From f99fd5abe39d6474685402f64ce1e075adf28466 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Sun, 28 Jul 2019 15:25:04 +0300 Subject: [PATCH] Futile attempts to make the lyx document compile Former-commit-id: d164c56e3eedb01db150844cc6eb33aabc065d0d --- lepaper/arrayscat.lyx | 33 ++++++++++++++---- lepaper/comparison.lyx | 44 +++++++++++++++--------- lepaper/examples.lyx | 24 ++++++++----- lepaper/finite-cs.lyx | 12 ++++--- lepaper/finite-old.lyx | 59 ++++++++++++++++++-------------- lepaper/finite.lyx | 58 +++++++++---------------------- lepaper/infinite-old.lyx | 44 +++++++++++++++++------- lepaper/infinite.lyx | 73 ++++++++++++++++------------------------ lepaper/intro.lyx | 24 ++++++++----- 9 files changed, 202 insertions(+), 169 deletions(-) diff --git a/lepaper/arrayscat.lyx b/lepaper/arrayscat.lyx index 36a9fbf..01b2c2e 100644 --- a/lepaper/arrayscat.lyx +++ b/lepaper/arrayscat.lyx @@ -5,18 +5,21 @@ \save_transient_properties true \origin unavailable \textclass article +\begin_preamble +\DeclareUnicodeCharacter{0428}{Ш } +\end_preamble \use_default_options true \maintain_unincluded_children false \language english \language_package default -\inputencoding auto-legacy +\inputencoding utf8 \fontencoding auto \font_roman "default" "TeX Gyre Pagella" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false \font_roman_osf true \font_sans_osf false @@ -26,10 +29,12 @@ \use_microtype false \use_dash_ligatures true \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \bibtex_command default \index_command default +\float_placement class +\float_alignment class \paperfontsize default \spacing single \use_hyperref true @@ -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 diff --git a/lepaper/comparison.lyx b/lepaper/comparison.lyx index 41e96c1..6257c19 100644 --- a/lepaper/comparison.lyx +++ b/lepaper/comparison.lyx @@ -1,29 +1,37 @@ -#LyX 2.1 created this file. For more info see http://www.lyx.org/ -\lyxformat 474 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header +\save_transient_properties true +\origin unavailable \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto -\fontencoding global -\font_roman TeX Gyre Pagella -\font_sans default -\font_typewriter default -\font_math auto +\inputencoding utf8 +\fontencoding auto +\font_roman "default" "TeX Gyre Pagella" +\font_sans "default" "default" +\font_typewriter "default" "default" +\font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false -\font_osf true -\font_sf_scale 100 -\font_tt_scale 100 +\font_roman_osf true +\font_sans_osf false +\font_typewriter_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures true \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \bibtex_command default \index_command default +\float_placement class +\float_alignment class \paperfontsize default \spacing single \use_hyperref true @@ -59,6 +67,8 @@ \suppress_date false \justification true \use_refstyle 1 +\use_minted 0 +\use_lineno 0 \index Index \shortcut idx \color #008000 @@ -67,10 +77,14 @@ \tocdepth 3 \paragraph_separation indent \paragraph_indentation default -\quotes_language swedish +\is_math_indent 0 +\math_numbering_side default +\quotes_style english +\dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default +\tablestyle default \tracking_changes false \output_changes false \html_math_output 0 diff --git a/lepaper/examples.lyx b/lepaper/examples.lyx index 40ab743..dee469a 100644 --- a/lepaper/examples.lyx +++ b/lepaper/examples.lyx @@ -1,5 +1,5 @@ -#LyX 2.3 created this file. For more info see http://www.lyx.org/ -\lyxformat 544 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header \save_transient_properties true @@ -7,27 +7,31 @@ \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto -\fontencoding global +\inputencoding utf8 +\fontencoding auto \font_roman "default" "TeX Gyre Pagella" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false -\font_osf true +\font_roman_osf true +\font_sans_osf false +\font_typewriter_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \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 diff --git a/lepaper/finite-cs.lyx b/lepaper/finite-cs.lyx index 28072a4..a6bfc45 100644 --- a/lepaper/finite-cs.lyx +++ b/lepaper/finite-cs.lyx @@ -7,16 +7,16 @@ \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto-legacy +\inputencoding utf8 \fontencoding auto \font_roman "default" "TeX Gyre Pagella" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false \font_roman_osf true \font_sans_osf false @@ -26,10 +26,12 @@ \use_microtype false \use_dash_ligatures false \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \bibtex_command default \index_command default +\float_placement class +\float_alignment class \paperfontsize default \spacing single \use_hyperref true @@ -77,7 +79,7 @@ \paragraph_indentation default \is_math_indent 0 \math_numbering_side default -\quotes_style swedish +\quotes_style english \dynamic_quotes 0 \papercolumns 1 \papersides 1 diff --git a/lepaper/finite-old.lyx b/lepaper/finite-old.lyx index 84eb30e..c6721bb 100644 --- a/lepaper/finite-old.lyx +++ b/lepaper/finite-old.lyx @@ -1,29 +1,37 @@ -#LyX 2.1 created this file. For more info see http://www.lyx.org/ -\lyxformat 474 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header +\save_transient_properties true +\origin unavailable \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto -\fontencoding global -\font_roman TeX Gyre Pagella -\font_sans default -\font_typewriter default -\font_math auto +\inputencoding utf8 +\fontencoding auto +\font_roman "default" "TeX Gyre Pagella" +\font_sans "default" "default" +\font_typewriter "default" "default" +\font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false -\font_osf true -\font_sf_scale 100 -\font_tt_scale 100 +\font_roman_osf true +\font_sans_osf false +\font_typewriter_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures false \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \bibtex_command default \index_command default +\float_placement class +\float_alignment class \paperfontsize default \spacing single \use_hyperref true @@ -59,6 +67,8 @@ \suppress_date false \justification true \use_refstyle 1 +\use_minted 0 +\use_lineno 0 \index Index \shortcut idx \color #008000 @@ -67,10 +77,14 @@ \tocdepth 3 \paragraph_separation indent \paragraph_indentation default -\quotes_language swedish +\is_math_indent 0 +\math_numbering_side default +\quotes_style english +\dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default +\tablestyle default \tracking_changes false \output_changes false \html_math_output 0 @@ -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 diff --git a/lepaper/finite.lyx b/lepaper/finite.lyx index 4672110..8dd3de6 100644 --- a/lepaper/finite.lyx +++ b/lepaper/finite.lyx @@ -1,5 +1,5 @@ -#LyX 2.3 created this file. For more info see http://www.lyx.org/ -\lyxformat 544 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header \save_transient_properties true @@ -7,27 +7,31 @@ \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto -\fontencoding global +\inputencoding utf8 +\fontencoding auto \font_roman "default" "TeX Gyre Pagella" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false -\font_osf true +\font_roman_osf true +\font_sans_osf false +\font_typewriter_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \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 @@ -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 diff --git a/lepaper/infinite-old.lyx b/lepaper/infinite-old.lyx index ffefe93..8e8296f 100644 --- a/lepaper/infinite-old.lyx +++ b/lepaper/infinite-old.lyx @@ -1,29 +1,37 @@ -#LyX 2.1 created this file. For more info see http://www.lyx.org/ -\lyxformat 474 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header +\save_transient_properties true +\origin unavailable \textclass article \use_default_options false \maintain_unincluded_children false \language english \language_package none -\inputencoding auto +\inputencoding utf8 \fontencoding default -\font_roman default -\font_sans default -\font_typewriter default -\font_math auto +\font_roman "default" "default" +\font_sans "default" "default" +\font_typewriter "default" "default" +\font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false -\font_osf false -\font_sf_scale 100 -\font_tt_scale 100 +\font_roman_osf false +\font_sans_osf false +\font_typewriter_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures true \graphics default \default_output_format default \output_sync 0 \bibtex_command default \index_command default +\float_placement class +\float_alignment class \paperfontsize default \spacing single \use_hyperref false @@ -48,6 +56,8 @@ \suppress_date false \justification true \use_refstyle 0 +\use_minted 0 +\use_lineno 0 \index Index \shortcut idx \color #008000 @@ -56,10 +66,14 @@ \tocdepth 3 \paragraph_separation indent \paragraph_indentation default -\quotes_language english +\is_math_indent 0 +\math_numbering_side default +\quotes_style english +\dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default +\tablestyle default \tracking_changes false \output_changes false \html_math_output 0 @@ -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 10–11" 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 diff --git a/lepaper/infinite.lyx b/lepaper/infinite.lyx index a91c95c..620e64c 100644 --- a/lepaper/infinite.lyx +++ b/lepaper/infinite.lyx @@ -1,5 +1,5 @@ -#LyX 2.3 created this file. For more info see http://www.lyx.org/ -\lyxformat 544 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header \save_transient_properties true @@ -7,27 +7,31 @@ \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto -\fontencoding global +\inputencoding utf8 +\fontencoding auto \font_roman "default" "TeX Gyre Pagella" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false -\font_osf true +\font_roman_osf true +\font_sans_osf false +\font_typewriter_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \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 @@ -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 @@ -241,7 +231,7 @@ reference "eq:W definition" \end_inset is the asymptotic behaviour of the translation operator, -\begin_inset Formula $S_{\vect0α\leftarrow\vect bβ}\sim\left|\vect r_{\vect b}\right|^{-1}e^{ik_{0}\left|\vect r_{\vect b}\right|}$ +\begin_inset Formula $S_{\vect 0α\leftarrow\vect bβ}\sim\left|\vect r_{\vect b}\right|^{-1}e^{ik_{0}\left|\vect r_{\vect b}\right|}$ \end_inset that makes the convergence of the sum quite problematic for any @@ -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} @@ -338,7 +327,7 @@ translation operator for spherical waves originating in \end_inset is in fact a function of a single 3d argument, -\begin_inset Formula $S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})=S(\vect0\leftarrow\vect r+\vect r_{\beta}-\vect r_{\alpha})=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha})$ +\begin_inset Formula $S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})=S(\vect 0\leftarrow\vect r+\vect r_{\beta}-\vect r_{\alpha})=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha})$ \end_inset . @@ -352,7 +341,7 @@ reference "eq:W integral" can be rewritten as \begin_inset Formula \[ -W_{\alpha\beta}(\vect k)=\left(2\pi\right)^{\frac{d}{2}}\uaft{(\dc{\basis u}S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0))\left(\vect k\right)} +W_{\alpha\beta}(\vect k)=\left(2\pi\right)^{\frac{d}{2}}\uaft{(\dc{\basis u}S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0))\left(\vect k\right)} \] \end_inset @@ -377,10 +366,10 @@ reference "eq:Dirac comb uaFt" for the Fourier transform of Dirac comb) \begin_inset Formula \begin{eqnarray} -W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\right)(\vect k)\nonumber \\ - & = & \frac{\left|\det\recb{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\left(\dc{\recb{\basis u}}^{(d)}\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\right)\left(\vect k\right)\nonumber \\ - & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\label{eq:W sum in reciprocal space}\\ - & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}e^{i\left(\vect k-\vect K\right)\cdot\left(-\vect r_{\beta}+\vect r_{\alpha}\right)}\left(\uaft{S(\vect{\bullet}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\nonumber +W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)(\vect k)\nonumber \\ + & = & \frac{\left|\det\recb{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\left(\dc{\recb{\basis u}}^{(d)}\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)\left(\vect k\right)\nonumber \\ + & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\label{eq:W sum in reciprocal space}\\ + & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}e^{i\left(\vect k-\vect K\right)\cdot\left(-\vect r_{\beta}+\vect r_{\alpha}\right)}\left(\uaft{S(\vect{\bullet}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\nonumber \end{eqnarray} \end_inset @@ -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 @@ -486,8 +471,8 @@ reference "eq:W sum in reciprocal space" \begin_inset Formula \begin{eqnarray} W_{\alpha\beta}\left(\vect k\right) & = & W_{\alpha\beta}^{\textup{S}}\left(\vect k\right)+W_{\alpha\beta}^{\textup{L}}\left(\vect k\right)\nonumber \\ -W_{\alpha\beta}^{\textup{S}}\left(\vect k\right) & = & \sum_{\vect R\in\basis u\ints^{d}}S^{\textup{S}}(\vect0\leftarrow\vect R+\vect r_{\beta}-\vect r_{\alpha})e^{i\vect k\cdot\vect R}\label{eq:W Short definition}\\ -W_{\alpha\beta}^{\textup{L}}\left(\vect k\right) & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S^{\textup{L}}(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\label{eq:W Long definition} +W_{\alpha\beta}^{\textup{S}}\left(\vect k\right) & = & \sum_{\vect R\in\basis u\ints^{d}}S^{\textup{S}}(\vect 0\leftarrow\vect R+\vect r_{\beta}-\vect r_{\alpha})e^{i\vect k\cdot\vect R}\label{eq:W Short definition}\\ +W_{\alpha\beta}^{\textup{L}}\left(\vect k\right) & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S^{\textup{L}}(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\label{eq:W Long definition} \end{eqnarray} \end_inset diff --git a/lepaper/intro.lyx b/lepaper/intro.lyx index 63172d3..f802303 100644 --- a/lepaper/intro.lyx +++ b/lepaper/intro.lyx @@ -1,5 +1,5 @@ -#LyX 2.3 created this file. For more info see http://www.lyx.org/ -\lyxformat 544 +#LyX 2.4 created this file. For more info see https://www.lyx.org/ +\lyxformat 583 \begin_document \begin_header \save_transient_properties true @@ -7,27 +7,31 @@ \textclass article \use_default_options true \maintain_unincluded_children false -\language finnish +\language english \language_package default -\inputencoding auto -\fontencoding global +\inputencoding utf8 +\fontencoding auto \font_roman "default" "TeX Gyre Pagella" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default -\use_non_tex_fonts true +\use_non_tex_fonts false \font_sc false -\font_osf true +\font_roman_osf true +\font_sans_osf false +\font_typewriter_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default -\default_output_format pdf4 +\default_output_format default \output_sync 0 \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