A variational-principle formulation of dissipative magnetohydrodynamics (DMHD) including thermal conduction and viscous dissipation as well as resistive decay is presented. The functional to be minimized is an extension of the generalized entropy-production (GEP) rate first discussed by I. Prigogine 2 [Nonequilibrium Thermodynamics, Variational Techniques, and Stability, edited by R. J. Donnelly, R. Herman, and I. Prigogine (University of Chicago Press, Chicago, 1966)]. Minimization of this functional at each instant of time results in the proper evolutionary behavior of the MHD fields while the correct boundary conditions are maintained. Steady-state solutions are obtained as a special case of the GEP functional minimization, which is fully consistent with earlier entropy formulations for the steady state. The method is illustrated with an explicit application to a simple, one-dimensional model of a reversed-field pinch.

A theoretical description of droplet growth and coarsening is presented for vapor condensing onto a partially wetting surface. Both individual droplet growth and coalescences are included in the description. The coupling of these growth mechanisms results in two characteristic lengths. The radii of individual droplets, nucleated onto the surface, increase as a power of time: R∼$t^m$. Diffusion-limited growth on the surface leads to a characteristic exponent m=(1/4. As a result of coalescences, however, the average droplet radius grows with an exponent of 3m. Further predictions of the theory are also discussed.

We have examined quasielastic light scattering off the crystal-melt interface of growing ice crystals using photon correlation spectroscopy. The intensity autocorrelation spectra exhibit two exponential decay rates with vastly different time constants. The fast decay is found only during growth and is similar to that observed by Bilgram and his co-workers. We have found several new features associated with the slow-decay component: (1) nonzero intercept of the decay constant Γ versus the square of the scattering vector $q^2$ during growth; (2) a liftoff layer that depends on the type of gaseous impurity; and (3) a direct relationship between the effective hydrodynamic radius of the slow component and the degree of its size polydispersity. These provide new evidence to support Cummins’s hypothesis that this component of the spectrum is caused by the segregation and precipitation of tiny gas bubbles at the crystal’s surface.

A recurrent problem in mathematical physics, for example, in the theory of critical phenomena, is the need to study the structure of physically interesting functions at a branch point of a complex structure usually called a ‘‘confluent singularity.’’ In such a neighborhood the function is necessarily multivalued. In addition, the value of such a function is sometimes required on a branch cut or even off the first Riemann sheet. Our approach to this problem is inspired by the Riemann (global) monodromy theorem and consists of using series expansions to form integral approximants (special case of Hermite-Padé approximants) to represent multivalued functions on multiple Riemann sheets. We prove an analogous local-monodromy-theorem, functional-representation results. We further identify the important ‘‘separation property’’ and use it to prove a convergence theorem for horizontal sequences of integral approximants. We make an extensive numerical investigation, using horizontal, diagonal, and constrained diagonal sequences, and find that these methods give excellent results on a wide variety of test functions of rather complex structure.

A one-dimensional model for hydrogen-bonded chains is investigated by including the dynamical degrees of freedom of the oxygens and thus generalizing the original Antonchenko-Davydov-Zolotaryuk model. Analytical solutions are derived within a continuum approximation up to second order so that rather narrow solutions could be derived accurately enough. Numerical simulations with a set of parameters derived from infrared spectra show stable low- and high-speed solutions separated by a forbidden gap. There exists also an intermediate velocity range where the initial pulse is unstable in the sense that it is transformed to a high-speed solution with the same energy. Discreteness effects are discussed.

A lattice model is used to investigate the surface behavior of smectic fluids close to the onset of smectic ordering. At the smectic-isotropic interface the nematic features of the smectic phase persist further into the bulk isotropic phase than the strictly smectic features. At the isotropic-vapor interface we find the possibility of a series of first-order layering transitions, each involving the addition of a smectic layer, in line with recent experimental results. However, at the nematic-vapor interface surface smectic order, if it exists, grows smoothly without layering transitions.

A rigid spherical pendulum supported by a universal joint has been studied both experimentally and numerically. By use of linear-capacitance transducers to sense pendulum displacement, dozens of rarely similar trajectories with diverse forms have been generated using an x-y recorder. A computer model was developed which is able to describe essentially all the observed motions of the pendulum. This computer model was used to perform a preliminary study of the motion of the pendulum in the limit of zero damping. It was found that the frictionless system can be regular or chaotic according to initial conditions.

We study the problem of the Fréedericksz transition under a rotating magnetic field by using a dynamical model which incorporates thermal fluctuations into the whole set of nematodynamic equations. In contrast to other geometries, nonuniform textures in the plane of the sample do not appear favored. The proper consideration of thermal noise enables us to describe the dynamics of orientational fluctuations both below and above the shifted instability.

We discuss the dynamics of the transient pattern formation process corresponding to the splay Fréedericksz transition. The emergence and subsequent evolution of the spatial periodicity is here described in terms of the temporal dependence of the wave numbers corresponding to the maxima of the structure factor. Situations of perpendicular as well as oblique field-induced stripes relative to the initial orientation of the director are both examined with explicit indications of the time scales needed for their appearance and posterior development.

