<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%  This file provides the asmejour class for formatting papers in a layout similar to ASME Journal papers.
%%  
%%  The asmejour.cls file should be used with the files asmejour.bst (for citations) and asmejour-template.tex.
%%
%%  This file's version and date are:
		\def\versionno{1.25}
		\def\versiondate{2025/04/07\space}
%%
%%  Author: John H. Lienhard V
%%          Department of Mechanical Engineering
%%          Massachusetts Institute of Technology
%%          Cambridge, MA 02139-4307 USA
%%
%%  This class was designed to approach the following aims:
%%
%%          1. Match ASME's current layout and font specifications
%%          2. With amsejour.bst, match ASME's reference formats and support DOI &amp; URL fields
%%          3. Provide hyperref compatibility for hyperlinks, pdf bookmarks, and metadata
%%          4. Support citations, footnotes, and bold face math in section headings
%%			5. Provide optional line numbers for editing and review
%%			6. Support balancing height of columns on the last page
%%			7. Provide copyright notices for government employees and government contractors
%%		    8. Enable various math features from the newtxmath or unicode-math packages 
%%		    9. Support inclusion of passages in languages other than English
%%
%%  This class is compatible with both pdfLaTeX and LuaLaTeX. All packages required by the class 
%%  are in standard distributions, such as TeX Live, and are also available at CTAN (https://ctan.org/).
%%  The use of a complete and up-to-date (Nov. 2022 or later) LaTeX distribution is strongly recommended;
%%		==&gt; Distributions older than Oct. 2020 are not supported. 
%%
%%  The title block is set by specific commands that are described in the asmejour-template.tex file.
%%
%%  The class defines abstract environment (with optional keywords) and a nomenclature environment.   
%%  (LaTeX must be run twice to align the columns in the nomenclature list).
%% 
 %=========================================================
%%
%% LICENSE:
%%
%% Copyright (c) 2025 John H. Lienhard
%%
%% Permission is hereby granted, free of charge, to any person obtaining a copy of this software and 
%% associated documentation files (the "Software"), to deal in the Software without restriction, 
%% including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 
%% and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 
%% subject to the following conditions:
%%
%% The above copyright notice and this permission notice shall be included in all copies or 
%% substantial portions of the Software.
%%
%% The software is provided "as is", without warranty of any kind, express or implied, including but 
%% not limited to the warranties of merchantability, fitness for a particular purpose and noninfringement. 
%% in no event shall the authors or copyright holders be liable for any claim, damages or other liability, 
%% whether in an action of contract, tort or otherwise, arising from, out of or in connection with the 
%% software or the use or other dealings in the software.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{asmejour}[\versiondate asmejour paper format (JHL)]

\LoadClass[twoside,9pt]{extarticle}% twocolumn format initiated by \maketitle command 2024/07/20

\newif\ifasmejour@pdftex
\newif\ifPDFtex
\ExplSyntaxOn
	\sys_if_engine_pdftex:T  { 
		\asmejour@pdftextrue
		\PDFtextrue % for end user   
	}
	\str_const:Nn \ClassName {asmejour}
	\prop_put:Nnn \g_msg_module_type_prop { \ClassName } { Class }
\ExplSyntaxOff

\RequirePackage{etoolbox}% patch amsmath and section headings


%%%%%%%%%%%%%  Some compatibility for older distributions  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\providecommand\IfFormatAtLeastTF{\@ifl@t@r\fmtversion}%  compare version to date; \If... added to latex 2020/10/01
\providecommand\IfPackageAtLeastTF{\@ifpackagelater}%     compare version to date; \If... added to latex 2020/10/01
\providecommand\IfPackageLoadedTF{\@ifpackageloaded}%     \If...added to latex 2021/11/15
\providecommand\ClassNoteNoLine[2]{\typeout{^^JClass Note #1: #2.^^J}}%  log &amp; terminal note... added to latex 2021/11/15

\IfFormatAtLeastTF{2020/10/01}{\relax}{%
	\ClassError{\ClassName}{Your LaTeX format is dated \fmtversion. Formats older than 2020-10-01 will throw errors and may fail entirely! Formats dated 2022-11-01 or later are strongly recommended for the asmejour class.}{Please UPDATE your LaTeX distribution. TeX Live is available for download at no charge: see \string https://www.tug.org/texlive/.}%
}

% Allow pre 2021/11/15 formats to see the graphicx alt= key without causing an error
\IfFormatAtLeastTF{2021/11/15}{
	\relax
}{ 
	\AtBeginDocument{
		\IfPackageLoadedTF{graphicx}{\define@key{Gin}{alt}{}}{\relax}
	}
}

% Enable pre-2020/10 formats to access essential macros later moved into LaTeX kernel
\ifdefined\NewDocumentCommand\else
  \RequirePackage{xparse}[2020/02/25]
\fi 

% kvoptions and fnpos may be loaded as fallbacks for pre-2022/11 formats


%%%%%%%%%%%%%% Options for the class %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ExplSyntaxOn
%\debug_on:n {all}

\msg_new:nnn { \ClassName } { mainlang } { Selecting~#1~as~the~primary~language }
\msg_new:nnn { \ClassName } { mathalfa } { Former~mathalfa~option~has~been~dropped;~instead,~load~mathalpha~package~in~your~preamble }

\newif\ifasmejour@mainset


%% Now create options and keys
\IfFormatAtLeastTF{2022/11/01}{
    \str_new:N  \asmejour@barcolor
    \str_set:Nn \asmejour@barcolor { black }% default
%   
    %% Set main language
    \cs_new:Nn \__asmejour_setupmain:n {
    	\PassOptionsToPackage{ main=#1 }{babel}
    	\asmejour@mainsettrue 
    	\msg_note:nnn { \ClassName } { mainlang } {#1}
    }
    \DeclareKeys[\ClassName]
    {
		balance 		.if	 	= asmejour@balance ,% 		Option to balance column height on last page [balance]
		balance 		.usage	= load ,
		barcolor		.store  = \asmejour@barcolor ,% 	Optional color for vertical bar in title block [barcolor= ], from xcolor package
		barcolor		.usage	= preamble ,
		captionpatch 	.if		= asmejour@captionpatch ,% 	Option to patch caption package for tagged pdf [captionpatch].  Experimental, 2025/03/31
		captionpatch 	.usage 	= load ,
		contractor 		.if		= asmejour@contractor ,% 	Option for government contractor copyright notice [contractor]
		contractor 		.usage	= load ,
		govt 			.if	 	= asmejour@govt ,% 			Option for copyright notice if all authors are government employees [govt]
		govt 			.usage	= load ,
		govtsome 		.if		= asmejour@govtsome ,% 		Option for copyright notice if some (not all) authors are government employees [govtsome]
		govtsome 		.usage	= load ,
		lineno 			.if	 	= asmejour@lineno ,% 		Option to obtain line numbers [lineno] 
		lineno 			.usage	= load ,
		main			.code	= \__asmejour_setupmain:n { #1 },%  Option to set main language (for babel) [main= ]
		main 			.usage	= preamble ,
		mathalfa		.code	= \msg_warning:nn { \ClassName } { mathalfa },% Warn about old [mathalfa= ] keyvalue; an imperfect fix. 2025/04/01 
		mathalfa		.usage	= load ,
		nocopyright 	.if	 	= asmejour@nocopyright ,% 	Option to omit ASME copyright notice [nocopyright]
		nocopyright		.usage	= load ,
		nofoot 			.if	 	= asmejour@nofoot ,% 		Option to omit ASME footers [nofoot]
		nofoot 			.usage	= load ,
		nolists 		.if	 	= asmejour@nolists ,% 		Option to omit lists of figures and tables [nolists]
		nolists 		.usage	= load ,
		singlecolumn 	.if	 	= asmejour@singlecolumn ,% 	Option for single column layout [singlecolumn]
		singlecolumn 	.usage	= load ,
    }    
	\DeclareUnknownKeyHandler[\ClassName]{\relax}% suppress warning about unused keys
	\ProcessKeyOptions
	
}{% And more compatibility code for distributions pre-2022/11     
    \RequirePackage{kvoptions}% this package loads kvsetkeys
    \SetupKeyvalOptions{
      family=\ClassName,
      prefix=asmejour@,
      setkeys=\kvsetkeys,
    }  
    %% Option to balance column height on last page [balance] 
    \DeclareBoolOption{balance}    
	%% Option to patch caption package for tagged pdf [captionpatch].  Experimental, 2025/03/31
    \DeclareBoolOption{captionpatch}   
    %% Option for government contractor copyright notice [contractor]
    \DeclareBoolOption{contractor}   
    %% Option for copyright notice if all authors are government employees [govt]
    \DeclareBoolOption{govt}    
    %% Option for copyright notice if some (not all) authors are government employees [govtsome]
    \DeclareBoolOption{govtsome}    
    %% Option to obtain line numbers [lineno] 
    \DeclareBoolOption{lineno}    
    %% Option to omit ASME copyright notice [nocopyright]
    \DeclareBoolOption{nocopyright}    
    %% Option to omit ASME footers [nofoot]
    \DeclareBoolOption{nofoot}    
    %% Option to omit lists of figures and tables
    \DeclareBoolOption{nolists}    
    %% Option for single column layout [singlecolumn], 2024/07/20
    \DeclareBoolOption{singlecolumn} 
      
    %% set key [barcolor=] to pass a color name defined by xcolor package
    \DeclareStringOption[black]{barcolor}    

    %% the key [main= ] to pass the choice of main language to babel
    \newif\ifasmejour@mainset
    \define@key{\ClassName}{main}{%
    	  \PassOptionsToPackage{main=#1,#1}{babel}% added #1 resolves conflicts between certain .ldf files under "main=".
    	  \asmejour@mainsettrue
	   	  \msg_note:nnn { \ClassName } { mainlang } {#1}
    }    
    %% the key [mathalfa= ] was dropped with v1.25; instead, load the mathalpha package in your preamble
    \define@key{\ClassName}{mathalfa}{%
	   	  \msg_note:nn { \ClassName } { mathalfa }
    }      
    %% Suppress warnings about unused global options, 2021/12/01
    \DeclareDefaultOption{}   
    \ProcessKeyvalOptions{\ClassName}
    
