Mathematica Simulation - Revision history

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Vanwdani at 18:00, 19 April 2017

2017-04-19T18:00:46Z

Vanwdani at 17:58, 19 April 2017

2017-04-19T17:58:09Z

Vanwdani at 17:55, 19 April 2017

2017-04-19T17:55:49Z

Vanwdani at 17:52, 19 April 2017

2017-04-19T17:52:45Z

Vanwdani: /* Setting up Mathematica for DC Theta-Phi Isotropic Cone */

2017-04-19T17:51:45Z

Setting up Mathematica for DC Theta-Phi Isotropic Cone

Vanwdani: /* Setting up Mathematica for DC Theta-Phi Isotropic Cone */

2017-04-19T17:50:34Z

Setting up Mathematica for DC Theta-Phi Isotropic Cone

Vanwdani: /* Setting up Mathematica for DC Theta-Phi Isotropic Cone */

2017-04-19T17:43:45Z

Setting up Mathematica for DC Theta-Phi Isotropic Cone

Vanwdani: /* Setting up Mathematica for DC Theta-Phi Isotropic Cone */

2017-03-13T15:15:58Z

Setting up Mathematica for DC Theta-Phi Isotropic Cone

Vanwdani: /* Setting up Mathematica for DC Theta-Phi Isotropic Cone */

2017-03-13T15:14:20Z

Setting up Mathematica for DC Theta-Phi Isotropic Cone

@@ Line 142: / Line 142: @@
 </pre>
-At \[Phi]=0, the condition of n=-959.637/(tan \[Theta]\[Degree] +2.14437)+430.189  should be met
+At <math>\phi </math>=0, the condition of n=-959.637/(tan <math>\theta^{\circ}</math> +2.14437)+430.189  should be met
 <pre>
@@ Line 154: / Line 154: @@
-This implies that for \[Theta]=40, we know that the wire number to be 108.538.  This corresponds to the position being in between 108.5 and 109.5, hence it falls into the 109 "bin".
+This implies that for <math>\theta=40^{\circ}</math>, we know that the wire number to be 108.538.  This corresponds to the position being in between 108.5 and 109.5, hence it falls into the 109 "bin".
 Testing the geometry

@@ Line 37: / Line 37: @@
 </pre>
-All of the conditions dependent on <math> \theta </math>and <math>\phi</math>
+All of the conditions dependent on <math> \theta </math> and <math>\phi</math>
 <pre>
@@ Line 81: / Line 81: @@
 </pre>
-We can define the x-y position on the DC plane as a function of \[Phi] for and limit the angles with the wall on the right and left hand sides.  By symmetry these angles are equal, but opposite in sign.  The range of <math>\phi</math> in the plane of the DC sector changes as <math>\theta</math> increases, so does <math>\phi</math> increase.
+We can define the x-y position on the DC plane as a function of <math>\phi</math> for and limit the angles with the wall on the right and left hand sides.  By symmetry these angles are equal, but opposite in sign.
 <pre>
@@ Line 118: / Line 118: @@
 </pre>
-This limiting condition will record the angle <math>\phi</math> in degrees within an array of wire number(1-112) horizontally  and angle <math>\theta (5\circ-40\circ )</math> vertically
+This limiting condition will record the angle <math>\phi</math> in degrees within an array of wire number(1-112) horizontally  and angle <math>\theta (5^{\circ}-40^{\circ} )</math> vertically
 <pre>

@@ Line 37: / Line 37: @@
 </pre>
-All of the conditions dependent on<math> \Theta </math>and \Phi
+All of the conditions dependent on <math> \theta </math>and <math>\phi</math>
 <pre>
@@ Line 81: / Line 81: @@
 </pre>
-We can define the x-y position on the DC plane as a function of \[Phi] for and limit the angles with the wall on the right and left hand sides.  By symmetry these angles are equal, but opposite in sign.  The range of \[Phi] in the plane of the DC sector changes as \[Theta] increases, so does \[Phi] increase.
+We can define the x-y position on the DC plane as a function of \[Phi] for and limit the angles with the wall on the right and left hand sides.  By symmetry these angles are equal, but opposite in sign.  The range of <math>\phi</math> in the plane of the DC sector changes as <math>\theta</math> increases, so does <math>\phi</math> increase.
 <pre>
@@ Line 105: / Line 105: @@
 </pre>
-The limit of \[Phi] increases in the plane of the DC sector changes as \[Theta] increases.
+The limit of <math>\phi</math> increases in the plane of the DC sector changes as <math>\theta</math> increases.
 <pre>
@@ Line 118: / Line 118: @@
 </pre>
-This limiting condition will record the angle \[Phi] in degrees within an array of wire number(1-112) horizontally  and angle \[Theta] (5\[Degree]-40\[Degree]) vertically
+This limiting condition will record the angle <math>\phi</math> in degrees within an array of wire number(1-112) horizontally  and angle <math>\theta (5\circ-40\circ )</math> vertically
 <pre>

