Skip to content
Toggle navigation
P
Projects
G
Groups
S
Snippets
Help
Uddeepta Deka
/
Updated Charged Lens
This project
Loading...
Sign in
Toggle navigation
Go to a project
Project
Repository
Issues
0
Merge Requests
0
Pipelines
Wiki
Snippets
Members
Activity
Graph
Charts
Create a new issue
Jobs
Commits
Issue Boards
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Charts
Commit
cf191802
authored
Sep 19, 2024
by
Uddeepta Deka
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
notebook with weak field calculation
parent
4cb82c43
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
691 additions
and
0 deletions
notebooks/charged_lens_weak_field_limit.nb
notebooks/charged_lens_weak_field_limit.nb
0 → 100644
View file @
cf191802
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 13.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 25797, 683]
NotebookOptionsPosition[ 22483, 614]
NotebookOutlinePosition[ 22920, 631]
CellTagsIndexPosition[ 22877, 628]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["Deflection angle in our model", "Subtitle",
CellChangeTimes->{{3.934959072259884*^9,
3.9349590860919943`*^9}},ExpressionUUID->"255fed1d-a31d-49ce-8ffb-\
24040a54a997"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"x", " ", "=", " ",
RowBox[{"{",
RowBox[{"x1", ",", " ", "x2"}], "}"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"nx", " ", "=", " ",
RowBox[{
RowBox[{"Norm", "[", "x", "]"}], "//", "ComplexExpand"}]}]}], "Input",
CellChangeTimes->{{3.934960087275403*^9, 3.934960148999646*^9}, {
3.935036877093408*^9, 3.935036881030464*^9}, {3.9350372749651003`*^9,
3.935037314250619*^9}},
CellLabel->"In[1]:=",ExpressionUUID->"01adbb2b-455b-45a5-ae75-e8e2ee8e9ef8"],
Cell[BoxData[
SqrtBox[
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}]]], "Output",
CellChangeTimes->{
3.934960150728792*^9, 3.935036883929147*^9, {3.9350372825001793`*^9,
3.935037315360223*^9}, 3.93503746295112*^9, 3.935717265710599*^9},
CellLabel->"Out[2]=",ExpressionUUID->"5b778830-824a-4684-8edd-195ff37ec9bb"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Psi]", " ", "=", " ",
RowBox[{
RowBox[{"Log", "[", "nx", "]"}],
RowBox[{"(",
RowBox[{"1", "+",
RowBox[{"\[Pi]", " ",
FractionBox["Q", "M"],
RowBox[{"Log", "[", "nx", "]"}]}]}], ")"}]}]}]], "Input",
CellChangeTimes->{{3.9267288464544487`*^9, 3.926728868272952*^9}, {
3.934960156593937*^9, 3.934960167718965*^9}, {3.9350373011274567`*^9,
3.935037302646393*^9}},
CellLabel->"In[3]:=",ExpressionUUID->"7decbc15-a9b4-4fa0-b56a-0557ec619f8b"],
Cell[BoxData[
RowBox[{
RowBox[{"Log", "[",
SqrtBox[
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}]], "]"}], " ",
RowBox[{"(",
RowBox[{"1", "+",
FractionBox[
RowBox[{"\[Pi]", " ", "Q", " ",
RowBox[{"Log", "[",
SqrtBox[
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}]], "]"}]}], "M"]}], ")"}]}]], "Output",
CellChangeTimes->{3.926728873218835*^9, 3.926731343897604*^9,
3.934959062773733*^9, 3.934960168642354*^9, 3.935036886112479*^9,
