ViewVC Help
View File | Revision Log | Show Annotations | View Changeset | Root Listing
root/group/trunk/nonperiodicVSS/friction.nb
Revision: 3943
Committed: Mon Sep 2 20:34:55 2013 UTC (11 years, 11 months ago) by kstocke1
File size: 16567 byte(s)
Log Message:

File Contents

# Content
1 (* Content-type: application/vnd.wolfram.mathematica *)
2
3 (*** Wolfram Notebook File ***)
4 (* http://www.wolfram.com/nb *)
5
6 (* CreatedBy='Mathematica 8.0' *)
7
8 (*CacheID: 234*)
9 (* Internal cache information:
10 NotebookFileLineBreakTest
11 NotebookFileLineBreakTest
12 NotebookDataPosition[ 157, 7]
13 NotebookDataLength[ 16369, 461]
14 NotebookOptionsPosition[ 14762, 404]
15 NotebookOutlinePosition[ 15116, 420]
16 CellTagsIndexPosition[ 15073, 417]
17 WindowFrame->Normal*)
18
19 (* Beginning of Notebook Content *)
20 Notebook[{
21 Cell[BoxData[
22 RowBox[{
23 RowBox[{"(*", " ",
24 RowBox[{"a", ",", " ", "b", ",", " ",
25 RowBox[{"r", " ", "in", " ", "units", " ", "of", " ", "meters"}]}], " ",
26 "*)"}], "\[IndentingNewLine]",
27 RowBox[{
28 RowBox[{
29 RowBox[{"a", " ", "=", " ", "0.0000000033"}], ";"}],
30 "\[IndentingNewLine]",
31 RowBox[{
32 RowBox[{"b", " ", "=", " ", "0.0000000013"}], ";"}],
33 "\[IndentingNewLine]",
34 RowBox[{
35 RowBox[{"r", " ", "=", " ", "0.0000000040"}], ";"}],
36 "\[IndentingNewLine]",
37 RowBox[{"(*", " ",
38 RowBox[{
39 "eta", " ", "in", " ", "units", " ", "of", " ", "Pa", "*", "s", " ", "or",
40 " ", "N", "*",
41 RowBox[{"s", "/",
42 RowBox[{"m", "^", "2"}]}]}], " ", "*)"}], "\[IndentingNewLine]",
43 RowBox[{
44 RowBox[{"eta", " ", "=", " ", "0.000334"}], ";"}], "\n",
45 RowBox[{
46 RowBox[{"ab", " ", "=", " ",
47 RowBox[{"Sqrt", "[",
48 RowBox[{
49 RowBox[{"(",
50 RowBox[{"a", "^", "2"}], ")"}], "-",
51 RowBox[{"(",
52 RowBox[{"b", "^", "2"}], ")"}]}], "]"}]}], ";"}],
53 "\[IndentingNewLine]",
54 RowBox[{
55 RowBox[{"v", " ", "=", " ",
56 RowBox[{"32", "*", "Pi", "*",
57 RowBox[{"eta", "/", "3"}]}]}], ";"}]}]}]], "Input",
58 CellChangeTimes->{{3.584807426161751*^9, 3.584807453166168*^9}, {
59 3.5848098994271517`*^9, 3.58480990098132*^9}, {3.584890669262165*^9,
60 3.5848906732045937`*^9}, 3.5848942046023273`*^9, 3.5848942364960403`*^9, {
61 3.584894394914665*^9, 3.584894407017727*^9}, {3.584894867879013*^9,
62 3.5848948703643208`*^9}, {3.584895906363385*^9, 3.584895906913582*^9}, {
63 3.586699807267563*^9, 3.586699811802783*^9}, {3.5867045314674397`*^9,
64 3.586704560779134*^9}, {3.586704640818076*^9, 3.586704681909463*^9}, {
65 3.5867047559862347`*^9, 3.586704766892249*^9}, {3.586704828026332*^9,
66 3.586704834460175*^9}, {3.586705096638748*^9, 3.586705109311314*^9}, {
67 3.586706477114703*^9, 3.58670647750175*^9}}],
68
69 Cell[BoxData[
70 RowBox[{"\[IndentingNewLine]",
71 RowBox[{"(*", " ",
72 RowBox[{"RESISTANCE", " ", "TENSORS"}], " ", "*)"}]}]], "Input",
73 CellChangeTimes->{{3.5848081048411083`*^9, 3.584808114547517*^9}}],
