commit 291b9f98a9b78cd406f5a23c49f70b8b6fbe3162
parent cd02848d183fa4ae0788183dd3b3df64deb075a0
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Wed, 20 Jun 2018 20:37:58 +0300
Second part WIP.
Diffstat:
5 files changed, 113 insertions(+), 710 deletions(-)
diff --git a/arma-slides.org b/arma-slides.org
@@ -23,6 +23,7 @@
\vfill\inserttitlegraphic%
\vfill\spbuInsertField{date}%
}
+\setbeamerfont{block title}{size=\small}
\frame{\maketitle}
#+end_export
@@ -499,7 +500,7 @@ arma.plot_nonlinear(file.path("build", "nit-standing"), args)
[[file:build/slides-nit-ru.pdf]]
-* Формула для поля давлений
+* Поле давлений под дискретно заданной взволнованной поверхностью
** Уравнения потенциального течения
#+begin_export latex
\begin{align*}
@@ -530,111 +531,87 @@ arma.plot_nonlinear(file.path("build", "nit-standing"), args)
}
#+end_export
-** Двухмерный случай
+** Трехмерный случай
-#+begin_export latex
-\small%
-\begin{minipage}{0.4\textwidth}
- \vspace{-\baselineskip}
- \begin{align*}
- & \phi_{xx}+\phi_{zz}=0\\
- & \zeta_t =
- \only<1>{\left(\zeta_x/\sqrt{1 + \zeta_x^2}-\zeta_x\right) \phi_x}%
- \only<2->{\rectemph{dzetadphi2}{\left(\zeta_x/\sqrt{1 + \zeta_x^2}-\zeta_x\right) \phi_x}}
- - \phi_z
- \end{align*}
-\end{minipage}
-\newline
-Решение в рамках линейной теории
+#+beamer: \small
+
+\begin{align*}
+ & \phi_{xx} + \phi_{yy} + \phi_{zz} = 0\\
+ & \zeta_t
+ = \underbrace{\fillrectemph{f1}{\left(\FracSqrtZetaY{\zeta_x} - \zeta_x\right)}}_{f_1} \phi_x
+ + \underbrace{\fillrectemph{f2}{\left(\FracSqrtZetaY{\zeta_y} - \zeta_y\right)}}_{f_2} \phi_y
+ - \underbrace{\fillrectemph{f3}{\FracSqrtZetaY{1}}}_{f_3} \phi_z
+\end{align*}
+
+Решение в рамках линейной теории:
\begin{equation*}
- \phi(x,z,t)
- =
- \InverseFourierX{
- \frac{\Sinh{2\pi u (z+h)}}{2\pi u \Sinh{2\pi u h}}
- \FourierX{-\zeta_t}{x}{u}
- }{u}{x}
- =
- \only<1>{\mathcal{W}(x,z)}
- \only<2->{\rectemph{windowFunc}{\mathcal{W}(x,z)}}
- \mathrel{*} \zeta_t(x,t)
+ \phi(x,y,z,t) = \mathcal{W}(x,y,z) \mathrel{*} \zeta_t(x,y,t)
\end{equation*}
-Общее решение
+
+Общее решение:
\begin{equation*}
- \boxed{
- \phi(x,z,t)
- =
- \InverseFourierX{
- \frac{\Sinh{2\pi u (z+h)}}{2\pi u}
- \frac{
- \FourierX{ \zeta_t / \left(i \:\!\:\! f(x) - 1\right) }{x}{u}
- }{
- \FourierX{ \FunSecond{\zeta(x,t)} }{x}{u}
- }
- }{u}{x}
- }
+ \phi(x,y,z,t)
+ =
+ \mathcal{W}(x,y,z)
+ \mathrel{*}
+ \frac{\zeta_t(x,y,t)}{i f_1(x,y,t) + i f_2(x,y,t) - f_3(x,y,t)}
\end{equation*}
-\only<2->{%
-\begin{tikzpicture}[remember picture,overlay]
- \node[fill=none,baseline,anchor=north,xshift=0cm,yshift=-1.2cm]
- (dzetadphiLabel) at (current page.north) {%
- \small нет в линейной теории%
- };
- \path[->,thick] (dzetadphiLabel.west) edge [bend right=20](dzetadphi2.north);
- \node[fill=spbuWhite2,anchor=north east,xshift=-0.2cm,yshift=-1.2cm]
- (windowFunctionGraph) at (current page.north east) {%
- \includegraphics[scale=0.4]{window-function-2}
- };
- \path[->,thick] (windowFunctionGraph.south) edge [bend right,out=0](windowFunc.north);
-\end{tikzpicture}
-}
-#+end_export
** Сравнение с линейной теорией
+
+*** Columns
+:PROPERTIES:
+:BEAMER_env: columns
+:BEAMER_opt: T
+:END:
+
+**** Линейная теория
+:PROPERTIES:
+:BEAMER_env: block
+:BEAMER_col: 0.4
+:END:
+
#+begin_export latex
-\centering
-\begin{columns}
- \begin{column}{0.15\textwidth}
- \only<1>{$A=1$м}%
- \only<2>{$A=2$м}%
- \only<3>{$A=4$м}%
- \end{column}
- \begin{column}{0.4\textwidth}