@@ Line 37: / Line 37: @@
 </pre>
-All of the conditions dependent on \Theta and \Phi
+All of the conditions dependent on<math> \Theta </math>and \Phi
 <pre>

@@ Line 37: / Line 37: @@
 </pre>
-All of the conditions dependent on \[Theta] and \[Phi]
+All of the conditions dependent on \Theta and \Phi
 <pre>

← Older revision		Revision as of 17:50, 19 April 2017
Line 80:		Line 80:
	R = 2.52934271645;		R = 2.52934271645;
	</pre>		</pre>
		+
		+	We can define the x-y position on the DC plane as a function of \[Phi] for and limit the angles with the wall on the right and left hand sides. By symmetry these angles are equal, but opposite in sign. The range of \[Phi] in the plane of the DC sector changes as \[Theta] increases, so does \[Phi] increase.
		+
		+	<pre>
		+	Limits = Table[\[Phi] /.
		+	NSolve[Sqrt[a^2 (1 - y^2/b^2)] - \[CapitalDelta]a ==
		+	Cot[29.5 \[Degree]] y + .09156 , \[Phi]], {\[Theta], 5, 40}];
		+	Lim = Table[0, {rows, 1, 36}];
		+	For[rows = 1, rows < 37, rows++,
		+	For[i = 1, i < 5, i++,
		+	If[Limits[[rows, i]] > 0 && Limits[[rows, i]] < 40,
		+	Lim[[rows]] = Limits[[rows, i]];
		+	];
		+	];
		+	];
		+	</pre>
		+
		+	The angle must have 4 subtracted to equal the line element numbering
		+
		+	<pre>
		+	In[33]:= Lim[[7 - 4]]
		+
		+	Out[33]= 23.4101
		+	</pre>
		+
		+	The limit of \[Phi] increases in the plane of the DC sector changes as \[Theta] increases.
		+
		+	<pre>
		+	In[34]:= Lim[1]
		+
		+	Out[34]= {20.076, 22.024, 23.4101, 24.448, 25.255, 25.9008, 26.4297,
		+	26.8711, 27.2453, 27.5667, 27.846, 28.0911, 28.3079, 28.5013,
		+	28.675, 28.8319, 28.9744, 29.1044, 29.2237, 29.3336, 29.4352,
		+	29.5294, 29.6171, 29.699, 29.7757, 29.8477, 29.9155, 29.9795,
		+	30.0399, 30.0973, 30.1517, 30.2034, 30.2528, 30.2999, 30.3449,
		+	30.388}[1]
		+	</pre>
		+
		+	This limiting condition will record the angle \[Phi] in degrees within an array of wire number(1-112) horizontally and angle \[Theta] (5\[Degree]-40\[Degree]) vertically
		+
		+	<pre>
		+	RightSolutions =
		+	Table[{\[Phi] /.
		+	Solve[Sqrt[a^2 (1 - y^2/b^2)] - \[CapitalDelta]a ==
		+	Tan[6 \[Degree]] y +
		+	x0forWireMiddles[number] , \[Phi]]}, {\[Theta], 5,
		+	40}, {number, 1, 112}];
		+	LineRight = Table[{\[Phi], columns}, {rows, 1, 36}, {columns, 1, 112}];
		+	For[rows = 1, rows < 37, rows++,
		+	For[columns = 1, columns < 113, columns++,
		+	For[i = 1, i < 5, i++,
		+	If[RightSolutions[[rows, columns, 1, i]] > 0 &&
		+	RightSolutions[[rows, columns, 1, i]] < Lim[[rows]],
		+	LineRight[[rows,
		+	columns]] = {RightSolutions[[rows, columns, 1, i]],
		+	columns + .5};
		+	];
		+	];
		+	];
		+	];
		+	</pre>
		+
		+	At \[Phi]=0, the condition of n=-959.637/(tan \[Theta]\[Degree] +2.14437)+430.189 should be met
		+
		+	<pre>
		+	In[38]:= f[\[Theta]for\[Phi]at0_] := -959.637/(
		+	Tan[\[Theta]for\[Phi]at0 \[Degree]] + 2.14437) + 430.189
		+
		+	In[39]:= f[40]
		+
		+	Out[39]= 108.538
		+	</pre>
		+
		+
		+	This implies that for \[Theta]=40, we know that the wire number to be 108.538. This corresponds to the position being in between 108.5 and 109.5, hence it falls into the 109 "bin".
		+
		+	Testing the geometry
		+	<pre>
		+	ClearAll[\[Theta]];
		+	\[Theta] = 40;
		+	ellipse40 =
		+	ContourPlot[(x + \[CapitalDelta]a)^2/a^2 + y^2/b^2 == 1, {y, -1,
		+	1}, {x, 1.2, 1.7}, Frame -> {True, True, False, False},
		+	PlotLabel ->
		+	"XY position on DC as a function of \[Phi] for \[Theta]=40\
		+	\[Degree]", FrameLabel -> {"y (meters)", "x (meters)"},
		+	ContourStyle -> Red, PlotLegends -> Automatic];
		+	Show[Table[
		+	ContourPlot[
		+	xWire == Tan[6 \[Degree]] yWire + x0forWires[number], {yWire, -1,
		+	1}, {xWire, 1.2, 1.7},
		+	FrameLabel -> {"y(meters)", "x(meters)"}], {number, 70, 109}],
		+	Table[ContourPlot[
		+	xWire ==
		+	Tan[6 \[Degree]] yWire + x0forWireMiddles[number2], {yWire, -1,
		+	1}, {xWire, 1.2, 1.7},
		+	ContourStyle -> {Dashing[Large]}], {number2, 70,
		+	109}], bottom, right, left, ellipse40]
		+	</pre>
		+
		+	[[File:40EllipseTest.png]]