3.9350373164276743`*^9, 3.935037463003686*^9, 3.935717267274866*^9},
CellLabel->"Out[3]=",ExpressionUUID->"56868050-f86a-4ede-89d3-176e43674a1c"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]Model", " ", "=", " ",
RowBox[{
RowBox[{"Grad", "[",
RowBox[{"\[Psi]", ",", " ",
RowBox[{"{",
RowBox[{"x1", ",", " ", "x2"}], "}"}]}], "]"}], "//",
"Simplify"}]}]], "Input",
CellChangeTimes->{{3.926728878636312*^9, 3.926728888403893*^9}, {
3.9349601715859423`*^9, 3.934960216623822*^9}, {3.93503732335916*^9,
3.935037324526396*^9}},
CellLabel->"In[4]:=",ExpressionUUID->"e1ec2aa2-699b-42f0-8479-7cf09c5d887e"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
FractionBox[
RowBox[{"x1", " ",
RowBox[{"(",
RowBox[{"M", "+",
RowBox[{"\[Pi]", " ", "Q", " ",
RowBox[{"Log", "[",
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}], "]"}]}]}], ")"}]}],
RowBox[{"M", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}], ")"}]}]], ",",
FractionBox[
RowBox[{"x2", " ",
RowBox[{"(",
RowBox[{"M", "+",
RowBox[{"\[Pi]", " ", "Q", " ",
RowBox[{"Log", "[",
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}], "]"}]}]}], ")"}]}],
RowBox[{"M", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}], ")"}]}]]}], "}"}]], "Output",
CellChangeTimes->{{3.926728883753319*^9, 3.926728888882772*^9},
3.9267313448582497`*^9, 3.9349590637390614`*^9, {3.934960184105431*^9,
3.9349602172614107`*^9}, 3.935036890661557*^9, {3.9350373178422194`*^9,
3.9350373249420013`*^9}, 3.935037466621924*^9, 3.9357172688252487`*^9},
CellLabel->"Out[4]=",ExpressionUUID->"68926dd4-28ea-4821-a543-c6d5b7de2f6b"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]ModelAbs", " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{"Norm", "[", "\[Alpha]Model", "]"}], "//", "ComplexExpand"}], " ",
"//", " ", "FullSimplify"}]}]], "Input",
CellChangeTimes->{{3.934960200640674*^9, 3.934960235743531*^9}},
CellLabel->"In[5]:=",ExpressionUUID->"cbf3372c-1db3-42f4-8673-70a079e23139"],
Cell[BoxData[
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{"M", "+",
RowBox[{"\[Pi]", " ", "Q", " ",
RowBox[{"Log", "[",
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}], "]"}]}]}], ")"}], "2"],
RowBox[{
SuperscriptBox["M", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["x1", "2"], "+",
SuperscriptBox["x2", "2"]}], ")"}]}]]]], "Output",
CellChangeTimes->{3.934960236228095*^9, 3.935037329136541*^9,
3.935037468273271*^9, 3.935717270295795*^9},
CellLabel->"Out[5]=",ExpressionUUID->"aabfcb8b-2f3a-4da4-b469-cbb81a817cbc"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Psi]1d", " ", "=", " ",
RowBox[{
RowBox[{"Log", "[", "\[Xi]", "]"}],
RowBox[{"(",
RowBox[{"1", "+",
RowBox[{"\[Pi]", " ",
FractionBox["Q", "M"],
RowBox[{"Log", "[", "\[Xi]", "]"}]}]}], ")"}]}]}]], "Input",
CellChangeTimes->{{3.934960399931669*^9, 3.9349604302457533`*^9}, {
3.935037343503847*^9, 3.935037346526232*^9}, {3.935037438388153*^9,
3.935037442194628*^9}},
