The driving current of a free-electron laser with a uniform helical undulator is calculated by solving a linearized Boltzmann equation which includes terms, generally neglected, representing the effect of the e-beam bending due to the finite radius of the electron wiggling. The current is used for writing the wave equation for the electromagnetic field amplified along the z axis of the wiggler. The space modulation of the current induced by the e-beam bending is eliminated by using a moving frame obtained by displacing the coordinate system, with its origin at the center of the wiggler entrance section, along the central trajectory of the electron beam. In this way, a parabolic wave equation is obtained similar to the well-known equation of high-gain lasers, with the addition of a term proportional to the wiggling radius and the transverse gradient of the field, which depends sinusoidally on z. For solving this generalized parabolic equation, the laser field is represented in the moving frame as a superposition of space harmonics whose longitudinal propagation constants differ by multiples of the wiggler period (Bloch-Floquet waves). The transverse profile of the field is accounted for by expanding it in a series of Gauss-Laguerre wave functions. Then, combining Bloch-Floquet waves with Gauss-Laguerre wave functions, three-dimensional mutually orthogonal modes are obtained. In the laboratory frame these modes appear as wiggling beams, which are used as the basis for transforming the wave equation into a homogeneous set of linear equations. A simple expression for the correction of the propagation constant due to the e-beam bending is presented together with the analytic expression of the field for the case of high Fresnel numbers.

We present a quantum theory of the nondegenerate parametric oscillator above threshold. The effect of signal and idler phase diffusion on the various types of external squeezing spectral measurements is discussed.

By treating a liquid metal as a mixture consisting of nuclei and electrons, we have derived a set of integral equations for calculating radial distribution functions (RDF’s) from the atomic number as the only input data; the internal atomic structure of an ion in a liquid metal is obtained self-consistently with the liquid structure at the same time. Here, we apply this formulation to liquid metallic lithium using further two approximations: (1) the local-field correction factor for electrons in a liquid metal is approximated by that of the jellium model, and (2) the ion-ion bridge function is replaced by that of the Percus-Yevick equation for a hard-sphere fluid. We calculate the structure factors at 470 and 595 K, which show excellent agreement with the experimental ones. Simultaneously we obtain the electron-ion RDF, which gives the charge distribution ρ(r) of a neutral pseudo- atom taking account of nonlinear screening. We extract a nonlinear pseudopotential $w_b^{\mathrm{nl}(\mathrm{r}}$) from the density ρ(r); this yields an interatomic interaction $v^{\mathrm{eff}(\mathrm{r}}$) giving the ion-ion RDF. Thus we determine the ion-ion and electron-ion RDF’s, the charge distribution ρ(r) of a pseudoatom, the pseudopotential $w_b^{\mathrm{nl}(\mathrm{r}}$), and the pair interaction $v^{\mathrm{eff}(\mathrm{r}}$) in a self-consistent manner; they are also regarded as consistent with experiment.

A mechanism has been found for nonlocal interaction of two spatially separated electromagnetic wave packets propagating with equal group velocities in a homogeneous plasma. The efficiency of the mechanism is sensitive to such parameters as the phase separation, width, and shape of the packets.

A theoretical model for the calculation of the K-shell photoabsorption edge in a dense plasma is described. In the model, degeneracy and continuum lowering contributions due to free electrons and neighboring ions were treated as perturbations on the continuum and the bound state. These contributions were evaluated using first-principles solid-state methods. The model was used to interpret recently observed shifts in the K-shell photoabsorption-edge energy in shock-compressed aluminum. The validity of the model was further examined through comparisons with two average-atom, self-consistent-field calculations and an augmented-plane-wave calculation.

Lattice-gas automata have been proposed as a new way of doing numerical calculations for hydrodynamic systems. Here, a lattice-gas simulation is run to see whether its behavior really does correspond, as proposed, to that of the Navier-Stokes equation. The geometry used is the two-dimensional version of laminar pipe flow. Three checks on the existing theory are performed. The parabolic profile of momentum density arising from the dynamics is quantitatively verified. So is the equation of state, which arises from the statistical mechanics of the system. Finally, the well-known logarithmic divergence in the viscosity is observed in the automaton and is shown to disagree with the earliest theoretical predictions in this system. Proper agreement is achieved, however, when the theory is extended to include three extra (recently discovered) conserved quantities. In this way, checks of both linear and nonlinear parts of the hydrodynamic description of lattice-gas automata have been achieved.

