-
Notifications
You must be signed in to change notification settings - Fork 4
/
qcriticalPlots.nb
1835 lines (1800 loc) · 75.7 KB
/
qcriticalPlots.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 11.2' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 77346, 1827]
NotebookOptionsPosition[ 74684, 1777]
NotebookOutlinePosition[ 75044, 1793]
CellTagsIndexPosition[ 75001, 1790]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{"(*",
RowBox[{"HVEDM", " ", "AdS", " ", "case"}], "*)"}]], "Input",
CellChangeTimes->{{3.768782978682901*^9,
3.768782989113742*^9}},ExpressionUUID->"f62957e6-f560-4eb6-a87b-\
de1b2a9f3455"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Block", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{"qcrit", ",", "\[Mu]extreme"}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"\[Mu]extreme", "[",
RowBox[{"rh_", ",", "z_", ",", "\[Theta]_"}], "]"}], ":=",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"2",
RowBox[{"(",
RowBox[{"2", "-", "\[Theta]"}], ")"}],
RowBox[{"(",
RowBox[{"2", "+", "z", "-", "\[Theta]"}], ")"}]}], "]"}],
RowBox[{"rh", "/",
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]"}], ")"}]}],
RowBox[{"Exp", "[",
RowBox[{"-",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"z", "-", "1", "+",
RowBox[{"\[Theta]", "/", "2"}]}], ")"}], "/", "2"}], "/",
RowBox[{"(",
RowBox[{"2", "-", "\[Theta]"}], ")"}]}], "]"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"rs_", ",", "rh_", ",", "\[Mu]_", ",", "z_", ",", "\[Theta]_"}],
"]"}], ":=",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"1", "-",
RowBox[{
RowBox[{"(",
RowBox[{"rh", "/", "rs"}], ")"}], "^",
RowBox[{"(",
RowBox[{"2", "+", "z", "-", "\[Theta]"}], ")"}]}], "+",
RowBox[{
RowBox[{"\[Mu]", "^", "2"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]"}], ")"}], "/", "2"}], "/",
RowBox[{"(",
RowBox[{"2", "-", "\[Theta]"}], ")"}]}], " ",
RowBox[{
RowBox[{"rh", "^",
RowBox[{"(",
RowBox[{
RowBox[{"2", "z"}], "-",
RowBox[{"2", "\[Theta]"}]}], ")"}]}], "/",
RowBox[{"rs", "^",
RowBox[{"(",
RowBox[{"2",
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]", "+", "1"}], ")"}]}], ")"}]}]}],
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"(",
RowBox[{"rh", "/", "rs"}], ")"}], "^",
RowBox[{"(",
RowBox[{"\[Theta]", "-", "z"}], ")"}]}]}], ")"}]}]}], "]"}], "/",
RowBox[{"(",
RowBox[{"\[Mu]", " ", "rs",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"(",
RowBox[{"rh", "/", "rs"}], ")"}], "^",
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]"}], ")"}]}]}], ")"}]}], ")"}]}]}],
";", "\[IndentingNewLine]",
RowBox[{"Print", "[", "\"\<1<=z<2 case\>\"", "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"1", ",", "0.1", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"0.1", ",", "1.75", ",", "\[Theta]"}], "]"}]}], ",",
"1.75", ",", "\[Theta]"}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Theta]", ",", "0", ",", "1.5"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\[Theta]", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}], ",",
RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[", "\"\<z>2 case\>\"", "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"1", ",", "0.1", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"0.1", ",", "3", ",", "\[Theta]"}], "]"}]}], ",", "3", ",",
"\[Theta]"}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Theta]", ",", "0", ",", "1.8"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\[Theta]", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}], ",",
RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], "]"}], ";"}]}],
