%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This is the document source index.tex. % Read this and then change it to your needs. But first make sure % that your editor window is wide enough to show the top line of % % signs above to its full width without wrapping % Note that this file is "compiled". In other words, it is turned % into a pdf file, web pages, or both. What you put in this file % determines what ends up in the pdf or on the web pages. % First is the header of the document. The actual document text % starts further down, below the \begin{document} line. But you must % get the header right too. % % Note that everything following a percent sign is ignored. That % includes explanatory comments like the ones you are reading right % now, as well as disabled formatting commands. To enable a disabled % formatting command, remove the percent sign. % % If you still have questions after looking at this example document, % and you will have, look at the intro_to_latex web page in the l2h % help-files subfolder next. % First a couple of notes about this particular example format: % % 1) If you want to use a program like TeXstudio or TeXmaker to edit % this document and turn it into a pdf, you must configure them to use % the so-called "DVI --> PS --> PDF" route. See the "editors" web % page in the l2h "help-files" folder for more. % % 2) Support for international characters is limited. It should be OK % for Western European languages other than Greek. (Greek mathematics % characters are *not* a problem for this template.) % % 3) This is set up to produce a book, not a scientific article. % % If any of the above is a problem, there are different examples % available. Just exit the editor with which you are reading this % example. Then remove the example, file index.tex, from your working % folder. When l2h_menu discovers that index.tex is gone, it will % give you a choice of versions for the new one. Reenter the editor % with the \ key. % The next line sets various options appropriate for books: \documentclass[12pt]{book} %%%%%%%%%%%%%%%%%%%%%%%%%% INTERNATIONIZATION %%%%%%%%%%%%%%%%%%%%%%%%%% % If you want to change the latex "build-in" names like "Figure", % "List of Figures", "Contents", etcetera, to another language see: % http://www.tex.ac.uk/cgi-bin/texfaq2html?label=fixnam % International Characters: % % This part explains how to insert international characters in your % document. So if you *only* write English and/or Dutch, you can skip % to the end of this section (i.e. to the blank line behind the % end{latexonly} line.) % % (We continue with the unlucky vast majority plus the author.) % % This version of the example document is set up to deal with the % characters of Western European languages, but NOT Greek. If you % need to write nontrivial amounts of Greek or nonWestern European % languages, you need to select another version of this document. Do % this by renaming or removing this document from your working folder % and then rerun l2h_menu in it. If l2h_menu does not find this % document, it will give you a choice of versions for a new one. % % (We continue with a Western European audience.) % % An international character, like say the n-tilde in Español can be % inserted either as in Espa\~nol, or as in Español. The first is the % standard LaTeX encoding. The second encoding is called "UTF-8" % encoding. UTF-8 encoding is nowadays standard: the help or % documentation of your editor should tell you how the put these % characters in. If not, update your editor. % % (The outdated UTF-16 encoding is not supported by l2h. You can % convert such a document into UTF-8 by putting it in the appropriate % subfolder of the "convert" folder of l2h and double-clicking the % convert_tex button. Other outdated encodings like latinX, % ISO-8859-X, Windows CPX, ... should still work, as long as there is % an appropriate converter in the "versions" folder of l2h. You will % need to change this internationalization section and $HTML_VERSION % in file "settings.pl". Look in the original latex2html manual in % the help-files folder for more details. Note that you will need to % modify file settings.pl, *not* .latex2html-init as the manual says.) % % A note for those who are only interested in the *web pages*, not in % the pdf version of the document. *Any* UTF-8 character that you put % in the *text* of the document, even Greek, Chinese, or whatever, % will make it correctly to the web pages. However, UTF-8 characters % that you put inside figures or mathematics will not be rendered. % Here you must use the LaTeX encoding, assuming there is one. Or % rewrite the mathematics to keep the international characters out of % it. And format figures like, say, % \begin{figure} % \begin{makeimage} % Stuff that does not use international characters, (except in % LaTeX encoding if one exists for the character). % \end{makeimage} % Blah blah freely using Greek, Chinese, ..., in UTF-8. % \begin{makeimage} % Stuff that does not use international characters, (except in % LaTeX encoding if one exists for the character). % \end{makeimage} % \caption{Blah blah freely using Greek, Chinese, ..., in UTF-8.} % \end{figure} % As a better solution, you may be able to find a graphics and/or % plotting program that can insert arbitrary UTF-8 characters into a % picture and save the result in .eps format. In that case, your % problem is solved. % % WARNING: Leave the following part, going up to the end{latexonly} % line, alone unless you have a very good reason. All this stuff is % bound to cause headaches. The author of l2h can attest. At least % leave it alone until you have verified that l2h can process this % document *as is*. % % WARNING: whatever is put in this section gets used to create the web % page images *instead* of the \usepackage[...]{inputenc} command that % latex2html would use otherwise. % % WARNING: The next two lines MUST be as given, do NOT touch them in ANY way: %begin{latexonly} % Start of the internationalization section: % % The following package allows latex to recognize various Western % European UTF-8 characters, like the ñ in Español: \usepackage[utf8]{inputenc} % % An alternative package that seems to have some more characters is % utf8x. To try it, put % before the \usepackage[utf8]{inputenc} line % above. And then remove the % from the line below: %\usepackage[utf8x]{inputenc} % No, it won't do Greek or nonWestern European. % % WARNING: The next two lines MUST be as given, do NOT touch them in ANY way: % End of the internationalization section. %end{latexonly} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%% BASIC PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%% % Hyperref is needed for putting active links in pdf files. \usepackage[final,ps2pdf]{hyperref} \hypersetup{ pdfborder={0 0 0.5}, citebordercolor={0.7 0.7 0.7}, filebordercolor={0.7 0.7 0.7}, linkbordercolor={0.7 0.7 0.7}, menubordercolor={0.7 0.7 0.7}, runbordercolor={0.7 0.7 0.7}, urlbordercolor={0 0 0}, pdfsubject={The Book on Miatas}, pdfkeywords={Quantum Mechanics} {Special Relativity} {Miatas} {Doppler effect}, breaklinks } %begin{latexonly} \usepackage[all]{hypcap}[2008/09/08]\renewcommand{\hypcapspace}{1pt} %end{latexonly} % Html defines the web-page related commands. % TO DISABLE, PUT A % IN FRONT OF THE NEXT LINE: \usepackage{html} % BUT THEN REMOVE THE LEADING % FROM THE NEXT TWO LINES: %\newcommand{\htmlimage}[2]{} %\newcommand{\latexhtml}[2]{#1} % This will also clobber any comment environments. So you will also % need to move \begin{comment}...