-
Notifications
You must be signed in to change notification settings - Fork 0
/
2007.02841_github.nb
1026 lines (996 loc) · 44.3 KB
/
2007.02841_github.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 45215, 1018]
NotebookOptionsPosition[ 43333, 978]
NotebookOutlinePosition[ 43728, 994]
CellTagsIndexPosition[ 43685, 991]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[StyleBox["On-shot diagnostic of electron beam-laser pulse \
interaction based on stochastic quantum radiation reaction", "Title",
FontWeight->"Regular",
FontColor->RGBColor[
0.2964217593652247, 0.6292210269321736, 0.2727702754253452]]], "Text",
CellChangeTimes->{{3.822636147120782*^9, 3.822636149053595*^9}, {
3.822636240732341*^9, 3.82263625191656*^9}, {3.822637212068983*^9,
3.822637212721833*^9}, 3.823094727278884*^9, {3.833550853313994*^9,
3.833550862795432*^9}, {3.833795877595468*^9, 3.833795921123438*^9}, {
3.8337976113677797`*^9, 3.8337976215952806`*^9}, {3.8368849167533627`*^9,
3.836884938754459*^9}, {3.836885017010099*^9, 3.83688501802005*^9}, {
3.838269556945876*^9, 3.8382695941735563`*^9}, {3.838269705424317*^9,
3.8382697091991663`*^9},
3.8831173137769127`*^9},ExpressionUUID->"93ad8efe-6512-48b9-bb54-\
8279fc4af6d0"],
Cell[TextData[{
StyleBox["Paper: arXiv: 2007.02841, by Matteo Tamburini\nNotebook: \
\[CapitalOAcute]scar Amaro, August 2021 + January 2023 @", "Section",
FontSize->24,
FontColor->GrayLevel[0]],
StyleBox[ButtonBox[" ",
BaseStyle->"Hyperlink",
ButtonData->{
URL["http://epp.ist.utl.pt/"], None},
ButtonNote->"http://epp.ist.utl.pt/"], "Section",
FontSize->24,
FontColor->GrayLevel[0]],
StyleBox[ButtonBox["GoLP-EPP",
BaseStyle->"Hyperlink",
ButtonData->{
URL["http://epp.ist.utl.pt/"], None},
ButtonNote->"http://epp.ist.utl.pt/"], "Section",
FontSize->24,
FontVariations->{"Underline"->True},
FontColor->GrayLevel[0]]
}], "Text",
CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9},
3.822636391632341*^9, {3.8226372468331547`*^9, 3.822637246833611*^9}, {
3.832755002125525*^9, 3.8327550028655148`*^9}, {3.8328159555988827`*^9,
3.8328159559877577`*^9}, {3.833550866979972*^9, 3.8335508675107203`*^9}, {
3.8337959288036613`*^9, 3.833795929749477*^9}, {3.836884940028832*^9,
3.836884940645474*^9}, {3.8382695643134193`*^9, 3.8382695830795717`*^9}, {
3.838269712757929*^9, 3.838269733266273*^9}, 3.88181907427205*^9, {
3.883117777672618*^9, 3.88311778570466*^9}},
FontSize->14,ExpressionUUID->"f080cb2d-b71f-46ba-aebc-8310b0d2b79a"],
Cell[TextData[{
StyleBox["Introduction", "Section",
FontSize->24,
FontWeight->"Bold",
FontColor->GrayLevel[0]],
StyleBox["\nContrary to CRR or MCRR, QRR through stochasticity will induce \
an asymmetry in the momentum space (x,y) orthogonal to propagation (z), with \
a visible increase along polarization (x), while in the remaining direction \
the divergence does not change significantly.", "Section",
FontSize->24,
FontColor->GrayLevel[0]]
}], "Text",
CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9,
3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
3.8230947324882936`*^9, 3.823094753820561*^9}, {3.833550870010079*^9,
3.8335508705241623`*^9}, {3.833552192734445*^9, 3.833552244447419*^9}, {
3.833795945276964*^9, 3.833795995813528*^9}, {3.833797624215995*^9,
3.833797700970443*^9}, {3.836884956779365*^9, 3.8368850450508223`*^9}, {
3.838269587610732*^9, 3.8382696377305927`*^9}, {3.838269737595594*^9,
3.838269819553781*^9}},
FontSize->14,ExpressionUUID->"f68e209f-1fc4-499a-adff-4329fa790445"],
Cell[CellGroupData[{
Cell["Figure 2", "Chapter",
CellChangeTimes->{{3.8326563117117662`*^9, 3.832656326417254*^9}, {