CellLabel->"In[6]:=",ExpressionUUID->"b88c3d2c-503d-4fc4-84ea-a209cd450322"],
Cell[BoxData[
RowBox[{
RowBox[{"Log", "[", "\[Xi]", "]"}], " ",
RowBox[{"(",
RowBox[{"1", "+",
FractionBox[
RowBox[{"\[Pi]", " ", "Q", " ",
RowBox[{"Log", "[", "\[Xi]", "]"}]}], "M"]}], ")"}]}]], "Output",
CellChangeTimes->{{3.934960408430624*^9, 3.934960435336372*^9}, {
3.935037333164751*^9, 3.9350373467765083`*^9}, {3.935037444095586*^9,
3.935037471203578*^9}, 3.935717271710202*^9},
CellLabel->"Out[6]=",ExpressionUUID->"837eb7a9-a71c-432b-8e38-39040e6d3a3f"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]1d", " ", "=", " ",
RowBox[{
RowBox[{"D", "[",
RowBox[{"\[Psi]1d", ",", " ", "\[Xi]"}], "]"}], " ", "//",
"Simplify"}]}]], "Input",
CellChangeTimes->{{3.934960437064498*^9, 3.934960455952656*^9}, {
3.935037364892002*^9, 3.9350373662291603`*^9}, {3.9350374759354153`*^9,
3.935037495442665*^9}, {3.935037579414577*^9, 3.935037579949833*^9}},
CellLabel->"In[7]:=",ExpressionUUID->"0338935b-422a-4d09-95da-1a0f245d8206"],
Cell[BoxData[
FractionBox[
RowBox[{"M", "+",
RowBox[{"2", " ", "\[Pi]", " ", "Q", " ",
RowBox[{"Log", "[", "\[Xi]", "]"}]}]}],
RowBox[{"M", " ", "\[Xi]"}]]], "Output",
CellChangeTimes->{
3.9349604563510857`*^9, 3.935037368159999*^9, {3.935037478526691*^9,
3.93503749574605*^9}, 3.935037580422165*^9, 3.935717272696322*^9},
CellLabel->"Out[7]=",ExpressionUUID->"3d114fb8-ddaa-4a4d-896e-21a61d63bfe4"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Deflection angle from the strong field calculations", "Subtitle",
CellChangeTimes->{{3.934959094738289*^9,
3.934959104547007*^9}},ExpressionUUID->"b822c0bc-05b3-46cb-be19-\
7dd38d39bc89"],
Cell["\<\
Refer to Eq. 10-13 in \
https://journals.aps.org/prd/pdf/10.1103/PhysRevD.66.024010\
\>", "Text",
CellChangeTimes->{{3.934959164530837*^9, 3.9349591910424223`*^9}, {
3.93495924878109*^9, 3.934959248895854*^9}, {3.934959358414825*^9,
3.934959360114464*^9}},ExpressionUUID->"01029359-303d-4c4a-88fd-\
1d171b0c422d"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]TheoryIntg", " ", "=", " ",
RowBox[{
RowBox[{
FractionBox["2",
RowBox[{" ",
RowBox[{"r", " ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"(",
FractionBox["r", "r0"], ")"}], "2"],
RowBox[{"(",
RowBox[{"1", "-",
FractionBox["rs", "r0"], "+",
FractionBox[
SuperscriptBox["rq", "2"],
SuperscriptBox["r0", "2"]]}], ")"}]}], "-",
RowBox[{"(",
RowBox[{"1", "-",
FractionBox["rs", "r"], "+",
FractionBox[
SuperscriptBox["rq", "2"],
SuperscriptBox["r", "2"]]}], ")"}]}], "]"}]}]}]], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"rq", "\[Rule]",
SqrtBox[
FractionBox[
RowBox[{
SuperscriptBox["Q", "2"], "G"}],
RowBox[{"4", " ", "\[Pi]", " ", "\[Epsilon]", " ",
SuperscriptBox["c", "4"]}]]]}], ",", " ",
RowBox[{"rs", "->", " ",
RowBox[{"2", "G", " ",
FractionBox["M",
SuperscriptBox["c", "2"]]}]}]}], "}"}]}], "//",
"FullSimplify"}]}]], "Input",
CellChangeTimes->{{3.93502618243648*^9, 3.9350262322657757`*^9}, {
