ViewVC Help
View File | Revision Log | Show Annotations | View Changeset | Root Listing
root/group/trunk/multipole/DipoleTensor.nb
Revision: 4195
Committed: Thu Jul 17 18:24:41 2014 UTC (9 years, 11 months ago) by gezelter
File size: 26212 byte(s)
Log Message:
Most recent version including dielectric stuff

File Contents

# User Rev Content
1 gezelter 4195 (*CacheID: 234*)
2     (* Internal cache information:
3     NotebookFileLineBreakTest
4     NotebookFileLineBreakTest
5     NotebookDataPosition[ 0, 0]
6     NotebookDataLength[ 26211, 815]
7     NotebookOptionsPosition[ 24416, 745]
8     NotebookOutlinePosition[ 24771, 761]
9     CellTagsIndexPosition[ 24728, 758]
10     WindowFrame->Normal*)
11    
12     (* Beginning of Notebook Content *)
13     Notebook[{
14     Cell[BoxData[{
15     RowBox[{
16     RowBox[{"rc", "=."}], ";"}], "\[IndentingNewLine]",
17     RowBox[{
18     RowBox[{"\[Kappa]", "=."}], ";"}], "\[IndentingNewLine]",
19     RowBox[{
20     RowBox[{
21     RowBox[{"f", "[",
22     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
23     RowBox[{
24     RowBox[{"Erfc", "[",
25     RowBox[{"\[Kappa]", " ", "r"}], "]"}], "/", "r"}]}],
26     ";"}], "\[IndentingNewLine]",
27     RowBox[{
28     RowBox[{
29     RowBox[{"g", "[",
30     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
31     RowBox[{
32     RowBox[{
33     RowBox[{"(",
34     RowBox[{
35     RowBox[{"-", "2"}], "*", "\[Kappa]"}], ")"}], "/",
36     RowBox[{"(",
37     RowBox[{
38     RowBox[{"E", "^",
39     RowBox[{"(",
40     RowBox[{
41     RowBox[{"r", "^", "2"}], "*",
42     RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
43     RowBox[{"Sqrt", "[", "Pi", "]"}], "*", "r"}], ")"}]}], "-",
44     RowBox[{
45     RowBox[{"Erfc", "[",
46     RowBox[{"r", "*", "\[Kappa]"}], "]"}], "/",
47     RowBox[{"r", "^", "2"}]}]}]}], " ", ";"}], "\[IndentingNewLine]",
48     RowBox[{
49     RowBox[{
50     RowBox[{"h", "[",
51     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=",
52     RowBox[{
53     RowBox[{
54     RowBox[{"(",
55     RowBox[{"4", "*", "\[Kappa]"}], ")"}], "/",
56     RowBox[{"(",
57     RowBox[{
58     RowBox[{"E", "^",
59     RowBox[{"(",
60     RowBox[{
61     RowBox[{"r", "^", "2"}], "*",
62     RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
63     RowBox[{"Sqrt", "[", "Pi", "]"}], "*",
64     RowBox[{"r", "^", "2"}]}], ")"}]}], "+",
65     RowBox[{
66     RowBox[{"(",
67     RowBox[{"4", "*",
68     RowBox[{"\[Kappa]", "^", "3"}]}], ")"}], "/",
69     RowBox[{"(",
70     RowBox[{
71     RowBox[{"E", "^",
72     RowBox[{"(",
73     RowBox[{
74     RowBox[{"r", "^", "2"}], "*",
75     RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
76     RowBox[{"Sqrt", "[", "Pi", "]"}]}], ")"}]}], "+",
77     RowBox[{
78     RowBox[{"(",
79     RowBox[{"2", "*",
80     RowBox[{"Erfc", "[",
81     RowBox[{"r", "*", "\[Kappa]"}], "]"}]}], ")"}], "/",
82     RowBox[{"r", "^", "3"}]}]}]}], ";"}], "\[IndentingNewLine]",
83     RowBox[{
84     RowBox[{
85     RowBox[{"s", "[",
86     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=",
87     RowBox[{
88     RowBox[{
89     RowBox[{"(",
90     RowBox[{
91     RowBox[{"-", "12"}], "*", "\[Kappa]"}], ")"}], "/",
92     RowBox[{"(",
93     RowBox[{
94     RowBox[{"E", "^",
95     RowBox[{"(",
96     RowBox[{
97     RowBox[{"r", "^", "2"}], "*",
98     RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
99     RowBox[{"Sqrt", "[", "Pi", "]"}], "*",
100     RowBox[{"r", "^", "3"}]}], ")"}]}], "-",
101     RowBox[{
102     RowBox[{"(",
103     RowBox[{"8", "*",
104     RowBox[{"\[Kappa]", "^", "3"}]}], ")"}], "/",
