% format file for An Introduction to Thermal Physics
% (for use with TeXtures)

\catcode`\@=11             % This allows us to modify PLAIN macros.
%% CM math fonts
%% chapter opening fonts:
\font\chapnumfont = cmssbx10 at 48pt
\font\chaptitlefont = cmss17 at 20pt
\font\chapchapfont = cmss17 at 14pt
%% These fonts are needed for math to work in all sizes
%% 14 points
\font\fourteenrm =cmr12 at 14pt
\font\fourteeni  =cmmi12 at 14pt  \skewchar\fourteeni='177
\font\fourteensy =cmsy10 at 14pt  \skewchar\fourteensy='60
\font\fourteenex =cmex10 at 14pt
\font\fourteenbf =cmbx12 at 14pt
\font\fourteensl =cmsl12 at 14pt
%% 12 points
\font\twelverm=cmr12 
\font\twelvei=cmmi12           \skewchar\twelvei='177
\font\twelvesy=cmsy10 at 12pt  \skewchar\twelvesy='60
\font\twelveex=cmex10 at 12pt
\font\twelvebf=cmbx12
\font\twelvett=cmtt12
\font\twelvesl=cmsl12
\font\twelveit=cmti12
\font\twelvemib=cmmib10 at 12pt  % for bold math in section headings
%% 11 points
\font\elevenrm=cmr10 at 11pt
\font\eleveni=cmmi10 at 11pt  \skewchar\eleveni='177
\font\elevensy=cmsy10 at 11pt \skewchar\elevensy='60
\font\elevenex=cmex10 at 11pt
\font\elevenbf=cmbx10 at 11pt
\font\eleventt=cmtt10 at 11pt
\font\elevensl=cmsl10 at 11pt
\font\elevenit=cmti10 at 11pt
%% 10 points
\font\tenrm=cmr10
\font\teni=cmmi10   \skewchar\teni='177
\font\tensy=cmsy10  \skewchar\tensy='60
\font\tenbf=cmbx10
\font\tentt=cmtt10
\font\tensl=cmsl10
\font\tenit=cmti10
\font\tenss=cmss10
\font\tenssb=cmssbx10
\font\tenmib=cmmib10
%% 9 points
\font\ninerm=cmr9
\font\ninei=cmmi9   \skewchar\ninei='177
\font\ninesy=cmsy9  \skewchar\ninesy='60
\font\nineex=cmex10 at 9pt
\font\ninebf=cmbx9
\font\ninesl=cmsl9
\font\ninett=cmtt9
\font\nineti=cmti9
\font\niness=cmss9
\font\ninessb=cmssbx10 at 9pt
\font\ninemib=cmmib10 at 9pt
%% 8 points
\font\eightrm=cmr8
\font\eighti=cmmi8  \skewchar\eighti='177
\font\eightsy=cmsy8 \skewchar\eightsy='60
\font\eightbf=cmbx8
%% 7 points
\font\sevenrm=cmr7
\font\seveni=cmmi7  \skewchar\seveni='177
\font\sevensy=cmsy7 \skewchar\sevensy='60
\font\sevenbf=cmbx7
%% 6 points
\font\sixrm=cmr6
\font\sixi=cmmi6  \skewchar\sixi='177
\font\sixsy=cmsy6 \skewchar\sixsy='60
\font\sixbf=cmbx6
%% 5 points
\font\fiverm=cmr5
\font\fivei=cmmi5  \skewchar\fivei='177
\font\fivesy=cmsy5 \skewchar\fivesy='60
\font\fivebf=cmbx5

\newskip\ttglue

% fourteenpoint needed only for chapter titles; limited math capability
\def\fourteenpoint{\def\rm{\fam0\fourteenrm}%
\textfont0=\fourteenrm \scriptfont0=\twelverm  \scriptscriptfont0=\tenrm
\textfont1=\fourteeni  \scriptfont1=\twelvei   \scriptscriptfont1=\teni
\textfont2=\fourteensy \scriptfont2=\twelvesy  \scriptscriptfont2=\tensy
\textfont3=\fourteenex \scriptfont3=\fourteenex
                       \scriptscriptfont3=\fourteenex
\fourteenbf}