- \begin{block}{\small Линейная теория}
- \includegraphics<1>{velocity-ref-1}
- \includegraphics<2>{velocity-ref-2}
- \includegraphics<3>{velocity-ref-4}
- \end{block}
- \end{column}
- \begin{column}{0.4\textwidth}
- \begin{block}{\small Новая формула}
- \includegraphics<1>{velocity-1}
- \includegraphics<2>{velocity-2}
- \includegraphics<3>{velocity-4}
- \end{block}
- \end{column}
-\end{columns}
+\includegraphics<1>{velocity-ref-1}
+\includegraphics<2>{velocity-ref-2}
+\includegraphics<3>{velocity-ref-4}
#+end_export
-** Сравнение с формулой для ВМА
+**** Новая формула
+:PROPERTIES:
+:BEAMER_env: block
+:BEAMER_col: 0.4
+:END:
+
#+begin_export latex
-\centering
-\begin{columns}[T]
- \begin{column}{0.45\textwidth}
- \begin{block}{\small Малая амплитуда}
- \vspace{0.25\baselineskip}%
- \includegraphics{low-amp-color}
- \end{block}
- \end{column}
- \begin{column}{0.45\textwidth}
- \begin{block}{\small Высокая амплитуда}
- \vspace{0.25\baselineskip}%
- \includegraphics{high-amp-color}
- \end{block}
- \end{column}
-\end{columns}
+\includegraphics<1>{velocity-1}
+\includegraphics<2>{velocity-2}
+\includegraphics<3>{velocity-4}
#+end_export
-** Выводы
+** Сравнение с формулой для ВМА
+
+*** Columns
+:PROPERTIES:
+:BEAMER_env: columns
+:BEAMER_opt: T
+:END:
+
+**** Малая амплитуда
+:PROPERTIES:
+:BEAMER_env: block
+:BEAMER_col: 0.45
+:END:
+[[file:graphics/slides/low-amp-color.eps]]
+
+**** Большая амплитуда
+:PROPERTIES:
+:BEAMER_env: block
+:BEAMER_col: 0.45
+:END:
+[[file:graphics/slides/high-amp-color.eps]]
+
+** Выводы :noexport:
Метод подходит для
- дискретно заданной $\zeta(x,y,t)$,
- волн произвольных амплитуд,
@@ -759,7 +736,6 @@ arma.plot_nonlinear(file.path("build", "nit-standing"), args)
** Апробация
-#+latex: \setbeamerfont{block title}{size=\small}
#+latex: \small
- Конференции: ISSW'14, HPCS'15, HPCS'16, HPCS'17.
diff --git a/graphics/slides/window-function-2.eps b/graphics/slides/window-function-2.eps
@@ -1,571 +0,0 @@
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-0 g
-0.8 w
-q 1 0 0 -1 0 240 cm
-43.281 15.602 m 43.281 198 l 283.84 198 l S Q
-Q Q
-showpage
-%%Trailer
-end restore
-%%EOF
diff --git a/math.tex b/math.tex
@@ -0,0 +1,34 @@
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsthm}
+
+% custom mathematical expressions
+\newcommand{\Var}[1]{\sigma_{#1}^2}
+\newcommand{\Fourier}[1]{\mathcal{F}\left\{#1\right\}}
+\newcommand{\InverseFourier}[1]{\mathcal{F}^{-1}\left\{#1\right\}}
+\newcommand{\Fun}[1]{\mathcal{D}_1\left(x,#1\right)}
+\newcommand{\FunSecond}[1]{\mathcal{D}_2\left(x,#1\right)}
+\newcommand{\FunThird}[1]{\mathcal{D}_2\left(x,#1\right)}
+\newcommand{\FunThreeD}[1]{\mathcal{D}_3\left(x,y,#1\right)}
+\newcommand{\Sinh}[1]{\cosh\left(#1\right)}
+\newcommand{\SinhX}[1]{\sinh\left(#1\right)}
+
+\newcommand{\FourierY}[2]{\mathcal{F}_{#2}\!\left\{#1\right\}}
+\newcommand{\InverseFourierY}[2]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}}
+
+\newcommand{\FourierX}[3]{\mathcal{F}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
+\newcommand{\InverseFourierX}[3]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
+
+% properly aligned version of sqrt for \zeta_y^2
+\newcommand{\SqrtZeta}[1]{\sqrt{\vphantom{\zeta_x^2}\smash[b]{#1}}}
+
+% normalisation
+\newcommand{\SqrtZetaX}{\sqrt{1 + \zeta_x^2}}
+\newcommand{\SqrtZetaY}{\SqrtZeta{1 + \zeta_x^2 + \zeta_y^2}}
+\newcommand{\FracSqrtZetaX}[1]{\frac{#1}{\SqrtZetaX{}}}
