We show, via simple geometrical arguments, the quantum-noise quenching in a correlated (spontaneous) emission laser (CEL). This noise quenching is a consequence of the correlation between noise sources which results in a multiplicative noise process. The steady-state distribution for the phase difference between the two electric fields in a CEL is compared and contrasted to that of a standard phase-locked laser. Noise quenching is shown to occur in the case of the CEL via an explicit solution of the Fokker-Planck equation.

A complete analytic solution is presented for the selection of symmetric Saffman-Taylor fingers, in the small–surface-tension limit. In a previous paper [Combescot et al., Phys. Rev. Lett. 56, 2036 (1986)] we showed that the selection can be understood in terms of a nonlinear eigenvalue problem that describes the region where ordinary perturbation theory fails to converge. This ‘‘inner’’ problem is completely solved by systematically studying the asymptotic series of the (formal) solution of the problem. Two methods are proposed to extract the selection mechanism from this asymptotic series. Numerical results agree very well with other existing numerical results, and, somewhat surprisingly, with the results that we obtained by a WKB solution of the inner problem. Last, we complete our WKB treatment by determining explicitly the additive constant appearing in the WKB formula.

Theoretical results are given for the ionization state, electrical conductivity, thermal conductivity, and thermoelectric coefficient for the entire Periodic Table over extreme ranges of temperature and density. A spherical average ion embedded in a uniform plasma background is used as a model to evaluate the electron densities of states, elastic scattering cross sections, and ionization states. These are then combined with one-component plasma structure factors to compute mean relaxation times and electrical resistivities according to an extended Ziman formula. The method of Lampe is used to compute thermal conductivities and thermoelectric coefficients from these values. Some experimental comparisons are made. The transport coefficients appear to be accurate for weakly and moderately correlated plasmas, but not for strongly correlated liquids or crystalline materials. The coefficients are tabulated as numerical functions of temperature and density. The tables extend in temperature from ${10}^{\mathrm{-}2}$ to ${10}^4$ eV. Density ranges depend upon atomic mass; lower limits range from ${10}^{\mathrm{-}4}$ to ${10}^{\mathrm{-}2}$ g/${\mathrm{cm}}^3$, and upper limits range from ${10}^5$ to ${10}^7$ g/${\mathrm{cm}}^3$. Indications are given of the regions of validity of the results.

Phase conjugation via degenerate four-wave mixing in a liquid suspension of dielectric microspheres is examined. An expression is derived for the nonlinear refractive index of such a medium, which is valid for up to moderately dense concentrations of microspheres. Examples are presented that show significantly higher phase-conjugate reflectivities than predicted by previous theories, even for low microsphere concentrations.

The power spectrum of the archetypal fluctuating bistable system, the underdamped double-well Duffing oscillator, is investigated both experimentally, with use of an electronic circuit, and theoretically. The experiment confirms previous analytic results for the structure of the spectrum, including the existence of three distinct peaks within a certain parameter range. The theory is extended to describe analytically the shape of the peak due to intrawell fluctuations for arbitrary noise intensities as well as certain other features of the spectrum. Good quantitative agreement of theory and experiment is demonstrated.

Several aspects of attractor reconstruction and analysis using the method of correlation integrals have been thoroughly investigated for a specific chaotic attractor. Requirements on the experimental data, the generation of the artificial phase space, and the evaluation of the correlation integral are considered in detail. In order to explain the surprisingly smooth behavior of the correlation integrals resulting in an unusually straightforward and accurate analysis, the global scaling properties of the attractor are derived. They indicate that specific aspects of the analysis are a direct consequence of the structure of the attractor. Moreover, the scaling properties provide a useful criterion for an optimum adaption of the length of the required time series to the particular attractor under consideration.

Correlation functions of one- and two-dimensional piecewise linear maps are analytically investigated. The asymptotic time behavior is shown to be given by the average inverse multiplier 〈${\mu }_1^{\mathrm{-}1}$(τ)〉, for one-dimensional maps with absolutely continuous invariant measure. The decay rate γ coincides with the generalized Lyapunov exponent Λ(scrq) at scrq=2, if the sign of the multiplier does not change during the time evolution, while, in general, it is larger than Λ(2). The analysis of two-dimensional maps reveals the importance of the average second multiplier 〈${\mu }_2$(τ)〉 and of the average ratio 〈${\mu }_2$(τ)/${\mu }_1$(τ)〉 which, in some cases, can provide the leading long-time contribution.

We present x-ray diffraction measurements of freely suspended single-orientation columnar-phase strands of 2,3,7,8,12,13-hexa(-n-tetradecanoyloxy)truxene [(${\mathrm{C}}_{13}$${\mathrm{H}}_{27}$COO${)}_6$-TX] which show a dramatic difference between the ordering of the rigid, planar central cores and the flexible hydrocarbon chain tails of the molecules. Diffraction from the strands reveals two types of behavior: the tails are highly disordered, producing a nearly isotropic scattering pattern, whereas the rigid cores are orientationally ordered and translationally disordered within the columns. High-resolution diffraction measurements show that the hexagonal lattice correlation length is greater than 4000 Å, corresponding to more than 200 columns.

