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Typography and minor stuff 

Former-commit-id: 2dcce31b7ef340e9068b8ca078521ae5a5e4911f
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Marek Nečada 2019-08-01 11:15:13 +03:00
parent 3ce28b21af
commit f65efdfe73
2 changed files with 19 additions and 55 deletions
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59
lepaper/finite.lyx
View File

@ -97,52 +97,6 @@
Finite systems
\end_layout
\begin_layout Itemize
motivation (classes of problems that this can solve: response to external
radiation, resonances, ...)
\begin_inset Separator latexpar
\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
theory
\begin_inset Separator latexpar
\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
T-matrix definition, basics
\begin_inset Separator latexpar
\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
How to get it?
\end_layout
\end_deeper
\begin_layout Itemize
translation operators (TODO think about how explicit this should be, but
I guess it might be useful to write them to write them explicitly (but
in the shortest possible form) in the normalisation used in my program)
\end_layout
\begin_layout Itemize
employing point group symmetries and decomposing the problem to decrease
the computational complexity (maybe separately)
\end_layout
\end_deeper
\end_deeper
\begin_layout Subsection
Motivation/intro
\end_layout
@ -660,9 +614,16 @@ TOOD H-field expansion here?
\end_inset
-matrices of particles with certain simple geometries (most famously spherical)
can be obtained analytically [Kristensson 2016, Mie], but in general one
can find them numerically by simulating scattering of a regular spherical
wave
can be obtained analytically
\begin_inset CommandInset citation
LatexCommand cite
key "kristensson_scattering_2016,mie_beitrage_1908"
literal "false"
\end_inset
, but in general one can find them numerically by simulating scattering
of a regular spherical wave
\begin_inset Formula $\vswfouttlm{\tau}lm$
\end_inset

15
lepaper/symmetries.lyx
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@ -7,7 +7,7 @@
\textclass article
\use_default_options true
\maintain_unincluded_children false
\language finnish
\language english
\language_package default
\inputencoding utf8
\fontencoding auto
@ -509,9 +509,10 @@ noprefix "false"
\lang english
\begin_inset Formula
\begin{align}
\vect E\left(\omega,R_{g}\vect r\right) & =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)+\outcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)\right).\label{eq:rotated E field expansion around outside origin}
\end{align}
\begin{multline}
\vect E\left(\omega,R_{g}\vect r\right)=\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)\right.+\\
+\left.\outcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)\right).\label{eq:rotated E field expansion around outside origin}
\end{multline}
\end_inset
@ -688,8 +689,10 @@ status open
\begin_inset Formula
\begin{align}
\vect E\left(\omega,R_{g}\vect r\right) & =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{\pi_{g}(p)}\right)\right)+\outcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{p}\right)\right)\right)\label{eq:rotated E field expansion around outside origin-1}\\
& =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm{\pi_{g}^{-1}(p)}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{p}\right)\right)+\outcoeffptlm{\pi_{g}^{-1}(p)}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{p}\right)\right)\right).
\vect E\left(\omega,R_{g}\vect r\right) & =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{\pi_{g}(p)}\right)\right)\right.+\label{eq:rotated E field expansion around outside origin-1}\\
& \quad+\left.\outcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{p}\right)\right)\right)\\
& =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm{\pi_{g}^{-1}(p)}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{p}\right)\right)\right.+\\
& \quad+\left.\outcoeffptlm{\pi_{g}^{-1}(p)}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{p}\right)\right)\right).
\end{align}
\end_inset