Skip to content

GitLab

Commit c19ac911 authored by Marcus Haberland's avatar Marcus Haberland
Browse files

git init

parent 91076733
Expand all Hide whitespace changes
Inline Side-by-side
Code.ipynb 0 → 100644
View file @ c19ac911
This source diff could not be displayed because it is too large. You can view the blob instead.
Differentiation.nb 0 → 100644
View file @ c19ac911
(* 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[ 19186, 537]
NotebookOptionsPosition[ 16590, 483]
NotebookOutlinePosition[ 17009, 499]
CellTagsIndexPosition[ 16966, 496]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"f", "[",
RowBox[{"K_", ",", "P_", ",", "\[Phi]_", ",", "f0_", ",", "t_"}], "]"}],
"=",
RowBox[{
RowBox[{"(", "f0", ")"}], "*",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"K", "/", "c"}], "*",
RowBox[{"Cos", "[",
RowBox[{
RowBox[{"2", "\[Pi]", "*",
RowBox[{"t", "/", "P"}]}], "+", "\[Phi]"}], "]"}]}]}],
")"}]}]}]], "Input",
CellChangeTimes->{{3.8465770652920523`*^9, 3.8465770717689853`*^9}, {
3.846577131510929*^9, 3.846577216793598*^9}, {3.8465772511117425`*^9,
3.846577260915845*^9}, {3.846577308925288*^9, 3.8465773340293303`*^9}, {
3.846837317405692*^9, 3.8468373403391542`*^9}, {3.8468422237937536`*^9,
3.8468422489367466`*^9}, {3.8468423139525204`*^9, 3.846842319376871*^9}},
CellLabel->"In[17]:=",ExpressionUUID->"cd236665-4b12-47d5-be32-e8f58207ec4a"],
Cell[BoxData[
RowBox[{"f0", " ",
RowBox[{"(",
RowBox[{"1", "-",
FractionBox[
RowBox[{"K", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t"}], "P"], "+", "\[Phi]"}],
"]"}]}], "c"]}], ")"}]}]], "Output",
CellChangeTimes->{
3.846577262007157*^9, {3.8465773142878847`*^9, 3.8465773352229557`*^9},
3.846837344577738*^9, 3.8468422590724773`*^9, 3.8468423228971276`*^9},
CellLabel->"Out[17]=",ExpressionUUID->"15100d70-78ee-4ee7-9a37-30cfd4871d3e"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{"dff", " ", "=", " ",
RowBox[{"D", "[",
RowBox[{
RowBox[{"f", "[",
RowBox[{"K", ",", "P", ",", "\[Phi]", ",", "f0", ",", "t"}], "]"}], ",",
"f0"}], "]"}]}], "\[IndentingNewLine]",
RowBox[{"dfK", " ", "=", " ",
RowBox[{"D", "[",
RowBox[{
RowBox[{"f", "[",
RowBox[{"K", ",", "P", ",", "\[Phi]", ",", "f0", ",", "t"}], "]"}], ",",
"K"}], "]"}]}]}], "Input",
CellChangeTimes->{{3.846577340451177*^9, 3.8465773585307775`*^9}, {
3.8465774049662333`*^9, 3.8465774141082907`*^9}, {3.846577512645645*^9,
3.846577531382092*^9}, {3.846837354473191*^9, 3.846837359189705*^9}, {
3.8468422814029555`*^9, 3.846842303413228*^9}, 3.846842354326686*^9},
CellLabel->"In[20]:=",ExpressionUUID->"b2396ad7-fd94-4c15-9528-b0bc92e86f3a"],
Cell[BoxData[
RowBox[{"1", "-",
FractionBox[
RowBox[{"K", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t"}], "P"], "+", "\[Phi]"}], "]"}]}],
"c"]}]], "Output",
CellChangeTimes->{{3.8465773481688013`*^9, 3.8465773588740954`*^9},
3.846577416298984*^9, 3.846577533345722*^9, 3.846577565486902*^9,
3.8468373646156683`*^9, 3.8468422726251698`*^9, {3.8468423059273543`*^9,
