We have developed a theoretical model that allows us to study the delay-time statistics of superfluorescent pulses for the case of collisional broadening with a Lorentzian line shape. Our model is based upon a more robust definition of delay time, based upon an energy rather than an intensity reference. We calculate the probability distribution of delay times in the initiation regime of superfluorescence, where the inversion is essentially constant. We find that, as the collisional dephasing rate is increased, the mean delay time increases and the distribution broadens. We compare our results with those for the case of inhomogeneous broadening with a Lorentzian line shape and find the unexpected result that the statistical behavior is identical.

The effects of radiation losses and atomic motion in a distributed feedback induced by Bragg reflections in an electron-beam-channeling x-ray laser are investigated. Standing-wave fields with nodes in the atomic sites are generated in this cavity-mirror structure in single crystals, thereby reducing the losses located close to the atomic sites. An explicit expression for the low-threshold gain is derived which depends on the absorption, temperature, and on the order of Bragg reflection. It is noted that diffraction from several sets of atomic planes which satisfy the Bragg condition simultaneously may further reduce the threshold gain. These distributed-feedback schemes have possible application in reducing beam high-current requirements by many orders of magnitude.

In a saturated two-level atomic system driven by a strong, near-resonant field, a large population difference between the two energy levels is recovered by an additional strong off-resonant laser field. This implies that the stimulated transition between the energy levels is inhibited by the additional laser field. This effect is attributed to the transverse resonance which has been extensively studied in the radio-frequency spectroscopy. It is also shown that the definite dispersion-free condition is realized when the intensities of the saturating field and the second field are the same.

The force distribution around a fractal aggregate in a shear flow is investigated. The steady-state Navier-Stokes equation is solved analytically on a model fractal boundary composed of a succession of small-amplitude sinusoidal buckles. It is found that the moments of the force distribution on the fractal scale as powers of the system size, yielding a nontrivial series of exponents, which implies an extremely broad, multifractal force profile. The forces normal and tangential to the boundary are both calculated. The experimental consequences for fractal structures in solution are discussed.

For a binary mixture of hard spheres in equilibrium, we reduce the expressions for the time-correlation functions between all single-particle fluctuations from the N-particle level to the (kinetic) two-particle level, using the revised Enskog theory.

It is generally recognized that a single Rayleigh-Taylor unstable mode grows exponentially, proportional to the initial amplitude, until the amplitude is about (1/10 to (1/5 of the wavelength. The growth then becomes nonlinear, and the mode evolves into spikes and bubbles. This paper considers how this picture of the transition to nonlinearity changes when, instead of there being a single mode, there is a full spectrum of modes. We argue that nonlinear behavior begins whenever the sum of modes over a specified small region of k space becomes comparable to the wavelength. In the case of a single mode, this reduces to the usual comparison of the mode’s amplitude with its wavelength λ. But if the modal amplitudes are smooth functions of k, the modes begin to saturate when their amplitude is comparable to ${\lambda }^2$/R times a dimensionless scale factor; here, R is the radius in spherical geometry, or the length of the surface in planar geometry. Given this new notion of the amplitude at which nonlinear saturation begins, we construct a simple model to estimate the net perturbation resulting from a broadband initial spectrum. We assume that modes grow exponentially until saturation occurs, and then the growth of the individual modes becomes linear in time. The model predictions in two and three dimensions are compared with Read and Young’s experiments [Atomic Weapons Research Establishment Report No. 011/83, Aldermasten, 1983 (unpublished)], and to Youngs’s calculations [Physica 12D, 32 (1984)]. The experimental results are used to set the single parameter characterizing the onset of nonlinearity. The model provides a complete description of a weak dependence on initial amplitude. The model can be easily extended to any situation for which one can estimate single-mode growths; results are presented regarding effects on multimode growth of spherical geometry, ablation stabilization, and interface coupling.

A new method for evaluating the critical exponent η and the critical correlation scaling function of a binary liquid mixture is presented by using small-angle x-ray scattering. The new procedure has the benefit that it is free from the uncertainties in collimation corrections, the effects of the cross-section factor, and the cell size used. The procedure was applied to the measurement and analysis of a binary critical mixture of perfluoromethyl-cyclohexane and n-heptane. The experimental data agree with the theory of Bray within experimental error [Phys. Lett. A 55, 453 (1976); Phys. Rev. Lett. 36, 285 (1976); Phys. Rev. B 14, 1248 (1976)]. The close agreement between present results and those of Chang and co-workers [Phys. Rev. Lett. 37, 1581 (1976); Phys. Rev. A 19, 866 (1979)] reconfirms that the binary liquid and the Ising model belong to the same universality class and also confirms the validity of the present procedure.

