A study is made of models for the phase-transition dynamics of systems in one space dimension with latent heat whose only field variables are an order parameter and temperature. The processes by which a material in the ordered state undergoes phase transition due to internal heating is explored by numerical simulation and analyses based thereon. Besides externally induced nucleation and transitions through a fine-grained phase-mixture state analogous to spinodal decomposition, there is a type of self-induced nucleation mechanism occurring in some parameter ranges.

The electroclinic effect and dielectric response have been investigated in the British Drug House material SCE12 over its entire 15-K smectic-A range. Near the smectic-A–smectic-${\mathit{C}}^{\mathrm{*}}$-phase transition both the electroclinic coefficient and dynamic response behave normally, the former diverging and the latter exhibiting a critical slowing down on approaching ${\mathit{T}}_{\mathit{A}\mathrm{-}\mathit{C}}^{\mathrm{*}}$ from above. Similar behavior is seen in the dielectric response. Approximately 10 to 12 K above ${\mathit{T}}_{\mathit{A}\mathrm{-}\mathit{C}}^{\mathrm{*}}$, however, it was found that the electroclinic relaxation time levels off and even begins to increase again on approaching the nematic–smectic-A transition from below. The magnitude of the electroclinic coefficient, however, decreases monotonically on approaching the nematic–smectic-A transition.

Near the sol-gel transition, gelling systems exhibit an extremely slow relaxation of thermally driven density fluctuations. We have made a detailed quasielastic light scattering study of the decay of density fluctuations in reacting silica sol-gels in the pre- and post-gel regimes, and at the gel point. In the pre-gel regime the dynamic structure factor S(q,t) for the branched polymer melt has a stretched exponential tail whose characteristic time diverges at the gel point. This critical slowing down is due to the divergence of the average cluster size and is distinct from the usual critical slowing down observed in second-order thermodynamic phase transitions, since the initial decay rate of S(q,t) is nondivergent at the gel point. In fact, at the gel point, S(q,t) becomes a power law, indicating a fractal time set in the scattered field. These observations are accounted for by considering the dynamics of percolation clusters, and in this connection the analogy to viscoelasticity is described. Beyond the gel point S(q,t) remains a power law, but the amplitude of the relaxing part of the intensity autocorrelation function diminishes. Finally, the dynamics of clusters diluted from the reaction bath is studied, and a crossover from power law to stretched exponential decay of S(q,t) is observed. It is shown that at infinite dilution the long-time tail of the correlation function describes the internal modes of a single percolation cluster.

The waterless microemulsion glycerol-AOT-isooctane [AOT, sodium bis(2-ethylhexyl) sulfosuccinate] was systematically studied as a function of temperature T, volume fraction (glycerol plus AOT) φ, molar ratio n=[glycerol]/[AOT], and the salt content ${\mathit{p}}_{\mathit{s}}$ in the glycerol. The properties studied are dynamic viscosity η, electric conductivity σ, and dielectric relaxation ${\mathrm{\epsilon }}_{\mathit{R}}^{\mathrm{*}}$. At fixed T, n, and ${\mathit{p}}_{\mathit{s}}$ an increase in the conductivity and dynamic viscosity is observed when the volume fraction increases. Dielectric relaxation may be represented as a generalized Davidson-Cole distribution of the relaxation time. The quantities (1/σ)(dσ/dφ) and (1/η)(dη/dφ) pass through a maximum, as does the static permittivity ${\mathrm{\epsilon }}_{\mathit{s}}$ (in the latter case the maximum is often followed by a minimum). At the same time the inverse of the characteristic frequency of dielectric relaxation 1/${\nu }_{\mathit{R}}$ passes through a maximum. The results are discussed in the framework of percolation theory. The application of the asymptotic laws of percolation is discussed. For viscosity, the analysis of the results provides a good comparison between theoretical and experimental values taking as critical percolation exponents μ’≃2 (for φ>${\mathrm{\phi }}_{\mathit{c}}$), where ${\mathrm{\phi }}_{\mathit{c}}$ is the percolation threshold and s’≃1.2 (φ<${\mathrm{\phi }}_{\mathit{c}}$), which are the values predicted by the dynamic theory of percolation. By determining the η(φ) curves for various conditions, we were able to establish the variations of ${\mathrm{\phi }}_{\mathit{c}}$(T), ${\mathrm{\phi }}_{\mathit{c}}$(n), and ${\mathrm{\phi }}_{\mathit{c}}$(${\mathit{p}}_{\mathit{s}}$). It was observed that ${\mathrm{\phi }}_{\mathit{c}}$ decreases when T and n increase or when ${\mathit{p}}_{\mathit{s}}$ decreases. This corresponds to an increase in the interactions between droplets within the system. Finally, according to the value of φ, the viscosity may increase or decrease with increasing temperature. This curious effect can be explained by appropriate application of percolation theory.