105     RowBox[{"(",
106     RowBox[{
107     RowBox[{"E", "^",
108     RowBox[{"(",
109     RowBox[{
110     RowBox[{"r", "^", "2"}], "*",
111     RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
112     RowBox[{"Sqrt", "[", "Pi", "]"}], "*", "r"}], ")"}]}], "-",
113     RowBox[{
114     RowBox[{"(",
115     RowBox[{"8", "*", "r", "*",
116     RowBox[{"\[Kappa]", "^", "5"}]}], ")"}], "/",
117     RowBox[{"(",
118     RowBox[{
119     RowBox[{"E", "^",
120     RowBox[{"(",
121     RowBox[{
122     RowBox[{"r", "^", "2"}], "*",
123     RowBox[{"\[Kappa]", "^", "2"}]}], ")"}]}], "*",
124     RowBox[{"Sqrt", "[", "Pi", "]"}]}], ")"}]}], "-",
125     RowBox[{
126     RowBox[{"(",
127     RowBox[{"6", "*",
128     RowBox[{"Erfc", "[",
129     RowBox[{"r", "*", "\[Kappa]"}], "]"}]}], ")"}], "/",
130     RowBox[{"r", "^", "4"}]}]}]}], ";"}], "\[IndentingNewLine]",
131     RowBox[{
132     RowBox[{
133     RowBox[{"f2", "[",
134     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
135     RowBox[{
136     RowBox[{"f", "[",
137     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ",
138     RowBox[{"f", "[",
139     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
140     RowBox[{
141     RowBox[{"(",
142     RowBox[{"r", "-", "rc"}], ")"}],
143     RowBox[{"g", "[",
144     RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}], "-",
145     RowBox[{
146     RowBox[{
147     RowBox[{"(",
148     RowBox[{"r", "-", "rc"}], ")"}], "^", "2"}], " ",
149     RowBox[{
150     RowBox[{"h", "[",
151     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "2"}]}], " ", "-", " ",
152     RowBox[{
153     RowBox[{
154     RowBox[{"(",
155     RowBox[{"r", "-", "rc"}], ")"}], "^", "3"}], " ",
156     RowBox[{
157     RowBox[{"s", "[",
158     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "6"}]}]}]}],
159     ";"}], "\[IndentingNewLine]",
160     RowBox[{
161     RowBox[{
162     RowBox[{"g2", "[",
163     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=", " ",
164     RowBox[{
165     RowBox[{"g", "[",
166     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-", " ",
167     RowBox[{"g", "[",
168     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
169     RowBox[{
170     RowBox[{"(",
171     RowBox[{"r", "-", "rc"}], ")"}],
172     RowBox[{"h", "[",
173     RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}], "-",
174     RowBox[{
175     RowBox[{
176     RowBox[{"(",
177     RowBox[{"r", "-", "rc"}], ")"}], "^", "2"}], " ",
178     RowBox[{
179     RowBox[{"s", "[",
180     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "2"}]}]}]}], " ",
181     ";"}], "\[IndentingNewLine]",
182     RowBox[{
183     RowBox[{
184     RowBox[{"h2", "[",
185     RowBox[{"r_", ",", "\[Kappa]_"}], "]"}], ":=",
186     RowBox[{
187     RowBox[{"h", "[",
188     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
189     RowBox[{"h", "[",
190     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], " ", "-", " ",
191     RowBox[{
192     RowBox[{"(",
193     RowBox[{"r", "-", "rc"}], ")"}],
194     RowBox[{"s", "[",
195     RowBox[{"rc", ",", "\[Kappa]"}], "]"}]}]}]}],
196     ";"}], "\[IndentingNewLine]",
197     RowBox[{
198     RowBox[{
199     RowBox[{"v21", "[",
200     RowBox[{"r_", ",", "method_"}], "]"}], ":=",
201     RowBox[{"Switch", "[",
202     RowBox[{"method", ",", "\[IndentingNewLine]", "BARE", ",", " ",
203     RowBox[{
204     RowBox[{"g", "[",
205     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}], ",", " ",
206     "\[IndentingNewLine]", "TSF", ",", " ",
207     RowBox[{
208     RowBox[{"g2", "[",
