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Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.
This paper is concerned with analyses of nonlinear waves in solid propellant rockets. Most attention is given to an approximate technique which inexpensively provides results which appear to be quite accurate at least up to amplitudes of ten percent. The connection with linear stability analysis is shown. Primarily to study nonlinear stability, or triggering, the method is extended to third order in the amplitude of wave motion; no explicit results have been obtained. Application of the approximate method to the behavior of pulses is described.
Two fluid model for laminar shocks and other nonlinear waves in warm plasmas
A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.
Two-stream and cross-stream effects on nonlinear wave stability with shock in collisionless plasma
Summaries are presented of research in basic plasma physics. Nonlinear waves and shock-like phenomena were studied which are pertinent to space physics applications, and include specific problems of magnetospheric and solar wind plasma physics.
One dimensional solution of nonlinear waves of rate sensitive, elastoplastic material
An investigation of the evolution of strongly nonlinear, low frequency (ion gyrofrequency), parallel propagating wave packets in a dispersive, collisionless, and low beta(= 8piP/B-squared = 0.3) plasma is undertaken using a hybrid numerical code. These strongly nonlinear wave packets have a transverse magnetic field strength, or wave amplitude, which is of order or greater the field strength along the direction of propagation, and their evolution can differ qualitatively from that of weakly nonlinear packets. The development of spreading fast wave (right helicity) and rarefraction regions competes strongly with steepening, and leads to a long time waveform which differs greatly from that for weak nonlinearity. Results are used to suggest that strongly nonlinear wave evolution occurs frequently in the earth's foreshock.
The mechanisms responsible for the transition of the circumpolar flow from its normal midwinter state to the preconditioned state that should evolve before a wavenumber-2 major warming are investigated, through a combination of observational, numerical and theoretical studies. Observations of Eliassen-Palm flux cross sections indicate that while wave zonal mean flow interaction theory could account for the qualitative evolution of the circumpolar flow during the warming, substantial nonlinear wave interactions were active during the cooling period, and these interactions significantly influenced the evolution of the circumpolar flow. Numerical experiments employing a truncated, semispectral model indicate that this cooling phenomenon is realistically reproducible in an idealized integration in which wave-wave interactions are present. Two different mechanisms are proposed to account for these nonlinearities.
We present results of the workshop's benchmark problems of the category 2. This category of problems is designed to test the nonlinear wave propagation properties of a computational scheme. We chose three high order spatially accurate algorithms for our computations. These are the Dispersion- Relation- Preserving (DRP) scheme proposed by Tam and his colleagues, a fourth order extension of the MacCormack scheme proposed by Gottlieb and Turkel and an Essentially Non Oscillatory (ENO) scheme proposed by Shu and Osher.
Three common finite difference schemes are used to examine the computation of one-dimensional nonlinear wave propagation. The schemes are studied for their responses to numerical parameters such as time step selection, boundary condition implementation, and discretization of governing equations. The performance of the schemes is compared and various numerical phenomena peculiar to each is discussed.
A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Wave equations coverning evolution of long nonlinear axially symmetric wave motion in inviscid rotating fluids
Solution of two fluid magnetohydrodynamic equations as nonlinear ionic waves providing mechanism for cosmic rays generation and for plasma penetration of magnetosphere
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.
The problem of vacillation in a baroclinically unstable flow field is studied through the time evolution of a single nonlinearly unstable wave. To this end a computer code is being developed to solve numerically for the time evolution of the amplitude of such a wave. The final working code will be the end product resulting from the development of a heirarchy of codes with increasing complexity. The first code in this series was completed and is undergoing several diagnostic analyses to verify its validity. The development of this code is detailed.