We present a predictive calculation of two-phase relative permeabilities in granular porous media formed from a dense random packing of equal spheres. The spatial coordinates of every sphere in the pack have been measured, enabling the microstructure of the medium to be completely determined. From these data we extract a network model that replicates the pore space. By compacting the packing or swelling individual spheres, we may generate model porous media of different porosities whose microstructure is also completely determined. We simulate both viscous- and capillary-dominated invasion of a nonwetting fluid into a wetting fluid contained in these media. During invasion we calculate the average hydraulic conductance of each phase to obtain the relative permeabilities as a function of fluid saturation. Because the microstructure is known, the calculations do not involve any adjustable parameters or supplementary measurements of pore structure. The computed relative permeabilities are successfully compared with experimental values previously measured on sand packs, bead packs, and a simple sandstone.

We have made a systematic survey of the behavior of colloidal polystyrene latex spheres (PLS’s) in critical mixtures of 2,6-lutidine plus water at temperatures where the liquid mixture separates into two immiscible phases. By varying the particle size, particle-surface charge density, and global PLS’s concentration, we observe a robust and reversible set of phenomena that include the partitioning of the particles into a preferred phase at temperatures close to ${\mathit{T}}_{\mathit{c}}$ with a subsequent population of the interface between the liquid phases as the temperature is quenched deeper into the two-phase region. These results are shown to be in good qualitative agreement with thermodynamic models if the models are extended to include the singular temperature dependence of the particle-liquid and liquid-liquid interactions near the critical point. We also observe crystalline ordering of particles on the interface when the population of PLS’s on the liquid-liquid interface is high.

The two models based on multiparticle diffusion-limited aggregation (DLA) are presented to study the morphological changes in diffusive systems. The first model, which takes into account the propagation of cations from the dissolving anode, is proposed for the Hecker effect, which appears in recent experiments of electrochemical deposition. The second model with two components, in which the one component is condensable and the other component is not, is presented to investigate the effect of an incondensable gas on the morphology of DLA. Computer simulation is performed for the deposition process on the plate in two dimensions. In the first model, it is shown that the morphological change of deposits occurs from a less dense structure at the inner region to a more dense structure at the outer region. In the second model, it is found that the morphological transitions appear from the dense structure, through the bay pattern, to the needle structure, with increasing concentration of incondensable gas.

The random-sequential adsorption of disks with two or more sizes onto a planar substrate has been investigated using computer simulations. For a binary mixture of large and small disks, we find that the large-disk coverage reaches its asymptotic value exponentially, while the small disk reaches its asymptotic value algebraically according to Feder’s law. For a uniform distribution of disk radii, the total coverage approaches its asymptotic value algebraically [ρ(∞)-ρ(t)∼${\mathit{t}}^{\mathrm{-}\mathit{p}}$, where ρ(t) is the coverage at time t], but the characteristic exponent p has an effective value smaller than 1/2. If the distribution of disk radii from which the disks are selected for attempted addition is Gaussian, then the exponent p has a very small effective value, and the distribution of adsorbed disks becomes very non-Gaussian if the initial Gaussian distribution is broad. Many of our simulation results can be understood in terms of the theoretical work of Talbot, Tarjus, and Schaff [Phys. Rev. A 40, 4808 (1980)], but other aspects of this work are beyond current theoretical approaches.

We have performed numerical simulations in an off-lattice version of the reversible particle-coalescence model. We have analyzed both two- and three-dimensional systems for several values of the coagulation and fragmentation rate constants. The numerical data support recent conjectures by Sorensen, Zhang, and Taylor [Phys. Rev. Lett. 59, 363 (1987)] on dynamical scaling behavior except at very early times, when we see crossover effects coming from the aggregation-dominated regime.

The morphology of structures formed during the two-dimensional aggregation of colloidal particles at a liquid surface has been studied. The aggregation was induced by adding ${\mathrm{CaCl}}_2$ solution to the aqueous subphase, the electrolyte concentration being varied to change the growth conditions. Under all conditions the clusters displayed self-similarity, the fractal dimension D determined by three independent methods concurring. For low subphase molarities the measured values of D were in accord with predictions for reaction-limited cluster-cluster aggregation, whereas at high molarities D agreed well with expectation for the diffusion-limited case. The cluster anisotropy was greater in the former regime than in the latter, again in accord with theoretical expectation. The change from one regime to the other occurred over a rather narrow range of electrolyte concentration.

