Rayleigh-Bloch Waves - Revision history

https://www.wikiwaves.org/index.php?action=history&feed=atom&title=Rayleigh-Bloch_Waves Rayleigh-Bloch Waves - Revision history 2026-04-17T18:29:50Z Revision history for this page on the wiki MediaWiki 1.43.1 https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=12687&oldid=prev Mpeter at 11:37, 23 September 2010 2010-09-23T11:37:17Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:37, 23 September 2010</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</td> <td colspan="2" class="diff-lineno">Line 5:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down an infinite array of bottom-mounted cylinders]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down an infinite array of bottom-mounted cylinders]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are observed for a very general class of arrays, where the medium is governed by the two-dimensional [[Helmholtz's Equation]] (cf. [[Linton and McIver 2002]]). In the water-wave context this means that the structures must have a depth dependence which can be removed (cf. [[Removing The Depth Dependence]]), so that the problem reduces to two dimensions. In the more general water-wave context, no Rayleigh-Bloch waves have been found. It seems likely that such waves will exist only for very special geometries and frequencies, but this remains only a conjecture at the present time. There are many off-shore structures which do support Rayleigh-Bloch waves, e.g. [[Bottom Mounted Cylinder|Bottom-Mounted Cylinders]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are observed for a very general class of arrays, where the medium is governed by the two-dimensional [[Helmholtz's Equation]] (cf. [[Linton and McIver 2002]]). In the water-wave context this means that the structures must have a depth dependence which can be removed (cf. [[Removing The Depth Dependence]]), so that the problem reduces to two dimensions. In the more general water-wave context, no Rayleigh-Bloch waves have been found <ins style="font-weight: bold; text-decoration: none;">(see [[Peter and Meylan 2007]] for a discussion)</ins>. It seems likely that such waves will exist only for very special geometries and frequencies, but this remains only a conjecture at the present time. There are many off-shore structures which do support Rayleigh-Bloch waves, e.g. [[Bottom Mounted Cylinder|Bottom-Mounted Cylinders]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Some more information on Rayleigh--Bloch waves can be found in [[Porter and Evans 1999]] and [[Linton and McIver 2002]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Some more information on Rayleigh--Bloch waves can be found in [[Porter and Evans 1999]] and [[Linton and McIver 2002]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> </table>

Mpeter https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=3081&oldid=prev Meylan at 07:15, 6 July 2006 2006-07-06T07:15:02Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:15, 6 July 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter and Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> \ k < \pi/R \ </math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[<ins style="font-weight: bold; text-decoration: none;">:Category:Infinite Array|</ins>Infinite Array]]. </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter and Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> \ k < \pi/R \ </math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down an infinite array of bottom-mounted cylinders]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down an infinite array of bottom-mounted cylinders]]</div></td></tr> </table>

Meylan https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2893&oldid=prev Meylan at 23:49, 17 June 2006 2006-06-17T23:49:40Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:49, 17 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l24">Line 24:</td> <td colspan="2" class="diff-lineno">Line 24:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category:<del style="font-weight: bold; text-decoration: none;">Linear Water-Wave Theory</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category:<ins style="font-weight: bold; text-decoration: none;">Infinite Array</ins>]]</div></td></tr> </table>

Meylan https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2556&oldid=prev Meylan at 01:40, 2 June 2006 2006-06-02T01:40:39Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:40, 2 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l23">Line 23:</td> <td colspan="2" class="diff-lineno">Line 23:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Linear Water-Wave Theory]]</ins></div></td></tr> </table>

Meylan https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2509&oldid=prev Meylan: Rayleigh-Bloch waves moved to Rayleigh-Bloch Waves 2006-06-01T11:28:04Z

