By Alexandr O. Ivanov, A. A. Tuzhilin

ISBN-10: 9810240600

ISBN-13: 9789810240608

ISBN-10: 9812810714

ISBN-13: 9789812810717

This e-book offers with the hot category of one-dimensional variational difficulties - the issues with branching strategies. as a substitute of utmost curves (mappings of a section to a manifold) we examine severe networks, that are mappings of graphs (one-dimensional mobilephone complexes) to a manifold. quite a few purposes of the procedure are provided, corresponding to a number of generalizations of the recognized Steiner challenge of discovering the shortest community spanning given issues of the airplane.

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**Extra info for Branching solutions to one-dimensional variational problems**

**Sample text**

At the lower frequencies, basement interaction is no longer negligible and the erroneous inputs show their effects. A series of S A F A R I runs were made to determine the degree of influence of the semi-infinite concrete basement at the four frequencies of interest. These additional runs were m a d e without the concrete basement. Instead, the bottom was modeled as a semi-infinite epoxy basement. The resulting transmission loss contour showed a negligible variation of the field at 25 and 30Hz, a somewhat poorer propagation at 20Hz, and a totally different field at 15Hz.

The best agreement was obtained at high frequencies and a typical result is shown in figure 2 0 for a source frequency of 110kHz . The plot shows the propagation loss as function of across slope range. There is excellent agreement between the measurements and the predictions at this frequency, and the only discrepancy occurs where the experimental levels reach the noise floor at a propagation loss of 12dB. Note that the shadow zone is clearly identified and tiiat the details of the interference pattern in the acoustic field is well predicted by the source image theory.

Downstope enhancement was atso investigated by Dosso and Chapman^** off the west coast of Canada. This experiment took ptace over the deep ocean basin, at a depth of 2500 meters, the continental siope, which was etevated nominally at 5 degrees, and the continental shelf, at an average depth of 150 meters. O n the continental slope, a pinnacle from an ocean bottom ridge is present. T w o ships were used in the experiment, the first ship dropped S U S charges which were detonated at a depth of 22 meters.

### Branching solutions to one-dimensional variational problems by Alexandr O. Ivanov, A. A. Tuzhilin

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