Remove file clashing with inconsistent OSX filesystem
This commit is contained in:
Jean-Sébastien
parent
3454aba504
commit
84531d125a
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-08 Tue 06:55 -->
|
||||
<!-- 2022-02-08 Tue 17:21 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -251,8 +251,8 @@ Table of contents
|
|||
<ul>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<details open="">
|
||||
<summary class="toc-open">
|
||||
<a href="./in.html#in">Introduction</a><span class="headline-id">in</span>
|
||||
|
||||
|
||||
|
|
@ -264,13 +264,17 @@ Table of contents
|
|||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<details open="">
|
||||
<summary class="toc-open">
|
||||
<a href="./in_t.html#in_t">Tips for the reader</a><span class="headline-id">in.t</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li class="toc-currentpage">
|
||||
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||
|
||||
|
|
@ -711,8 +715,8 @@ Table of contents
|
|||
</li>
|
||||
<li>
|
||||
|
||||
<details open="">
|
||||
<summary class="toc-open">
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./emsm.html#emsm">Electromagnetostatics in matter</a><span class="headline-id">emsm</span>
|
||||
|
||||
|
||||
|
|
@ -724,8 +728,8 @@ Table of contents
|
|||
</li>
|
||||
<li>
|
||||
|
||||
<details open="">
|
||||
<summary class="toc-open">
|
||||
<details>
|
||||
<summary>
|
||||
<a href="./emsm_esm.html#emsm_esm">Electrostatics in matter</a><span class="headline-id">emsm.esm</span>
|
||||
|
||||
|
||||
|
|
@ -735,8 +739,8 @@ Table of contents
|
|||
<a href="./emsm_esm_p.html#emsm_esm_p">Polarization</a><span class="headline-id">emsm.esm.p</span>
|
||||
|
||||
</li>
|
||||
<li class="toc-currentpage">
|
||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
||||
<li>
|
||||
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1612,53 +1616,60 @@ Table of contents
|
|||
</ul>
|
||||
</details>
|
||||
</nav>
|
||||
<ul class="navigation-links"><li>Prev: <a href="emsm_esm_p.html">Polarization <small>[emsm.esm.p]</small></a></li><li>Next: <a href="emsm_esm_fpo.html">The Field of a Polarized Object <small>[emsm.esm.fpo]</small></a></li><li>Up: <a href="emsm_esm.html">Electrostatics in matter <small>[emsm.esm]</small></a></li></ul><div id="outline-container-emsm_esm_d" class="outline-4">
|
||||
<h4 id="emsm_esm_d">Dielectrics<a class="headline-permalink" href="./emsm_esm_d.html#emsm_esm_d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<ul class="navigation-links"><li>Prev: <a href="in_t.html">Tips for the reader <small>[in.t]</small></a></li><li>Next: <a href="in_t_c.html">Contextual colors <small>[in.t.c]</small></a></li><li>Up: <a href="in_t.html">Tips for the reader <small>[in.t]</small></a></li></ul><div id="outline-container-in_t_l" class="outline-4">
|
||||
<h4 id="in_t_l">Section and equation labelling<a class="headline-permalink" href="./in_t_l.html#in_t_l"><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><span class="headline-id">emsm.esm.d</span></h4>
|
||||
<div class="outline-text-4" id="text-emsm_esm_d">
|
||||
</svg></a><span class="headline-id">in.t.l</span></h4>
|
||||
<div class="outline-text-4" id="text-in_t_l">
|
||||
<p>
|
||||
Let's quickly pause to give a classification of the types of responses that might be expected from
|
||||
materials.
|
||||
\subsubsection*{Permanent polarization:} here, \({\bf P} \neq 0\) even if \({\bf E} = 0\).
|
||||
These are the {\bf electrets}.
|
||||
For labelling sections and equations, I've preferred to use a semantic
|
||||
format instead of traditional numbers.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
\subsubsection*{Nonlinear dielectrics:}
|
||||
\[
|
||||
P_i = \sum_j \alpha_{ij} E_j + \sum_{jk} \beta_{ijkl} E_j E_k E_l + ...
|
||||
\]
|
||||
(even-order terms usually absent, but could be there in principle).
|
||||
\subsubsection*{Linear dielectrics:} only linear term is there. Most general:
|
||||
\[
|
||||
P_i = \varepsilon_0 \chi_{ij} E_j
|
||||
\label{Gr(4.38)}
|
||||
\]
|
||||
where \({\bf \chi}\) is the {\bf electric susceptibility tensor} (it's a tensor of rank 2),
|
||||
which cannot depend on \({\bf E}\) (otherwise we go back to the nonlinear case).
|
||||
Common in crystals, leading to for example double refraction.
|
||||
\subsubsection*{Linear isotropic dielectrics:} at a given point, the electrical properties of
|
||||
the dielectric are independent of the direction of \({\bf E}\) (isotropy). Liquids fall into
|
||||
this category. We here have
|
||||
</p>
|
||||
<div class="main div" id="org4bcb7c7">
|
||||
<p>
|
||||
\[
|
||||
{\bf P} = \varepsilon_0 \chi_e {\bf E}
|
||||
\]
|
||||
This has a number of advantages: the labelling is
|
||||
</p>
|
||||
|
||||
<ul class="org-ul">
|
||||
<li>easier to remember in the long run</li>
|
||||
<li>stable under tree structure modifications</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p>
|
||||
but also come with some things which need getting used to:
|
||||
</p>
|
||||
|
||||
<ul class="org-ul">
|
||||
<li>the loss of clear notion of ordering</li>
|
||||
<li>abbreviations being as short as possible, thus needing learning</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p>
|
||||
<b>Section labelling</b>: floated right next to the title of any section, you will see the
|
||||
label together with a permalink (pointing to the main site's version
|
||||
of that particular section). Under a section's headline, you will also
|
||||
sometimes see references (in small gray letters) to corresponding sections
|
||||
in complemetary <a href="./a_l.html#a_l">literature</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<b>Equation labelling</b>: similarly to sections, some (but not all)
|
||||
equations also carry a semantic label, given in parentheses to the right
|
||||
of the equation. As per sections, a permalink is also given, together
|
||||
with corresponding equation numbers in complementary literature.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
|
||||
<hr><div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-08 Tue 06:55</p>
|
||||
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
|
||||
Loading…
Reference in New Issue