In the preceding paper we derived a new theory of the dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, and DT) in which the electrical asymmetry appears directly in the electronic Hamiltonian (in an appropriate Born-Oppenheimer separation) and the dipole moment may be computed as a purely electronic property. In the present paper we describe variation-perturbation calculations and convergence studies on the dipole moment for HD, which is found to have the value 8.51×${10}^{\mathrm{-}4}$ debye at 1.40 a.u. Using the two alternative formulations of the electronic problem, we can provide a test of basis-set adequacy and convergence of the results, and such convergence studies are reported here. We have also computed vibration-rotation transition matrix elements and these are compared with experimental and other theoretical results.

We present a three-dimensional formulation of the cw free-electron laser amplifier in the small-signal domain. The formalism is used to calculate expressions for the power gain in both small-gain and large-gain situations, and differences from the corresponding formulas of the one-dimensional theory are studied in detail for an input optical beam of Gaussian cross section. In the small-gain case, the maximum of the gain profile is shifted from that of the one-dimensional theory, in accord with previous results. In the large-gain case, we show that the primary effect of diffraction of the fields is conveniently expressed in terms of radially dependent shifts in the resonance frequency and the overall phase. This leads to the result that an optical beam, as it amplifies in the electron-wiggler system, undergoes a smaller diffractive spreading than what it would have in free space.

With the help of time-dependent solutions, their power spectra, Poincaré maps, and the complete set of Lyapunov exponents, we have carried out a detailed investigation of the bifurcation routes of three attractors in a single-mode model of a laser with injected signal. In addition to a sequence of ordinary period-doubling bifurcations leading to chaos, we have observed subcritical and supercritical Hopf bifurcations of limit cycles. We have also observed the sudden disappearance of trajectories due to the coalescence of a pair of stable and unstable tori and the possible collision of a limit cycle with an unstable torus.

In the newly synthesized compound MORA12 [S-4-0-(6 methyl)octylresorcylidene-4’-dodecylaniline], we observed a novel intermediate phase (which we call $P^{\mathrm{*}}$) between two tilted smectic liquid-crystal phases, $C^{\mathrm{*}}$ and X. The $C^{\mathrm{*}}$ phase has a helicoidal structure whereas the X phase does not. In the $P^{\mathrm{*}}$ phase the layer spacing increases continuously from 32.3 Å to nearly 37 Å in a 10 °C temperature interval. This is a large temperature dependence of a lattice parameter which we attribute to the onset of hexagonal (as opposed to rectangular) in-plane ordering for which there is no easy axis for tilt: The tilt angle decreases as the degree of hexagonal in-plane order increases. The X phase is a true ferroelectric phase with a bistable electro-optic response whereas $P^{\mathrm{*}}$, being helielectric, is not bistable. Furthermore, for fields larger than 1 V/μm, the switching times in $C^{\mathrm{*}}$ and $P^{\mathrm{*}}$ increased with increasing voltages.

We consider a one-dimensional stochastic process described by a master equation and calculate the time-dependent distribution function. The time evolution of the system is given by the conditional probability h(x,t‖$x_0$), where x and $x_0$ are continuous variables. Assuming a quite general dependence of the transition probability $W_{\Omega }$(x→x’) on a parameter Ω, we show that the backward form of the master equation can be used to calculate arbitrary conditional averages 〈f(x)‖$x_0$${〉}_t$ up to any given power in ${\Omega }^{\mathrm{-}1}$. This general expansion procedure will be used to construct h(x,t‖$x_0$) itself. We show that—introducing a new stochastic variable y—the conditional probability h(x,t‖$x_0$) can be expanded into a series of Hermite functions. The coefficients of this expansion, $b_n$(t), which depend on the expansion parameter Ω, can be uniquely determined via a recursion relation. We show that in the limit Ω→∞ all coefficients $b_n$(t) vanish, except $b_0$, which is time independent. In this limit a Gaussian distribution for the conditional probability is obtained, which is in agreement with the so-called linear noise approximation.

Quantitative measurements of the parameter dependence of the onset of an interior crisis are reported for a sinusoidally-driven nonlinear diode-inductor circuit. The measurements are in reasonable agreement with the predictions of Grebogi, Ott, and Yorke.