\end{comment} stuff behind the % \end{document} line. % Epsf is a good way to include figures, and is preferred here: \usepackage{epsf} % Float is wanted to prevent latex from putting figures wherever it wants: %\usepackage{float} % Graphics is needed to manipulate figures (resize, rotate, ...): \usepackage{graphicx} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% DOCUMENT OPTIONS %%%%%%%%%%%%%%%%%%%%%%%%%%% % In general, when you need more information on something done by a % package, searching the web for the package name is definitely % something to try. Almost all packages have pdf instructions. % The next two lines allow the book index to be made: \usepackage{makeidx} \makeindex % TO DISABLE, PUT % SIGNS IN FRONT OF THE TWO LINES ABOVE, AND % ALSO ONE IN FRONT OF THE \printindex LINE NEAR THE END OF THIS % DOCUMENT. % Natbib takes care of the format of bibliographic references nicely: \usepackage[square,numbers]{natbib} % Options in the square brackets must be separated by commas as in the % example above. Some more important ones are: % square: uses square brackets instead of parentheses in citations. % numbers: uses numerical references instead of author-year. % super: uses superscript numbers for references. % comma: separates a list of references using commas. % sort: sorts a list of references in the bibliography order. % sort&compress: also compresses say 3,4,5,6 into 3-6 % (See the documentation of the natbib package for more details) % To add links from the index to the citations in the text, remove the % leading percent sign from the next line: %\citeindextrue % For the web pages, this will also create links from the entries in % the bibliography to where they are cited in the text. To do the % same for the pdf, use the backref or pagebackref option for the % hyperref package. % Additional math symbols from the American Mathematical Society (AMS): %\usepackage{amsfonts} %includes \mathbb{U} for blackboard bold uppercase %\usepackage{amssymb} %complete AMS symbol definition, includes amsfonts %\usepackage[mathscr]{eucal} %makes Euler script available as \mathscr %\usepackage{amsbsy} %allows bolding of additional characters % Poor man's bold: \pmb{TEXT} will simulate bold face if the % characters in TEXT are not available in bold face. Use only if % \textbf{TEXT}, or \mathbf{TEXT} in math, does not work. \newcommand{\pmb}[1]{\setbox0=\hbox{#1}\kern-.025em\copy0\kern-\wd0% \kern.05em\copy0\kern-\wd0\kern-.025em\raise.0433em\box0} % Note: the AMS packages above will normally give you *real* bold % characters. Find their documentation on the web. % If you need a figure or table to be sideways, think again. That is % very ugly and irritating to the readers. Instead, try to resize it, % split it into two, or drop something. However, if there is really % nothing that can be done, remove the % from the next line: %\usepackage{rotating} % Then in the{figure} or {table} environment, replace {figure} or {table} % by {sidewaysfigure} respectively {sidewaystable}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FORMATTING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Vmargin is a relatively simple way to set page margins. \usepackage[USletter]{vmargin} \setpapersize{USletter} % use A4 in Europe \setmargins{1.65in}{1in}{5.625in}{8.42361in} % left, top margins, width, height {\headheight}{20pt}{\footheight}{30pt} % 20pt=headsep, 30pt=footskip \setlength{\marginparwidth}{70pt}% width of \marginpar{...} notes in the margin % Note: lines more than about 72 characters long are hard to read. % Important note: pdf readers like Adobe Acrobat tend to shrink the % page when printing it. You need to select an option in the print % menu to avoid that. Or live with a shrunken page. % Remove the leading % sign to have a doubly spaced document: %\latexhtml{\linespread{1.5}}{} % rounds to 2 :) % Note: to still have some block of text single-spaced, use: %{\latexhtml{\baselineskip=16pt plus 3pt}{} BLOCK OF TEXT } % Remove the leading % sign to have 1 blank line between paragraphs: %\setlength{\parskip}{1\baselineskip plus 0.3ex} % Remove the leading % sign to have a 1/4 inch paragraph indentation: %\setlength{\parindent}{1.5em} % The next lines define more compact itemize and enumerate % environments called itemize* and enumerate*. The blank space % between the list items is set equal to \parskip as set above. % Note: If \parskip is not 0\baselineskip, and you want no space % between items, then set \parskip to 0\baselineskip immediately % before the list, and set it back to what it was in the text % following the list. Do that following the format above. Do the % same with \parindent, if you do not want paragraphs in the list to % be indented. \newenvironment{itemize*} {\begin{list}{$\bullet$}{ \setlength{\topsep}{0ex}\setlength{\partopsep}{\parskip} \setlength{\itemsep}{0pt plus 0.2ex}\setlength{\parsep}{\parskip} \setlength{\leftmargin}{\leftmargini}\setlength{\rightmargin}{\leftmargin} \setlength{\listparindent}{\parindent}\setlength{\itemindent}{0em} \setlength{\labelsep}{\labelsep} \setlength{\labelwidth}{\leftmargin}\addtolength{\labelwidth}{-\labelsep}}} {\end{list}} \newenvironment{enumerate*} {\begin{list}{\arabic{enumi}.}{ \setlength{\topsep}{0ex}\setlength{\partopsep}{\parskip} \setlength{\itemsep}{0pt plus 0.2ex}\setlength{\parsep}{\parskip} \setlength{\leftmargin}{\leftmargini}\setlength{\rightmargin}{\leftmargin} \setlength{\listparindent}{\parindent}\setlength{\itemindent}{0em} \setlength{\labelsep}{\labelsep} \setlength{\labelwidth}{\leftmargin}\addtolength{\labelwidth}{-\labelsep} \usecounter{enumi}}} {\end{list}} % Use \newoddpage at the end of a chapter or other major unit to % leave the next page blank if it is an even page (i.e. a left-hand % page in a book): \newcommand{\newoddpage}{% \latexhtml{\newpage\markboth{}{} \ifodd\arabic{page}\else\strut\thispagestyle{empty}\newpage\fi}{}} % If the last line on a page is the first line of a new paragraph, % it's called club line. If the first line of a page is the last line % of a paragraph, it is called a widow line. If you want LaTeX to % spend additional effort to avoid those, remove the leading percents % from the next two lines: %\widowpenalty=9999 %\clubpenalty=9999 % Set LateX to number subsubsections. % To disable, put a % in front of the next line: \setcounter{secnumdepth}{3} % To set a nonwhite page color for the pdf, adjust the red, green and % blue values, with values from 0 to 1, then remove the leading percent: %\latexhtml{\usepackage[dvips]{color}\pagecolor[rgb]{1.,0.941,0.651}}{} % To change the page color of the web pages, index.css must be % changed. Using the l2h menu is one way to do that. The web color % must be hexadecimal, ({1.,0.941,0.651} becomes #FFF0A6). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PICTURES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % IMPORTANT: You normally need to include "pictures", (like data % plots, photographs, etcetera), in your document. This section tells % you what format these must be in. % \latexhtml{ % The next two lines specify in which format pictures must be for % the *pdf* version of your document. In particular, they require % that you provide every picture in "eps" format: \newcommand{\putpicture}[1]{\epsffile{#1.eps}} \newcommand{\pdfengine}{latex} }{ % The next two lines specify in which format pictures must be for % the *web pages* version of your document. In particular, they % require that you provide every picture in "eps" format: \newcommand{\putpicture}[1]{\epsffile{#1.eps}} \newcommand{\webengine}{latex} } % The above is not a big deal: % % Suppose that you have, say, a jpg picture, but you need an eps one. % Well, there is a folder named "convert" inside the l2h folder. It % has a subfolder "any_eps". Put a copy of your jpg picture inside % that folder and double-click "convert_jpg". Bingo, an eps version of % your picture is produced. Just put it in with your document. % % Conversely, suppose you have an eps picture, but you need an noneps % one. Simply put a copy of the eps picture inside the "eps_pdf" % subfolder and double-click "convert_eps". Bingo, a pdf version will % be produced. % % You can instead use a commercial program like Adobe Photoshop, or a % free one like the gimp, to turn jpg, gif, png, ... pictures into eps % ones or vice-versa. See the "images" web page inside the l2h % "help-files" folder for more. % % See the "plots" web page for more on how to make data plots in eps % format. There are also additional examples in the "plots" subfolder % of example subfolder. These latter examples show exactly how the % plots in this document were made using gnuplot. % A note for these who would want to mess around with the definitions % of \pdfengine and \webengine above. The first "word", (i.e. up to % the first space, if any), must be an executable file in your path, % (as set by init.bat), when l2h is running. Do not use any quotes in % the definition. Further requirements for MS Windows users: The % default extension is .exe, so {latex} really means {latex.exe} say. % If the executable has extension .cmd, it must be specified, like in % {latex.cmd} say. If the executable has extension .bat, it must be % specified *and* the executable needs to be preceded by the word % "call", like in {call latex.bat} say. Also, if there is a path % name, use the normal \, not /, in it. You cannot have spaces in the % path name either: say {C:\Program Files\latex.exe} does not work but % {C:\PROGRA~1\latex.exe} is OK. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WEB PAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % THIS BLOCK DETERMINES THE SETTINGS FOR THE WEB PAGES. IGNORE IT IF % YOU ARE NOT PLANNING TO CREATE WEB PAGES OF THE DOCUMENT. % In a \[re]newcommand{\command}{...}, do *NOT* forget the brackets % around {\command}. (Yes, this is a latex2html quirk.) % Hthtml simplifies making active url links, see the latex2html web % page inside the help-files folder. Enable by removing the next %: %\usepackage{hthtml} % Then you can also create a \weblink{TEXT}{URL} command for active % links to the web by removing the % signs from the next 3 lines: %\latexhtml %{\newcommand{\weblink}[2]{\href{#2}{#1}\htlink{{}}{#2}}} %{\newcommand{\weblink}[2]{\htlink{#1}{#2}}} % and a \weburl{URL} command by doing the same for the next 3 lines: %\latexhtml %{\newcommand{\weburl}[1]{\url{#1}}} %{\newcommand{\weburl}[1]{\hturl{#1}}} % This defines the form of the web page data command: \newcommand{\webpages}[2]{} % Change the language of some titles like "Table of Contents". See % subfolder "versions" in l2h for what languages are defined: \webpages{TITLES_LANGUAGE}{english} % The following lines describe the short strings that go into the top % and bottom bars of web pages. Change the texts as needed. Note % that the strings are in html format. % % Warning: you cannot use the characters <, >, {, }, or & in the text % (besides in html code). Instead use < for <, > for >, { % for {, } for }, and & for &. Note that   is blank % space and © the copyright symbol. % % To insert a link named LINKNAME with address LINKURL, in the desired % place use LINKNAME. See the example % links below. Omit class=runnerb for a background (page) color bar. % % To insert an image NAME.EXT (e.g. mylogo.jpg), put NAME.EXT inside % the "keep" subfolder of web-pages. (In the web-pages folder itself, % it is likely to be deleted eventually.) Then below, in the desired % place, use . To find % the right values of numbers NNN and NN, you can, for example, open % the image with your web browser. The correct values will be shown % in the browser top bar. % \webpages{TITLE}{Why White Miatas are Faster} % used for the top web page only \webpages{TOP_LEFT_TEXT}{ Why White Miatas are Faster} \webpages{TOP_CENTER_TEXT}{ } \webpages{TOP_RIGHT_TEXT}{© Leon van Dommelen } \webpages{TOP_BORDER}{4} % use 0 for no border, 1 for a thin frame \webpages{TOP_CLASS}{class=runner} % omit class=runner for background color \webpages{BOT_LEFT_TEXT}{ FAMU-FSU College of Engineering} \webpages{BOT_CENTER_TEXT}{ } \webpages{BOT_RIGHT_TEXT}{Processed with l2h } \webpages{BOT_BORDER}{3} % use 0 for no border, 1 for a thin frame \webpages{BOT_CLASS}{class=runnerb} % omit class=runnerb for background color \webpages{NAVIGATION_HEIGHT}{80} % navigation frame height in a frames version % Where people end up if they back out of the document web pages. % You may want to have this point to your home page: \webpages{EXTERNAL_UP_LINK}{../index.html} % or your home page url? \webpages{EXTERNAL_UP_TITLE}{Format selection page} % or: Home page? % The digit in the next line determines how small the web pages are % made. If it is 3, a web page contains an entire chapter. If it is % 4, it contains only a single section, 5 a subsection, etcetera \webpages{MAX_SPLIT_DEPTH}{4} % Using \label{sec:NAME} after a sectioning command allows you to refer % to that sectional unit as \ref{sec:NAME}. Using \secname{NAME} % does the same, but that also uses NAME as the name of the corresponding % web page. And you do not have to type the colon. :) % Do avoid using spaces in NAME. \newcommand{\secname}[1]{\label{sec:#1}} % \webpagename{sec_title}{NAME} is for unnumbered sectional units: \newcommand{\webpagename}[2]{} % If you do NOT want to use this naming scheme, and revert to % latex2html default web page names node0001.html, node0002.html, ..., % you need to remove the stuff inside the next latexonly block: %begin{latexonly} \newwrite\wpnames\immediate\openout\wpnames=index.pl \makeatletter\catcode`\~=12 \renewcommand{\secname}[1]{\def\ls{$fnam =~ s/^}\def\lsb{$/#1/;}% \immediate\write\wpnames{\ls\@currentlabel\lsb}\label{sec:#1}} \renewcommand{\webpagename}[2]{% \def\ls{$fname =~ s/^#1$/#2/;}\immediate\write\wpnames{\ls}} \catcode`\~=\active\makeatother %end{latexonly} % Use \picfrbox inside "picture" environments instead of \framebox. % (Yes, this is a latex2html quirk.) \def\picfrbox(#1,#2){\framebox(#1,#2)} \begin{imagesonly} \def\picfrbox(#1,#2){\framebox(#1,#2)} \end{imagesonly} % If you are planning to hyphenate your web pages, here are some % things that might be useful. % % To prevent a part of your document from being hyphenated, (maybe % because it is in a different language), enclose it between \nowebhypbeg % and \nowebhypend tags. Make sure the enclosed part does not extend from % one web page to the other or neither web page will be hyphenated at all. \newcommand{\nowebhypbeg}{\latexhtml{} {\begin{rawhtml}\end{rawhtml}}} \newcommand{\nowebhypend}{\latexhtml{} {\begin{rawhtml}\end{rawhtml}}} % % To explicitly create a potential web-page hyphenation point somewhere % use \1 (\0 through \9 do not produce erroneous space in latex2html): \newcommand{\1}{\latexhtml{\-}{\begin{rawhtml}­\end{rawhtml}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%% PLEASE FILL IN THE BASIC DOCUMENT DATA %%%%%%%%%%%%%%%% % Put the document author(s) between the curly brackets, % (if there are multiple authors, separate them by \and commands): \author{Leon van Dommelen \and L.L. van Dommelen} % In case a name contains a letter, call it a, with an accent, write % it as \`a, \'a, \^a, \"a, \~a, \=a, \.a, \u{a}, \v{a}, \H{a}, % \t{aa}, \c{a}, \d{a}, or \b{a} for grave, acute, circumflex, % umlaut, tilde, macron, dot, breve, check, long-umlaut, tie-after, % cedilla, dot-under, or bar-under respectively. To get rid of the % normal dot above an accented i, write the i as \i. % Enter the document title between the curly