of stable or splitting tips in directions parallel and perpendicular to the grooves. We demonstrate that the effective anisotropy governing the stability of the tips is a result of a complex interplay between the local anisotropy and the driving force.

We show that the heat flow in the tail sections of needle-crystal solutions of dendritic growth becomes increasingly anisotropic. As a result, the dominant behavior in an outer expansion for the tails reduces to that of a very simple physical model which admits the exact Ivantsov solutions as well as a continuous family of solutions for nonzero capillary length. The model provides a useful testing ground for newly developed analytical and numerical methods for velocity selection.

Several types of fumed-silica aggregates with differing surface areas were studied over a wide range of spatial resolution by employing both light and neutron scattering. At intermediate length scales, between 100 and 1000 Å, the aggregates are mass fractals with $D_m$≊1.7–2.0, in basic agreement with simulations of aggregating clusters. At short length scales below 100 Å where the nature of the surfaces of the primary particles dominates the scattering, some of the samples appear to be fractally rough. In particular, a higher surface area seems to be correlated not with smaller primary particles in the aggregates, as previously assumed, but with fractally rough surfaces having $D_s$ as high as 2.5. These may be the first materials discovered to have both mass and surface fractal structure.