We report on the characterization of ultrashort (<10 psec at 1 keV), high-brightness (${10}^{20}$ photons/sec ${\mathrm{mm}}^2$eV into 2π sr at 1 keV) x-ray pulses. The pulses are generated by exciting a preformed laser-produced plasma using an ∼1 GW, picosecond laser pulse. Time-resolved measurements of the x-ray emission from a solid Au target are presented as well as the variation in the yield with laser energy and the angle of incidence. Time-integrated x-ray emission yields and spectra are presented for Si, Ti, and Au solid targets. Physical mechanisms responsible for the x-ray generation are discussed.

We report the first observations of cellular and dendritic growth at the smectic-B–smectic-A interface of the liquid crystal 4O8. Experimentally, 4O8 is seen to be an intermediate case between the solid-liquid and the nematic-isotropic interfaces studied previously. Based on this similarity, we propose a classification of interface behavior based on the latent heat of transition.

Topological correlations in a coarsening two-dimensional soap froth or polycrystalline network are studied by computer simulation. With use of a continuum model, grain growth in very large systems of over ${10}^5$ grains can be simulated. The correlations found between the size or the number of vertices of adjacent grains are in accordance with semiempirical rules of metallurgy. The average grain size grows in proportion to the square root of time, as predicted by mean-field theory. This result, that correlation effects do not modify the growth exponent, is consistent with dynamical scaling and agrees with simulations done on a lattice.

The Ising chain in a random field is investigated in the region of parameter settings where the measure related to the free-energy distribution is a fractal. The multifractal spectrum is calculated by means of a perturbation expansion in terms of the strength of the random field by exploiting the connection with the problem of a non-natural measure of a one-dimensional map. It is shown that the multifractal spectrum and the distribution of the free-energy fluctuations of finite chains are connected.

A Gibbs-type partition of the chaotic motion is introduced. The distribution function of the spectral density defined on such partition is Gaussian. The variance of this distribution is the Fourier transform of the correlation function. We demonstrate this by direct numerical computations for the simple models of chaos. These results are the consequence of translational invariance and should be valid for the general case of chaotic motion described by differential equations.

The probability measure generated by typical chaotic orbits of a dynamical system can have an arbitrarily fine-scaled interwoven structure of points with different singularity scalings. Recent work has characterized such measures via a spectrum of fractal dimension values. In this paper we pursue the idea that the infinite number of unstable periodic orbits embedded in the support of the measure provides the key to an understanding of the structure of the subsets with different singularity scalings. In particular, a formulation relating the spectrum of dimensions to unstable periodic orbits is presented for hyperbolic maps of arbitrary dimensionality. Both chaotic attractors and chaotic repellers are considered.

A new procedure for computing the equilibrium director pattern in a liquid-crystal-display cell subjected to an applied voltage is presented. It uses the simulated-anneal method which is based on the Metropolis Monte Carlo algorithm. The usefulness of the technique is illustrated by the simulation of three representative, but totally different kinds of liquid-crystal devices.

This paper shows that the level crossing rate of a process y(t) which results from nonlinear filtering of non-Markov dichotomous noise x(t) can be expressed as N${¯}_l$=β[1-$F^2$(l)]p(l), where p(y) is the density of y(t), β is an inverse time parameter, and F(y) is a nonlinearity in the system equation ẏ+βF(y)=βx. Four examples are given in which Monte Carlo methods are used to establish the veracity of the theoretical results. In a fifth example, the theoretical result is obtained by time averaging. The new result is compared with the crossing rate for Gaussian processes and it is found that N${¯}_l$∼B(l)p(l) in each case, where B(y) is the second conditional moment in the extended Fokker-Planck equation for p(y).

We present a density-functional theory for the growth of equilibrium nematic and smectic-A wetting layers near free surfaces. In the nematic case our theory predicts complete wetting, with the integrated order parameter diverging logarithmically as one approaches the ordering temperature from the isotropic phase. When a smectic phase is approached from the isotropic phase, we find a discrete series of metastable surface phases with integral numbers of layers of smectic order, and incomplete wetting with one or two first-order layering transitions among these surface phases. These results agree qualitatively with recent experiments.

