source: altifloat/doc/ocean_modelling/elsarticle-template-harv.tex @ 187

%% 
%% Copyright 2007, 2008, 2009 Elsevier Ltd
%% 
%% This file is part of the 'Elsarticle Bundle'.
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%% It may be distributed under the conditions of the LaTeX Project Public
%% License, either version 1.2 of this license or (at your option) any
%% later version.  The latest version of this license is in
%%    http://www.latex-project.org/lppl.txt
%% and version 1.2 or later is part of all distributions of LaTeX
%% version 1999/12/01 or later.
%% 
%% The list of all files belonging to the 'Elsarticle Bundle' is
%% given in the file `manifest.txt'.
%% 
%% Template article for Elsevier's document class `elsarticle'
%% with harvard style bibliographic references
%% SP 2008/03/01

\documentclass[preprint,12pt,authoryear]{elsarticle}

%% Use the option review to obtain double line spacing
%% \documentclass[authoryear,preprint,review,12pt]{elsarticle}

%% Use the options 1p,twocolumn; 3p; 3p,twocolumn; 5p; or 5p,twocolumn
%% for a journal layout:
%% \documentclass[final,1p,times,authoryear]{elsarticle}
%% \documentclass[final,1p,times,twocolumn,authoryear]{elsarticle}
%% \documentclass[final,3p,times,authoryear]{elsarticle}
%% \documentclass[final,3p,times,twocolumn,authoryear]{elsarticle}
%% \documentclass[final,5p,times,authoryear]{elsarticle}
%% \documentclass[final,5p,times,twocolumn,authoryear]{elsarticle}

%% For including figures, graphicx.sty has been loaded in
%% elsarticle.cls. If you prefer to use the old commands
%% please give \usepackage{epsfig}

%% The amssymb package provides various useful mathematical symbols
\usepackage{amssymb}
\usepackage{multimedia}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{multimedia}
\usepackage{graphics}
\usepackage{bbm}
\usepackage{pstricks}
\usepackage{amsthm}
 \usepackage{graphics}
 \usepackage{pgf}
 \usepackage{wrapfig} 
 \usepackage{mathtools} 
 \newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|}
 \newcommand{\bo}[1]{\mathbf{#1}}
%\newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|}
\newcommand{\dif}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\diff}[2]{\frac{\partial^2 #1}{\partial {#2}^2}}
\newcommand{\odif}[2]{\frac{d #1}{d #2}} 
\newcommand{\odiff}[2]{\frac{d^2 #1}{d #2^2}}

%% The amsthm package provides extended theorem environments
%% \usepackage{amsthm}

%% The lineno packages adds line numbers. Start line numbering with
%% \begin{linenumbers}, end it with \end{linenumbers}. Or switch it on
%% for the whole article with \linenumbers.
%% \usepackage{lineno}

\journal{Ocean Modellling}

\begin{document}

\begin{frontmatter}

%% Title, authors and addresses

%% use the tnoteref command within \title for footnotes;
%% use the tnotetext command for theassociated footnote;
%% use the fnref command within \author or \address for footnotes;
%% use the fntext command for theassociated footnote;
%% use the corref command within \author for corresponding author footnotes;
%% use the cortext command for theassociated footnote;
%% use the ead command for the email address,
%% and the form \ead[url] for the home page:
%% \title{Title\tnoteref{label1}}
%% \tnotetext[label1]{}
%% \author{Name\corref{cor1}\fnref{label2}}
%% \ead{email address}
%% \ead[url]{home page}
%% \fntext[label2]{}
%% \cortext[cor1]{}
%% \address{Address\fnref{label3}}
%% \fntext[label3]{}

\title{Modeling Surface Currents in the Eastern Levantine Mediterranenan Using Surface Drifters and Satellite Altimetry Data}

%% use optional labels to link authors explicitly to addresses:
%% \author[label1,label2]{}
%% \address[label1]{}
%% \address[label2]{}

\author{Leila Issa, Julien Brajard, Pierre-Marie Poulain, Laurent Mortier, Dan Hayes, Milad Fakhri}

\address{}

\begin{abstract}
%% Text of abstract

\end{abstract}

\begin{keyword}
%% keywords here, in the form: keyword \sep keyword

%% PACS codes here, in the form: \PACS code \sep code

%% MSC codes here, in the form: \MSC code \sep code
%% or \MSC[2008] code \sep code (2000 is the default)

\end{keyword}

\end{frontmatter}

%% \linenumbers

%% main text
\section{Introduction}
\label{}
\section{Data}
\section{Method}
\begin{itemize} 

\item $\vec{U_0}=\vec{U}_{b}+\vec{\delta U},$ $\vec{U}_b=\textcolor{red}{\vec{U}_{alt}}$ and $\vec{r}=\vec{r}^{\,b}+\vec{\delta r}$
\item Model and Linear tangent (forward Euler for the numerical integration, and bilinear Lagrange interpolation in space for instance):  
\small{
\begin{align} \notag
&\vec{r}^{\,b}_i(k\delta t)=\vec{r}^{\,b}_i((k-1)\delta t)+2\delta t \, interp(\vec{U}^b, \vec{r}^{\,b}_i((k-1)\delta t)),\,\,\,\,\, \text{\textcolor{blue}{model}}  \\  \notag
&\vec{\delta r}_i(k\delta t) = \vec{\delta r}_i((k-1)\delta t) + 2 \delta t \, \{ interp(\textcolor{green}{\vec{\delta U}},\vec{r}^{\,b}_i((k-1)\delta t)) \\ \notag 
&+ \vec{\delta {r}}_i((k-1)\delta t) \cdot \partial _{(x,y)} interp (\vec{U}^b,\vec{r}^{\,b}_i((k-1)\delta t))\}  \,\,\, \text{\textcolor{blue}{tangent}} \notag
\end{align}
initialized with observations, for $k=1,2,3, \cdots $ and $i=1, \cdots N_{drift}$ 
}
%\vec{r}(0)= \vec{r}^{o}(0)$
\item Perform sequences of optimization
\[\mathcal{J}(\textcolor{green}{\delta \vec{U}})= \frac{1}{2} \left \{ \sum _i \sum_{m=1}^{P} \vectornorm{\vec{r}^{\,b}_i+\delta \vec{r}_i(\textcolor{green}{\delta \vec{U}}) -\vec{r}_i^{\,o}(m\Delta t) }^2 +\vectornorm{ \textcolor{green}{\vec{\delta U}} }^2_{\bo{B}}  \right\}   \]
$P$ depends on $T_{L}/\Delta t$. $T_L$ characteristic of autocorrelation of drifters (typical 1-3 days) 

%+\sum_{i,m=1}^{m=P} \vectornorm{\vec{r}^{\,b}+\delta \vec{r}(\textcolor{green}{\delta \vec{u}}) -\vec{r}_i^{\,o}(m\Delta t) }^2   \right]   \]
\end{itemize}




\section{Twin Experiments}
\section{Experiment with Real Data}
%% The Appendices part is started with the command \appendix;
%% appendix sections are then done as normal sections
%% \appendix

%% \section{}
%% \label{}

%% If you have bibdatabase file and want bibtex to generate the
%% bibitems, please use
%%
%%  \bibliographystyle{elsarticle-harv} 
%%  \bibliography{<your bibdatabase>}

%% else use the following coding to input the bibitems directly in the
%% TeX file.

\begin{thebibliography}{00}

%% \bibitem[Author(year)]{label}
%% Text of bibliographic item

\bibitem[ ()]{}

\end{thebibliography}
\end{document}

\endinput
%%
%% End of file `elsarticle-template-harv.tex'.