3.832656759272208*^9, 3.8326567620349483`*^9}, {3.8326569412336063`*^9,
3.832656945761533*^9}, {3.8326612651442423`*^9, 3.832661265897476*^9}, {
3.836884947670759*^9, 3.836884953331353*^9}, {3.836885004822013*^9,
3.8368850224940968`*^9}, {3.838269623022902*^9, 3.8382696245591507`*^9}, {
3.8831173434295807`*^9,
3.883117344669546*^9}},ExpressionUUID->"9193af5d-6504-4a5e-a140-\
06b33034f4ff"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{"Clear", "[",
RowBox[{
"m", ",", "px", ",", "py", ",", "\[Sigma]x", ",", "\[Sigma]y", ",", "p",
",", "\[Theta]", ",", "dNd\[Theta]"}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"n", "=",
RowBox[{"Exp", "[",
RowBox[{
RowBox[{"-", "0.5"}],
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"px", "^", "2"}], "/",
RowBox[{"\[Sigma]x", "^", "2"}]}], "+",
RowBox[{
RowBox[{"py", "^", "2"}], "/",
RowBox[{"\[Sigma]y", "^", "2"}]}]}], ")"}]}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"px", "=",
RowBox[{"p", " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"py", "=",
RowBox[{"p", " ",
RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"p", " ", "n"}], ",",
RowBox[{"{",
RowBox[{"p", ",", "0", ",", "\[Infinity]"}], "}"}]}], "]"}], "//",
"Normal"}]}], "Input",
CellChangeTimes->{{3.838266172731187*^9, 3.838266253498448*^9}, {
3.8382664160162487`*^9, 3.838266442746367*^9}, {3.838266481110908*^9,
3.838266481457018*^9}},
CellLabel->"In[23]:=",ExpressionUUID->"fca623fe-807b-4fc2-9059-3578f87315ad"],
Cell[BoxData[
FractionBox["1",
RowBox[{
FractionBox[
RowBox[{"1.`", " ",
SuperscriptBox[
RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}],
SuperscriptBox["\[Sigma]y", "2"]], "+",
FractionBox[
RowBox[{"1.`", " ",
SuperscriptBox[
RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}],
SuperscriptBox["\[Sigma]x", "2"]]}]]], "Output",
CellChangeTimes->{{3.838266221200605*^9, 3.838266262410089*^9},
3.838266488143621*^9},
CellLabel->"Out[27]=",ExpressionUUID->"00a25449-7bba-41b4-a68c-9f8d3d2feb0d"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{"dNd\[Theta]", "[",
RowBox[{"\[Theta]_", ",", "\[Sigma]x_", ",", "\[Sigma]y_"}], "]"}], ":=",
FractionBox["1",
RowBox[{
FractionBox[
SuperscriptBox[
RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"],
SuperscriptBox["\[Sigma]y", "2"]], "+",
FractionBox[
SuperscriptBox[
RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"],
SuperscriptBox["\[Sigma]x", "2"]]}]]}], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"approximate", " ", "choices", " ", "of", " ",
RowBox[{"\[Sigma]y", "/", "\[Sigma]x"}], " ", "to", " ", "match", " ",
"Figure", " ", "2"}], " ", "*)"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"dNd\[Theta]norm", "[",
RowBox[{"\[Theta]_", ",", "\[Sigma]x_", ",", "\[Sigma]y_"}], "]"}], ":=",
RowBox[{
RowBox[{"dNd\[Theta]", "[",
RowBox[{"\[Theta]", ",", "\[Sigma]x", ",", "\[Sigma]y"}], "]"}], "/",
RowBox[{"NIntegrate", "[",
RowBox[{
RowBox[{"dNd\[Theta]", "[",
RowBox[{"\[Theta]\[Theta]", ",", "\[Sigma]x", ",", "\[Sigma]y"}], "]"}],
",",
RowBox[{"{",
RowBox[{"\[Theta]\[Theta]", ",", "0", ",",
RowBox[{"2", "\[Pi]"}]}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"dNd\[Theta]norm", "[",
RowBox[{"\[Theta]", ",", "1", ",", "1"}], "]"}], ",",
RowBox[{"dNd\[Theta]norm", "[",
RowBox[{"\[Theta]", ",", "1.9", ",", "1"}], "]"}], ",",
RowBox[{"dNd\[Theta]norm", "[",
RowBox[{"\[Theta]", ",", "2.6", ",", "1"}], "]"}], ",",
RowBox[{"dNd\[Theta]norm", "[",
RowBox[{"\[Theta]", ",", "3.8", ",", "1"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[Theta]", ",", "0", ",",
RowBox[{"2", "\[Pi]"}]}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<\[Theta]\>\"", ",", "\"\<dN/d\[Theta]\>\""}], "}"}]}], ",",
