The closed set of general-relativistic hydrodynamical equations describing a strongly magnetized collisionless plasma with an anisotropic pressure tensor is derived. Consideration is based on the ‘‘3+1’’ formulation of magnetohydrodynamics and the orthonormal tetrad technique. The model is the further generalization of the theory of Chew, Goldberger, and Low [Proc. R. Soc. London Ser. A 236, 1204 (1954)] for the general-relativistic case. In ultrarelativistic limit the equations of state are obtained, which differ noticeably from those known previously.

A one-dimensional model, including pulse propagation and detailed ionization dynamics, is developed in order to calculate the spectrum of an intense femtosecond laser pulse transmitted through an atmospheric-density noble gas. The spectrum is broadened and blueshifted due to self-phase-modulation resulting from a combination of optical-field-induced ionization and collisional ionization. Different features in the spectrum can be used to indicate the relative importance of the two ionization mechanisms. The calculations are in good agreement with the recent experimental results of Wood, Siders, and Downer [Phys. Rev. Lett. 67, 3523 (1991)], but indicate that a significant degree of defocusing occurs as a result of plasma generation. The simulations could possibly be used as a test of various theoretical models for optical-field-induced ionization.

The tunneling-ionization model predicts that fully ionized plasmas with controllable perpendicular (${\mathit{T}}_{\mathrm{\perp }}$) and negligible longitudinal temperature (${\mathit{T}}_{\mathrm{\parallel }}$) can be produced. The validity of these predictions has been studied through experiments and supporting theory and simulations. Emission of odd harmonics of the laser frequency, indicative of a stepwise ionization process, has been observed. X-ray measurements show that the plasma temperature is higher for a circularly polarized laser-produced plasma compared to when linear polarization is used. Analytically we find that the growth of the stimulated Raman (SRS) and Compton scattering (SCS) instabilities are suppressed during the ionization phase. A higher ${\mathit{T}}_{\mathrm{\parallel }}$ than expected from the single-particle-tunneling model was observed after the ionization phase through SCS fluctuation spectra. The maximum achievable plasma density is found to be limited by ionization induced refraction. One-dimensional (1D) simulations show that, after the ionization phase, the initial ${\mathit{T}}_{\mathrm{\parallel }}$ is low as expected from the single particle model and SRS density fluctuations grow to large values. In 2D simulations, however, ${\mathit{T}}_{\mathrm{\parallel }}$ at the end of the ionization phase is already much higher and only SCS is seen to grow. The simulations indicate that stochastic heating and the Weibel instability play an important role in plasma heating in all directions and in making the plasma isotropic. Two-dimensional simulations also confirm that refraction plays a crucial role in determining the maximum electron density that can be obtained in such plasmas.

The coupling impedance of a hole in a thick-wall beam pipe has been calculated for hole dimensions that are small compared to the wavelength. In particular, the longitudinal and transverse coupling impedances are shown to be proportional to the difference between the transverse magnetic susceptibility and the electric polarizability of the inside surface of the hole, and these quantities are themselves proportional to the cube of the hole dimensions.

The longitudinal and transverse impedance of many holes in a thick-wall liner have been calculated for hole dimensions that are small compared to the wavelength. These are shown to be small compared with the corresponding resistive wall impedances of the liner at the frequency of the lowest transverse coupled-bunch mode. Estimates are made of the effect of the propagation of TEM modes in the coaxial region between the liner and beam pipe, and these can be neglected for a sufficiently thick liner. Estimates are also made of the possible coherent effect of uniformly spaced holes.

A number of authors have reported poor scaling with size N in numerical studies of the neural-network-based algorithm for the ‘‘traveling-salesman’’ problem proposed by Hopfield and Tank [Biol. Cybern. 52, 141 (1984)]. In this paper, the scaling with N of a closely related algorithm for solving bipartite list matching is analyzed in an expansion in powers of 1/lnN. A self-averaging solution is obtained by assuming row and column exchange symmetry and directly evaluating the partition function. This yields a prediction for the error rate that increases proportionally to lnN for fixed values of the control parameters, confirmed here for this model by numerical simulation. The same result can be derived using the replica method, assuming that the solutions are replica symmetric. The analysis predicts that scaling the inhibitory coupling with ${\mathit{N}}^{\mathrm{\delta }}$, δ>0, drives the error rate asymptotically to 0 with increasing N.

