Based on the model of the equilibrium electron beam, the electron cyclotron system (ECS), a unified single-particle approach is developed for the free-electron-maser (gyrotron, cyclotron autoresonance maser, and gyropeniotron) amplifiers. The dispersion equation is derived in detail in terms of the coupling of the ECS with the waveguide field. Unlike the previous model of the beamlet and its treatment, here the variation rate of the perturbed current to the gyroradius is considered. This approach can be used to analyze the gyroradius spread. Results show the existence of the gyropeniotron interaction, even when the gyrotron interaction extinguishes. The gyropeniotron instability is demonstrated to be based on the radial resonance of the electrons with the perturbation fields. The special case of a thin axis-encircling electron beam is discussed, and it is found that the gyrotron instability and the gyropeniotron instability cannot simultaneously appear for the given initial parameters and the azimuthal mode index.

A previously published analysis [J. L. Hirshfield, Phys. Rev. A 44, 6845 (1991)] of the first-order transfer of power into fields of a ${\mathrm{TE}}_{0\mathit{m}}$ rectangular waveguide from a relativistic electron beam carrying spatiotemporal modulation is extended to ${\mathrm{TE}}_{\mathit{l}\mathit{m}}$ modes. Non-axis-encircling orbits, circularly polarized excitations, and competing modes are incorporated into the expanded analysis. Selection rules and phase-matching conditions are found that govern the power transfer; these are shown to allow wave power to increase quadratically with both the interaction length and the dc beam current. Examples of fifth-harmonic conversion are presented for both ${\mathrm{TE}}_{32}$ and ${\mathrm{TE}}_{03}$ modes, the latter in a square waveguide supporting a circularly polarized wave. Power levels of 100 kW or more at 94 GHz appear to be achievable in a conceptual fifth-harmonic device using a 200-kV, 1-A beam. The circularly polarized mode appears to be relatively free of mode competition. Devices with lower beam energies are also shown to be capable of fifth-harmonic operation at 94 GHz, albeit with lower output power than for devices with higher beam energies.

The beam-breakup instability is analyzed for a high-current electron beam transported in an anharmonic ion channel. A multicomponent model of transverse beam motion is used to treat the damping effect of nonlinear focusing. An analytic dispersion relation is obtained, and growth rates are calculated for specific beam and channel profiles. The instability is completely suppressed when a stability criterion obtained from the dispersion relation is satisfied. The analytic results are in good agreement with the results of a particle-simulation code. Nonlinear development of the instability is discussed briefly.

The transverse wake field in a dielectric wake-field accelerator for drive beams with a small nonaxisymmetric component (l≠0) has been calculated in the ultrarelativistic limit. It is found that for the lth azimuthal mode, where l>0, the transverse component is comparable to the longitudinal component. This implies that these devices will be subject to a beam-breakup instability as the drive current becomes large.

With the help of molecular dynamics we study the properties of a string of ions that is confined by an external harmonic potential and that initially is cold in the beam direction but warm in the transverse one. Under the influence of the mutual Coulomb repulsion, intrabeam scattering leads to a flow of energy from the transverse to the longitudinal direction. Depending on the density and the initial transverse temperature ${\mathit{T}}_{\mathrm{\perp }0}$, three regimes can be distinguished: a fast transient increase of the longitudinal temperature ${\mathit{T}}_{\mathrm{\perp }0}$ in a fraction of a betatron period, a slow linear increase in some ten betatron periods, and a fast exponential increase followed by complete thermal equilibration. If ${\mathit{T}}_{\mathrm{\perp }0}$ is large, linear order is lost and thermal equilibrium is postponed to large times. Fourier analyses show that the energy flows into the long-wavelength modes of the collective string excitations. A comparison of calculated heating rates with achievable cooling rates reveals that maintaining linear order in a storage ring is marginal.

As light propagates in an optically inhomogeneous medium, bending and twisting of the beam cause the rotation of the polarization plane. This is the well-known Rytov-Vladimirsky effect or Berry phase. Considering this effect as the result of an interaction between the spin of the photon (polarization) and its orbital motion, one can expect the reverse effect. In fact, the additional angular shift of a trajectory of the circularly polarized beam (CPB) was recently studied for the particular case of an optical fiber. In this paper the spin-orbit interaction Hamiltonian is obtained both in geometrical optics and in wave optics. We have calculated also the effect of the transverse shift of CPB under refraction on the boundary of two media. The expressions for the angular shift of a trajectory of CPB in optical fibers with two types of refractive-index profiles have been obtained. Geometrical optics expressions can be applied for the typical waveguides only at lengths less than 0.05 cm. However, using the geometric optical picture we can successfully describe statistical properties of speckle patterns of laser radiation as it propagates at a considerable distance.

Actual and gedanken experiments aiming to test properties of the Lorentz-Dirac equation are discussed. It is shown that a kind of gedanken experiment, where a charge accelerates in an external field-free region, cannot be carried out in the laboratory. The numerical algorithm utilized for solving the resultant singular problem is discussed.

We study kink-impurity interactions in the ${\mathrm{\phi }}^4$ model, extending our previous results [Zhang Fei, Y. Kivshar, and L. Vázquez, Phys. Rev. A 45, 6019 (1992)] to the case where the kink has an internal degree of freedom which may be excited due to scattering. We demonstrate numerically that the kink may be reflected by an attractive impurity when its velocity lies in some ‘‘windows,’’ and this effect is due to a resonant energy exchange between the kink translational mode, its internal mode, and the impurity mode. We observe additional features in the resonant interactions, e.g., quasiresonances at some intermediate velocities and ‘‘three-bounce’’ resonances. We also develop an analytical approach taking into account three dynamical variables and show that such a collective-coordinate model may explain qualitatively the resonance structures observed in numerical simulations.

