diff --git a/.gitignore b/.gitignore index c4abc9c51a26473dbbddd1c8bc0f34451a8965cc..963c17cfe8d79c85e12945fb35c6d1d99bb2ba92 100644 --- a/.gitignore +++ b/.gitignore @@ -32,3 +32,11 @@ *.dot *.pdf *.jpg + +# latex output +*.aux +*.log +*.out +*.pdf +*.toc + diff --git a/docs/SelfArx.cls b/docs/SelfArx.cls new file mode 100644 index 0000000000000000000000000000000000000000..23b8a932f6c93940eddfecd8de09f7632b5acc55 --- /dev/null +++ b/docs/SelfArx.cls @@ -0,0 +1,229 @@ +% --------------------------------------------------------------------- +% Conference proceedings and article templates for +% personal open-archiving activities +% September 2012 +% --------------------------------------------------------------------- + +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{SelfArx}[25/01/2012, v1.0] +\RequirePackage{ifthen} +\RequirePackage{calc} +\AtEndOfClass{\RequirePackage{microtype}} +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} +\ProcessOptions* +\LoadClass{article} +\RequirePackage{ifpdf} % Needed to pick between latex and pdflatex + +%---------------------------------------------------------------------- +% FONTS +%---------------------------------------------------------------------- + +\RequirePackage{times} % Loads the Times-Roman Fonts +\RequirePackage{mathptmx} % Loads the Times-Roman Math Fonts + +%---------------------------------------------------------------------- +% VARIOUS USEFUL PACKAGES +%---------------------------------------------------------------------- + +\RequirePackage[utf8]{inputenc} +\RequirePackage{amsmath,amsfonts,amssymb} +\RequirePackage{graphicx,xcolor} +\RequirePackage[english]{babel} +\RequirePackage{booktabs} + +%---------------------------------------------------------------------- +% MARGINS +%---------------------------------------------------------------------- + +\RequirePackage[left=2cm,% + right=2cm,% + top=2.25cm,% + bottom=2.25cm,% + headheight=11pt,% + letterpaper]{geometry}% + +%---------------------------------------------------------------------- +% FIGURES AND TABLES CAPTIONS +%---------------------------------------------------------------------- + +\RequirePackage[labelfont={bf,sf,small},% + labelsep=period,% + justification=raggedright]{caption} +\setlength{\abovecaptionskip}{0pt} +\setlength{\belowcaptionskip}{0pt} + +%---------------------------------------------------------------------- +% PAGE HEADER +%---------------------------------------------------------------------- + +\RequirePackage{fancyhdr} % Needed to define custom headers/footers +\RequirePackage{lastpage} % Number of pages in the document +\pagestyle{fancy} % Enables the custom headers/footers +% Headers +\lhead{}% +\chead{}% +\rhead{\small\sffamily\bfseries\@PaperTitle\ --- \thepage/\pageref{LastPage}} +% Footers +\lfoot{}% +\cfoot{}% +\rfoot{}% +\renewcommand{\headrulewidth}{0pt}% % No header rule +\renewcommand{\footrulewidth}{0pt}% % No footer rule + +%---------------------------------------------------------------------- +% SECTION/SUBSECTION/PARAGRAPH SET-UP +%---------------------------------------------------------------------- + +\RequirePackage[explicit]{titlesec} +\titleformat{\section} + {\color{color1}\large\sffamily\bfseries} + {} + {0em} + {\colorbox{color2!10}{\parbox{\dimexpr\linewidth-2\fboxsep\relax}{\centering\arabic{section}. #1}}} + [] +\titleformat{name=\section,numberless} + {\color{color1}\large\sffamily\bfseries} + {} + {0em} + {\colorbox{color2!10}{\parbox{\dimexpr\linewidth-2\fboxsep\relax}{\centering#1}}} + [] +\titleformat{\subsection} + {\color{color1}\sffamily\bfseries} + {\thesubsection} + {0.5em} + {#1} + [] +\titleformat{\subsubsection} + {\sffamily\small\bfseries} + {\thesubsubsection} + {0.5em} + {#1} + [] +\titleformat{\paragraph}[runin] + {\sffamily\small\bfseries} + {} + {0em} + {#1} +\titlespacing*{\section}{0pc}{3ex \@plus4pt \@minus3pt}{5pt} +\titlespacing*{\subsection}{0pc}{2.5ex \@plus3pt \@minus2pt}{0pt} +\titlespacing*{\subsubsection}{0pc}{2ex \@plus2.5pt \@minus1.5pt}{0pt} +\titlespacing*{\paragraph}{0pc}{1.5ex \@plus2pt \@minus1pt}{10pt} + +%---------------------------------------------------------------------- +% TABLEOFCONTENTS SET-UP +%---------------------------------------------------------------------- +\newlength{\tocsep} +\setlength\tocsep{1.5pc} % Sets the indentation of the sections in the table of contents +\setcounter{tocdepth}{3} % Three levels in the table of contents section: sections, subsections and subsubsections + +\usepackage{titletoc} +\contentsmargin{0cm} +\titlecontents{section}[\tocsep] + {\addvspace{4pt}\small\bfseries\sffamily} + {\contentslabel[\thecontentslabel]{\tocsep}} + {} + {\hfill\thecontentspage} + [] +\titlecontents{subsection}[\tocsep] + {\addvspace{2pt}\sffamily} + {\contentslabel[\thecontentslabel]{\tocsep}} + {} + {\ \titlerule*[.5pc]{.