We reconsider the theory of pulse propagation in free-electron lasers operating with arbitrary gain. We show that the dynamics can be accounted for by collective longitudinal excitations of supermode type and discuss their properties. We study the interplay between the optical-packet longitudinal dimension and the electron-beam energy spread, along with the induced gain depression. Semianalytical formulas for the gain, pulse length, etc., are presented.

Both the Raman, coherent Compton, and Compton regimes of high-gain ion-ripple Lasers (IRL’s) are studied. The IRL works by coupling a negative-energy beam wave (or ponderomotive potential) to an electromagnetic wave by means of the ion ripple (backward Raman scattering or backward coherent Compton scattering) or by amplification of an em wave by negative Landau damping (backward Compton scattering). By employing fluid theory, the dispersion relation for wave coupling is derived and used to calculate the radiation frequency and linear growth rate. The nonlinear saturation mechanism is explored. A multidimensional (one dimension in space, three dimensions in momenta and fields) particle-in-cell simulation code was developed to verify the ideas, scaling laws, and nonlinear mechanisms. The effect of momentum spread is also studied; there is a slow decrease in the growth rate and efficiency as well as broadening of the radiation spectrum. This scheme may provide tunable sources of coherent high-power radiation. By proper choice of device parameters, sources of microwaves, optical, and perhaps even x rays can be made. An ion ripple in a plasma can provide a very short undulator wavelength (e.g., ∼${10}^{\mathrm{-}2}$ cm) and strong dc electric fields (e.g., ∼${10}^{10}$ V/m; equivalent to a magnetic field of 30 T). The plasma also produces an ion channel that provides guiding of electron and laser beams. The IRL’s may generate high-power (e.g., >1 MW), coherent, short-wavelength photons with relatively low beam energy (e.g., ∼10 MeV) and possibly low beam quality requirement. The availability of tunable sources for wide wavelength regimes, coherence and high power, as well as lower cost and simplicity of equipment are emphasized.

We present an analytic expression of the harmonic bunching produced by the dispersive section of a free-electron laser (FEL) optical klystron operating in the high-gain exponential regime. This model allows the evaluation of the operating constraints and limits, the possible optimizations and advantages of such a device with respect to the conventional FEL configuration, i.e., shortening of the overall length and reduction of the induced energy spread, provided that the initial energy spread is smaller than the one required for the normal high-gain FEL operator. The analytical expressions derived here are confirmed by the numerical solution of the full nonlinear set of equations for the FEL.

It is demonstrated that an external ac field may support stable propagation of solitons and cnoidal waves in a chain of interacting particles in the presence of friction, provided that the drive amplitude exceeds a certain threshold value. The effect is analyzed in the general form, and is then considered in detail both for the Toda lattice with weak friction and for a string of hard beads with arbitrary friction. The effects disappears in the continuum limit.

We study how well perceptrons learn to solve problems for which there is no perfect answer (the usual case), taking as examples a rule with a threshold, a rule in which the answer is not a monotonic function of the overlap between question and teacher, and a rule with many teachers (a ‘‘hard’’ unlearnable problem). In general there is a tendency for first-order transitions, even using spherical perceptrons, as networks compromise between conflicting requirements. Some existing learning schemes fail completely–occasionally even finding the worst possible solution; others are more successful. High-temperature learning seems more satisfactory than zero-temperature algorithms and avoids ‘‘overlearning’’ and ‘‘overfitting,’’ but care must be taken to avoid ‘‘trapping’’ in spurious free-energy minima. For some rules examples alone are not enough to learn from, and some prior information is required.

Following similar work in polaron theory, Davydov has proposed soliton formation and propagation as a mechanism for energy storage and transport in proteins. This paper deals with the energetics of soliton disappearance and is of interest for polaron theory as well. A semiclassical Davydov model is used, for which exact wave functions can be determined. The results in a special case equal those obtained with the full quantum-mechanical model. Monte Carlo simulations show that thermal destabilization is not associated with transitions to exciton states, as is usually assumed in the literature, and that it involves instead disordered states with energies intermediate between those of the minimum energy soliton state and those of the exciton states. At biological temperatures, the Davydov system exhibits ‘‘universal’’ (i.e., parameter independent) behavior.