← Older revision		Revision as of 17:43, 19 April 2017
Line 2:		Line 2:


−	<~~center~~>[[~~File~~:~~Part1d~~.~~pdf~~]]</~~center~~>	+	We can define the constraints of the plane the DC is in
		+
		+	<pre>
		+	right = ContourPlot[
		+	x2 == Cot[29.5 \[Degree]] y + .09156, {y, -1, 1}, {x2, 0, 1.8},
		+	Frame -> {True, True, False, False},
		+	PlotLabel -> "Right side limit of DC as a function of X and Y",
		+	FrameLabel -> {"y (meters)", "x (meters)"}, ContourStyle -> Black,
		+	PlotLegends -> Automatic];
		+
		+	left = ContourPlot[
		+	x2 == -Cot[29.5 \[Degree]] y + .09156, {y, -1, 1}, {x2, 0, 1.8},
		+	Frame -> {True, True, False, False},
		+	PlotLabel -> "Right side limit of DC as a function of X and Y",
		+	FrameLabel -> {"y (meters)", "x (meters)"}, ContourStyle -> Black,
		+	PlotLegends -> Automatic];
		+
		+	</pre>
		+
		+
		+	We can define the x coordinate of the wires as they cross the midpoint plane as shown earlier.
		+
		+	<pre>
		+	x0forWires[number_] := .23168 + .01337*(number);
		+	</pre>
		+
		+
		+	We can define the point midway between two parallel lines as the point where one wire is recorded versus its next highest neighbor
		+
		+	<pre>
		+	x0forWireMiddles[
		+	number_] := ((.23168 + .01337(number)) + (.23168 + .01337(number \
		+	+ 1)))/2;
		+	</pre>
		+
		+	All of the conditions dependent on \[Theta] and \[Phi]
		+
		+	<pre>
		+
		+	\[CapitalDelta]a :=
		+	FullSimplify[(R Sin[\[Theta] \[Degree]])/
		+	2 (Csc[65 \[Degree] - \[Theta] \[Degree]] -
		+	Csc[115 \[Degree] - \[Theta] \[Degree]]), \[Theta] > 0];
		+	e := Sin[25 \[Degree]]/Cos[\[Theta] \[Degree]];
		+	a := FullSimplify[(R Sin[\[Theta] \[Degree]])/
		+	2 (Csc[65 \[Degree] - \[Theta] \[Degree]] +
		+	Csc[115 \[Degree] - \[Theta] \[Degree]]), \[Theta] > 0];
		+	rD1 := Simplify[(a e - \[CapitalDelta]a) Tan[
		+	65 \[Degree]] Cos[\[Theta] \[Degree]], \[Theta] > 0];
		+	rD2 := Simplify[(a e + \[CapitalDelta]a) Tan[
