A study is presented of the transmission characteristics of low-finesse ring and Fabry-Perot optical cavities containing sodium vapor and operated below the threshold for optical bistability. Novel features are observed in the transmission signals obtained as the laser light frequency is swept through resonance with a sodium D transition. The ring cavity transmission peaks display a broad absorption profile except for the peak which is tuned to the center of the profile which is almost completely transmitted. A similarly tuned cavity transmission peak in the Fabry-Perot étalon is split into three, with the central peak being very narrow. A theoretical description for each cavity is developed in terms of a Λ-type, three-state model for the atomic energy levels associated with the transition. Using parameter values based on the experimental conditions, theoretical transmission signals for the linear cavity are obtained which are in good detailed agreement with the experimental results. For the ring cavity, agreement is also good except for the degree of absorption of the central peak.

We discuss the problem of a dynamical system with delayed feedback, a hybrid bistable device, characterized by n response times and described by an nth-order differential-delay equation (DDE). Starting from a linear-stability analysis of the DDE we show the effects of the second-order differential terms on the position of the first bifurcation and on the frequency of the resulting self-oscillation. We also consider the effects of the third-order differential terms on the first bifurcation. Experimental results are shown to support the linear analysis. A numerical solution of the second-order DDE is also presented and a comparison is established with the first-order case.

When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.

The electron temperature dependence of the dissociative recombination of ${\mathrm{NO}}^{+}$ ions with electrons has been redetermined with use of a microwave-afterglow–mass-spectrometer apparatus employing microwave heating of electrons. We resolve the discrepancy between previous microwave-afterglow measurements of the recombination coefficient α(${\mathrm{NO}}^{+}$) at high electron temperatures made by Huang, Biondi, and Johnsen [Phys. Rev. A 11, 901 (1975)] (α∼$T_e^{\mathrm{-}0.37}$) and the trapped-ion results of Walls and Dunn [J. Geophys. Res. 79, 1911 (1974)] (α∼$T_e^{\mathrm{-}0.85}$). It is found that the electron temperature attained by microwave heating in the experiments of Huang et al. is lower than they calculated, due to neglect of the effect of inelastic collisions of electrons with minority nitric oxide molecules. Also, their assumption of spatially uniform electron temperatures is not warranted.

An improved data-analysis technique is described which allows accurate determination of the recombination coefficient at elevated electron temperatures. Using this analysis, the recombination coefficient is found to follow the relation α(${\mathrm{NO}}^{+}$) =(4.2±0.2)×${10}^{\mathrm{-}7}$(${\mathrm{T}}_{\mathrm{e}}$[K]/300${)}_{0.08}^{\mathrm{-}(0.75\mathrm{}\pm 0.6}$) ${\mathrm{cm}}^3$/s over the electron temperature range, 295 K≤$T_e$≤4500 K at $T_n$=$T_{+}$=295 K. The afterglow data now support the trapped-ion results of Walls and Dunn.

A novel perturbation method for calculating electron-energy distributions in weakly ionized plasmas with large inelastic collision cross sections is suggested. In contrast to the conventional two-term spherical-harmonics expansion, valid only in weakly anisotropic situations, the two-term expansion, developed here, is applicable uniformly for an arbitrary degree of anisotropy, thus describing both almost-isotropic and beamlike distribution functions. The procedure is basically an expansion of the integral form of the kinetic equation in powers of parameter δ=eE/mvν (E, v, and ν being the electric field, electron velocity, and total collision frequency) and is similar to that conventionally applied in WKB treatments of waves in weakly nonuniform environments. The predictions of the theory are compared with the results of an improved Monte Carlo simulation scheme, employing such advanced methods as Russian roulette, splitting, and ‘‘null’’ collisions.

We present preliminary experiments which indicate a dramatic effect of external noise on superfluid turbulence in thermal counterflow. This turbulent system is in many ways ideal for the study of noise-driven nonlinear dynamical systems. It contains a well-defined continuous transition (the T-I–T-II transition), and noise can be easily imposed on the driving heat current. Previous work has shown that the superfluid turbulence system is described by a single nonlinear amplitude equation, and it can be expected to show some of the rich noise-induced behavior found in theoretical treatments of such systems. We find that external noise dramatically modifies the T-I–T-II transition and induces bistability.