3.846842356010291*^9}},
CellLabel->"Out[20]=",ExpressionUUID->"b8c8020d-a3bf-431a-be58-750c4040245f"],
Cell[BoxData[
RowBox[{"-",
FractionBox[
RowBox[{"f0", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t"}], "P"], "+", "\[Phi]"}], "]"}]}],
"c"]}]], "Output",
CellChangeTimes->{{3.8465773481688013`*^9, 3.8465773588740954`*^9},
3.846577416298984*^9, 3.846577533345722*^9, 3.846577565486902*^9,
3.8468373646156683`*^9, 3.8468422726251698`*^9, {3.8468423059273543`*^9,
3.8468423560162745`*^9}},
CellLabel->"Out[21]=",ExpressionUUID->"f18ad73b-162e-4f55-b46f-5132e2f7841d"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[""], "Input",
CellChangeTimes->{3.8465775615572042`*^9},
NumberMarks->False,ExpressionUUID->"a540fa33-6a88-4736-aa90-5a554f5a205b"],
Cell[BoxData[
TagBox[
StyleBox[
DynamicModuleBox[{$CellContext`c$$ = -8., $CellContext`P$$ = -2., \
$CellContext`\[Phi]$$ = -2, $CellContext`$11$$ = -2, Typeset`show$$ = True,
Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu",
Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ =
"\"untitled\"", Typeset`specs$$ = {{
Hold[$CellContext`c$$], -8, 8}, {
Hold[$CellContext`P$$], -2, 2}, {
Hold[$CellContext`\[Phi]$$], -2, 2}, {{
Hold[$CellContext`$11$$], Manipulate`Dump`ReEvaluateInit,
RawBoxes[
SubscriptBox["f", "0"]]}, -2, 2}}, Typeset`size$$ = {
199., {59., 64.37072977247917}}, Typeset`update$$ = 0, Typeset`initDone$$,
Typeset`skipInitDone$$ = True},
DynamicBox[Manipulate`ManipulateBoxes[
1, StandardForm,
"Variables" :> {$CellContext`c$$ = -8, $CellContext`P$$ = -2, \
$CellContext`\[Phi]$$ = -2, $CellContext`$11$$ = -2},
"ControllerVariables" :> {},
"OtherVariables" :> {
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
Typeset`skipInitDone$$}, "Body" :>
Plot[$CellContext`dfK, {$CellContext`t, -8, 8}],
"Specifications" :> {{$CellContext`c$$, -8, 8}, {$CellContext`P$$, -2,
2}, {$CellContext`\[Phi]$$, -2,
2}, {{$CellContext`$11$$, Manipulate`Dump`ReEvaluateInit,
RawBoxes[
SubscriptBox["f", "0"]]}, -2, 2}}, "Options" :> {},
"DefaultOptions" :> {}],
ImageSizeCache->{470., {140.13403328722342`, 145.86596671277658`}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
UnsavedVariables:>{Typeset`initDone$$},
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]], "Output",
CellChangeTimes->{3.8465775377535367`*^9},
CellLabel->"Out[10]=",ExpressionUUID->"13e38cd2-2a18-4fd0-a487-25353ca8cd44"]
}, Closed]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"dfP", " ", "=", " ",
RowBox[{"D", "[",
RowBox[{
RowBox[{"f", "[",
RowBox[{"K", ",", "P", ",", "\[Phi]", ",", "t"}], "]"}], ",", "P"}],
"]"}]}]], "Input",
CellChangeTimes->{{3.846577426806892*^9, 3.8465774270518703`*^9}, {
3.846577516970455*^9, 3.8465775187486367`*^9}, {3.846577572360089*^9,
3.8465775726216717`*^9}, 3.8468373710191526`*^9},
CellLabel->"In[3]:=",ExpressionUUID->"885058cf-75d4-47bb-98dc-f2956bf3ece7"],
Cell[BoxData[
RowBox[{"-",
FractionBox[
RowBox[{"2", " ", "K", " ", "\[Pi]", " ", "t", " ",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t"}], "P"], "+", "\[Phi]"}], "]"}],