RowBox[{"ImageSize", "\[Rule]", "300"}], ",",
RowBox[{"PlotLegends", "\[Rule]",
RowBox[{"{",
RowBox[{
"\"\<\[Sigma]x=\[Sigma]y\>\"", ",", "\"\<\[Sigma]x=1.9\[Sigma]y\>\"",
",", "\"\<\[Sigma]x=2.6\[Sigma]y\>\"", ",",
"\"\<\[Sigma]x=3.8\[Sigma]y\>\""}], "}"}]}], ",",
RowBox[{"PlotStyle", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"Black", ",", "Dashed"}], "}"}], ",", "Blue", ",", "Green",
",", "Red"}], "}"}]}], ",",
RowBox[{"PlotPoints", "->", "3"}], ",",
RowBox[{"Frame", "\[Rule]", "True"}], ",",
RowBox[{"PlotRange", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0.61"}], "}"}]}]}], "]"}]}], "Input",
CellChangeTimes->{{3.8382664765331373`*^9, 3.838266497513851*^9}, {
3.838266543999444*^9, 3.8382665443307543`*^9}, {3.838266642671278*^9,
3.8382666430051117`*^9}, {3.838266955762106*^9, 3.8382670061604643`*^9},
3.8384504994794083`*^9, {3.8831175347691927`*^9, 3.883117549903524*^9}, {
3.883117652242876*^9, 3.883117753105294*^9}, {3.883117853830345*^9,
3.883117882095052*^9}},
CellLabel->"In[34]:=",ExpressionUUID->"6b2356cd-d661-4982-8aa1-070bfa492f1a"],
Cell[BoxData[
TemplateBox[{
GraphicsBox[{{{{}, {},
TagBox[{
Directive[
Opacity[1.],
AbsoluteThickness[1.6],
GrayLevel[0],
Dashing[{Small, Small}]],
LineBox[{{3.141592653589793*^-6, 0.15915494309189518`}, {
0.37770245310557365`, 0.15915494309189515`}, {0.7554017646184937,
0.15915494309189515`}, {1.5108003876443339`,
0.15915494309189512`}, {3.021597633696014, 0.15915494309189515`}, {
4.652389899641474, 0.15915494309189518`}, {6.283182165586933,
0.15915494309189518`}}]},
Annotation[#, "Charting`Private`Tag$241548#1"]& ],
TagBox[{
Directive[
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 0, 1]],
LineBox[CompressedData["
1:eJw1lek71AsbgMdOhLGMJeubvYlQ6HT0PJKlhUoLuSwZoYTkkDP2StRpU8oa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"]]},
Annotation[#, "Charting`Private`Tag$241548#2"]& ],
TagBox[{
Directive[
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 1, 0]],
LineBox[CompressedData["
1:eJw1lek/FPoegMfSINsMZqzZl6bEQZfOKb6/IqlEyVKu5TSOkqXkhmSJEkop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"]]}, Annotation[#, "Charting`Private`Tag$241548#3"]& ],
TagBox[{
Directive[
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[1, 0, 0]],
LineBox[CompressedData["
1:eJw1lfk/FPgfx8dNzmGMqxXlSCa5Soe8P1KirFpZOsQaS6JDdmLlTui0kRCV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"]]},
Annotation[#, "Charting`Private`Tag$241548#4"]& ]}}, {}}, {
DisplayFunction -> Identity, Ticks -> {Automatic, Automatic},
AxesOrigin -> {0, 0},
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
GridLines -> {None, None}, DisplayFunction -> Identity,
PlotRangePadding -> {{
Scaled[0.02],
Scaled[0.02]}, {0, 0}}, PlotRangeClipping -> True, ImagePadding ->
All, DisplayFunction -> Identity, AspectRatio ->
NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True},
AxesLabel -> {
FormBox["\"\[Theta]\"", TraditionalForm],
FormBox["\"dN/d\[Theta]\"", TraditionalForm]}, AxesOrigin -> {0, 0},
DisplayFunction :> Identity, Frame -> {{True, True}, {True, True}},
FrameLabel -> {{None, None}, {None, None}},
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
GridLines -> {None, None}, GridLinesStyle -> Directive[
GrayLevel[0.5, 0.4]], ImageSize -> 300,
Method -> {
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}},
"DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange -> {{0., 6.283182165586933}, {0, 0.61}}, PlotRangeClipping ->
True, PlotRangePadding -> {{
Scaled[0.02],
Scaled[0.02]}, {Automatic, Automatic}},
Ticks -> {Automatic, Automatic}}],
FormBox[
FormBox[
TemplateBox[{
