Measurements have been made of electron-impact ionization and excitation of Balmer lines in low-current, steady-state discharges of hydrogen and deuterium. Results were obtained from spatial scans of ${\mathrm{H}}_{\mathrm{\alpha }}$ lines for E/N ranging from 250 Td to 10 kTd. Here E is the electric field, N is the gas density, and 1 Td=${10}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$. Ionization and excitation coefficients versus E/N are presented for E/N between 250 and 1800 Td, and Nd (where d denotes the gap length) between 2.3×${10}^{22}$ and 1.7×${10}^{21}$ ${\mathrm{m}}^{\mathrm{-}2}$. Excitation coefficients obtained for ${\mathrm{H}}_{\mathrm{\alpha }}$ and ${\mathrm{D}}_{\mathrm{\alpha }}$ are placed on an absolute scale using a standard tungsten lamp calibrated against the blackbody radiation standard. The ionization coefficients are compared with previous experimental and theoretical data, while the excitation coefficients are compared with the calculated values.

The plasma heating by radio-frequency (rf) waves in the lower hybrid range of frequency has been studied using Langmuir and magnetic probes and also a Faraday cup. The plasma was confined in a mirror magnetic structure called LISA. It has been shown that the plasma heating rate depends on the resonant volume created by the ambient magnetic field. Also, the plasma potential drops due to the presence of the rf wave. The plasma we have considered was weakly ionized (<1%) due to the presence of a 28-MHz rf source. The quality factor of the machine is comparable to the lower hybrid Landau one.

Time-dependent functions giving distributions over instantaneous values of electron momenta and energies in a laser field are derived. These distribution functions are found for arbitrary values of the ratio of the electron thermal velocity to the electron oscillation velocity. They are necessary in studies of laser-radiation interaction with plasma, laser-plasma x-ray lasers, etc.

The intensity ratio of the electric quadrupole 3${\mathit{p}}^6$3${\mathit{d}}^{10}$-3${\mathit{p}}_{3/2}^5$4${\mathit{f}}_{7/2}$(J=2) line to the electric dipole 3${\mathit{p}}^6$3${\mathit{d}}^{10}$-3${\mathit{p}}_{1/2}^5$4s line is used as a density diagnostic of a highly ionized uranium laser-produced plasma for electron densities of ${10}^{19}$-${10}^{23}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Calculations show that this ratio is insensitive to the plasma temperature in the range of 1000–4000 eV. Self-absorption of the lines is shown to be unimportant in this density range. Experimental line ratios are compared to the predictions of a Ni-like uranium-ion model that includes 138 excited levels. The densities inferred from this analysis applied to a measured line ratio yield densities of (4.0±0.5)×${10}^{22}$ ${\mathrm{cm}}^{\mathrm{-}3}$. This is in good agreement with models of x-ray production in laser-produced plasmas.

This work extends a previous analysis of the x-ray spectrum of a laser-produced uranium plasma [P. Mandelbaum et al., Phys. Rev. A 44, 5752 (1991)] to the longer-wavelength range (3.8<λ<4.4 Å) which includes the 3d-4p transitions. Detailed analysis of the spectrum has been performed using the hullac computer code and the unresolved-transition-array formalism. 3d-4p transitions emitted from ions belonging to the Co-like (${\mathrm{U}}^{+65\mathrm{}}$) through As-like (${\mathrm{U}}^{+59\mathrm{}}$) isoelectronic sequences are identified in the spectrum, in good agreement with the previous analysis of the spectrum emitted at shorter wavelengths.

A self-consistent analysis of wiggler-field errors in free-electron lasers is described using the three-dimensional simulation code wigglin. A random variation is chosen for the pole-to-pole wiggler amplitude, and a continuous map is used between the pole faces. On average, increases in the root-mean-square value of the field causes a decrease in the interaction efficiency; however, this is relatively benign for the specific case studied, and particular error distributions can result in efficiency enhancements.

Discrete quadrupole focusing systems are subject to an electromagnetic instability wherein the growing transverse motion of the beam interacts with the quadrupole field and the ${\mathrm{TE}}_{11}$ waveguide mode. The dispersion relation is derived, which is a matrix equation of infinite dimensions. We show that an appropriately truncated matrix equation is able to give exact growth rates. Furthermore, analytical growth rates are obtained and instability boundaries are established. Numerical solutions of the dispersion relation show that the overall stability properties are not favorable for long-pulse, high-current electron beams. The stability properties of ion beams are also discussed.