3.935026639612649*^9, 3.935026640547823*^9}, {3.935026994042377*^9,
3.935026994096809*^9}, {3.935027142398926*^9, 3.935027157037257*^9}, {
3.9350272334474916`*^9, 3.9350272337724237`*^9}, {3.935027585737118*^9,
3.935027611833548*^9}, {3.935027878441781*^9, 3.935027945888442*^9}},
CellLabel->"In[1]:=",ExpressionUUID->"95a6de8c-dac0-4329-9e47-4008c97af5bd"],
Cell[BoxData[
FractionBox[
RowBox[{"4", " ",
SqrtBox["\[Pi]"]}],
RowBox[{"r", " ",
SqrtBox[
FractionBox[
RowBox[{
RowBox[{"4", " ", "\[Pi]", " ",
RowBox[{"(",
RowBox[{"r", "-", "r0"}], ")"}], " ",
SuperscriptBox["r0", "2"], " ",
RowBox[{"(",
RowBox[{"r", "+", "r0"}], ")"}]}], "+",
FractionBox[
RowBox[{"8", " ", "G", " ", "M", " ", "\[Pi]", " ", "r0", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["r", "3"]}], "+",
SuperscriptBox["r0", "3"]}], ")"}]}],
RowBox[{
SuperscriptBox["c", "2"], " ", "r"}]], "+",
FractionBox[
RowBox[{"G", " ",
SuperscriptBox["Q", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["r", "4"], "-",
SuperscriptBox["r0", "4"]}], ")"}]}],
RowBox[{
SuperscriptBox["c", "4"], " ",
SuperscriptBox["r", "2"], " ", "\[Epsilon]"}]]}],
SuperscriptBox["r0", "4"]]]}]]], "Output",
CellChangeTimes->{
3.9350262426554403`*^9, {3.935026637668475*^9, 3.935026665760429*^9},
3.935026722044826*^9, 3.935026995249744*^9, {3.9350271085387783`*^9,
3.935027158167038*^9}, 3.9350272044343557`*^9, 3.935027235284246*^9, {
3.93502759145653*^9, 3.93502761884758*^9}, 3.935027947394401*^9,
3.935028212819545*^9, 3.935037606769106*^9, 3.935037645368924*^9,
3.935039146608048*^9, 3.935717276013521*^9, 3.935723226263226*^9,
3.935723562292046*^9},
CellLabel->"Out[1]=",ExpressionUUID->"2346b8e6-8fdd-4d1c-8a7e-3660c7a8c50f"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]TheoryIntgGSeries", " ", "=", " ",
RowBox[{
RowBox[{"Series", "[",
RowBox[{"\[Alpha]TheoryIntg", ",",
RowBox[{"{",
RowBox[{"G", ",", " ", "0", ",", " ", "1"}], "}"}]}], "]"}], "//",
"Simplify"}]}]], "Input",
CellChangeTimes->CompressedData["
1:eJxTTMoPSmViYGAQBWIQffVnyObywLeOVZ/WbwfRayR89oFovZ5wMC11/q5S
BZAW62FQBtGbmldbguhDXuvBtOyaZ8kgmklaNhVExz2MqgHRX87GQmjpo30g
eoXTSTDdVBL5uhZI19xvBtNP7KZ8ANErLs0C058OXvtyIuito07TXTAt5n9R
+CSQvvT7Cpi23fFREkTzeH4D0y1bdSNA9JZd3NEgesWsCzNAtN6VK2DaTiFf
7hSQ5r5UBKZ5rP7cOQ2kc75x3AXRW2dUfwLRh7XqwPQas9scZ4D0j53snCDa
THaeMoie5LEITK/orlMH0adyloHpGMOva88C6Rn6LOtANAAKQbJv
"],
CellLabel->"In[23]:=",ExpressionUUID->"2b1d853c-f777-458f-8011-cedff647f874"],
Cell[BoxData[
InterpretationBox[
RowBox[{
FractionBox["2",
RowBox[{"r", " ",
SqrtBox[
RowBox[{
RowBox[{"-", "1"}], "+",
FractionBox[
SuperscriptBox["r", "2"],
SuperscriptBox["r0", "2"]]}]]}]], "+",
FractionBox[
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-",
SuperscriptBox["Q", "2"]}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["r", "3"], "+",
RowBox[{
SuperscriptBox["r", "2"], " ", "r0"}], "+",
RowBox[{"r", " ",
SuperscriptBox["r0", "2"]}], "+",
SuperscriptBox["r0", "3"]}], ")"}]}], "+",
RowBox[{"8", " ",
