Variation Analysis of Spatial Solitons of Power-Law Nonlinearity

We consider arbitrary angle interactions between spatial solitons and the planar boundary between two optical materials with a single power-law nonlinear refractive index. Extensive analysis has uncovered a wide range of new qualitative phenomena in non-Kerr regimes. A universal Helmholtz-Snell law describing soliton refraction is derived using exact solutions to the governing equation as a nonlinear basis. New predictions are tested through exhaustive computations, which have uncovered substantially enhanced Goos-Hänchen shifts at some non-Kerr interfaces. Helmholtz nonlinear surface waves are analyzed theoretically, and their stability properties are investigated numerically for the first time. Interactions between surface waves and obliquely incident solitons are also considered. Novel solution behaviours have been uncovered, which depend upon a complex interplay between incidence angle, medium mismatch parameters, and the power-law nonlinearity exponent.

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Analysis of power law assumptions for short-period comets and Kuiper bodies

International Astronomical Union Colloquium ◽

10.1017/s0252921100031584 ◽

1999 ◽

Vol 173 ◽

pp. 289-293 ◽

Cited By ~ 1

Author(s):

J.R. Donnison ◽

L.I. Pettit

Keyword(s):

Power Law ◽

Pareto Distribution ◽

Limited Data ◽

Short Period ◽

Probability Plots ◽

Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

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Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

Journal of Speech and Hearing Research ◽

10.1044/jshr.1101.169 ◽

1968 ◽

Vol 11 (1) ◽

pp. 169-178 ◽

Cited By ~ 4

Author(s):

Alan Gill ◽

Charles I. Berlin

Keyword(s):

Power Law ◽

Response Magnitude ◽

Single Units ◽

Spectral Content ◽

Hearing Sensitivity ◽

Subjective Magnitude ◽

Orderly Fashion ◽

Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

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