The excitation and decay of autoionizing states of multiply charged ions in plasmas can play an important role in the determination of both the distribution of the various charge states and the spectrum of the emitted radiation. All previous theoretical treatments for low-density plasmas are based on the conventional expressions for the Auger and fluorescence branching ratios, in which the autoionization and radiative decay rates are assumed to be additive. Using a two-level atom model, Armstrong, Theodosiou, and Wall and also Haan and Cooper have investigated the effects of the interaction between the final continuum states which result from the autoionization and radiative decay modes. They have shown that this interaction produces an interference which can alter the relative probabilities for decay into the two alternative continuum channels. In the present investigation, the general properties of angular momentum and spherical tensor operators are employed to extend the theory of this interference to the case in which each of the atomic levels consists of a set of 2J+1 degenerate magnetic sublevels, where J is the total electronic angular momentum. In the case where this interference involves only a single term in the partial-wave expansion for the electron-continuum state, the expressions obtained for the Auger and fluorescence branching ratios are in agreement with those derived in the previous investigations. When several terms in the electron-continuum partial-wave expansion are involved, the Auger and fluorescence branching ratios contain terms corresponding to the interference between different partial-wave components analogous to those which occur in the expression for the photoelectron angular distribution asymmetry parameter. The electromagnetic interaction between the final continuum states of the combined atom plus quantized radiation field system may be expressed in terms of the matrix elements for either the photoelectric transition or the inverse radiative recombination process connecting the final atomic states. Finally, the corrected expressions are obtained for the resonant electron-impact excitation rates and the intensities of the dielectronic satellite lines resulting from the decay of autoionizing states of multiply charged ions in plasmas. The modifications to the conventional expression for the satellite line intensities may be interpreted as terms corresponding to the interference between the direct radiative recombination and dielectronic recombination processes together with radiative corrections to the dielectronic recombination process.

We present numerical solutions of the Navier-Stokes equations for the time evolution of axisymmetric flows between concentric cylinders of three different radius ratios η in the range 0.5<η<0.9 after the Reynolds number R is suddenly increased from a subcritical to a supercritical value in the range of ε=R/$R_c$-1 between 0.01 and 0.1. Such a procedure generates a propagating interface between the stable Taylor vortex state that grows first near a rigid nonrotating end plate and the unstable homogeneous circular Couette flow which is formed in the bulk of the annulus very shortly after increasing the driving. Step up from stationary flow states at finite subcritical driving and sudden starts from rest are simulated. We determine for both cases the behavior of the Ekman vortex system near an annulus end. The time evolution of the unstable circular Couette flow in the bulk is found to agree perfectly with the analytical solution for an infinite annulus. We discuss the effect of inhomogeneities that break the translational symmetry in axial direction, thereby generate local vortex flow, and thus compete against front propagation in the destruction of the homogeneous flow state. The evolution of the intensity and the structure of the vortex pattern behind the moving interface and various other properties of the fronts are determined in quantitative detail and compared with theoretical and experimental results. The axial intensity profiles of the Taylor vortex fronts are about 20% sharper than those we have derived from the lowest-order amplitude equation. In agreement with the latter, the front extension suitably defined varies as ∼${\epsilon }^{\mathrm{-}1/2}$ and the propagation ve- locity varies as ∼${\epsilon }^{1/2}$ in the driving range considered here.

We present an analytic theory of Richtmyer-Meshkov instabilities in an arbitrary number N of stratified fluids subjected to a shock. Following our earlier work on Rayleigh-Taylor instabilities, the theory assumes incompressible flow in which a shock is treated as an impulsive acceleration. We discuss the special cases N=2 and N=3, and illustrate both Rayleigh-Taylor and Richtmyer-Meshkov instabilities by examples patterned after inertial-confinement-fusion implosions.

A peculiar route to chaos is known experimentally for magnetic parallel pumping. The periods of auto-oscillations become irregular at the onset of chaos, without previous cascades of period-doubling bifurcations. This route to chaos has been found by the simulation of parallel pumping of a single spin interacting with a cavity or, for multispin systems, coupled by exchange.

The eigenvalue problem for two particles interacting through the potential being the superposition of the attractive Coulomb potential (-A/r) and the Yukawa potential B exp(-Cr)/r of arbitrary strength B and screening parameter C is solved by variational means. The energy levels $E_{\mathrm{nl}}$ for the states 1s through 7i are calculated as functions of B and C. It is shown that for a given principal quantum number n the energy eigenvalues increase (decrease) with increasing azimuthal quantum number l if the Yukawa potential is attractive (repulsive), i.e., for l>l’: $E_{\mathrm{nl}}$≥$E_{\mathrm{nl}\mathcal{’}}$ if B<0, and $E_{\mathrm{nl}}$≤$E_{\mathrm{nl}\mathcal{’}}$ if B>0. It leads to the crossing of the energy levels with n≥2. For B>0 the levels with larger n and l become lower than those with smaller n and l, e.g., $E_{3d}$<$E_{2s}$, $E_{4f}$<$E_{2s}$, and $E_{4f}$<$E_{3p}$. For B<0 and certain intervals of C the levels with larger n but smaller l lie below those with smaller n and larger l, e.g., $E_{4s}$<$E_{3d}$, $E_{5s}$<$E_{4f}$, and $E_{5p}$<$E_{4f}$. The values of B and C for which the lowest-energy levels cross over are estimated. Moreover, the splitting of the 2s and 2p levels (the Lamb shift) is discussed.