How thermodynamic properties of fractal objects cross over to the corresponding thermodynamic properties of nonfractal ‘‘Euclidean’’ objects is an open question of considerable recent interest. We study how the ground-state entropy σ of the Ising antiferromagnet on a family of two-dimensional fractals ‘‘crosses over’’ to the ground-state entropy of a triangular lattice. The fractal family studied is a generalization of the simple Sierpiński gasket. We find that σ varies smoothly with a parameter b (which labels each member of the fractal family) and approaches for large b the value ${\sigma }_{\mathrm{Baxter}=0.333\mathrm{}24272...}$ calculated by Baxter and Tsang for the hard-hexagon problem on the triangular lattice and confirmed by Baxter to be an exact value.

An adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal cholesteryl nonanoate in a temperature range covering all phase transitions involving the three different blue phases occurring in this substance. Results for the temperature dependence of the enthalpy and the heat capacity are reported. It is found that all three of the blue phases are thermodynamically stable and that all the phase transitions observed are first order.

The best possible constraints on the static response in terms of the two-particle correlation functions, which follow from their integral representation, are analyzed for homogeneous states of multicomponent systems of charged particles. The static mass-response function (MRF) and mass-structure factor (MSF) satisfy a new long-wavelength sum rule which, together with the generalization of the compressibility sum rule, implies that the MRF-MSF relationship reaches the ‘‘classical limit’’ at length scales exceeding $L_{\mathrm{cl}=\mathrm{ħ}{v}_T/\mathrm{T}}$, where $v_T$ is the (isothermal) velocity of sound. The bounds on the static inverse dielectric function (SIDF) and the charge-structure factor allow both positive and negative values of ${\varepsilon }^{\mathrm{-}1}$(k,0). The long-wavelength limit is no longer classical. If the charged particles are confined to neutral clusters whose charge exchange may be neglected (atomic limit states), a Clausius-Mossotti-like inequality (with the cluster polarizability replaced by a lower bound to it) follows from the bounds on the dielectric constant. Assuming perfect screening [${\mathrm{\epsilon }}^{\mathrm{-}1}$=${\lim }_{\mathit{k}\to 0}$${\mathrm{\epsilon }}^{\mathrm{-}1}$(k,0)], the second moment of the charge-correlation function is bracketed by the Stillinger-Lovett (SL) condition and its quantum generalization. For the one-component plasma, the second moment satisfies the quantum SL condition. Using Monte Carlo data, we obtain upper bounds on the values of the plasma parameters $r_s$ and Γ, above which the long-wavelength SIDF is negative.

Calculations of the photoionization cross section of Kr 3p have been performed at four different levels of approximation, from the central-field Hartree-Slater to the 20-channel relativistic-random-phase approximation. The results show unequivocally that the structure that appears at the central-field level is not an artifact of the calculation but persists through the most sophisticated level of approximation.

It is shown that the semirelativistic approach, when applied consistently to atomic calculations involving the Thomas-Reiche-Kuhn sum rule or its applications, may lead to very inaccurate results.

Hillery [Opt. Commun. 62, 135 (1987)] has recently shown that the squeezing of the square of the field amplitude is a nonclassical effect. In this paper we show that the interaction of coherent light with a nonlinear medium modeled as a nonabsorbing anharmonic oscillator gives rise to this type of squeezing. We also show that this squeezing can be interpreted in terms of the Lie algebra of SU(1,1).

Direct experimental evidence for the suppression of period doubling by near-resonant perturbations is presented. The phenomenon is analyzed with use of the dissipative standard map approximation. Experimental results are compared with their numerically simulated counterparts.

Total and resonance electron-impact cross sections are obtained for Na in six-state (6CC) and four-state close-coupling (4CC) approximations for the electron energy range 3.5≤E≤150 eV. Accurate configuration-interaction target wave functions are employed to represent the ground state 3 ${}_{}{}^2{}_{}{}^{}S$ and the excited states $3^2$P°, 3 ${}_{}{}^2{}_{}{}^{}D$,$4^2$S, 4 ${}_{}{}^2{}_{}{}^{}°$, and 4 ${}_{}{}^2{}_{}{}^{}D$. The 4CC results are in excellent agreement with calculated and measured total cross sections for E≤5 eV. Above 10 eV our 6CC resonance cross sections are in accord with measurement, and disagreements among experimental measurements of total cross sections are resolved. We also find that the cross section σ(3s→4d) is much larger than hitherto anticipated. The mechanism responsible is suggested.