+\newcommand{\FracSqrtZetaY}[1]{\frac{#1}{\SqrtZetaY{}}}
+
+% wave vector
+\newcommand{\Kvec}{\vec{k}}
+\newcommand{\Kveclen}{\lvert\smash[b]{\Kvec}\rvert}
+
diff --git a/preamble.tex b/preamble.tex
@@ -1,8 +1,5 @@
\usepackage{graphicx}
\usepackage{booktabs}
-\usepackage{amsmath}
-\usepackage{amssymb}
-\usepackage{amsthm}
\usepackage{hyperref}
\usepackage{tikz}
\usepackage{cite}
@@ -43,35 +40,7 @@
% multiple bibliographies
\usepackage[resetlabels]{multibib}
-% custom mathematical expressions
-\newcommand{\Var}[1]{\sigma_{#1}^2}
-\newcommand{\Fourier}[1]{\mathcal{F}\left\{#1\right\}}
-\newcommand{\InverseFourier}[1]{\mathcal{F}^{-1}\left\{#1\right\}}
-\newcommand{\Fun}[1]{\mathcal{D}_1\left(x,#1\right)}
-\newcommand{\FunSecond}[1]{\mathcal{D}_2\left(x,#1\right)}
-\newcommand{\FunThird}[1]{\mathcal{D}_2\left(x,#1\right)}
-\newcommand{\FunThreeD}[1]{\mathcal{D}_3\left(x,y,#1\right)}
-\newcommand{\Sinh}[1]{\cosh\left(#1\right)}
-\newcommand{\SinhX}[1]{\sinh\left(#1\right)}
-
-\newcommand{\FourierY}[2]{\mathcal{F}_{#2}\!\left\{#1\right\}}
-\newcommand{\InverseFourierY}[2]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}}
-
-\newcommand{\FourierX}[3]{\mathcal{F}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
-\newcommand{\InverseFourierX}[3]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
-
-% properly aligned version of sqrt for \zeta_y^2
-\newcommand{\SqrtZeta}[1]{\sqrt{\vphantom{\zeta_x^2}\smash[b]{#1}}}
-
-% normalisation
-\newcommand{\SqrtZetaX}{\sqrt{1 + \zeta_x^2}}
-\newcommand{\SqrtZetaY}{\SqrtZeta{1 + \zeta_x^2 + \zeta_y^2}}
-\newcommand{\FracSqrtZetaX}[1]{\frac{#1}{\SqrtZetaX{}}}
-\newcommand{\FracSqrtZetaY}[1]{\frac{#1}{\SqrtZetaY{}}}
-
-% wave vector
-\newcommand{\Kvec}{\vec{k}}
-\newcommand{\Kveclen}{\lvert\smash[b]{\Kvec}\rvert}
+\include{math}
% org-mode friendly commands
\newcommand{\orgcmidrule}[2]{\cmidrule(lr){#1}\cmidrule(lr){#2}}
diff --git a/slides-preamble.tex b/slides-preamble.tex
@@ -20,22 +20,11 @@
\graphicspath{{build/}{graphics/slides/}}
-% custom mathematical expressions
-\newcommand{\Var}[1]{\sigma_{#1}^2}
-\newcommand{\Fourier}[1]{\mathcal{F}\left\{#1\right\}}
-\newcommand{\InverseFourier}[1]{\mathcal{F}^{-1}\left\{#1\right\}}
-\newcommand{\Fun}[1]{\mathcal{D}_1\left(x,#1\right)}
-\newcommand{\FunSecond}[1]{\mathcal{D}_2\left(x,#1\right)}
-\newcommand{\FunThird}[1]{\mathcal{D}_2\left(x,#1\right)}
-\newcommand{\Sinh}[1]{\cosh\left(#1\right)}
-
-\newcommand{\FourierX}[3]{\mathcal{F}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
-\newcommand{\InverseFourierX}[3]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
-
+\include{math}
% tikz helper macros
\definecolor{markBlue}{HTML}{40C0F0}
-\definecolor{markRed}{HTML}{C00000}
+\definecolor{markRed}{HTML}{E5C6C5}
\definecolor{markBlueFg}{HTML}{226680}
\newcommand*{\circleemph}[2]{%
\begin{tikzpicture}[baseline=(#1tmp.base),remember picture]
@@ -49,5 +38,11 @@
\node[overlay,rectangle,fill=none,ultra thick,draw=none, inner xsep=0.5mm, inner ysep=1mm] (#1) at (#1tmp) {$\displaystyle#2$};%
\end{tikzpicture}
}
+\newcommand*{\fillrectemph}[2]{%
+ \begin{tikzpicture}[baseline=(#1tmp.base),remember picture]
+ \node[fill=none,inner sep=0mm] (#1tmp) {$\displaystyle\phantom{#2}$};%
+ \node[overlay,rectangle,fill=markRed,ultra thick,draw=none, inner xsep=0mm, inner ysep=0.5mm] (#1) at (#1tmp) {$\displaystyle#2$};%
+ \end{tikzpicture}
+}
\AtBeginSection[]{\frame{\sectionpage}}
