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Update 2022-03-24 08:43

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Jean-Sébastien
2022-03-24 08:43:21 +01:00
parent 1d852e7213
commit 50704eba07
211 changed files with 1506 additions and 3143 deletions
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build/ems_ca_sv_car.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-22 Tue 10:52 -->
<!-- 2022-03-24 Thu 08:42 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
</summary>
<ul>
<li>
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
</li>
@@ -1613,7 +1613,7 @@ Table of contents
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a><span class="headline-id">ems.ca.sv.car</span></h5>
<div class="outline-text-5" id="text-ems_ca_sv_car">
<div class="example div" id="org98b3764">
<div class="example div" id="org4f7c0e6">
<p>
</p>
@@ -1659,14 +1659,14 @@ This thus falls back onto a 2d problem. We need to solve the 2d Laplace equatio
<p>
Let us look for solutions in the form
</p>
<div class="eqlabel" id="orgc28ff62">
<div class="eqlabel" id="orgf3cdb2d">
<p>
<a id="Lap_sv_car"></a><a href="./ems_ca_sv_car.html#Lap_sv_car"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org1acbd09">
<div class="alteqlabels" id="org5ac02b7">
<ul class="org-ul">
<li>Gr (3.23)</li>
</ul>
@@ -1685,14 +1685,14 @@ individual term in the Laplace equation equals a constant,
and that these constants add up to zero. We can thus put (the sign choice anticipates
the solution somewhat)
</p>
<div class="eqlabel" id="org8e7ab92">
<div class="eqlabel" id="orgca3ea46">
<p>
<a id="Lap_sv_car_sep"></a><a href="./ems_ca_sv_car.html#Lap_sv_car_sep"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org86925b3">
<div class="alteqlabels" id="orgf06d4b4">
<ul class="org-ul">
<li>Gr (3.26)</li>
</ul>
@@ -1716,14 +1716,14 @@ Let's look first of all at the solutions of <a href="./ems_ca_sv_car.html#Lap_sv
Since this is a second-order linear differential equation, there are two linearly
independent solutions. The most general solution for \(X\) and \(Y\) can be written
</p>
<div class="eqlabel" id="orgd404b3a">
<div class="eqlabel" id="orge369796">
<p>
<a id="Lap_sv_car_solXY"></a><a href="./ems_ca_sv_car.html#Lap_sv_car_solXY"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org30886f9">
<div class="alteqlabels" id="org6d1469c">
<ul class="org-ul">
<li>Gr (3.27)</li>
</ul>
@@ -1780,14 +1780,14 @@ C_n = \frac{2}{a} \int_0^a dy ~\phi_0(y) \sin(n\pi y/a)
<p>
<b>Specific example</b>: say that \(\phi_0(y) = \phi_0\), <i>i.e.</i> just a constant. Then,
</p>
<div class="eqlabel" id="orgf5c8f3f">
<div class="eqlabel" id="org050a3b2">
<p>
<a id="Cn"></a><a href="./ems_ca_sv_car.html#Cn"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org5ad8bf2">
<div class="alteqlabels" id="orgea3f86c">
<ul class="org-ul">
<li>Gr (3.35)</li>
</ul>
@@ -1841,7 +1841,7 @@ The solution for the specific case \(\phi_0 (y) = \phi_0\) is thus
</p>
<div class="example div" id="org8b40fc1">
<div class="example div" id="orge4fea76">
<p>
<b>Example: rectangular pipe</b>
</p>
@@ -1898,14 +1898,14 @@ The full solution is then a linear combination of complete set of functions,
The coefficients must be chosen such that \((iii)\) is fulfilled, \(\phi(b,y) = \phi_0\).
This simple case of a constant value \(\phi_0\) gives us the same relation as <a href="./ems_ca_sv_car.html#Cn">Cn</a>, so
</p>
<div class="eqlabel" id="org4c670ac">
<div class="eqlabel" id="org4b471b1">
<p>
<a id="p_recpipe"></a><a href="./ems_ca_sv_car.html#p_recpipe"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgdedd5fd">
<div class="alteqlabels" id="org0968599">
<ul class="org-ul">
<li>Gr (3.42)</li>
</ul>
@@ -1941,7 +1941,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-03-22 Tue 10:52</p>
<p class="date">Created: 2022-03-24 Thu 08:42</p>
<p class="validation"></p>
</div>