209     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}], ",",
210     "\[IndentingNewLine]", "SP", ",", " ",
211     RowBox[{
212     RowBox[{
213     RowBox[{"g", "[",
214     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}], " ", "-", " ",
215     RowBox[{
216     RowBox[{"g", "[",
217     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "rc"}]}], ",",
218     "\[IndentingNewLine]", "GSF", ",", " ",
219     RowBox[{
220     RowBox[{
221     RowBox[{"g", "[",
222     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}], " ", "-", " ",
223     RowBox[{
224     RowBox[{"g", "[",
225     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "rc"}], " ", "-", " ",
226     RowBox[{
227     RowBox[{"(",
228     RowBox[{"r", "-", "rc"}], ")"}],
229     RowBox[{"(",
230     RowBox[{
231     RowBox[{
232     RowBox[{"h", "[",
233     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "rc"}], " ", "-", " ",
234     RowBox[{
235     RowBox[{"g", "[",
236     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/",
237     RowBox[{"rc", "^", "2"}]}]}], ")"}]}]}]}], "\[IndentingNewLine]",
238     "]"}]}], ";"}], "\[IndentingNewLine]",
239     RowBox[{
240     RowBox[{
241     RowBox[{"v22", "[",
242     RowBox[{"r_", ",", " ", "method_"}], "]"}], ":=", " ",
243     RowBox[{"Switch", "[",
244     RowBox[{"method", ",", " ", "\[IndentingNewLine]", "BARE", ",",
245     RowBox[{
246     RowBox[{"h", "[",
247     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
248     RowBox[{
249     RowBox[{"g", "[",
250     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}]}], ",", " ",
251     "\[IndentingNewLine]", "TSF", ",", " ",
252     RowBox[{
253     RowBox[{"h2", "[",
254     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
255     RowBox[{
256     RowBox[{"g2", "[",
257     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}]}], ",", " ",
258     "\[IndentingNewLine]", "SP", ",", " ",
259     RowBox[{
260     RowBox[{"h", "[",
261     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
262     RowBox[{
263     RowBox[{"g", "[",
264     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}], " ", "-",
265     RowBox[{"(",
266     RowBox[{
267     RowBox[{"h", "[",
268     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
269     RowBox[{
270     RowBox[{"g", "[",
271     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "rc"}]}], ")"}]}], ",",
272     " ", "\[IndentingNewLine]", "GSF", ",", " ",
273     RowBox[{
274     RowBox[{"h", "[",
275     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "-",
276     RowBox[{
277     RowBox[{"g", "[",
278     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "/", "r"}], " ", "-",
279     RowBox[{"(", " ",
280     RowBox[{
281     RowBox[{"h", "[",
282     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
283     RowBox[{
284     RowBox[{"g", "[",
285     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "rc"}]}], ")"}], " ",
286     "-", " ",
287     RowBox[{
288     RowBox[{"(",
289     RowBox[{"r", "-", "rc"}], ")"}],
290     RowBox[{"(",
291     RowBox[{
292     RowBox[{"s", "[",
293     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "-",
294     RowBox[{
295     RowBox[{"h", "[",
296     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/", "rc"}], " ", "+", " ",
297     RowBox[{
298     RowBox[{"g", "[",
299     RowBox[{"rc", ",", "\[Kappa]"}], "]"}], "/",
300     RowBox[{"rc", "^", "2"}]}]}], ")"}]}]}]}], "\[IndentingNewLine]",
301     "]"}]}], ";"}], "\[IndentingNewLine]",
302     RowBox[{
303     RowBox[{
304     RowBox[{"R", "[", "\[Alpha]_", "]"}], " ", ":=",
305     RowBox[{"r", " ",
