Futile attempts to make the lyx document compile

Former-commit-id: d164c56e3eedb01db150844cc6eb33aabc065d0d
This commit is contained in:
Marek Nečada 2019-07-28 15:25:04 +03:00
parent 0f1ce6122e
commit f99fd5abe3
9 changed files with 202 additions and 169 deletions

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@ -5,18 +5,21 @@
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@ -26,10 +29,12 @@
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@ -270,12 +275,12 @@
\begin_inset FormulaMacro
\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1}_{#2#3#4}}
\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1,#2#3#4}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1}_{#2#3#4}}
\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1,#2#3#4}}
\end_inset
@ -290,7 +295,7 @@
\begin_inset FormulaMacro
\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1}_{#2#3#4}}
\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1,#2#3#4}}
\end_inset
@ -397,6 +402,11 @@ These are compatibility macros for the (...)-old files:
\end_inset
\begin_inset FormulaMacro
\newcommand{\Kp}{K}
\end_inset
\end_layout
\begin_layout Title
@ -675,6 +685,17 @@ literal "true"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand include
filename "infinite-old.lyx"
literal "true"
\end_inset
\end_layout
\begin_layout Standard

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@ -1,29 +1,37 @@
#LyX 2.1 created this file. For more info see http://www.lyx.org/
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@ -59,6 +67,8 @@
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@ -67,10 +77,14 @@
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@ -1,5 +1,5 @@
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@ -63,6 +67,7 @@
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@ -73,11 +78,12 @@
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@ -7,16 +7,16 @@
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@ -77,7 +79,7 @@
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@ -1,29 +1,37 @@
#LyX 2.1 created this file. For more info see http://www.lyx.org/
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@ -59,6 +67,8 @@
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@ -67,10 +77,14 @@
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@ -81,12 +95,10 @@
\begin_body
\begin_layout Subsection
\lang english
The multiple-scattering problem
\begin_inset CommandInset label
LatexCommand label
name "sub:The-multiple-scattering-problem"
name "subsec:The-multiple-scattering-problem"
\end_inset
@ -94,8 +106,6 @@ name "sub:The-multiple-scattering-problem"
\end_layout
\begin_layout Standard
\lang english
In the
\begin_inset Formula $T$
\end_inset
@ -147,6 +157,7 @@ where
LatexCommand cite
after "chapter 7"
key "kristensson_scattering_2016"
literal "true"
\end_inset
@ -183,8 +194,6 @@ The expansion coefficients
\end_layout
\begin_layout Standard
\lang english
At a given frequency, assuming the system is linear, the relation between
the expansion coefficients in the VSWF bases is given by the so-called
@ -226,6 +235,7 @@ th nanoparticles) its elements drop very quickly to negligible values with
\begin_inset CommandInset citation
LatexCommand cite
key "SCUFF2,reid_efficient_2015"
literal "true"
\end_inset
@ -233,8 +243,6 @@ key "SCUFF2,reid_efficient_2015"
\end_layout
\begin_layout Standard
\lang english
The singular VSWFs originating at
\begin_inset Formula $\vect R_{n}$
\end_inset
@ -262,6 +270,7 @@ Analytical expressions for the translation operator
\begin_inset CommandInset citation
LatexCommand cite
key "xu_efficient_1998"
literal "true"
\end_inset
@ -269,8 +278,6 @@ key "xu_efficient_1998"
\end_layout
\begin_layout Standard
\lang english
If we write the field incident onto the
\begin_inset Formula $n$
\end_inset

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@ -1,5 +1,5 @@
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@ -7,27 +7,31 @@
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@ -63,6 +67,7 @@
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@ -73,11 +78,12 @@
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@ -92,8 +98,6 @@ Finite systems
\end_layout
\begin_layout Itemize
\lang english
motivation (classes of problems that this can solve: response to external
radiation, resonances, ...)
\begin_inset Separator latexpar
@ -104,8 +108,6 @@ motivation (classes of problems that this can solve: response to external
\begin_deeper
\begin_layout Itemize
\lang english
theory
\begin_inset Separator latexpar
\end_inset
@ -115,8 +117,6 @@ theory
\begin_deeper
\begin_layout Itemize
\lang english
T-matrix definition, basics
\begin_inset Separator latexpar
\end_inset
@ -126,23 +126,17 @@ T-matrix definition, basics
\begin_deeper
\begin_layout Itemize
\lang english
How to get it?
\end_layout
\end_deeper
\begin_layout Itemize
\lang english
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
\lang english
employing point group symmetries and decomposing the problem to decrease
the computational complexity (maybe separately)
\end_layout
@ -150,8 +144,6 @@ employing point group symmetries and decomposing the problem to decrease
\end_deeper
\end_deeper
\begin_layout Subsection
\lang english
Motivation
\end_layout
@ -167,8 +159,6 @@ The basic idea of MSTMM is quite simple: the driving electromagnetic field
\end_layout
\begin_layout Subsection
\lang english
Single-particle scattering
\end_layout
@ -227,8 +217,6 @@ todo define
\end_layout
\begin_layout Standard
\lang english
Throughout this text, we will use the same normalisation conventions as
in
\begin_inset CommandInset citation
@ -242,20 +230,14 @@ literal "true"
\end_layout
\begin_layout Subsubsection
\lang english
Spherical waves
\end_layout
\begin_layout Standard
\lang english
\begin_inset Note Note
status open
\begin_layout Plain Layout
\lang english
TODO small note about cartesian multipoles, anapoles etc.
(There should be some comparing paper that the Russians at META 2018 mentioned.)
\end_layout
@ -266,8 +248,6 @@ TODO small note about cartesian multipoles, anapoles etc.
\end_layout
\begin_layout Subsubsection
\lang english
T-matrix definition
\end_layout
@ -276,26 +256,18 @@ Absorbed power
\end_layout
\begin_layout Subsubsection
\lang english
T-matrix compactness, cutoff validity
\end_layout
\begin_layout Subsection
\lang english
Multiple scattering
\end_layout
\begin_layout Subsubsection
\lang english
Translation operator
\end_layout
\begin_layout Subsubsection
\lang english
Numerical complexity, comparison to other methods
\end_layout