We report x-ray scattering measurements around the smectic-$A_1$-to-nematic phase transition of ${\mathrm{C}}_8$${\mathrm{H}}_{17}$O-φ-OOC-φ-${\mathrm{OCH}}_2$-φ-CN, where φ is the phenylene functional group. Critical fluctuations occur at the smectic-$A_1$ monolayer wave vector ${\mathrm{q}}_2$ and noncritical bilayer fluctuations at the incommensurate wave vector ${\mathrm{q}}_1$≊${0.56\mathrm{q}}_2$. This is different from the situation at the surface where the two wave vectors are commensurate with ${\mathrm{q}}_1$${=(1/2\mathrm{q}}_2$. For both types of layering the correlation lengths for the bulk were found to be equal to the penetration depths at the surface. The critical behavior of the monolayer fluctuations is described by the critical exponents γ for the susceptibility and ${\nu }_{?}$ for the correlation length, which are both close to their tricritical values. This is unexpected for the large nematic temperature range involved.

Transient behaviors of a nonlinear model system perturbed by external white noises are studied numerically. Results derived with both Stratonovich and Ito interpretations of stochastic calculi demonstrate that instability occurs at a transition point associated with a critical value of the noise parameter. It is found that the critical slowing down familiar in the equilibrium systems occurs near this nonequilibrium instability point. It is also found that for both calculi and over a broad range of initial conditions, the relaxation time diverges with an exponent which is in accord with the classical mean-field value.

Following an analogy to the formalism of statistical mechanics, an entropy function and a free energy are introduced for multifractals. These functions give a full description of the scaling behaviors of multifractals. The method of Halsey et al. [Phys. Rev. A 33, 1141 (1986)] for characterizing multifractals can naturally be interpreted by the use of these functions. For the invariant set of a dynamical system, these functions are furthermore related to the measure-theoretic (Kolmogolov-Sinai) entropy, the topological entropy, and the Lyapunov exponent.

A theoretical criterion is offered for the design of a temperature schedule for simulated annealing. It is based on a measure of distance in probability space. Implementation requires a knowledge of the heat capacity and the relaxation time. A method of calculating these quantities for a combinatorial problem is outlined. The theoretical structure involved seems to point to an information-theoretic measure of computational effort in certain probabilistic algorithms.

The collision strengths for electric monopole collisional excitation of the outermost subshell of highly stripped closed-shell ions are examined and found to scale nearly hydrogenically. The collision strength near threshold for the principal monopole excitation process (in the distorted-wave approximation) is written as Ω(Z)=${\xi }_{\mathrm{nl}}$(Z)${\mathrm{\eta }}_{\mathrm{nl}}$(Z)${\mathrm{N}}_{\mathrm{nl}}$${\mathrm{I}}_{\mathrm{H}/\mathrm{\Delta }\mathrm{E}\left(\mathrm{Z}\right)}$, where ${\xi }_{\mathrm{nl}}$(Z) is near 0.3, 0.5, and 0.6 for the He-like (1s–2s), Ne-like (2p–3p), and Ni-like (3d–4d) sequences, respectively, and where ${\eta }_{\mathrm{nl}}$(Z) accounts for mixing effects and is near unity at low Z. The excitation process in nickel-like ions is more effective per electron than for neonlike ions and is favorable to the development of x-ray lasers below 44 Å. The extension of the monopole excitation scheme to Nd-like ions appears very attractive for longer wavelengths.

In a single- , nondegenerate- , band model, the electron density ρ(r) is the sum of the squares of the Wannier function of the band, summed over all lattice sites. X-ray scattering is then determined by the convolution of the momentum eigenfunction of the band, which is the Fourier transform of the Wannier function with itself. Invoking the one-body potential V(r) of density functional theory, a formally exact link is established between ρ(r) and V(r).

In the case of resonant two-photon autoionization of ${\mathrm{H}}_2$, the influence of laser bandwidth on the photoelectron angular distribution is seen to be large at lower intensities (∼${10}^6$ W/${\mathrm{cm}}^2$), but gradually disappears towards higher intensities. At very high intensities (∼${10}^{12}$ W/${\mathrm{cm}}^2$), the ac Stark shift of the resonant intermediate state is found to affect the distribution significantly. It has also been found that the Stark-shifted line shape of the intermediate state tends to be symmetrical around zero detuning on increasing the laser bandwidth.

The role of chirp and pulse area in squeezed-state generation is analyzed on the analytically soluble example of a parametric down-conversion. It is shown that the chirp decreases the amount of squeezing.

It is shown that for rotating binary liquids in the extreme Soret regime there is a critical Taylor number below which convection sets in as zero-wave-number rolls. Above the critical Taylor number a finite wave number is selected and the critical wave number depends on the rotation speed. Experimental possibilities are discussed.

Application of the variational Hartree method to a system of N bosons interacting via Skyrme-type forces allows us to describe the single-boson wave function for the ground-state condensate in terms of the nonlinear time-independent Schrödinger equation, ${\mathit{\nabla }}^2$φ=${\mathrm{\varepsilon }}_1$φ-A‖φ${\mathrm{\Vert }}^2$φ+B‖φ${\mathrm{\Vert }}^4$φ. In one dimension, not only is φ found by analytic integration of this equation, but the single-boson separation energy, the Hartree potential energy, the kinetic energy, and the mean-square radius are also all evaluated in closed form. The resulting expressions show that the model exhibits the property of saturation.

It is experimentally observed that first-order optical Fréedericksz transitions can be induced by two laser beams which interact incoherently in a homeotropically aligned nematic film. The observed bistable behavior of the system is in good agreement with the theory.

Multifractality in growth processes has been illustrated using different measures. Here their influence on the f(α) function is evaluated, invoking generic properties of simple two-scale sets.