306     RowBox[{"Switch", "[",
307     RowBox[{"\[Alpha]", ",", " ", "\[IndentingNewLine]", "1", ",",
308     RowBox[{
309     RowBox[{"Sin", "[", "\[Theta]", "]"}],
310     RowBox[{"Cos", "[", "\[Phi]", "]"}]}], " ", ",", "\[IndentingNewLine]",
311     "2", ",",
312     RowBox[{
313     RowBox[{"Sin", "[", "\[Theta]", "]"}],
314     RowBox[{"Sin", "[", "\[Phi]", "]"}]}], " ", ",", "\[IndentingNewLine]",
315     "3", ",",
316     RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}]}],
317     ";"}], "\[IndentingNewLine]",
318     RowBox[{
319     RowBox[{
320     RowBox[{"T", "[",
321     RowBox[{"\[Alpha]_", ",", "\[Beta]_", ",", " ", "method_"}], "]"}], " ", ":=",
322     " ",
323     RowBox[{
324     RowBox[{
325     RowBox[{"KroneckerDelta", "[",
326     RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "*", " ",
327     RowBox[{"v21", "[",
328     RowBox[{"r", ",", " ", "method"}], "]"}]}], "+", " ",
329     RowBox[{
330     RowBox[{"R", "[", "\[Alpha]", "]"}],
331     RowBox[{"R", "[", "\[Beta]", "]"}],
332     RowBox[{"(",
333     RowBox[{
334     RowBox[{"v22", "[",
335     RowBox[{"r", ",", "method"}], "]"}], "/",
336     RowBox[{"r", "^", "2"}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
337     RowBox[{
338     RowBox[{"TBare", " ", "=", " ",
339     RowBox[{"MatrixForm", "[",
340     RowBox[{"Table", "[",
341     RowBox[{
342     RowBox[{"Table", "[",
343     RowBox[{
344     RowBox[{"Integrate", "[",
345     RowBox[{
346     RowBox[{
347     RowBox[{"r", "^", "2"}],
348     RowBox[{"Integrate", "[",
349     RowBox[{
350     RowBox[{"Integrate", "[",
351     RowBox[{
352     RowBox[{
353     RowBox[{"Sin", "[", "\[Theta]", "]"}],
354     RowBox[{"T", "[",
355     RowBox[{"i", ",", "j", ",", "BARE"}], "]"}]}], ",",
356     RowBox[{"{",
357     RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
358     ",",
359     RowBox[{"{",
360     RowBox[{"\[Phi]", ",", "0", ",",
361     RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
362     RowBox[{"{",
363     RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
364     RowBox[{"{",
365     RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
366     RowBox[{"{",
367     RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
368     ";"}], "\[IndentingNewLine]",
369     RowBox[{
370     RowBox[{"TSP", " ", "=", " ",
371     RowBox[{"MatrixForm", "[",
372     RowBox[{"Table", "[",
373     RowBox[{
374     RowBox[{"Table", "[",
375     RowBox[{
376     RowBox[{"Integrate", "[",
377     RowBox[{
378     RowBox[{
379     RowBox[{"r", "^", "2"}],
380     RowBox[{"Integrate", "[",
381     RowBox[{
382     RowBox[{"Integrate", "[",
383     RowBox[{
384     RowBox[{
385     RowBox[{"Sin", "[", "\[Theta]", "]"}],
386     RowBox[{"T", "[",
387     RowBox[{"i", ",", "j", ",", "SP"}], "]"}]}], ",",
388     RowBox[{"{",
389     RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
390     ",",
391     RowBox[{"{",
392     RowBox[{"\[Phi]", ",", "0", ",",
393     RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
394     RowBox[{"{",
395     RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
396     RowBox[{"{",
397     RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
398     RowBox[{"{",
399     RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
400     ";"}], "\[IndentingNewLine]",
401     RowBox[{
402     RowBox[{"TGSF", " ", "=", " ",
403     RowBox[{"MatrixForm", "[",
404     RowBox[{"Table", "[",
405     RowBox[{
406     RowBox[{"Table", "[",
407     RowBox[{
408     RowBox[{"Integrate", "[",
409     RowBox[{
410     RowBox[{
411     RowBox[{"r", "^", "2"}],
412     RowBox[{"Integrate", "[",