The kinetics of aggregation of colloidal particles at an air-water interface have been investigated. The cluster size distribution and its various moments exhibited scaling with time and cluster size in accord with simulations in which the sticking probability for clusters of size i and j was proportional to (ij${)}^{\mathrm{\sigma }}$. Modification of the growth conditions caused systematic variation of the scaling exponents, due to changes in the sticking probability exponent σ. The various scaling exponents satisfied a constraint derived from the critical nature of the nonequilibrium aggregation process. Under all experimental conditions the observed kinetics exhibited a crossover from slow to rapid growth, as expected for reaction limited cluster-cluster aggregation. This implies that the probability of irreversible particle-particle reaction was always very small.

Time-dependent aspects of the structural self-similarity of colloidal aggregates formed in a two-dimensional system at a liquid-air interface are considered. The aggregation was induced by the addition of ${\mathrm{CaCl}}_2$ to the aqueous phase, the electrolyte concentration governing the growth conditions. At all subphase molarities large clusters, necessarily formed late in the aggregation process, showed evidence of internal reorganization, the fractal dimension of the cores of the clusters being significantly larger than that for the global cluster structure. Early in the aggregation process, during a regime of slow cluster growth, the overall cluster morphology resembled that of reaction-limited cluster-cluster aggregation for all ${\mathrm{CaCl}}_2$ concentrations. However, during the later, rapid growth phase the fractal dimensions of the clusters fell at high subphase molarities, becoming compatible with expectation for diffusion-limited aggregation. It is shown that all of these observations are in accord with the hypothesis that the intrinsic particle-particle reaction probability, while experimentally variable, was small under all conditions. A possible explanation for this hypothesis is discussed.

The neutral-hydrogen density in a hot pinch plasma and in the surrounding halo is investigated spectroscopically, and its influence on the ionization dynamics of impurity ions is analyzed. The results are employed in the analysis of effective-ionization-rate coefficients, which are derived for Si viii to Si xii from the time evolution of the respective ions in the plasma.

A one-dimensional model incorporating Maxwell’s equations and tunneling ionization is used to predict the plasma temperature after the passage of an intense femtosecond laser pulse through an atmospheric-density noble gas. These calculations are of relevance to a new class of proposed recombination x-ray lasers that use optical-field-induced ionization to generate an initially cold plasma. The residual plasma temperature is determined under a range of relevant conditions, and is found to be minimized for short laser pulses, short wavelengths, and the lowest intensity consistent with reaching the desired ionization stage. Even under optimum conditions, the predicted temperature is significantly greater than that required for high efficiency in the transient-gain regime.

In an earlier paper [Phys. Rev. A 44, 5122 (1991)], we presented a Helmholtz-free-energy model for nonideal mixtures of hydrogen atoms and molecules. In the present paper, we extend this model to describe an interacting mixture of ${\mathrm{H}}_2$, H, ${\mathrm{H}}^{+}$, and ${\mathit{e}}^{\mathrm{-}}$ in chemical equilibrium. This general model describes the phenomena of dissociation and ionization caused by pressure and temperature effects, as encountered in astrophysical situations and high-pressure experiments. The present model is thermodynamically unstable in the pressure-ionization regime and predicts the existence of a plasma phase transition with a critical point at ${\mathit{T}}_{\mathit{c}}$=15 300 K, ${\mathit{P}}_{\mathit{c}}$=0.614 Mbar, and ${\mathrm{\rho }}_{\mathit{c}}$=0.35 g/${\mathrm{cm}}^3$. The transition occurs between a weakly ionized phase and a partially (≊50%) ionized phase. Molecular dissociation and pressure ionization occur in the same narrow density range; atoms play a minor role in pressure ionization. In the high-density phase, complete pressure ionization is reached gradually. The sensitivity of the coexistence curve and of the critical point to model parameters and assumptions is discussed in detail.