"\"\[Sigma]x=\[Sigma]y\"", "\"\[Sigma]x=1.9\[Sigma]y\"",
"\"\[Sigma]x=2.6\[Sigma]y\"", "\"\[Sigma]x=3.8\[Sigma]y\""},
"LineLegend", DisplayFunction -> (FormBox[
StyleBox[
StyleBox[
PaneBox[
TagBox[
GridBox[{{
TagBox[
GridBox[{{
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
GrayLevel[0],
Dashing[{Small, Small}]], {
LineBox[{{0, 10}, {40, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
GrayLevel[0],
Dashing[{Small, Small}]], {}}}, AspectRatio -> Full,
ImageSize -> {40, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 0, 1]], {
LineBox[{{0, 10}, {40, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full,
ImageSize -> {40, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 1, 0]], {
LineBox[{{0, 10}, {40, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full,
ImageSize -> {40, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[1, 0, 0]], {
LineBox[{{0, 10}, {40, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full,
ImageSize -> {40, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}},
GridBoxAlignment -> {
"Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
AutoDelete -> False,
GridBoxDividers -> {
"Columns" -> {{False}}, "Rows" -> {{False}}},
GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
GridBoxSpacings -> {
"Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
AutoDelete -> False,
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
"Grid"], Alignment -> Left, AppearanceElements -> None,
ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
"ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
False], TraditionalForm]& ),
InterpretationFunction :> (RowBox[{"LineLegend", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
GrayLevel[0],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
FrameStyle -> GrayLevel[0.], FrameTicks -> None,
PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}]],
StyleBox[
RowBox[{"GrayLevel", "[", "0", "]"}], NumberMarks ->
False]], Appearance -> None, BaseStyle -> {},
BaselinePosition -> Baseline, DefaultBaseStyle -> {},
ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
GrayLevel[0];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["GrayLevelColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
GrayLevel[0], Editable -> False, Selectable -> False],
",",
RowBox[{"Dashing", "[",
RowBox[{"{",
RowBox[{"Small", ",", "Small"}], "}"}], "]"}]}], "]"}],
",",
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[0, 0, 1],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
FrameStyle -> RGBColor[0., 0., 0.6666666666666666],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}]],
StyleBox[
RowBox[{"RGBColor", "[",
RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks ->
False]], Appearance -> None, BaseStyle -> {},
BaselinePosition -> Baseline, DefaultBaseStyle -> {},
ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0, 0, 1];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[0, 0, 1], Editable -> False, Selectable ->
False]}], "]"}], ",",
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[0, 1, 0],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
FrameStyle -> RGBColor[0., 0.6666666666666666, 0.],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}]],
StyleBox[
RowBox[{"RGBColor", "[",
RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks ->
False]], Appearance -> None, BaseStyle -> {},
BaselinePosition -> Baseline, DefaultBaseStyle -> {},
ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0, 1, 0];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[0, 1, 0], Editable -> False, Selectable ->
False]}], "]"}], ",",
