A precise interpretation of oblique collisions of plane ion-acoustic solitons in a double-plasma device is given for clarifying the mechanisms of resonant interaction of solitons. The amplitude increment of the new waves produced by the interaction of two waves is shown to be different, depending on whether the two waves have linear or nonlinear natures.

Parameters of an electron component of plasma produced by two types of the gas-discharge arc sources (V. I. Davidenko et al., Sov. Phys. Tech. Phys. 28, 160 (1983) [Zh. Tekh. Fiz. 53, 258 (1983)]; G. I. Dimov, A. A. Ivanov, and G. V. Roslyakov, Sov. J. Plasma Phys. 8, 546 (1982) [Fiz. Plazmy 8, 970 (1982)]) are given. An analysis is made of the hypothesis [E. V. Shun’ko, Phys. Lett. A 147, 37 (1990)] that under special conditions, related to the configurations of these sources, the isotropic thermal motion of plasma electrons is stratified into separate localized electron currents due to a filamentation, its mechanism being similar to the current instability.

The dynamic properties for electrons in the localized coherent Langmuir wave fields have been investigated numerically. The Poincaré map and the absolute diffusion coefficient account for the existence of regular islands embedded within stochastic regions of phase space. The relative diffusion behavior illustrates that the localized coherent Langmuir wave packets can lead to the formation of a microscale correlation for electrons in phase space. The time evolution of relative quantities further shows that such a microscale correlation has the characteristic of phase-space particle-density granulations, although the electric fields are regular. Finally, the two-point correlation function has been measured by use of the particle simulation technique. That the strong peak behavior of the correlation function can occur only for sufficiently small ${\mathit{r}}^0$ and ${\mathit{u}}^0$ has been displayed by the simulated results. All these phenomena indicate that the microscale correlation effects (defined also as ‘‘clumps’’) indeed exist in our dynamic system.

We describe a nonperturbative numerical technique for solving the Hamilton-Jacobi equation of a nonlinear Hamiltonian system. We find the time-periodic solutions that yield accurate approximations to invariant tori. The method is suited to the case in which the perturbation to the underlying integrable system has a periodic and not necessarily smooth dependence on the time. This case is important in accelerator theory, where the perturbation is a periodic step function in time. The Hamilton-Jacobi equation is approximated by its finite-dimensional Fourier projection with respect to angle variables, then solved by Newton’s method. To avoid Fourier analysis in time, which is not appropriate in the presence of step functions, we enforce time periodicity of solutions by a shooting algorithm. The method is tested in soluble models, and finally applied to a nonintegrable example, the transverse oscillations of a particle beam in a storage ring, in two degrees of freedom. In view of the time dependence of the Hamiltonian, this is a case with ‘‘21/2 degrees of freedom,’’ in which phenomena like Arnol’d diffusion can occur.

A singular system with primary and secondary constraints of the second kind is investigated by two different methods, and exact agreement is observed.

Using a nonorthogonal helical coordinate system, we obtain exact free-space solutions for both the Helmholtz and paraxial Helmholtz equations. At optical frequencies the helical Helmholtz solutions can be interpreted as helical beams characterized by a constant pitch angle and beam radius. These solutions are shown to be generalizations of the family of scalar nondiffracting beams known as Bessel beams. They are similar to Bessel beams in some ways, such as an invariant intensity distribution profile in any plane normal to their axis of propagation, but have a nonconstant order. The paraxial helical Helmholtz equation is cast into two different forms, one assuming propagation along the helical axis and one assuming propagation along the original cylindrical axis. The first is solved using a paraxial form of the above helical beam family while a solution of the second form is a helical Gaussian.

The fractal character of fracture surfaces of thick-walled pressure vessels produced in the final fast fracture that terminates low-cycle-fatigue tests is compared with that of fracture surfaces produced in Charpy impact tests in samples of the same high-strength and -toughness steel (ASTM A723) alloy. Slit island analysis yielded fractal dimensions near 1.25 for the Charpy specimens, which is typical of high-strength steel alloys previously studied; however, extremely high fractal dimensions near 1.40 were determined for the low-cycle-fatigue specimens. The distributions of island and lake areas and of island and lake perimeters on random sections exhibit hyperbolic distributions analogous to those found for geographic islands and lakes.

Motivated by the perturbative dynamic renormalization-group analysis of Wolf [Phys. Rev. Lett. 67, 1783 (1991)], who recently examined Villain’s anisotropic generalization of the noisy Burgers equation appropriate to the kinetic roughening of vicinal surfaces [J. Phys. (Paris) I 1, 19 (1991)], we have performed extensive numerical simulations of this stochastic partial differential equation in an attempt to investigate Wolf’s claim of logarithmic, rather than algebraic, roughness. Our work provides direct confirmation of his dramatic predictions, complementing the evidence provided by simulations of various microscopic growth models.

For the problem of a two- and three-dimensional deterministic sandpile automaton, analytical formulas are derived which express the relation between the period of an attracting orbit and the number of grain spillings in the self-organized critical state. Numerical results for lattices up to sizes 19×19 and 9×9×9 are given. A generalization to lattices in arbitrary dimensions is also presented.

We have discovered substructures consisting of branches at each step of the devil’s staircase of the sine circle map. These substructures are found to follow the hierarchy of the Farey tree. We develop a formalism to relate the rational winding number W=p/q to the number of branches in these substructures.

