From the resonance theory to the statistical model
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Theories and numerical experiments regarding secular resonances are reviewed. The basic dynamics and the positions of secular resonances are discussed, and secular perturbation theories for the nu16 resonance case, the nu6 resonance, and the nu5 resonance are addressed. What numerical experiments have revealed about asteroids located in secular resonances, the stability of secular resonances, variations of eccentricities and inclinations, and chaotic orbits is considered. Resonant transport of meteorites is discussed.
Kinetic theory for resonant four-wave processes in turbulent ensemble of dispersive systems
Analytical theories have been devised for the three resonant pairs in Saturn's satellite system: Enceladus-Dione, Titan-Hyperion, and Mimas-Tethys. An algebraic manipulation language was adopted to calculate the theories; use of the canonically invariant Hori-Lie (1966) theory in noncanonical variables made it possible to perform direct computations of perturbations in such quantities as longitude, latitude and radius vector. Important terms at the 1-100 km level have been found second-order terms of the resonant satellite are calculated.
Performance of folded Fabry-Perot quasi-optical ring resonator diplexers with different geometries of reflecting surfaces is investigated both theoretically and experimentally. Design of optimum surface geometry for minimum diffraction, together with the figure of merit indicating improvement in performance, are given.
The ring systems of Jupiter, Saturn and Uranus have been studied particularly since the Voyager flights, in order to obtain more information on the rings' origin and structure. These ring systems all have satellites but the structure and number of satellites are different. Jupiter, with its two satellites, has a ring that is roughly 6000 km wide while Uranus has nine ringlets, most of which are no wider than tens of kilometers and which are separated by empty space. The three planetary ring systems also show distinctions in composition; for example, the rings of Saturn are thought to be icy while Jupiter's consist mostly of rocky material. The effect that countless particles, which make up each ring and interact with each other through collisions and gravitational attractions, have on the system's energy and angular momentum has been discussed. Spiral density waves and spiral bending waves, are explained by the resonance theory. Further study is needed in this area since the resonance theory does not account for all observed ring structures.
Contrary to the claim by von Uexkuell et al. (1983), their observations of upward phase propagation of umbral oscillations in the chromosphere are in agreement with the photospheric resonance theory of Thomas and Scheuer (1982) and in contradiction to the chromospheric resonance theory of Zhugzhda et al. (1983). Other observational evidence also indicates that the fundamental 3-min umbral oscillation is due to a photospheric resonance, although the closely-spaced multiple peaks sometimes seen in the power spectrum of chromospheric oscillations may well be due to chromospheric resonances.
An adaptive fuzzy system using the concept of the Adaptive Resonance Theory (ART) type neural network architecture and incorporating fuzzy c-means (FCM) system equations for reclassification of cluster centers was developed. The Adaptive Fuzzy Leader Clustering (AFLC) architecture is a hybrid neural-fuzzy system which learns on-line in a stable and efficient manner. The system uses a control structure similar to that found in the Adaptive Resonance Theory (ART-1) network to identify the cluster centers initially. The initial classification of an input takes place in a two stage process; a simple competitive stage and a distance metric comparison stage. The cluster prototypes are then incrementally updated by relocating the centroid positions from Fuzzy c-Means (FCM) system equations for the centroids and the membership values. The operational characteristics of AFLC and the critical parameters involved in its operation are discussed. The performance of the AFLC algorithm is presented through application of the algorithm to the Anderson Iris data, and laser-luminescent fingerprint image data. The AFLC algorithm successfully classifies features extracted from real data, discrete or continuous, indicating the potential strength of this new clustering algorithm in analyzing complex data sets. The hybrid neuro-fuzzy AFLC algorithm will enhance analysis of a number of difficult recognition and control problems involved with Tethered Satellite Systems and on-orbit space shuttle attitude controller.
Here, we present a time-dependent Schrödinger equation approach within a nonrelativistic quantum electrodynamics framework to investigate resonant x-ray scattering driven by intense x-ray pulses. This method enables us to explore how coherent x-ray electron dynamics influence scattering signals from Ne + . We account for both resonance fluorescence and elastic scattering channels, while also considering competing photoionization and inner-shell decay processes. By computing the angular distribution and energy spectrum of scattered photons, we uncover interference effects between elastic scattering and resonance fluorescence pathways. Notably, this interference results in a small asymmetry in the energy spectrum. We discuss the experimental potential for detecting signatures of interference. Our findings demonstrate that the x-ray Rabi dynamics can be used to control scattering responses and provide insights into interference mechanisms and scattering efficiency in high-intensity x-ray regimes.
Impedance and radiation field in surrounding hot plasma interacting with electrically short antenna
Intensity of radiation transfer in Doppler broadened resonance line expressed in terms of appropriate H-functions assuming semi-infinite atmosphere
Quasi-linear behavior of collisionless relativistic plasma in uniform magnetic field, discussing resonant diffusion and turbulent waves effects
Nonlinear integrodifferential kinetic equation for weak turbulence of resonant four wave processes, considering spectral energy density
The aim of the symposium was to bring together investigators with interests in low latitude hydromagnetic waves in order to review the present state of knowledge in this area of magnetospheric physics. Of particular importance is the means by which wave energy is transferred to low latitudes to produce geomagnetic pulsations on the ground. The group of contributed papers reviewed shows that definitive experiments are underway and new theories capable of providing resonant wave energy at low latitudes are being developed. Particular topics covered by the review include solar wind control, wave spectra, array studies of wave parameters, storm time waves, and global wave resonance theory involving the coupling of compressional and transverse waves in the magnetosphere.
A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented herein is easily extended to many layer structures where it is more accurate than other existing transfer matrix or Wentzel-Kramers-Brillouin (WKB) models. The transmission resonances are compared to the bound-state energies calculated for a finite square well under bias using either an asymmetric square-well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound-state energies. The calculations were then applied to a new superlattice structure, the variably spaced superlattice energy filter, which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.
The Resonance Island Jump (RIJ) scheme for transition crossing in HSR (or the CERN SPS [1, 2]) is radically new, and untested. Beam experiments in RHIC will be necessary if the RIJ scheme is to be considered as a serious alternative to upgrading the first order linear jump scheme currently implemented in RHIC [3]. This note outlines the planning and the theoretical foundations that are necessary for such a beam experiment, perhaps to be performed in 2024.
One of the long-standing uncertainties in the wave-resonance theory of coronal heating is the stability of the resonance layer. The wave motions in the resonance layer produce highly localized shear flows which vary sinusoidally in time with the resonance period. This configuration is potentially susceptible to the Kelvin-Helmholtz instability (KHI), which can enhance small-scale structure and turbulent broadening of shear layers on relatively rapid ideal timescales. We have investigated numerically the response of a characteristic velocity profile, derived from resonance absorption models, to finite fluid perturbations comparable to photospheric fluctuations. We find that the KHI primarily should affect long (approximately greater than 6 x 10(exp 4) km) loops where higher velocity flows (M approximately greater than 0.2) exist in resonance layers of order 100 km wide. There, the Kelvin-Helmholtz growth time is comparable to or less than the resonance quarter-period, and the potentially stabilizing magnetic effects are not felt until the instability is well past the linear growth stage. Not only is the resonance layer broadened by the KHI, but also the convective energy transport out of the resonance layer is increased, thus adding to the efficiency of the wave-resonance heating process. In shorter loops, e.g., those in bright points and compact flares, the stabilization due to the magnetic field and the high resonance frequency inhibit the growth of the Kelvin-Helmholtz instability beyond a minimal level.