LSUsimulations - Revision history

Joel2: /* 1st Video */

2024-10-25T18:34:09Z

1st Video

← Older revision		Revision as of 14:34, 25 October 2024
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	</table>		</table>
	</td></tr></table>		</td></tr></table>
	<font color="red">Resolution …</font>		<font color="red">Resolution …</font>   <math>[128, 128, 128]</math> in <math>[\varpi, Z, \varphi]</math>
	<ul>		<ul>
	<li>Radial:   Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53. Hence, ample room was allowed for radial expansion of the model as it deformed into a two-armed spiral, then bar-like, configuration.</li>		<li>Radial:   Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53. Hence, ample room was allowed for radial expansion of the model as it deformed into a two-armed spiral, then bar-like, configuration.</li>

Joel2: /* Model A */

2024-10-25T18:26:15Z

Model A

← Older revision		Revision as of 14:26, 25 October 2024
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	<table border="0" align="right" cellpadding="10" width="30%"><tr><td align="center">		<table border="0" align="right" cellpadding="10" width="30%"><tr><td align="center">
	<table border="1" align="center" cellpadding="5">		<table border="1" align="center" cellpadding="5">
	<tr><td align="center">Table 1 extracted from p. 1057 of<br />{{ CT2000figure }}</td></tr		<tr><td align="center">Table 1 extracted from p. 1057 of …<br />{{ CT2000figure }}</td></tr
	><tr><td align="center">[[File:CT2000Table01.png\|~~350px~~\|CT2000 Table 1]]</td></tr>		><tr><td align="center">[[File:CT2000Table01.png\|300px\|CT2000 Table 1]]</td></tr>
	</table></td></tr></table>The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')		</table></td></tr></table>The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')

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	====1<sup>st</sup> Video====		====1<sup>st</sup> Video====

	Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character. The icon shown here, on the left, ~~links~~ to a YouTube video that shows the nonlinear development of this instability.		Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character. The caption of the icon shown here, on the left, contains a link to a YouTube video that shows the nonlinear development of this instability.

	<table border="0" align="left" cellpadding="20"><tr><td align="center">		<table border="0" align="left" cellpadding="10"><tr><td align="center">
	<table border="0" align="center" cellpadding="1">		<table border="0" align="center" cellpadding="1">
	<tr><td align="center">Model A Barmode Instability</td></tr>		<tr><td align="center">Model A Barmode Instability</td></tr>
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	<font color="red">Resolution …</font>		<font color="red">Resolution …</font>
	<ul>		<ul>
	<li>Radial:   Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53. Hence, ample room was allowed for radial expansion of the model as it deformed into a bar-like configuration.</li>		<li>Radial:   Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53. Hence, ample room was allowed for radial expansion of the model as it deformed into a two-armed spiral, then bar-like, configuration.</li>
	<li>Vertical:   Although the model was initially quite flat — ~~with~~ a pole-to equatorial ratio of <math>0.5</math>, meaning that the vertical extent above its equatorial plane was substantially less than 53 vertical zones — it was evolved on a grid that contained 128 vertical zones in this "northern" hemisphere.</li>		<li>Vertical:   Although the model was initially quite flat — having a pole-to-equatorial axis ratio, <math>c/a = 0.208</math>, meaning that the vertical extent above its equatorial plane was substantially less than 53 vertical zones — it was evolved on a grid that contained 128 vertical zones in this "northern" hemisphere. (Our technique for solving the Poisson equation imposed this grid size.) We assumed reflection symmetry through the equatorial plane, so it was not necessary to include an additional 128 zones in the "southern" hemisphere.</li>
			<li>Azimuthal:   In the azimuthal direction, each grid zone had an angular extent of <math>2\pi/256</math>. However, by forcing the evolution to maintain a two-fold "π-symmetry" only 128 grid zones were required to evolve the system with this resolution.</li>
	</ul>		</ul>

			This evolution is viewed from an inertial frame of reference in which the initial symmetry (vertical) axis is tipped somewhat toward the viewer. As a consequence, even though the initial model is axisymmetric, it appears to be slightly ellipsoidal in even the earliest frames of the video. After "ejecting" a small portion of its mass into a "circumstellar" disk/ring, the model settles down into a ''nearly'' steady-state, rotating bar-like configuration that, for all intents and purposes is a compressible analog of a Riemann ellipsoid. (This is the theme of the {{ CT2000 }} publication.)