brackets, % (note the use of \\ to start a new line): \title{A Theoretical Investigation \\ Into The Increased Speed Of White Miatas \\ Due To Surface-Photon Interaction} % Remember: to force a new line in plain text, use \\, \newline, or % \linebreak[4]. Similarly use \newpage or \pagebreak[4] to force a % new page. (The difference is whether or not LaTeX will stretch the % broken line to the right margin, or the broken page to the bottom of % the page. The 4 means you really insist; use less if not.) % % As long as I mention page breaking: If you ever have to change a % page number to, say, 24, use \setcounter{page}{24} just before where % latex "cuts the page" in question. % % Also, if latex starts "hoarding" figures and tables, instead of % placing them, use \clearpage to stop it. % If the date is not set here, the processing date is inserted: \date{April 1, 2013} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} % Here we start the actual document! :) % Fix to get the math images properly scaled on the web pages: \latexhtml{}{\setlength{\textheight}{8.42361in}\setlength{\textwidth}{5.625in} \setlength{\vsize}{8.42361in}\setlength{\hsize}{5.625in}} % When running a spell check, you want to avoid having the spell % checker try to spell-check every LaTeX command. The easiest way is % to use an LaTeX editor like TeXstudio that has spell and grammar % checking build in. If using emacs, use M-x ispell-buffer for a % LaTeX-aware spell check. In gedit, the best is to select "Highlight % Misspelled Words" in the tools menu. Or highlight the paragraph(s) % that you want to have spell-checked with the mouse and select "Check % Spelling". % Establish small roman numeral numbering \frontmatter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TITLE PAGE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \nowebhypbeg \maketitle \nowebhypend %%%%%%%%%%%%%%%%%%%%%%%%%%%% COPYRIGHT PAGE %%%%%%%%%%%%%%%%%%%%%%%%%%%% \thispagestyle{empty} % no page number, header, or footer \vspace*{\fill} % some stretchable blank space % The title of the page \begin{center} {\Huge Copyright} \end{center} \vspace*{0.5in} % half an inch of additional space % A single paragraph of text Copyright \copyright{} 2013 Leon van Dommelen. All responsibility for the contents of this book rests fully with the reader. \vspace*{\fill} % some stretchable blank space \vspace*{\fill} % some stretchable blank space %%%%%%%%%%%%%%% TABLES OF CONTENTS, FIGURES, AND TABLES %%%%%%%%%%%%%%%% % Let's have a table of contents: \newoddpage \phantomsection % fix to get active links in the pdf to work properly \renewcommand{\contentsname}{Contents} % Title of the table of contents \tableofcontents % And a list of figures: \newoddpage \phantomsection\addcontentsline{toc}{section}{List of Figures} \renewcommand{\listfigurename}{List of Figures} % Title of the list \renewcommand{\figurename}{Figure} % what it is called in the captions \listoffigures % And a list of tables: \newoddpage \phantomsection\addcontentsline{toc}{section}{List of Tables} \renewcommand{\listtablename}{List of Tables} % Title of the list \renewcommand{\tablename}{Table} % what it is called in the captions \listoftables %%%%%%%%%%%%%%%%%%%%%% START OF THE MAIN DOCUMENT %%%%%%%%%%%%%%%%%%%%%% % Start normal arabic page numbering \newoddpage \mainmatter \newoddpage % For more on page headers and footers, see: % http://en.wikibooks.org/wiki/LaTeX/Page_Layout % First chapter title and its label: \chapter{Introduction}\secname{intro}% \index{intro} % The \index command above adds an entry in the index called "intro" % with the page number of the current page. To get the link properly % positioned on the web pages, make sure you have the trailing percent % on the \chapter line like above and put all index extries on the % next line. Do not break the line between index entries, even when % commenting away the end-of-line. (Yes, a latex2html quirk.) You % could use \index{intro|emph} to get the page number in the index in % italics, and \index{intro|textrm} to get it underlined. (This is % enabled that way at the end of this file.) % Note: if you put a latex command inside a sectional title, or a % figure or table caption, you may sometimes have to precede it by % \protect. So if you get into trouble with a title or caption, % try that. \begin{figure}[htbp]\latexhtml{\par}{} \centering % Image bozo.jpg was made by my digital camera. To create bozo.eps, % I put a copy of bozo.jpg in the "any_eps" folder, inside the l2h % "convert" folder, and double-clicked "convert.jpg". See web-page % "images", inside the l2h "help-files" folder, for more details: \resizebox{1in}{!}{\putpicture{bozo}} % The next line puts in 1 inch of horizontal space: \hspace{1in} % Modified version of the image: \resizebox{1in}{!}{\putpicture{nobozo}} % Do not use multiple captions in the same figure; latex2html does % not handle it correctly: \caption{A white Miata and a nonwhite one.} % The \label below creates a mnemonic "fig:bozo" for this figure. % The actual numbers are put in by latex. That means that you do not % have to change hundreds of numbers when you add or delete a figure, % equation, or whatever in a big document. It also cuts down on % mistakes: \label{fig:bozo} \end{figure} % The below \index command creates a subitem "Miata" in the "intro" % index entry: The Miata\index{intro!Miata} is a sports car developed by the Japanese % Note the use of the mnemonic "fig:bozo" as defined in the figure above: car manufacturer Mazda. Figure \ref{fig:bozo} shows a white and a nonwhite Miata. % Use \footnote{...} for footnotes: The Miata\footnote{Mazda refers to the Miata commonly as the MX-5. % Use \emph{...} for emphasis (italics) and similarly \textbf{...} for bold: The designation \emph{Miata} has been dropped altogether in recent years.} was introduced in the USA market in 1990. It is definitely important to recognize that the Miata was primarily designed for the USA\index{USA Market!Miata} market. However, it was also very successful in other markets. Here are some languages in which the praises of the Miata\index{Miata!international acclaim} were sung: \begin{center} English \\ (Spanish) Español \latexhtml {% This is for the pdf version of the document: % See the Internationalization part at the start of this file for more. \\ (Greek) % not supported by the utf8 and utf8x packages \\ (Russian) % not supported by the utf8 and utf8x packages \\ (CJK) % not supported by the utf8 and utf8x packages \\ (High UTF-8) % not supported by the utf8 and utf8x packages } {% And this is for the web pages version of the document: % Note that unicode characters simply pass through to the web pages. % (Unfortunately, that is no longer true if you put the characters % inside mathematics, or inside figures other than in the captions.) % See the Internationalization part at the start of this file for more. \\ (Greek) Ελληνικά \\ (Russian) Русский \\ (CJK) 中日韓 \\ (High UTF-8) 𐑍𐑎𐑏 } \end{center} Needless to say, white was a Miata color from the beginning. However, early white Miatas had a problem where the paint would peel off the cars. This was the stage at which the issue of Miata-photon interaction first received significant popular attention. Owners with peeling paint\index{paint!speed relation}\index{peel|see{paint}} noticed that their cars did not only look worse. The cars also became very noticeably slower when the paint peeled off. Since then, the increased speed of white Miatas became well known among knowledgeable owners. However, some others doubted the association and acquired grey, black, and even red Miatas. While these Miatas would still drive at reasonable speeds, they had difficulty competing with the white ones when maximum performance was an issue. % Example table. The table environment merely allows the position of % the table to be changed from h (here) to t (top of page), b (bottom % of page), or to p (a separate page with just tables and figures). \begin{table}[htbp] \centering \caption[First-generation Miata colors produced, in cars.]