This paper describes a method for measuring distributions of turbulent diffusivity in less than an hour. The measurement is rapid enough to aid in designing devices that make use of the turbulent diffusion of mass, heat, or momentum. It may be useful as a measurement of the degree of turbulence in the blood of patients with cardiovascular diseases. It consists of subtracting the natural logarithms of the pixel values of a magnetic-resonance image of turbulent fluid from those of stationary fluid. The pixel values of the resulting image are multiplied by a constant to yield diffusivities. The accuracy of the measurement is within the range of diffusivities (1) upstream as far as the speed of the fluid multiplied by the time $T_E$ between exciting the spin system and recording the signal, (2) in the direction of the gradient of diffusivity as far as $T_E$ multiplied by 5 times the gradient of the diffusivity, and (3) in the direction of the phase-encoding magnetic field gradient as far as the negative of the component of velocity in the phase-encoding direction multiplied by the time between phase encoding and recording the signal. In a 32×32-${\mathrm{cm}}^2$ image of a jet of water with a nozzle velocity of 4.5 m ${\mathrm{s}}^{\mathrm{-}1}$ and Reynolds number of 18 000, made with a $T_E$ of 15 ms, the distance of (1) ranged from 0 to 6.7 cm, of (2) ranged from 0 to 0.3 cm, and of (3) ranged from 0 to 0.4 cm. These distances are bounds; the actual spatial misregistration was less. The signal-to-noise ratio ranged from 10 to 15 for diffusivities from 0.02 to 0.7 ${\mathrm{cm}}^2$ ${\mathrm{s}}^{\mathrm{-}1}$. .AE

We present a quantitative comparison between recent theoretical predictions and an experimental study of the transition from traveling waves to steady overturning convection in a water-isopropanol mixture presenting a negative value of the separation ratio. The observed velocity for this transition is not in agreement with the predicted value.

Using a six-center Lennard-Jones (12-6) pair potential, we modeled lead liquid at two different thermodynamic states by molecular-dynamics (MD) computations. While the static structure factor is found to agree with experiment at both states, the pressure is reproduced only for the lower temperature. Self-diffusion and shear viscosity are in reasonable agreement with experimental results. However, the thermal conductivity is predicted far too low. We emphasize the following points: (i) the chosen multiple-center pair potential has only three free parameters that were fitted by about ten test MD runs, each of which required only 3 min on a supercomputer; (ii) the production computations for the structure factor and the self-diffusion were carried out with 500 molecules, while the transport coefficients were obtained by runs with 32 molecules. Thus our findings stand in sharp contrast to recent calculations of Dzugutov, Larsson, and Ebbsjö [Phys. Rev. A 38, 3609 (1988)] who claimed that a seven-parameter pair potential and a very large number of particles are required to model liquid lead by MD computations.

Radiation cooling of laser-produced aluminum plasmas by highly ionized gold atoms was studied experimentally. The plasma was produced by irradiating 500-μm-diam glass spheres coated with two layers of aluminum and an intermediate gold layer of varying thickness. The 24-beam Omega laser system at a laser wavelength of 351 nm and intensity in the range (2–3)×${10}^{14}$ W/${\mathrm{cm}}^2$ was used to produce the plasma. Electron temperatures were determined spectroscopically by measuring the 1s-2p–to–1$s^2$-1s2p line ratio in Al xiii and Al xii. With no gold layer the electron temperature of highly ionized aluminum is found to be close to 1400 eV. The introduction of a 0.01-μm layer of gold reduced the electron temperature to approximately 1100 eV, and with a 0.05-μm gold layer it was reduced to 700 eV. A gold layer also reduced the temperature of the sodium plasma produced from the glass as measured using Na x and Na xi line ratios. Time-resolved x-ray measurements showed additional evidence of cooling. Measurements of total x-ray emission and radiative energy calculations from a hydrodynamic code showed a 50% increase in radiated energy with the addition of 0.05-μm gold layer.

The cumulant expansion of the density matrix proposed by Fujiwara, Osborn, and Wilk [Phys. Rev. A 25, 14 (1982)], which represents a formal resummation of the Wigner-Kirkwood (WK) ħ expansion, permits computationally efficient Monte Carlo simulations for calculating quantum-mechanical averages of quasiclassical systems. The resulting radial distribution function and various thermodynamic averages are reported for the Lennard-Jones model, at different thermodynamic conditions and for a number of values of the reduced quantum parameter $q^{\mathrm{*}}$, and compared with WK and path-integral Monte Carlo results. The range of validity of the approximation can be predicted by the features of the effective pair interaction potential.

One-dimensional systems of annihilating and coalescing random walks and Brownian motions with arbitrary initial configurations of particles are studied. Exact results are derived for site-occupancy probabilities (densities), local fluctuations in these probabilities, and distributions of nearest-neighbor distances. Two types of initial configuration are investigated in detail: the homogeneous Poisson process and a one-parameter family of pairwise clustered locations. The systems studied can be regarded as simple models of diffusion-controlled chemical reactions and hence the exact results derived here can be compared with the predictions of traditional, deterministic models that are based on simplifying assumptions about the evolution of the spatial structure of the systems. It is shown that, although the asymptotic behavior of the annihilating systems does depend on the structure of the initial configuration, the deterministic approximations are not able to detect this dependence, and the approximation is poor when the particles are initially highly clustered.