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[1, 0, 0],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
FrameStyle -> RGBColor[0.6666666666666666, 0., 0.],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}]],
StyleBox[
RowBox[{"RGBColor", "[",
RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks ->
False]], Appearance -> None, BaseStyle -> {},
BaselinePosition -> Baseline, DefaultBaseStyle -> {},
ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[1, 0, 0];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[1, 0, 0], Editable -> False, Selectable ->
False]}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",",
RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"{", "}"}]}], ",",
RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
Editable -> True], TraditionalForm], TraditionalForm]},
"Legended",
DisplayFunction->(GridBox[{{
TagBox[
ItemBox[
PaneBox[
TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline},
BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"],
"SkipImageSizeLevel"],
ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}},
GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}},
AutoDelete -> False, GridBoxItemSize -> Automatic,
BaselinePosition -> {1, 1}]& ),
Editable->True,
InterpretationFunction->(RowBox[{"Legended", "[",
RowBox[{#, ",",
RowBox[{"Placed", "[",
RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
CellChangeTimes->{
3.838266654234283*^9, 3.8382669763677*^9, 3.838267013244052*^9,
3.838450508914034*^9, 3.883117558305148*^9, {3.883117660819686*^9,
3.883117754849415*^9}, 3.883117964866239*^9},
CellLabel->"Out[36]=",ExpressionUUID->"9ae97bea-5f22-44be-9547-49cbfa6a7c2e"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
RowBox[{"As", " ", "you", " ", "would", " ", "expect"}], ",", " ",
RowBox[{
RowBox[{"peaks", " ", "happen", " ", "at", " ",
RowBox[{"\[Pi]", "/", "2"}], " ", "and", " ", "3",
RowBox[{"\[Pi]", "/", "2"}], " ", "for", " ", "\[Sigma]x"}], ">",
"\[Sigma]y"}]}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"d\[Theta]", "=",
RowBox[{"D", "[",
RowBox[{
FractionBox["1",
RowBox[{
FractionBox[
SuperscriptBox[
RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"],
SuperscriptBox["\[Sigma]y", "2"]], "+",
FractionBox[
SuperscriptBox[
RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"],
SuperscriptBox["\[Sigma]x", "2"]]}]], ",", "\[Theta]"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{"d\[Theta]", "==", "0"}], ",", "\[Theta]"}], "]"}]}]}]], "Input",\
CellChangeTimes->{{3.8384505055093327`*^9, 3.838450574712607*^9}},
CellLabel->"In[9]:=",ExpressionUUID->"0bb965bd-d19f-4328-9c6e-c2d5cdf0fc73"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\[Theta]", "\[Rule]",
TemplateBox[{
RowBox[{"2", " ", "\[Pi]", " ",
TemplateBox[{"1"}, "C"]}],
RowBox[{
TemplateBox[{"1"}, "C"], "\[Element]",
TemplateBox[{}, "Integers"]}]},
"ConditionalExpression"]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[Theta]", "\[Rule]",
TemplateBox[{
RowBox[{
RowBox[{"-",
FractionBox["\[Pi]", "2"]}], "+",
RowBox[{"2", " ", "\[Pi]", " ",
TemplateBox[{"1"}, "C"]}]}],
RowBox[{
TemplateBox[{"1"}, "C"], "\[Element]",
TemplateBox[{}, "Integers"]}]},
"ConditionalExpression"]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[Theta]", "\[Rule]",
TemplateBox[{
RowBox[{
FractionBox["\[Pi]", "2"], "+",
RowBox[{"2", " ", "\[Pi]", " ",
TemplateBox[{"1"}, "C"]}]}],
RowBox[{
TemplateBox[{"1"}, "C"], "\[Element]",
TemplateBox[{}, "Integers"]}]},
"ConditionalExpression"]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[Theta]", "\[Rule]",
TemplateBox[{
RowBox[{"\[Pi]", "+",
RowBox[{"2", " ", "\[Pi]", " ",
TemplateBox[{"1"}, "C"]}]}],
