Skip to content

Commit 5360bc9

Browse files
arsenovicarsenovic
committed
deploy: 6558ace 
1 parent 0433cb4 commit 5360bc9

7 files changed

Lines changed: 528 additions & 1113 deletions

File tree

β€ŽMaxwellsOperator.htmlβ€Ž

Lines changed: 22 additions & 21 deletions
Original file line numberDiff line numberDiff line change
@@ -7797,7 +7797,7 @@
77977797
</head>
77987798
<body class="jp-Notebook" data-jp-theme-light="true" data-jp-theme-name="JupyterLab Light">
77997799
<main>
7800-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=22b39c7e">
7800+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=2ffcdef7">
78017801
<div class="jp-Cell-inputWrapper" tabindex="0">
78027802
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78037803
</div>
@@ -7811,7 +7811,7 @@
78117811
</div>
78127812
</div>
78137813
</div>
7814-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=3be2e242">
7814+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=4e5345e4">
78157815
<div class="jp-Cell-inputWrapper" tabindex="0">
78167816
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78177817
</div>
@@ -7838,7 +7838,7 @@ <h2 id="Idea">Idea<a class="anchor-link" href="#Idea">ΒΆ</a></h2><p>Consider the
78387838
</div>
78397839
</div>
78407840
</div>
7841-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=e7be62c1">
7841+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=38f038a9">
78427842
<div class="jp-Cell-inputWrapper" tabindex="0">
78437843
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78447844
</div>
@@ -7854,24 +7854,25 @@ <h2 id="Curvature">Curvature<a class="anchor-link" href="#Curvature">ΒΆ</a></h2>
78547854
<p>$$e^{\tau \partial_a}e^{\epsilon \partial_{b}} \stackrel{?}{=}
78557855
e^{\tau \partial_a+\epsilon \partial_{b}} $$</p>
78567856
<p>This is true when $\tau$ and $\epsilon$ are small, but small compared to what? Compared to the curvature. This is what we are assuming by a <em>linear</em> vector manifold. One way to measure curvature, would be to move along $a$ then $b$, then back along $-a$ <em>then</em> $-b$. Basically reverse your steps in a different order to get back to the start.<br>
7857-
$$\Delta f
7858-
= e^{-\tau \partial_a}e^{-\epsilon \partial_b}e^{\tau \partial_a}e^{\epsilon \partial_b}f -f
7859-
=( e^{-\tau \partial_a}e^{-\epsilon \partial_b}e^{\tau \partial_a}e^{\epsilon \partial_b}-1)f
7860-
= (R\tilde{R} -1)f $$
7861-
Another method is to compare the difference in $f$ at some nearby point, going either way .</br></p>
7862-
<p>$$\Delta f
7863-
= e^{\tau \partial_a}e^{\epsilon \partial_b}f -e^{\epsilon \partial_b}e^{\tau \partial_a}f
7864-
= (R -\tilde R )f
7865-
$$
7866-
Lets see if we can re-work this in terms of conjugation, because conjugation is dank.
7857+
\begin{align*}
7858+
\Delta f &amp;= e^{-\tau \partial_a}e^{-\epsilon \partial_b}e^{\tau \partial_a}e^{\epsilon \partial_b}f -f\\
7859+
&amp;=( e^{-\tau \partial_a}e^{-\epsilon \partial_b}e^{\tau \partial_a}e^{\epsilon \partial_b}-1)f\\
7860+
&amp;= (R\tilde{R} -1)f \\
7861+
\end{align*}</br></p>
7862+
<p>Another method is to compare the difference in $f$ at some nearby point, going either way .</p>
7863+
<p>\begin{align*}
7864+
\Delta f &amp;= e^{\tau \partial_a}e^{\epsilon \partial_b}f -e^{\epsilon \partial_b}e^{\tau \partial_a}f \\
7865+
&amp;= (R -\tilde R )f
7866+
\end{align*}</p>
7867+
<p>Lets see if we can re-work this in terms of conjugation, because conjugation is dank.
78677868
$$ e^{\tau \partial_a}e^{\epsilon \partial_b} fe^{\tilde{\epsilon \partial_b}}e^{\tilde{\tau \partial_a}}
78687869
=f(x+\tau a +\epsilon b -\epsilon b -\tau a ) =f(x) $$
78697870
which is a dumb thing to write when we are in a linear space.</p>
78707871
</div>
78717872
</div>
78727873
</div>
78737874
</div>
7874-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=beb91872">
7875+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=9ea08369">
78757876
<div class="jp-Cell-inputWrapper" tabindex="0">
78767877
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78777878
</div>
@@ -7921,7 +7922,7 @@ <h3 id="Exponetial-of-a--Differential">Exponetial of a Differential<a class="an
79217922
</div>
79227923
</div>
79237924
</div>
7924-
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=d8f732f4">
7925+
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=b483f33e">
79257926
<div class="jp-Cell-inputWrapper" tabindex="0">
79267927
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79277928
</div>
@@ -7936,7 +7937,7 @@ <h3 id="Exponetial-of-a--Differential">Exponetial of a Differential<a class="an
79367937
</div>
79377938
</div>
79387939
</div>
7939-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=69ca9687">
7940+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=d8155952">
79407941
<div class="jp-Cell-inputWrapper" tabindex="0">
79417942
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79427943
</div>
@@ -7947,7 +7948,7 @@ <h2 id="Ortho-not-Normal">Ortho-not-Normal<a class="anchor-link" href="#Ortho-no
79477948
</div>
79487949
</div>
79497950
</div>
7950-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=58e6795e">
7951+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=d87112c0">
79517952
<div class="jp-Cell-inputWrapper" tabindex="0">
79527953
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79537954
</div>
@@ -7957,7 +7958,7 @@ <h2 id="Curvature--on-a-sphere">Curvature on a sphere<a class="anchor-link" hre
79577958
</div>
79587959
</div>
79597960
</div>
7960-
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=4fd53812">
7961+
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=bf7a0b5b">
79617962
<div class="jp-Cell-inputWrapper" tabindex="0">
79627963
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79637964
</div>
@@ -7994,7 +7995,7 @@ <h2 id="Curvature--on-a-sphere">Curvature on a sphere<a class="anchor-link" hre
79947995
</div>
79957996
</div>
79967997
</div>
7997-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=54d4ca61">
7998+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=98a2257d">
79987999
<div class="jp-Cell-inputWrapper" tabindex="0">
79998000
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
80008001
</div>
@@ -8010,7 +8011,7 @@ <h2 id="Transmission-line-Model">Transmission line Model<a class="anchor-link" h
80108011
</div>
80118012
</div>
80128013
</div>
8013-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=ffa842bf">
8014+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=9a495a6d">
80148015
<div class="jp-Cell-inputWrapper" tabindex="0">
80158016
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
80168017
</div>
@@ -8025,7 +8026,7 @@ <h2 id="Others">Others<a class="anchor-link" href="#Others">ΒΆ</a></h2><p>How ca
80258026
</div>
80268027
</div>
80278028
</div>
8028-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=c39b79bf">
8029+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=286f074f">
80298030
<div class="jp-Cell-inputWrapper" tabindex="0">
80308031
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
80318032
</div>