<p><a href="/index.php/Rayleigh-Bloch_waves" class="mw-redirect" title="Rayleigh-Bloch waves">Rayleigh-Bloch waves</a> moved to <a href="/index.php/Rayleigh-Bloch_Waves" title="Rayleigh-Bloch Waves">Rayleigh-Bloch Waves</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:28, 1 June 2006</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Meylan https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2508&oldid=prev Meylan at 11:27, 1 June 2006 2006-06-01T11:27:52Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:27, 1 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[<del style="font-weight: bold; text-decoration: none;">Porter_Evans_05|</del>Porter <del style="font-weight: bold; text-decoration: none;">& </del>Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> \ k < \pi/R \ </math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter <ins style="font-weight: bold; text-decoration: none;">and </ins>Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> \ k < \pi/R \ </math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down an infinite array of bottom-mounted cylinders]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down an infinite array of bottom-mounted cylinders]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are observed for a very general class of arrays, where the medium is governed by the two-dimensional [[Helmholtz's Equation]] (cf. [[<del style="font-weight: bold; text-decoration: none;">Linton_Mciver_02|</del>Linton <del style="font-weight: bold; text-decoration: none;">& </del>McIver 2002]]). In the water-wave context this means that the structures must have a depth dependence which can be removed (cf. [[Removing The Depth Dependence]]), so that the problem reduces to two dimensions. In the more general water-wave context, no Rayleigh-Bloch waves have been found. It seems likely that such waves will exist only for very special geometries and frequencies, but this remains only a conjecture at the present time. There are many off-shore structures which do support Rayleigh-Bloch waves, e.g. [[Bottom Mounted Cylinder|Bottom-Mounted Cylinders]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are observed for a very general class of arrays, where the medium is governed by the two-dimensional [[Helmholtz's Equation]] (cf. [[Linton <ins style="font-weight: bold; text-decoration: none;">and </ins>McIver 2002]]). In the water-wave context this means that the structures must have a depth dependence which can be removed (cf. [[Removing The Depth Dependence]]), so that the problem reduces to two dimensions. In the more general water-wave context, no Rayleigh-Bloch waves have been found. It seems likely that such waves will exist only for very special geometries and frequencies, but this remains only a conjecture at the present time. There are many off-shore structures which do support Rayleigh-Bloch waves, e.g. [[Bottom Mounted Cylinder|Bottom-Mounted Cylinders]].</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Some more information on Rayleigh--Bloch waves can be found in [[<del style="font-weight: bold; text-decoration: none;">Porter_Evans_99|</del>Porter <del style="font-weight: bold; text-decoration: none;">& </del>Evans <del style="font-weight: bold; text-decoration: none;">(</del>1999<del style="font-weight: bold; text-decoration: none;">)</del>]] and [[<del style="font-weight: bold; text-decoration: none;">Linton_Mciver_02|</del>Linton <del style="font-weight: bold; text-decoration: none;">& </del>McIver <del style="font-weight: bold; text-decoration: none;">(</del>2002<del style="font-weight: bold; text-decoration: none;">)</del>]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Some more information on Rayleigh--Bloch waves can be found in [[Porter <ins style="font-weight: bold; text-decoration: none;">and </ins>Evans 1999]] and [[Linton <ins style="font-weight: bold; text-decoration: none;">and </ins>McIver 2002]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Rayleigh-Bloch wavenumber <math>\beta</math> is the value for which the operator</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Rayleigh-Bloch wavenumber <math>\beta</math> is the value for which the operator</div></td></tr> </table>

Meylan https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2444&oldid=prev Mpeter at 10:17, 1 June 2006 2006-06-01T10:17:04Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:17, 1 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\ <del style="font-weight: bold; text-decoration: none;"> </del>Q_j = \mathrm{e}^{\mathrm{i} j R \beta}. <del style="font-weight: bold; text-decoration: none;">\</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\ Q_j = \mathrm{e}^{\mathrm{i} j R \beta}.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td></tr> </table>