413     RowBox[{
414     RowBox[{"Integrate", "[",
415     RowBox[{
416     RowBox[{
417     RowBox[{"Sin", "[", "\[Theta]", "]"}],
418     RowBox[{"T", "[",
419     RowBox[{"i", ",", "j", ",", "GSF"}], "]"}]}], ",",
420     RowBox[{"{",
421     RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
422     ",",
423     RowBox[{"{",
424     RowBox[{"\[Phi]", ",", "0", ",",
425     RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
426     RowBox[{"{",
427     RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
428     RowBox[{"{",
429     RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
430     RowBox[{"{",
431     RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
432     ";"}], "\[IndentingNewLine]",
433     RowBox[{
434     RowBox[{"TTSF", " ", "=", " ",
435     RowBox[{"MatrixForm", "[",
436     RowBox[{"Table", "[",
437     RowBox[{
438     RowBox[{"Table", "[",
439     RowBox[{
440     RowBox[{"Integrate", "[",
441     RowBox[{
442     RowBox[{
443     RowBox[{"r", "^", "2"}],
444     RowBox[{"Integrate", "[",
445     RowBox[{
446     RowBox[{"Integrate", "[",
447     RowBox[{
448     RowBox[{
449     RowBox[{"Sin", "[", "\[Theta]", "]"}],
450     RowBox[{"T", "[",
451     RowBox[{"i", ",", "j", ",", "TSF"}], "]"}]}], ",",
452     RowBox[{"{",
453     RowBox[{"\[Theta]", ",", "0", ",", "Pi"}], "}"}]}], "]"}],
454     ",",
455     RowBox[{"{",
456     RowBox[{"\[Phi]", ",", "0", ",",
457     RowBox[{"2", " ", "Pi"}]}], "}"}]}], "]"}]}], ",",
458     RowBox[{"{",
459     RowBox[{"r", ",", "0", ",", "rc"}], "}"}]}], "]"}], ",",
460     RowBox[{"{",
461     RowBox[{"j", ",", "1", ",", "3"}], "}"}]}], "]"}], ",",
462     RowBox[{"{",
463     RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}], "]"}]}],
464     ";"}], "\[IndentingNewLine]",
465     RowBox[{
466     RowBox[{"QBARE", " ", "=",
467     RowBox[{"3",
468     RowBox[{
469     RowBox[{"Part", "[",
470     RowBox[{"TBare", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
471     RowBox[{"(",
472     RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
473     RowBox[{
474     RowBox[{"QTSP", " ", "=", " ",
475     RowBox[{"3",
476     RowBox[{
477     RowBox[{"Part", "[",
478     RowBox[{"TSP", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
479     RowBox[{"(",
480     RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
481     RowBox[{
482     RowBox[{"QGSF", " ", "=", " ",
483     RowBox[{"3",
484     RowBox[{
485     RowBox[{"Part", "[",
486     RowBox[{"TGSF", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
487     RowBox[{"(",
488     RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
489     RowBox[{
490     RowBox[{"QTSF", " ", "=", " ",
491     RowBox[{"3",
492     RowBox[{
493     RowBox[{"Part", "[",
494     RowBox[{"TTSF", ",", "1", ",", "1", ",", "1"}], "]"}], "/",
495     RowBox[{"(",
496     RowBox[{"4", " ", "Pi"}], ")"}]}]}]}], ";"}]}], "Input",
497     CellChangeTimes->{{3.613731558054296*^9, 3.613732200209785*^9},
498     3.6137322781282454`*^9, {3.61373233169027*^9, 3.613732397354877*^9}, {
499     3.613732488348338*^9, 3.6137327713906393`*^9}, {3.613732810835518*^9,
500     3.613732821957967*^9}, {3.613732862763562*^9, 3.613732913141625*^9}, {
501     3.61373295595298*^9, 3.613733106904414*^9}, {3.613733177027177*^9,
502     3.613733199740512*^9}, {3.61373326352699*^9, 3.6137332727080936`*^9}, {
503     3.613733425731758*^9, 3.6137335719815893`*^9}, {3.613733605778666*^9,
504     3.613733648768111*^9}, {3.613733776819376*^9, 3.6137338150569887`*^9}, {
505     3.6137338699918118`*^9, 3.61373393057332*^9}, {3.613733985426153*^9,