The time correlation functions involving heat and particle fluxes in a binary argon-krypton mixture with Lennard-Jones interactions are found using both isoenergetic and isokinetic equilibrium molecular dynamics simulations. The heat-current–diffusion-current cross function does not appear to have been evaluated before. The Green-Kubo integral of this function has nearly canceling positive and negative parts and so is not a good way of obtaining the Soret or Dufour coefficient. Integration of the diffusion-current autocorrelation function yields a value for the mutual diffusion coefficient in agreement with an earlier nonequilibrium simulation but at variance with previous isoenergetic (or Newtonian) equilibrium simulation results. It is conjectured on the basis of these results that isokinetic simulations may have smaller system-size dependence than isoenergetic ones.

We have studied mass transport in a turbulent flow with large coherent structures—turbulent Taylor vortices. A pulse of dye is injected in fluid contained between concentric cylinders (with the inner one rotating and the outer one fixed), and the time dependence of the dye concentration at two axial positions is then determined from optical absorption measurements. The measurements have been made for radius ratios η ranging from 0.494 to 0.875, and at Reynolds numbers R ranging from 50 to 1000 times that corresponding to the onset of Taylor vortex flow. Transport in the axial direction is found to be modeled very well by a one-dimensional diffusion process with the reflections at the ends of the annulus and the finite injection time of the dye taken into account. (The time scale for the transport in the radial and azimuthal directions is short compared with that in the axial direction.) The effective axial diffusion coefficient D in the parameter range studied is of the order of 1 ${\mathrm{cm}}^2$/s, or greater, orders of magnitude larger than molecular diffusion coefficients. For a fixed R and η, D increases linearly with the axial wavelength λ of the Taylor vortices. The Reynolds-number dependence of the wavelength-independent scaled diffusion coefficient $D^{\mathrm{*}}$=(2d/λ)D (where d is the gap between the cylinders), is described by a power law $D^{\mathrm{*}}$∝$R^{\beta }$. Measurements for different parameter regions yield 0.69<β<0.86, while theory suggests a larger value, β=1.

We show how bounded quantum systems in the presence of time-periodic fields can mimic random behavior in spite of their almost periodic character. We calculate the distribution of values taken by observables in the course of time, and demonstrate how they become asymptotically Gaussian in the large-N limit but with constant variance and a posteriori, δ-correlated noise. Thus, unlike a priori processes, the quantum dynamics of bounded systems remains nondiffusive while appearing to be random.

We have carried out high-resolution x-ray scattering and heat-capacity studies of the nematic (N)→smectic-A (SmA) transitions in 4’-(4’’-n-alkoxybenzyloxy)-4-cyanostilbene with the alkyl chain of length 7 (T7) and 8 (T8). The material T7 exhibits only a single nematic–to–smectic-$A_1$ transition where the Sm$A_1$ period is commensurate with the molecular length l. T8 exhibits with decreasing temperature the doubly reentrant sequence N-Sm$A_d$-N-Sm$A_1$ where the Sm$A_d$ period is incommensurate with d∼1.2l. For both T7 and T8 we find second-order N-Sm$A_1$ transitions with identical reduced amplitudes and exponents; the critical exponents so obtained are γ=1.22±0.06, ${\nu }_{?}$=0.69±0.03, ${\nu }_{\perp }$=0.63±0.03, and α=0.06±0.06. These are close, but not identical, to those expected for an ideal XY transition and they give ${\nu }_{?}$+2${\nu }_{\perp }$+α-2=0.01±0.15, in good agreement with anisotropic hyperscaling. The lower N-Sm$A_d$ transition in T8 gives γ=1.53±0.1, ${\nu }_{?}$=0.88±0.05, and ${\nu }_{\perp }$=0.76±0.05, in disagreement with all models. The heat capacity associated with this transition is too small to yield a reliable value for the critical exponent α. In the reentrant nematic phase of T8, the Sm$A_d$ and Sm$A_1$ fluctuations are essentially independent; the Sm$A_d$ fluctuations change over from being SmA-like to SmC-like with decreasing temperature in the reentrant nematic phase.

The concept of the absolute half-cell potential is discussed from a simple thermodynamic point of view and defined as -ΔG/ne for the half-cell reaction, treating the electron like other individual chemical species. With the standard reference state of the electron taken as the free electron at rest at infinity, the absolute half-cell potential is simply the Fermi level of the electrons in the half-cell lead wire. This potential can be simply measured with a Kelvin probe by determining the vacuum potential level over the electrolyte relative to the Fermi level of the half-cell lead. Since the probe cannot determine potentials absolutely, it must be calibrated using a material whose work function is known. Using this procedure we obtain for the standard hydrogen half-cell, $E_{\mathrm{abs}\left(\mathrm{SHE}\right)=4.456\mathrm{}\pm 0.025}$ eV, assuming our Hg as used in calibration has a work function of 4.495 eV.

