Typography and minor stuff

Former-commit-id: 2dcce31b7ef340e9068b8ca078521ae5a5e4911f

lepaper/finite.lyx

@@ -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 be obtained analytically 
- can find them numerically by simulating scattering of a regular spherical
+\begin_inset CommandInset citation
- wave 
+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
 

lepaper/symmetries.lyx

@@ -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}
+\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)+\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}
+\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.+\\
-\end{align}
++\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}\\
+\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}\\
- & =\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).
+ & \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