506     3.613733985628289*^9}, {3.613734054134171*^9, 3.6137340588514023`*^9}, {
507     3.6137371511302147`*^9, 3.613737188118826*^9}, {3.613815304031159*^9,
508     3.613815306899302*^9}, {3.613815415274508*^9, 3.613815450160325*^9}, {
509     3.613815535717202*^9, 3.613815604127789*^9}, {3.613815665097225*^9,
510     3.613815673383039*^9}, {3.613816023942026*^9, 3.6138160527230864`*^9}, {
511     3.613825536655637*^9, 3.613825555245915*^9}, {3.613825660601698*^9,
512     3.6138256692518787`*^9}, {3.613825968874196*^9, 3.613826000721004*^9}, {
513     3.6138263115515537`*^9, 3.613826312408416*^9}, {3.613826919678602*^9,
514     3.613826920319913*^9}, {3.613827178556149*^9, 3.6138272197490597`*^9}, {
515     3.614594522437893*^9, 3.61459456139437*^9}}],
516    
517     Cell[CellGroupData[{
518    
519     Cell[BoxData[
520     RowBox[{"Expand", "[", "QBARE", "]"}]], "Input",
521     CellChangeTimes->{{3.6138263631875963`*^9, 3.613826368246337*^9},
522     3.6139024316559362`*^9}],
523    
524     Cell[BoxData[
525     RowBox[{
526     RowBox[{"-",
527     FractionBox[
528     RowBox[{"2", " ",
529     SuperscriptBox["\[ExponentialE]",
530     RowBox[{
531     RowBox[{"-",
532     SuperscriptBox["rc", "2"]}], " ",
533     SuperscriptBox["\[Kappa]", "2"]}]], " ", "rc", " ", "\[Kappa]"}],
534     SqrtBox["\[Pi]"]]}], "+",
535     RowBox[{"Erf", "[",
536     RowBox[{"rc", " ", "\[Kappa]"}], "]"}]}]], "Output",
537     CellChangeTimes->{3.613826419489653*^9, 3.613827358701158*^9,
538     3.613902416523858*^9, 3.6139057770507097`*^9, 3.613988354332242*^9,
539     3.614594677651219*^9}]
540     }, Open ]],
541    
542     Cell[CellGroupData[{
543    
544     Cell[BoxData[
545     RowBox[{"Expand", "[", "QTSP", "]"}]], "Input",
546     CellChangeTimes->{{3.613826369100939*^9, 3.613826374086033*^9}}],
547    
548     Cell[BoxData[
549     RowBox[{
550     RowBox[{"-",
551     FractionBox[
552     RowBox[{"2", " ",
553     SuperscriptBox["\[ExponentialE]",
554     RowBox[{
555     RowBox[{"-",
556     SuperscriptBox["rc", "2"]}], " ",
557     SuperscriptBox["\[Kappa]", "2"]}]], " ", "rc", " ", "\[Kappa]"}],
558     SqrtBox["\[Pi]"]]}], "-",
559     FractionBox[
560     RowBox[{"4", " ",
561     SuperscriptBox["\[ExponentialE]",
562     RowBox[{
563     RowBox[{"-",
564     SuperscriptBox["rc", "2"]}], " ",
565     SuperscriptBox["\[Kappa]", "2"]}]], " ",
566     SuperscriptBox["rc", "3"], " ",
567     SuperscriptBox["\[Kappa]", "3"]}],
568     RowBox[{"3", " ",
569     SqrtBox["\[Pi]"]}]], "+",
570     RowBox[{"Erf", "[",
571     RowBox[{"rc", " ", "\[Kappa]"}], "]"}]}]], "Output",
572     CellChangeTimes->{3.613988356366749*^9, 3.6145946819255857`*^9}]
573     }, Open ]],
574    
575     Cell[BoxData["Q"], "Input",
576     CellChangeTimes->{{3.613907587432749*^9, 3.6139075875102386`*^9}}],
577    
578     Cell[CellGroupData[{
579    
580     Cell[BoxData[
581     RowBox[{"Expand", "[", "QGSF", "]"}]], "Input",
582     CellChangeTimes->{{3.6138263748828497`*^9, 3.613826377787304*^9}, {
583     3.613830939552072*^9, 3.613830971126011*^9}, {3.613905875167797*^9,
584     3.6139058760662394`*^9}}],
585    
586     Cell[BoxData[
587     RowBox[{
588     RowBox[{"-",
589     FractionBox[
590     RowBox[{"2", " ",
591     SuperscriptBox["\[ExponentialE]",
592     RowBox[{
593     RowBox[{"-",
594     SuperscriptBox["rc", "2"]}], " ",
595     SuperscriptBox["\[Kappa]", "2"]}]], " ", "rc", " ", "\[Kappa]"}],
596     SqrtBox["\[Pi]"]]}], "-",
597     FractionBox[
598     RowBox[{"4", " ",
599     SuperscriptBox["\[ExponentialE]",
600     RowBox[{
601     RowBox[{"-",
602     SuperscriptBox["rc", "2"]}], " ",