RowBox[{
TemplateBox[{"1"}, "C"], "\[Element]",
TemplateBox[{}, "Integers"]}]},
"ConditionalExpression"]}], "}"}]}], "}"}]], "Output",
CellChangeTimes->{{3.838450510187015*^9, 3.83845053188415*^9}, {
3.8384505645218983`*^9, 3.8384505753775673`*^9}},
CellLabel->"Out[10]=",ExpressionUUID->"b8e1f482-0aaa-4ef2-b7d6-df7a5eb25ac2"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{
"sqrt", " ", "of", " ", "max", " ", "and", " ", "min", " ", "gives", " ",
"\[Delta]"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"Refine", "[",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"dNd\[Theta]", "[",
RowBox[{
RowBox[{"\[Pi]", "/", "2"}], ",", "\[Sigma]x", ",", "\[Sigma]y"}],
"]"}], "/",
RowBox[{"dNd\[Theta]", "[",
RowBox[{"\[Pi]", ",", "\[Sigma]x", ",", "\[Sigma]y"}], "]"}]}], "]"}],
",",
RowBox[{"{",
RowBox[{
RowBox[{"\[Sigma]x", ">", "0"}], ",",
RowBox[{"\[Sigma]y", ">", "0"}]}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.838450622235145*^9, 3.838450663572372*^9}, {
3.838450977279395*^9,
3.838450988568372*^9}},ExpressionUUID->"18867fde-3704-4182-8aff-\
5bc34349f26a"],
Cell[BoxData[
FractionBox["\[Sigma]x", "\[Sigma]y"]], "Output",
CellChangeTimes->{{3.838450625725717*^9, 3.8384506639579372`*^9}},
CellLabel->"Out[17]=",ExpressionUUID->"4680d356-b595-4ea2-80c0-2381b3b0d9cb"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
"taking", " ", "data", " ", "from", " ", "Fig2", " ", "with", " ",
"Webplot", " ", "digitizer", " ", "allows", " ", "us", " ", "to", " ",
"compute", " ", "the", " ", "asymmetry"}], " ", "*)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"max", "=",
RowBox[{"{",
RowBox[{"0.2997", ",", "0.42199", ",", "0.58887"}], "}"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"min", "=",
RowBox[{"{",
RowBox[{"0.09752", ",", "0.07331", ",", "0.052299"}], "}"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"\[Delta]", "=",
RowBox[{"Sqrt", "[",
RowBox[{"max", "/", "min"}], "]"}]}], "\[IndentingNewLine]",
RowBox[{"Asym", "=",
RowBox[{
RowBox[{"(",
RowBox[{"\[Delta]", "-", "1"}], ")"}], "/",
RowBox[{"(",
RowBox[{"\[Delta]", "+", "1"}], ")"}]}]}]}]}]], "Input",
CellChangeTimes->{{3.8384508768613663`*^9, 3.838451008535913*^9}, {
3.883117572919712*^9,
3.88311759270354*^9}},ExpressionUUID->"ed2f8166-390a-44de-a872-\
5898fca2dfbe"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
"1.7530589695202097`", ",", "2.3992166684182767`", ",",
"3.3555446528690447`"}], "}"}]], "Output",
CellChangeTimes->{
3.838450968180387*^9, {3.838451005875023*^9, 3.83845100916203*^9}},
CellLabel->"Out[27]=",ExpressionUUID->"75433f62-9fac-4dc9-82ea-10eaf8b95b86"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
"0.27353535752684927`", ",", "0.4116291501563389`", ",",
"0.5408151771139396`"}], "}"}]], "Output",
CellChangeTimes->{
3.838450968180387*^9, {3.838451005875023*^9, 3.838451009163913*^9}},
CellLabel->"Out[28]=",ExpressionUUID->"60d9405f-f45a-497c-95be-ca2b5f82a960"]
}, Open ]]
}, Open ]]
},
WindowSize->{1386, 762},
WindowMargins->{{Automatic, 260}, {Automatic, 166}},
FrontEndVersion->"12.3 for Mac OS X x86 (64-bit) (July 9, 2021)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"b59bfc57-ad5a-4457-8f36-48f3339f7f1d"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 885, 14, 135, "Text",ExpressionUUID->"93ad8efe-6512-48b9-bb54-8279fc4af6d0"],
Cell[1446, 36, 1304, 29, 79, "Text",ExpressionUUID->"f080cb2d-b71f-46ba-aebc-8310b0d2b79a"],
Cell[2753, 67, 1142, 21, 145, "Text",ExpressionUUID->"f68e209f-1fc4-499a-adff-4329fa790445"],
Cell[CellGroupData[{
Cell[3920, 92, 504, 8, 69, "Chapter",ExpressionUUID->"9193af5d-6504-4a5e-a140-06b33034f4ff"],