74
75 Cell[BoxData[
76 RowBox[{"(*", " ",
77 RowBox[{"sphere", " ", "rotation"}], " ", "*)"}]], "Input",
78 CellChangeTimes->{{3.5848955452222424`*^9, 3.584895552580024*^9}}],
79
80 Cell[CellGroupData[{
81
82 Cell[BoxData[
83 RowBox[{"XiS", " ", "=", " ",
84 RowBox[{"8.", "*", "Pi", "*", "eta", "*",
85 RowBox[{"(",
86 RowBox[{"r", "^", "3"}], ")"}]}]}]], "Input",
87 CellChangeTimes->{{3.584895562690569*^9, 3.584895581538089*^9}}],
88
89 Cell[BoxData["5.372374765050834`*^-28"], "Output",
90 CellChangeTimes->{3.5848955833332977`*^9, 3.584895910460045*^9,
91 3.586699817892194*^9, 3.586704684940571*^9, 3.586704772274445*^9,
92 3.586704844305737*^9, 3.586705113459869*^9, 3.586706480803813*^9}]
93 }, Open ]],
94
95 Cell[BoxData[
96 RowBox[{
97 RowBox[{"S", " ", "=", " ",
98 RowBox[{
99 RowBox[{"(",
100 RowBox[{"2", "/", "ab"}], ")"}], "*",
101 RowBox[{"Log", "[",
102 RowBox[{
103 RowBox[{"(",
104 RowBox[{"a", "+", "ab"}], ")"}], "/", "b"}], "]"}]}]}], ";"}]], "Input",\
105
106 CellChangeTimes->{{3.584895591890572*^9, 3.584895628889739*^9}}],
107
108 Cell[BoxData[
109 RowBox[{"(*", " ",
110 RowBox[{"ellipsoid", " ", "axial", " ",
111 RowBox[{"rotation", " ", "--"}], " ", "about", " ", "long", " ", "axis"}],
112 " ", "*)"}]], "Input",
113 CellChangeTimes->{{3.584807845501628*^9, 3.584807881963066*^9},
114 3.58480810065349*^9, {3.584810005255805*^9, 3.584810006597301*^9}}],
115
116 Cell[BoxData[{
117 RowBox[{
118 RowBox[{"nXiA", " ", "=", " ",
119 RowBox[{
120 RowBox[{"(",
121 RowBox[{"ab", "^", "2"}], ")"}], "*",
122 RowBox[{"(",
123 RowBox[{"b", "^", "2"}], ")"}]}]}], ";"}], "\[IndentingNewLine]",
124 RowBox[{
125 RowBox[{"dXiA", " ", "=", " ",
126 RowBox[{"(",
127 RowBox[{
128 RowBox[{"2", "*", "a"}], " ", "-", " ",
129 RowBox[{
130 RowBox[{"(",
131 RowBox[{"b", "^", "2"}], ")"}], "*", "S"}]}], ")"}]}], ";"}]}], "Input",\
132
133 CellChangeTimes->{{3.584894479745336*^9, 3.584894547193737*^9}}],
134
135 Cell[CellGroupData[{
136
137 Cell[BoxData[
138 RowBox[{"XiA", " ", "=", " ",
139 RowBox[{"v", " ", "*",
140 RowBox[{"(", " ",
141 RowBox[{"nXiA", "/", "dXiA"}], ")"}]}]}]], "Input",
142 CellChangeTimes->{{3.584807580926756*^9, 3.5848076774271517`*^9}, {
143 3.584893446441492*^9, 3.584893456926993*^9}, {3.584893513019639*^9,
144 3.5848935374433117`*^9}, {3.5848937295629377`*^9, 3.5848937320361967`*^9}, {
145 3.5848940598863373`*^9, 3.5848940827349033`*^9}, {3.584894124697816*^9,
146 3.584894131830501*^9}, {3.5848944118465767`*^9, 3.584894413689575*^9}, {
147 3.584894553484161*^9, 3.5848945620889597`*^9}}],
148
149 Cell[BoxData["3.5988069933435006`*^-29"], "Output",
150 CellChangeTimes->{
151 3.58480767838589*^9, 3.584812369332225*^9, 3.58489067890679*^9,
152 3.584893466947144*^9, {3.584893515809536*^9, 3.5848935380765*^9},
153 3.584893667613534*^9, 3.584893745846806*^9, 3.584893991496749*^9, {
154 3.5848940686270847`*^9, 3.584894083689426*^9}, 3.584894132885084*^9,
