From f65efdfe73ddf3c1f96f856989678c0c3e30ee08 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Thu, 1 Aug 2019 11:15:13 +0300 Subject: [PATCH] Typography and minor stuff Former-commit-id: 2dcce31b7ef340e9068b8ca078521ae5a5e4911f --- lepaper/finite.lyx | 59 +++++++----------------------------------- lepaper/symmetries.lyx | 15 ++++++----- 2 files changed, 19 insertions(+), 55 deletions(-) diff --git a/lepaper/finite.lyx b/lepaper/finite.lyx index 1f2d76c..711f2fd 100644 --- a/lepaper/finite.lyx +++ b/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 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 diff --git a/lepaper/symmetries.lyx b/lepaper/symmetries.lyx index 9016d58..19175fc 100644 --- a/lepaper/symmetries.lyx +++ b/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} -\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