    %% Turn off these keys now that we're done with them
    \NewDocumentCommand\asmejour@DisableOption{m}{%
		\DisableKeyvalOption[%
			action=ignore,%
			class=\ClassName%
		]{#1}{\asmejour@KeyFamily}%
    }
    \def\asmejour@KeyFamily{}
    \NewDocumentCommand\asmejour@DisableKeys{&gt;{\SplitList{;}}m}{\ProcessList{#1}{\asmejour@DisableOption}}
    \asmejour@DisableKeys{singlecolumn;lineno;balance;nolists;nocopyright;nofoot;govt;govtsome;contractor;barcolor;main;mathalfa}
}

%% if main language was not was chosen explicitly, default to English
\ifasmejour@mainset\relax\else
	\PassOptionsToPackage{main=english}{babel}%
	\ClassNoteNoLine{\ClassName}{Selecting~English~as~the~primary~language,~since~main=~not~set}%
\fi

\ExplSyntaxOff


%%%%%%%%%  Various font-related options  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% option for upright integral signs, rather than default slanted integrals, [upint]
\def\UpInt{}% default slanted integrals in STIX Two Math font with unicode-math
\DeclareOption{upint}{%
	\ifasmejour@pdftex
		\PassOptionsToPackage{upint}{newtxmath}% this option exists in newtxmath
	\else
		\def\UpInt{+ss08}% upright integrals in STIX Two Math font and Lete Sans Math fonts
	\fi
}

%% Select larger small capitals font from newtxtext, set as default 2025/03/30
\ifasmejour@pdftex
	\PassOptionsToPackage{largesc=true}{newtxtext} 
\fi

%% Option to allow hyphenation of typewriter font [hyphenate]
\DeclareOption{hyphenate}{%
	\ifasmejour@pdftex
		\PassOptionsToPackage{hyphenate}{inconsolata}% hyphenate is a key via xkeyval in inconsolata
		\ClassNoteNoLine{\ClassName}{Allowing hyphenation of typewriter font}%
	\else
		\ClassWarningNoLine{\ClassName}{The [hyphenate] option is only supported with pdftex. It will be ignored}%
	\fi
}

%% Option to enforce monospacing of words the typewriter font [mono]
\def\MonoNotMono{WordSpace={1,1,1}}% rescale fontspec's tt font to match pdf tt font, 2024/07/30
\DeclareOption{mono}{%
	\ifasmejour@pdftex
		\PassOptionsToPackage{mono}{inconsolata}% mono is a key via xkeyval in inconsolata
	\else
		\def\MonoNotMono{WordSpace={1,0,0},PunctuationSpace={3}}% 2024/07/30, these are actually default WordSpace values
	\fi
}

%% Option for unslashed zero typewriter font [var0]
\def\ssztwo{}% for Inconsolatazi4; default uses slashed zero, +ss02 uses regular zero
\DeclareOption{var0}{%
	\ifasmejour@pdftex
		\PassOptionsToPackage{var0}{inconsolata}% var0 is a key via xkeyval in inconsolata
	\else
		\def\ssztwo{+ss02}% stylistic alternate for regular zero
	\fi
}

%% Suppress warnings about keys as unused global options
\DeclareOption*{}
\ProcessOptions \relax


%%%%%%%%%%%%  Page size, bibliography, graphics, color  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\RequirePackage[paperheight=285.7mm, paperwidth=215.900mm, left=21.100mm, right=21.100mm, top=15.9mm, bottom = 24mm, footskip=8mm]{geometry}
\setlength\columnsep{4.5mm}
\setlength\parindent{3.5mm}
%% ASME's pdf pages are 11.25 in. tall, not 11.00 in.

\RequirePackage[sort&amp;compress,numbers]{natbib} 
\AtBeginDocument{\def\NAT@space{\relax}}%   ASME puts no space between numerical references (2020/04/05)
\setlength\bibsep{0pt plus 1pt minus 0pt}%  ASME keeps this tight
\renewcommand*{\bibfont}{\footnotesize}

\RequirePackage{graphicx} 
\RequirePackage[dvipsnames,svgnames,x11names]{xcolor}% removed obsolete options, 2023/10/23


%%%%%%%%%%%%%  Table related   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\RequirePackage{array} 

\RequirePackage{dcolumn}%  column alignment on decimal places
	\newcolumntype{d}[1]{D{.}{.}{#1}}
	% NB: The above conflicts with babel's Spanish language option which makes "." an active character.
    % Instead: use "," as the decimal separator, choose columntype "," (as in "12,234"), and put
    % 	\newcolumntype{,}[1]{D{,}{,}{#1}} in your preamble.


%% make \hline in tables heavier than default 0.4pt
\setlength\arrayrulewidth{0.5\p@}

%% use double-rules for top and bottom of tables, per ASME style
\RequirePackage{booktabs}
    \renewcommand*{\toprule}{\specialrule{0.5pt}{0pt}{\doublerulesep}\specialrule{0.5pt}{0pt}{3pt}}
    \renewcommand*{\midrule}{\specialrule{0.5pt}{2pt}{3pt}}
    \renewcommand*{\bottomrule}{\specialrule{0.5pt}{1pt}{\doublerulesep}\specialrule{0.5pt}{0pt}{0pt}}


%%%%%%%%%%%%%  Font related   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\RequirePackage{mathtools}% loads and extends amsmath
\RequirePackage[]{babel}%   supports languages other than English, if used.

\ifasmejour@pdftex
    \RequirePackage[T1]{fontenc}
 	%% ASME word separation is greater than newtxtext defaults so change these parameters.  
 	%%     increased shrink from 0.08, 2021/01/30; add this helvetica scaling 2022/06/26
	\RequirePackage[helvratio=0.91, spacing=0.3em, stretch=0.18em, shrink=0.10em]{newtxtext}% default {0.25em,0.2em,0.1em}
	\RequirePackage[varl,varqu]{inconsolata}% sans typewriter font; restored varl, varqu 2020/08/10 
	\RequirePackage[]{newtxmath}
	\RequirePackage{bm}%  load after all math for expanded access to bold math
%
\else
    % Revised 2025/04/01
    \RequirePackage[warnings-off={mathtools-colon,mathtools-overbracket}]{unicode-math}
    % suppress tiresome warnings about lack of integration between mathtools and unicode-math
    % unicode-math loads the fontspec package
%
	\def\FontWarning{For luaLaTeX, you MUST have these OpenType fonts installed on your computer: TeX Gyre Termes X, TeX Gyre Termes Math, TeX Gyre Heros, Inconsolatazi4, XTISMath-Bold, LeteSansMath-Bold, LeteSansMath, and STIXTwoMath. All are in TeX Live and CTAN. If you DON'T have these fonts, you will see warning or ERROR messages}
%		    
	\IfFontExistsTF{TexGyreTermesX-regular.otf}{}{  \ClassErrorNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{texgyretermes-math.otf}{}{ 		\ClassErrorNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{texgyreheros-regular.otf}{}{    \ClassErrorNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{Inconsolatazi4-Regular.otf}{}{  \ClassErrorNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{XITSMath-Bold.otf}{}{  			\ClassWarningNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{LeteSansMath-Bold.otf}{}{  		\ClassWarningNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{LeteSansMath.otf}{}{  			\ClassWarningNoLine{\ClassName}{\FontWarning} }
	\IfFontExistsTF{STIXTwoMath-Regular.otf}{}{  	\ClassErrorNoLine{\ClassName}{\FontWarning} }
	%
	% The newtx package includes a modified version of TeXGyreTermes called TexGyreTermesX, which could be loaded instead.
    \setmainfont{TeXGyreTermesX}[% Presumes these are system fonts! In CTAN (under the newtx heirarchy)
		WordSpace = {1.20,1.44,1.2},% This stretch matches newtxtext fontdimens (reset 2024/07/30)
    	PunctuationSpace = {1.33},% reset 2024/07/30
	    Extension = .otf,
    	UprightFont = *-Regular,
    	ItalicFont = *-Italic,
    	BoldFont = *-Bold,
    	BoldItalicFont = *-BoldItalic,
		Numbers = Lining,
		]
    \setsansfont{texgyreheros}[% Presumes these are system fonts! Available at: http://www.gust.org.pl/projects/e-foundry/tex-gyre
		WordSpace = {1,1,1.0036},%% This stretch matches newtxtext fontdimens (reset 2024/07/30)
    	PunctuationSpace = {1.0036},% reset 2024/07/30
    	Scale=0.91,% same as for newtx; former value 0.9 too small 2022/01/15
		Extension = .otf,
    	UprightFont = *-regular,
    	ItalicFont = *-italic,
    	BoldFont = *-bold,
    	BoldItalicFont = *-bolditalic,
		Numbers = Lining,
		]        
   \setmonofont{Inconsolatazi4}[% This otf font ships with the LaTeX Inconsolata package (it's in TeX Live)
        Scale=1.0,% rescaled 1.05, 2022/03/10; reset to 1 2024/07/30, based on fontdimen6 (and all others!)
        Extension = .otf,
        UprightFont = *-Regular,
        ItalicFont = *-Regular,% has no italic face
        BoldFont = *-Bold, 
    	BoldItalicFont = *-Bold,% has no italic face
        RawFeature = {+ss01,\ssztwo,-ss03},
        \MonoNotMono,% WordSpace and PunctuationSpace are set in the class option [mono]
        ]
	\setmathfont{texgyretermes-math}[% Presumes it's installed! http://www.gust.org.pl/projects/e-foundry/tex-gyre
    	Scale=MatchUppercase,
	    Extension = .otf,
		]
	\ExplSyntaxOn
    \IfFontExistsTF{XITSMath-Bold.otf}{    
        \setmathfont{XITSMath-Bold.otf}[Scale=MatchUppercase,version=bold]% font is missing \cdot U+22C5
        \setmathfontface\mathrm{XITSMath-Bold.otf}[Scale=MatchUppercase,version=bold] 
		\AddToHook{begindocument/end} % this command added to LaTeX, 2020/10
         {
          \NewCommandCopy{\standardcdot}{\cdot} % thanks to Enrico Gregorio and David Carlisle for this solution
          \cs_set_protected:Npn \cdot
           {
            \str_if_eq:vnTF { math@version } { bold }
             { \cdotp }			% U+00B7
             { \standardcdot }	% U+22C5
           }
         }
	}{
	    \ClassWarningNoLine{\ClassName}{XITS Math Bold font not found, falling back to Tex Gyre Termes Math with FakeBold}%
		\setmathfont{texgyretermes-math}[Scale=MatchUppercase,version=bold,FakeBold=3.5]
        \setmathfontface\mathrm{texgyretermes-math}[Scale=MatchUppercase,version=bold,FakeBold=3.5] 
    }
    \ExplSyntaxOff
%	        
    % set up sans and sansbold math fonts
    \IfFontExistsTF{LeteSansMath-Bold.otf}% the bold version was released a few months after the regular, but we need both.
    {
        \setmathfont{LeteSansMath-Bold}[% In TeX Live. A newer math font (2024/05), boldface sans serif
            Scale=MatchUppercase,
	       	Extension = .otf,
			RawFeature={\UpInt},
            version=sansbold,
        ]
        \setmathfontface\mathrm{LeteSansMath-Bold.otf}[
        	Scale=MatchUppercase,
			version=sansbold
		]
        \setmathfont{LeteSansMath}[
            Scale=MatchUppercase,
	       	Extension = .otf,
			RawFeature={\UpInt},
            version=sans,
            BoldFont = *-Bold,
            NFSSFamily=lsm,
        ]
        \setmathfontface\mathrm{LeteSansMath.otf}[
        	Scale=MatchUppercase,
			version=sans,
		]
        \setmathfontface\mathbf{LeteSansMath-Bold.otf}[
        	Scale=MatchUppercase,
			version=sans,
		]
        \setmathfont{STIXTwoMath-Regular}[% In TeX Live. Substitution for bigger integrals (similar to newtxmath)
	       	Extension = .otf,
            Scale=MatchUppercase,
            RawFeature={\UpInt},
            BoldFont=*, 
            range={"0222B-"02233,"02A0B-"02A1C,}, 
        ] 
    }{
    	\ClassWarningNoLine{\ClassName}{Lete Sans Math Bold font not found, falling back to Fira Math with FakeBold}%
		\setmathfont{FiraMath-Regular}[% 2020 version of Regular is in TeX Live
            Scale=MatchUppercase,
	       	Extension = .otf,
            version=sansbold,
            FakeBold = 4,
    	]
        \setmathfontface\mathrm{FiraMath-Regular.otf}[
        	Scale=MatchUppercase,
			version=sansbold,
			FakeBold = 4,
		]
		\setmathfont{FiraMath-Regular}[% 2020 version of Regular is in TeX Live
            Scale=MatchUppercase,
	       	Extension = .otf,
            version=sans,
            NFSSFamily=fsm,
            BoldFont=*, 
			BoldFeatures = {FakeBold=4},
        ]
        \setmathfontface\mathrm{FiraMath-Regular.otf}[
        	Scale=MatchUppercase,
			version=sans,
		]     
        \setmathfontface\mathbf{FiraMath-Regular.otf}[
        	Scale=MatchUppercase,
			version=sans,
			FakeBold=4,
		]     
        \setmathfont{STIXTwoMath-Regular}[% In TeX Live. Subst. bigger integrals (similar to newtxmath) + cal,scr,frak
	       	Extension = .otf,
            Scale=MatchUppercase,
    		BoldFont = *,
            RawFeature={\UpInt},
            range={"0222B-"02233,"02A0B-"02A1C,frak,bffrak,cal,bfcal,scr,bfscr}
        ]
	}
%
    \setmathfontface\mathsf{texgyreheros-bold.otf}[Scale=0.91,version=sansbold]       % for sf     
    \setmathfontface\mathit{texgyreheros-bolditalic.otf}[Scale=0.91,version=sansbold] % for it
    \setmathfontface\mathtt{Inconsolatazi4-Bold.otf}[Scale=1.0,version=sansbold] 	  % for tt

