Severity: Warning
Message: file_get_contents(https://...@pubfacts.com&api_key=b8daa3ad693db53b1410957c26c9a51b4908&a=1): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
Line Number: 176
Backtrace:
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 176
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 250
Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3122
Function: getPubMedXML
File: /var/www/html/application/controllers/Detail.php
Line: 575
Function: pubMedSearch_Global
File: /var/www/html/application/controllers/Detail.php
Line: 489
Function: pubMedGetRelatedKeyword
File: /var/www/html/index.php
Line: 316
Function: require_once
We show the existence of natural subsurface channels that guide acoustic waves for periodic arrays of spherical grains under the influence of gravity. Downward propagation of acoustic rays can be stopped altogether as a result of a caustic whose origin lies in the continuous bending of rays as a result of a gravitationally induced increase of rigidity with depth. Upward propagation of acoustic rays, on the other hand, is attenuated by Bragg reflection arising from the continuous diminishing of rigidity in the direction of the surface, resulting in a vertical propagation constant that approaches a limited allowed value. Waves with different frequencies are shown to travel at different depths below the surface. The key conditions for the manifestation of the predicted wave modes are microscopic periodicity and macroscopic inhomogeneity of the medium.
Download full-text PDF |
Source |
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http://dx.doi.org/10.1103/PhysRevE.78.036602 | DOI Listing |
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