SuperscriptBox["c", "2"], " ", "M", " ", "\[Pi]", " ", "r", " ", "r0",
" ",
RowBox[{"(",
RowBox[{
SuperscriptBox["r", "2"], "+",
RowBox[{"r", " ", "r0"}], "+",
SuperscriptBox["r0", "2"]}], ")"}], " ", "\[Epsilon]"}]}], ")"}],
" ", "G"}],
RowBox[{"4", " ",
SuperscriptBox["c", "4"], " ", "\[Pi]", " ",
SuperscriptBox["r", "3"], " ",
SqrtBox[
RowBox[{
RowBox[{"-", "1"}], "+",
FractionBox[
SuperscriptBox["r", "2"],
SuperscriptBox["r0", "2"]]}]], " ",
SuperscriptBox["r0", "2"], " ",
RowBox[{"(",
RowBox[{"r", "+", "r0"}], ")"}], " ", "\[Epsilon]"}]], "+",
InterpretationBox[
SuperscriptBox[
RowBox[{"O", "[", "G", "]"}], "2"],
SeriesData[$CellContext`G, 0, {}, 0, 2, 1],
Editable->False]}],
SeriesData[$CellContext`G, 0, {
2 $CellContext`r^(-1) (-1 + $CellContext`r^2 $CellContext`r0^(-2))^
Rational[-1, 2], Rational[1, 4] $CellContext`c^(-4)
Pi^(-1) $CellContext`r^(-3) (-1 + $CellContext`r^2 $CellContext`r0^(-2))^
Rational[-1,
2] $CellContext`r0^(-2) ($CellContext`r + $CellContext`r0)^(-1) \
$CellContext`\[Epsilon]^(-1) (-$CellContext`Q^2 ($CellContext`r^3 + \
$CellContext`r^2 $CellContext`r0 + $CellContext`r $CellContext`r0^2 + \
$CellContext`r0^3) +
8 $CellContext`c^2 $CellContext`M
Pi $CellContext`r $CellContext`r0 ($CellContext`r^2 + $CellContext`r \
$CellContext`r0 + $CellContext`r0^2) $CellContext`\[Epsilon])}, 0, 2, 1],
Editable->False]], "Output",
CellChangeTimes->{
3.9350266220343113`*^9, {3.935026670008518*^9, 3.935026675296225*^9},
3.935026727866353*^9, 3.935027030705665*^9, 3.9350271112057037`*^9,
3.935027164336194*^9, 3.935027240309205*^9, 3.935027481325735*^9, {
3.935027654519971*^9, 3.935027661970907*^9}, 3.935027962123082*^9, {
3.935028000152595*^9, 3.935028009439591*^9}, {3.9350281971966476`*^9,
3.9350282161225*^9}, 3.935028342726095*^9, 3.935037608099319*^9,
3.935037650856675*^9, 3.9350391546112537`*^9, 3.935039326011801*^9,
3.935039365204525*^9, {3.9357172796287193`*^9, 3.935717287386078*^9},
3.935717535075841*^9, 3.935717584228724*^9, {3.935718082365869*^9,
3.935718104790546*^9}, 3.9357185990078497`*^9, 3.935719667995173*^9,
3.9357232407480087`*^9, 3.9357234124559937`*^9, {3.935723564835615*^9,
3.9357235925491133`*^9}, 3.935723805902494*^9, 3.935723837516152*^9,
3.935726960586087*^9},
CellLabel->"Out[23]=",ExpressionUUID->"39abd69d-becc-4aa1-a631-3e7555b43cf6"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]Theory", " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{"\[Alpha]TheoryIntgGSeries", ",",
RowBox[{"{",
RowBox[{"r", ",", " ", "r0", ",", " ", "\[Infinity]"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"r0", "\[Element]", "Reals"}], ",", " ",
RowBox[{"r0", ">", "0"}]}], "}"}]}]}], "]"}], "-", "\[Pi]"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"G", "\[Rule]", "1"}], ",", " ",
RowBox[{"c", "\[Rule]", "1"}]}], "}"}]}], "//",
"FullSimplify"}]}]], "Input",
CellChangeTimes->{{3.9350268665069036`*^9, 3.935026899662031*^9}, {
3.935027049303677*^9, 3.935027085629859*^9}, {3.93502753613266*^9,