The human erythrocyte readily changes its shape in response to mechanical stress. Geometrical methods are used to analyze this effect in three experiments: thermal shape fluctuation (flicker), electrodeformation, and tank treading, which is the circulation of the membrane around the interior fluid in a shear flow. Comparison with existing data indicates that both flicker and tank treading represent the motion of a fluid membrane. At the same time it is a solid membrane (i.e., possessing a shear modulus) that resists large-scale shape change. This combination of fluid and solid membrane properties is in some ways paradoxical.

In the search for networks that implement the winner-take-all function dynamically in a robust way, we study in this paper a class of models that includes short-range diffusive interactions. The analysis is based on a combination of numerical simulations and analytic results obtained by the application of field-theoretical methods. An examination of the ground-state properties reveals that the implementation of robust competition in dimensions higher than one requires a nonstandard diffusive interaction of at least fourth order.

The statistical mechanics of two-layered perceptrons with N input units, K hidden units, and a single output unit that makes a decision based on a majority rule (Committee Machine) are studied. Two architectures are considered. In the nonoverlapping case the hidden units do not share common inputs. In the fully connected case each hidden unit is connected to the entire input layer. In both cases the network realizes a random dichotomy of P inputs. The statistical properties of the space of solutions as a function of P is studied, using the replica method, and by numerical simulations, in the regime where N≫K. In the nonoverlapping architecture with continuously varying weights the capacity, defined as the maximal number of P per weight, (${\mathrm{\alpha }}_{\mathit{c}}$) is calculated under a replica-symmetric (RS) ansatz. At large K, ${\mathrm{\alpha }}_{\mathit{c}}$ diverges as ${\mathit{K}}^{1/2}$ in contradiction with the rigorous upper bound, ${\mathrm{\alpha }}_{\mathit{c}}$<C lnK, where C is a proportionality constant, derived by Mitchison and Durbin [Biol. Cybern. 60, 345 (1989)]. This suggests a strong replica-symmetry-breaking effect.

The instability of the RS solution is shown to occur at a value of α which remains finite in the large-K limit. A one-step replica-symmetry-breaking (RSB) ansatz is studied for K=3 and in the limit K goes to infinity. The results indicate that ${\mathrm{\alpha }}_{\mathit{c}}$(K) diverges with K, probably logarithmically. The occurrence of RSB far below the capacity limit is confirmed by comparison of the theoretical results with numerical simulations for K=3. This symmetry breaking implies that unlike the single-layer perceptron case, the space of solutions of the two-layer perceptron breaks, beyond a critical value of α, into many disjoint subregions. The entropies of the connected subregions are almost degenerate, their relative difference being of order 1/N. In the case of a nonoverlapping Committee Machine with binary, i.e., ±1 weights, ${\mathrm{\alpha }}_{\mathit{c}}$≤1 is an upper bound for all K. The RS theory predicts ${\mathrm{\alpha }}_{\mathit{c}}$=0.92 for K=3 and ${\mathrm{\alpha }}_{\mathit{c}}$=0.95 for the large-K limit.

The theoretical prediction (for K=3) is in excellent agreement with the numerical estimate based on an exhaustive search in the space of solutions for small N. These results indicate that in the binary case there is no RSB in the space of solutions below the maximal capacity. In the fully connected architecture, the solution’s phase space has a global permutation symmetry (PS) reflecting the invariance under permuting the hidden units. The order parameters that signal the spontaneous breaking of this symmetry are defined. The RS theory shows that for small α the PS is maintained. For larger values of α<${\mathrm{\alpha }}_{\mathit{c}}$ the symmetry is broken, inplying the breaking of the solution space into disjoint regions. These regions are related by permutation symmetry, hence they are fully degenerate with respect to their entropies and statistical properties. This prediction has been tested by simulations of the K=3 case, calculating the order parameters by random walks in the space of solutions. They yield good evidence for existence of a phase with broken permutation symmetry at values of α≥2. Finally, both theory and simulations show that for a typical fully connected network the connections joining the same input to a pair of hidden units are negatively correlated.