	=See Also=		=See Also=

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Joel2: /* 1st Video */

2024-10-25T17:58:16Z

1st Video

← Older revision		Revision as of 13:58, 25 October 2024
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	Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character. The icon shown here, on the left, links to a YouTube video that shows the nonlinear development of this instability.		Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character. The icon shown here, on the left, links to a YouTube video that shows the nonlinear development of this instability.

	<table border="0" align="left" cellpadding="2">		<table border="0" align="left" cellpadding="20"><tr><td align="center">
			<table border="0" align="center" cellpadding="1">
	<tr><td align="center">Model A Barmode Instability</td></tr>		<tr><td align="center">Model A Barmode Instability</td></tr>
	<tr>		<tr>
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	</tr>		</tr>
	</table>		</table>
			</td></tr></table>
			<font color="red">Resolution …</font>
			<ul>
			<li>Radial:   Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53. Hence, ample room was allowed for radial expansion of the model as it deformed into a bar-like configuration.</li>
			<li>Vertical:   Although the model was initially quite flat — with a pole-to equatorial ratio of <math>0.5</math>, meaning that the vertical extent above its equatorial plane was substantially less than 53 vertical zones — it was evolved on a grid that contained 128 vertical zones in this "northern" hemisphere.</li>
			</ul>

	=See Also=		=See Also=

	{{ SGFfooter }}		{{ SGFfooter }}

Joel2: /* Model A */

2024-10-25T17:44:57Z

Model A

← Older revision		Revision as of 13:44, 25 October 2024
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	The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.		The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.

			====1<sup>st</sup> Video====

			Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character. The icon shown here, on the left, links to a YouTube video that shows the nonlinear development of this instability.

	<table border="0" align="left" cellpadding="2">		<table border="0" align="left" cellpadding="2">
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	<tr>		<tr>
	<td align="center">		<td align="center">
	[[File:VideoCoverModelABarmodeInstability.png\|250px\|Model A ~~Barmode~~ Instability]]		[[File:VideoCoverModelABarmodeInstability.png\|250px\|Model A Bar-mode Instability]]
	</td>		</td>
	</tr>		</tr>

Joel2: /* Model A */

2024-10-25T17:32:51Z

Model A

← Older revision		Revision as of 13:32, 25 October 2024
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	The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.		The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.

	<b>YouTube</b> video:  [https://www.youtube.com/watch?v=BhRUqZe0Ly4 ~~Model A~~] ~~evolution:~~		<table border="0" align="left" cellpadding="2">
			<tr><td align="center">Model A Barmode Instability</td></tr>
			<tr>
			<td align="center">
			[[File:VideoCoverModelABarmodeInstability.png\|250px\|Model A Barmode Instability]]
			</td>
			</tr>
			<tr>
			<td align="center">
			<b>YouTube</b> video:  [https://www.youtube.com/watch?v=BhRUqZe0Ly4 BhRUqZe0Ly4]
			</td>
			</tr>
			</table>

	=See Also=		=See Also=

	{{ SGFfooter }}		{{ SGFfooter }}

Joel2: /* Model A */

2024-10-25T17:20:38Z

Model A

← Older revision		Revision as of 13:20, 25 October 2024
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	===Model A===		===Model A===

	<table border="1" align="right" cellpadding="5" width="30%">		<table border="0" align="right" cellpadding="10" width="30%"><tr><td align="center">
			<table border="1" align="center" cellpadding="5">
	<tr><td align="center">Table 1 extracted from p. 1057 of<br />{{ CT2000figure }}</td></tr		<tr><td align="center">Table 1 extracted from p. 1057 of<br />{{ CT2000figure }}</td></tr
	><tr><td align="center">[[File:CT2000Table01.png\|350px\|CT2000 Table 1]]</td></tr>		><tr><td align="center">[[File:CT2000Table01.png\|350px\|CT2000 Table 1]]</td></tr>
	</table>The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')		</table></td></tr></table>The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')

	The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.		The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.