3.935027541684339*^9}, {3.935027717945545*^9, 3.935027722079101*^9}, {
3.935723503245549*^9, 3.93572351055457*^9}, {3.935723838738455*^9,
3.9357238397053967`*^9}},
CellLabel->"In[24]:=",ExpressionUUID->"9d341fab-79ff-4fb9-9b75-6791602f06e1"],
Cell[BoxData[
RowBox[{
FractionBox[
RowBox[{"4", " ", "M"}], "r0"], "-",
FractionBox[
RowBox[{"3", " ",
SuperscriptBox["Q", "2"]}],
RowBox[{"16", " ",
SuperscriptBox["r0", "2"], " ", "\[Epsilon]"}]]}]], "Output",
CellChangeTimes->{{3.93502707098386*^9, 3.9350270790826397`*^9},
3.935027114189205*^9, 3.935027178368826*^9, 3.93502724437468*^9,
3.935027552342515*^9, 3.935027723796625*^9, {3.935027980586608*^9,
3.935028013077425*^9}, 3.9350282263991613`*^9, 3.9350283474154863`*^9,
3.935037612801614*^9, 3.935037655620305*^9, 3.9350391757395906`*^9,
3.935039336043063*^9, 3.935039373926477*^9, 3.9357173001129007`*^9,
3.935717539923349*^9, 3.935717591762699*^9, {3.935718086901164*^9,
3.9357181126199703`*^9}, 3.9357186025412273`*^9, 3.935719676829406*^9,
3.935723254768239*^9, 3.935723427315572*^9, 3.935723517883444*^9, {
3.935723574998715*^9, 3.935723597494371*^9}, 3.9357238133460197`*^9,
3.935723858354121*^9, 3.935726964822887*^9},
CellLabel->"Out[24]=",ExpressionUUID->"bcdfc849-0e62-4c14-8a9d-bf181102a713"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]TheoryX", "=",
RowBox[{
RowBox[{"\[Alpha]Theory", " ",
FractionBox[
RowBox[{"Dl", " ", "Dls"}],
RowBox[{"\[Xi]0", " ", "Ds"}]]}], "/.",
RowBox[{"{",
RowBox[{"r0", "\[Rule]",
RowBox[{"\[Xi]0", " ", "\[Chi]"}]}], "}"}]}]}]], "Input",
CellChangeTimes->{{3.9350299884032917`*^9, 3.9350301236201067`*^9}, {
3.935030319932406*^9, 3.9350303608491383`*^9}, {3.935030400715679*^9,
3.9350304124022284`*^9}, {3.93503050493639*^9, 3.9350305342780933`*^9}, {
3.935717340826592*^9, 3.935717346156402*^9}, {3.935717567128707*^9,
3.935717575080031*^9}},
CellLabel->"In[25]:=",ExpressionUUID->"44e73b9e-a984-4c6c-abe6-59a9459f11c7"],
Cell[BoxData[
FractionBox[
RowBox[{"Dl", " ", "Dls", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
FractionBox[
RowBox[{"3", " ",
SuperscriptBox["Q", "2"]}],
RowBox[{"16", " ", "\[Epsilon]", " ",
SuperscriptBox["\[Xi]0", "2"], " ",
SuperscriptBox["\[Chi]", "2"]}]]}], "+",
FractionBox[
RowBox[{"4", " ", "M"}],
RowBox[{"\[Xi]0", " ", "\[Chi]"}]]}], ")"}]}],
RowBox[{"Ds", " ", "\[Xi]0"}]]], "Output",
CellChangeTimes->{
3.935030007484617*^9, {3.9350300680674257`*^9, 3.935030124140223*^9},
3.935030362221737*^9, 3.9350304133432083`*^9, 3.935030538574332*^9,
3.9350376137855453`*^9, 3.935037659336377*^9, 3.935039184749331*^9,
3.935039340826103*^9, 3.935039378542783*^9, 3.935717305742334*^9,
3.93571734835791*^9, {3.935717540923568*^9, 3.935717594394017*^9}, {
3.93571808878161*^9, 3.935718115577442*^9}, 3.935718605501642*^9,
3.935719680792975*^9, 3.935723263966981*^9, 3.935723431249311*^9,
3.9357235771729918`*^9, 3.93572360756811*^9, 3.9357238169961042`*^9,
3.9357238609156933`*^9, 3.935726965767631*^9},