    \setmathfontface\mathsf{texgyreheros-regular.otf}[Scale=0.91,version=sans]  	% for sf     
    \setmathfontface\mathit{texgyreheros-italic.otf}[Scale=0.91,version=sans]		% for it
    \setmathfontface\mathtt{Inconsolatazi4-Regular.otf}[Scale=1.0,version=sans]		% for tt
%%
    \setoperatorfont\normalfont % to enable sans or bold operators, etc.
\fi
  
%% Relative to size9.clo: leading reduced to 10 pt; displayskips made greater
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@ixpt{10\p@}%               % &lt;== was \@xipt
   \abovedisplayskip 10\p@ \@plus5\p@ \@minus4\p@%      % &lt;== was 8\p@ 4,4...
   \abovedisplayshortskip 3\p@ \@plus1\p@ \@minus1\p@%  % &lt;== was \z@ \@plus3\p@ (3pt stretch)
   \belowdisplayshortskip 10\p@ \@plus5\p@ \@minus4\p@% % &lt;== was 5\p@ 3, 3
   \belowdisplayskip \abovedisplayskip%
   \let\@listi\@listI}
\normalsize

%% The article class calls \sloppy in two-column mode (\tolerance 9999, \emergencystretch 3em)
%% These adjustments affect line breaking; the values below are intended to produce
%% fewer lines with large spaces, without creating the problems of using \fussy in two-column mode.
\tolerance 2500
\emergencystretch 3em 

%% Fonts for author and title only: TeX Gyre Heros Condensed (qhvc, regular is qhv)
\DeclareFontFamily{T1}{qhvc}{}% qhvc is not TU encoded
\DeclareFontShape{T1}{qhvc}{m}{n}{&lt;-&gt; s*[0.91] ec-qhvcr}{} %% see t1qhvc.fd; 0.9--&gt;0.94 2022/01/15; 0.94--&gt;0.91 2022/06/26
\DeclareFontShape{T1}{qhvc}{b}{n}{&lt;-&gt; s*[0.91] ec-qhvcb}{} %% see t1qhvc.fd; 0.9--&gt;0.94 2022/01/15; 0.94--&gt;0.91 2022/06/26
\newcommand*{\CondSans}{\fontencoding{T1}\fontfamily{qhvc}\selectfont}% remove extra \selectfont, 2023/10/21
\newcommand\Condhuge{\@setfontsize\huge{14}{14}}        %... for author names only
\newcommand*{\CondSansBold}{\renewcommand\bfdefault{b}\fontencoding{T1}\fontfamily{qhvc}\selectfont\bfseries} 
\newcommand\CondHuge{\@setfontsize\Huge{26.5}{26.5}}    %... for title only
  
\ifasmejour@pdftex    
    %% sans math version, potential value with PGFPlots, etc., 2021/01/25 %%%
    \DeclareMathVersion{sans}
    \SetSymbolFont{letters}{sans}{OML}{ntxsfmi}{m}{it}
    \SetSymbolFont{lettersA}{sans}{U}{ntxsfmia}{m}{it}
    \IfFormatAtLeastTF{2016/01/05}{%
    	\SetSymbolFont{symbols}{sans}{LMS}{ntxsy}{m}{n}
    	}{\relax}
    \SetSymbolFont{largesymbols}{sans}{LMX}{ntxexx}{m}{n}
    \SetSymbolFont{largesymbolsTXA}{sans}{U}{ntxexa}{m}{n}
    \SetSymbolFont{operators}{sans}{OT1}{\sfdefault}{m}{n}% fixed encoding 2025/04/04
    \SetMathAlphabet{\mathsf}{sans}{\encodingdefault}{\sfdefault}{m}{n}% make upright 2021/01/31.
%
    %% sans serif italic and sans serif bold italic math
    \DeclareMathVersion{sansbold}
    \SetSymbolFont{letters}{sansbold}{OML}{ntxsfmi}{b}{it}
    \SetSymbolFont{lettersA}{sansbold}{U}{ntxsfmia}{b}{it}
    \SetSymbolFont{symbols}{sansbold}{LMS}{ntxsy}{b}{n}
    \SetSymbolFont{largesymbols}{sansbold}{LMX}{ntxexx}{b}{n}%  added 2021/01/26
    \SetSymbolFont{largesymbolsTXA}{sansbold}{U}{ntxexa}{b}{n}% added 2021/01/26
    \SetSymbolFont{operators}{sansbold}{OT1}{\sfdefault}{\bfdefault}{n}% fixed encoding 2025/04/04
    \SetMathAlphabet{\mathsf}{sansbold}{\encodingdefault}{\sfdefault}{b}{n}% \mathsf is upright
%
\fi

%%%%%%%%%%%%%%  Sans serif upright greek and sans mathversion  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% revised 2025/04/03
%
\ifasmejour@pdftex
    %% Provide sans-serif *upright* Greek letters, following a suggestion by Michael Sharpe (March 2019).
    %% Following Sharpe's newtxsf implementation of the STIX fonts, under the LaTeX Project Public License.
    %% (Note that \mathversion{sansbold} provides sans-serif *italic* Greek letters.)
    