155 3.584894209263301*^9, 3.5848944220659027`*^9, 3.584894562584774*^9,
156 3.5848956426941223`*^9, 3.584895912816411*^9, 3.586699824159266*^9,
157 3.586704688787434*^9, 3.5867047762806807`*^9, 3.58670484784446*^9,
158 3.586705115994009*^9, 3.586706483628399*^9}]
159 }, Open ]],
160
161 Cell[BoxData[
162 RowBox[{"\[IndentingNewLine]",
163 RowBox[{"(*", " ",
164 RowBox[{"ellipsoid", " ", "equatorial", " ",
165 RowBox[{"rotation", " ", "--"}], " ", "about", " ", "short", " ",
166 "axes"}], " ", "*)"}]}]], "Input",
167 CellChangeTimes->{{3.5848078641082973`*^9, 3.584807887971993*^9}, {
168 3.584810008477813*^9, 3.58481001069223*^9}}],
169
170 Cell[BoxData[{
171 RowBox[{
172 RowBox[{"nXiB", " ", "=", " ",
173 RowBox[{
174 RowBox[{"(",
175 RowBox[{"a", "^", "4"}], ")"}], "-",
176 RowBox[{"(",
177 RowBox[{"b", "^", "4"}], ")"}]}]}], ";"}], "\[IndentingNewLine]",
178 RowBox[{
179 RowBox[{"dXiB", " ", "=", " ",
180 RowBox[{
181 RowBox[{
182 RowBox[{"(",
183 RowBox[{
184 RowBox[{"2", "*",
185 RowBox[{"(",
186 RowBox[{"a", "^", "2"}], ")"}]}], "-",
187 RowBox[{"(",
188 RowBox[{"b", "^", "2"}], ")"}]}], ")"}], "*", "S"}], " ", "-", " ",
189 RowBox[{"(",
190 RowBox[{"2", "*", "a"}], ")"}]}]}], ";"}]}], "Input",
191 CellChangeTimes->{{3.584894566445219*^9, 3.5848945876718807`*^9}, {
192 3.5848946888115788`*^9, 3.5848947150455017`*^9}}],
193
194 Cell[CellGroupData[{
195
196 Cell[BoxData[
197 RowBox[{"XiB", " ", "=", " ",
198 RowBox[{"v", " ", "*", " ",
199 RowBox[{"(",
200 RowBox[{"nXiB", "/", "dXiB"}], ")"}]}]}]], "Input",
201 CellChangeTimes->{{3.584807667200397*^9, 3.5848076699441557`*^9}, {
202 3.5848077499771643`*^9, 3.584807786900511*^9}, {3.584893547107358*^9,
203 3.584893579226317*^9}, {3.58489389632187*^9, 3.584893901176014*^9}, {
204 3.584893943459343*^9, 3.584893946518909*^9}, {3.584894088000602*^9,
205 3.5848941203441153`*^9}, 3.5848944172115498`*^9, {3.584894722257359*^9,
206 3.584894733911747*^9}}],
207
208 Cell[BoxData["9.010843062329251`*^-29"], "Output",
209 CellChangeTimes->{
210 3.584807788832862*^9, 3.584812370076736*^9, 3.5848906801945047`*^9,
211 3.5848935801190357`*^9, 3.5848936688170233`*^9, 3.5848939033674097`*^9, {
212 3.58489396555275*^9, 3.584893992584134*^9}, 3.5848940700482283`*^9, {
213 3.584894103054511*^9, 3.584894120965992*^9}, 3.584894210383068*^9,
214 3.584894423252715*^9, 3.584894734499061*^9, 3.58489564491859*^9,
215 3.584895914221643*^9, 3.5866998271353817`*^9, 3.586704693130818*^9,
216 3.586704778769905*^9, 3.586704850366987*^9, 3.586705118085232*^9,
217 3.586706485967189*^9}]
218 }, Open ]],
219
220 Cell[BoxData["\[IndentingNewLine]"], "Input",
221 CellChangeTimes->{3.584887428382176*^9, 3.584891660811152*^9}],
222
223 Cell[BoxData[
224 RowBox[{"\[IndentingNewLine]",
225 RowBox[{"(*", " ",
226 RowBox[{"FRICTION", " ", "FACTORS", " ", "via", " ", "Wikipedia"}], " ",
227 "*)"}]}]], "Input",