We present a theoretical approach for describing clustering and percolation phenomena in an assembly of nonspherical particles. The theory is based upon calculations of an orientation-dependent pair connectedness function. We show how this function may be approximated using a perturbation expansion in which the reference system is an assembly of spherical particles. The reference system is treated via the connectivity Ornstein-Zernike equation in the Percus-Yevick approximation. Although such an approach might appear to be limited to particles of small anisotropy, we find that as the particle anisotropy increases, the regime of interest (i.e., densities below percolation) moves to lower densities where the theory is increasingly accurate. Results are presented for systems of randomly distributed ellipsoids with aspect ratios varying from unity to 5:1 and are compared with Monte Carlo simulations. The approach successfully describes the pair connectedness function, mean cluster size, and percolation threshold. In principle, the formalism is capable of describing the connectivity of randomly distributed particle systems over a wide range of particle anisotropy, including the limiting cases of randomly distributed spheres and infinitely extended rods.

We use the method of cell-to-cell mapping to locate attractors, basins, and saddle nodes in the phase plane of a driven Josephson junction. The cell-mapping method is discussed in some detail, emphasizing its ability to provide a global view of the phase plane. Our computations confirm the existence of a previously reported interior crisis. In addition, we observe a boundary crisis for a small shift in one parameter. The cell-mapping method allows us to show both crises explicitly in the phase plane, at low computational cost.

We have analyzed a two-dimensional lattice-gas model of cylindrical molecules which can exhibit four possible orientations. The Hamiltonian of the model contains positional and orientational energy interaction terms. The ground state of the model has been investigated on the basis of Karl’s theorem. Monte Carlo simulation results have confirmed the predicted ground state. The model is able to reproduce, with appropriate values of the Hamiltonian parameters, both, a smectic-nematic-like transition and a nematic-isotropic-like transition. We have also analyzed the phase diagram of the system by mean-field techniques and Monte Carlo simulations. Mean-field calculations agree well qualitatively with Monte Carlo results but overestimate transition temperatures.

A functional-integral expression for the stochastic-mechanics transition probability is obtained. The form of this transition probability indicates that, contrary to the general consensus, interference plays an essential role in the evolution of the probability density in stochastic mechanics.

Our previous results [Phys. Rev. A 37, 2843 (1988)], based on the concept of sojourn time, for the transmission and reflection time delays in one-dimensional scattering by a potential barrier are compared to the corresponding results of E. H. Hauge, J. P. Falck, and T. A. Fjedly [Phys. Rev. B 36, 4203 (1987)], based on the idea of following the time evolution of the mean position of wave packets. It is shown that the mean-position approach agrees with the more general sojourn-time approach in the limit of well-defined momentum, and that, in general, the two approaches appear to be related in a classical-like manner.

Analytic expressions for the diagonal matrix elements 〈nl‖(r-$r^e$${)}^s$‖nl〉 (s=1,2) in rotating Morse oscillators, which are assured to give the correct numerical values which were calculated by numerical integration, have been obtained. Further, an algorithm for computing the matrix elements of arbitrary powers of q, 〈n’l‖(r-$r^e$${)}^s$‖nl〉, is proposed and examined for the case s=2 and shown to produce fairly good results.

The problem of finding the class of wave packets ψ that minimizes the quantum-mechanical uncertainty product ${\Delta }_x$${\Delta }_p$ is treated via the constrained variational principle. This leads to a harmonic-oscillator-type wave equation for ψ whose explicit solutions are obtained when the potential V has, or does not have, an infinite step. The method can be fruitfully applied to the quantum cosmology of the inflationary universe.

A distorted-wave Born approximation has been adopted to perform calculations of the cross sections for electron- and positron-impact excitations in positive heliumlike ions initially from their metastable excited states. 2 ${}_{}{}^1{}_{}{}^{}n$ ${}_{}{}^1{}_{}{}^{}P$ and $2^3$S→$n^3$P (n=2,3) transitions in each ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$ heliumlike ion are considered. The calculated total excitation cross-section results are compared with other previously reported theoretical estimates.

We present theoretical, differential, and total cross sections for electron impact excitation of the lowest autoionizing levels of various lithiumlike ions (viz., ${\mathrm{Be}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, ${\mathrm{O}}^{5+}$, and ${\mathrm{Ne}}^{7+}$). For these ions, the autoionizing level of interest results from excitation of an inner-shell electron. A distorted-wave Born approximation (with exchange) is used for the calculation. The present results are compared with previous theoretical calculations and it is concluded that the Coulomb-Born approach is unreliable, particularly near threshold.

We report the observation of the two-photon decay of the $2^1$$S_0$ level in heliumlike ${\mathrm{Ni}}^{26+}$ and a measurement of the lifetime of this state. We find a lifetime of 150(16) ps, in agreement with the theoretical calculation of G. W. F. Drake [Phys. Rev. A 34, 2871 (1986)] which yields 154.3(5) ps.

Radiation trapping currently creates one of the major limitations on population inversion, gain, and size in x-ray lasers. The resulting increase in lower-level population may be reduced by photodepletion to higher energy levels. A natural energy match between hydrogenic lasing ions of nuclear charge Z, for n=2 to 4 or 6 excitation, and Z/2 radiating ions provides a scalable system for even-Z elements.