    \DeclareSymbolFont{lettersAB}{U}{ntxsfmia}{m}{it}
    \SetSymbolFont{lettersAB}{normal}{U}{ntxsfmia}{m}{it}
    \SetSymbolFont{lettersAB}{bold}{U}{ntxsfmia}{b}{it}
    \SetSymbolFont{lettersAB}{sans}{U}{ntxsfmia}{m}{it}
    \SetSymbolFont{lettersAB}{sansbold}{U}{ntxsfmia}{b}{it}
    
    \DeclareMathSymbol{\sfGamma}{\mathalpha}{lettersAB}{0}% adjust to avoid overwriting newtxmath commands, 2021/01/25
    \DeclareMathSymbol{\sfDelta}{\mathalpha}{lettersAB}{1}
    \DeclareMathSymbol{\sfTheta}{\mathalpha}{lettersAB}{2}
    \DeclareMathSymbol{\sfLambda}{\mathalpha}{lettersAB}{3}
    \DeclareMathSymbol{\sfXi}{\mathalpha}{lettersAB}{4}
    \DeclareMathSymbol{\sfPi}{\mathalpha}{lettersAB}{5}
    
    \DeclareMathSymbol{\sfSigma}{\mathalpha}{lettersAB}{6}
    \DeclareMathSymbol{\sfUpsilon}{\mathalpha}{lettersAB}{7}
    \DeclareMathSymbol{\sfPhi}{\mathalpha}{lettersAB}{8}
    \DeclareMathSymbol{\sfPsi}{\mathalpha}{lettersAB}{9}
    \DeclareMathSymbol{\sfOmega}{\mathalpha}{lettersAB}{10}
    
    \DeclareMathSymbol{\sfalpha}{\mathalpha}{lettersAB}{11}
    \DeclareMathSymbol{\sfbeta}{\mathalpha}{lettersAB}{12}
    \DeclareMathSymbol{\sfgamma}{\mathalpha}{lettersAB}{13}
    \DeclareMathSymbol{\sfdelta}{\mathalpha}{lettersAB}{14}
    \DeclareMathSymbol{\sfepsilon}{\mathalpha}{lettersAB}{15}
    
    \DeclareMathSymbol{\sfzeta}{\mathalpha}{lettersAB}{16}
    \DeclareMathSymbol{\sfeta}{\mathalpha}{lettersAB}{17}
    \DeclareMathSymbol{\sftheta}{\mathalpha}{lettersAB}{18}
    \DeclareMathSymbol{\sfiota}{\mathalpha}{lettersAB}{19}
    \DeclareMathSymbol{\sfkappa}{\mathalpha}{lettersAB}{20}
    
    \DeclareMathSymbol{\sflambda}{\mathalpha}{lettersAB}{21}
    \DeclareMathSymbol{\sfmu}{\mathalpha}{lettersAB}{22}
    \DeclareMathSymbol{\sfnu}{\mathalpha}{lettersAB}{23}
    \DeclareMathSymbol{\sfxi}{\mathalpha}{lettersAB}{24}
    \DeclareMathSymbol{\sfpi}{\mathalpha}{lettersAB}{25}
    
    \DeclareMathSymbol{\sfrho}{\mathalpha}{lettersAB}{26}
    \DeclareMathSymbol{\sfsigma}{\mathalpha}{lettersAB}{27}
    \DeclareMathSymbol{\sftau}{\mathalpha}{lettersAB}{28}
    \DeclareMathSymbol{\sfupsilon}{\mathalpha}{lettersAB}{29}
    \DeclareMathSymbol{\sfphi}{\mathalpha}{lettersAB}{30}
    
    \DeclareMathSymbol{\sfchi}{\mathalpha}{lettersAB}{31}
    \DeclareMathSymbol{\sfpsi}{\mathalpha}{lettersAB}{32}
    \DeclareMathSymbol{\sfomega}{\mathalpha}{lettersAB}{33}
    \DeclareMathSymbol{\sfvarepsilon}{\mathalpha}{lettersAB}{34}
    \DeclareMathSymbol{\sfvartheta}{\mathalpha}{lettersAB}{35}
    
    \DeclareMathSymbol{\sfvarpi}{\mathord}{lettersAB}{36}% added these 2021/01/25
    \DeclareMathSymbol{\sfvarrho}{\mathord}{lettersAB}{37}
    \DeclareMathSymbol{\sfvarsigma}{\mathord}{lettersAB}{38}
    \DeclareMathSymbol{\sfvarphi}{\mathord}{lettersAB}{39}
    \DeclareMathSymbol{\sfitvarkappa}{\mathalpha}{lettersAB}{40}
    \DeclareMathSymbol{\sfvarkappa}{\mathalpha}{lettersAB}{40}
    \DeclareMathSymbol{\sfitnabla}{\mathalpha}{lettersAB}{42}
    \DeclareMathSymbol{\sfnabla}{\mathalpha}{lettersAB}{43}
    \DeclareMathSymbol{\sfhslash}{\mathalpha}{lettersAB}{52}% this is not upright
    \DeclareMathSymbol{\sfhbar}{\mathalpha}{lettersAB}{53}%   this is not upright
\else
    \IfFontExistsTF{LeteSansMath-Bold}
    {
        \DeclareSymbolFont{lsmgreek}{TU}{lsm}{m}{n}% NFSSFamily lsm set above
        \SetSymbolFont{lsmgreek}{normal}{TU}{lsm}{m}{n}
        \SetSymbolFont{lsmgreek}{bold}{TU}{lsm}{b}{n}
        \def\ac@sansgreek{\symlsmgreek}
    }{
        \DeclareSymbolFont{fsmgreek}{TU}{fsm}{m}{n}% NFSSFamily fsm set above
        \SetSymbolFont{fsmgreek}{normal}{TU}{fsm}{m}{n}
        \SetSymbolFont{fsmgreek}{bold}{TU}{fsm}{b}{n}
        \def\ac@sansgreek{\symfsmgreek}
    }
    % uppercase greek
    \Umathchardef\sfAlpha="0   \ac@sansgreek "0391
    \Umathchardef\sfBeta="0    \ac@sansgreek "0392
    \Umathchardef\sfGamma="0   \ac@sansgreek "0393
    \Umathchardef\sfDelta="0   \ac@sansgreek "0394
    \Umathchardef\sfEpsilon="0 \ac@sansgreek "0395
    \Umathchardef\sfZeta="0    \ac@sansgreek "0396
    \Umathchardef\sfEta="0     \ac@sansgreek "0397
    \Umathchardef\sfTheta="0   \ac@sansgreek "0398
    \Umathchardef\sfIota="0    \ac@sansgreek "0399
    \Umathchardef\sfKappa="0   \ac@sansgreek "039A
    \Umathchardef\sfLambda="0  \ac@sansgreek "039B
    \Umathchardef\sfMu="0      \ac@sansgreek "039C
    \Umathchardef\sfNu="0      \ac@sansgreek "039D
    \Umathchardef\sfXi="0      \ac@sansgreek "039E
    \Umathchardef\sfOmicron="0 \ac@sansgreek "039F
    \Umathchardef\sfPi="0      \ac@sansgreek "03A0
    \Umathchardef\sfRho="0     \ac@sansgreek "03A1
    \Umathchardef\sfSigma="0   \ac@sansgreek "03A3
    \Umathchardef\sfTau="0     \ac@sansgreek "03A4
    \Umathchardef\sfUpsilon="0 \ac@sansgreek "03A5
    \Umathchardef\sfPhi="0     \ac@sansgreek "03A6
    \Umathchardef\sfChi="0     \ac@sansgreek "03A7
    \Umathchardef\sfPsi="0     \ac@sansgreek "03A8
    \Umathchardef\sfOmega="0   \ac@sansgreek "03A9
    %
    % lowercase greek, upright forms selected
    \Umathchardef\sfalpha="0   \ac@sansgreek "03B1 
    \Umathchardef\sfbeta="0    \ac@sansgreek "03B2 
    \Umathchardef\sfgamma="0   \ac@sansgreek "03B3 
    \Umathchardef\sfdelta="0   \ac@sansgreek "03B4 
    \Umathchardef\sfvarepsilon="0 \ac@sansgreek "03B5 % see note below
    \Umathchardef\sfzeta="0    \ac@sansgreek "03B6 
    \Umathchardef\sfeta="0     \ac@sansgreek "03B7 
    \Umathchardef\sftheta="0   \ac@sansgreek "03B8 
    \Umathchardef\sfiota="0    \ac@sansgreek "03B9 
    \Umathchardef\sfkappa="0   \ac@sansgreek "03BA 
    \Umathchardef\sflambda="0  \ac@sansgreek "03BB 
    \Umathchardef\sfmu="0      \ac@sansgreek "03BC 
    \Umathchardef\sfnu="0      \ac@sansgreek "03BD 
    \Umathchardef\sfxi="0      \ac@sansgreek "03BE 
    \Umathchardef\sfomicron="0 \ac@sansgreek "03BF 
    \Umathchardef\sfpi="0      \ac@sansgreek "03C0 
    \Umathchardef\sfrho="0     \ac@sansgreek "03C1 
    \Umathchardef\sfvarsigma="0 \ac@sansgreek "03C2 
    \Umathchardef\sfsigma="0   \ac@sansgreek "03C3 
    \Umathchardef\sftau="0     \ac@sansgreek "03C4 
    \Umathchardef\sfupsilon="0 \ac@sansgreek "03C5 
    \Umathchardef\sfphi="0     \ac@sansgreek "03C6 
    \Umathchardef\sfchi="0     \ac@sansgreek "03C7 
    \Umathchardef\sfpsi="0     \ac@sansgreek "03C8 
    \Umathchardef\sfomega="0   \ac@sansgreek "03C9
    %
    % character variants
    \Umathchardef\sfvartheta="0  \ac@sansgreek "03D1
    \Umathchardef\sfvarphi="0    \ac@sansgreek "03D5
    \Umathchardef\sfvarpi="0     \ac@sansgreek "03D6 
    \Umathchardef\sfvarkappa="0  \ac@sansgreek "03F0 
    \Umathchardef\sfvarrho="0    \ac@sansgreek "03F1 
    \Umathchardef\sfvarTheta="0  \ac@sansgreek "03F4
    \Umathchardef\sfepsilon="0   \ac@sansgreek "03F5 % this is the lunate form
    %
    % uppercase bold greek
    \Umathchardef\sfbfAlpha="0   \ac@sansgreek "1D6A8
    \Umathchardef\sfbfBeta="0    \ac@sansgreek "1D6A9
    \Umathchardef\sfbfGamma="0   \ac@sansgreek "1D6AA
    \Umathchardef\sfbfDelta="0   \ac@sansgreek "1D6AB
    \Umathchardef\sfbfEpsilon="0 \ac@sansgreek "1D6AC
    \Umathchardef\sfbfZeta="0    \ac@sansgreek "1D6AD
    \Umathchardef\sfbfEta="0     \ac@sansgreek "1D6AE
    \Umathchardef\sfbfTheta="0   \ac@sansgreek "1D6AF
    \Umathchardef\sfbfIota="0    \ac@sansgreek "1D6B0
    \Umathchardef\sfbfKappa="0   \ac@sansgreek "1D6B1
    \Umathchardef\sfbfLambda="0  \ac@sansgreek "1D6B2
    \Umathchardef\sfbfMu="0      \ac@sansgreek "1D6B3
    \Umathchardef\sfbfNu="0      \ac@sansgreek "1D6B4
    \Umathchardef\sfbfXi="0      \ac@sansgreek "1D6B5
    \Umathchardef\sfbfOmicron="0 \ac@sansgreek "1D6B6
    \Umathchardef\sfbfPi="0      \ac@sansgreek "1D6B7
    \Umathchardef\sfbfRho="0     \ac@sansgreek "1D6B8
    \Umathchardef\sfbfvarTheta="0 \ac@sansgreek "1D6B9
    \Umathchardef\sfbfSigma="0   \ac@sansgreek "1D6BA
    \Umathchardef\sfbfTau="0     \ac@sansgreek "1D6BB
    \Umathchardef\sfbfUpsilon="0 \ac@sansgreek "1D6BC
    \Umathchardef\sfbfPhi="0     \ac@sansgreek "1D6BD
    \Umathchardef\sfbfChi="0     \ac@sansgreek "1D6BE
    \Umathchardef\sfbfPsi="0     \ac@sansgreek "1D6BF
    \Umathchardef\sfbfOmega="0   \ac@sansgreek "1D6C0
	%
    % lowercase bold greek, upright forms selected
    \Umathchardef\sfbfalpha="0   \ac@sansgreek "1D6C2
    \Umathchardef\sfbfbeta="0    \ac@sansgreek "1D6C3
    \Umathchardef\sfbfgamma="0   \ac@sansgreek "1D6C4 
    \Umathchardef\sfbfdelta="0   \ac@sansgreek "1D6C5
    \Umathchardef\sfbfvarepsilon="0 \ac@sansgreek "1D6C6 % see note below
    \Umathchardef\sfbfzeta="0    \ac@sansgreek "1D6C7
    \Umathchardef\sfbfeta="0     \ac@sansgreek "1D6C8
    \Umathchardef\sfbftheta="0   \ac@sansgreek "1D6C9
    \Umathchardef\sfbfiota="0    \ac@sansgreek "1D6CA
    \Umathchardef\sfbfkappa="0   \ac@sansgreek "1D6CB
    \Umathchardef\sfbflambda="0  \ac@sansgreek "1D6CC
    \Umathchardef\sfbfmu="0      \ac@sansgreek "1D6CD
    \Umathchardef\sfbfnu="0      \ac@sansgreek "1D6CE
    \Umathchardef\sfbfxi="0      \ac@sansgreek "1D6CF
    \Umathchardef\sfbfomicron="0 \ac@sansgreek "1D6D0
    \Umathchardef\sfbfpi="0      \ac@sansgreek "1D6D1
    \Umathchardef\sfbfrho="0     \ac@sansgreek "1D6D2
    \Umathchardef\sfbfvarsigma="0 \ac@sansgreek "1D6D3
    \Umathchardef\sfbfsigma="0   \ac@sansgreek "1D6D4
    \Umathchardef\sfbftau="0     \ac@sansgreek "1D6D5
    \Umathchardef\sfbfupsilon="0 \ac@sansgreek "1D6D6
    \Umathchardef\sfbfphi="0     \ac@sansgreek "1D6D7
    \Umathchardef\sfbfchi="0     \ac@sansgreek "1D6D8
    \Umathchardef\sfbfpsi="0     \ac@sansgreek "1D6D9
    \Umathchardef\sfbfomega="0   \ac@sansgreek "1D6DA    
	%
    % character variants, bold
    \Umathchardef\sfbfepsilon="0  \ac@sansgreek "1D6DC % this is the lunate form
    \Umathchardef\sfbfvartheta="0 \ac@sansgreek "1D6DD
    \Umathchardef\sfbfvarkappa="0 \ac@sansgreek "1D6DE 
    \Umathchardef\sfbfvarphi="0   \ac@sansgreek "1D6DF
    \Umathchardef\sfbfvarrho="0   \ac@sansgreek "1D6E0
	\Umathchardef\sfbfvarpi="0    \ac@sansgreek "1D6E1
\fi