228 CellChangeTimes->{{3.584887434985119*^9, 3.58488743942144*^9}, {
229 3.5848907429833384`*^9, 3.584890746521543*^9}}],
230
231 Cell[BoxData[{
232 RowBox[{
233 RowBox[{"xi", " ", "=",
234 RowBox[{
235 RowBox[{"Sqrt", "[",
236 RowBox[{
237 RowBox[{"(",
238 RowBox[{"p", "^", "2"}], ")"}], "-", "1"}], "]"}], "/", "p"}]}],
239 ";"}], "\[IndentingNewLine]",
240 RowBox[{
241 RowBox[{"s", " ", "=", " ",
242 RowBox[{"2", "*",
243 RowBox[{
244 RowBox[{"ArcTanh", "[", "xi", "]"}], "/", "xi"}]}]}],
245 ";"}], "\[IndentingNewLine]",
246 RowBox[{
247 RowBox[{"p", " ", "=", " ",
248 RowBox[{"a", "/", "b"}]}], ";"}], "\[IndentingNewLine]",
249 RowBox[{
250 RowBox[{"re", " ", "=", " ",
251 RowBox[{
252 RowBox[{"(",
253 RowBox[{"a", "*",
254 RowBox[{"(",
255 RowBox[{"b", "^", "2"}], ")"}]}], ")"}], "^",
256 RowBox[{"(",
257 RowBox[{"1", "/", "3"}], ")"}]}]}], ";"}], "\[IndentingNewLine]",
258 RowBox[{
259 RowBox[{"eqSphere", " ", "=", " ",
260 RowBox[{"8", "*", "Pi", "*", "eta", "*",
261 RowBox[{"(",
262 RowBox[{"re", "^", "3"}], ")"}]}]}], ";"}]}], "Input",
263 CellChangeTimes->{{3.584887453255073*^9, 3.584887474611525*^9}, {
264 3.584887518352754*^9, 3.5848875201183167`*^9}, {3.5848875705654163`*^9,
265 3.584887612684559*^9}, {3.584891207938551*^9, 3.5848912105877657`*^9}, {
266 3.58489477575947*^9, 3.584894789206271*^9}, {3.5848948909071417`*^9,
267 3.5848949045983353`*^9}, {3.584895894748207*^9, 3.58489594161933*^9}, {
268 3.584895989916945*^9, 3.584896035299241*^9}}],
269
270 Cell[BoxData[""], "Input",
271 CellChangeTimes->{{3.5848876347988167`*^9, 3.584887638277546*^9}}],
272
273 Cell[BoxData[
274 RowBox[{"(*", " ",
275 RowBox[{"ellipsoid", " ", "axial", " ", "friction", " ",
276 RowBox[{"factor", " ", "--"}], " ", "about", " ", "long", " ", "axis"}],
277 " ", "*)"}]], "Input",
278 CellChangeTimes->{{3.58488764265452*^9, 3.584887652272901*^9}, {
279 3.58489128903328*^9, 3.5848912914194727`*^9}}],
280
281 Cell[CellGroupData[{
282
283 Cell[BoxData[
284 RowBox[{"Fax", " ", "=", " ",
285 RowBox[{
286 RowBox[{"(",
287 RowBox[{"4", "/", "3"}], ")"}], "*",
288 RowBox[{
289 RowBox[{"(",
290 RowBox[{"xi", "^", "2"}], ")"}], "/",
291 RowBox[{"(",
292 RowBox[{"2", "-",
293 RowBox[{"(",
294 RowBox[{"s", "/",
295 RowBox[{"(",
296 RowBox[{"p", "^", "2"}], ")"}]}], ")"}]}], ")"}]}]}]}]], "Input",
297 CellChangeTimes->{{3.58488765759788*^9, 3.584887700018955*^9}, {
298 3.5848879174727783`*^9, 3.584887938981941*^9}, {3.584890603482909*^9,
299 3.5848906063233852`*^9}, 3.584890946638309*^9, {3.584894926277274*^9,
300 3.584894983989938*^9}}],
301
302 Cell[BoxData["0.7687260259259584`"], "Output",
303 CellChangeTimes->{
304 3.58488770586084*^9, {3.58488792206218*^9, 3.584887939492504*^9},
305 3.584890608261299*^9, 3.5848906924156*^9, 3.584890948261269*^9,
306 3.584891214003551*^9, 3.584893997414321*^9, 3.584894794095375*^9,
307 3.5848948750854387`*^9, 3.584894906946406*^9, {3.584894984628289*^9,