A mechanism is proposed for the excitation of solitons in nonlinear dispersive media. The mechanism employs an external pumping wave with a varying phase velocity, which provides a continuous resonant excitation of a nonlinear wave in the medium. Two different schemes of a continuous resonant growth (continuous phase locking) of the induced nonlinear wave are suggested. The first of them requires a definite time dependence of the pumping-wave phase velocity and is relatively sensitive to the initial wave phase. The second employs the dynamic autoresonance effect and is insensitive to the exact time dependence of the pumping-wave phase velocity. It is demonstrated analytically and numerically, for a particular example of a driven Korteweg–de Vries (KdV) equation with periodic boundary conditions, that as the nonlinear wave grows, it transforms into a soliton, which continues growing and accelerating adiabatically. A fully nonlinear perturbation theory is developed for the driven KdV equation to follow the growing wave into the strongly nonlinear regime and describe the soliton formation.

Numerical and analytical methods are used to study a model for the multiple scattering of photons in the presence of randomly reflecting inclusions. The photons are injected into a semi-infinite medium near its surface, and are absorbed by the surface or within the medium. In the medium the photons can diffuse only through voids between the reflecting inclusions, where the void structure has been modeled as a fractal object. Our analytical approach is based on an analogy between the kinetics of a continuous-time random-walk model and the movement of random walkers on fractals. For the case of nonabsorbing media, we find the survival of photons within the medium after n steps to be S(n)∝${\mathit{n}}_{\mathit{w}}^{\mathrm{-}1+1/\mathit{d}}$ and the intensity profile at a distance ρ from the injection point to be Γ(ρ)∝${\mathrm{\rho }}_{\mathit{w}}^{\mathrm{-}\mathit{d}}$, where ${\mathit{d}}_{\mathit{w}}$ is the diffusion exponent for fractals. For the case of absorbing media, Γ(ρ) scales as ${\mathrm{\mu }}^{\mathrm{\theta }}$${\mathrm{\rho }}^{\mathrm{-}\lambda }$ exp(-γ${\mathrm{\mu }}_{\mathit{w}}^{1/\mathit{d}}$ρ), where μ is the absorption coefficient of the fractal medium, θ and λ are exponents related to the fractal dimensions, and γ is a constant. We also calculate the mean time and the average maximal depth of photons that emerge at a distance ρ.

The force-free magnetic-field condition ∇×H=αH is expressed in terms of a flux function Ψ; α is then also a function of Ψ, and with suitable restrictions the resulting equations can be separated and solved. The case of spherical coordinates yields four sets of solutions that are shown to be dependent and equivalent to a simple generalization of those given by Chandrasekhar [Proc. Natl. Acad. Sci. U.S 42, 1 (1956)]. Similarly, the case of cylindrical coordinates results in a generalization of the solution given by Furth, Levine, and Waniek [Rev. Sci. Instrum. 28, 949 (1957)].

The objective of this paper is the establishment of a formal theory of the scattering of time-harmonic electromagnetic waves from impenetrable, immobile obstacles, with given linear, homogeneous, and generally nonlocal, boundary conditions of Leontovich (i.e., impedance) type for the wave on the obstacle’s surface ∂Ω. As in an analogous treatment of acoustic-wave diffraction by the author [G.E. Hahne, Phys. Rev. A 43, 976 (1991); 43, 990 (1991)], the theory is modeled on the theory of the complete Green’s function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. For each nonzero free-space wave number ${\mathit{k}}_0$, the electromagnetic field is described kinematically in terms of a six-component entity comprising the direct sum of the electric and the magnetic three-vector field at each point of position space; an electromagnetic source is described correspondingly as a six-component entity comprising the direct sum of the time-harmonic electric and magnetic current distributions. Accordingly, the Green’s function and the T operator are 6×6 matrices of two-point, complex-valued, ${\mathit{k}}_0$-dependent functions.

A simplified expression is obtained for the T operator for a general case of nonlocal, homogeneous Leontovich boundary conditions for the electromagnetic wave on ∂Ω. Analogous to the acoustic case, all the nonelementary operators that enter the expression for the T operator are formally simple, rational algebraic functions of a certain invertible, linear, ${\mathit{k}}_0$-dependent operator Z${\mathrm{̆}}_{\mathit{k}0}^{+}$, which is called the radiation impedance operator; Z${\mathrm{̆}}_{\mathit{k}0}^{+}$ is an operator of the class that maps the linear space of complex tangent-vector fields on ∂Ω onto itself. The nonlocal operator Z${\mathrm{̆}}_{\mathit{k}0}^{+}$ is defined only implicitly, in that, apart from a simple transformation made for technical reasons, it is the operator that maps the tangential magnetic field on ∂Ω of an outgoing-wave solution to the source-free Maxwell equations into the uniquely corresponding tangential electric field.