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@ -1,29 +1,37 @@
#LyX 2.1 created this file. For more info see http://www.lyx.org/
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@ -48,6 +56,8 @@
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@ -56,10 +66,14 @@
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@ -73,7 +87,7 @@
Periodic systems and mode analysis
\begin_inset CommandInset label
LatexCommand label
name "sub:Periodic-systems"
name "subsec:Periodic-systems"
\end_inset
@ -160,6 +174,7 @@ reference "eq:multiple scattering per particle a"
\begin_inset CommandInset citation
LatexCommand cite
key "linton_lattice_2010"
literal "true"
\end_inset
@ -273,6 +288,7 @@ try points of the Brillouin zone can be found e.g.
LatexCommand cite
after "chapters 1011"
key "dresselhaus_group_2008"
literal "true"
\end_inset
@ -323,6 +339,7 @@ We analyse the symmetries of the system in the same VSWF representation
LatexCommand cite
after "eq. (11.19)"
key "dresselhaus_group_2008"
literal "true"
\end_inset
@ -342,6 +359,7 @@ key "dresselhaus_group_2008"
\begin_inset CommandInset citation
LatexCommand cite
key "schulz_point-group_1999"
literal "true"
\end_inset
@ -359,6 +377,7 @@ key "schulz_point-group_1999"
LatexCommand cite
after "eq. (4.28)"
key "dresselhaus_group_2008"
literal "true"
\end_inset
@ -440,6 +459,7 @@ Each mode at the
LatexCommand cite
after "eq. (2.51)"
key "dresselhaus_group_2008"
literal "true"
\end_inset

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@ -1,5 +1,5 @@
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@ -63,6 +67,7 @@
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@ -73,11 +78,12 @@
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@ -92,14 +98,10 @@ Infinite periodic systems
\end_layout
\begin_layout Subsection
\lang english
Formulation of the problem
\end_layout
\begin_layout Standard
\lang english
Assume a system of compact EM scatterers in otherwise homogeneous and isotropic
medium, and assume that the system, i.e.
both the medium and the scatterers, have linear response.
@ -139,14 +141,10 @@ where
\end_layout
\begin_layout Standard
\lang english
...
\end_layout
\begin_layout Standard
\lang english
\begin_inset Formula
\[
\sum_{β}(\delta_{αβ}-T_{α}S_{α\leftarrowβ})A_{β}=T_{α}P_{0α}.
@ -158,14 +156,10 @@ where
\end_layout
\begin_layout Standard
\lang english
Now suppose that the scatterers constitute an infinite lattice
\end_layout
\begin_layout Standard
\lang english
\begin_inset Formula
\[
\sum_{\vect bβ}(\delta_{\vect{ab}}\delta_{αβ}-T_{\vect aα}S_{\vect aα\leftarrow\vect bβ})A_{\vect bβ}=T_{\vect aα}P_{0\vect aα}.
@ -225,14 +219,10 @@ W_{\alpha\beta}(\vect k)\equiv\sum_{\vect b}S_{\vect 0α\leftarrow\vect bβ}e^{i
\end_layout
\begin_layout Subsection
\lang english
Computing the Fourier sum of the translation operator
\end_layout
\begin_layout Standard
\lang english
The problem evaluating
\begin_inset CommandInset ref
LatexCommand eqref
@ -253,8 +243,6 @@ reference "eq:W definition"
status open
\begin_layout Plain Layout
\lang english
Note that
\begin_inset Formula $d$
\end_inset
@ -274,8 +262,6 @@ Note that
\end_layout
\begin_layout Standard
\lang english
Let us re-express the sum in
\begin_inset CommandInset ref
LatexCommand eqref
@ -284,11 +270,14 @@ reference "eq:W definition"
\end_inset
in terms of integral with a delta comb
\begin_inset FormulaMacro
\renewcommand{\basis}[1]{\mathfrak{#1}}
\end_inset
\end_layout
\begin_layout Standard
\lang english
\begin_inset Formula
\begin{equation}
W_{\alpha\beta}(\vect k)=\int\ud^{d}\vect r\dc{\basis u}(\vect r)S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})e^{i\vect k\cdot\vect r}.\label{eq:W integral}
@ -390,8 +379,6 @@ W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(
status open
\begin_layout Plain Layout
\lang english
Factor
\begin_inset Formula $\left(2\pi\right)^{\frac{d}{2}}$
\end_inset
@ -424,8 +411,6 @@ whole
\end_layout
\begin_layout Standard
\lang english
However, Fourier transform is linear, so we can in principle separate
\begin_inset Formula $S$
\end_inset

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\bibtex_command default
\index_command default
\float_placement class
\float_alignment class
\paperfontsize default
\spacing single
\use_hyperref true
@ -63,6 +67,7 @@
\justification true
\use_refstyle 1
\use_minted 0
\use_lineno 0
\index Index
\shortcut idx
\color #008000
@ -73,11 +78,12 @@
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style swedish
\quotes_style english
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tablestyle default
\tracking_changes false
\output_changes false
\html_math_output 0