{First-generation Miata colors produced, in cars. Data compiled by John Emerson. Figures provided by Marketing Division of Mazda Corporation, Irvine, CA. Posted on miata.net. Data are resorted in order of increasing car speed, scaled with rated engine power. Data for 1990-1991 white Miatas are applicable until the paint peels off.} \label{tab:colors} \vspace*{.15in} % 0.15 inch of blank space % The tabular environment produces the actual table. Inside % mathematics, a table (like say a matrix), is called an array. But % the idea is the same. % The string lrrrrrrrrr means that there is a left-aligned column, % followed by 9 right-aligned ones. A centered column would be a c. {\setlength{\tabcolsep}{3.3pt}% reduces space between columns \begin{tabular}{lrrrrrrrrr} % \hline is a horizontal line. You could put | characters in the % lrrrrrrrrr string above to produce vertical lines. That is ugly. % Refrain. \hline\hline % Note that table columns are separated by & and the line ended by \\. Year: &1990 &1991 &1992 &1993 &1994 &1995 &1996 &1997 &all~~~\\ \hline % classic red Classic red &29195 &16000 &11729 &8415 &6013 &4888 &4006 &3950 &84196 \\ % brilliant black, but always dirty: Black & & &4626 &6111 &5741 &4877 &4063 &3702 &29120 \\ % british racing green, dark: BRG green & &3997 & & & & & & &3997 \\ % 1997 marina green, dark: Marina green & & & & & & & &3000 &3000 \\ % 1996 starlight blue, very dark: Starlight blue& & & & & & &3000 & &3000 \\ % 1995 merlot, dark purple: Merlot & & & & & &3500 & & &3500 \\ % 1997 twilight blue, dark: Twilight blue & & & & & & & &1500 &1500 \\ % montego blue, darkish: Montego blue & & & & &3003 &2818 &5742 &4571 &16134 \\ % sunburst yellow, light: Yellow & & &1515 & & & & & &1515 \\ % mariner blue, quite light: Mariner blue &6540 &3633 &2096 &1082 & & & & &13351 \\ % laguna blue, light: Laguna blue & & & & &1788 &440 & & &2228 \\ % silver stone metallic: Silver stone &3481 &5802 &1475 & & & & & &10758 \\ % chaste white: Chaste white & & & & &3565 &2945 &2160 &1929 &10599 \\ % crystal white: Crystal white &12420 &8855 &5195 &5874 & &122 & & &32466 \\ \hline Totals &51636 &38287 &26636 &21482 &20110 &19590 &18971 &18652 &215364\\ \hline\hline \end{tabular}} \end{table} Table \ref{tab:colors} lists the various colors in which the first-generation Miata was produced. They are sorted by car speed, relative to engine power. (Table \ref{tab:colors2} shows the same data sorted by total cars produced.) At first, some features of table \ref{tab:colors} may seem surprising. For example, you might reasonable assume that black Miatas would be slower than red ones. After all, black will absorb all colors of light, while red absorbs only nonred ones. However, black Miatas are notoriously difficult to keep clean. Because of the great variations in surface temperatures, dirt gets \lq\lq{}baked\rq\rq{} on. So black Miatas reflect a good deal of light due to the dirt. \begin{table}[htbp] \centering \caption{Like the first table, but sorted by total cars produced.} \label{tab:colors2} \latexhtml{\vspace*{.15in}}{}% \setlength{\unitlength}{1pt}\setlength{\tabcolsep}{3.3pt}% % In my opinion, LaTeX tables look better than html ones. To force % latex2html to use an image of the LaTeX table, it can be put % inside a picture environment like here. See the next figure for % more on this environment. \begin{picture}(405,237)(-202,0)%\htmlimage{scale=1.6}{}% %\put(-202,0){\framebox(405,237){}} % used for testing picture size \put(0,0){\makebox(0,0)[b]{\begin{tabular}{lrrrrrrrrr}\hline\hline Year: &1990 &1991 &1992 &1993 &1994 &1995 &1996 &1997 &all~~~\\ \hline % 1997 twilight blue, dark: Twilight blue & & & & & & & &1500 &1500 \\ % sunburst yellow, light: Yellow & & &1515 & & & & & &1515 \\ % laguna blue, light: Laguna blue & & & & &1788 &440 & & &2228 \\ % 1997 marina green, dark: Marina green & & & & & & & &3000 &3000 \\ % 1996 starlight blue, very dark: Starlight blue& & & & & & &3000 & &3000 \\ % 1995 merlot, dark purple: Merlot & & & & & &3500 & & &3500 \\ % british racing green, dark: BRG green & &3997 & & & & & & &3997 \\ % chaste white: Chaste white & & & & &3565 &2945 &2160 &1929 &10599 \\ % silver stone metallic: Silver stone &3481 &5802 &1475 & & & & & &10758 \\ % mariner blue, quite light: Mariner blue &6540 &3633 &2096 &1082 & & & & &13351 \\ % montego blue, darkish: Montego blue & & & & &3003 &2818 &5742 &4571 &16134 \\ % brilliant black, but always dirty: Black & & &4626 &6111 &5741 &4877 &4063 &3702 &29120 \\ % crystal white: Crystal white &12420 &8855 &5195 &5874 & &122 & & &32466 \\ % classic red Classic red &29195 &16000 &11729 &8415 &6013 &4888 &4006 &3950 &84196 \\ \hline Totals &51636 &38287 &26636 &21482 &20110 &19590 &18971 &18652 &215364\\ \hline\hline \end{tabular}}} \end{picture} \end{table} You might also wonder why the slower colors, and especially red, sold quite a large number of cars. The reason is psychological. A significant number of owners are somewhat wary of the speed of their Miatas. In private communications, Miata owners have told me that it feels \lq\lq{}somewhat scary, so without a roof in a small, fast, car.\rq\rq{} The reduced speed of red Miatas provides some sense of reassurance. Many red Miata owners also end up installing a hardtop on a semi-permanent basis. At the other side of the list, you find the hard-core enthusiasts who go for speed. (To be sure, some white Miata owners might also be attracted by the fact that the white Miatas do not need much effort to look clean. But surely, that is a small minority.) Another observation that may be surprising at first is why a yellow Miata might best several blue ones. After all, photon energy increases from red to yellow to green to blue. Actually, the yellow Miata has a lot of white thrown in. And various blue Miatas are really dark. While they do emit some blue, they absorb colors of all wavelengths. \begin{figure}[htbp]\latexhtml{\par}{} \centering \setlength{\unitlength}{1pt} % 72 pt = 1 inch % % The picture environment allows you to put labels, arrows, circles, % etcetera, in your figures. While gnuplot will put in labels, these % tend to clash with the style of the document fonts and with the % document font sizes. % % Using a picture environment allows you to put every label just % where you want it. And put every plot where you want it. % But it does require some trial and error to get the positions of % the labels just right. % % (If you think it is too much work, just let gnuplot put in the % labels and then position plots "curves" and "stretch" just like % "bozo" and "nobozo" were put in figure 1.) % % In this figure, the picture width is 400 units and the height 140. % The coordinates of the far left bottom point are 0 and 0. That % means that in "(x,y)" coordinate pairs, 0 < "x" < 400 and % 0 < "y" < 140. % % For more info, see http://en.wikibooks.org/wiki/LaTeX/Picture % \begin{picture}(400,140)(0,0) % The following \picfrbox command, when uncommented, puts a frame % around the total picture area. That is helpful when % experimenting in verifying that everything stays within the % limits defined above: %\put(0,0){\picfrbox(400,140){}} % The next line puts plot 'curves.eps' such that its bottom left % point ([bl]) is at coordinates 19 horizontally and 0 vertical. % Taking into account that the plot has