"\[IndentingNewLine]", "]"}]], "Input",
CellChangeTimes->{{3.7687829618095503`*^9, 3.768783066326708*^9}, {
3.768783098817932*^9, 3.768783123262689*^9}, {3.7687831650780993`*^9,
3.7687832477321243`*^9}, {3.7687833956137342`*^9,
3.768783436162868*^9}},ExpressionUUID->"21c5d56c-8196-425e-9939-\
80f2dfc31416"],
Cell[CellGroupData[{
Cell[BoxData["\<\"1<=z<2 case\"\>"], "Print",
CellChangeTimes->{{3.768783236674155*^9, 3.768783249492634*^9}, {
3.768783415544139*^9,
3.768783436494228*^9}},ExpressionUUID->"c560d338-ca77-4ba8-ba9c-\
a1c8d023175c"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVj3tUjAkYxictkeSyydJlNd83X83Mpu9DVLu8r6xIpbBKV7qabqNaii50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"]]},
Annotation[#, "Charting`Private`Tag$3955#1"]& ]}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox[
TagBox["\[Theta]", HoldForm], TraditionalForm],
FormBox["qc", TraditionalForm]},
AxesOrigin->{0., 0.},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{All, All},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Print",
CellChangeTimes->{{3.768783236674155*^9, 3.768783249492634*^9}, {
3.768783415544139*^9,
3.768783436570326*^9}},ExpressionUUID->"28931079-edbd-4efa-98a0-\
ff50dc309c01"],
Cell[BoxData["\<\"z>2 case\"\>"], "Print",
CellChangeTimes->{{3.768783236674155*^9, 3.768783249492634*^9}, {
3.768783415544139*^9,
3.7687834365782967`*^9}},ExpressionUUID->"8e0d1b06-7384-44e7-b86b-\
2c99bd9f424a"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVkGk41Asfhke02RreQtmLssUJkdDvZyJnRpZhGFmyZJcsnawdRLJlSZSS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"]]},
Annotation[#, "Charting`Private`Tag$3999#1"]& ]}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox[
TagBox["\[Theta]", HoldForm], TraditionalForm],
FormBox["qc", TraditionalForm]},
AxesOrigin->{0., 0.},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{All, All},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Print",
CellChangeTimes->{{3.768783236674155*^9, 3.768783249492634*^9}, {
3.768783415544139*^9,
3.768783436665758*^9}},ExpressionUUID->"6153253b-d855-4aa3-93c8-\
d7f56fd0c1cc"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Block", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{"qcrit", ",", "\[Mu]extreme"}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"\[Mu]extreme", "[",
RowBox[{"rh_", ",", "z_", ",", "\[Theta]_"}], "]"}], ":=",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"2",
RowBox[{"(",
RowBox[{"2", "-", "\[Theta]"}], ")"}],
RowBox[{"(",
RowBox[{"2", "+", "z", "-", "\[Theta]"}], ")"}]}], "]"}],
RowBox[{"rh", "/",
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]"}], ")"}]}],
RowBox[{"Exp", "[",
RowBox[{"-",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"z", "-", "1", "+",
RowBox[{"\[Theta]", "/", "2"}]}], ")"}], "/", "2"}], "/",
RowBox[{"(",
RowBox[{"2", "-", "\[Theta]"}], ")"}]}], "]"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"rs_", ",", "rh_", ",", "\[Mu]_", ",", "z_", ",", "\[Theta]_"}],
"]"}], ":=",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"1", "-",
RowBox[{
RowBox[{"(",
RowBox[{"rh", "/", "rs"}], ")"}], "^",
RowBox[{"(",
RowBox[{"2", "+", "z", "-", "\[Theta]"}], ")"}]}], "+",
RowBox[{
RowBox[{"\[Mu]", "^", "2"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]"}], ")"}], "/", "2"}], "/",
RowBox[{"(",
RowBox[{"2", "-", "\[Theta]"}], ")"}]}], " ",
RowBox[{
RowBox[{"rh", "^",
RowBox[{"(",
RowBox[{
RowBox[{"2", "z"}], "-",
RowBox[{"2", "\[Theta]"}]}], ")"}]}], "/",
RowBox[{"rs", "^",
RowBox[{"(",
RowBox[{"2",
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]", "+", "1"}], ")"}]}], ")"}]}]}],
