Field of degenerate modes

1978 ◽  
Vol 21 (7) ◽  
pp. 747-749
Author(s):  
T. I. Bichutskaya
Keyword(s):  
Degenerate Modes

Properties of leaky and degenerate modes in a prism–film coupler with waveguide structure

2003 ◽  
Vol 94 (11) ◽  
pp. 7025-7030 ◽  
Author(s):  
Xi-Jing Zhang ◽  
Xi-Zhi Fan ◽  
Jun Yan ◽  
Fei Xu ◽  
Xiao-Yuan Lou ◽  
...  
Keyword(s):  
Waveguide Structure ◽  
Degenerate Modes

Chaotic mode competition in parametrically forced surface waves

1985 ◽  
Vol 158 ◽  
pp. 381-398 ◽  
Author(s):  
S. Ciliberto ◽  
J. P. Gollub
Keyword(s):  
Fluid Layer ◽  
Chaotic Regime ◽  
Mode Competition ◽  
Sampling Techniques ◽  
Onset Of Chaos ◽  
Chaotic Mode ◽  
The Stability ◽  
Degenerate Modes ◽  
Local Sampling ◽  
Slow Timescale

Vertical forcing of a fluid layer leads to standing waves by means of a subharmonic instability. When the driving amplitude and frequency are chosen to be near the intersection of the stability boundaries of two nearly degenerate modes, we find that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. We utilize digital image-processing methods to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques to study the onset of chaos in some detail. Reconstruction of the attractors in phase space shows that in the chaotic regime the dimension of the attractor is fractional and at least one Lyapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition.

Novel rat-race coupler design of arbitrary coupling coefficient using substrate integrated waveguide cavity

2018 ◽  
Vol 10 (8) ◽  
pp. 861-869 ◽  
Author(s):  
Min-Hua Ho ◽  
Yi-Hao Hong ◽  
Jen-Chih Li
Keyword(s):  
Transmission Lines ◽  
Coupling Coefficient ◽  
Substrate Integrated Waveguide ◽  
Cavity Field ◽  
Arbitrary Coupling ◽  
Degenerate Mode ◽  
Quarter Wavelength ◽  
Small Phase ◽  
Hybrid Coupler ◽  
Degenerate Modes

AbstractThe contribution of this paper is to propose a novel rat-race hybrid coupler of arbitrary coupling coefficient. Traditionally, the rat-race hybrid couplers are built by various loop-alike transmission-lines of multiple quarter-wavelength, and in this paper, we approach the coupler design by using a circular substrate integrated waveguide (SIW) cavity (SIWC). The employed SIWC supports two mutually orthogonal degenerate modes, and cavity field is formed by the two modes in an arbitrary weighting ratio which defines the proposed rat-race coupler's coupling coefficient. The cavity is excited by a microstrip combined coupling slot with the microstrip along a specifically chosen direction. The energy of each degenerate mode can be solely extracted by an associated subminiature version A (SMA) whose position is carefully determined. The isolation between the coupling slots is assured by their perpendicular layout, and the isolation between the SMA probes is obtained by the orthogonality of the two degenerate modes. Experiments are conducted on the 3- and 10-dB coupling coefficient samples to verify this novel rat-race coupler design. The measurements agree well with the simulations, and circuit's good performance is observed in terms of coupling precision, isolations, and small phase imbalances.

Normalkoordinatenanalyse und Frequenzberechnungen für die isotopomeren closo-Hydrohexaborate 11Bn10B6-nH62- , n = 0 – 6 / Normal Coordinate Analysis and Frequency Calculations of Isotopomeric closo-Hydrohexaborates 11Bn10B6-nH62- , n = 0 – 6

1990 ◽  
Vol 45 (5) ◽  
pp. 641-646 ◽  
Author(s):  
J. Thesing ◽  
W. Preetz
Keyword(s):  
Potential Energy Distribution ◽  
Geometric Isomers ◽  
Normal Coordinate ◽  
Valence Force Field ◽  
Small Coupling ◽  
Atomic Displacements ◽  
Symmetry Coordinates ◽  
Statistical Frequency ◽  
Degenerate Modes ◽  
Ir And Raman

Normal coordinate analyses for the ten isotopomers Cs211Bn10B6-nH6, n = 0 — 6, including the pairs of geometric isomers for n = 2, 3, 4 have been performed, based on a general valence force field. The shift of the bands as well as the splitting of degenerate modes by lowered symmetry due to exchange of 10B by 11B or H by D is exactly calculated by a set of six force constants. The characteristic band patterns observed in the IR and Raman spectra of Cs2B6H6 with natural abundance of B isotopes (80.22% 11B, 19.78% 10B) measured at 10 K are explained by the superposition of the calculated spectra of the different isotopomers present, according to their statistical frequency distribution. The calculated atomic displacements and the potential energy distribution on the symmetry coordinates reveal only a small coupling (PED < 10%) between the cage (in-phase displacements of H and B) and substituent vibrations (anti-phase motions of B and H). Based on the normal coordinate analyses previously obtained assignments for several bands are revised.

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