		+	65 \[Degree]] Cos[\[Theta] \[Degree]], \[Theta] > 0];
		+	xD1 := Simplify[rD1 Cos[\[Phi] \[Degree]]];
		+	yD1 := Simplify[rD1 Sin[\[Phi] \[Degree]]];
		+	zD1 := Simplify[rD1 Cot[\[Theta] \[Degree]], \[Theta] > 0];
		+	xD2 := Simplify[rD2 Cos[\[Phi] \[Degree]], \[Theta] > 0];
		+	yD2 := Simplify[rD2 Sin[\[Phi] \[Degree]], \[Theta] > 0];
		+	zD2 := Simplify[rD2 Cot[\[Theta] \[Degree]], \[Theta] > 0];
		+	xP := Simplify[(R Cos[\[Phi] \[Degree]])/(Cot[\[Theta] \[Degree]] +
		+	Cos[\[Phi] \[Degree]] Cot[65 \[Degree]]), \[Theta] > 0];
		+	yP := Simplify[(R Sin[\[Phi] \[Degree]])/(Cot[\[Theta] \[Degree]] +
		+	Cos[\[Phi] \[Degree]] Cot[65 \[Degree]]), \[Theta] > 0];
		+	zP := Simplify[(R Cot[\[Theta] \[Degree]])/(Cot[\[Theta] \[Degree]] +
		+	Cos[\[Phi] \[Degree]] Cot[65 \[Degree]]), \[Theta] > 0];
		+	x1 := Simplify[(rD2^2 - rD1^2 +
		+	Cot[\[Theta] \[Degree]]^2 (rD2^2 - rD1^2) - 2 xP (xD2 - xD1) -
		+	2 yP (yD2 - yD1) - 2 zP (zD2 - zD1))/(4 a e) - a e, \[Theta] >
		+	0];
		+	x := Simplify[x1 - \[CapitalDelta]a + a e, \[Theta] > 0];
		+	xCenter := x + \[CapitalDelta]a;
		+	n := -957.412/(Tan[\[Theta] \[Degree]] + 2.14437) + 430.626;
		+	D2P := Simplify[((xD2 - xP)^2 + (yD2 - yP)^2 + (zD2 -
		+	zP )^2)^.5, \[Theta] > 0] // N
		+	D1P := Simplify[((xP - xD1)^2 + (yP - yD1)^2 + (zP -
		+	zD1)^2)^.5, \[Theta] > 0] // N;
		+	y := Simplify[(D1P^2 - x1^2)^.5, \[Theta] > 0] // N;
		+	b := Simplify[a Sqrt[1 - e^2], \[Theta] > 0] // N;
		+	R = 2.52934271645;
		+	</pre>

← Older revision		Revision as of 15:15, 13 March 2017
Line 1:		Line 1:
	==Setting up Mathematica for DC Theta-Phi Isotropic Cone==		==Setting up Mathematica for DC Theta-Phi Isotropic Cone==
−
−	~~<center>[[File:FirstPass.pdf]]</center>~~
−


	<center>[[File:Part1d.pdf]]</center>		<center>[[File:Part1d.pdf]]</center>

← Older revision		Revision as of 15:14, 13 March 2017
Line 5:		Line 5:


−	<center>[[File:~~SecondPass~~.pdf]]</center>	+	<center>[[File:Part1d.pdf]]</center>