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"(",
RowBox[{"rh", "/", "rs"}], ")"}], "^",
RowBox[{"(",
RowBox[{"\[Theta]", "-", "z"}], ")"}]}]}], ")"}]}]}], "]"}], "/",
RowBox[{"(",
RowBox[{"\[Mu]", " ", "rs",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"(",
RowBox[{"rh", "/", "rs"}], ")"}], "^",
RowBox[{"(",
RowBox[{"z", "-", "\[Theta]"}], ")"}]}]}], ")"}]}], ")"}]}]}],
";", "\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"1", ",", "0.1", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"0.1", ",", "z", ",", "1"}], "]"}]}], ",", "z", ",", "1"}],
"]"}], ",",
RowBox[{"{",
RowBox[{"z", ",", "1.5", ",", "15"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"z", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], "]"}], ";"}]}],
"\[IndentingNewLine]", "]"}]], "Input",
CellChangeTimes->{{3.768739678786416*^9, 3.7687397561513157`*^9}, {
3.768739887319951*^9, 3.768740090551032*^9}, {3.768740277783934*^9,
3.768740517360342*^9}, {3.768783294749133*^9, 3.7687833631175127`*^9}, {
3.768783449683344*^9, 3.7687834625902243`*^9}, {3.768834713805646*^9,
3.768834719587509*^9}},ExpressionUUID->"3c075b31-4643-4cf4-b327-\
7ee416a4ade8"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVkH080wkAh5dTOO+xjggLM5sfJZ3LaN/JhLPmrVBq8lIyLxMS2o+jJJmP
aDV1FV15C13XG13pxF1J9elFJ6WdJCm96KQWsXN/PJ/nj+e/hxaVHBSrRqFQ
+DP8747XH30pFCWn8uusMLuTNDAOFHSPGyg5OGVYWttCQzHXRDhCU3JYq/l6
rndoCJGz0/5eoeRM5w71ZH+m4QUv72jDbiVHjcrPOOG3EHOq9MfC9L9w2hua
JOKxhfAJZf58xmKCw+5jGQ2tskFXu/BdlMdXTuw1j/MtDnZ4pKnzp6aIAnlp
guysniNuifJ1o0vV0D3YX3vwmDPYRV7Vn+rV4bjDfPv9jO8xP7rBbdHYHCSu
Pq8hG3fDRMbpzgRjLWSmMuP9EjjwXRkeIojWxp0paQHXyxNG9/2dRDW6MBln
Hr340gsK+RP1og59tGYukcZkrYSuVFNUo2GIoiu0xh+i/XBqZDRgr+lcHDo1
VUl15UODMa3QphuBF7FU1aodgMNtinihrzH2bfl6KKI+EE5fdNJcwqko4M9e
tJ8djEmpXnZfzjyojIUXwqZDsIuylEmr+g53fqfGOHSugb5h3ZqXTSZgt3RU
/pMfhnvkaG7uA1PYeA67pqStRXnRLsbhwfkIieSYVARHQDr29nahjjns9+7c
TSRsAM8t28zIaQFCi5d9FHtHYspizZDFcgscDfTQrPHfiLeR6qenoi1x+9Y6
1eeUKCRb5U44sq3gcq2ufWtxNLxzSlMa26xwe5i6vaIuBs3FRZtlwTQYy2gj
/OFYsLawzFuf0IBn1Prq+Zvh9vG8ICB5ITbZSmr3i+Ng9y6oZxHFGntKuowz
bm4B9eKBBUG7reEzVeUTOk+EY44dA32mNpC2WhvuKkyAfbp8U+1xG8zq8Ssb
GElEGTNn+TWGLXgm3tXywGQcKBHIeJds8aHyS/pisXjm71/1Wp50COIOma5y
SoH7L3Yc14d0vLlib2KmvhVPg53KTm6wQ2idqtPx7lasT/VdFvXCDgMP7N8J
j6Qik8sXFmYwQJ981dv+Uxpkis8r3qsYWDm+j5cZkQ4+s7jmark9/jClCKsE
2/B80FmosGFiYip/VpNXBrKSch96NDCReNK3S81pOxqrL96cw2FBVX2kKH1J
JvobZaTBDRau21LKmhyy8K91QUHcKge8SqSU3KBn45hPpC6z3wHlN/l7zrrv
AN/9WZBDHAG4P6b7e0swdFlctTeeQN2kXDnpJ0GuB2X0dQKB9qQurwaBBL8t
t5TWpRBgWzX464VLYMJdf52eTaCggmv2SCTBIK+XTSshIM97cSlvnwRZgns2
884R2Jkk8nB5KoHx3cjU9AsEgpsliWPPJGgMGG3rbiZweVrL9OyQBP2B+sLy
KwR+jT0zsGRUAl4Iv8LgOoFbH2hc9jckDMI7dbUfE2DNbl280Z5EfW9YRHwf
AZ1zPy5gOJJYsXa4vlNBIMyqZ+d7ZxLb1mn4FD4n0OykeSPHnUTfel7e7LcE
hpZesqwWzHRF992Y9wSO95q/EYeQ0BfGWHZ8IBDvedXFPZyEZ2T+5bxPBE4k
Dbp1R5F40j9Xe0BJoL85Q1m5mUTaxuPh3EkCbQ9FzkkJJPQGFtdWThFo0eoc
ZqeQqIlq+6RSESirOGj27TYS/wH3bBrT
"]]},
Annotation[#, "Charting`Private`Tag$325036#1"]& ]}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox[
TagBox["z", HoldForm], TraditionalForm],
FormBox["qc", TraditionalForm]},
AxesOrigin->{0., 0.},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0., 15}, {0., 487.3774677202101}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Print",
CellChangeTimes->{
3.768783365670196*^9, {3.768783457531637*^9, 3.768783470247149*^9}, {
3.7688347154940443`*^9,
3.768834720271649*^9}},ExpressionUUID->"70764102-4f92-4308-ad82-\
15f547c0ccc1"]
}, Open ]],
Cell[BoxData[
RowBox[{"(*", " ",
RowBox[{"BIAdS", " ", "plots"}], " ", "*)"}]], "Input",