β€ŽOperatorClass.htmlβ€Ž

Lines changed: 13 additions & 13 deletions
Original file line numberDiff line numberDiff line change
@@ -7797,7 +7797,7 @@
77977797
</head>
77987798
<body class="jp-Notebook" data-jp-theme-light="true" data-jp-theme-name="JupyterLab Light">
77997799
<main>
7800-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=44b377a5">
7800+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=4fba0b99">
78017801
<div class="jp-Cell-inputWrapper" tabindex="0">
78027802
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78037803
</div>
@@ -7811,7 +7811,7 @@
78117811
</div>
78127812
</div>
78137813
</div>
7814-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=ab530d44">
7814+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=7b0043ab">
78157815
<div class="jp-Cell-inputWrapper" tabindex="0">
78167816
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78177817
</div>
@@ -7823,7 +7823,7 @@ <h2 id="Context">Context<a class="anchor-link" href="#Context">ΒΆ</a></h2><p>Geo
78237823
</div>
78247824
</div>
78257825
</div>
7826-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=47dca8da">
7826+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f7880e54">
78277827
<div class="jp-Cell-inputWrapper" tabindex="0">
78287828
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78297829
</div>
@@ -7848,7 +7848,7 @@ <h2 id="Context">Context<a class="anchor-link" href="#Context">ΒΆ</a></h2><p>Geo
78487848
</div>
78497849
</div>
78507850
</div>
7851-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=0b1bc5fd">
7851+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=29bd1b4b">
78527852
<div class="jp-Cell-inputWrapper" tabindex="0">
78537853
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78547854
</div>
@@ -7858,7 +7858,7 @@ <h2 id="Implementation">Implementation<a class="anchor-link" href="#Implementati
78587858
</div>
78597859
</div>
78607860
</div>
7861-
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=3905f162">
7861+
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=ff239a4c">
78627862
<div class="jp-Cell-inputWrapper" tabindex="0">
78637863
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
78647864
</div>
@@ -7930,7 +7930,7 @@ <h2 id="Implementation">Implementation<a class="anchor-link" href="#Implementati
79307930
</div>
79317931
</div>
79327932
</div>
7933-
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=9cb977b1">
7933+
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=1cce2476">
79347934
<div class="jp-Cell-inputWrapper" tabindex="0">
79357935
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79367936
</div>
@@ -7940,7 +7940,7 @@ <h2 id="Test">Test<a class="anchor-link" href="#Test">ΒΆ</a></h2>
79407940
</div>
79417941
</div>
79427942
</div>
7943-
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=d795eec5">