" ",
RowBox[{"(",
RowBox[{
SubscriptBox["f", "0"], "+",
RowBox[{"t", " ",
SubscriptBox["f", "1"]}]}], ")"}]}],
RowBox[{"c", " ",
SuperscriptBox["P", "2"]}]]}]], "Output",
CellChangeTimes->{3.846577428353319*^9, 3.8465775743791556`*^9,
3.8468373735274806`*^9},
CellLabel->"Out[3]=",ExpressionUUID->"67d293f6-1e09-4caf-81cd-4079e76c8cb3"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"df\[Phi]", " ", "=", " ",
RowBox[{"D", "[",
RowBox[{
RowBox[{"f", "[",
RowBox[{"K", ",", "P", ",", "\[Phi]", ",", "t"}], "]"}], ",", "\[Phi]"}],
"]"}]}]], "Input",
CellChangeTimes->{{3.84657744084962*^9, 3.84657744354318*^9}, {
3.84657752192662*^9, 3.8465775233198137`*^9}, {3.84657762960233*^9,
3.846577631591188*^9}, 3.846837379132104*^9},
CellLabel->"In[4]:=",ExpressionUUID->"07f94485-1306-4bb2-99a6-ee184147e89e"],
Cell[BoxData[
FractionBox[
RowBox[{"K", " ",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t"}], "P"], "+", "\[Phi]"}], "]"}],
" ",
RowBox[{"(",
RowBox[{
SubscriptBox["f", "0"], "+",
RowBox[{"t", " ",
SubscriptBox["f", "1"]}]}], ")"}]}], "c"]], "Output",
CellChangeTimes->{3.846577446519346*^9, 3.8465776344682217`*^9,
3.8468373805004435`*^9},
CellLabel->"Out[4]=",ExpressionUUID->"6874ce41-42cf-4b6b-be5d-107be9053fca"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{"dfK", ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "t1"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.846577473288022*^9, 3.846577485953947*^9}, {
3.846577583869754*^9, 3.8465776029542418`*^9}, {3.846837736729806*^9,
3.846837736901641*^9}},
CellLabel->"In[9]:=",ExpressionUUID->"b578157a-d909-496c-a3ef-8b67d2c2ce4c"],
Cell[BoxData[
RowBox[{
FractionBox["1",
RowBox[{"4", " ", "c", " ",
SuperscriptBox["\[Pi]", "2"]}]],
RowBox[{"P", " ",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "4"}], " ", "\[Pi]", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}], "]"}], " ",
RowBox[{"Sin", "[",
FractionBox[
RowBox[{"\[Pi]", " ", "t1"}], "P"], "]"}], " ",
SubscriptBox["f", "0"]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"P", " ",
RowBox[{"Cos", "[", "\[Phi]", "]"}]}], "-",
RowBox[{"P", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}], "-",
RowBox[{"2", " ", "\[Pi]", " ", "t1", " ",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}]}], ")"}], " ",
SubscriptBox["f", "1"]}]}], ")"}]}]}]], "Output",
CellChangeTimes->{3.8465776045121326`*^9, 3.8468373874685636`*^9,
3.8468377390994453`*^9},
CellLabel->"Out[9]=",ExpressionUUID->"b7d3533b-8c5c-4dfc-81f6-d31294b8dbd0"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{"dfP", ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "t1"}], "}"}]}], "]"}], "//",
"Simplify"}]], "Input",
CellChangeTimes->{{3.8465779927783885`*^9, 3.8465780280180845`*^9}, {
3.8468377598933363`*^9, 3.8468377600026846`*^9}},
CellLabel->"In[10]:=",ExpressionUUID->"fd6c8356-719f-4e62-90f2-90e70b9636bf"],
Cell[BoxData[
RowBox[{
FractionBox["1",
RowBox[{"2", " ", "c", " ", "P", " ",