CellChangeTimes->{{3.768783825060652*^9,
3.768783835145598*^9}},ExpressionUUID->"78807abb-a5c0-416a-baf2-\
f25df1dea14c"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Block", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{"m", ",", "f", ",", "qcrit", ",", "\[Mu]extreme"}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"m", "[",
RowBox[{"\[Beta]_", ",", "\[Gamma]_", ",", "\[Mu]_"}], "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"-",
RowBox[{"\[Beta]", "^", "2"}]}], "/", "2"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{"Sqrt", "[",
RowBox[{"1", "+",
RowBox[{"\[Gamma]", " ",
RowBox[{"\[Mu]", "^", "2"}]}]}], "]"}]}], ")"}], "/", "6"}], "/",
"\[Gamma]"}], "+", "1", "+",
RowBox[{
RowBox[{
RowBox[{"\[Mu]", "^", "2"}], "/", "3"}],
RowBox[{"Hypergeometric2F1", "[",
RowBox[{
RowBox[{"1", "/", "4"}], ",",
RowBox[{"1", "/", "2"}], ",",
RowBox[{"5", "/", "4"}], ",",
RowBox[{
RowBox[{"-", "\[Gamma]"}], " ",
RowBox[{"\[Mu]", "^", "2"}]}]}], "]"}]}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"f", "[",
RowBox[{"z_", ",", "\[Beta]_", ",", "\[Gamma]_", ",", "\[Mu]_"}], "]"}],
":=",
RowBox[{
RowBox[{
RowBox[{"\[Mu]", "^", "2"}], " ",
RowBox[{
RowBox[{"z", "^", "4"}], "/", "3"}], " ",
RowBox[{"Hypergeometric2F1", "[",
RowBox[{
RowBox[{"1", "/", "4"}], ",",
RowBox[{"1", "/", "2"}], ",",
RowBox[{"5", "/", "4"}], ",",
RowBox[{
RowBox[{"-",
RowBox[{"z", "^", "4"}]}], " ", "\[Gamma]", " ",
RowBox[{"\[Mu]", "^", "2"}]}]}], "]"}]}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{"Sqrt", "[",
RowBox[{"1", "+",
RowBox[{"\[Gamma]", " ",
RowBox[{"\[Mu]", "^", "2"}], " ",
RowBox[{"z", "^", "4"}]}]}], "]"}]}], ")"}], "/", "6"}], "/",
"\[Gamma]"}], "-", " ",
RowBox[{
RowBox[{"m", " ", "[",
RowBox[{"\[Beta]", ",", "\[Gamma]", ",", "\[Mu]"}], "]"}],
RowBox[{"z", "^", "3"}]}], "+", "1", "-",
RowBox[{
RowBox[{"\[Beta]", "^", "2"}], " ",
RowBox[{
RowBox[{"z", "^", "2"}], "/", "2"}]}]}]}], ";", "\[IndentingNewLine]",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"zs_", ",", "\[Beta]_", ",", "\[Gamma]_", ",", "\[Mu]_"}],
"]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"f", "[",
RowBox[{"zs", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Mu]"}], "]"}],
"]"}], "/", "zs"}], "/",
RowBox[{"(",
RowBox[{"\[Mu]", "*",
RowBox[{"(",
RowBox[{
RowBox[{"Hypergeometric2F1", "[",
RowBox[{
RowBox[{"1", "/", "4"}], ",",
RowBox[{"1", "/", "2"}], ",",
RowBox[{"5", "/", "4"}], ",",
RowBox[{
RowBox[{"-", "\[Gamma]"}], " ",
RowBox[{"\[Mu]", "^", "2"}]}]}], "]"}], "-",
RowBox[{"zs", " ",
RowBox[{"Hypergeometric2F1", "[",
RowBox[{
RowBox[{"1", "/", "4"}], ",",
RowBox[{"1", "/", "2"}], ",",
RowBox[{"5", "/", "4"}], ",",
RowBox[{
RowBox[{"-", "\[Gamma]"}], " ",
RowBox[{"\[Mu]", "^", "2"}], " ",
RowBox[{"zs", "^", "4"}]}]}], "]"}]}]}], ")"}]}], ")"}]}]}],
";", "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Mu]extreme", "[",
RowBox[{"\[Beta]_", ",", "\[Gamma]_"}], "]"}], ":=",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"1", "/", "\[Gamma]"}],
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"1", "+",
RowBox[{
RowBox[{"(",
RowBox[{"6", "-",
RowBox[{"\[Beta]", "^", "2"}]}], ")"}], "\[Gamma]"}]}], ")"}],
"^", "2"}], "-", "1"}], ")"}]}], "]"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[", "\"\<0<=\[Beta]<=Sqrt[6] case\>\"", "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"0.1", ",", "2", ",", "\[Gamma]", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"2", ",", "\[Gamma]"}], "]"}]}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Gamma]", ",", "0", ",", "10"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\[Gamma]", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[", "\"\<\[Beta]>Sqrt[6] case\>\"", "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"0.1", ",", "5", ",", "\[Gamma]", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"5", ",", "\[Gamma]"}], "]"}]}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Gamma]", ",",