\def\twelvepoint{\def\rm{\fam0\twelverm}%
  \textfont0=\twelverm \scriptfont0=\ninerm  \scriptscriptfont0=\sixrm
  \textfont1=\twelvei  \scriptfont1=\ninei   \scriptscriptfont1=\sixi
  \textfont2=\twelvesy \scriptfont2=\ninesy  \scriptscriptfont2=\sixsy
  \textfont3=\twelveex \scriptfont3=\twelveex \scriptscriptfont3=\twelveex
  \textfont\itfam=\twelveit \def\it{\fam\itfam\twelveit}%
  \textfont\slfam=\twelvesl \def\sl{\fam\slfam\twelvesl}%
  \textfont\ttfam=\twelvett \def\tt{\fam\ttfam\twelvett}%
  \textfont\bffam=\twelvebf \scriptfont\bffam=\eightbf
  \scriptscriptfont\bffam=\sixbf \def\bf{\fam\bffam\twelvebf}%
  \tt \ttglue=.5em plus.25em minus.15em
  \normalbaselineskip=14.4pt%
  \setbox\strutbox=\hbox{\vrule height9.7pt depth4.7pt width0pt}%
  \normalbaselines\rm \b@gheight=12pt}

\def\elevenpoint{\def\rm{\fam0\elevenrm}%
  \textfont0=\elevenrm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm
  \textfont1=\eleveni  \scriptfont1=\seveni  \scriptscriptfont1=\fivei
  \textfont2=\elevensy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy
  \textfont3=\elevenex \scriptfont3=\elevenex   \scriptscriptfont3=\elevenex
  \textfont\itfam=\elevenit \def\it{\fam\itfam\elevenit}%
  \textfont\slfam=\elevensl \def\sl{\fam\slfam\elevensl}%
  \textfont\ttfam=\eleventt \def\tt{\fam\ttfam\eleventt}%
  \textfont\bffam=\elevenbf \scriptfont\bffam=\sevenbf
  \scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\elevenbf}%
  \tt \ttglue=.5em plus.25em minus.15em
  \normalbaselineskip=13.2pt%
  \setbox\strutbox=\hbox{\vrule height9.1pt depth4.1pt width0pt}%
  \normalbaselines \b@gheight=11pt\rm}

\def\tenpoint{\def\rm{\fam0\tenrm}%
  \textfont0=\tenrm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm
  \textfont1=\teni  \scriptfont1=\seveni  \scriptscriptfont1=\fivei
  \textfont2=\tensy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy
  \textfont3=\tenex \scriptfont3=\tenex   \scriptscriptfont3=\tenex
  \textfont\itfam=\tenit \def\it{\fam\itfam\tenit}%
  \textfont\slfam=\tensl \def\sl{\fam\slfam\tensl}%
  \textfont\ttfam=\tentt \def\tt{\fam\ttfam\tentt}%
  \textfont\bffam=\tenbf \scriptfont\bffam=\sevenbf
  \scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\tenbf}%
  \tt \ttglue=.5em plus.25em minus.15em
  \normalbaselineskip=12.5pt% % could take this down to 12
  \setbox\strutbox=\hbox{\vrule height8.5pt depth3.5pt width0pt}%
  \abovedisplayskip=11pt plus 4pt minus 7pt
  \belowdisplayskip=11pt plus 4pt minus 7pt
  \abovedisplayshortskip=0pt plus 4pt
  \belowdisplayshortskip=7pt plus 4pt minus 3pt
  %\let\big=\tenbig 
  \normalbaselines \b@gheight=10pt\rm}

\def\ninepoint{\def\rm{\fam0\ninerm}%
  \textfont0=\ninerm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm
  \textfont1=\ninei  \scriptfont1=\seveni  \scriptscriptfont1=\fivei
  \textfont2=\ninesy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy
  \textfont3=\nineex  \scriptfont3=\nineex   \scriptscriptfont3=\nineex
  \textfont\itfam=\nineti \def\it{\fam\itfam\nineti}%
  \textfont\slfam=\ninesl \def\sl{\fam\slfam\ninesl}%
  \textfont\ttfam=\ninett \def\tt{\fam\ttfam\ninett}%
  \textfont\bffam=\ninebf \scriptfont\bffam=\sevenbf
  \scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\ninebf}%
  \tt \ttglue=.5em plus.25em minus.15em
  \normalbaselineskip=11pt  % could increase this to 11.5
  \setbox\strutbox=\hbox{\vrule height8pt depth3pt width0pt}%
  \abovedisplayskip=7pt plus 4pt minus 4.5pt
  \belowdisplayskip=7pt plus 4pt minus 4.5pt
  \abovedisplayshortskip=0pt plus 4pt
  \belowdisplayshortskip=5pt plus 4pt minus 2.5pt
  %\let\big=\ninebig 
  \normalbaselines \b@gheight=9pt\rm}