SuperscriptBox["\[Pi]", "2"]}]],
RowBox[{"K", " ",
RowBox[{"(",
RowBox[{
RowBox[{"\[Pi]", " ",
RowBox[{"(",
RowBox[{
RowBox[{"2", " ", "\[Pi]", " ", "t1", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}], "+",
RowBox[{"P", " ",
RowBox[{"(",
RowBox[{
RowBox[{"Sin", "[", "\[Phi]", "]"}], "-",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}], ")"}]}]}], ")"}], " ",
SubscriptBox["f", "0"]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["P", "2"], " ",
RowBox[{"Cos", "[", "\[Phi]", "]"}]}], "-",
RowBox[{
RowBox[{"(",
RowBox[{
SuperscriptBox["P", "2"], "-",
RowBox[{"2", " ",
SuperscriptBox["\[Pi]", "2"], " ",
SuperscriptBox["t1", "2"]}]}], ")"}], " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}], "-",
RowBox[{"2", " ", "P", " ", "\[Pi]", " ", "t1", " ",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}]}], ")"}], " ",
SubscriptBox["f", "1"]}]}], ")"}]}]}]], "Output",
CellChangeTimes->{{3.8465780242521315`*^9, 3.8465780288097444`*^9},
3.8468373930818577`*^9, 3.846837766456029*^9},
CellLabel->"Out[10]=",ExpressionUUID->"4bb4a4d9-8046-402e-95a4-0e417f69d25a"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{"df\[Phi]", ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "t1"}], "}"}]}], "]"}], "//",
"Simplify"}]], "Input",
CellChangeTimes->{{3.846578398997497*^9, 3.846578401643093*^9}, {
3.846837770284807*^9, 3.8468377704878826`*^9}},
CellLabel->"In[11]:=",ExpressionUUID->"0c0f99c8-7a55-4fc8-b9ca-116d7ce38334"],
Cell[BoxData[
RowBox[{
FractionBox["1",
RowBox[{"4", " ", "c", " ",
SuperscriptBox["\[Pi]", "2"]}]],
RowBox[{"K", " ", "P", " ",
RowBox[{"(",
RowBox[{
RowBox[{"4", " ", "\[Pi]", " ",
RowBox[{"Sin", "[",
FractionBox[
RowBox[{"\[Pi]", " ", "t1"}], "P"], "]"}], " ",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}], "]"}], " ",
SubscriptBox["f", "0"]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ", "\[Pi]", " ", "t1", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}], "+",
RowBox[{"P", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+",
RowBox[{"Sin", "[",
RowBox[{
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}],
"]"}]}], ")"}]}]}], ")"}], " ",
SubscriptBox["f", "1"]}]}], ")"}]}]}]], "Output",
CellChangeTimes->{3.8465784040165195`*^9, 3.8468374003210516`*^9,
3.8468377733374743`*^9},
CellLabel->"Out[11]=",ExpressionUUID->"112d4f4a-1d3b-4885-b5e3-c46cdaa44046"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"f", "[",
RowBox[{"K", ",", "P", ",", "t", ",", "\[Phi]"}], "]"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "t1"}], "}"}]}], "]"}], "//",
"Simplify"}]], "Input",
CellChangeTimes->{{3.8465785439829903`*^9, 3.8465785967087507`*^9}, {
3.8468377783360643`*^9, 3.8468377785391417`*^9}},
CellLabel->"In[12]:=",ExpressionUUID->"f98bd923-a771-4ccd-87d8-eaecd6f324a2"],
Cell[BoxData[
FractionBox[
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"c", " ", "t1"}], "+",
RowBox[{"K", " ",
RowBox[{"Sin", "[",
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "\[Phi]"}], "P"], "]"}]}], "-",