Accurate nonrelativistic calculations of ionization energies and hyperfine structures for the 3s and the 3p states, and of the dipole transition 3s-3p, are presented for Na, using wave functions obtained in the coupled-cluster approach including single and double excitations (CCSD). Agreement with experimental results is at the percent level, corresponding to an error in the correlation contribution of approximately 5%. Certain three-body cluster contributions to the 3s ionization energy and the 3s hyperfine structure are evaluated and are found to account for the main part of the discrepancies between the values obtained from CCSD calculations and the experimental results.

We extend the solvability theory of dendritic growth to the case of systems without reflection symmetry. We show that these systems exhibit a double selection of growth velocity and growth direction. These results are obtained both via numerical solution of the integro-differential shape equation and via the asymptotic Kruskal-Segur reduction to a differential equation in the complex plane.

The large variability in the ramified structure of diffusion-limited-aggregation clusters suggests an analogy between their branches and the phase-space valleys of spin glasses. We define the overlap q of two growth sites, and study numerically the overlap function q(x) of two- and three-dimensional aggregates. For isotropic aggregates we find that the average overlap decreases as a power law when their mass N increases, indicating that the number of branches increases with N, and that the overlap function and its fluctuations obey a scaling law. Analytical results are presented for the infinite-dimensional limit on the Cayley tree. For anisotropic aggregates with b-fold symmetry (b=2, 3, and 4), the average overlap obtained numerically has a finite limit for large N, and the overlap function is in very good agreement with analytical calculations on a simplified model.

Several recent theories involve a modification of the Schrödinger equation, which dynamically suppresses coherent superpositions of macroscopically different states and so avoids Schrödinger’s cat paradox. It is shown that these theories violate energy conservation and are incompatible with the existence of equilibrium and steady states. The reasons for these troubles are pointed out.

Several aspects of the columnar structure encountered in vapor deposition at oblique particle incidence are studied through a combination of theoretical analysis and computer simulations. First, a general macroscopic theory of columnar growth is presented that yields, among other results, an expression for the columnar growth angle. We then focus on the role of noise in columnar growth, using two simple square-lattice ballistic deposition models–finite-density deposition and noise-reduced deposition–in which the amount of fluctuations in the growth process can be tuned by varying a control parameter. In both models faceting of the column tips stabilizes the columnar morphology. In the finite-density model, we find a faceting transition related to directed percolation. Some characteristics of columnar growth are retrieved within a mean-field approximation. Simulations carried out on d-dimensional hypercubic lattices up to d=6 indicate that the deposit density converges to its mean-field value in the limit d→∞.

Numerical simulations are reported on a ballistic deposition model that interpolates between the weak- and strong-coupling limits of the stochastic Burgers equation introduced by M. Kardar, G. Parisi, and Y. C. Zhang [Phys. Rev. Lett. 56, 889 (1986)]. The model, which is built on a d-dimensional cubic lattice, considers a random deposition of two kinds of particles, with concentrations c and 1-c, that stick to the deposit or may slide on it by no more than one lattice spacing. Evidence is given for the existence of a phase transition, when varying c, in d=3 and 4, but not in d=2, in agreement with an analytical prediction due to Halpin-Healy [Phys. Rev. Lett. 62, 442 (1989)]. The transition is investigated by analyzing, as a function of c, the scaling exponents of the surface thickness as well as the compactness of the bulk of the deposit. An analytical mean-field approach is proposed that describes most of the features of the phase transition.

This work deals with the global instability mechanism of solidification from melt. It leads to a wave theory for solving long-standing problems–the pattern formation of dendritic growth and the selection of the tip velocity. One of the most important results drawn from the present work is that the selection condition of the dendrite’s tip velocity can be found even in the absence of the anisotropy of surface tension. Two distinct sets of unstable global modes for the system are obtained: (1) the global trapped wave (GTW) modes, which describe the characteristics of waves trapped in the region between the tip point and the turning point; (2) modes that display a mechanism involving wave emission at the turning point and signal reflections between the turning point and the leading edge of the tip, abbreviated as WEASR. Uniformly valid asymptotic expansions for the GTW modes and the quantum conditions of corresponding eigenvalues are derived. The requirement that the total perturbed interfacial energy must be finite eventually rules out all the WEASR modes. The presence of the self-sustaining GTW mode in the system, however, very well explains the origin and persistence of the pattern formation in dendrite growth. A unique global neutral stable state is found, which gives the tip velocity at the later stage of growth. The present theory shows good agreement with the available experimental data for a nearly isotropic material.

We analyze the effect of space-correlated disorder on diffusion in a one-dimensional continuous disordered medium. We calculate the frequency-dependent diffusion coefficient using a method based on a perturbative treatment around an effective homogeneous medium. Exact results for disorder modeled by a two-level process and by a generalized Poisson process are obtained. We show that, in the Poisson case, changes in the correlation length can induce essential changes in the diffusive behavior of the medium, from strong to weak disorder or vice versa.

An alternative density-functional theory, the generalized local-spin-density-functional (G-LSD) theory, is proposed based on the boundary conditions and sum rule of the Fermi-correlation factor in the Hartree-Fock (HF) limit. It avoids the physical restrictions to the boundary conditions and the sum rule used in the generalized exchange local-spin-density-functional (GX-LSD) theory completely, the homogeneous electron-density approximation in the Hartree-Fock-Slater (HFS) theory and in the Gáspár-Kohn-Sham (GKS) theory partly, and the time-consuming step to search for the optimal exchange parameter for each atom or ion in the Xα and Ξa theories. The alternative G-LSD theory generates the GX-LSD, HFS, GKS, Xα, and Ξa theories, when additional approximations or certain Fermi-hole shapes or high electron-density limit in a system are used. Theoretically, the G-LSD theory is more rigorous than the GX-LSD, HFS, GKS, and Ξa theories. Numerically, the statistical total energies for atoms in the G-LSD theory are in excellent agreement with the HF results, when the Gopinathan, Whitehead, and Bogdanovic [Phys. Rev. A 14, 1 (1976)] Fermi-hole parameters are used.

Gold disk targets were irradiated with and without induced spatial incoherence (ISI) at λ=0.526 μm and intensities of (1–5)×${10}^{14}$ W/${\mathrm{cm}}^2$. The distribution of laser energy on target and M-band x-ray (2–4 keV) pinhole images of the target were smoothed with ISI. Absorption of laser energy was increased by 5–10 % with ISI. Soft-x-ray conversion efficiency with and without ISI were equal within the data scatter and uncertainty of ∼10%.

Absorption spectroscopy can be used to diagnose compressed layers in spherical targets imploded by means of high-intensity laser irradiation [B. Yaakobi et al., Opt. Commun. 34, 213 (1980)]. In appropriately designed experiments, absorption lines are formed by 1s-2p absorption transitions in the heliumlike through fluorinelike species of certain ions in the shell that surrounds the strong continuum source in the compressed core of the target. These transitions form a distinct, broad linelike absorption band for each ion species. The areal density of each species can be inferred from the attenuation in the spectrum within its respective absorption band and from the known cross sections for each 1s-2p transition. Earlier analyses have assumed that all such transitions begin from states in the ground configuration of each species [A. Hauer et al., Phys. Rev. A 34, 411 (1986)], but, in fact, most of the absorption can be due to satellite absorption transitions originating from states in excited configurations which are, in total, less opaque than transitions originating from the ground configuration. As a result, the opacity becomes temperature dependent through the temperature dependence of the populations of excited configurations. This is illustrated for the specific case of chlorine, and approximate results, based on the screened hydrogenic approximation, are obtained for other elements. Estimates of areal density that include only the ground configuration can be too low by as much as 33%.

The suppression of current-driven ion cyclotron waves is studied in finite geometry. The mode structure equation for the interacting waves, which includes the nonlinear correction terms due to ponderomotive effects, is solved using the perturbation technique. From the resultant dispersion relation, expressions for real and imaginary parts of the frequency are obtained. It is found that the lower-hybrid pump causes a downward shift in the frequency of the cyclotron wave and enhances the ion cyclotron damping, thereby stabilizing it.

We develop a novel approach to dynamical particle correlations in a classical one-component plasma system. A self-consistent integral equation is obtained for the dynamical local field to be determined. We show that this dynamical local field possesses the following properties: (i) it simultaneously satisfies the conservation and compressibility sum rules; (ii) it has the requisite constant values depending on frequency for large wave numbers; and (iii) it develops an algebraic tail in the high-frequency limit for small wave numbers.

The objective of this paper is the establishment of a formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles; the time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green’s function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface ∂Ω of an impenetrable obstacle. With ${\mathit{k}}_0$ as the free-space wave number of the signal, a simplified expression is obtained for the ${\mathit{k}}_0$-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on ∂Ω. All the nonelementary operators that enter the expression for the T operator are formally simple, rational algebraic functions of a certain invertible linear operator Z${\mathrm{̌}}_{\mathit{k}0}$, which is called the radiation impedance operator, and which maps any sufficiently well-behaved, complex-valued function on ∂Ω into another such function on ∂Ω. The nonlocal operators Z${\mathrm{̌}}_{\mathit{k}0}$ and Z${\mathrm{̌}}_{\mathit{k}0}^{\mathrm{-}1}$ are defined only implicitly, in that Z${\mathrm{̌}}_{\mathit{k}0}^{\mathrm{-}1}$ is the operator that maps the limiting-value function on ∂Ω of an outgoing-wave solution to the scalar Helmholtz equation into the uniquely corresponding limiting-normal-derivative function, and Z${\mathrm{̌}}_{\mathit{k}0}$ does the inverse operation. Previous appearances in the literature of these operators, or their analogs for other elliptic, linear partial-differential equation systems, are cited. An analytical study of the dominant singularities of the operators (considered as two-point kernels on a smooth ∂Ω), and of their behavior in the geometrical acoustics limit, is the subject of a second paper [G. E. Hahne, following paper, Phys. Rev. A 43, 1990 (1991)].

This second paper of a series deals with special aspects of transition- (T-) operator theory for diffraction of time-harmonic, acoustic scalar waves from an impenetrable obstacle with surface ∂Ω. It was shown in the first paper [G. E. Hahne, preceding paper, Phys. Rev. A 43, 976 (1991)] that the computation of the T operator and complete Green’s function for the case of ‘‘sound-hard’’ (Neumann-type) and ‘‘sound-soft’’ (Dirichlet-type) boundary conditions on ∂Ω reduces to the determination of the ‘‘radiation impedance’’ operator Z${\mathrm{̌}}_{\mathit{k}0}$ and the ‘‘radiation admittance’’ operator Z${\mathrm{̌}}_{\mathit{k}0}^{\mathrm{-}1}$, respectively, characteristic of ∂Ω at wave number ${\mathit{k}}_0$. In this paper, the short-wavelength and the long-wavelength behavior of these operators as two-point kernels on a smooth ∂Ω are studied for pairs of points that are close together. First, an exact, closed-form expression is obtained for both Z${\mathrm{̌}}_{\mathit{k}0}$ and Z${\mathrm{̌}}_{\mathit{k}0}^{\mathrm{-}1}$ for ∂Ω=a plane, on the basis of which a ‘‘tangent-plane’’ approximation to Z${\mathrm{̌}}_{\mathit{k}0}$ and to Z${\mathrm{̌}}_{\mathit{k}0}^{\mathrm{-}1}$ for diffraction from a general smooth-surfaced, convex obstacle is proposed. This approximation is shown to lead, by means of the method of stationary phase, to the familiar ‘‘physical optics’’ approximation and to the geometrical acoustics limit for diffraction with Neumann-type and with Dirichlet-type boundary conditions. Second, the dominant singularities in Z${\mathrm{̌}}_{\mathit{k}0}$ and in Z${\mathrm{̌}}_{\mathit{k}0}^{\mathrm{-}1}$ are obtained for smooth ∂Ω, and the results are compared to analogous results for ∂Ω as a sphere inferred from the spherical harmonic expansions of the two operators.

The leading-order contributions to the transition amplitudes in adiabatically driven quantum systems are presented in closed form for a physical class of Hamiltonians that have a specified scaling property. For smooth parametric variations the transition amplitudes are beyond all orders of perturbation in the parameter of slowness. The quantum and classical cases are contrasted. Specific applications include the particle in a box and the harmonic oscillator.