Invasion percolation was first proposed as a theoretical model for the flow of two immiscible, incompressible fluids through porous media. The model leads to both global and local predictions as to the final state of such a flow, which can be studied experimentally. Nondestructive measurement techniques which reveal detailed spatial information (without destroying the sample)—such as tomography for three-dimensional systems—typically involve a resolution length that is large compared with the smallest relevant length scales of the medium. Monte Carlo methods are described which are designed to enable one to use computer simulations of invasion percolation in order to analyze the spatially smeared data which one is likely to encounter in such an experiment. Special attention is drawn to those experimental tests which would shed light on the validity of the model.

The effect of stirring on the transitions between multiple steady states is analyzed in exothermic reactions giving rise to ignition and explosion, as well as in reactions occurring under isothermal conditions. It is found that, to first order, deviations from perfectly effective stirring amount to a renormalization of the value of the heat- or mass-transfer coefficients, whereas higher-order corrections introduce a coupling between stirring and the effects of chemical kinetics.

We present a method for estimating line broadening in the framework of a general average-atom model. This method is an extension of our previous work [Phys. Rev. A 29, 2789 (1984)]. It can reproduce the overall shapes of the ‘‘hilly features’’ present in spectra of hot dense plasmas in local thermodynamic equilibrium. Calculations are presented for a hafnium plasma, and the results are compared with experimental ones.

A new method is presented for solving the space-independent Boltzmann-Enskog equation describing the motions of a heavy tagged particle (A) in the medium of light bath particles (B). It is shown how in the case of inverse-power-law repulsive interactions the transport equation can be transformed into a set of partial differential equations which are then solved successively to give the conditional average of an arbitrary physical quantity as a power series in the mass ratio ${\Omega }^{\mathrm{-}1}$=$m_B$/($m_A$+$m_B$). The method is explicitly developed to first order in ${\Omega }^{\mathrm{-}1}$, which shows the effects of fluctuations, and in the linear noise approximation the time-dependent distribution function itself is obtained. The velocity autocorrelation function of a tagged particle is evaluated to order ${\Omega }^{\mathrm{-}2}$ where one finds corrections to a single exponential decay.

Noise-driven self-excited oscillators in their quasisinusoidal regime are treated within a functional-integral approach. The zero modes are eliminated from the generating functional with a change of variables to collective coordinates. The van der Pol oscillator is analyzed as a prototype of such systems. The main generating functional is introduced, taking from the Lagrangian the nonfluctuating terms and linearizing the resulting integral in the neighborhood of the limit-cycle solution of the oscillator. By functional differentiation the response and correlation functions associated with the problem are calculated from the main generating functional. Some well-established properties of these noise-driven oscillators are easily recovered with this method.

Exact calculations for a quantum oscillator linearly coupled to a thermal reservoir are presented. Explicit results (variances and correlations) for the response and the spontaneous fluctuations are evaluated for two different models of the heat bath; a reservoir with a spectrum which is similar to that of acoustic phonons and another which is analogous to optic phonons. The low-temperature behavior is shown to depend sensitively on the spectral density of the thermal reservoir. The mass and the frequency of the oscillator become renormalized through the coupling to the bath. These renormalizations are intrinsically frequency dependent. Moreover, the commonly used form of Ehrenfest’s equation for the dynamics of the linearly damped oscillator is shown to only be a reasonable approximation within certain frequency regimes.

High-resolution volumetric measurements have been made on pure 8¯S5. The molar-volume variations show a classical second-order smectic-A–smectic-C transition. These data are very well described by a mean-field Landau model and are inconsistent with the critical behavior of the three-dimensional XY model. The thermal-expansion coefficient ${\alpha }_p$ has been calculated and Δ${\alpha }_p$=(0.50±0.02)×${10}^{\mathrm{-}4}$ ${\mathrm{K}}^{\mathrm{-}1}$ at the phase transition estimated.

It is demonstrated that Eberly and Singh’s notion of partial stationarity of a quantum system can be reconciled with Mandelstam and Tamm’s approach to deriving energy-time inequalities. The result of this merger is an improved stationarity time, which provides a more precise measure of the degree of stationarity of the system under study, and which permits a sharper statement of the energy-time uncertainty relation than that given by Eberly and Singh.

It is argued that energy transfer between two quantum systems is subject to the uncertainty relation Δ$E_2$Δ$E_2$≥ħR/2, where Δ$E_1$ and Δ$E_2$ are the uncertainties in the energies of the systems and R is the rate of energy transfer between them.