From 70e1e197601043a93aa1cf7b9160215a4e931920 Mon Sep 17 00:00:00 2001 From: Fiete Winter Date: Fri, 15 Nov 2019 10:42:00 +0100 Subject: [PATCH] add figure from appendix B.1 --- B_derivations/fig01/README.md | 24 +++++++ B_derivations/fig01/fig1.pdf | Bin 0 -> 35762 bytes B_derivations/fig01/fig1.png | Bin 0 -> 147864 bytes B_derivations/fig01/fig1.tex | 125 +++++++++++++++++++++++++++++++++ B_derivations/fig01/fig2.pdf | Bin 0 -> 36049 bytes B_derivations/fig01/fig2.png | Bin 0 -> 172937 bytes B_derivations/fig01/fig2.tex | 127 ++++++++++++++++++++++++++++++++++ B_derivations/fig01/fig3.pdf | Bin 0 -> 36243 bytes B_derivations/fig01/fig3.png | Bin 0 -> 191100 bytes B_derivations/fig01/fig3.tex | 127 ++++++++++++++++++++++++++++++++++ 10 files changed, 403 insertions(+) create mode 100644 B_derivations/fig01/README.md create mode 100644 B_derivations/fig01/fig1.pdf create mode 100644 B_derivations/fig01/fig1.png create mode 100644 B_derivations/fig01/fig1.tex create mode 100644 B_derivations/fig01/fig2.pdf create mode 100644 B_derivations/fig01/fig2.png create mode 100644 B_derivations/fig01/fig2.tex create mode 100644 B_derivations/fig01/fig3.pdf create mode 100644 B_derivations/fig01/fig3.png create mode 100644 B_derivations/fig01/fig3.tex diff --git a/B_derivations/fig01/README.md b/B_derivations/fig01/README.md new file mode 100644 index 0000000..96aef3c --- /dev/null +++ b/B_derivations/fig01/README.md @@ -0,0 +1,24 @@ +![Fig](fig1.png) +![Fig](fig2.png) +![Fig](fig3.png) + +minimum and maximum wavenumber vector for circular region -- case 1 + +Bash: +```Bash +$ pdflatex fig1.tex +``` + +minimum and maximum wavenumber vector for circular region -- case 2 + +Bash: +```Bash +$ pdflatex fig2.tex +``` + +minimum and maximum wavenumber vector for circular region -- case 3 + +Bash: +```Bash +$ pdflatex fig3.tex +``` diff --git a/B_derivations/fig01/fig1.pdf b/B_derivations/fig01/fig1.pdf new file mode 100644 index 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sV{At~+_klrGq&@%=j85oOkY)96d@+bO>52|3p_ujrKYP|qGJ8{KV2{=;s5{u literal 0 HcmV?d00001 diff --git a/B_derivations/fig01/fig1.tex b/B_derivations/fig01/fig1.tex new file mode 100644 index 0000000..ac0aa0d --- /dev/null +++ b/B_derivations/fig01/fig1.tex @@ -0,0 +1,125 @@ +% minimum and maximum wavenumber vector for circular region -- case 1 + +%***************************************************************************** +% Copyright (c) 2019 Fiete Winter * +% Institut fuer Nachrichtentechnik * +% Universitaet Rostock * +% Richard-Wagner-Strasse 31, 18119 Rostock, Germany * +% * +% This file is part of the supplementary material for Fiete Winter's * +% PhD thesis * +% * +% You can redistribute the material and/or modify it under the terms of the * +% GNU General Public License as published by the Free Software Foundation * +% , either version 3 of the License, or (at your option) any later version. * +% * +% This Material is distributed in the hope that it will be useful, but * +% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY * +% or FITNESS FOR A PARTICULAR PURPOSE. * +% See the GNU General Public License for more details. * +% * +% You should have received a copy of the GNU General Public License along * +% with this program. If not, see . * +% * +% http://github.com/fietew/phd-thesis fiete.winter@gmail.com * +%***************************************************************************** + +\documentclass{standalone} + +\usepackage{import} +\input{../../preamble/standalone} + +\begin{document} + +\begin{tikzpicture} +\pgfmathsetmacro{\Rvec}{1.0} +\pgfmathsetmacro{\Rdashed}{2.5} + +\pgfmathsetmacro{\Rls}{5.0} + +\pgfmathsetmacro{\Ru}{\Rls-0.1} + +\pgfmathsetmacro{\phider}{0} +\pgfmathsetmacro{\Rder}{2.0} + + +\pgfmathsetmacro{\phips}{-30} +\pgfmathsetmacro{\Rps}{2} + +\pgfmathsetmacro{\rl}{0.7} +\pgfmathsetmacro{\Rl}{0.85} +\pgfmathsetmacro{\phil}{70} + +\pgfmathsetmacro{\phimin}{-180} +\pgfmathsetmacro{\phimax}{+0} + +\coordinate (origin) at (0,0); + +\fill[fill=black!30] (\phil:\rl) circle (\Rl); +\coordinate (center) at (\phil:\rl); +\node[circle, fill=black, inner sep=1pt, label={90:$\sfpos[subscript=h]$}] + at (center) {}; + +\draw(center) -- +(180:\Rl) node[midway,above=-3pt,sloped]{\footnotesize +$\sfR[subscript=h]$}; + +\node[above right=0.25cm of center]{$\sfcircle[subscript=h]$}; + +%%\coordinate (xmin) at (\phimin:\Rmax); +%%\coordinate (xmax) at (\phimax:\Rmax); +% +\coordinate (kmax) at (\phimax:\Rvec); +\coordinate (kmin) at (\phimin:\Rvec); + +%\draw(center) -- (xmax) node[midway,above=-3pt,sloped]{\footnotesize $R_l$}; +%\draw(center) -- (xmin); + +%\dotMarkRightAngle[size=4pt](center,xmax,origin); +%\dotMarkRightAngle[size=4pt](origin,xmin,center); + +\draw[draw=black] ($(-70:\Rls)+(0,\Rls)$) arc (-70:-110:\Rls); +\draw[draw=black,-latex'] ($(-75:\Ru)+(0,\Rls)$) arc (-75:-70:\Ru) +node[above, sloped, midway] {$u$}; + +\foreach \phils in {-105, -100, -95, -85, -80, -75} +{ + \node[loudspeaker, + fill=activecolor, + transform shape, + rotate=\phils-180, + anchor=cone] at ($(\phils:\Rls)+(0,\Rls)$) {}; +} + +\node[loudspeaker, + fill=activecolor, + transform shape, + rotate=90, + anchor=cone, + label={180:$\sfpossec$}] (ls) {}; + +\coordinate[label={-90:$\sftangentsec$}] (derivative) at (\phider:\Rder); +\draw[-latex'] (0,0) -- (derivative); + +\coordinate[label={90:$\sfnormalsec$}] (nls) at (0,\Rder); +\draw[-latex'] (0,0) -- (nls); + +\coordinate (kmaxu) at ($(derivative)!(kmax)!(0,0)$); + +\draw[draw=red, thick] (kmaxu) -- (0,0) +node[below=0.75cm, pos=0.25,anchor=south] +{\color{red}$\sfknorm^{\max}_{\sfgreens,\sftangentsec}$}; +\draw[dashed] (kmaxu) -- (kmax); + +\coordinate (kminu) at ($(derivative)!(kmin)!(0,0)$); + +\draw[draw=blue, thick] (kminu) -- (0,0) +node[below=0.75cm, pos=0.35, anchor=south] +{\color{blue}$\sfknorm^{\min}_{\sfgreens,\sftangentsec}$}; +\draw[dashed] (kminu) -- (kmin); + +\draw[red, thick] (0,0) -- (kmax); +\draw[blue, thick] (0,0) -- (kmin); +% +\end{tikzpicture} +% +\end{document} diff --git a/B_derivations/fig01/fig2.pdf b/B_derivations/fig01/fig2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..baff74c941f8a3b4be799421e7fd6a5a52b64f37 GIT binary patch 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znL^*Sp)pSU$G?O`c(7RG)ZYK7{QNdRRfP92v{i>A7H+06Bs3s+WOCI&t?@sRB(v;O~jAcAY}8YfbEO!#SuiyaOQ4!fK3b2m#fH!BGX z7c1-=jv!b-oDVF*Cn%^dARqw|mk@^VfCVMMV4M%k*Z(-d-q8|n?fw6Kg7Za&BKCv_ re_g@J(puuFm5VFf(E&$WNrg|~kucNk7lh*2<2a9%HI>Q~OyB-L7iOXz literal 0 HcmV?d00001 diff --git a/B_derivations/fig01/fig2.tex b/B_derivations/fig01/fig2.tex new file mode 100644 index 0000000..0a537e9 --- /dev/null +++ b/B_derivations/fig01/fig2.tex @@ -0,0 +1,127 @@ +% minimum and maximum wavenumber vector for circular region -- case 2 + +%***************************************************************************** +% Copyright (c) 2019 Fiete Winter * +% Institut fuer Nachrichtentechnik * +% Universitaet Rostock * +% Richard-Wagner-Strasse 31, 18119 Rostock, Germany * +% * +% This file is part of the supplementary material for Fiete Winter's * +% PhD thesis * +% * +% You can redistribute the material and/or modify it under the terms of the * +% GNU General Public License as published by the Free Software Foundation * +% , either version 3 of the