a blank margin, this leaves % enough space below and to the left of the plot to put in labels. \put(19,0){\makebox(0,0)[bl]{\putpicture{curves}}} % For the plot 'stretch.eps', it is more convenient to specify the % location of its bottom right ([br]) point. The "x" value is 410 and % not 400 since the plot has a 10 point white margin at the right: \put(410,0){\makebox(0,0)[br]{\putpicture{stretch}}} % change to a smaller font: {\small % put labels on the curves (the [l] causes left-alignment of the label % to the specified position) \put(50,110){\makebox(0,0)[l]{$a(t)/a(0)$}} \put(150,112){\makebox(0,0)[l]{$v_{\rm p,w}(t)$}} \put(150,61){\makebox(0,0)[l]{$v_{\rm p,r}(t)$}} % Put in labels for the two left axes ([r] is right alignment): \put(27,15){\makebox(0,0)[r]{0\%}} \put(27,135.5){\makebox(0,0)[r]{100\%}} \put(274.5,15){\makebox(0,0)[r]{0}} \put(274.5,135.5){\makebox(0,0)[r]{1}} \put(275,90){\makebox(0,0)[r]{$v_{\rm p}/v_{\rm p,w}$}} % Put in labels for the two bottom axes (b and t are bottom and % top alignment; if there are no l or r inside [], these % labels are horizontally centered around the specified point): \put(30,3){\makebox(0,0)[b]{0}} \put(94,3){\makebox(0,0)[b]{10}} \put(140,0.5){\makebox(0,0)[bl]{$t$ (seconds)}} \put(276.8,3){\makebox(0,0)[b]{0}} \put(397,3){\makebox(0,0)[b]{1}} \put(340,0){\makebox(0,0)[b]{$v_{\rm i}/v_{\rm i,w}$}} } % end smaller font \end{picture} % If you also provide a shortened caption inside [], like the one % below, make sure there is NO LINEBREAK BETWEEN ] AND {. (Yes, a % latex2html quirk.) \caption[Speed difference between a white and a red Miata.]{Left: Speed difference between a white and a red Miata. This uses plot units. Right: the nonlinear stretching used to clarify the speed difference.} \label{fig:curves} \end{figure} % The tilde ~ in "Fig.~" below prevents the abbreviation point from % being regarded as the end of a sentence. (After such an end point % additional blank space would be inserted.) You could instead use % "Fig.\ " if you wanted to allow a line break behind the point. The left-hand graph in Fig.~\ref{fig:curves} compares the speed $v(t)$ of a red Miata to that of a white one. Here $v$ is the velocity and $t$ the time in seconds from rest. Subscripts w and r indicate the white and red Miatas, respectively. The velocity is taken relative to the terminal velocity of the white Miata. The acceleration $a(t)$, relative to the initial one $a(0)$, is also plotted. (The relative acceleration\index{acceleration} is the same for the Miatas, although the absolute acceleration of the red Miata is of course less.) For simplicity, CVT\index{CVT mode} mode is assumed. To clarify the speed difference, the velocity has been plotted on a slightly nonlinear scale. The right-hand graph shows this scaling. In it, $v_{\rm{i}}$ is the indicated speed and $v_{\rm{p}}$ the plotted speed. Note that this correction is reminiscent of the difference between indicated airspeed and true airspeed in aviation. The plotted speed takes here the place of the true airspeed in aviation. Mathematically, the velocity correction is given by \begin{displaymath} \frac{v_{\rm p}}{v_{\rm p,w}} = \frac{1+e^{1990^2(v_{\rm i}-v_{\rm i,w})/v_{\rm i,w}}}{2} \end{displaymath} Note that 1990 is the model year of the first Miatas. For convenience, the above curve can be approximated as piecewise linear. The purpose of this paper is to shed some theoretical light on the described empirical observations. It will be shown that special relativity combined with quantum mechanics directly implies the speed advantage of white Miatas. Therefore, the speed difference is not an experimental aberration but a scientific fact. \newoddpage % Do not use mathematics inside section titles. There would be big % font size issues on the web pages. In the worst case, fake it using % italics, like in \emph{x}: \chapter{Theoretical Background}\secname{theory} % Note the references to sections and the bibliographical citations: The Miata-light interaction is obviously described by the two pillars of modern physics, special relativity and quantum mechanics. Since the reader is surely well aware of quantum electrodynamics, either in % Use \lq{} and \rq{} for left and right quotes; they look better on % the web pages: Feynman\rq{}s path integral\index{Feynman|emph} approach or in canonical formulation, it needs no introduction. However, a few key results will be summarized in subsections \ref{sec:specrel} and \ref{sec:quantum} for ready reference. For more information, see % Bibliographical references are inserted using the cite command. % The key, like Feynman06 here, is whatever you put in the % references.bib file. (See \bibliography at the end of this file). \citep[pp.~1-152]{Feynman06}. A more easily accessible source may be \citep{QMFE}. \section{Special relativity} \secname{specrel} The speed of any Miata is small, but not vanishingly small, compared to the speed of light. (There are some mathematical issues associated with the previous statement that will be addressed in a planned second volume of this book.) Therefore relativistic mechanics must be used. Einstein\rq{}s famous relation\index{Einstein|emph} % Note that ^{...} creates a superscript and _{...} a subscript. % The \label allows you to refer to this equation elsewhere by the % mnemonic \ref{eq:emc2}. Do *not* put the \label on a line by % itself, but *do* put a % behind it, (yes, a latex2html quirk): \begin {equation} E = m c^{2} \label{eq:emc2}% \end {equation} % If you just want mathematics without an equation number, use % the displaymath environment. For a multiline equation, see below. implies that a moving Miata picks up additional mass. However, the principle of relativity, as first formulated by % the following index entry uses the unaccented string Poincare as the sort % key in the index, but the accented version behind @ is actually printed: Poincar\'e\index{Poincare@Poincar\'e|emph}, allows the viewpoint of a driver inside the Miata. Physics is the same regardless of the relative motion of the observers. The driver viewpoint will frequently be used in the current paper to simplify the arguments. % Note that mathematics inside the text is enclosed between dollar % signs. Also note \sqrt for square root and \frac for fraction. The most important relation for the purpose of this paper is the relativistic Doppler shift. The equation that governs the difference in observed wavelength $\lambda$ of light, and the corresponding difference in observed frequency $\omega$, between moving observers is % The eqnarray environment is good for lining up equations on separate % lines, or for splitting a long single equation over separate lines. % Note that the center (equals signs) column is surrounded by & and &, % and that a new line is started with \\. The \nonumber is used to % prevent an equation number from being inserted in that line. If you % do not want equation numbers at all, use the eqnarray* environment % instead. {\setlength{\jot}{9pt}% extra space between the rows \begin{eqnarray} \lambda_v & = & \lambda_0 \sqrt{\frac{c + v}{c - v}} \nonumber \\ \omega_v & = & \omega_0 \sqrt{\frac{c - v}{c + v}} \label{eq:relds}% \end{eqnarray}} % For equations with a long left-hand side, you sometimes want to allow % the left hand side to stick out over the right hand side. Use the % \lefteqn{...} command to do so. To see it in action, remove the % leading % signs from the next eqnarray: %\begin{eqnarray*} % \lefteqn{\langle\Psi_1(\vec r_1,S_{z1},\vec r_2,S_{z2};t)| % \Psi_2(\vec r_1,S_{z1},\vec r_2,S_{z2};t)\rangle =} \\ % &&\!