Semiclassical limits for the dynamics of the Wigner function, and for the dynamics of the low-order moments of physical interest, are discussed in fluid-dynamical terms. The harmonic-oscillator solution yields local Maxwellian (ideal) fluid-dynamical behavior, and this is extended to locally quadratic problems in a straightforward manner. Coherent states are shown to have a particularly simple fluid-dynamical interpretation, and coherence may be easily demonstrated for mixed states having an arbitrary degree of uncertainty in the field variables. The semiclassical behavior of pure and mixed states is conveniently discussed in terms of coherent and incoherent limits, and the origin of quantum-mechanical behavior in the simple low-order approximations proposed is simply explained. The relation to the pure-state theory of Madelung is made explicit. A recently proposed method for the solution of a certain hierarchy of quantum-fluid-dynamical equations is analyzed in detail, and is demonstrated to be inconsistent with these semiclassical limits.

Observations of line-emission Doppler broadening and Doppler shift are used to determine the velocity distributions, parallel and perpendicular to the anode surface, of neutral particles and multiply charged ions in a surface-flashover-produced plasma in a magnetically insulated ion diode. The velocity distributions were found to be nearly Maxwellian with thermal energies of ≃8 eV for neutral particles, ≃20 eV for singly charged ions, and 20–80 eV for doubly and triply charged ions. The plasma-pressure gradient in the magnetic field, obtained from the observed ion temperature and density, and a suggested anomalous plasma conductivity that is approximately ten times lower than the classical conductivity are shown to explain the fast plasma expansion with respect to the magnetic field. Elastic collisions of the 7-eV electrons with the hotter ions cause electron heating. The observed ion velocities in the plasma parallel to the anode account for ≃(1/3 of the velocities in the same directions observed in the diode acceleration gap in a previous experiment.

The magnetic field in the anode plasma of a magnetically insulated ion-beam diode has been measured as a function of time by the observation of Zeeman splitting of line emission. With use of this technique, the plasma was found to be penetrated by the magnetic field applied in the diode early in the pulse. The diamagnetic effect of the electron flow in the diode acceleration gap was found to be much larger than that calculated from one-dimensional solutions for the magnetically insulated gap. However, it agrees with the measured ion current density and the observed electric field distributions across the diode gap that showed significant electron flow beyond the calculated electron-sheath region. The penetration of the diamagnetic signal into the plasma indicates an anomalous plasma conductivity that is at least ten times lower than the classical conductivity.

Experiments on the stability of the circular interface formed in a Hele-Shaw cell when air displaces a viscous oil have shown that available theories underestimate the wavelength of the most unstable wave when the capillary number ($N_{\mathrm{ca})}$ is large. Apparently this is caused by a modification of the interface boundary condition by three-dimensional effects. At small values of $N_{\mathrm{ca}}$ the results overlap several of the theories and we are unable to choose among them on the basis of the present experiments.

Extensive quasielastic-light-scattering, small-angle neutron scattering, and neutron-spin-echo (NSE) spectroscopic measurements have been performed on a three-component microemulsion system containing bis(2-ethylhexylsulfosuccinate) (AOT) (surfactant), ${\mathrm{D}}_2$O, and decane (oil) at two temperatures in the one-phase region. By fixing the molar ratio of water to AOT at w=40.61, the average radius of spherical surfactant coated water droplets can be maintained at 58 Å with a polydispersity index of 22%. The volume fraction φ of the droplets can be continuously varied from 0.1 to 0.75, spanning the entire range from the dilute gas all the way to the close-packed glass by adjusting the oil content of the microemulsion. The static structure factors and the time-dependent density correlation functions of these densely packed spherical droplets were systematically measured as a function of the volume fraction.

As φ increases from 0.1 to 0.75, the structure factor gradually evolves from a smooth function of the order unity into a highly oscillatory function, with the height of the first diffraction peak around 2 and higher, similar to that of a dense liquid. At the same time the time-dependent density correlation function exhibits pronounced nonexponential relaxation. The Kohlrausch-Williams-Watts (KWW) stretched exponential function, exp[-(t/T${)}^{\beta }$], has been shown to fit the density correlation function over most of the time range of the measurements, which covers nearly three decades, at Q values of about ${10}^{\mathrm{-}3}$ A${̊}^{\mathrm{-}1}$, typical in a light scattering experiment. The exponent β, starting from an initial value of unity at φ=0.1, gradually decreases to about 0.6 at ${\phi }_c$∼0.65 and increases thereafter. The relaxation time T shows a trend to diverge at φ∼${\phi }_c$, approximately following the Vogel-Fulcher law. These features bear striking similarity to a glasslike transition predicted by recent mode-mode coupling theories of dense liquids. The KWW function also fits very well the time-dependent density correlation function at φ=0.6, measured by NSE (Q∼0.2 A${̊}^{\mathrm{-}1}$). Thus, the KWW function is shown to be valid for the Q range spanning from 0.001 to 0.2 A${̊}^{\mathrm{-}1}$. The relaxation time, to a good approximation, scales like $Q^{\mathrm{-}2/\beta }$.

