Apps/DysonPotential - Revision history

Jet53man: /* Dyson's Figures */

2021-10-06T22:40:21Z

Dyson's Figures

← Older revision		Revision as of 18:40, 6 October 2021
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	<table border="1" cellpadding="5" align="center">		<table border="1" cellpadding="5" align="center">
	<tr><td align="center" colspan="2" bgcolor="lightgreen">		<tr><td align="center" colspan="2" bgcolor="lightgreen">
	'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of <br />[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />		'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of <br />
	''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />		{{ Dyson1893figure }}
			<!--
			[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
			''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184
			-->
			<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />
	[[File:PermissionsRectYellow.png\|75px\|link=Appendix/Permissions#Dyson1893]]		[[File:PermissionsRectYellow.png\|75px\|link=Appendix/Permissions#Dyson1893]]
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Jet53man: /* Our Attempt to Replicate */

2021-09-23T18:22:29Z

Our Attempt to Replicate

← Older revision		Revision as of 14:22, 23 September 2021
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	<table border="1" align="center" cellpadding="8">		<table border="1" align="center" cellpadding="8">
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			''Top Panel''<br />(as above) '''Figure 3 extracted without modification from p. 65 of <br />[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
			''II.  The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />
			[[File:PermissionsRectYellow.png\|75px\|link=Appendix/Permissions#Dyson1893]]
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	<td rowspan="1" align="left" valign="bottom">		<td rowspan="1" align="left" valign="bottom">
	~~[[File:PermissionsRectYellow.png\|75px\|link=Appendix/Permissions#Dyson1893]]<br />~~
	[[File:RoverD5over2.png\|800px\|center\|The Potential Exterior to an Anchor Ring; R/d = 2.5]]		[[File:RoverD5over2.png\|800px\|center\|The Potential Exterior to an Anchor Ring; R/d = 2.5]]
	</td>		</td>

Jet53man: /* Our Attempt to Replicate */

2021-09-23T18:11:07Z

Our Attempt to Replicate

← Older revision		Revision as of 14:11, 23 September 2021
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	<td rowspan="1" align="left" valign="bottom">		<td rowspan="1" align="left" valign="bottom">
			[[File:PermissionsRectYellow.png\|75px\|link=Appendix/Permissions#Dyson1893]]<br />
	[[File:RoverD5over2.png\|800px\|center\|The Potential Exterior to an Anchor Ring; R/d = 2.5]]		[[File:RoverD5over2.png\|800px\|center\|The Potential Exterior to an Anchor Ring; R/d = 2.5]]
	</td>		</td>

Jet53man: /* Dyson's Figures */

2021-09-23T17:48:09Z

Dyson's Figures

← Older revision		Revision as of 13:48, 23 September 2021
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	<table border="0" cellpadding="8" align="center"><tr><td align="center">		<table border="0" cellpadding="8" align="center"><tr><td align="center">
	<table border="1" cellpadding="5" align="center">		<table border="1" cellpadding="5" align="center">
	<tr><td align="center" colspan="2">		<tr><td align="center" colspan="2" bgcolor="lightgreen">
	'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of <br />[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />		'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of <br />[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
	''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />		''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />
	[[File:~~PermissionsBanner~~.png\|75px\|link=Appendix/Permissions#Dyson1893]]		[[File:PermissionsRectYellow.png\|75px\|link=Appendix/Permissions#Dyson1893]]
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Jet53man: /* Dyson (1893) */

2021-09-20T22:29:39Z

Dyson (1893)

← Older revision		Revision as of 18:29, 20 September 2021
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	{\| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"		{\| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
	\|-		\|-
	! style="height: ~~150px~~; width: ~~150px~~; background-color:#ffeeee;" \|[[H_BookTiledMenu#Toroidal_.26_Toroidal-Like\|<b>Dyson<br />(1893)</b>]]		! style="height: 125px; width: 125px; background-color:#ffeeee;" \|[[H_BookTiledMenu#Toroidal_.26_Toroidal-Like\|<b>Dyson<br />(1893)</b>]]
	\|}		\|}

Jet53man: /* Dyson's Figures */

2021-09-15T22:50:41Z

Dyson's Figures

← Older revision		Revision as of 18:50, 15 September 2021
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	<table border="1" cellpadding="5" align="center">		<table border="1" cellpadding="5" align="center">
	<tr><td align="center" colspan="2">		<tr><td align="center" colspan="2">
	'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />		'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of <br />[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
	''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />		''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]<br />
	[[File:PermissionsBanner.png\|75px\|link=Appendix/Permissions#Dyson1893]]		[[File:PermissionsBanner.png\|75px\|link=Appendix/Permissions#Dyson1893]]
	</td></tr>		</td></tr>

Jet53man: /* Dyson's Figures */

2021-09-15T22:45:30Z

Dyson's Figures

← Older revision		Revision as of 18:45, 15 September 2021
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	'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />		'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
	''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />		''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />
	[[File:PermissionsBanner.png\|75px\|link=~~Apps~~/~~MaclaurinSpheroids~~]]		[[File:PermissionsBanner.png\|75px\|link=Appendix/Permissions#Dyson1893]]
	</td></tr>		</td></tr>
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Jet53man: /* Our Attempt to Replicate */