\! % \sum_{S_{z1} = \pm\frac12\hbar} \sum_{S_{z2} = \pm\frac12\hbar} % \int_{{\rm all}\ \vec r_1} \int_{{\rm all}\ \vec r_2} % \Psi_1^*(\vec r_1,S_{z1},\vec r_2,S_{z2};t) % \Psi_2(\vec r_1,S_{z1},\vec r_2,S_{z2};t) % \,{\rm D}^3 \vec r_1 \,{\rm D}^3 \vec r_2 %\end{eqnarray*} Here the subscript 0 stands for the emitter of the light, and subscript $v$ for an observer moving with speed $v$ away from the emitter. If the observer moves towards the emitter, $v$ is negative. (To be true, the formulae above apply whether the observer 0 is emitting the light or not. But in most practical applications, observer 0 is indeed the emitter.) Of course, Miatas do not drive in vacuum but in the atmosphere. Fortunately, this effect may be ignored as secondary on light propagation as long as no % Note that subscripts, and superscripts, can only be used inside a % math enclosure: significant H$_{2}$O in liquid form is present. (In any case, Miatas are known to disagree with these so-called \lq\lq{}rain\rq\rq{} conditions.) However, the atmosphere is very important because of aerodynamic drag. These issues will be addressed further in subsection \ref{sec:aero}. \section{Quantum mechanics} \secname{quantum} % Note the umlaut: Schr\"odinger\index{Schrodinger@Schr\"odinger|emph}, in his famous equation, associated energy with the partial time differentiation operator, and linear momentum with the partial space differentiation operator in a given direction: % \!, \,, \:, \;, \quad, and \qquad provide increasing amounts of % blank space in equations (\! is negative!): \begin{equation} E\quad\Longleftrightarrow\quad i\hbar\frac{\partial}{\partial t} \qquad p_x\quad\Longleftrightarrow\quad -i\hbar\frac{\partial}{\partial x} \label{eq:se}% \end{equation} Here $\hbar$ is the scaled Planck\rq{}s constant and $i$ is $\sqrt{-1}$. The above results are of critical importance for this paper, because the Miata-light interaction is due to exchange of the energy and momentum of photons\index{photon|textrm} of light. Therefore, it is helpful to make the above relations specific for photons: \begin{equation} E = \hbar\omega \qquad p = \hbar \frac{\omega}{c} \label{eq:photon}% \end{equation} These expressions are known as the Planck-Einstein\index{Planck|emph} and de Broglie\index{de Broglie|emph} relations. They may be derived by applying Schr\"odinger\rq{}s associations on a complex, propagating monochromatic light wave. As is well known, the first expression is consistent with Einstein\rq{}s relation (\ref{eq:emc2}) in view of the fact that photons have zero rest mass. \section{Aerodynamics}\secname{aero}% \index{aerodynamics!intro} The primary factor limiting the maximum speed of a Miata is aerodynamic resistance. This resistance is related to boundary layers along the surface of the Miata in which the air is being dragged along. Going downstream, this air forms a wake behind the Miata. The wake is the primary cause of resistance, \citep[see][pp.~570-571]{Prandtl61}\index{Prandtl|emph}. The wake is always relatively wide because the boundary layer separates from the surface at some point, \citep{VanD81,VanD_Shen82,VanD_Cowley90}. This greatly increases the aerodynamic resistance. Controlling separation remains a difficult % Note the use of \citet to get the author(s) listed in the text: problem, as discussed by \citet{Shen_Xiao90}. There is also the problem that the boundary layer is normally turbulent. By itself, turbulence will increase drag due to its thermodynamically irreversible mechanics, \citep{Walker88}. However, often transition to turbulence decreases drag instead because it also tends to delay separation. The high speed of, in particular, white Miatas, will also bring in compressibility effects, \citep{Ackeret_Feldmann_Rott47}. Note that such effects are largest in elevated speed areas such as near the top of the windshield header. \newoddpage \chapter{Photon-Surface Interactions} \secname{mechanisms} % If you really, really, want to insist that a figure is placed % exactly where you put it, uncomment the \usepackage{float} line % in the header and then replace the [htbp] below with [H]: \begin{figure}[htbp]\latexhtml{\par}{} \centering % For images including bitmaps (photographs, or more general % pictures in .jpg, .gif, .bmp, etcetera, format) the next line is % needed for better image quality on the web pages: \htmlimage{extrascale=3,notransparent}{} % Compare the quality of this picture on the web pages with the first % figure. It is better. Look at the noses of the Miatas! \setlength{\unitlength}{1pt} % 1 pt = 1 inch / 72 % Here the picture width is 400 units and the height 55. The coordinates % of the far left bottom point are -200 and 0. That means that in "(x,y)" % coordinate pairs, -200 < "x" < 200 and 0 < "y" < 55. \begin{picture}(400,55)(-200,0) \thinlines %\put(-200,0){\picfrbox(400,55){}} % The next line puts picture bozo.eps such that its bottom center % point ([b]) is at coordinates -100 horizontally and 0 vertical. % So it is centered in the left half of the graph. \put(-100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{bozo}}}} % Similarly, the bottom center of nobozo.eps is at +100 and 0: \put(100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{nobozo}}}} % Put in the arrows using \put(x,y){\vector(rw,rh){length}} where % -4 < rw < 4 and -4 < rh < 4 are the relative width and height. % The values rh and rw must be in whole units with no common divisor. % The "length" is measured horizontally unless the arrow is vertical, % (rw = 0), in whih case it is measured vertically. \put(-150,26){\vector(3,-1){30}} \put(-120,16){\vector(1,1){20}} \put(50,26){\vector(3,-1){30}} \put(80,16){\vector(2,3){10}} % (For lines without arrow heads, use \line instead of \vector.) % Put in the "photon gamma" labels (note the use of the \makebox with % a [r] to right-align the string to the specified (x,y), near the % start of the arrows): \put(-152,27){\makebox(0,0)[r]{photon $\gamma$}} \put(48,27){\makebox(0,0)[r]{photon $\gamma$}} % In rare cases, some part of your figure might be improperly % clipped on the web pages. Putting a tiny rule in the problem % corner can fix that, like say: \put(-200,0){\rule{.2pt}{.2pt}} \end{picture} % If you also provide a shortened caption inside [], like the one % below, make sure there is NO LINEBREAK BETWEEN ] AND {. (Yes, a % latex2html quirk.) \caption[Photon-surface interaction mechanisms.]{Photon-surface interaction mechanisms. They depend on photon wavelength. Photos \copyright{} Leon van Dommelen.} \label{fig:bozo2} \end{figure} At this stage, the photon-surface interaction can be understood to the required detail. Figure \ref{fig:bozo2} above shows how an incoming photon of light, $\gamma$, interacts with a white and a nonwhite Miata. The white Miata will reflect or emit photons of all colors. However, a red Miata will mostly emit red photons. If a red Miata absorbs a blue photon and releases its energy as heat, the momentum of the photon is gone. The red Miata has effectively stopped the photon. Because of Newton\rq{}s third law, action equals minus reaction, the red Miata experiences an opposite force slowing it down. That would hold even if all the photon energy was emitted again as omnidirectional infrared radiation. On the other hand, as illustrated in figure \ref{fig:bozo2}, the white Miata leaves the backward moving momentum of the photon largely intact, assuming a predominantly specular emission. The vertical momentum does change more significantly. But that merely presses the white Miata more strongly onto the road, providing an additional measure of safety at its higher speeds. (As the Planck-Einstein and the Broglie relations show, photon energy is proportional to momentum. It is not proportional to square momentum, as Newtonian