We have recently studied a random walk on a comblike structure as an analog of diffusion on a fractal structure. In our earlier work, the comb was assumed to have a deterministic structure, the comb having teeth of infinite length. In the present paper we study diffusion on a one-dimensional random comb, the length of whose teeth are random variables with an asymptotic stable law distribution φ(L)∼$L^{\mathrm{-}(1+\gamma )}$ where 0<γ≤1. Two mean-field methods are used for the analysis, one based on the continuous-time random walk, and the second a self-consistent scaling theory. Both lead to the same conclusions. We find that the diffusion exponent characterizing the mean-square displacement along the backbone of the comb is $d_w$=4/(1+γ) for γ<1 and $d_w$=2 for γ≥1. The probability of being at the origin at time t is $P_0$(t)∼$t^{\mathrm{-}{d}_s/2\mathrm{}}$ for large t with $d_s$=(3-γ)/2 for γ<1 and $d_s$=1 for γ>1. When a field is applied along the backbone of the comb the diffusion exponent is $d_w$=2/(1+γ) for γ<1 and $d_w$=1 for γ≥1. The theoretical results are confirmed using the exact enumeration method.

We present a quantitative theory of the scaling properties of Julia sets, using them as a case model for nontrivial fractal sets off the borderline of chaos. It is shown that generally the theory has a ‘‘macroscopic’’ part which consists of the generalized dimensions of the set, or its spectrum of scaling indexes, and a ‘‘microscopic’’ part which consists of scaling functions. These two facets are formally and computationally equivalent to thermodynamics and statistical mechanics in the theory of many-body systems. We construct scaling functions for the Julia sets and argue that basically there are two different approaches to this construction, which we term the Feigenbaum approach and the Ruelle-Bowen-Sinai approach. For the cases considered here the two approaches converge, meaning that we can map the theory onto Ising models with finite-range interactions. The largest eigenvalue of the appropriate transfer matrix furnishes the thermodynamic functions.

The diffusion-limited aggregation of oriented anisotropic particles is explored with use of computer simulations and scaling theory. The time-dependent cluster-size distribution (in both two- and three-dimensional systems) can be well represented by the dynamic scaling form for the cluster-size distribution $N_s$(t)=$s^{\mathrm{-}2}$f(s/S(t)) where $N_s$(t) is the number of clusters of size s at time t. The mean cluster size S(t) diverges as S(t)∼$t^z$. The value of the exponent z is found to agree with the mean-field Smoluchowski result z=1/(1-γ) in d≥$d_c$=2 dimensions, where $d_c$ is the upper critical dimension, and γ is the exponent describing the dependence of the diffusion coefficient on the cluster mass. Below $d_c$, we find that our results agree with the expression z=d/(2-dγ). At high particle densities, a crossover from two or three dimensions to one-dimensional behavior is observed.

Bifurcation diagrams of the driven van der Pol oscillator are given showing mode-locking and period-doubling cascades. At low driving amplitudes locking regions occur following Farey sequences. At high driving amplitudes this relationship is destroyed due to the appearance of period-doubling cascades and coexisting attractors. A generalization of the winding number is used to compute devil’s staircases and winding-number diagrams of period-doubling cascades. The winding numbers at the period-doubling bifurcation points constitute an alternating sequence that converges at the accumulation point of the cascade.

A new method for the calculation of first-passage times for non-Markovian processes is presented. In addition to the general formalism, some familiar examples are worked out in detail.

For the rf-driven Josephson junction, the dynamical behavior is studied near a period-doubling transition. The center-manifold theorem simplifies the problem and enables us to study only a first-order system, the parameters of which are expressed in terms of the Josephson-junction parameters.

In this investigation, term values in sodium are found by numerical integration of Schrödinger’s wave equation. Effective core polarizabilities are determined by fitting calculations to experimental data. The fit includes quantum defects in low-angular-momentum states which were not previously used. When penetration and exchange are taken into account and the effective dipole and quadrupole polarizabilities are corrected for nonadiabatic effects, the dipole and quadrupole polarizabilities are found to be 0.998(100) and 1.36(40) a.u., respectively. Quantum defects and fine structure are also calculated for states not included in the initial fit and are found to be in good agreement with experimental results.

We show how the exact solvability of some of the well-known one-dimensional quantum systems arises from an underlying SU(2) dynamical symmetry.

A new 1/N expansion is developed that is more easily tractable. Accurate large-order results are shown for the anharmonic oscillator.