An attempt is made to study learning in neural networks with local minima. For small learning parameters η, the transition time from one mimimum to another is asymptotically given by exp(η̃/η), with η̃, a constant independent of η, called the reference learning parameter. A general scheme to calculate the reference learning parameter is presented. This scheme is valid for a large class of learning rules.

It is shown that an ionic channel in biological membranes is a self-organized nonequilibrium dynamic system functioning in a multistable regime. The different components of such a regime can be compared with discrete conductivity levels of the ionic channel. For the case of a channel with two binding sites we have shown that such an effect is a consequence of organization of the conformational channel structure at the expense of the energy of an ion flux itself. The possibility of the control of the channel functioning due to the external electric field is also considered. Calculations show that one may effectively modulate channel lifetimes in their open and closed states using the applied field. It is also shown that the ensemble of channels which mutually interact in a cooperative manner via the bulk solution under the sufficiently strong dependence of the rate constants upon the conformational variable may possess various types of dynamic behavior such as monostability, bistability, and relaxation oscillations.

The initial events of protein folding can be described by the time evolution of a neural network through the use of polymer-kinetics theory, where the fundamental variables are residue contacts. The contact energies are analogous to chemical activation potentials. The resulting recurrent neural network behaves like a partially frustrated spin system interacting with a random external field. A dynamical phase diagram is derived from numerical studies of the model, and the basins of attraction for the network are studied.

We analyze the generalization ability of an iterated-map neural network when an extensive number of patterns is stored through a Hebbian learning mechanism. We show that the model is able to create a concept representative of a set of correlated patterns if a critical minimum number of patterns is presented. This critical number depends on the correlation among the patterns, the slope of the transfer function at the origin, and the ratio between the number of memories and the total number of neurons.

We report the observation of stochastic resonance in a parametrically driven bistable magnetoelastic buckling-ribbon experiment. We have found that the parametric addition of white noise increases the signal-to-noise ratio of the response of the ribbon by 10 to 12 dB relative to that of the ribbon with no externally added noise. We have also observed a characteristic spectrum for the probability of residence times for this weakly bistable system.

We study the fluctuations in the density of time periods of the closed orbits of a model chaotic system. The work is motivated by a similar study on integrable systems [D. Biswas (unpublished)], where the existence of universalities in the fluctuation measures is established. We find that the nearest-neighbor spacing distribution exhibits linear repulsion and is well approximated by a one-parameter additive random matrix model. The spectral rigidity is more revealing and clearly shows that the fluctuations lie between those of Poisson-distributed periods and the Gaussian orthogonal ensemble of matrices. The question of universalities, however, remains open. This study should serve as a guide in settling the issue.

We examine the effect of edges on the random, sequential, irreversible filling of sites on a lattice. In particular, we focus upon the distance that the edge effect propagates into the bulk and how this varies depending upon the length of the filling species for some simple one- and two-dimensional processes on a square lattice. Primary consideration is given to the saturation state. We find that for random n-mer filling, the edge effect propagates approximately 2n to 3n sites into the lattice. Additionally, we find that the effect of an edge will propagate farther along an adjacent edge (in a corner).

The rotating spiral pattern seen in a variety of excitable systems is known to undergo a secondary instability referred to as tip meandering. In the limit of a small (but nonzero) diffusion-constant ratio for a two-component reaction-diffusion model of an excitable medium, we derive the existence of this instability; this requires solving the linear problem defined by expanding about the spiral-core steady-state solution found by Bernoff [Physica D 53, 125 (1991)]. We comment on how these results might lead to a full theory of core meandering.

We show that two successive symmetry breakings can lead to the formation of hybrid topological defects in nonequilibrium systems. A phase-jump line with end points in two-dimensional periodic structures turns out to be a kind of hybrid topological defect. The dynamics of a hybrid defect is also discussed in a variational system.

We show that chaotic dynamics occur in a pair of weakly nonlinear coupled active oscillators when nonisochronism, the dependence of oscillation frequencies on amplitudes, is included. The strange attractor in this system develops from a nearby homoclinic orbit, the same mechanism that leads to chaos in coupled active-passive modes. After analytically determining the most likely parameter region for such a homoclinic orbit, we found the neighboring region of chaos predicted by Shilnikov’s theorem. These coupled oscillators also exhibit multistability and unexpected three-frequency oscillations.

A method for identification of the irreducible cluster of atoms critically involved in inelastic structural alterations has been developed. The method is based on analysis of diagonal minors of the Hessian matrix for the transitory saddle-point configurations of atom clusters. The method provides a basis for handling large amounts of numerical data obtained in detailed atomic-level simulations and leads to a substantial reduction of complexity of involved structural information.

We study the phenomenon of slip length using molecular dynamics and direct simulation Monte Carlo simulations of a dilute gas. Our work extends the range of Knudsen numbers that have been previously studied. In a recent paper, Bhattacharya and Lie [Phys. Rev. 43, 761 (1991)] suggest a logarithmic dependence of slip length on Knudsen number. By a simple redefinition of the mean free path, we obtain good agreement between simulation results and Maxwell theory for slip length. The anomalies seen by Bhattacharya and Lie appear to be due to their definition of the mean free path.