RowBox[{"2", "/",
RowBox[{"(",
RowBox[{
RowBox[{"5", "^", "2"}], "-", "6"}], ")"}]}], ",", "10"}], "}"}],
",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\[Gamma]", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[", "\"\<Branch cut 0<=\[Beta]<=Sqrt[6]\>\"", "]"}],
";", "\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"0.1", ",", "\[Beta]", ",", "10", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"\[Beta]", ",", "10"}], "]"}]}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Beta]", ",", "0", ",",
RowBox[{"Sqrt", "[", "6", "]"}]}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\[Beta]", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], "]"}], ";",
"\[IndentingNewLine]",
RowBox[{
"Print", "[",
"\"\<Branch cut \[Beta]\[GreaterEqual] \!\(\*SqrtBox[FractionBox[\(2 \
\((1 + 3\\\ \[Gamma])\)\), \(\[Gamma]\)]]\)\>\"", "]"}], ";",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"qcrit", "[",
RowBox[{"0.1", ",", "\[Beta]", ",", "10", ",",
RowBox[{"0.75",
RowBox[{"\[Mu]extreme", "[",
RowBox[{"\[Beta]", ",", "10"}], "]"}]}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Beta]", ",",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"2",
RowBox[{
RowBox[{"(",
RowBox[{"1", "+",
RowBox[{"3", "\[Gamma]"}]}], ")"}], "/", "\[Gamma]"}]}], "]"}],
"/.",
RowBox[{"{",
RowBox[{"\[Gamma]", "\[Rule]", "10"}], "}"}]}], ",",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{"20",
RowBox[{
RowBox[{"(",
RowBox[{"1", "+",
RowBox[{"3", "\[Gamma]"}]}], ")"}], "/", "\[Gamma]"}]}], "]"}],
"/.",
RowBox[{"{",
RowBox[{"\[Gamma]", "\[Rule]", "10"}], "}"}]}]}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\[Beta]", ",", "qc"}], "}"}]}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], "]"}], ";"}]}],
"\[IndentingNewLine]", "]"}]], "Input",
CellChangeTimes->{{3.7687835521896477`*^9, 3.768783787764545*^9}, {
3.7688281571218767`*^9,
3.768828161349102*^9}},ExpressionUUID->"16e5d08b-4c1b-4438-bfe0-\
19c6a18b1fdd"],
Cell[CellGroupData[{
Cell[BoxData["\<\"0<=\[Beta]<=Sqrt[6] case\"\>"], "Print",
CellChangeTimes->{{3.76878377083335*^9, 3.768783789215413*^9},
3.7688281620952*^9},ExpressionUUID->"6327216c-cba9-47ed-8223-357c82f3f5ff"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV13k4VO8XAPCxM8yYQXGvJYwilLUQuSchZMtSyhaKkKWiFLK0SCgk/KzZ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"]]},
Annotation[#, "Charting`Private`Tag$2153#1"]& ]}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox[
TagBox["\[Gamma]", HoldForm], TraditionalForm],
FormBox["qc", TraditionalForm]},
AxesOrigin->{0., 0.},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 10}, {0., 6.775144317321754}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Print",
CellChangeTimes->{{3.76878377083335*^9, 3.768783789215413*^9},
3.7688281624852037`*^9},ExpressionUUID->"47670cb4-e255-4df9-a138-\
8f26429b628e"],
Cell[BoxData["\<\"\[Beta]>Sqrt[6] case\"\>"], "Print",
CellChangeTimes->{{3.76878377083335*^9, 3.768783789215413*^9},
3.768828162492598*^9},ExpressionUUID->"fa3bb2cd-9686-4133-88b7-\
f8c5e174de53"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV13k41N8XB/DPjGGY7EUqS0wrflG0CecgrUqlSIQspZJIfamQpI2KUFQq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