2021-09-15T21:57:12Z

Our Attempt to Replicate

← Older revision		Revision as of 17:57, 15 September 2021
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	====Our Attempt to Replicate====		====Our Attempt to Replicate====
	First, let's test the accuracy of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D Dyson's (1893a)] "series expansion" expression for the elliptic integrals, <math>~K(\mu)</math> and <math>~E(\mu)</math>; in the following table, the high-precision evaluations labeled "''Numerical Recipes''" have been drawn from the tabulated data that is provided in our [[2DStructure/ToroidalCoordinateIntegrationLimits#Evaluation_of_Elliptic_Integrals\|accompanying discussion]] of incomplete elliptic integrals. Drawing from our [[Appendix/~~Equation_templates~~#Complete_Elliptic_Integrals\|accompanying set of Key mathematical relations]] — in which <math>~k</math>, rather than <math>~\mu</math>, represents the function modulus — the relevant series-expansion expressions are:		First, let's test the accuracy of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D Dyson's (1893a)] "series expansion" expression for the elliptic integrals, <math>~K(\mu)</math> and <math>~E(\mu)</math>; in the following table, the high-precision evaluations labeled "''Numerical Recipes''" have been drawn from the tabulated data that is provided in our [[2DStructure/ToroidalCoordinateIntegrationLimits#Evaluation_of_Elliptic_Integrals\|accompanying discussion]] of incomplete elliptic integrals. Drawing from our [[Appendix/SpecialFunctions#Complete_Elliptic_Integrals\|accompanying set of Key mathematical relations]] — in which <math>~k</math>, rather than <math>~\mu</math>, represents the function modulus — the relevant series-expansion expressions are:
	<div align="center">		<div align="center">
	{{ Math/EQ_EllipticIntegral01 }}<br />		{{ Math/EQ_EllipticIntegral01 }}<br />

Jet53man: /* Dyson's Figures */

2021-09-15T21:50:13Z

Dyson's Figures

← Older revision		Revision as of 17:50, 15 September 2021
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	Figures 1 - 6 from [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D Dyson (1893a)] — replicated immediately below — show his resulting set of contours for six cases: Tori (anchor rings) having aspect ratios of <math>~a/c = 0, 1/5, 2~~/5, 3/5, 4~~/5, 1</math>. Click on an image to view the contour plot at higher resolution. In what follows we present results from our own evaluation of this "V<sub>2</sub>" function for the single case of an anchor ring having <math>~a/c = 2/5</math>.		Figures 1, 2, 3, & 6 from [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D Dyson (1893a)] — replicated immediately below — show his resulting set of contours for six cases: Tori (anchor rings) having aspect ratios of <math>~a/c = 0, 1/5, 2/5, 1</math>. Click on an image to view the contour plot at higher resolution. In what follows we present results from our own evaluation of this "V<sub>2</sub>" function for the single case of an anchor ring having <math>~a/c = 2/5</math>.


	<table border="0" cellpadding="8" align="center"><tr><td align="center">		<table border="0" cellpadding="8" align="center"><tr><td align="center">
	<table border="1" cellpadding="5" align="center">		<table border="1" cellpadding="5" align="center">
	<tr><td align="center" colspan="3">		<tr><td align="center" colspan="2">
	'''Figures 1 - 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />		'''Figures 1, 2, 3, & 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
	''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />		''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />
	[[File:PermissionsBanner.png\|75px\|link=Apps/MaclaurinSpheroids]]		[[File:PermissionsBanner.png\|75px\|link=Apps/MaclaurinSpheroids]]
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	[[File:RoverD5over1.png\|300px\|center\|The Potential Exterior to an Anchor Ring; R/d = 5]]		[[File:RoverD5over1.png\|300px\|center\|The Potential Exterior to an Anchor Ring; R/d = 5]]
	~~</td>~~
	~~<td>~~
	~~[[File:RoverD5over2.png\|300px\|center\|The Potential Exterior to an Anchor Ring; R/d = 2.5]]~~
	</td>		</td>
	</tr>		</tr>
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	<td>		<td>
	[[File:~~RoverD5over3~~.png\|300px\|center\|The Potential Exterior to an Anchor Ring; R/d = 1.667]]		[[File:RoverD5over2.png\|300px\|center\|The Potential Exterior to an Anchor Ring; R/d = 1.667]]
	~~</td>~~
	~~<td>~~
	~~[[File:RoverD5over4.png\|300px\|center\|The Potential Exterior to an Anchor Ring; R/d = 1.25~~]]
	</td>		</td>
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Jet53man: /* Dyson's Figures */

2021-09-15T21:32:21Z

Dyson's Figures

← Older revision		Revision as of 17:32, 15 September 2021
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	<table border="1" cellpadding="5" align="center">		<table border="1" cellpadding="5" align="center">
	<tr><td align="center" colspan="3">		<tr><td align="center" colspan="3">
	'''Figures 1 - 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<~~p><~~/p>		'''Figures 1 - 6 extracted without modification from pp. 63-66 of [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]'''<br />
	''The Potential of an Anchor Ring'', Phil. Trans. Royal Soc. London. A., Vol. 184		''The Potential of an Anchor Ring''<br /> Phil. Trans. Royal Soc. London. A., Vol. 184<br />
			[[File:PermissionsBanner.png\|75px\|link=Apps/MaclaurinSpheroids]]
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