CellLabel->"Out[25]=",ExpressionUUID->"fbc8fad4-43e3-4ad5-97e0-ada8139d5904"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]TheoryXGeomUnits", " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"\[Alpha]TheoryX", "/.",
RowBox[{"{",
RowBox[{"Dls", " ", "\[Rule]",
FractionBox[
RowBox[{
SuperscriptBox["\[Xi]0", "2"], "Ds"}],
RowBox[{"4", " ", "M", " ", "Dl"}]]}], "}"}]}], "/.",
RowBox[{"{",
RowBox[{"Q", "\[Rule]",
SqrtBox[
RowBox[{"8", " ", "M", " ", "\[Xi]0", " ",
FractionBox["Qeff", "\[Pi]"]}]]}], "}"}]}], "/.",
RowBox[{"{",
RowBox[{"\[Epsilon]", "\[Rule]",
FractionBox["1",
RowBox[{"4", " ", "\[Pi]"}]]}], "}"}]}], "//",
"FullSimplify"}]}]], "Input",
CellChangeTimes->{{3.9357190388166*^9, 3.935719102852594*^9},
3.935719268765457*^9, {3.935719586941434*^9, 3.9357196332370462`*^9}, {
3.935723538013443*^9, 3.935723547002122*^9}, {3.935723619657971*^9,
3.935723636527114*^9}},
CellLabel->"In[26]:=",ExpressionUUID->"47cdfdef-8db8-4012-9b94-35261792dad1"],
Cell[BoxData[
RowBox[{
RowBox[{"-",
FractionBox[
RowBox[{"3", " ", "Qeff"}],
RowBox[{"2", " ",
SuperscriptBox["\[Chi]", "2"]}]]}], "+",
FractionBox["1", "\[Chi]"]}]], "Output",
CellChangeTimes->{{3.935719095535082*^9, 3.9357191034073267`*^9},
3.9357192706744003`*^9, 3.9357196341610603`*^9, 3.935719683668853*^9,
3.935723316174766*^9, 3.93572343294619*^9, {3.935723583738428*^9,
3.935723637112855*^9}, 3.935723818758154*^9, 3.935723862520755*^9,
3.935726967220913*^9},
CellLabel->"Out[26]=",ExpressionUUID->"799dd8e9-3983-4f2e-92ed-b2ac37b8c688"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]TheoryXGeomUnits", "/.",
RowBox[{"Qeff", "\[Rule]", "0"}]}]], "Input",
CellChangeTimes->{{3.9350376723850822`*^9, 3.935037699742826*^9}, {
3.935719121043541*^9, 3.9357191442199717`*^9}, 3.9357192439720984`*^9, {
3.935719283900131*^9, 3.935719289465973*^9}, {3.935719733905694*^9,
3.9357197340967693`*^9}},
CellLabel->"In[27]:=",ExpressionUUID->"3b865eeb-c50f-4753-a7dc-81dbc3255e16"],
Cell[BoxData[
FractionBox["1", "\[Chi]"]], "Output",
CellChangeTimes->{{3.935037681106112*^9, 3.9350377002897*^9},
3.935039351442196*^9, 3.9357173604134817`*^9, 3.93571754289249*^9,
3.935717577510191*^9, {3.935719123072431*^9, 3.935719144399374*^9},
3.935719289919183*^9, {3.935719724029995*^9, 3.935719734475545*^9},
3.9357233279802713`*^9, 3.935723435931785*^9, 3.935723585994747*^9,
3.93572364040154*^9, 3.935723820784243*^9, 3.935723863648588*^9,
3.935726968575989*^9},
CellLabel->"Out[27]=",ExpressionUUID->"91753962-d2be-49b6-a4f2-b85c8051c12f"]
}, Open ]]
}, Open ]]
},
WindowSize->{1920, 953},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
TaggingRules-><|"TryRealOnly" -> False|>,
FrontEndVersion->"13.0 for Mac OS X ARM (64-bit) (February 4, 2022)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"e2ffb407-981d-4199-a6de-1c86c7cdaf68"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 177, 3, 53, "Subtitle",ExpressionUUID->"255fed1d-a31d-49ce-8ffb-24040a54a997"],