}\ \thecontentspage} + [] +\titlecontents*{subsubsection}[\tocsep] + {\footnotesize\sffamily} + {} + {} + {} + [\ \textbullet\ ] + +%---------------------------------------------------------------------- +% MULTIPLE AUTHOR SET +%---------------------------------------------------------------------- + +\newcount\@authcnt +\newcount\@tmpcnt\@tmpcnt\z@ + +\def\@affiliation{% + \ifnum\@tmpcnt<\@authcnt + \global\advance\@tmpcnt1 + \raggedright \csname @auth\romannumeral\the\@tmpcnt\endcsname\hfill\\% + \let\next\@affiliation \vskip1pt + \else + \let\next\relax + \fi +\next} + +\newcommand{\affiliation}[1]{% + \global\advance\@authcnt1 + \expandafter\gdef\csname @auth\romannumeral\the\@authcnt\endcsname + {#1}} + + +%---------------------------------------------------------------------- +% LIST CONTROL +%---------------------------------------------------------------------- + +\RequirePackage{enumitem} +%\setlist{nolistsep} % Uncomment to remove spacing between items in lists (enumerate, itemize) + +%---------------------------------------------------------------------- +% ABSTRACT+AUTHOR FRAME +%---------------------------------------------------------------------- + +\newcommand{\PaperTitle}[1]{\def\@PaperTitle{#1}} +\newcommand{\Archive}[1]{\def\@Archive{#1}} +\newcommand{\Authors}[1]{\def\@Authors{#1}} +\newcommand{\JournalInfo}[1]{\def\@JournalInfo{#1}} +\newcommand{\Abstract}[1]{\def\@Abstract{#1}} +\newcommand{\Keywords}[1]{\def\@Keywords{#1}} + +% --------------------------------------------------------------------- + +\renewcommand{\@maketitle}{% +\twocolumn[ + {% + \thispagestyle{empty}% + \vskip-36pt% + {\raggedleft\small\sffamily\bfseries\@JournalInfo\\\@Archive\par}% + \vskip20pt% + {\raggedright\color{color1}\sffamily\bfseries\fontsize{20}{25}\selectfont \@PaperTitle\par}% + \vskip10pt% + %{\raggedright\color{color1}\sffamily\fontsize{12}{16}\selectfont \@Authors\par}% + \vskip18pt% + %\fcolorbox{color1}{white}{% + %\parbox{\textwidth-2\fboxsep-2\fboxrule}{\centering% + %\colorbox{color2!10}{% + %\parbox{\textwidth-4\fboxsep-2\fboxrule}{% + %\ifx\@Keywords\@empty% + %\sffamily\textbf{\abstractname}\\\@Abstract% + %\else% + %\sffamily\textbf{\abstractname}\\\@Abstract\\[4pt]% + %\textbf{\keywordname}\\\@Keywords% + %\fi% + %}% + %}% + %\vskip4pt% + %\begingroup% + %\raggedright\sffamily\small% + %\footnotesize\@affiliation\par% + %\endgroup%% + %}% + %}% + %\vskip25pt + } +]% +}% + +%---------------------------------------------------------------------- +% REFERENCES +%---------------------------------------------------------------------- + +% Remove brackets from numbering in List of References +\renewcommand{\@biblabel}[1]{\bfseries\color{color1}\textsuperscript{[#1]}} +%\setlength{\bibitemsep}{0cm} +\let\oldbibliography\thebibliography +\renewcommand{\thebibliography}[1]{% +\addcontentsline{toc}{section}{\refname}% +\oldbibliography{#1}% +\setlength\itemsep{0pt}}% diff --git a/docs/formulation.tex b/docs/formulation.tex new file mode 100644 index 0000000000000000000000000000000000000000..93183fc00f847ed50e0526de711fe97ec1837e89 --- /dev/null +++ b/docs/formulation.tex @@ -0,0 +1,14 @@ +\section*{Introduction} + +The cable equation is a nonlinear parabolic PDE that can be written in the form +\begin{equation} + c_m \pder{V}{t} = \frac{1}{2ar_{L}} \pder{}{x} \left( a^2 \pder{V}{x} \right) - i_m + i_e, +\end{equation} +where +\begin{itemize} + \item $V$ is the potential relative to the ECM $[mV]$ + \item $a$ is the cable radius \todo{units} + \item $c_m$ is the {specific membrane capacitance}, approximately the same for all neurons $\approx 10~nF/mm^2$. Related to \emph{membrane capacitance} $C_m$ by the relationship $C_m=c_{m}A$, where $A$ is the surface area of the cell. + \item $i_m$ is the membrane current \todo{units} + \item $r_L$ is intracellular resistivity, typical value $1~k\Omega$ +\end{itemize} diff --git a/docs/makefile b/docs/makefile new file mode 100644 index 0000000000000000000000000000000000000000..c0e8e4d56f169461af19a7154f07867ca806afd3 --- /dev/null +++ b/docs/makefile @@ -0,0 +1,12 @@ +report.pdf : *.tex + pdflatex report.tex + +force : report.pdf + pdflatex report.tex + +clean : + rm -f *.pdf + rm -f *.log + rm -f *.out + rm -f *.aux + rm -f *.toc diff --git a/docs/report.tex b/docs/report.tex new file mode 100644 index 0000000000000000000000000000000000000000..fdc2cca75baaec1ca7702cb73d4f493bb96ac5d5 --- /dev/null +++ b/docs/report.tex @@ -0,0 +1,108 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Stylish Article +% LaTeX Template +% Version 2.0 (13/4/14) +% +% This template has been downloaded from: +% http://www.LaTeXTemplates.com +% +% Original author: +% Mathias Legrand (legrand.mathias@gmail.com) +% +% License: +% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/) +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%---------------------------------------------------------------------------------------- +% PACKAGES AND OTHER DOCUMENT CONFIGURATIONS +%---------------------------------------------------------------------------------------- + +\documentclass[fleqn,10pt]{SelfArx} % Document font size and equations flushed left + +\usepackage{xspace} +\usepackage{color} + +%---------------------------------------------------------------------------------------- +% COLUMNS +%---------------------------------------------------------------------------------------- + +\setlength{\columnsep}{0.55cm} % Distance between the two columns of text +\setlength{\fboxrule}{0.75pt} % Width of the border around the abstract + +%---------------------------------------------------------------------------------------- +% COLORS +%---------------------------------------------------------------------------------------- + +\definecolor{color1}{RGB}{0,0,90} % Color of the article title and sections +\definecolor{color2}{RGB}{0,20,20} % Color of the boxes behind the abstract and headings + +%---------------------------------------------------------------------------------------- +% PLOTTING and DRAWING +%---------------------------------------------------------------------------------------- +\usepackage{tikz} +\usetikzlibrary{positioning} +\usetikzlibrary{shapes,arrows,backgrounds,fit,shapes.geometric,calc} +\usetikzlibrary{pgfplots.groupplots} +\usepackage{pgfplots} +\usepackage{pgfplotstable} + +%---------------------------------------------------------------------------------------- +% HYPERLINKS +%---------------------------------------------------------------------------------------- + +\usepackage{hyperref} % Required for hyperlinks +\hypersetup{hidelinks,colorlinks,breaklinks=true,urlcolor=color2,citecolor=color1,linkcolor=color1,bookmarksopen=false,pdftitle={Title},pdfauthor={Author}} + +%---------------------------------------------------------------------------------------- +% CUSTOM COMMANDS +%---------------------------------------------------------------------------------------- + +\newcommand{\HWtwelve}{HW12\xspace} +\newcommand{\HWtwelves}{HW12$^*$\xspace} +\newcommand{\HWeight}{HW8\xspace} +\newcommand{\HWsix}{HW6\xspace} +\newcommand{\HWfour}{HW4\xspace} +\newcommand{\SBeight}{SB8\xspace} + +\newcommand{\HWtwelvecode}{E5-2690v3\xspace} +\newcommand{\HWtwelvescode}{E5-2680v3\xspace} +\newcommand{\HWeightcode}{E5-1660v3\xspace} +\newcommand{\HWsixcode}{E5-1650v3\xspace} +\newcommand{\HWfourcode}{E5-1620v3\xspace} +\newcommand{\SBeightcode}{E5-2670\xspace} + +\newcommand{\todo}[1]{\textbf{\textcolor{blue}{TODO: #1}}} % add a comment to the article + +\newcommand{\tbl}[1]{\textbf{Table \ref{#1}}\xspace} +\newcommand{\fig}[1]{\textbf{Figure \ref{#1}}\xspace} +\newcommand{\eq}[1]{\textbf{(\ref{#1})}\xspace} +\newcommand{\ssec}[1]{\textbf{\S\ref{#1}}\xspace} + +\newcommand{\pder}[2]{\frac{\partial{#1}}{\partial{#2}}} + +%---------------------------------------------------------------------------------------- +% ARTICLE INFORMATION +%---------------------------------------------------------------------------------------- + +\JournalInfo{CSCS} % name of "journal" on upper right corner +\Archive{working document} + +\PaperTitle{Cable Equation} + +%=============================================================================== + +\begin{document} + +\flushbottom % Makes all text pages the same height +\maketitle % Print the title and authors +\tableofcontents + +\thispagestyle{empty} % Removes page numbering from the first page + +%------------------------------------------------ +\input{formulation.tex} + + +\end{document} +