% and simple cheat to avoid errors when switching from luatex to pdftex with the template example
\providecommand*\mitDelta{\Delta}


%%%%%%%%%%%%%%%%%  Some adjustments to math layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\setlength{\jot}{10pt}% &lt;== default is 3pt

%% multline has an extra \jot above it, so subtract from \abovedisplayskip to remove imbalance
%%		see: https://tex.stackexchange.com/a/637071/119566 

\AddToHook{env/multline/begin}{\addtolength\abovedisplayskip{-10pt}}% 2025/04/06 increase to 10pt from 7pt, use hooks rather than etoolbox
\AddToHook{env/multline/end}{\addtolength\abovedisplayskip{+10pt}}

\allowdisplaybreaks   % ASME allows these breaks


%%%%%%%%%%%%%%%%%  Equation and Line Numbering  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% ASME puts equation tags in blue
\patchcmd{\tagform@}{(\ignorespaces#1\unskip\@@italiccorr)}{\color{blue}(\ignorespaces#1\unskip\@@italiccorr)}{}{}

% To free \eqref from the normal font (e.g., for use in section headings or captions). Revised 2024/07/28
\renewcommand{\eqref}[1]{\textup{\hbox{\m@th{(\ignorespaces\ref{#1}\unskip\@@italiccorr)}}}}
%
% amsmath def:  \newcommand{\eqref}[1]{\textup{\tagform@{\ref{#1}}}}
%				\def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip\@@italiccorr)}}
%				\def\maketag@@@#1{\hbox{\m@th\normalfont#1}}

%% Italicize alph part of subequation numbers. Revised 2023/10/20
\patchcmd{\subequations}{\theparentequation\alph{equation}}{\theparentequation\itshape\alph{equation}}{}{}


%%%%% lineno related %%%%

\ifasmejour@lineno
    \RequirePackage[switch,mathlines]{lineno}%
    \renewcommand{\linenumberfont}{\normalfont\scriptsize\color{red}}% 
    \AtBeginDocument{\linenumbers}%
    \ifasmejour@balance
		\ClassWarningNoLine{\ClassName}{Package lineno loaded, so final column balancing will be disabled}%
	\fi
	%%% Patch to allow line numbering in AMS math environments.
	%%% This patch is for lineno versions earlier than v5.2 [2023/05/19]. As of mid-2023, the lineno package
	%%% 	has been corrected to account for the AMS math environments.  Retaining temporarily for backward compatibility.
	%%% postdisplaypenalty adjusted to avoid extra line number at end, see: https://tex.stackexchange.com/a/461192/ 
	\IfPackageAtLeastTF{lineno}{2023/05/19}{\relax}{
    	\NewDocumentCommand{\asmejour@losepostpenalty}{}{\patchcmd{\linenomathWithnumbers}{\advance\postdisplaypenalty\linenopenalty}{}{}{}}
    	%
        \NewDocumentCommand{\asmejour@FixAMSMath}{m}{%
        	\AtBeginEnvironment{#1}{\asmejour@losepostpenalty\linenomath}%
        	\AtEndEnvironment{#1}{\endlinenomath}%
        	\AtBeginEnvironment{#1*}{\asmejour@losepostpenalty\linenomath}%
        	\AtEndEnvironment{#1*}{\endlinenomath}%
        }
    	\NewDocumentCommand{\asmejour@FixAll}{&gt;{\SplitList{;}}m}{\ProcessList{#1}{\asmejour@FixAMSMath}}
    	\asmejour@FixAll{align;alignat;gather;flalign;multline}
	}
%
\else
    \ProvideDocumentEnvironment{linenomath}{}{}{}%
    \ifasmejour@balance          %    balancing by flushend can produce weird errors.
    	\RequirePackage{flushend}%    flushend package is NOT compatible with lineno.
    	\AtEndDocument{\flushcolsend}%
		\ClassNoteNoLine{\ClassName}{Calling flushend package to balance column height on last page}%
    \fi%
\fi

\providecommand{\@LN@col}[1]{\relax}% avoid errors in the aux file when lineno is dropped
\providecommand{\@LN}[2]{\relax}

%% ASME page proofs seem to align the line number at top of the line, rather than bottom as done here.


%%%%%%%%%%%%%%%%%  Footer Set Up  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%  footer text names  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\JourName}[1]{\gdef\@JourName{#1}}
\providecommand\@JourName{\hbox{ }}

\NewDocumentCommand{\PaperYear}{m}{%
      \gdef\@PaperYear{#1}%
      }
\providecommand\@PaperYear{\the\year}

\def\@PreprintStringL{PREPRINT}% updated 2024/07/24
\def\@PreprintStringR{PREPRINT}

\NewDocumentCommand{\PreprintString}{m o}{%
    \IfNoValueTF{#2}{%
		\gdef\@PreprintStringL{#1}%
		\gdef\@PreprintStringR{#1}%
	}{%
	\ifx R#2{\gdef\@PreprintStringR{#1}}\fi
	\ifx L#2{\gdef\@PreprintStringL{#1}}\fi
	}
}

\newcommand{\PaperNumber}[1]{\gdef\@PaperNumber{#1-}}
\providecommand\@PaperNumber{\relax}

%%%%%%  Fancyhdr  %%%%%%%%%%%%%%%%%%%%%%%%%

\RequirePackage{fancyhdr}% options revised 2024/07/23
\pagestyle{fancy}

\fancyhf{}% clear all header and footer fields
\renewcommand{\headrulewidth}{0pt} 
\renewcommand{\footrulewidth}{0pt}
\ifasmejour@nofoot
    \fancyfoot[CE,CO]{\thepage}
\else
    \fancyfoot[RE]{\large\bfseries\sffamily Transactions of the ASME} 
    \fancyfoot[LO]{\large\bfseries\sffamily Journal of \@JourName} 
    \fancyfoot[RO]{\large\sffamily \@PreprintStringR\space\space\bfseries/\space\space\@PaperNumber\thepage}
    \fancyfoot[LE]{\large\sffamily {\bfseries \@PaperNumber\thepage\space\space/}\space\space\@PreprintStringL\ }
\fi

\fancypagestyle{title}{% is an odd page
    \fancyhf{}% clear all header and footer fields
    \renewcommand{\headrulewidth}{0pt}
    \renewcommand{\footrulewidth}{0pt}
    \ifasmejour@nofoot
        \fancyfoot[CO]{\thepage}
    \else
	    \fancyfoot[RO]{\large\sffamily \@PreprintStringR\space\space\bfseries/\space\space\@PaperNumber\thepage} 
	    \fancyfoot[LO]{\large\bfseries\sffamily Journal of \@JourName}
        \ifasmejour@nocopyright
        	\fancyfoot[CO]{}
    	\else
    	    \fancyfoot[CO]{\large\bfseries\sffamily Copyright \textcopyright\ \@PaperYear\ by ASME}
    	\fi
    \fi	
}