603     SuperscriptBox["\[Kappa]", "2"]}]], " ",
604     SuperscriptBox["rc", "3"], " ",
605     SuperscriptBox["\[Kappa]", "3"]}],
606     RowBox[{"3", " ",
607     SqrtBox["\[Pi]"]}]], "-",
608     FractionBox[
609     RowBox[{"2", " ",
610     SuperscriptBox["\[ExponentialE]",
611     RowBox[{
612     RowBox[{"-",
613     SuperscriptBox["rc", "2"]}], " ",
614     SuperscriptBox["\[Kappa]", "2"]}]], " ",
615     SuperscriptBox["rc", "5"], " ",
616     SuperscriptBox["\[Kappa]", "5"]}],
617     RowBox[{"3", " ",
618     SqrtBox["\[Pi]"]}]], "+",
619     RowBox[{"Erf", "[",
620     RowBox[{"rc", " ", "\[Kappa]"}], "]"}]}]], "Output",
621     CellChangeTimes->{
622     3.613826419640369*^9, 3.6138270566935883`*^9, 3.6138273666891203`*^9, {
623     3.613830943408469*^9, 3.6138309716792517`*^9}, 3.613905783149455*^9,
624     3.613905876406279*^9, 3.613988358482745*^9, 3.614594685371746*^9}]
625     }, Open ]],
626    
627     Cell[CellGroupData[{
628    
629     Cell[BoxData[
630     RowBox[{"Expand", "[", "QTSF", "]"}]], "Input",
631     CellChangeTimes->{{3.61382637871056*^9, 3.61382638209606*^9}}],
632    
633     Cell[BoxData["1"], "Output",
634     CellChangeTimes->{3.613826419723484*^9, 3.6138273774842777`*^9,
635     3.6139057853066607`*^9, 3.613988360907867*^9, 3.614594688339691*^9}]
636     }, Open ]],
637    
638     Cell[CellGroupData[{
639    
640     Cell[BoxData[
641     RowBox[{
642     RowBox[{"QGSF", "/.",
643     RowBox[{"rc", "\[Rule]", "11.5"}]}], " ", "/.",
644     RowBox[{"\[Kappa]", "\[Rule]", "0.2"}]}]], "Input",
645     CellChangeTimes->{{3.613826607232987*^9, 3.6138266182268*^9}}],
646    
647     Cell[BoxData["0.8175716808656065`"], "Output",
648     CellChangeTimes->{3.613827062575906*^9, 3.613827398725811*^9,
649     3.613905789167375*^9, 3.6139075965611973`*^9, 3.613907713580661*^9,
650     3.6139883631950703`*^9}]
651     }, Open ]],
652    
653     Cell[CellGroupData[{
654    
655     Cell[BoxData[
656     RowBox[{"Limit", "[",
657     RowBox[{"QBARE", ",",
658     RowBox[{"\[Kappa]", "\[Rule]", "0"}]}], "]"}]], "Input",
659     CellChangeTimes->{{3.6145954324899607`*^9, 3.614595438979292*^9}}],
660    
661     Cell[BoxData["0"], "Output",
662     CellChangeTimes->{3.614595439312615*^9}]
663     }, Open ]],
664    
665     Cell[CellGroupData[{
666    
667     Cell[BoxData[
668     RowBox[{"Limit", "[",
669     RowBox[{"QTSP", ",",
670     RowBox[{"\[Kappa]", "\[Rule]", "0"}]}], "]"}]], "Input",
671     CellChangeTimes->{{3.614595446545167*^9, 3.61459545529193*^9}}],
672    
673     Cell[BoxData["0"], "Output",
674     CellChangeTimes->{3.614595456000258*^9}]
675     }, Open ]],
676    
677     Cell[CellGroupData[{
678    
679     Cell[BoxData[
680     RowBox[{"Limit", "[",
681     RowBox[{"QGSF", ",",
682     RowBox[{"\[Kappa]", "\[Rule]", "0"}]}], "]"}]], "Input",
683     CellChangeTimes->{{3.614595464309478*^9, 3.614595469692217*^9}}],
684    
685     Cell[BoxData["1"], "Output",
686     CellChangeTimes->{3.6145954699957027`*^9}]
687     }, Open ]],
688    
689     Cell[CellGroupData[{
690    
691     Cell[BoxData[
692     RowBox[{"Limit", "[",
693     RowBox[{"QTSF", ",",
694     RowBox[{"\[Kappa]", "\[Rule]", "0"}]}], "]"}]], "Input",
695     CellChangeTimes->{{3.614595479813127*^9, 3.614595487321061*^9}}],
696    
697     Cell[BoxData["1"], "Output",
698     CellChangeTimes->{3.614595487675913*^9}]
699     }, Open ]],
700    
701     Cell[CellGroupData[{
702    
703     Cell[BoxData[
704     RowBox[{"Expand", "[",
705     RowBox[{"h", "[",
706     RowBox[{"r", ",", "\[Kappa]"}], "]"}], "]"}]], "Input",