The paper concludes with a derivation of an expression for the differential scattering cross section for plane electromagnetic waves in terms of certain matrix elements of the T operator for the obstacle, and a proposal for a class of Leontovich boundary conditions that, if realized, would yield exactly zero scattering amplitude at a given ${\mathit{k}}_0$. There are four appendixes: The first appendix recapitulates the theory of the free-space Green’s function for the time-harmonic Maxwell field and the relationship of this Green’s function to certain linear functional operators defined on the space of tangent-vector fields on the obstacle’s boundary. The second appendix establishes mathematical conditions on the defining operators for the Leontovich boundary conditions, which conditions are sufficient to guarantee the uniqueness and existence of the complete Green’s function, and reciprocity for the Green’s functions of purely outgoing-wave type. The third appendix argues that any of a certain class of time-harmonic, linear electromagnetic scattering problems admits to a partial decoupling into a separate problem for the region interior and the region exterior to a dividing surface; a complete set of interior solutions determines exactly one equivalence class of Leontovich boundary conditions for the exterior electromagnetic field, so that the solution of a scattering problem then reduces to a problem in functional analysis in the space of tangent-vector fields on the dividing surface, as described in the main part of the paper. The fourth appendix describes a linear network analog to the formal scattering theory established herein.

It is shown how the dynamics of a discrete-time leaky-integrator (time-summating) neural network with quantal synaptic noise may be formulated in terms of a random iterated function system. Conditions are derived for which the limiting behavior of the system is described by an invariant probability measure on the space of membrane potentials. Such an invariant measure typically has a fractal-like structure, which is illustrated by a simple example of a single neuron with inhibitory feedback. The effects of synaptic noise on the response characteristics of the neuron are also considered. Finally, learning in networks with synaptic noise is discussed.

Recently Corvera, Laradji, and Zuckermann (unpublished) showed that the multistate lattice model due to Pink, Green, and Chapman [Biochemistry 20, 6692 (1981)] with parameters obtained from fitting to thermodynamic data for saturated phospholipid bilayers does not exhibit a phase transition but could instead be described in terms of short-range fluctuations close to a critical point. We have extended the Pink-Green-Chapman model by including hydrophobic mismatch interactions between the lipid acyl-chain conformational states. We used Monte Carlo techniques to examine the phase behavior of the extended model and found that it exhibits first-order phase transitions above a critical value of the mismatch parameter. The results are discussed in relation to previous theoretical work as well as experimental measurements on lipid bilayers.

We report a detailed analytical and numerical model study of pattern formation during the development of visual maps, namely, the formation of topographic maps and orientation and ocular dominance columns in the striate cortex. Pattern formation is described by a stimulus-driven Markovian process, the self-organizing feature map. This algorithm generates topologically correct maps between a space of (visual) input signals and an array of formal ‘‘neurons,’’ which in our model represents the cortex. We define order parameters that are a function of the set of visual stimuli an animal perceives, and we demonstrate that the formation of orientation and ocular dominance columns is the result of a global instability of the retinoptic projection above a critical value of these order parameters. We characterize the spatial structure of the emerging patterns by power spectra, correlation functions, and Gabor transforms, and we compare model predictions with experimental data obtained from the striate cortex of the macaque monkey with optical imaging. Above the critical value of the order parameters the model predicts a lateral segregation of the striate cortex into (i) binocular regions with linear changes in orientation preference, where iso-orientation slabs run perpendicular to the ocular dominance bands, and (ii) monocular regions with low orientation specificity, which contain the singularities of the orientation map. Some of these predictions have already been verified by experiments.

A two-layer feedforward network of McCulloch-Pitts neurons with N inputs and K hidden units is analyzed for N→∞ and K finite with respect to its ability to implement p=αN random input-output relations. Special emphasis is put on the case where all hidden units are coupled to the output with the same strength (committee machine) and the receptive fields of the hidden units either enclose all input units (fully connected) or are nonoverlapping (tree structure). The storage capacity is determined generalizing Gardner’s treatment [J. Phys. A 21, 257 (1988); Europhys. Lett. 4, 481 (1987)] of the single-layer perceptron. For the treelike architecture, a replica-symmetric calculation yields ${\mathrm{\alpha }}_{\mathit{c}}$∝ √K for a large number K of hidden units. This result violates an upper bound derived by Mitchison and Durbin [Biol. Cybern. 60, 345 (1989)]. One-step replica-symmetry breaking gives lower values of ${\mathrm{\alpha }}_{\mathit{c}}$.