\newdimen\b@gheight \b@gheight=10pt
\def\big#1{{\hbox{$\left#1\vbox to 0.85\b@gheight{}\right.\n@space$}}}
\def\Big#1{{\hbox{$\left#1\vbox to 1.15\b@gheight{}\right.\n@space$}}}
\def\bigg#1{{\hbox{$\left#1\vbox to 1.45\b@gheight{}\right.\n@space$}}}
\def\Bigg#1{{\hbox{$\left#1\vbox to 1.75\b@gheight{}\right.\n@space$}}}

\catcode`\@=12              % at signs are no longer letters

% end of font stuff

\tenpoint
\parskip=0pt  % no stretch

\hsize=30pc\hoffset=.8in
\vsize=47pc\voffset=.375in
\parindent=15pt


% running heads (actual headings are set by chapter and section macros):

\def\TLcrop{\llap{\smash{\raise.585in\hbox{\special{illustration 
                       topcrop}}}\hskip1.91in}}
\def\TRcrop{\llap{\smash{\raise.585in\hbox{\special{illustration 
                       topcrop}}}\hskip1.305in}}
\def\BLcrop{\llap{\smash{\lower.73in\hbox{\special{illustration
                       bottomcrop}}}\hskip1.91in}}
\def\BRcrop{\llap{\smash{\lower.73in\hbox{\special{illustration
                       bottomcrop}}}\hskip1.305in}}

\def\rheadfont{\ninerm}
\def\pagenofont{\ninebf}
\newif\ifchapterbegin
%\headline={\ifchapterbegin\ifodd\pageno\TRcrop\else\TLcrop\fi\hfill\else
%    \ifodd\pageno\TRcrop\rightheadline
%    \else\TLcrop\leftheadline\fi\fi}
%\footline={\ifchapterbegin\ifodd\pageno\BRcrop\else\BLcrop\fi
%               \hss{\pagenofont\folio}\hss\global\chapterbeginfalse
%    \else\ifodd\pageno\BRcrop\hfill
%         \else\BLcrop\hfill\fi\fi}
\headline={\ifchapterbegin\hfill\else
    \ifodd\pageno\rightheadline
    \else\leftheadline\fi\fi}
\footline={\ifchapterbegin
               \hss{\pagenofont\folio}\hss\global\chapterbeginfalse
    \else\hfill\fi}


% variables to store numbers:

\newcount\chapternumber
\newcount\sectionnumber
\newcount\problemnumber
\newcount\partnumber
\newcount\figurenumber
\newcount\tablenumber

\newif\ifappendix

\newskip\pagenoskip  % amount by which page number sticks out
\pagenoskip=3pc


% chapter and section macros:

\def\chapnum{\ifappendix\appletter\else\number\chapternumber\fi}

\def\chapter#1#2{\vfill\eject\appendixfalse\chapterbegintrue
  \global\chapternumber=#1\global\sectionnumber=0
  \global\problemnumber=0\global\equanumber=0
  \global\figurenumber=0\global\tablenumber=0
  \gdef\leftheadline{\llap{\rlap{\pagenofont\folio}\hskip\pagenoskip}{\rheadfont
   Chapter #1\hskip1pc #2}\hfill}%
  \vglue 1.5in\noindent{\chapnumfont#1\ }%
  \vtop{\hsize=22pc\def\ {\hfil\break}\baselineskip=24pt\chaptitlefont\noindent #2}
%  \vglue 1.5in\leftline{{\chapchapfont Chapter\ }{\chapnumfont#1}}%
%  \vskip12pt\leftline{\chaptitlefont#2}%
  \vskip-\pagetotal\vskip3.0in}

\def\appendix#1#2{\vfill\eject\appendixtrue\chapterbegintrue
  \gdef\appletter{#1}\global\sectionnumber=0
  \global\problemnumber=0\global\equanumber=0
  \global\figurenumber=0\global\tablenumber=0
  \gdef\leftheadline{\llap{\rlap{\pagenofont\folio}\hskip\pagenoskip}{\rheadfont
   Appendix #1\hskip1pc #2}\hfill}%
  \vglue 1.5in\noindent{\chapnumfont#1\ }%
  \vtop{\hsize=22pc\def\ {\hfil\break}\baselineskip=24pt\chaptitlefont\noindent #2}
%  \vglue 1.5in\leftline{{\chapchapfont Appendix\ }{\chapnumfont#1}}%
%  \vskip12pt\leftline{\chaptitlefont#2}%
  \vskip-\pagetotal\vskip3.0in}