Cell[CellGroupData[{
Cell[782, 29, 508, 11, 52, "Input",ExpressionUUID->"01adbb2b-455b-45a5-ae75-e8e2ee8e9ef8"],
Cell[1293, 42, 354, 8, 36, "Output",ExpressionUUID->"5b778830-824a-4684-8edd-195ff37ec9bb"]
}, Open ]],
Cell[CellGroupData[{
Cell[1684, 55, 504, 12, 47, "Input",ExpressionUUID->"7decbc15-a9b4-4fa0-b56a-0557ec619f8b"],
Cell[2191, 69, 710, 19, 70, "Output",ExpressionUUID->"56868050-f86a-4ede-89d3-176e43674a1c"]
}, Open ]],
Cell[CellGroupData[{
Cell[2938, 93, 476, 11, 30, "Input",ExpressionUUID->"e1ec2aa2-699b-42f0-8479-7cf09c5d887e"],
Cell[3417, 106, 1269, 35, 61, "Output",ExpressionUUID->"68926dd4-28ea-4821-a543-c6d5b7de2f6b"]
}, Open ]],
Cell[CellGroupData[{
Cell[4723, 146, 349, 7, 30, "Input",ExpressionUUID->"cbf3372c-1db3-42f4-8673-70a079e23139"],
Cell[5075, 155, 653, 19, 71, "Output",ExpressionUUID->"aabfcb8b-2f3a-4da4-b469-cbb81a817cbc"]
}, Open ]],
Cell[CellGroupData[{
Cell[5765, 179, 510, 12, 47, "Input",ExpressionUUID->"b88c3d2c-503d-4fc4-84ea-a209cd450322"],
Cell[6278, 193, 500, 11, 49, "Output",ExpressionUUID->"837eb7a9-a71c-432b-8e38-39040e6d3a3f"]
}, Open ]],
Cell[CellGroupData[{
Cell[6815, 209, 470, 9, 30, "Input",ExpressionUUID->"0338935b-422a-4d09-95da-1a0f245d8206"],
Cell[7288, 220, 422, 9, 51, "Output",ExpressionUUID->"3d114fb8-ddaa-4a4d-896e-21a61d63bfe4"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[7759, 235, 197, 3, 53, "Subtitle",ExpressionUUID->"b822c0bc-05b3-46cb-be19-7dd38d39bc89"],
Cell[7959, 240, 329, 7, 35, "Text",ExpressionUUID->"01029359-303d-4c4a-88fd-1d171b0c422d"],
Cell[CellGroupData[{
Cell[8313, 251, 1655, 44, 74, "Input",ExpressionUUID->"95a6de8c-dac0-4329-9e47-4008c97af5bd"],
Cell[9971, 297, 1602, 42, 95, "Output",ExpressionUUID->"2346b8e6-8fdd-4d1c-8a7e-3660c7a8c50f"]
}, Open ]],
Cell[CellGroupData[{
Cell[11610, 344, 747, 16, 30, "Input",ExpressionUUID->"2b1d853c-f777-458f-8011-cedff647f874"],
Cell[12360, 362, 3287, 79, 73, "Output",ExpressionUUID->"39abd69d-becc-4aa1-a631-3e7555b43cf6"]
}, Open ]],
Cell[CellGroupData[{
Cell[15684, 446, 1054, 25, 30, "Input",ExpressionUUID->"9d341fab-79ff-4fb9-9b75-6791602f06e1"],
Cell[16741, 473, 1081, 20, 55, "Output",ExpressionUUID->"bcdfc849-0e62-4c14-8a9d-bf181102a713"]
}, Open ]],
Cell[CellGroupData[{
Cell[17859, 498, 696, 15, 50, "Input",ExpressionUUID->"44e73b9e-a984-4c6c-abe6-59a9459f11c7"],
Cell[18558, 515, 1203, 26, 67, "Output",ExpressionUUID->"fbc8fad4-43e3-4ad5-97e0-ada8139d5904"]
}, Open ]],
Cell[CellGroupData[{
Cell[19798, 546, 1017, 26, 57, "Input",ExpressionUUID->"47cdfdef-8db8-4012-9b94-35261792dad1"],
Cell[20818, 574, 589, 13, 54, "Output",ExpressionUUID->"799dd8e9-3983-4f2e-92ed-b2ac37b8c688"]
}, Open ]],
Cell[CellGroupData[{
Cell[21444, 592, 430, 7, 30, "Input",ExpressionUUID->"3b865eeb-c50f-4753-a7dc-81dbc3255e16"],
Cell[21877, 601, 578, 9, 74, "Output",ExpressionUUID->"91753962-d2be-49b6-a4f2-b85c8051c12f"]
}, Open ]]
}, Open ]]
}
]
*)
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment