The Stokes equation system and Ohm’s law were solved within periodic bicontinuous porous media of simple-cubic (sc) symmetry. The results were used to test the permeability scaling law proposed by Johnson, Koplik, and Schwartz [Phys. Rev. Lett. 57, 2564 (1986)], which uses a length parameter Λ to relate the Darcy permeability k and formation factor F. We found that the scaling law M==8Fk/${\mathrm{\Lambda }}^2$≊1 was obeyed by many bicontinuous porous media within the sc crystallographic family. However, this is not valid when the constrictions in the porous media approach an orificelike aspect: The scaling law is not universal.

Electrostatic properties of polymers have been studied by numerical measurement of the capacitance, polarizability of unrestricted, and self-avoiding random walks of length L=2,4,8,...,128. Asymptotic values of the depolarization coefficients have been found. The electrostatic shapes of random walks have been shown to be significantly more aspherical than could be predicted from the components of the squared radius of gyration. Proportionality coefficients of various scaling properties have been established, and a very strong correlation between the shape tensor and the polarizability tensor has been found.

Series expansions for the time-dependent coverage in random sequential adsorption on a lattice are reviewed. A transformation is carried out, resulting in combinatorial expressions in which only nonrepeating lattice walks are required. Convergence is greatly accelerated, and application is made to the asymptotic coverage of previously solved lattices as well as Bethe lattices and cactuses, or Bethe lattices with the bonds replaced by triangles. The method is extended to multisite correlations as well.

Adaptive-network growth has been obtained by a diffusion-limited-aggregation model in which particles of the cluster that do not connect active regions (regions in which deposition is occurring) to the seed or origin of the cluster are removed from the cluster. In the computer simulation of this model, the accumulated ‘‘score’’ associated with each of the ${\mathit{N}}_{\mathit{b}}$ particles connecting a deposited particle to the seed is increased by 1/${\mathit{N}}_{\mathit{b}}$ when the particle is added. At the same time, the scores of all particles in the cluster are decreased by an amount 1/${\mathit{N}}_{\mathit{m}}$, which is a parameter of the model. Particles with scores less than zero are then removed from the cluster. This model leads to the formation of clusters that reach a stationary state in which the cluster size s(t) fluctuates about a constant value controlled by the parameter ${\mathit{N}}_{\mathit{m}}$. The number of particles N(r) within a distance r from the seed is given by N(r)∼${\mathit{r}}^{\gamma }$, where the exponent (fractal dimensionality) γ≃1.25. The scaling of the cluster size with ${\mathit{N}}_{\mathit{m}}$ is described by s¯(t)=${\mathit{N}}_{\mathit{m}}^{\nu }$f(t/${\mathit{N}}_{\mathit{m}}^{\nu }$), where t is the time (number of particles that have contacted the cluster). The exponent ν has a value of about 0.75. The score of each surviving particle is a measure μ(r) that also exhibits interesting scaling behavior.

In laser-plasma experiments, conditions in an embedded layer in a target shell can be inferred from the spectral attenuation of x-ray continuum radiation by the layer [B. Yaakobi et al., Opt. Commun. 34, 213 (1980)]. In such experiments, absorption lines are formed by 1s-2p absorption transitions in heliumlike through fluorinelike species of certain ions in the layer to be diagnosed. The areal density of each species can be inferred from the attenuation in the spectrum within its respective band, provided the average 1s-2p absorption cross sections for each species are known and provided competing line-forming mechanisms are taken into account. In photoelectric fluorescence, which is one such potentially important competing mechanism, the formation of a 1s vacancy by photoionization is followed by 2p-1s spontaneous emission within the same spectral range as the 1s-2p absorption band of the same ion. The importance of photoelectric fluorescence depends on the supply of ionizing photons, which is sensitive to the design of the experiment. This process should be considered when analyzing experiments where the continuum is hardened by high core temperatures, by opacity effects, or by core components that radiate efficiently at ionizing energies.

It is shown that when a light pulse is incident upon an underdense relativistic ionization front, the light pulse can be simultaneously upshifted in frequency and compressed in duration. The reflection and transmission coefficients are examined. Examples for both overdense and underdense fronts are given to show that a relativistic ionization front can generate tunable radiation from millimeter to ultraviolet wavelengths.

We develop a model for the Helmholtz free energy of fluid hydrogen at high density and high temperature. This model aims at describing both pressure and temperature dissociation and ionization and bears directly on equations of state of partially ionized plasmas, as encountered in astrophysical situations and high-pressure experiments. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. In the present model, the strong interactions are described with realistic potentials and are computed with a modified Weeks-Chandler-Andersen fluid perturbation theory that reproduces Monte Carlo simulations to better than 3%. Perturbations of the internal partition functions of H and ${\mathrm{H}}_2$ arising in the nonideal fluid are treated self-consistently with a recently developed occupation probability formalism. Theoretical Hugoniot curves derived from our model are in excellent agreement with experimental data. Pressure dissociation occurs over a narrow density range above 0.5 g/${\mathrm{cm}}^3$ and is remarkably temperature insensitive. Molecules remain the dominant species even at high densities.