% for front matter:
\def\nonumchapter#1{\vfill\eject\appendixfalse\chapterbegintrue
  \gdef\leftheadline{\llap{\rlap{\pagenofont\folio}\hskip\pagenoskip}{\rheadfont
   #1}\hfill}%
  \gdef\rightheadline{\hfill{\rheadfont #1}%
    \rlap{\hskip\pagenoskip\llap{\pagenofont\folio}}}
  \vglue .9in\noindent{\chapnumfont\vphantom{9}}%
  \vtop{\hsize=20pc\def\ {\hfil\break}\baselineskip=24pt\chaptitlefont\noindent #1}
  \vskip-\pagetotal\vskip2.4in}

\def\endmatter#1{\vfill\eject\appendixfalse\chapterbegintrue
  \gdef\leftheadline{\llap{\rlap{\pagenofont\folio}\hskip\pagenoskip}{\rheadfont
   #1}\hfill}%
  \gdef\rightheadline{\hfill{\rheadfont #1}%
    \rlap{\hskip\pagenoskip\llap{\pagenofont\folio}}}
  \vglue .9in\noindent{\chapnumfont\vphantom{9}}%
  \vtop{\hsize=20pc\def\ {\hfil\break}\baselineskip=24pt\chaptitlefont\noindent #1}
  \vskip-\pagetotal\vskip2.4in}

\newskip\beforesectionskip
\beforesectionskip=20pt plus 10pt minus 4pt
\newskip\aftersectionskip
\aftersectionskip=7pt plus 2pt minus 1pt

\def\section#1{\dimen0=\pagetotal\advance\dimen0 by 1.5in
  \ifdim\dimen0>\pagegoal       % if no room on current page
     \ifdim\pagetotal>\pagegoal % if already past ideal length
       \vskip\beforesectionskip\goodbreak % try to invoke o.r.
       \else\vfill\eject\fi     % otherwise force break
     \else\vskip\beforesectionskip\fi
%\vskip\beforesectionskip\goodbreak
  \global\advance\sectionnumber by 1
  \gdef\rightheadline{\hfill
    {\rheadfont\chapnum.\number\sectionnumber\hskip1pc #1}%
    \rlap{\hskip\pagenoskip\llap{\pagenofont\folio}}}
  \noindent
  {\twelvepoint\bf \chapnum.\number\sectionnumber\ \ #1}\vskip\aftersectionskip}

\newskip\beforesubsectionskip
\beforesubsectionskip=12pt plus 6pt minus 2pt
\newskip\aftersubsectionskip
\aftersubsectionskip=4pt plus 1pt minus 1pt

\def\subsection#1{\dimen0=\pagetotal\advance\dimen0 by 1.0in
  \ifdim\dimen0>\pagegoal       % if no room on current page
     \ifdim\pagetotal>\pagegoal % if already past ideal length
       \vskip\beforesubsectionskip\goodbreak % try to invoke o.r.
       \else\vfill\eject\fi     % otherwise force break
     \else\vskip\beforesubsectionskip\fi
%\vskip\beforesubsectionskip\goodbreak
     \noindent{\bf #1}\vskip\aftersubsectionskip}


% problems:
\def\problem#1{\global\advance\problemnumber by 1
               \global\partnumber=96
               {\vskip6pt plus 4pt minus 1pt\goodbreak\narrower\noindent
               \ninepoint
               {\bf Problem \chapnum.\number\problemnumber.} 
                #1\par}}
\def\part{\global\advance\partnumber by 1
            \vskip 3pt plus 1pt minus 1pt\itemitem{\bf(\char\the\partnumber)}}

\def\probname#1{\xdef#1{\hbox{\chapnum.\number\problemnumber}}}
% give a problem a name for later reference

% tables:

\def\table#1#2{\midinsert\vskip-0pt$$#1$$\medskip
       \global\advance\tablenumber by 1
       {\narrower\ninepoint
       \noindent{\bf Table \chapnum.\number\tablenumber.} #2\par}
       \endinsert}

\def\tabletop#1#2{\topinsert\vskip-\abovedisplayskip\vskip3pt$$#1$$\medskip
       \global\advance\tablenumber by 1
       {\narrower\ninepoint
       \noindent{\bf Table \chapnum.\number\tablenumber.} #2\par}
       \endinsert}