We study the persistence of self-trapping in the presence of arbitrary large perturbations. We obtain the phase diagram for a nonlinear dimer interacting with a third linear impurity site and show that the abrupt Kenkre-Campbell transition is sustained. In addition to the ‘‘free’’ and ‘‘self-trapped’’ regimes we find a ‘‘chaotic’’ regime for some well-defined values of the nonlinearity and linear coupling parameters.

We compare exact and semiclassical Husimi distributions for the single eigenstates of a one-dimensional resonant Hamiltonian. We find that both distributions concentrate near the unstable fixed points even when these points are made complex by suitably varying a parameter.

An interference asymmetry in the angular distribution of the Ly-α quenching radiation emitted by ${\mathrm{He}}^{+}$ ions in the metastable 2${\mathit{s}}_{1/2}$ state is measured to high precision to obtain the lifetime of the 2${\mathit{p}}_{1/2}$ state. The derived lifetime of (0.997 17±0.000 75)×${10}^{\mathrm{-}10}$ s is the most accurate available for a fundamental atomic system. A detailed discussion of systematic corrections is included. The result is in good agreement with theory, thereby confirming the theory of radiative transition probabilities to ±0.075%, and indicating that differences between theory and experiment for the alkali metals must be due to either inadequate wave functions or experimental errors.

Atomic self-motion in liquid lead was studied on the molecular dynamics model of 16 384 particles using the effective pair potential which was derived earlier from the measured structure factor. The simulation was carried out at two temperatures, 623 and 1170 K, the former being close to the melting point. At 623 K, the deviation of the incoherent intermediate-scattering function ${\mathit{F}}_{\mathit{s}}$(Q,t) from its Langevin approximation, for long enough times, was found to display a characteristic pattern of Q dependence which resembles that of the static structure factor S(Q). Some elements of this picture of Q dependence were also found in the high-temperature region. These results indicate that sizable effects of coupling between the diffusion process and the structural relaxation, known to be characteristic of supercooled-liquid dynamics, are well defined in the normal-liquid domain and they may be found even in the temperature region well above the melting point.

Two distinct renormalization-group (RNG) approaches have been applied to Navier-Stokes turbulence: ε-RNG and recursive RNG. ε-RNG takes into account only nonlocal interactions and utilizes an infinitesimal subgrid (unresolvable scale) shell limit. Recursive RNG takes into account both nonlocal and local interactions and does not require an infinitesimal subgrid shell limit to be taken. The role of local interactions and the introduction of RNG-induced nonlinearities are discussed and clarified.

Starting from an initial state with an electron energy ${\mathit{p}}_0^2$/2m+ħ${\mathrm{\omega }}_{\mathit{c}}$/2, a vacuum-laser field, and a coherent wiggler field, I discuss photon statistics in a free-electron laser with an axial-guide magnetic field. It is found that the axial field can weaken the squeezing, enhance the positive (for θ>0) and negative (for θ<0) gain, and strengthen the bunching (for θ>0) and antibunching (for θ<0).

The 2×2-matrix-valued first-order linear differential equation appears when we solve the modified Korteweg–de Vries (MKdV) equation. This linear differential equation is regarded as a fictitious quantum equation. On the other hand, it is known that the dynamics of an elastic rod is governed by the MKdV equation. In this paper, after we construct a Dirac equation on an elastic rod embedded into (2+1)-dimensional space-time, we show that this linear differential equation is naturally introduced through this Dirac equation. Then we can explain the reason why the classical nonlinear differential equation is associated physically with quantum mechanics. In other words, we prove that fictitious quantum mechanics related to the soliton is real quantum mechanics on the soliton as a base space. We also argue that the Berry phase of the Dirac particle is related to the Lax pair ${\mathit{L}}_{\mathrm{\tau }}$=i[L,B].

Caccamo and Giacoppo, in a recent Rapid Communication [Phys. Rev. A 42, 6285 (1990)], use the energy-equation form of the mean spherical approximation to model liquid-liquid equilibria for mixtures containing ions. They calculate critical exponents numerically and find classical values, in apparent agreement with some experimental data. We comment that the critical exponents are known a priori to be classical in this form of the approximation, and that therefore the comparison with experimental exponents is not meaningful.

We respond that analyticity of the Gibbs free energy, constituting the basic argument of Harvey and Levelt Sengers’s Comment, is not a priori known in our calculational scheme, and hence the value of the critical exponent cannot be anticipated. We also clarify the procedure to follow in order to implement an investigation of the critical consolute point via the ‘‘compressibility route.’’