A Robinson-type theorem concerning beam damping is proved, based directly on Liouville’s theorem. The theorem so obtained is somewhat general: The radiating particles need not be relativistic, and they need not form a beam, the emitted radiation may be arbitrary (not necessarily electromagnetic), provided only that the emission process is short enough and not too violent. The proof makes no reference to transfer matrices, nor to properties of the guiding forces (which need not be electromagnetic), except that they are derivable from a Hamiltonian. Then in general the sum of the instantaneous damping coefficients is Σ=${\mathrm{\Sigma }}_{\mathit{i}=1\mathrm{}}^3$${\mathit{a}}_{\mathit{i}}$=1/2${\mathrm{\Sigma }}_{\mathit{i}=1\mathrm{}}^3$∂k${\mathrm{̇}\mathrm{¯}}_{\mathit{i}}$/∂${\mathit{p}}_{\mathit{i}}$ =1/2∇${\mathrm{¯}}_{\mathit{p}}$k̇¯, where k̇ is the time rate of momentum given up by a particle of momentum p¯ and i=1,2,3 denotes the three components. When k̇¯ is parallel to p¯, and k̇=${\mathit{tsum}}_{\mathit{n}=\mathit{M}}^{\mathit{N}}$k̇(n), where k̇(n)∼${\mathit{p}}^{\mathit{n}}$, then Σ=${\mathit{tsum}}_{\mathit{n}}$(2+n)k̇(n)/2p. If, further, the emitting and emitted particles are both ultrarelativistic, and the sum of powers reduces to a single second-order term (as during photon emission by ultrarelativistic electrons in storage rings), then Σ=4ɛ̇/2E, where ɛ̇ is the power radiated out by particles of energy E. Taking the usual time average for quasi-harmonically oscillating beams gives 〈Σ${\mathrm{〉}}_{\mathit{T}}$=4ɛ̇/2E: Robinson’s original result. Special cases are discussed, including certain ones where the sum of the damping partition numbers ≠4.

The spectrum of Schottky noise in ion storage rings is analyzed as density fluctuations in effectively one-dimensional plasmas. Strong-coupling effects in these plasmas are discussed in relation to experimental observations.

An asymptotic calculation for the electromagnetic fields at frequencies near low-order high-Q morphology-dependent resonances in a large dielectric sphere is reported. Employing local coordinates in the radial and angular directions, our method takes advantage of the special field distribution within the sphere. Closed-form formulas for the resonance frequencies are derived. Our results turn out to be identical with those obtained in recent independent studies in which these formulas are extracted from Mie’s exact solution. Our method is interesting in that it does not require the knowledge of the exact solution to the entire problem and can be extended to fully nonlinear cases.

This paper addresses the question of magnetic energy in mutiply connected domains. It is shown that the magnetic energy must in general include a boundary term that is usually assumed to vanish. The physical interpretation of this term is discussed in terms of de Rham’s theorems.

A statistical-mechanics approach has been recently used to develop a theoretical framework to describe the process of supervised learning and the emergence of generalization ability in layered neural networks. This theory has yielded a powerful tool: a recursion relation that predicts the generalization ability of trained networks as a function of the size of the training set. The recursion relation results from an annealed approximation to the correct quenched averaging over all possible training sets of fixed size. Here we investigate a simple learning problem for which both the quenched and annealed calculations are performed analytically. Comparison between the corresponding results establishes the range of validity of the annealed approximation.

The transmission of information through a nonlinear noisy neuron has been computed with the following results. The mutual information between input and output signals is, in the large-noise limit, rigorously given by the mean-squared variance of the fluctuations of the output of the nonlinear neuron. The changes of synaptic strengths that tend to maximize the mutual information are qualitatively similar to those obtained by Hebbian learning of the nonlinear neuron. If noise is added homogeneously to all inputs, its strength becomes multiplied by the number of synapses leading, even in the presence of weak noise, to a ‘‘noise breakdown,’’ for which all synaptic strengths tend to the same value during learning.

Using Gardner’s approach [J. Phys. A 21, 257 (1988)], we calculate optimal storage of exponentially correlated patterns in neural-network memories.

A quantum-activated rate process in the presence of a nonlinear dissipative environment is studied with a Feynman path-integral technique. The nonlinear dissipation arises from specific nonlinear couplings between the reaction coordinate and a many-dimensional bath of effective harmonic oscillators. Such coupling results in a nonlinear influence functional for the effective Feynman path integral along the reaction coordinate. Large nonlinear effects on the rate constant are found at low temperatures.

Using the Melnikov-function approach, we obtain the threshold condition for the occurrence of Smale-horseshoe chaos in the parametrically driven Duffing oscillator. A detailed description of the homoclinic bifurcation sets in the five-dimensional parameter space involved in the system is provided.