%%%%%% Footnotes %%%%%%%%%%%%%%%%%%%%%%%%%%%

\RequirePackage{footmisc}%
\IfPackageAtLeastTF{footmisc}{2022/02/05}{
	 	\PassOptionsToPackage{belowfloats}{footmisc}%
	}{	\RequirePackage{fnpos}
		\makeFNbottom
		\makeFNbelow
	}%
\setlength\footnotemargin{4mm}% reduce indentation of footnotes, from footmisc
\setlength{\skip\footins}{12pt plus 2pt minus 1pt}

\renewcommand{\footnoterule}{%
  \kern -3pt
  \hrule width 0.5in height 0.5pt
  \kern 2pt
}

%% Produces an unmarked footnote about the revision date. 
%% This command is invoked by \date as part of \maketitle below.
%% Text can be anything given as the argument to \date{..}.
\NewDocumentCommand{\revfootnote}{m}{\begin{NoHyper}\def\@thefnmark{}\@footnotetext{\hspace{-3pt}#1}\end{NoHyper}}% \gdef --&gt;\def 2021/12/23

%% The above has been offset per style and modified to eliminate missing anchor warning from hyperref that the following \def would cause
%%\def\revfootnote{\gdef\@thefnmark{}\@footnotetext}


%% include a comma for sequential footnotes
\ExplSyntaxOn
	\cs_new:Npn   \__asmejour_NoteComma:n { \peek_meaning:NT \footnote { \textsuperscript{\mdseries,} } }
	\cs_new_eq:NN \__asmejour_savefootnote \footnote
	\cs_gset_protected:Npn \footnote #1    { \__asmejour_savefootnote{#1}\__asmejour_NoteComma:n } 
\ExplSyntaxOff


%%%%%%%%%  Caption Related  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\RequirePackage[labelfont={sf,bf},hypcap=false]{caption}
\RequirePackage[hypcap=false,list=true]{subcaption}

%% This option is experimental and documented only here, 2025/04/01
%% 	 purpose is to allow tagged pdf based on current latex-lab code
%%   subcaptions are not specifically addressed in this patch
%% 	 babel [spanish] option is NOT compatible with tagging.
\ifasmejour@captionpatch
%%  see github discussion of this patch by Ulrike Fischer
%% 	https://github.com/latex3/tagging-project/issues/720#issuecomment-2386568711
	\ExplSyntaxOn
	\IfPackageLoadedTF{tagpdf}{% this test may need to be removed once latex-lab moves to kernel code
        \RemoveFromHook{begindocument}[latex-lab-testphase-float]
        \socket_new_plug:nnn{tagsupport/parbox/before}{caption}
          {   
           \tagpdfparaOn %restart para tagging
           \tl_if_empty:NTF\@current@float@struct
            {     
             \tag_struct_begin:n{tag=Caption,firstkid}
            }
            {
             \tag_struct_begin:n{tag=Caption,parent=\@current@float@struct,firstkid}
            } 
          }
        \socket_new_plug:nnn{tagsupport/parbox/after}{caption}
          {
           \tag_struct_end:   
          }
        \l@addto@macro\caption@beginex@hook{%
          \tagpdfparaOff %leavevmode in parbox should not start paragraph structure
          \AssignSocketPlug{tagsupport/parbox/before}{caption}
          \AssignSocketPlug{tagsupport/parbox/after}{caption}}
	}{}
	\ExplSyntaxOff
\fi

\DeclareCaptionTextFormat{boldmath}{\mathversion{sansbold}#1}
\DeclareCaptionTextFormat{sansmath}{\mathversion{sans}#1}% ASME's subcaptions actually do not allow math...

\captionsetup[figure]{labelfont={sf,bf},textfont={sf,bf},textformat=boldmath,labelsep=quad}
\captionsetup[table]{labelfont={sf,bf},textfont={sf,bf},textformat=boldmath,labelsep=quad,skip=0.5\baselineskip} 

%% 2021/01/30: ASME only labels subfigures with a sans serif, italic (a), (b),... no caption text or math, no bold face.
\captionsetup[subfigure]{labelfont={sf},textfont={sf},textformat=sansmath,labelformat=simple}% default: =parens
\renewcommand\thesubfigure{(\textit{\alph{subfigure}})}

\captionsetup[subtable]{labelfont={sf},textfont={sf},textformat=sansmath,labelformat=simple} 
\renewcommand\thesubtable{(\textit{\alph{subtable}})}


%%%%%%%%%%%%  Section Headings  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Revised 2025/03/30, removing titlesec package

\renewcommand\section{\@startsection {section}{1}{\z@}%
                                   {14pt \@plus 3pt \@minus 2pt}%
                                   {3pt \@plus 2pt \@minus 1pt}%
                                   {\mathversion{bold}\bfseries\large\raggedright}}
\renewcommand\subsection{\@startsection {subsection}{2}{3.5mm}%
                                   {12pt \@plus 3pt \@minus 2pt}%
                                   {-0.5em}%
                                   {\mathversion{bold}\normalsize\bfseries\raggedright}}
\renewcommand\subsubsection{\@startsection {subsubsection}{3}{3.5mm}%
                                   {12pt \@plus 3pt \@minus 2pt}%
                                   {-0.5em}%
                                   {\itshape\normalsize}}
\patchcmd{\thesection}{\@arabic\c@section}{\@arabic\c@section}{}{}
\patchcmd{\thesubsection}{\thesection.\@arabic\c@subsection}{\@arabic\c@section.\@arabic\c@subsection}{}{}
\patchcmd{\@seccntformat}{\quad}{\hspace*{1em}}{}{} 
\let\paragraph\subsubsection

% note, 2025/04/07: \mathversion{bold} gets tagged as a formula in display headings, which \@xsect, etc. handle differently. Unclear why this happens.

% Insert period at end of subsection and subsubsection titles
% Would prefer a more streamlined approach, but no simple hook for #8 in \section
\let\oldsubsection\subsection
\RenewDocumentCommand{\subsection}{s o m}{%
  \IfBooleanTF{#1} % starred version
    {\IfNoValueTF{#2}
        {\oldsubsection*{#3.}} % no optional arg
        {\oldsubsection*[#2]{#3.}}%
    }
    {\IfNoValueTF{#2}
        {\oldsubsection{#3.}} % no optional arg
        {\oldsubsection[#2]{#3.}}%
    }%
}
\let\oldsubsubsection\subsubsection
\RenewDocumentCommand{\subsubsection}{s o m}{%
  \IfBooleanTF{#1} % starred version
    {\IfNoValueTF{#2}
        {\oldsubsubsection*{#3.}} % no optional arg
        {\oldsubsubsection*[#2]{#3.}}%
    }
    {\IfNoValueTF{#2}
        {\oldsubsubsection{#3.}} % no optional arg
        {\oldsubsubsection[#2]{#3.}}%
    }%
}

% Special handling of the appendices            
% Assumes that appendices are the last technical content in paper
% Tagging code, if loaded, uses \@kernel@tag@hangfrom
\ExplSyntaxOn
\cs_new_protected:Nn \__asmejour_change_hangindent: {
    \cs_if_exist:NT \@kernel@tag@hangfrom {
		  \cs_new_eq:NN  \__asmejour_sav@kernel@tag@hangfrom \@kernel@tag@hangfrom
		  % modify command in latex-lab-sec
          \cs_gset_protected:Npn \@app@kernel@tag@hangfrom ##1
          {
            \tagstructbegin{tag=\l__tag_para_tag_tl}
            \cs_if_exist_use:N \__tag_gincr_para_begin_int:
            \tagstructbegin{tag=Lbl}
            \setbox\@tempboxa
             \hbox
              {
                \bool_lazy_and:nnT
                {\tag_if_active_p:}
                {\g__tag_mode_lua_bool}
                {\tagmcbegin{tag=Lbl}}
                {##1}
              }
            \tag_suspend:n{hangfrom}
        %   \hangindent \wd\@tempboxa\noindent %% &lt;== changing this line only
            \hangindent 0pt\noindent
            \tag_resume:n{hangfrom}
            \tagmcbegin{}\box\@tempboxa\tagmcend\tagstructend\tagmcbegin{}
          }
		  \cs_set_eq:NN  \@kernel@tag@hangfrom \@app@kernel@tag@hangfrom
	}
          \cs_new_eq:NN \__asmejour_sav@hangfrom \@hangfrom
          \cs_gset_protected:Npn \@app@hangfrom ##1
          {
            \setbox\@tempboxa\hbox{{##1}}%
         %  \hangindent \wd\@tempboxa\noindent\box\@tempboxa} %% &lt;== changing this line only
            \hangindent 0pt\noindent\box\@tempboxa
          }   
}

\providecommand*{\appendicesname}{Appendices}
\renewcommand{\appendix}{
    \par
    \__asmejour_change_hangindent:
    \setcounter{section}{0}
    \setcounter{subsection}{0}
    \@addtoreset{equation}{section}
    \pdfbookmark[1]{\appendicesname}{appendices}
    \gdef\theequation{\@Alph\c@section\@arabic\c@equation}
    \gdef\thesection{\@Alph\c@section}
    \gdef\thesubsection{\@Alph\c@section.\@arabic\c@subsection}
	\AddToHook{cmd/section/before}{
		\gdef\@seccntformat##1{\appendixname\ \csname the##1\endcsname :\hspace{0.5em}}
		\def\@hangfrom{\@app@hangfrom}
		\def\@kernel@tag@hangfrom{\@app@kernel@tag@hangfrom}
	}
    \AddToHook{cmd/subsection/before}{ % added to Latex 2020/10/01 
	    \gdef\@seccntformat##1{\csname the##1\endcsname.\hspace{0.5em}}
    	\def\@hangfrom{\__asmejour_sav@hangfrom}
		\def\@kernel@tag@hangfrom{\__asmejour_sav@kernel@tag@hangfrom}
    }
}
\ExplSyntaxOff

%  natbib's \bibsection controls section heading for References. 
%		If you wish to customize the title of the reference list put \renewcommand{\refname}{Other Title} 
%		into the .tex file, after the preamble (before the other bib commands near the end)