7943+
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=f6c28cf1">
79447944
<div class="jp-Cell-inputWrapper" tabindex="0">
79457945
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79467946
</div>
@@ -7978,14 +7978,14 @@ <h2 id="Test">Test<a class="anchor-link" href="#Test">ΒΆ</a></h2>
79787978
<div class="jp-OutputArea-child jp-OutputArea-executeResult">
79797979
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[2]:</div>
79807980
<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
7981-
<pre>(3.78 + 5.89e-08 πžβ‚€β‚ + 5.16e-09 πžβ‚€β‚‚ + 3.78e-08 πžβ‚€β‚ƒ + -9.25e-10 πžβ‚β‚‚ + -9.34e-08 πžβ‚β‚ƒ + -6.92e-09 πžβ‚‚β‚ƒ + 2.41e-25 πžβ‚€β‚β‚‚β‚ƒ,
7982-
3.78 + 5.89e-08 πžβ‚€β‚ + 5.16e-09 πžβ‚€β‚‚ + 3.78e-08 πžβ‚€β‚ƒ + -9.25e-10 πžβ‚β‚‚ + -9.34e-08 πžβ‚β‚ƒ + -6.92e-09 πžβ‚‚β‚ƒ + 2.41e-25 πžβ‚€β‚β‚‚β‚ƒ,
7983-
3.78 + 1.5e-07 πžβ‚€β‚ + 5.17e-09 πžβ‚€β‚‚ + 4.1e-08 πžβ‚€β‚ƒ + -9.68e-09 πžβ‚β‚‚ + -1.82e-07 πžβ‚β‚ƒ + -7.02e-09 πžβ‚‚β‚ƒ + 2.12e-24 πžβ‚€β‚β‚‚β‚ƒ)</pre>
7981+
<pre>(5.2 + 2.75e-08 πžβ‚€β‚ + 1.79e-08 πžβ‚€β‚‚ + 4.84e-08 πžβ‚€β‚ƒ + 1.09e-08 πžβ‚β‚‚ + -1.56e-09 πžβ‚β‚ƒ + -6.99e-09 πžβ‚‚β‚ƒ + 1.54e-24 πžβ‚€β‚β‚‚β‚ƒ,
7982+
5.2 + 2.75e-08 πžβ‚€β‚ + 1.79e-08 πžβ‚€β‚‚ + 4.84e-08 πžβ‚€β‚ƒ + 1.09e-08 πžβ‚β‚‚ + -1.56e-09 πžβ‚β‚ƒ + -6.99e-09 πžβ‚‚β‚ƒ + 1.54e-24 πžβ‚€β‚β‚‚β‚ƒ,
7983+
5.2 + 4.93e-08 πžβ‚€β‚ + 4.95e-08 πžβ‚€β‚‚ + 1.05e-07 πžβ‚€β‚ƒ + 2.71e-09 πžβ‚β‚‚ + -2.76e-08 πžβ‚β‚ƒ + 4.55e-08 πžβ‚‚β‚ƒ + 4.62e-24 πžβ‚€β‚β‚‚β‚ƒ)</pre>
79847984
</div>
79857985
</div>
79867986
</div>
79877987
</div>
7988-
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=37f306d3">
7988+
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=d0b541da">
79897989
<div class="jp-Cell-inputWrapper" tabindex="0">
79907990
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
79917991
</div>
@@ -8006,12 +8006,12 @@ <h2 id="Test">Test<a class="anchor-link" href="#Test">ΒΆ</a></h2>
80068006
<div class="jp-OutputArea-child jp-OutputArea-executeResult">
80078007
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[3]:</div>
80088008
<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
8009-
<pre>3.33e+02 + 1.81e+02 πžβ‚€β‚ + 0.00344 πžβ‚€β‚‚ + 6.32 πžβ‚€β‚ƒ + -17.5 πžβ‚β‚‚ + -1.78e+02 πžβ‚β‚ƒ + -0.194 πžβ‚‚β‚ƒ + 3.76e-15 πžβ‚€β‚β‚‚β‚ƒ</pre>
8009+
<pre>1.22e+03 + 43.5 πžβ‚€β‚ + 63.1 πžβ‚€β‚‚ + 1.12e+02 πžβ‚€β‚ƒ + -16.4 πžβ‚β‚‚ + -52.1 πžβ‚β‚ƒ + 1.05e+02 πžβ‚‚β‚ƒ + 6.16e-15 πžβ‚€β‚β‚‚β‚ƒ</pre>
80108010
</div>
80118011
</div>
80128012
</div>
80138013
</div>
8014-
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=fec4745b">
8014+
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=7832359e">
80158015
<div class="jp-Cell-inputWrapper" tabindex="0">
80168016
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
80178017
</div>

0 commit comments

Comments
Β (0)