Some theorems relating the Dirac δ function to both Fermi and Bose distributions are presented in this paper. Several potential applications of these theorems are discussed in detail. In particular, an inverse problem for determining the density of states of Fermi systems is solved with a closed-form expression.

A two-dimensional cellular pattern (lattice) created by electrohydrodynamic convection of a nematic liquid crystal exhibits limit cycle oscillations. We found a localized target pattern of wave fronts emitted from a self-organized oscillating center. The localized structure has a life cycle: it arises from a uniform state, grows, and collapses from nucleating defects at its center. This phenomenon is caused by an interaction between the waves and deformations of the underlying lattice, and is different from that in localized traveling waves.

The stability of two-dimensional well-defined needle growth is considered beyond the perturbative approach, until singularity formation, when surface tension may no longer be neglected. The needle growth is shown to be represented by the development of a single dominant Fourier mode, and the conditions under which all other modes are negligibly small, and not influenced by this dominant one, are derived. The dominant mode divides the Fourier spectrum into two parts with different criteria for stability. It is shown that for modes higher than the dominant one the initial smoothness (i.e., the decay of the Fourier spectrum with wave numbers) should be at least exponential for needle stability, whereas for modes lower than the dominant one the condition for stability is more restrictive in that the initial law of decay should be faster than Gaussian.

The hexagonal cell parameter a of the system sodium dodecyl lauryl sulfate and water as a function of volume concentration ${\mathit{c}}_{\mathit{v}}$ in phase ${\mathit{H}}_{\mathrm{\alpha }}$ shows the functional behavior expected for micelles of finite length: a∝${\mathit{c}}_{\mathit{v}}^{\mathrm{-}1/3}$. The interpretation of x-ray data based on finite micelles leads to an alternative description of the hexagonal phase ${\mathit{H}}_{\mathrm{\alpha }}$: spherocylindrical micelles of constant radius with length that may grow along the range of the ${\mathit{H}}_{\mathrm{\alpha }}$ phase. Results are compared with recent statistical-mechanical calculations for the isotropic I-${\mathit{H}}_{\mathrm{\alpha }}$ transition. The absence of diffraction in the direction perpendicular to the hexagonal plane is ascribed to polydispersity of micellar length, which also is a necessary condition for the occurrence of direct I-${\mathit{H}}_{\mathrm{\alpha }}$ transitions.

Considering the standard Landau model we demonstrate that the phase diagrams for the lock-in to the uniform and dimerized ordering contain a class of periodic configurations. They are formed as sequences of local commensurate and incommensurate modulation. The simplest representatives are calculated numerically. Being stable in narrow ranges of the control parameters, these configurations might be the source of global hysteresis and memory effects frequently seen in particular systems.

We (i) describe the complete ${\mathrm{Li}}^{+}$-adduct mass spectrum of the ${\mathrm{CH}}_4$ microwave discharge plasma, obtained by ion attachment techniques, (ii) give evidence that many radicals are produced in the plasma, and (iii) present a preliminary spectral identification analysis. The identified species are ${\mathrm{C}}_{\mathit{n}}$${\mathrm{H}}_{2\mathit{n}\mathrm{-}1}$ (n=2–13), ${\mathrm{C}}_{\mathit{n}}$${\mathrm{H}}_{2\mathit{n}+1\mathrm{}}$ (n=2–13), ${\mathrm{C}}_{\mathit{n}}$${\mathrm{H}}_{\mathit{n}}$ (n=2,4,5,6), and so on.

The Fokker-Planck equation for a magnetic well with neutral-beam pumping is rigorously solved under the assumption of a Maxwellian field-particle distribution, using the separable variables and moment approach. The results agree with the numerical code within 20% even if the pumping effect is strong. This method is applicable to a variety of cases, as long as the isotropic field-particle distribution function is adopted.

Laser acceleration of electrons is considered. A general formulation of the problem is developed that would allow the recently proposed accelerator based on nonlinear amplification of inverse bremsstrahlung electron acceleration (NAIBEA) to function with any state of polarization and shape of the laser pulse, and any kind of applied field. Analytical estimates as well as numerical analysis for the case of an applied magnetic field are made. It is found that electrons, injected with few tens of mega-electron-volts, can be accelerated to giga-electron-volt energies using a NAIBEA accelerator of a length of few meters.

A free-electron laser was configured as an autoaccelerator to test the principle of accelerating electrons by stimulated absorption of radiation (λ=1.65 mm) by an electron beam (750 kV) traversing an undulator. Radiation is produced in the first section of a constant period undulator (${\mathit{l}}_{\mathit{w}1}$=1.43 cm) and then absorbed (∼40%) in a second undulator, having a tapered period (${\mathit{l}}_{\mathit{w}2}$=1.8–2.25 cm), which results in the acceleration of a subgroup (∼9%) of electrons to ∼1 MeV.

The effect of intrinsic fluctuations in systems exhibiting deterministic chaos is analyzed. It is suggested that the conclusions of the recent series of papers by Fox and Keizer [Phys. Rev. Lett. 64, 249 (1990); Phys. Rev. A 41, 2969 (1990); 42, 1946 (1990); 43, 1709 (1991)] on the breakdown of the deterministic description need to be reassessed.