License, or (at your option) any later version. * +% * +% This Material is distributed in the hope that it will be useful, but * +% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY * +% or FITNESS FOR A PARTICULAR PURPOSE. * +% See the GNU General Public License for more details. * +% * +% You should have received a copy of the GNU General Public License along * +% with this program. If not, see . * +% * +% http://github.com/fietew/phd-thesis fiete.winter@gmail.com * +%***************************************************************************** + +\documentclass{standalone} + +\usepackage{import} +\input{../../preamble/standalone} + +\begin{document} + +\begin{tikzpicture} +\pgfmathsetmacro{\Rvec}{1.0} +\pgfmathsetmacro{\Rdashed}{2.5} + +\pgfmathsetmacro{\Rls}{5.0} + +\pgfmathsetmacro{\Ru}{\Rls-0.1} + +\pgfmathsetmacro{\phider}{0} +\pgfmathsetmacro{\Rder}{2.0} + + +\pgfmathsetmacro{\phips}{-30} +\pgfmathsetmacro{\Rps}{2} + +\pgfmathsetmacro{\rl}{1.4} +\pgfmathsetmacro{\Rl}{0.85} +\pgfmathsetmacro{\phil}{30} + +\pgfmathsetmacro{\Rmax}{sqrt(\rl*\rl - \Rl*\Rl)} +\pgfmathsetmacro{\phimin}{\phil+asin(\Rl/\rl)} +\pgfmathsetmacro{\phimax}{0} + +\coordinate (origin) at (0,0); + +\fill[fill=black!30] (\phil:\rl) circle (\Rl); +\coordinate (center) at (\phil:\rl); +\node[circle, fill=black, inner sep=1pt, label={90:$\sfpos[subscript=h]$}] + at (center) {}; + +\node[above right=0.25cm of center]{$\sfcircle[subscript=h]$}; + +\draw[dashed] (0,0) -- (\phimin:\Rdashed); + +\coordinate (xmin) at (\phimin:\Rmax); +\coordinate (xmax) at (\phimax:\Rmax); + +\coordinate (kmax) at (\phimax:\Rvec); +\coordinate (kmin) at (\phimin:\Rvec); + +\draw(center) -- (xmin) node[midway,below=-3pt,sloped]{\footnotesize $ +\sfR[subscript=h]$}; + +\dotMarkRightAngle[size=4pt](origin,xmin,center); + +\draw[draw=black] ($(-70:\Rls)+(0,\Rls)$) arc (-70:-110:\Rls); +\draw[draw=black,-latex'] ($(-75:\Ru)+(0,\Rls)$) arc (-75:-70:\Ru) +node[above, sloped, midway] {$u$}; + +\foreach \phils in {-105, -100, -95, -85, -80, -75} +{ + \node[loudspeaker, + fill=activecolor, + transform shape, + rotate=\phils-180, + anchor=cone] at ($(\phils:\Rls)+(0,\Rls)$) {}; +} + +\node[loudspeaker, + fill=activecolor, + transform shape, + rotate=90, + anchor=cone, + label={180:$\sfpossec$}] (ls) {}; + +\coordinate[label={-90:$\sftangentsec$}] (derivative) at (\phider:\Rder); +\draw[-latex'] (0,0) -- (derivative); + +\coordinate[label={90:$\sfnormalsec$}] (nls) at (0,\Rder); +\draw[-latex'] (0,0) -- (nls); + +\coordinate (kmaxu) at ($(derivative)!(kmax)!(0,0)$); + +\draw[draw=red, thick] (kmaxu) -- (0,0) +node[below=0.75cm, pos=0.25,anchor=south] +{\color{red}$\sfknorm^{\max}_{\sfgreens,\sftangentsec}$}; +\draw[dashed] (kmaxu) -- (kmax); + +\coordinate (kminu) at ($(derivative)!(kmin)!(0,0)$); +\coordinate (kmint) at ($(nls)!(kmin)!(0,0)$); + +%\draw[red, thick] (0,0) -- (kmax); +% +\draw[draw=blue, thick] (kmint) -- (kmin) node[above=0.75cm, +pos=0,anchor=north] {\color{blue}$\sfknorm^{\min}_{\sfgreens,\sftangentsec}$}; + +\draw[dashed] (kminu) -- (kmin); + + +\draw[-latex',blue, thick] (origin) -- (kmin); +% +\end{tikzpicture} +% +\end{document} diff --git a/B_derivations/fig01/fig3.pdf b/B_derivations/fig01/fig3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..37be0e77976b225bd89f1c046e241dca72fcd015 GIT binary patch literal 36243 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b/B_derivations/fig01/fig3.tex @@ -0,0 +1,127 @@ +% minimum and maximum wavenumber vector for circular region -- case 3 + +%***************************************************************************** +% Copyright (c) 2019 Fiete Winter * +% Institut fuer Nachrichtentechnik * +% Universitaet Rostock * +% Richard-Wagner-Strasse 31, 18119 Rostock, Germany * +% * +% This file is part of the supplementary material for Fiete Winter's * +% PhD thesis * +% * +% You can redistribute the material and/or modify it under the terms of the * +% GNU General Public License as published by the Free Software Foundation * +% , either version 3 of the License, or (at your option) any later version. * +% * +% This Material is distributed in the hope that it will be useful, but * +% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY * +% or FITNESS FOR A PARTICULAR PURPOSE. * +% See the GNU General Public License for more details. * +% * +% You should have received a copy of the GNU General Public License along * +% with this program. If not, see . * +% * +% http://github.com/fietew/phd-thesis fiete.winter@gmail.com * +%***************************************************************************** + +\documentclass{standalone} + +\usepackage{import} +\input{../../preamble/standalone} + +\begin{document} + +\begin{tikzpicture} +\pgfmathsetmacro{\Rvec}{1.0} +\pgfmathsetmacro{\Rdashed}{2.2} + +\pgfmathsetmacro{\Rls}{5.0} + +\pgfmathsetmacro{\Ru}{\Rls-0.1} + +\pgfmathsetmacro{\phider}{0} +\pgfmathsetmacro{\Rder}{2.0} + + +\pgfmathsetmacro{\phips}{-30} +\pgfmathsetmacro{\Rps}{2} + +\pgfmathsetmacro{\rl}{1.4} +\pgfmathsetmacro{\Rl}{0.85} +\pgfmathsetmacro{\phil}{80} + +\pgfmathsetmacro{\Rmax}{sqrt(\rl*\rl - \Rl*\Rl)} +\pgfmathsetmacro{\phimin}{\phil+asin(\Rl/\rl)} +\pgfmathsetmacro{\phimax}{\phil-asin(\Rl/\rl)} + +\coordinate (origin) at (0,0); + +\fill[fill=black!30] (\phil:\rl) circle (\Rl); +\coordinate (center) at (\phil:\rl); +\node[circle, fill=black, inner sep=1pt, label={90:$\sfpos[subscript=h]$}] + at (center) {}; + +\node[above right=0.25cm of center]{$\sfcircle[subscript=h]$}; + +\draw[dashed] (0,0) -- (\phimin:\Rdashed); +\draw[dashed] (0,0) -- (\phimax:\Rdashed); + +\coordinate (xmin) at (\phimin:\Rmax); +\coordinate (xmax) at (\phimax:\Rmax); + +\coordinate (kmax) at (\phimax:\Rvec); +\coordinate (kmin) at (\phimin:\Rvec); + +\draw(center) -- (xmax) node[midway,above=-3pt,sloped]{\footnotesize +$\sfR[subscript=h]$}; +\draw(center) -- (xmin); + +\dotMarkRightAngle[size=4pt](center,xmax,origin); +\dotMarkRightAngle[size=4pt](origin,xmin,center); + +\draw[draw=black] ($(-70:\Rls)+(0,\Rls)$) arc (-70:-110:\Rls); +\draw[draw=black,-latex'] ($(-75:\Ru)+(0,\Rls)$) arc (-75:-70:\Ru) +node[above, sloped, midway] {$u$}; + +\foreach \phils in {-105, -100, -95, -85, -80, -75} +{ + \node[loudspeaker, + fill=activecolor, + transform shape, + rotate=\phils-180, + anchor=cone] at ($(\phils:\Rls)+(0,\Rls)$) {}; +} + +\node[loudspeaker, + fill=activecolor, + transform shape, + rotate=90, + anchor=cone, + label={180:$\sfpossec$}] (ls) {}; + +\coordinate[label={-90:$\sftangentsec$}] (derivative) at (\phider:\Rder); +\draw[-latex'] (0,0) -- (derivative); + +\coordinate[label={90:$\sfnormalsec$}] (nls) at (0,\Rder); +\draw[-latex'] (0,0) -- (nls); + +\coordinate (kmaxu) at ($(derivative)!(kmax)!(0,0)$); + +\draw[draw=red, thick] (kmaxu) -- (0,0) +node[below=0.75cm, pos=0,anchor=south] +{\color{red}$\sfknorm^{\max}_{\sfgreens,\sftangentsec}$}; +\draw[dashed] (kmaxu) -- (kmax); + +\coordinate (kminu) at ($(derivative)!(kmin)!(0,0)$); + +\draw[draw=blue, thick] (kminu) -- (0,0) +node[below=0.75cm, pos=0,anchor=south] +{\color{blue}$\sfknorm^{\min}_{\sfgreens,\sftangentsec}$}; +\draw[dashed] (kminu) -- (kmin); + +\draw[-latex',red, thick] (0,0) -- (kmax); +\draw[-latex',blue, thick] (0,0) -- (kmin); +% +\end{tikzpicture} +% +\end{document}