308 3.5848950094024963`*^9}, 3.584895649579417*^9, 3.5848960393110647`*^9,
309 3.586699830645979*^9, 3.5867046965751457`*^9, 3.58670478211369*^9,
310 3.58670485421113*^9, 3.586705120876774*^9, 3.586706489578327*^9}]
311 }, Open ]],
312
313 Cell[BoxData[
314 RowBox[{"\n",
315 RowBox[{"(*", " ",
316 RowBox[{"ellipsoid", " ", "equatorial", " ", "friction", " ",
317 RowBox[{"factor", " ", "--"}], " ", "about", " ", "short", " ", "axes"}],
318 " ", "*)"}]}]], "Input",
319 CellChangeTimes->{{3.584887710741127*^9, 3.584887713271037*^9},
320 3.584887813383315*^9, {3.584891294243541*^9, 3.5848912960435057`*^9}}],
321
322 Cell[CellGroupData[{
323
324 Cell[BoxData[
325 RowBox[{"Feq", " ", "=", " ",
326 RowBox[{
327 RowBox[{"(",
328 RowBox[{"4", "/", "3"}], ")"}], " ", "*", " ",
329 RowBox[{
330 RowBox[{"(",
331 RowBox[{
332 RowBox[{
333 RowBox[{"(",
334 RowBox[{"1", "/", "p"}], ")"}], "^", "2"}], " ", "-", " ",
335 RowBox[{"p", "^", "2"}]}], ")"}], "/",
336 RowBox[{"(",
337 RowBox[{"2", " ", "-", " ",
338 RowBox[{"s", "*",
339 RowBox[{"(",
340 RowBox[{"2", " ", "-", " ",
341 RowBox[{
342 RowBox[{"(",
343 RowBox[{"1", "/", "p"}], ")"}], "^", "2"}]}], ")"}]}]}],
344 ")"}]}]}]}]], "Input",
345 CellChangeTimes->{{3.584887727157157*^9, 3.584887769116691*^9}, {
346 3.584887926989279*^9, 3.584887942885796*^9}, {3.584890609957733*^9,
347 3.584890611532776*^9}, 3.584890951791182*^9}],
348
349 Cell[BoxData["1.924768288590935`"], "Output",
350 CellChangeTimes->{
351 3.5848877700852623`*^9, {3.584887929629698*^9, 3.5848879434378977`*^9},
352 3.584890612056086*^9, 3.5848906935323477`*^9, 3.584890952137286*^9,
353 3.584891216311064*^9, 3.584893998534431*^9, 3.584894876538658*^9,
354 3.5848950109231567`*^9, 3.584895650617403*^9, 3.584896040714982*^9,
355 3.5866998334559813`*^9, 3.586704697863037*^9, 3.5867047835855827`*^9,
356 3.586704856869244*^9, 3.586705122378854*^9, 3.5867064906482763`*^9}]
357 }, Open ]],
358
359 Cell[BoxData[
360 RowBox[{"\[IndentingNewLine]",
361 RowBox[{"(*", " ",
362 RowBox[{"ellipsoid", " ", "axial", " ", "rotational", " ", "friction"}],
363 " ", "*)"}]}]], "Input",
364 CellChangeTimes->{{3.58489104521352*^9, 3.584891053491618*^9}, {
365 3.584891299813236*^9, 3.5848913004309483`*^9}}],
366
367 Cell[CellGroupData[{
368
369 Cell[BoxData[
370 RowBox[{"fAx", " ", "=", " ",
371 RowBox[{"Fax", " ", "*", " ", "eqSphere"}]}]], "Input",
372 CellChangeTimes->{{3.584891056631095*^9, 3.584891064865149*^9}}],
373
374 Cell[BoxData["3.5988069933435135`*^-29"], "Output",
375 CellChangeTimes->{3.5848910656263733`*^9, 3.584891217398337*^9,
376 3.58489400012298*^9, 3.584895019483296*^9, 3.584895652455336*^9,
377 3.584896042503642*^9, 3.586699834607826*^9, 3.586704699166651*^9,
378 3.586704785006289*^9, 3.586704858291555*^9, 3.5867051235852127`*^9,
379 3.586706492338463*^9}]
380 }, Open ]],
381
382 Cell[BoxData[
383 RowBox[{"(*", " ",