In a recent paper, Bartelt and Privman [Phys. Rev. A 44, R2227 (1991)], presented an exact solution for the kinetics of a random sequential adsorption on a continuous one-dimensional line of a mixture of fixed-size and pointlike particles. We derive the asymptotic law for the coverage in arbitrary dimension D for this mixture. We show that the result for the one-dimensional system is specific and different from the general formula for D≥2.

The sensitivity of chaotic systems to small perturbations can be used to rapidly direct orbits to a desired state (the ‘‘target’’). We formulate a particularly simple procedure for doing this for cases in which the system is describable by an approximately one-dimensional map, and demonstrate that the procedure is effective even in the presence of noise.

The growth of interfaces in a discrete solid-on-solid model driven by quenched random fields have been simulated in (1+1) dimensions. It is found that the interface width initially grows with time t as ${\ln }^2$(t), and with a power law ${\mathit{t}}^{1/2}$ for long times. The crossover time increases sharply with increasing randomness.

Considering one-dimensional diffusion as a sequence of exchange processes between occupied and vacant sites, the long-time limit of the mean-square displacement of the diffusants is shown to be easily calculable as the net effect of the random walk of the vacancies.

The phase-slip process, which occurs as the instantaneous variation of the phase of the order parameter on a multiple of 2π for one-dimensionally distributed systems, is studied in detail. The general analytical results are supplemented by a computer simulation of the phase-slip process for the case of the Ginzburg-Landau equation.

An effect of polymers on vorticity of a fluid was offered as a possible explanation of turbulent drag reduction [Y. Rabin and B. J. A. Zielinska, Phys. Rev. Lett. 63, 512 (1989)]. We show that this effect is attributable to the increased viscosity due to the polymers. We note another effect that may be relevant for drag reduction.

A numerical scheme has been introduced and implemented for realizing the zero-noise limit in discrete Laplacian growth processes such as diffusion-limited aggregation and dielectric breakdown. The results clearly demonstrate the possibility of branching in the absence of noise. The formalism provides essentially exact results that can be compared with future experimental, numerical, and theoretical studies.

We discuss an electrochemical effect involving laser ablation of metals in a gas environment of ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, or ${\mathrm{H}}_2$O and the subsequent interaction of metal atoms with these gases to form hydrides and oxides. Under a suitably applied electric field in the cell during ablation, the hydride and oxide particles collect on one of the electrodes to form a macroscopic dendritic aggregation directly from the gas phase. Laser ablation followed by coagulation produces electrically neutral oxide and hydride aerosol particles, which have permanent electric dipole moments. The dendritic aggregation is due to the migration of these electric dipoles in a spatially varying electric field.

In the present work we perform analytical and numerical investigations on the conditions under which there occurs stochastic exchange of energy between unidirectionally magnetized electrons and perpendicular electromagnetic waves that propagate with ordinary-mode polarization. It is observed that for low amplitudes of the fluctuating field, the electronic dynamics is essentially regular for small initial energies. On the other hand, for larger energies, the dynamics may be chaotic. It is also shown that stochastic energy excursions may be larger than resonant ones.

The transient motion of dissipative systems depends on the eigenvalues of the Jacobian of the map representing the system. In the high bifurcation limit of period-doubling systems, these eigenvalues approach universal curves in the period-doubling interval. We calculate these curves for two-dimensional iterative maps and compare with experimental measurements of the eigenvalues.

The Q-state Potts model of neural networks, extended to include biased patterns, is studied for extensive loading α. Within the replica-symmetric approximation, mean-field equations are written down for general Q and arbitrary temperature T. The critical storage capacity is discussed for Q=3 and two classes of representative bias parameters. The complete T-α phase diagram is presented. A tricritical point is found in the spin-glass transition for Q>6, depending on α. Contrary to the Hopfield model, the critical lines do not converge to the same T as α→0. A stability analysis is made.