The approximate quantum numbers A and T in the (K,T${)}^{\mathit{A}}$ classification scheme of doubly excited helium states have been evaluated. A strong mixing of the symmetrized and antisymmetrized components has been found in the A=0 states. A direct verification supporting rotorlike structures has also been found.

The decay of silver and hafnium atoms with a vacancy in the K shell by the emission of photon pairs which continuously share the transition energy was studied. Radioactive decay of ${}_{}{}^{109}{}_{}{}^{}\mathrm{Cd}$ and of ${}_{}{}^{179}{}_{}{}^{}\mathrm{Ta}$ was used to generate K-shell vacancy states in silver and hafnium atoms, respectively. A pair of germanium detectors in a 180° geometry and a fast-slow coincidence system with a (128×512×512)-channel three-parameter pulse-height analyzer were used in the measurements. Two-dimensional spectra of numbers of events as functions of amplitudes of coincident pulses from the two detectors were analyzed. Surface fitting of two-dimensional spectra and curve fitting of sum spectra were applied to deduce the number of events. The differential transition probabilities of 2s→1s, 3s→1s, 3d→1s, and 4sd→1s two-photon decay per decay of a K-shell vacancy have been determined. For silver they are compared with the results of relativistic self-consistent-field calculations of Mu and Crasemann [Phys. Rev. A 38, 4585 (1988)] and of Tong, Li, Kissel, and Pratt [Phys. Rev. A 42, 1442 (1990)]. The results for silver and hafnium are compared with the results of nonrelativistic calculations for hydrogenic silver and hafnium ions. The 3d→1s two-photon decays show the resonance effect, in accordance with the theoretical predictions.

Graphical representations of three-particle wave functions obtained by direct solution of the Schrödinger equation with the correlation-function hyperspherical-harmonic (CFHH) method are obtained and analyzed for ground and excited states of the helium atom and for the ground state of the μdd mesomolecular ion. The inclusion of adequate singular and cluster-correlation behavior is shown to be of crucial importance for a proper description of the wave function. In the CFHH method the wave function is a product of a correlation function and of a smooth factor expanded into hyperspherical-harmonic (HH) functions. While the HH expansion by itself is not able to reproduce a correct form of the wave function, the inclusion of the correlations results in its proper description even for low values of the maximal global momenta ${\mathit{K}}_{\mathit{m}}$.

Absolute oscillator strengths for the photoabsorption of argon, krypton, and xenon in both the discrete and continuum regions have been measured. The results are compared where possible with previously published experimental and theoretical data. The present work is a continuation of recently reported measurements for helium [Chan et al., Phys. Rev. A 44, 186 (1991)] and neon [Chan et al., Phys. Rev. A 45, 1420 (1992)] obtained using the dipole (e,e) method at both low and high resolution. Using the low-resolution dipole (e,e) spectrometer [with a full width at half maximum (FWHM) of about 1 eV], absolute photoabsorption oscillator strength spectra for the valence and inner shells of argon, krypton, and xenon were obtained up to equivalent photon energies of 500, 380, and 398 eV, respectively. The high-resolution dipole (e,e) spectrometer (FWHM of 0.048 eV) was employed to obtain absolute photoabsorption oscillator strengths for the discrete electronic transitions from the ground states to the ${\mathit{ms}}^2$${\mathit{mp}}^5$ns and ${\mathit{ms}}^2$${\mathit{mp}}^5$nd ${(}^2$${\mathit{P}}_{3/2,1/2}$) manifolds where m=3, 4, and 5 for argon, krypton, and xenon, respectively. The absolute optical oscillator strength scales were obtained by single-point continuum normalization of the Bethe-Born converted electron-energy-loss spectra using the recently reported absolute optical data of Samson and Yin [J. Opt. Soc. Am. B 6, 2326 (1989)] for argon, krypton, and xenon atoms. High-resolution absolute photoabsorption oscillator strengths were also obtained in the energy regions of the autoionizing resonances corresponding to excitation of the inner-valence s electrons of argon, krypton, and xenon.

The self-energy correction for an electron bound in an electrostatic potential is examined in coordinate space. The binding potential is assumed to be spherically symmetric and local but not necessarily Coulomb. Subtractions that remove infinite renormalization terms and lower-order terms are given as operators in coordinate space in order to facilitate the numerical evaluation of the level shift. This approach is expected to be applicable to calculations of finite-nuclear-size corrections and electron-screening corrections to the self-energy, and to calculations of higher-order quantum-electrodynamic corrections where the self-energy diagram is part of a more complex external-field Feynman diagram.