In the fully connected committee machine there are in general correlations among different hidden units. As the limit of capacity is approached, the hidden units are anticorrelated: One hidden unit attempts to learn those patterns which have not been learned by the others. These correlations decrease as 1/K, so that for K→∞ the capacity per synapse is the same as for the tree architecture, whereas for small K we find a considerable enhancement for the storage per synapse. Numerical simulations were performed to explicitly construct solutions for the tree as well as the fully connected architecture. A learning algorithm is suggested. It is based on the least-action algorithm, which is modified to take advantage of the two-layer structure. The numerical simulations yield capacities p that are slightly more than twice the number of degrees of freedom, while the fully connected net can store relatively more patterns than the tree. Various generalizations are discussed. Variable weights from hidden to output give the same results for the storage capacity as does the committee machine, as long as K=O(1). We furthermore show that thresholds at the hidden units or the output unit cannot increase the capacity, as long as random unbiased patterns are considered. Finally we indicate how to generalize our results to other Boolean functions.

The effective-field model for the dynamics of DNA polymer in solution has been extended to include the effect of monovalent counterions surrounding the polymer. The effect of site-bound counterions as compared to the area-bound counterions has been included specifically by explicitly introducing degrees of freedom for the counterions associated with a monomer and coupling these to the DNA degrees of freedom via appropriate interactions. Stability of the system for all vibrational modes was used as a criterion to find possible equilibrium positions of the site-bound counterions. The normal-mode spectrum of DNA homopolymer poly(dA)-poly(dT) with different monovalent counterion species is calculated. Based on an analysis of the eigenvectors, a mode around 25 ${\mathrm{cm}}^{\mathrm{-}1}$ is found to have a strong plasmonlike character, i.e., a large electric dipole moment associated with longitudinal collective oscillations of the DNA-water-counterion system. Further analysis of eigenvectors with strong counterion motion gives information about effective force constants binding counterions to the polymer backbone. The effect of varying counterion species and the degree of the site-bound character of counterions was also investigated by examining the variation of frequencies of various modes with similar characteristic motions.

The Ornstein-Zernike equation is used to analyze adsorption at, and the forces between, solutes and walls in near-critical fluids. The density profile is shown to decay exponentially with the bulk correlation length. The forces between solutes and between walls are also exponentially long ranged with the bulk correlation length, and are always attractive for identical solutes.

In this paper we study directed polymers in (1+1)-dimensional random media with special emphasis on P(x,t), the probability distribution to reach a transverse distance x for a polymer of length t. P(x,t) follows the scaling form P(x,t)∼〈${\mathit{x}}^2$(t)${\mathrm{〉}}^{\mathrm{-}1/2}$f(ξ), where 〈${\mathit{x}}^2$(t)〉 is the transverse mean-square displacement, which asymptotically obeys 〈${\mathit{x}}^2$(t)〉∼${\mathit{t}}^{4/3}$, and ξ is the scaling variable ξ=x/〈${\mathit{x}}^2$(t)${\mathrm{〉}}^{1/2}$. The numerical results indicate that f(ξ)≃exp(-c${\xi }^{\mathrm{\delta }}$), where the exponent δ evolves with ξ such that δ≃2 for ξ→0 and δ≳2.5 for ξ≫1, demonstrating an ‘‘enhanced’’ Gaussian behavior. We discuss these results in the context of enhanced diffusion.

It is argued that one should expect a fluid of symmetrically charged hard spheres (the restricted primitive model) to have an Ising-like critical point. It is further noted that the presence of a repulsive ${\mathit{r}}^{\mathrm{-}4}$ ion-ion interaction term (of the sort found in real ionic systems as a result of solvent-averaged ion-dipole-ion interaction) will prevent such a critical point from developing, although competing terms that suppress its effect may also be present in real electrolytes.

We apply the lattice-gas cellular automata of Frisch, Hasslacher, and Pomeau [Phys. Rev. Lett. 56, 1505 (1986)] to the problem of modeling non-Newtonian fluids. Using an approach based on Hénon’s work, we calculate the extensional viscosity of a lattice gas. We then propose a simple model of suspended particles and a model of interparticle forces within the lattice-gas framework. We calculate the shear and extensional viscosities for each of these models.