\def\tableNarrowCap#1#2{\midinsert\vskip-0pt$$#1$$\medskip
       \global\advance\tablenumber by 1
       {\narrower\narrower\ninepoint
       \noindent{\bf Table \chapnum.\number\tablenumber.} #2\par}
       \endinsert}

% table with caption at right.  parameters are table, width, caption
\def\tableRightCap#1#2#3{
  \dimen0=\hsize \advance\dimen0 by -#2 \advance\dimen0 by -3.5\parindent
  \global\advance\tablenumber by 1
  \midinsert
  \vskip-\abovedisplayskip
  $$
  \vcenter{#1}
  \hskip1.5\parindent\vcenter{\hsize=\dimen0\noindent\ninepoint
  \tolerance=800
  {\bf Table \chapnum.\number\tablenumber.} #3}
  $$
  \vskip-\belowdisplayskip
  \endinsert}

\newcount\tablecount
\def\nexttable{\tablecount=\tablenumber
                \advance\tablecount by 1
                \chapnum.\number\tablecount}
\def\nextnexttable{\tablecount=\tablenumber
                \advance\tablecount by 2
                \chapnum.\number\tablecount}
\def\lasttable{\chapnum.\number\tablenumber}
\def\lastlasttable{\tablecount=\tablenumber
                \advance\tablecount by -1
                \chapnum.\number\tablecount}
\def\tablename#1{\xdef#1{\hbox{\chapnum.\number\tablenumber}}}

\def\tablerule{\noalign{\vskip2pt\hrule\vskip4pt}}


% figures:

% main figure macro.  parameters are filename, vsize, hsize, caption
\def\figure#1#2#3#4{\midinsert\vglue#2
  \dimen0=#3\noindent\hskip.5\hsize\hskip-.5\dimen0
  \special{illustration #1}\par\medskip
  \global\advance\figurenumber by 1
  {\narrower\ninepoint
   \noindent{\bf Figure \chapnum.\number\figurenumber.} #4\par}
  \endinsert}

% version that makes the caption narrower, for use in problems:
\def\figureNarrowCap#1#2#3#4{\midinsert\vglue#2
  \dimen0=#3\noindent\hskip.5\hsize\hskip-.5\dimen0
  \special{illustration #1}\par\medskip
  \global\advance\figurenumber by 1
  {\narrower\narrower\ninepoint
   \noindent{\bf Figure \chapnum.\number\figurenumber.} #4\par}
  \endinsert}

% figure with caption to right.  #4 is horizontal shift to left
\def\figureRightCap#1#2#3#4#5{\dimen0=\hsize
  \advance\dimen0 by -#3
  \advance\dimen0 by -3\parindent
  \global\advance\figurenumber by 1
  \midinsert
  \vskip-\abovedisplayskip
  $$
  \hskip-#4
  \vcenter to #2{\vfill\hbox to #3{\special{illustration #1}\hfill}}
  \hskip#4
  \hskip\parindent\vcenter{\hsize=\dimen0\noindent\ninepoint
  \tolerance=1200
  {\bf Figure \chapnum.\number\figurenumber.} #5}
  $$
  \vskip-\belowdisplayskip
  \endinsert}
% increase the tolerance for the caption in both of these macros

% figure with caption to left.
\def\figureLeftCap#1#2#3#4#5{\dimen0=\hsize
  \advance\dimen0 by -#3
  \advance\dimen0 by -3\parindent
  \global\advance\figurenumber by 1
  \midinsert
  \vskip-\abovedisplayskip
  $$
  \vcenter{\hsize=\dimen0\noindent\ninepoint
  \tolerance=800
  {\bf Figure \chapnum.\number\figurenumber.} #5}
  \hskip\parindent
  \hskip-#4
  \vcenter to #2{\vfill\hbox to #3{\special{illustration #1}\hfill}}
  \hskip #4
  $$
  \vskip-\belowdisplayskip
  \endinsert}

\newcount\figurecount
\def\nextfigure{\figurecount=\figurenumber
                \advance\figurecount by 1
                \chapnum.\number\figurecount}
\def\nextnextfigure{\figurecount=\figurenumber
                \advance\figurecount by 2
                \chapnum.\number\figurecount}
\def\lastfigure{\chapnum.\number\figurenumber}
\def\lastlastfigure{\figurecount=\figurenumber
                    \advance\figurecount by -1
                    \chapnum.\number\figurecount}
\def\figname#1{\xdef#1{\hbox{\chapnum.\number\figurenumber}}}