physics would suggest. So if a red Miata re-emitted all incoming photon energy as radiation, and if that radiation was predominantly specular with respect to the incoming photon, then there would not be a difference between the Miatas. Unfortunately, neither condition is true.) You might of course wonder whether the advantage of the white Miata would not be offset by photons coming from other directions. There is something to that. It should be stressed that a Miata, of any color, in an equilibrium situation with blackbody radiation coming from all directions, will \emph{not} experience a net force. Any other statement would obviously violate the second law of thermodynamics. And this paper would never suggest it would not. Only the highest standards of scientific integrity are applied in this work. However, for a \emph{moving} Miata, the photons coming from the front are \emph{blue-shifted}. That is described by the relativistic Doppler shift (\ref{eq:relds}). This increases their energy, and as a result, a moving Miata on an otherwise equilibrium earth experiences a photon drag slowing it down. Photons like the example in figure \ref{fig:bozo2} dominate. As a result, the Miata will experience a photon drag. But a white Miata will experience less drag because it slows down the dominant photons less. It is also interesting to look at nonequilibrium situations. In particular, on sunny days the photon distribution is far from a blackbody one. Photons come predominantly from a concentrated source: the sun. Now if the sun is in front of the Miata, figure \ref{fig:bozo2} showed that a white Miata experiences less photon drag. You might now of course conjecture that if the sun is in the back, then this advantage could reverse. That in that case, a red Miata might have an advantage. Unfortunately, that is not true. Figure \ref{fig:bozo3} shows what happens. In this case, there is a \lq\lq{}solar sail\rq\rq{} effect\index{solar sail effect}. This effect, well established for interstellar travel, actually provides a propulsive force for the Miata. Now if a photon is simply absorbed by a red Miata, its momentum adds to that red Miata. But if a photon is reflected by a white Miata, \emph{double} its momentum is added to that white Miata. Of course, the real situation is more complex. A white Miata is not a perfect reflector, and a red Miata not a perfect absorber. Figure \ref{fig:bozo3} tries to capture the average situation. Still, the white Miata experiences a much greater solar sail effect. \begin{figure}[htbp]\latexhtml{\par}{} \centering \htmlimage{extrascale=3,notransparent}{} \setlength{\unitlength}{1pt} \begin{picture}(400,55)(-200,0) \thinlines %\put(-200,0){\picfrbox(400,55){}} \put(-100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{bozo}}}} \put(100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{nobozo}}}} \put(-58,24){\vector(-3,-1){30}} \put(-88,14){\vector(4,-1){27}} \put(142,24){\vector(-3,-1){30}} \put(112,14){\vector(1,-1){10}} \put(-56,25){\makebox(0,0)[l]{photon $\gamma$}} \put(144,25){\makebox(0,0)[l]{photon $\gamma$}} \end{picture} \caption{The solar sail effect.} \label{fig:bozo3} \end{figure} There is another important effect that Miata owners often ignore. The high-energy radiation absorbed by a red Miata comes out primarily as heat. Now heated air at the surface of the red Miata wants to rise away from the Miata because it is lighter than the surrounding air at the same pressure. Clearly, that will promote separation, the primary effect limiting the speed of a Miata. True, the rising air will also promote turbulence, which might delay separation a bit. However, it is to be expected that global buoyancy will dominate and separation will be promoted. This will greatly increase the aerodynamic drag of a red Miata. \begin{figure}[htbp] \centering % Here the latex is kept simple. The labels were put in by gnuplot, % so all we need to do is insert the plot and add a caption. \putpicture{contour} \caption[G\"ortler vortex system in the boundary layer on a white Miata at speed.]{G\"ortler vortex system in the boundary layer on a white Miata at speed. Inferred from theoretical observations by Van Dommelen and Yapalparvi.} \label{fig:contour} \end{figure} On the other hand, current work by the author and Yapalparvi, (in progress), suggests that the lower surface temperatures of a white Miata will generate a \lq\lq{}G\"ortler\rq\rq{} vortex system that may be very efficient in delaying separation. Figure \ref{fig:contour} shows the expected motion of the system. Note that this represents just a very small segment of the thin boundary layer, looking upstream. With the advantageous photon interaction, in addition to the enhancement of the aerodynamics\index{aerodynamics!enhancement} by the G\"ortler system, the much higher speed of white Miatas is clearly fully explained. \newoddpage \chapter{Concluding Remarks} \secname{conclusion} The claim that white Miatas are noticeably faster than other ones, and in particular red ones, is commonly considered with considerable skepticism. It is often argued that this experimental observation is due to observational bias of some Miata owners and is not supported by independent verification. The analysis in this paper, however, clearly shows that such skepticism\index{skepticism!unjustified} is unjustified. For solid theoretical reasons, white Miatas cannot be anything else than faster than other colors. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% APPENDICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Any \chapter chapters after this point will be formatted as % appendices, numbered A, B, ... \appendix \newoddpage \chapter{More Details} \secname{more} This appendix has deliberately been left empty, to convey the sense of peace and quiet that comes from driving a Miata. %%%%%%%%%%%%%%%%%%%%%%% REFERENCES/BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%% % This sets the name of the references section: \renewcommand{\bibname}{References} % If your references include additional items *not* cited in the text, % replace {References} above by {Bibliography}. % Note: use the \nocite command to add such references to the list. % The next line sets the style of the bibliographical references (see % the documentation of the natbib package for more details): \bibliographystyle{plainnat} % {plainnat} means sorted alphabetically. {unsrtnat} is in order of % appearance, and {abbrvnat} is a more compact version of {plainnat}. \newoddpage % The references need to be put in a file references.bib % You can open this file with an editor to see example references. % Then add your own references to it following these examples. \bibliography{references} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% INDEX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newoddpage {% limits the scope of the index related commands %begin{latexonly} % The next line is to assure correct active links to the index: \phantomsection % And we add the index to the contents as if it was a chapter: \addcontentsline{toc}{chapter}{Index} % The following lines are a fix to allow page numbers in the index that are % shown emphasized or underlined and are still active. Note that we disable % the textrm command in the index this way; sorry about that. \renewcommand{\emph}[1]{\textit{\hyperpage{#1}}} % for \index{...|emph} entries \renewcommand{\textrm}[1]{\underline{\hyperpage{#1}}} % for \index{..|textrm} % Print the actual index in a smaller font: \footnotesize %end{latexonly} \printindex }% end of the scope of the index related commands %%%%%%%%%%%%%%%%%%%%%%%%%%% END OF DOCUMENT %%%%%%%%%%%%%%%%%%%%%%%%%%%% % All done: \end{document}