The turbulent mixing generated at the surface of an inertial-confinement fusion target affected by the Rayleigh-Taylor instability is studied with the use of a simple, nonlinear diffusion model. In order to study the turbulent mixing at the ablation front, a reduced growth rate of the Rayleigh-Taylor instability is used in the model. It is found that, compared with the classical layered fluids, turbulent mixing at the ablation front is significantly suppressed because of the ablative stabilization effect. With the use of a constant-acceleration model, we conclude that targets imploded with an in-flight aspect ratio less than about 50 to 70 survive without suffering shell breakup as a result of the turbulent mixing.

The Zubarev formalism is applied to a two-temperature plasma to obtain the generalized law of mass action. This is done for arbitrary heat flow between the electrons and the internal states of the heavy particles on one hand and the kinetic degrees of freedom of the heavy particles on the other hand. In the case of zero heat flow the results previously reported are recovered. Applying the outcome of the calculation to a simple plasma of Rydberg atoms and ions, the Saha equation is changed. The difference can be expressed in a correction factor that depends on the mass ratio of the electron to the heavy particle, the difference in temperature, and the specific atomic structure. For argon plasmas the correction factor is small. For hydrogen plasma the results indicate a correction on the order of 10%, depending on the plasma conditions.

Four-wave mixing in plasmas using ponderomotive and thermal nonlinearities has been extensively studied. Plasmas have received considerable attention since they become more efficient four-wave-mixing and phase-conjugation media at longer wavelengths (far infrared, 10 μm, to radio wave, 10 m). In this paper, the prospect of using an ionization nonlinearity in weakly ionized plasmas for degenerate four-wave mixing and phase conjugation is discussed. Like the thermal pressure nonlinearity, the ionization nonlinearity results from the heating of the plasma by the beat wave. However, as the local temperature increases, more neutral species are ionized by electron-impact ionization to form a beat-wave grating structure; instead of pushing the electrons into a grating structure (as with the thermal and ponderomotive nonlinearities), the electron density grating is created directly by ionization. Numerical estimates of the phase-conjugate reflectivity indicate reflectivities in the range of ${10}^{\mathrm{-}4–}$${10}^{\mathrm{-}3}$ are possible in a weakly ionized steady-state gas-discharge plasma. The reflectivity is limited to this range due to the onset of an ionization instability (striations). Larger reflectivities may be possible for pulsed plasma sources.

We have already presented results on the stochastic cooling of the axial motion of samples of N particles stored in a Penning trap. We now complete our previous results, discussing a simple method also to cool stochastically the radial motion of the particles.

We present a detailed analysis of a subharmonically seeded single-pass free-electron laser (FEL) utilizing two wiggler magnets separated by a dispersion section. To be specific, suppose the seed to be laser light at 300 nm. A first wiggler is used to energy modulate the electron beam. This is followed by a dispersion section to produce spatial bunching, and a second wiggler resonant to 100 nm. Upon passing through the second wiggler, the prebunched electron beam first radiates coherently, and then this radiation is exponentially amplified. Finally, a tapered section is used to extract additional power from the electron beam. In this manner we can achieve pulses of duration ≊10 psec with 1 mJ per pulse in ${10}^{\mathrm{-}4}$ bandwidth, with continuously tunable wavelength in the range 100–300 nm. We present the analytical tools we have employed for the preliminary estimate of the system performance and of the optimization of the parameters. We describe our modification of the simulation code tda to include harmonic generation and discuss its use in analyzing the subharmonically seeded FEL. The analytic and computer-simulation calculations are in good agreement. We discuss in detail the physical process in the system and the optimization of parameters.

The homogenization of a beam with a transversely nonuniform initial density distribution is examined by masking the ouput from a Pierce electron gun into five parallel beamlets, which are then propagated down a channel of periodically spaced solenoid focusing magnets. Experimental measurements, theoretical predictions, and PIC simulations are in excellent agreement for averaged beam quantities such as rms emittance and envelope radius. In addition, the fine-structure characteristic of the nonlinear evolution of the beam, including the formation of downstream images, is reproduced in detail by the simulations.

A description of the steady-state nonlinear behavior of a Compton free-electron-laser (FEL) amplifier is presented, in which the radiation field is written in both linear and nonlinear regimes as the sum of three coupled ‘‘normal modes.’’ In the linear regime these modes reduce themselves to the noninteracting modes of the usual linear theory. The two linearly stable modes turn out to be nonlinearly unstable, because their amplitudes grow exponentially as the FEL enters into the nonlinear regime. We derive a self-contained system of three nonlinear dynamical equations for these modes in two different approaches. The system is then reduced to comparatively simple forms in which only cubic nonlinearities appear. In this way, we are able to describe the FEL saturation process and the first peak in the amplitude of the radiation field with a good degree of accuracy. The large-amplitude oscillations in the field intensity, which are the main feature of the FEL nonlinear dynamics, are also reproduced through the nonlinear coupling between the normal modes.