% unnumbered figure with no caption, placed right here:
\def\figurehere#1#2#3{\goodbreak\medskip\vglue#2
  \dimen0=#3\noindent\hskip.5\hsize\hskip-.5\dimen0
  \special{illustration #1}
  \medskip}


% equation numbering:
\newif\ifdraft
\def\draft{\global\drafttrue}
\newcount\equanumber
\equanumber=0
\def\eqname#1{
  \global\advance\equanumber by 1
  \xdef#1{\hbox{\chapnum.\number\equanumber}}
  (#1)
  \ifdraft\rlap{\ninett\ \string#1}\fi}
\def\eq{\eqname\?}
\def\eqn{\eqno\eqname}
\let\eqnalign=\eqname

% footnotes:
\def\foot#1{$^*$\footnote{}{\ninepoint\llap{$^*$}#1}}
\def\footdagger#1{$^\dagger$\footnote{}{\ninepoint\llap{$^\dagger$}#1}}
\def\footddagger#1{$^\ddagger$\footnote{}{\ninepoint\llap{$^\ddagger$}#1}}


% sub-paragraph with narrower margins:
\def\setoff#1{\medskip{\narrower\noindent#1\medskip}}


% font conventions:
\def\defterm{\bf}
\def\em{\it}
\def\cite{\sl}

% hyphenation
\hyphenation{macro-state}
\hyphenation{macro-states}
\hyphenation{mon-atomic}
\hyphenation{mole-cule}
\hyphenation{mole-cules}
\hyphenation{iso-therm}

% abbreviations:
\def\deg{$^\circ$}
\def\degC{\deg C}
\def\Navo{N_{\mskip-2mu\rm A}}
\def\muBohr{\mu_{\rm B}}
\def\dbar{\kern.2em\bar{\phantom{o}}\kern-.67em d\kern.1em}
\def\d{\partial}
\def\Nup{N_\uparrow}
\def\Ndown{N_\downarrow}
\def\UsubA{U_{\mskip-3mu A}}
\def\UsubB{U_{\mskip-2mu B}}
\def\SsubA{S_{\mskip-2.5mu A}}
\def\SsubB{S_{\mskip-2mu B}}
\def\VsubA{V_{\mskip-3.5mu A}}
\def\VsubB{V_{\mskip-1.5mu B}}
\def\NsubA{N_{\mskip-2mu A}}
\def\NsubB{N_{\mskip-1.5mu B}}
\def\TsubA{T_{\mskip-2mu A}}
\def\TsubB{T_{\mskip-1.5mu B}}
\def\UsubR{U_{\mskip-2mu R}}
\def\VsubR{V_{\mskip-2mu R}}
\def\NsubR{N_{\mskip-2mu R}}
\def\SsubR{S_{\mskip-1.5mu R}}
\def\GApure{G_{\!A}^\circ}
\def\GBpure{G_{\!B}^\circ}
\def\Re{\mathop{\rm Re}\nolimits}
\def\Im{\mathop{\rm Im}\nolimits}
\def\erf{\mathop{\rm erf}\nolimits}
\def\P{{\cal P}}
\def\D{{\cal D}}
\def\nFD{\overline{n}_{\lower1pt\hbox{$\scriptstyle\rm FD$}}}
\def\nBE{\overline{n}_{\lower1pt\hbox{$\scriptstyle\rm BE$}}}
\def\nPl{\overline{n}_{\lower1pt\hbox{$\scriptstyle\rm Pl$}}}
\def\eF{\epsilon_{\lower1pt\hbox{$\scriptstyle\rm F$}}}
\def\TsubF{T_{\rm F}}
\def\TsubD{T_{\rm D}}
\def\clustertwo{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clustertwo}}\hskip10pt}
\def\clusterlambda{\hskip2pt\lower8.0pt\hbox{\special{illustration 
   clusterlambda}}\hskip27pt}
\def\clustertriangle{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clustertriangle}}\hskip27pt}
\def\clusterT{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clusterT}}\hskip41pt}
\def\clusterpi{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clusterpi}}\hskip25pt}
\def\clustersquare{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clustersquare}}\hskip26pt}
\def\clustersquarediag{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clustersquarediag}}\hskip26pt}
\def\clustersquarex{\hskip2pt\lower8.8pt\hbox{\special{illustration 
   clustersquarex}}\hskip26pt}