RowBox[{"K", " ",
RowBox[{"Sin", "[",
RowBox[{"t1", "+",
FractionBox[
RowBox[{"2", " ", "\[Pi]", " ", "\[Phi]"}], "P"]}], "]"}]}]}], ")"}],
" ",
RowBox[{"(",
RowBox[{
SubscriptBox["f", "0"], "+",
RowBox[{"\[Phi]", " ",
SubscriptBox["f", "1"]}]}], ")"}]}], "c"]], "Output",
CellChangeTimes->{{3.8465785820854836`*^9, 3.846578599400714*^9},
3.8468374063926363`*^9, 3.846837780800908*^9},
CellLabel->"Out[12]=",ExpressionUUID->"0d1b6639-1ee9-4593-90ed-ff48da452e3d"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{"dff", ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "t1"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.8468424927435446`*^9, 3.846842529932545*^9}, {
3.8468425620096583`*^9, 3.8468425924926023`*^9}},
CellLabel->"In[25]:=",ExpressionUUID->"6b6e893d-02c0-4960-b3b4-3beab27b7e61"],
Cell[BoxData[
RowBox[{"t1", "-",
FractionBox[
RowBox[{"K", " ", "P", " ",
RowBox[{"Cos", "[",
RowBox[{
FractionBox[
RowBox[{"\[Pi]", " ", "t1"}], "P"], "+", "\[Phi]"}], "]"}], " ",
RowBox[{"Sin", "[",
FractionBox[
RowBox[{"\[Pi]", " ", "t1"}], "P"], "]"}]}],
RowBox[{"c", " ", "\[Pi]"}]]}]], "Output",
CellChangeTimes->{{3.8468425114475*^9, 3.8468425325413866`*^9}, {
3.8468425644393864`*^9, 3.846842593371865*^9}},
CellLabel->"Out[25]=",ExpressionUUID->"54115c14-6f37-4004-8564-379f695f4d23"]
}, Open ]]
},
WindowSize->{574.8, 579.6},
WindowMargins->{{Automatic, -4.7999999999999545`}, {Automatic, 0}},
FrontEndVersion->"12.3 for Microsoft Windows (64-bit) (June 19, 2021)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"f7eef99b-ed39-4411-b818-2152a788e3f7"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 884, 21, 43, "Input",ExpressionUUID->"cd236665-4b12-47d5-be32-e8f58207ec4a"],
Cell[1467, 45, 541, 14, 63, "Output",ExpressionUUID->"15100d70-78ee-4ee7-9a37-30cfd4871d3e"]
}, Open ]],
Cell[CellGroupData[{
Cell[2045, 64, 795, 17, 78, "Input",ExpressionUUID->"b2396ad7-fd94-4c15-9528-b0bc92e86f3a"],
Cell[2843, 83, 552, 13, 55, "Output",ExpressionUUID->"b8c8020d-a3bf-431a-be58-750c4040245f"],
Cell[3398, 98, 550, 13, 55, "Output",ExpressionUUID->"f18ad73b-162e-4f55-b46f-5132e2f7841d"]
}, Open ]],
Cell[CellGroupData[{
Cell[3985, 116, 146, 2, 28, "Input",ExpressionUUID->"a540fa33-6a88-4736-aa90-5a554f5a205b"],
Cell[4134, 120, 2199, 45, 305, "Output",ExpressionUUID->"13e38cd2-2a18-4fd0-a487-25353ca8cd44"]
}, Closed]],
Cell[CellGroupData[{
Cell[6370, 170, 472, 10, 39, "Input",ExpressionUUID->"885058cf-75d4-47bb-98dc-f2956bf3ece7"],
Cell[6845, 182, 621, 18, 56, "Output",ExpressionUUID->"67d293f6-1e09-4caf-81cd-4079e76c8cb3"]
}, Open ]],
Cell[CellGroupData[{
Cell[7503, 205, 472, 10, 43, "Input",ExpressionUUID->"07f94485-1306-4bb2-99a6-ee184147e89e"],
Cell[7978, 217, 508, 15, 55, "Output",ExpressionUUID->"6874ce41-42cf-4b6b-be5d-107be9053fca"]
}, Open ]],
Cell[CellGroupData[{
Cell[8523, 237, 391, 8, 43, "Input",ExpressionUUID->"b578157a-d909-496c-a3ef-8b67d2c2ce4c"],
Cell[8917, 247, 1301, 38, 87, "Output",ExpressionUUID->"b7d3533b-8c5c-4dfc-81f6-d31294b8dbd0"]