We have studied the amplitude and temporal correlations of intensity fluctuations of multiply scattered light transmitted through a colloidal suspension. When the coherence length ${\mathit{l}}_{\mathit{c}}$ of the incident light becomes comparable to the width of the probability distribution of photon-path lengths, both the amplitude and dynamics of intensity fluctuations become functions of ${\mathit{l}}_{\mathit{c}}$. In this article we present a simple theory that relates these coherence effects to the photon path-length distribution P(L). We have tested this theory using P(L) calculated from computer simulations and from the diffusion approximation, and find that our theory qualitatively accounts for the observed dependences on coherence length. Our results indicate when the effects of finite laser coherence must be taken into account in quasielastic multiple scattering. In the few-scattering regime of quasielastic multiple scattering, we find that the intensity autocorrelation function generally has a stretched-exponential form, and we discuss the origin of this behavior.

In this paper we apply optimal control theory to nonlinear classical systems for the design of electric fields that interact with the systems so that an ensemble of classical trajectories are manipulated in some desired way. Control of selective unimolecular bond dissociation is demonstrated in the classical regime on a model linear triatomic molecule with spreading of the ensemble of trajectories held to a minimum for closer agreement between quantum and classical mechanics. Control was also demonstrated over trajectories in a highly chaotic two-dimensional system. It was found in the cases studied that a high degree of control was attained in situations where the dynamics are chaotic in the absence of a controlling field.

Traditional approaches to the asymptotic behavior of coupled wave equations have difficulties in the formulation of a consistent version of the Bohr-Sommerfeld quantization conditions. These difficulties can be circumvented by using the Weyl calculus to diagonalize the matrix of wave operators. In analyzing the diagonalized wave equations, geometric phases enter in an important way, especially in the development of Bohr-Sommerfeld quantization rules. It turns out that a version of Berry’s phase is incorporated into the symplectic structure in the ray phase space, influencing the classical Hamiltonian orbits, the construction of solutions to the Hamiltonian-Jacobi equation, and the computation of action integrals. Noncanonical coordinates in the ray phase space are useful in carrying out these calculations and in making the construction of eigenvalues and wave functions manifestly gauge invariant.

Frozen-solution EPR spectra from the cupric site in the protein azurin were measured at 6, 9, and 35 GHz, and subjected to a model-independent analysis. Anomalies in the splittings and shapes of the hyperfine peaks of the low-field quartet are faithfully simulated when a correlated distribution in spin-Hamiltonian parameters is employed, with Δ${\mathit{A}}_{11}$/Δ${\mathit{g}}_{11}$=-0.08 ${\mathrm{cm}}^{\mathrm{-}1}$ and ${\mathrm{\sigma }}_{\mathit{g}}$=0.009. A hybrid-orbital ‘‘united-atom’’ model is used as the basis for a perturbation calculation of the spin-Hamiltonian parameters. With a simple assumption relating the spreads in the hybridization parameters, these spreads and Δ${\mathit{A}}_{11}$/Δ${\mathit{g}}_{11}$ are computed from the model. Equipartition is applied to estimate force constants for the protein modes responsible for the distribution in site geometry. With hybridization parameters in ranges constrained to produce agreement between the calculated and observed magnetic-resonance properties, a force constant at the upper end of those for bending modes is obtained for tetrahedral displacement, and a stiffer one, consistent with stretch, is found for displacement around the symmetry axis.

The temperature sensitivity of hydration forces between ${\mathrm{Mn}}^{2+}$-DNA helices in ordered arrays has been used to measure the entropic part of the interaction free-energy versus helix separation. This entropy is positive, and like the hydration force itself, grows exponentially as helices move closer. Measured forces show an abrupt transition between regions of interactions with quite different characteristic decay lengths, with a discontinuous change in interhelical spacing. However, both the entropic and enthalpic components of the interaction free-energy maintain smooth single-exponential variation across this transition.

Measurements are reported of the evolution of bioconvective patterns in shallow, dense cultures of microorganisms subjected to varying gravity. Various statistical properties of this random, quasi-two-dimensional structure have been found: Aboav’s law is obeyed, the average vertex angles follow predictions for regular polygons, and the area of a pattern varies linearly with its number of sides. As gravity varies between 1 g and 1.8g (g=9.8 m ${\mathrm{s}}^{\mathrm{-}1}$), these statistical properties continue to hold despite a tripling of the number of polygons and a reduced average polygon dimension by a third. This work compares with experiments on soap foams, Langmuir monolayer foams, metal grains, and simulations.