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trinitree88
2009-Nov-15, 04:24 PM
There are different ways of modeling gravitational waves, and depending upon how you expect them to behave, different ways of trying to detect them. Our current best money is spent on laser interferometers....giant versions of the Michelson device used to search for the "luminiferous ether" many moons ago, which ultimately led to the discovery of Special Relativity by Einstein.
Nevertheless groups try different experimental set-ups. One of the first was Joe Weber's bar type detector at U. Maryland. Piezoelectric sensors recorded distortions of a large suspended aluminum cylinder. Contemporary LIGO's should be more sensitive by far, enabling the detection of coalescing massive objects, and asymmetrical supernovae light years distant. However we don't see them yet, and theorists need some help trying to unravel the complex mathematics showing that a Weber type wave is actually a superposition of several Mathieu type waves. The proof is left as an exercise for the student. Homework, and probably a lot of gratitude from the authors. SEE:http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.2295v1.pdf

Cougar
2009-Nov-15, 07:08 PM
There are different ways of modeling gravitational waves...

Hmm. Interesting....


...Plane waves carry a well defined linear momentum in the x and y directions, Bessel waves carry a well defined orbital angular momentum, Mathieu waves carry a well defined composition of orbital angular and x-linear momenta, while Weber waves carry a composition of orbital angular and y-linear momenta...

trinitree88
2009-Nov-16, 01:08 PM
Hmm. Interesting....


...Plane waves carry a well defined linear momentum in the x and y directions, Bessel waves carry a well defined orbital angular momentum, Mathieu waves carry a well defined composition of orbital angular and x-linear momenta, while Weber waves carry a composition of orbital angular and y-linear momenta...

Cougar. Yep. At the time of construction of the bar type detectors, I believe the expectation was that a passing g-wave ought to first distort the bar in the x direction, followed by a contiguous distortion in the y-axis, or the inverse of that. Without an expectation of the correct sequence, including these others, the algorithms to search for signal/noise ratios might miss a real one. Interesting to me,too. We'll see if they research the old data. pete

hhEb09'1
2009-Nov-16, 01:52 PM
However we don't see them yet, and theorists need some help trying to unravel the complex mathematics showing that a Weber type wave is actually a superposition of several Mathieu type waves. The proof is left as an exercise for the student. Homework, and probably a lot of gratitude from the authors. SEE:http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.2295v1.pdfJust author, no? B. M. Rodriguez-Lara
A normalization for the finite energy Weber-Gauss beams was presented based on their Bessel-Gauss decomposition. It has been shown that it is not feasible to efficiently construct a Weber-Gauss beam through the finite superposition of just a few Bessel-Gauss beams.

Finding a close analytical form for the normalization integral straight from the configuration or phase space representation of a Weber beam and the analysis pertaining the generation of Weber beams as the superposition of Mathieu beams is left as an open problem due to the complexity of the calculations involved.