Molecular-dynamics simulation results on soft-sphere fluids are presented that show the systematic changes in the equation of state, pair distribution function, self-diffusion coefficient, and various time-correlation functions with density at constant temperature in the metastable density region beyond the normal liquid range. At a characteristic density in this region, a decrease in the compressibility is observed along with a change in the density variation of the self-diffusion coefficient and the onset of a slowly decaying component in the density-correlation function. We interpret these behaviors as manifestations of a transition in which the particle dynamics changes its basic character, from collisions among particles undergoing continuous fluidlike displacements to barrier hopping of individual particles trapped in local-potential-energy minima. It is also concluded that this transition is distinct from the glass transition that occurs at a higher density.

Using detailed asymptotic analyses of the dynamics of the phase-field model, we show that the major sharp-interface models (Stefan, modified Stefan, Hele-Shaw, etc.) all arise as limiting cases of the phase-field equations. The scaling of the physical parameters in the microscopics leads to distinct macroscopic models with critical differences.

Through a sequence of time-dependent transformations and time substitution, we evaluate the propagator of a harmonically bound charged particle with time-dependent mass in a time-varying electromagnetic field by relating it to those of free particles. From this propagator we derive the wave functions. The propagators beyond and at caustics are then investigated, respectively, by including the Maslov phase factor and by using the modified semigroup property. Finally, we calculate explicitly the propagator for the constant-damping case.

We use a hybrid-orbital ‘‘united-atom’’ model to calculate the effect of an applied electric field upon hyperfine interactions in cupric sites of low symmetry. This electric-field-induced change can produce a shift in electron-paramagnetic-resonance frequency which is of the same order as the frequency shift due to the effect of the electric field upon the g tensor. We describe how these shifts are manifested in the linear-electric-field effect (LEFE) upon a spin-echo measurement. This LEFE can be used to assist in the determination of the electronic structure of the metal-ligand complex for a site of low symmetry, as is often found for the cupric ion in biological molecules.

Modulated phases that occur in tilted chiral smectic liquid crystals are discussed within mean-field theory in thin films and in bulk. A chiral term in the free energy containing three order parameters and one gradient can make the free energy of certain defects negative or the bend elastic constant negative. Assuming various possible behaviors for these defect energies we find either a striped state with parallel defect walls or a lattice of hexagonal unit cells containing disclinations bounded by intersecting defect walls in films. Rather different transitions to the striped phase occur when this elastic constant is either positive or zero. The multicritical point that separates these two transitions is discussed. Finally, possible modulated phases in bulk, three-dimensional systems are discussed and it is shown that, because of a competition between two different modulations, the transitions to the new modulated phases are always first order. Possible consequences for designing molecules for chiral smectic-C phases with increased polarizations are discussed.

We calculate the position autocorrelation and magnetic moment of a charged particle at finite temperatures moving in two dimensions in the presence of a magnetic field and a dissipative environment. We show that the time-dependent position-autocorrelation function does not change qualitatively from the free-particle behavior. This implies that orbital magnetic moment of a charged particle is zero at all temperatures.

Gels are highly compressible elastic bodies near the volume phase transition. They undergo large elastic deformations that cannot be described within the usual elastic theory. A theoretical framework is proposed to incorporate a nonlinear elastic theory into the Ginzburg-Landau theory of phase transition. Then we analyze patterns emerging on the upper surface of uniaxially deformed gels whose lower surface is clamped to a substrate. On the upper surface a two-dimensional spinodal decomposition is shown to occur when the elongation ratio exceeds a critical value. If the gel is uniaxially stretched and sufficiently compressible, the surface eventually folds itself, yielding periodic cusps in the late stage of the coarsening process. The folded parts are singular surfaces like cracks in solids accompanied by large strains. Developing some mathematical techniques, we properly take into account a drastic change of the boundary conditions at the folded parts, but elastic deformations inside the gel are treated within a linear theory around uniaxial homogeneous states. We also find that the cusp pattern exists only in a limited region of the parameter space, outside which it is still an open question as to what kinds of patterns emerge in final stages of the spinodal decomposition. We expect corrugated surfaces without folding when the gel is uniaxially stretched and rather incompressible or when it is uniaxially compressed near the critical point.

Nonuniversal dynamics introduced by Swendsen and Wang [Phys. Rev. Lett. 58, 86 (1987)] is studied in a mean-field Ising model. Numerical simulation data indicate that z, the dynamical critical exponent, is 0.98±0.08. A modified version of this dynamics in which only large clusters are flipped apparently gives the same exponent, although the amplitude is reduced by a factor of 1/2. In addition, a theoretical argument is presented which gives z=1 and provides insight into the dynamics.