384 RowBox[{
385 "ellipsoid", " ", "equatorial", " ", "rotational", " ", "friction"}], " ",
386 "*)"}]], "Input",
387 CellChangeTimes->{{3.5848910141246853`*^9, 3.584891022193733*^9}, {
388 3.5848913017358427`*^9, 3.5848913022309103`*^9}}],
389
390 Cell[CellGroupData[{
391
392 Cell[BoxData[
393 RowBox[{"fEq", " ", "=", " ",
394 RowBox[{"Feq", " ", "*", " ", "eqSphere"}]}]], "Input",
395 CellChangeTimes->{{3.584891025068652*^9, 3.584891029821259*^9}}],
396
397 Cell[BoxData["9.010843062329284`*^-29"], "Output",
398 CellChangeTimes->{3.584891030572219*^9, 3.584891218233328*^9,
399 3.584894001208784*^9, 3.584895020435354*^9, 3.584895653375164*^9,
400 3.58489604404213*^9, 3.5866998356785097`*^9, 3.586704701890503*^9,
401 3.5867047871298437`*^9, 3.586704859378227*^9, 3.586705125437768*^9,
402 3.586706494141871*^9}]
403 }, Open ]]
404 },
405 WindowSize->{740, 876},
406 WindowMargins->{{437, Automatic}, {62, Automatic}},
407 FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (July 22, \
408 2012)",
409 StyleDefinitions->"Default.nb"
410 ]
411 (* End of Notebook Content *)
412
413 (* Internal cache information *)
414 (*CellTagsOutline
415 CellTagsIndex->{}
416 *)
417 (*CellTagsIndex
418 CellTagsIndex->{}
419 *)
420 (*NotebookFileOutline
421 Notebook[{
422 Cell[557, 20, 1920, 46, 133, "Input"],
423 Cell[2480, 68, 204, 4, 43, "Input"],
424 Cell[2687, 74, 164, 3, 27, "Input"],
425 Cell[CellGroupData[{
426 Cell[2876, 81, 223, 5, 27, "Input"],
427 Cell[3102, 88, 254, 3, 30, "Output"]
428 }, Open ]],
429 Cell[3371, 94, 335, 11, 27, "Input"],
430 Cell[3709, 107, 318, 6, 27, "Input"],
431 Cell[4030, 115, 524, 17, 43, "Input"],
432 Cell[CellGroupData[{
433 Cell[4579, 136, 568, 10, 27, "Input"],
434 Cell[5150, 148, 615, 9, 30, "Output"]
435 }, Open ]],
436 Cell[5780, 160, 343, 7, 43, "Input"],
437 Cell[6126, 169, 717, 22, 43, "Input"],
438 Cell[CellGroupData[{
439 Cell[6868, 195, 540, 10, 27, "Input"],
440 Cell[7411, 207, 599, 9, 30, "Output"]
441 }, Open ]],
442 Cell[8025, 219, 109, 1, 43, "Input"],
443 Cell[8137, 222, 284, 6, 43, "Input"],
444 Cell[8424, 230, 1342, 37, 88, "Input"],
445 Cell[9769, 269, 94, 1, 27, "Input"],
446 Cell[9866, 272, 311, 6, 27, "Input"],
447 Cell[CellGroupData[{
448 Cell[10202, 282, 615, 17, 27, "Input"],
449 Cell[10820, 301, 561, 8, 27, "Output"]
450 }, Open ]],
451 Cell[11396, 312, 364, 7, 43, "Input"],
452 Cell[CellGroupData[{
453 Cell[11785, 323, 782, 23, 27, "Input"],
454 Cell[12570, 348, 500, 7, 27, "Output"]
455 }, Open ]],
456 Cell[13085, 358, 289, 6, 43, "Input"],
457 Cell[CellGroupData[{
458 Cell[13399, 368, 169, 3, 27, "Input"],
459 Cell[13571, 373, 350, 5, 30, "Output"]
460 }, Open ]],
461 Cell[13936, 381, 264, 6, 27, "Input"],
462 Cell[CellGroupData[{
463 Cell[14225, 391, 169, 3, 27, "Input"],
464 Cell[14397, 396, 349, 5, 30, "Output"]
465 }, Open ]]
466 }
467 ]
468 *)
469
470 (* End of internal cache information *)