This paper describes various procedures for extracting an underlying multiplicative process from the thermodynamic description of multifractals (i.e., its $D_q$ curve), and points out the associated pitfalls of such procedures. We extend previous work by Feigenbaum, Jensen, and Procaccia [Phys. Rev. Lett. 57, 1567 (1986)] using transfer matrices to the case of singular measures, and develop the corresponding thermodynamic formalism. We find that the extraction procedure based solely on information from the $D_q$ curves allows for an infinity of cascade processes and that additional dynamical information is required to remove this degeneracy. In addition, we find that different multiplicative processes with only three free parameters produce excellent fits to all the $D_q$ curves studied in this paper, which further confuses the inversion process when it is applied to experimental data. We then examine the application of these procedures to a variety of computer and laboratory experiments, such as the period-doubling attractor, the golden-mean circle-map attractor, and a reanalysis of Rayleigh-Bénard experiments corresponding to these examples. Finally we consider laboratory experiments on open flows in two different circumstances. The first deals with velocity measurements in the wake of an oscillating cylinder and has dynamics closely related to that of the circle map. The second case corresponds to the spatial distribution of turbulent energy dissipation in several flows (grid turbulence, wakes, and boundary layers in the laboratory and atmosphere), where the underlying dynamics are presently not well understood. In each of these examples we highlight the above-mentioned ambiguities and, in cases where additional information is available, apply the procedure to extract basic underlying length scales of the phenomena.

Breathing vibrational modes near a junction of DNA double helices poly(dA)-poly(dT) and poly(dG)-poly(dC), in the B confirmation are studied theoretically using the Green’s-function technique. The thermal mean-square displacement amplitude of the average hydrogen-bond stretch is found reduced on the A-T base-pair side of the junction, while it is enhanced on the G-C base-pair side due to local-mode contributions.

Experimental data for the pressure dependence of the critical temperature (${\mathrm{dT}}_c$/dP) are reported for several microemulsions of n-dodecane, water, n-pentanol, and sodium dodecylsulfate, with critical points along a critical line ending at a critical end point (CEP). Negative ${\mathrm{dT}}_c$/dP values, substantially decreasing near the CEP, are obtained for all the microemulsions investigated. Using two-scale-factor universality and combining ${\mathrm{dT}}_c$/dP with correlation-length critical-amplitude ${\xi }_0$ values, we also find that a density anomaly is very likely unobservable experimentally. From the negative sign of ${\mathrm{dT}}_c$/dP it can also be concluded that if there is any critical contribution of the density anomaly to the refractive index n, it must be opposite to the anomaly recently reported for n by Rebbouh and Lalanne [J. Chem. Phys. 90, 1175 (1989)].

We report a high-resolution x-ray scattering study of the nematic–smectic-A transition around the tricritical point in mixtures of heptyloxypentylphenylthiobenzoate and octyloxycyanobiphenyl. Unusually large susceptibility and correlation length critical exponents are observed; this is explained as a clear example of Fisher renormalization. The underlying exponents, over a large range of impurity concentrations, are in good agreement with those observed previously in homologous mixture tricritical studies.

A study is reported that was designed to search for the existence of a ‘‘1/f’’-noise component in the α-decay process. The experimental design was carefully optimized since simply attaining the Poisson variance limit is difficult when high-precision observations are made. Measurements indicate a ‘‘flicker floor’’ of (2.1±3.7)×${10}^{\mathrm{-}11}$. This result is not inconsistent with a complete lack of a 1/f component and is in marked contrast with an earlier reported value of 1×${10}^{\mathrm{-}7}$. .AE

A matrix approximant to the generalized Frobenius-Perron equation is presented, the largest eigenvalues of which approach the most important eigenvalues of the operator (e.g., the so-called free energy). It is pointed out that also certain eigenfunctions not accessible to iteration of the continuous problem can easily be obtained in the discretized formalism. For general one-dimensional maps the spectrum of generalized entropies is shown to appear as the largest eigenvalue of a truncated version of the matrix. The statistical interpretation of the eigenfunction associated with the free energy is given in terms of configuration probabilities of spin chains.

The chirality-induced biaxiality is measured at the uniaxial-to-biaxial cholesteric phase transition of the lyotropic system including potassium laurate, decanol, ${\mathrm{H}}_2$O, and some chiral agent. The measurement of an induced biaxiality in a cholesteric uniaxial liquid crystal is reported. The corresponding susceptibility coefficient c/‖$a_0$‖ is deduced to be 5×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^2$ K, which leads to consistent values of the bare correlation length, ${\xi }_0$∼130 Å at the normal transition and ${\xi }_0$<100 Å at the reentrant one. The measurements moreover show that the uniaxial-to-biaxial cholesteric phase transition is not second order as is the uniaxial-to-biaxial nematic phase transition, but continuous. This change is interpreted to be an effect of the elastic field of chirality present in the cholesteric phases.

We present a theory of fully connected neural networks that incorporates mechanisms of dynamical self-control of recognition process. Using a functional integral technique, we formulate mean-field dynamics for such systems.