Joel2: /* Model A */

2024-10-25T17:17:36Z

Model A

← Older revision		Revision as of 13:17, 25 October 2024
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	===Model A===		===Model A===
	The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')

	The initial values of various "Model A" parameters are provided in Table 1 (p. 1057) of {{ CT2000 }}. For example, the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>.		<table border="1" align="right" cellpadding="5" width="30%">
			<tr><td align="center">Table 1 extracted from p. 1057 of<br />{{ CT2000figure }}</td></tr
			><tr><td align="center">[[File:CT2000Table01.png\|350px\|CT2000 Table 1]]</td></tr>
			</table>The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')

			The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of {{ CT2000 }} — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, <math>\rho_\mathrm{max}/\bar\rho = 5.66</math>; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>. For comparison — see the first column of numbers — in a [[SSC/Structure/Polytropes/Numerical#Chandrasekhar\|nonrotating, spherically symmetric <math>n = \tfrac{3}{2}</math> polytrope]], <math>\rho_\mathrm{max}/\bar\rho = 5.99</math> and <math>T_\mathrm{rot}/\|W\| = 0.0</math>.

	<b>YouTube</b> video:  [https://www.youtube.com/watch?v=BhRUqZe0Ly4 Model A] evolution:		<b>YouTube</b> video:  [https://www.youtube.com/watch?v=BhRUqZe0Ly4 Model A] evolution:

Joel2: /* Simulations Performed by John Cazes */

2024-10-25T00:24:01Z

Simulations Performed by John Cazes

← Older revision		Revision as of 20:24, 24 October 2024
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	The initial values of various "Model A" parameters are provided in Table 1 (p. 1057) of {{ CT2000 }}. For example, the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>.		The initial values of various "Model A" parameters are provided in Table 1 (p. 1057) of {{ CT2000 }}. For example, the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>.

			<b>YouTube</b> video:  [https://www.youtube.com/watch?v=BhRUqZe0Ly4 Model A] evolution:

	=See Also=		=See Also=

	{{ SGFfooter }}		{{ SGFfooter }}

Joel2 at 00:12, 25 October 2024

2024-10-25T00:12:26Z

← Older revision		Revision as of 20:12, 24 October 2024
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	===Model A===		===Model A===
	The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. ~~Thus~~, ~~this model~~ sits on the so-called <math>n'=0</math> sequence, as ~~defined~~ by {{ ~~Stoeckly65full~~ }} and as implemented by, for example, {{ ~~OM68full~~ }}, and {{ ~~BO73full~~ }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')		The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by {{ Stoeckly65full }}. With this in mind, it is clear that "Model A" sits on the so-called <math>n'=0</math> sequence, as introduced by {{ OM68full }}, and as implemented, for example, by {{ BO73full }}, and by {{ PDD96full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')

			The initial values of various "Model A" parameters are provided in Table 1 (p. 1057) of {{ CT2000 }}. For example, the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, <math>T_\mathrm{rot}/\|W\| = 0.30</math>.

	=See Also=		=See Also=

	{{ SGFfooter }}		{{ SGFfooter }}

Joel2 at 23:50, 24 October 2024

2024-10-24T23:50:39Z

← Older revision		Revision as of 19:50, 24 October 2024
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	==Simulations Performed by John Cazes==		==Simulations Performed by John Cazes==

	Here we summarize the results of numerical simulations that John Cazes performed as part of [https://digitalcommons.lsu.edu/gradschool_disstheses/6982/ his doctoral dissertation research], which was completed in 1999.		Here we summarize the results of numerical simulations that John Cazes performed as part of [https://digitalcommons.lsu.edu/gradschool_disstheses/6982/ his doctoral dissertation research], which was completed in 1999. A portion of this work has been published by {{ CT2000full }} in an article titled, "<i>Self-Gravitating Gaseous Bars.   I. Compressible Analogs of Riemann Ellipsoids with Supersonic Internal Flows.</i>"

			===Model A===
			The initial configuration of "Model A" is an axisymmetric, <math>n = \tfrac{3}{2}</math> polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius, <math>\varpi</math>, has the same function as a uniformly rotating, <math>n=0</math> polytrope — that is, the same as a Maclaurin spheroid. Thus, this model sits on the so-called <math>n'=0</math> sequence, as defined by {{ Stoeckly65full }} and as implemented by, for example, {{ OM68full }}, and {{ BO73full }}. (See our [[AxisymmetricConfigurations/SolutionStrategies#Uniform-Density_Initially_(n'_=_0)\|additional discussion of ''Simple Rotation Profiles]].'')

	=See Also=		=See Also=

	{{ SGFfooter }}		{{ SGFfooter }}