Mpeter https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2443&oldid=prev Mpeter at 10:16, 1 June 2006 2006-06-01T10:16:24Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:16, 1 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter_Evans_05|Porter & Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> \ k < \pi/R \ </math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter_Evans_05|Porter & Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> \ k < \pi/R \ </math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down <del style="font-weight: bold; text-decoration: none;">and </del>infinite array of bottom-mounted cylinders]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down <ins style="font-weight: bold; text-decoration: none;">an </ins>infinite array of bottom-mounted cylinders]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are observed for a very general class of arrays, where the medium is governed by the two-dimensional [[Helmholtz's Equation]] (cf. [[Linton_Mciver_02|Linton & McIver 2002]]). In the water-wave context this means that the structures must have a depth dependence which can be removed (cf. [[Removing The Depth Dependence]]), so that the problem reduces to two dimensions. In the more general water-wave context, no Rayleigh-Bloch waves have been found. It seems likely that such waves will exist only for very special geometries and frequencies, but this remains only a conjecture at the present time. There are many off-shore structures which do support Rayleigh-Bloch waves, e.g. [[Bottom Mounted Cylinder|Bottom-Mounted Cylinders]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are observed for a very general class of arrays, where the medium is governed by the two-dimensional [[Helmholtz's Equation]] (cf. [[Linton_Mciver_02|Linton & McIver 2002]]). In the water-wave context this means that the structures must have a depth dependence which can be removed (cf. [[Removing The Depth Dependence]]), so that the problem reduces to two dimensions. In the more general water-wave context, no Rayleigh-Bloch waves have been found. It seems likely that such waves will exist only for very special geometries and frequencies, but this remains only a conjecture at the present time. There are many off-shore structures which do support Rayleigh-Bloch waves, e.g. [[Bottom Mounted Cylinder|Bottom-Mounted Cylinders]].</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15">Line 15:</td> <td colspan="2" class="diff-lineno">Line 15:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>and appropriate boundary conditions at the body surfaces, has an</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>and appropriate boundary conditions at the body surfaces, has an</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>eigenvalue in the interval <math>(k,\pi/R]</math>. This corresponds to a wave</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>eigenvalue in the interval <math> <ins style="font-weight: bold; text-decoration: none;">\ </ins>(k,\pi/R] <ins style="font-weight: bold; text-decoration: none;">\ </ins></math>. This corresponds to a wave</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>travelling down the array with phase factor </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>travelling down the array with phase factor </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del>Q_j = \mathrm{e}^{\mathrm{i} j R \beta}.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">\ </ins>Q_j = \mathrm{e}^{\mathrm{i} j R \beta}. <ins style="font-weight: bold; text-decoration: none;">\</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An example is given in the plot.</div></td></tr> </table>

Mpeter https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2442&oldid=prev Mpeter at 10:15, 1 June 2006 2006-06-01T10:15:46Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:15, 1 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter_Evans_05|Porter & Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math>k < \pi/R</math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves ([[Porter_Evans_05|Porter & Evans 2005]]). Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math> <ins style="font-weight: bold; text-decoration: none;">\ </ins>k < \pi/R <ins style="font-weight: bold; text-decoration: none;">\ </ins></math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down and infinite array of bottom-mounted cylinders]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down and infinite array of bottom-mounted cylinders]]</div></td></tr> </table>

Mpeter https://www.wikiwaves.org/index.php?title=Rayleigh-Bloch_Waves&diff=2438&oldid=prev Mpeter at 09:25, 1 June 2006 2006-06-01T09:25:29Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:25, 1 June 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves [[Porter_Evans_05|Porter & Evans <del style="font-weight: bold; text-decoration: none;">(</del>2005<del style="font-weight: bold; text-decoration: none;">)</del>]]. Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math>k < \pi/R</math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Rayleigh-Bloch waves are waves which travel along an [[Infinite Array]]. Generally, they propagate along the array with a dominant wavenumber which is greater than that for freely-propagating waves and they decay exponentially away from the array. They have other names (guided waves, surface waves) in acoustics and electromagnetics. Only in very exceptional cases are they excited by plane incident waves <ins style="font-weight: bold; text-decoration: none;">(</ins>[[Porter_Evans_05|Porter & Evans 2005]]<ins style="font-weight: bold; text-decoration: none;">)</ins>. Rayleigh-Bloch waves (if they can be supported by the structure) will be excited in a [[Semi-Infinite Array]] provided that <math>k < \pi/R</math> (where <math>k</math> is the wavenumber of the incident wave and <math>R</math> is the body spacing of the array). </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down and infinite array of bottom-mounted cylinders]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:RB_wiki.jpg|thumb|right|Rayleigh-Bloch wave travelling down and infinite array of bottom-mounted cylinders]]</div></td></tr> </table>

Mpeter