}, Open ]],
Cell[CellGroupData[{
Cell[10255, 290, 386, 9, 43, "Input",ExpressionUUID->"fd6c8356-719f-4e62-90f2-90e70b9636bf"],
Cell[10644, 301, 1899, 54, 124, "Output",ExpressionUUID->"4bb4a4d9-8046-402e-95a4-0e417f69d25a"]
}, Open ]],
Cell[CellGroupData[{
Cell[12580, 360, 385, 9, 43, "Input",ExpressionUUID->"0c0f99c8-7a55-4fc8-b9ca-116d7ce38334"],
Cell[12968, 371, 1377, 40, 87, "Output",ExpressionUUID->"112d4f4a-1d3b-4885-b5e3-c46cdaa44046"]
}, Open ]],
Cell[CellGroupData[{
Cell[14382, 416, 465, 11, 43, "Input",ExpressionUUID->"f98bd923-a771-4ccd-87d8-eaecd6f324a2"],
Cell[14850, 429, 788, 23, 56, "Output",ExpressionUUID->"0d1b6639-1ee9-4593-90ed-ff48da452e3d"]
}, Open ]],
Cell[CellGroupData[{
Cell[15675, 457, 347, 7, 43, "Input",ExpressionUUID->"6b6e893d-02c0-4960-b3b4-3beab27b7e61"],
Cell[16025, 466, 549, 14, 79, "Output",ExpressionUUID->"54115c14-6f37-4004-8564-379f695f4d23"]
}, Open ]]
}
]
*)
LISA.py 0 → 100644
View file @ c19ac911
import numpy as np
from scipy import interpolate
import matplotlib.pyplot as plt
import PhenomA as pa
# constants
fm = 3.168753575e-8 # LISA modulation frequency
YEAR = 3.15581497632e7 # year in seconds
AU = 1.49597870660e11 # Astronomical unit (meters)
Clight = 299792458. # speed of light (m/s)
##########################################################
################# Noise Curve Methods ####################
##########################################################
def LoadTransfer(self, file_name):
"""
Load the data file containing the numerically calculate transfer function
(sky and polarization averaged)
"""
try: # try to read in the data file
transfer_data = np.genfromtxt(file_name) # read in the data
except: # If file isn't successfully read in, use approximate transfer function
print("Warning: Could not find transfer function file!")
print(" \tApproximation will be used...")
self.FLAG_R_APPROX = True
return
f = transfer_data[:,0]*self.fstar # convert to frequency
R = transfer_data[:,1]*self.NC # response gets improved by more data channels
# create an interpolation function; attach to LISA object
self.R_INTERP = interpolate.splrep(f, R, s=0)
self.FLAG_R_APPROX = False
return
def Pn(self, f):
"""
Caclulate the Strain Power Spectral Density
"""
# single-link optical metrology noise (Hz^{-1}), Equation (10)
P_oms = (1.5e-11)**2*(1. + (2.0e-3/f)**4)
# single test mass acceleration noise, Equation (11)
P_acc = (3.0e-15)**2*(1. + (0.4e-3/f)**2)*(1. + (f/(8.0e-3))**4)
# total noise in Michelson-style LISA data channel, Equation (12)
Pn = (P_oms + 2.*(1. + np.cos(f/self.fstar)**2)*P_acc/(2.*np.pi*f)**4)/self.Larm**2
return Pn
def SnC(self, f):
"""
Get an estimation of the galactic binary confusion noise are available for
Tobs = {0.5 yr, 1 yr, 2 yr, 4yr}
Enter Tobs as a year or fraction of a year
"""
Tobs = self.Tobs
NC = self.NC
# Fix the parameters of the confusion noise fit
if (Tobs < .75*YEAR):
est = 1
elif (0.75*YEAR < Tobs and Tobs < 1.5*YEAR):
est = 2