%%%%%%%%%%%%%%%%%%%%  List environments  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Revised 2025/03/30, removing enumitem

\renewcommand\labelenumi{(\theenumi)}	% cf. article.cls
\setlength\leftmargini{2em}				% reset here b/c @twocolumn not yet invoked

% No extra space between list items (cf. size9.clo)
\AddToHook{begindocument/end}{
    \AddToHook{cmd/@listi/after}{
    	\parsep  0\p@
    	\itemsep 0\p@
    }
}
%\AtBeginDocument{
%    \patchcmd{\@listi}{\parsep 4\p@ \@plus 2\p@ \@minus \p@}{\parsep  0\p@}{}{}
%    \patchcmd{\@listi}{\itemsep \parsep}{\itemsep 0\p@}{}{}
%}

%%%%%%%%%%%%%%%%%  Hyperref  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ifasmejour@pdftex
    %%% to assist with unicode glyph mapping, following M. Sharpe's recommendation in the newtx documentation. 
    %%% as of 2024/07/28, these are still necessary with \DocumentMetadata{pdfstandard=A-3u}.
    \InputIfFileExists{glyphtounicode-cmr.tex}{}{} 	%% additional mappings
    \InputIfFileExists{glyphtounicode-cmex.tex}{}{} %% additional mappings in latex-lab.
    \InputIfFileExists{glyphtounicode-ntx.tex}{}{} 	%% additional mappings
\fi

%%%

\RequirePackage[psdextra]{hyperref} % provide most hyperref options via \hypersetup, but also per documentation
									% set [psdextra] here (for additional math support in bookmarks) 2021/12/23
\hypersetup{%
	pdfborder={0 0 0}, 
	bookmarksnumbered=true,
	bookmarksopen=true,
	bookmarksopenlevel=1,
	colorlinks=true,
	linkcolor=blue, 
	citecolor=blue,  
	urlcolor=blue,   
	filecolor=red, % added 2021/12/23, to make certain broken links more apparent
	pdfnewwindow=true,
	pdfpagelayout=SinglePage, % was TwoPageRight, changed 2020/08/12
	pdfdisplaydoctitle=true,
}
	
\urlstyle{same}                % don't switch to typewriter font
\RequirePackage{doi}           % supports nasty characters in some doi's
\renewcommand{\doitext}{doi:~} % change from default, {doi:}, to this for ASME specification

\providecommand*{\toclevel@subfigure}{1}%  &lt;== to address unknown bookmark level of subfigure. 2021/12/24
\providecommand\hrefurl[2]{\href{#1}{#2}}% &lt;== in case no \DocumentMetadata{..}


%%%%%% Adjustments to accommodate hyperref bookmarks %%%%%%%%%%%%%%%%%%%%%%

%%%     Recent development of \pdfstring has removed all robust commands from bookmarks (2021/12/23).
%%%     By mid-2024, no errors are thrown except for \bm; however, these commands still serve to suppress warnings.
%%%	    Math shift by $..$ still creates a warning, but I am leaving that in place. To avoid, use \( .. \) instead.

%% Since \bm is useful in headings, this fix will reduce frequency with which
%% alternate pdfstrings must be given in section command as \section[pdfstring]{texstring}
\pdfstringdefDisableCommands{%
    \def\bm#1#{\relax}%
}

%% Let's disable \( and \) in pdf bookmarks, 2020/02/28
\pdfstringdefDisableCommands{%
    \def\({\relax}%
    \def\){\relax}%
}

%% Let's just remove citations from pdf bookmarks
\pdfstringdefDisableCommands{%
    \def\cite{\@gobble}%
}

%% Ensure that tag color does not follow \eqref into bookmarks, 2020/02/28
\pdfstringdefDisableCommands{%
    \def\eqref#1{(\ref*{#1})}%
}

%% Let's make sure footnotes in section headings don't break pdf bookmarks.
%\robustify{\footnote} % the redefined footnote above is protected, 2023/10/21
\pdfstringdefDisableCommands{%
    \def\footnote#1{}%
}


%%%%%%%%%%%%%  Define some section and other names for special environments  %%%%%%%%%%%%%%%%%%%%%%%%

\providecommand{\nomname}{Nomenclature}  
\providecommand{\keywordname}{Keywords}
\providecommand{\CAwords}{Corresponding Author.}


%%%%%%%%%%%%%  Nomenclature Environment   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Nomenclature environment in ASME Journal Style.
%% Run twice to get proper label width.
%% Set first optional argument (a dimension) to override automatic label width (e.g., if one label too wide)
%% Second argument can be used to rename the section, e.g., to List of Symbols.

\newlength\widest
\newlength\asmejour@widest
\newlength\nomenwidth
\newlength\savitemsep

\NewDocumentCommand{\entry}{m m}{%
	\ifblank{#2}{%
		\ClassError{\ClassName}{The command \protect\entry should have two arguments. For subheadings, use \protect\EntryHeading}{It appears that you gave only one argument to \protect\entry.  You must include a second argument.}
	}{%
		\item[\hfill#1${} = {}$]#2%
		\@itempenalty=-\@lowpenalty%
		\setlength\itemsep\savitemsep%
		\settowidth\asmejour@widest{#1${} = {}$}%
		\ifdim\asmejour@widest&gt;\widest \global\setlength\widest\asmejour@widest\fi%
    }
}

%% A separate command command for nomenclature subheadings
\NewDocumentCommand\EntryHeading{m}{%
             \itemsep12\p@ plus 4\p@ minus 4\p@
             \goodbreak\item[\bfseries#1\hfill]\mbox{}\itemsep3\p@ plus 1\p@ minus 1\p@\@itempenalty=1000% add \mbox for tagged pdf, 2023/10/20
}

\newlength\savwidest
\NewDocumentEnvironment{nomenclature}{O{\nomenwidth} O{\nomname} }{
        \setlength{\widest}{0em}
        \section*{#2}
        \raggedright
        \begin{list}{}{%
             \setlength{\topsep}{0pt}
             \setlength{\partopsep}{0pt}
             \setlength{\itemsep}{0pt}
             \setlength{\parsep}{\itemsep}
             \setlength{\labelsep}{0em}
             \setlength{\labelwidth}{#1}
             \setlength{\leftmargin}{\labelwidth}
             \addtolength{\leftmargin}{\labelsep}
			 \setlength\savitemsep\itemsep % EntryHeading changes \itemsep from 0pt
         }%
   }{%
   \immediate\write\@auxout{\global\savwidest=\the\widest}% after the preamble, the aux file will set this value...
   \end{list}\ignorespacesafterend
} 
\AtBeginDocument{
	\setlength{\nomenwidth}{\savwidest} % ...and this will set nomenwidth to the saved widest label width
}

      
%%%%%%%%%%%%%%%%  List of figures and list of tables  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% ASME requires these lists for production. 
\ifasmejour@nolists
	\ClassNoteNoLine{\ClassName}{Omitting lists of figures and tables}%
\else
    \AtEndDocument{%
		\twocolumn[%
			\listoffigures
			\listoftables
		]%
	}%
\fi


%%%%%%%%%%%%%%%%  Author/Title/Abstract block  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% convert to expl3 2024/08/19
\ExplSyntaxOn

\coffin_new:N \g__asmejour_authorblock_coffin
\coffin_new:N \g__asmejour_ruleblock_coffin
\coffin_new:N \g__asmejour_abstract_coffin
\coffin_new:N \g__asmejour_title_coffin
\coffin_new:N \g__asmejour_firstrowauthorblock_coffin

\dim_new:N   \g__asmejour_coffinsep_dim %%% vert space between aut coffins
\dim_gset:Nn \g__asmejour_coffinsep_dim {4.5mm}

\dim_new:N   \g__asmejour_coffinspace_dim %%% vert space between title/abst coffins
\dim_gset:Nn \g__asmejour_coffinspace_dim {6.75mm}

\dim_new:N \g__asmejour_rulecofheight_dim
\dim_new:N \g__asmejour_titleheight_dim

\cs_new:Nn \__asmejour_internallinenumbers:n 
{
       \ifasmejour@lineno
          \str_if_in:nnT {#1} {R} { \rightlinenumbers* }
          \str_if_in:nnT {#1} {r} { \rightlinenumbers* }
	 	  \cs_set:Npn \thelinenumber { \@roman\c@linenumber }
		  \internallinenumbers
	   \fi
}

%% In case tagging is not loaded, 2025/04/06
\cs_if_exist:NF \tag_struct_begin:n
	{ 
	  \cs_new:Npn \tag_struct_begin:n #1 { \scan_stop: } 
	  \cs_new:Nn  \tag_struct_end:       { \scan_stop: } 
	}

%% This command is used in the .tex file
\NewDocumentCommand\SetAuthorBlock{m m}{
	\__asmejour_setauthorblock:nn { #1 } { #2 }
}
\int_gzero_new:N  \g__asmejour_authorno_int
\seq_new:N  \g__asmejour_author_seq
\msg_new:nnn { \ClassName } { missingauthor } { Missing~author~name,~check~\SetAuthorBlock~command[s]! }


%% Attach each successive authorblock to the list, which is saved in \g__asmejour_firstrowauthorblock_coffin
\cs_if_exist:NF \str_set:Ne { \cs_generate_variant:Nn \str_set:Nn {Ne} }

\cs_new:Nn \__asmejour_setauthorblock:nn {
   \int_gincr:N  \g__asmejour_authorno_int
   \tl_if_empty:nT {#1} { 
		\msg_warning:nn { \ClassName } { missingauthor } 
		}
   \seq_gput_right:Nn \g__asmejour_author_seq {#1}
   \str_set:Ne \ltmpa_str { Author~\int_use:N \g__asmejour_authorno_int }
   \tag_struct_begin:n{tag=Div, title-o={ \ltmpa_str } }
   \vcoffin_gset:Nnn   \g__asmejour_authorblock_coffin {48.2mm} 
	{
	   \__asmejour_internallinenumbers:n {}
	   \raggedleft\sffamily
	   {\Condhuge\CondSansBold \tl_trim_spaces:n { #1 } }\\ 
	   \CondSans#2
	}
	\tag_struct_end:
    \int_compare:nNnTF { \g__asmejour_authorno_int } =  { 1 } 
    {
    	\coffin_gjoin:NnnNnnnn \g__asmejour_firstrowauthorblock_coffin { hc } { b } \g__asmejour_authorblock_coffin { hc } {t } { 0pt } { 0pt } 
        \dim_gset:Nn \g__asmejour_rulecofheight_dim  { \coffin_ht:N \g__asmejour_firstrowauthorblock_coffin  +  \coffin_dp:N \g__asmejour_firstrowauthorblock_coffin }
     }{
    	\coffin_gjoin:NnnNnnnn \g__asmejour_firstrowauthorblock_coffin { hc } { b } \g__asmejour_authorblock_coffin {hc } {t } { 0pt } { - \dim_use:N \g__asmejour_coffinsep_dim }
        \dim_gset:Nn \g__asmejour_rulecofheight_dim  { \coffin_ht:N \g__asmejour_firstrowauthorblock_coffin  +  \coffin_dp:N \g__asmejour_firstrowauthorblock_coffin }
    }     
}
%% Standard coffin poles are (l hc r t T vc b B). See xcoffins documentation. 