707     CellChangeTimes->{{3.614595726057316*^9, 3.6145957369270573`*^9}}],
708    
709     Cell[BoxData[
710     RowBox[{"h", "[",
711     RowBox[{"r", ",", "\[Kappa]"}], "]"}]], "Output",
712     CellChangeTimes->{{3.6145957290402822`*^9, 3.614595737188229*^9},
713     3.614595821337948*^9}]
714     }, Open ]],
715    
716     Cell[CellGroupData[{
717    
718     Cell[BoxData[
719     RowBox[{"s", "[",
720     RowBox[{"r", ",", "\[Kappa]"}], "]"}]], "Input",
721     CellChangeTimes->{{3.6145957525304213`*^9, 3.614595789766198*^9}}],
722    
723     Cell[BoxData[
724     RowBox[{"s", "[",
725     RowBox[{"r", ",", "\[Kappa]"}], "]"}]], "Output",
726     CellChangeTimes->{3.614595790131374*^9}]
727     }, Open ]],
728    
729     Cell[CellGroupData[{
730    
731     Cell[BoxData[
732     RowBox[{"Expand", "[",
733     RowBox[{
734     RowBox[{"s", "[",
735     RowBox[{"r", ",", "\[Kappa]"}], "]"}], ",",
736     RowBox[{"{",
737     RowBox[{"r", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input",
738     CellChangeTimes->{{3.614595791670055*^9, 3.614595812670266*^9}}],
739    
740     Cell[BoxData[
741     RowBox[{"s", "[",
742     RowBox[{"r", ",", "\[Kappa]"}], "]"}]], "Output",
743     CellChangeTimes->{{3.614595794966937*^9, 3.614595812909087*^9}}]
744     }, Open ]]
745     },
746     WindowSize->{884, 1337},
747     WindowMargins->{{Automatic, 355}, {Automatic, 0}},
748     FrontEndVersion->"10.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (June 27, \
749     2014)",
750     StyleDefinitions->"Default.nb"
751     ]
752     (* End of Notebook Content *)
753    
754     (* Internal cache information *)
755     (*CellTagsOutline
756     CellTagsIndex->{}
757     *)
758     (*CellTagsIndex
759     CellTagsIndex->{}
760     *)
761     (*NotebookFileOutline
762     Notebook[{
763     Cell[400, 13, 17508, 501, 845, "Input"],
764     Cell[CellGroupData[{
765     Cell[17933, 518, 159, 3, 28, "Input"],
766     Cell[18095, 523, 541, 15, 58, "Output"]
767     }, Open ]],
768     Cell[CellGroupData[{
769     Cell[18673, 543, 128, 2, 28, "Input"],
770     Cell[18804, 547, 777, 24, 58, "Output"]
771     }, Open ]],
772     Cell[19596, 574, 95, 1, 28, "Input"],
773     Cell[CellGroupData[{
774     Cell[19716, 579, 230, 4, 28, "Input"],
775     Cell[19949, 585, 1278, 38, 58, "Output"]
776     }, Open ]],
777     Cell[CellGroupData[{
778     Cell[21264, 628, 126, 2, 28, "Input"],
779     Cell[21393, 632, 165, 2, 28, "Output"]
780     }, Open ]],
781     Cell[CellGroupData[{
782     Cell[21595, 639, 218, 5, 28, "Input"],
783     Cell[21816, 646, 208, 3, 28, "Output"]
784     }, Open ]],
785     Cell[CellGroupData[{
786     Cell[22061, 654, 190, 4, 28, "Input"],
787     Cell[22254, 660, 70, 1, 28, "Output"]
788     }, Open ]],
789     Cell[CellGroupData[{
790     Cell[22361, 666, 186, 4, 28, "Input"],
791     Cell[22550, 672, 70, 1, 28, "Output"]
792     }, Open ]],
793     Cell[CellGroupData[{
794     Cell[22657, 678, 187, 4, 28, "Input"],
795     Cell[22847, 684, 72, 1, 28, "Output"]
796     }, Open ]],
797     Cell[CellGroupData[{
798     Cell[22956, 690, 187, 4, 28, "Input"],
799     Cell[23146, 696, 70, 1, 28, "Output"]
800     }, Open ]],
801     Cell[CellGroupData[{
802     Cell[23253, 702, 186, 4, 28, "Input"],
803     Cell[23442, 708, 179, 4, 28, "Output"]
804     }, Open ]],
805     Cell[CellGroupData[{
806     Cell[23658, 717, 152, 3, 28, "Input"],
807     Cell[23813, 722, 127, 3, 28, "Output"]
808     }, Open ]],
809     Cell[CellGroupData[{
810     Cell[23977, 730, 269, 7, 28, "Input"],
811     Cell[24249, 739, 151, 3, 28, "Output"]
812     }, Open ]]
813     }
814     ]
815     *)
816