% build comma-separated list of author names
\cs_if_exist:NF \tl_set:Ne   { \cs_generate_variant:Nn \tl_set:Nn   {Ne} }
\cs_if_exist:NF \seq_item:NV { \cs_generate_variant:Nn \seq_item:Nn {NV} }
\tl_new:N     \g_asmejour_authors_tl
\tl_gset:Nn   \g_asmejour_authors_tl \c_empty_tl
\cs_new_protected:Nn \__asmejour_concataut: { 
	\int_set:Nn  \l_tmpa_int {1}
	\tl_clear:N  \l_tmpb_tl 
	\int_do_until:nNnn { \l_tmpa_int } &gt; { \g__asmejour_authorno_int }
	{
		\tl_set:Ne  \l_tmpb_tl { \seq_item:NV \g__asmejour_author_seq \l_tmpa_int }
        \regex_replace_all:nnN  { \cA\~ } {\ } \l_tmpb_tl 		  % replace ~ by space in author list
        \tl_replace_all:Nnn \l_tmpb_tl { \affil } { \use_none:n  }% include in case of carry-over from asmeconf
    	\tl_remove_all:Nn   \l_tmpb_tl { \JointFirstAuthor }      % include in case of carry-over from asmeconf
    	\tl_remove_all:Nn  \l_tmpb_tl { \CorrespondingAuthor }    % takes no argument in asmejour, unlike asmeconf
    	\int_compare:nNnT   { \l_tmpa_int } &lt; { \g__asmejour_authorno_int } {
        	\tl_put_right:Nn \l_tmpb_tl { ,~ }
    		}
		\tl_gput_right:NV  \g_asmejour_authors_tl \l_tmpb_tl
		\int_incr:N  \l_tmpa_int  
	}
	%\iow_term:e { Authors:~ \tl_use:N \g_asmejour_authors_tl } % diagnostic only		
}

\cs_new:Nn \__asmejour_settitle:n 
{
	\cs_gset:Npn \@title {#1} % 2024/07/30 (make this standard command available)
	\tag_struct_begin:n{tag=Title, title=Title}
	\vcoffin_gset:Nnn \g__asmejour_title_coffin {114mm} 
	{
		\__asmejour_internallinenumbers:n {R}
		\vskip 0.5mm % &lt;== ASME doesn't align bar and text
		\noindent\CondHuge\CondSansBold\raggedright
		#1
		\par
	}
	\tag_struct_end:
}

%% \keywords command is used in the .tex file
\cs_new:Npn \__asmejour_keywords {\relax}
\NewDocumentCommand{\keywords}{m}{% removed g option, 2021/01/30
	\cs_gset:Npn \__asmejour_keywords { \par\vskip\baselineskip\noindent{\keywordname :}~#1 }
}

\cs_new:Nn \__asmejour_setabstract:n
{
    \tag_struct_begin:n{tag=Div, title=Abstract}
    \vcoffin_gset:Nnn \g__asmejour_abstract_coffin {114mm}
    {
	   \__asmejour_internallinenumbers:n {R}
       \noindent\itshape
       #1
       \__asmejour_keywords\par 
       \vskip 4mm % &lt;== at bottom of abstract to extend rule
    }
	\tag_struct_end:
}

%% Now assemble and typeset the author, title, and abstract coffins
\cs_new:Nn 	\__asmejour_constructauthorblock: {
	\coffin_gjoin:NnnNnnnn \g__asmejour_title_coffin { l } { b } \g__asmejour_abstract_coffin { l } {t } { 0pt } { - \dim_use:N \g__asmejour_coffinspace_dim } 
    \dim_gset:Nn \g__asmejour_titleheight_dim  { \coffin_ht:N \g__asmejour_title_coffin + \coffin_dp:N \g__asmejour_title_coffin }
	\if_dim:w \g__asmejour_titleheight_dim &gt; \g__asmejour_rulecofheight_dim
		\dim_gset:Nn \g__asmejour_rulecofheight_dim { \g__asmejour_titleheight_dim }
	\else:
		\dim_add:Nn  \g__asmejour_rulecofheight_dim {7.0mm} 
	\fi:
	\hcoffin_gset:Nn \g__asmejour_ruleblock_coffin { \color{\asmejour@barcolor}\rule{2.1mm}{ \dim_use:N \g__asmejour_rulecofheight_dim } }
	\coffin_gjoin:NnnNnnnn \g__asmejour_firstrowauthorblock_coffin { vc } { r } \g__asmejour_ruleblock_coffin {vc } { l } { \dim_use:N \g__asmejour_coffinsep_dim } { 0pt } 
	\coffin_gjoin:NnnNnnnn \g__asmejour_firstrowauthorblock_coffin { vc } { r } \g__asmejour_title_coffin {vc } { l } { \dim_use:N \g__asmejour_coffinsep_dim } { 0pt } 
    \coffin_typeset:Nnnnn  \g__asmejour_firstrowauthorblock_coffin { l }{t }{ 0pt }{ 0pt }
    \__asmejour_concataut:
    \cs_gset:Npn \@author { \tl_use:N \g_asmeconf_authors_tl }
}

\ExplSyntaxOff

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Corresponding author gets footnote #1 and subsequent notes are 2, 3, ....
%% ASME apparently does not recognize joint first authors...so I have not coded that functionality

%% Flag for corresponding author (only one expected, although this code supports more than one)
\newif\ifasmejour@CA

%% ASME prefers email to be in address block, not CA footnote; removed option 2021/01/30
\NewDocumentCommand{\CorrespondingAuthor}{}{%
	\global\asmejour@CAtrue%
	\def\@makefnmark{\hbox{\@textsuperscript{\sffamily\@thefnmark}}}%
	\footnotemark%
	\addtocounter{footnote}{-1}% in case of more than one CA
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% make the title block

\ExplSyntaxOn

%% space between title block an start of two-column text
\skip_new:N   \g__asmejour_AbstractSep_skip
\skip_gset:Nn \g__asmejour_AbstractSep_skip {12.5mm plus 2mm minus 2mm }

\NewDocumentCommand\AbstractSep{m}{
	\skip_gset:Nn \g__asmejour_AbstractSep_skip {#1}
}

\cs_new:Npn \__asmejour_maketitle:  
{
    \thispagestyle{title}%
    \ifasmejour@singlecolumn % added 2024/07/20
    	\__asmejour_constructauthorblock: 
      	\vskip \g__asmejour_AbstractSep_skip 
    \else	
        \twocolumn[
    	\__asmejour_constructauthorblock:
    	\vskip \g__asmejour_AbstractSep_skip
        ]
    \fi
    \ifasmejour@CA 
    	\addtocounter{footnote}{1}
    	\footnotetext{\CAwords}
    \fi
    \DateFootnote
    \ifasmejour@contractor\revfootnote{The~United~States~Government~retains,~and~by~accepting~the~article~for~publication,~the~publisher~acknowledges~that~the~United~States~Government~retains,~a~non-exclusive,~paid-up,~irrevocable,~worldwide~license~to~publish~or~reproduce~the~published~form~of~this~work,~or~allow~others~to~do~so,~for~United~States~Government~purposes.}%
    \fi
    \ifasmejour@govt\revfootnote{This~material~is~declared~a~work~of~the~U.~S.~Government~and~is~not~subject~to~copyright~protection~in~the~United~States.~Approved~for~public~release;~distribution~is~unlimited.}%
    \fi
    \ifasmejour@govtsome\revfootnote{This~work~was~authored~in~part~by~a~U.~S.~Government~employee~in~the~scope~of~his/her~employment.~ASME~disclaims~all~interest~in~the~U.~S.~Government's~contribution.}%
    \fi
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Redefine titling commands from standard LaTeX article class

\RenewDocumentCommand{\maketitle}{}{\__asmejour_maketitle:}
\RenewDocumentCommand{\title}{m}{ \__asmejour_settitle:n {#1} }
\RenewDocumentCommand{\author}{m}{
	\msg_error:nn { \ClassName }{ authornotused }
}
\msg_new:nnnn { \ClassName } { authornotused }{ In~the~asmejour~class,\\ the~\author~command~is~not~used.\\ Use~\SetAuthorBlock{Name}{Address}~for~each~author~instead. } { The~\author~command~is~not~defined~in~the~asmejour~class.~Use~\SetAuthorBlock{Name}{Address}~as~described~in~the~documentation. }

\RenewDocumentEnvironment{abstract}{+b}{\gdef\tmp{ \__asmejour_setabstract:n {#1} }\aftergroup\tmp}{\ignorespacesafterend} 
%% Thanks to David Carlisle for the suggestion of \gdef\tmp{...

%% Put date as an unnumbered footnote at bottom of first column
%% If \date command is not used, default to \DateFootnote
\bool_new:N 	  \g__asmejour_date_bool
\bool_gset_true:N \g__asmejour_date_bool
\tl_new:N   \g__asmejour_date_tl 
\tl_gset:Nn \g__asmejour_date_tl { \today }
\tl_new:N   \DateFootnote
\tl_gset:Nn \DateFootnote { 
	\if_bool:N \g__asmejour_date_bool \revfootnote{\g__asmejour_date_tl} \else: \fi: 
}
\RenewDocumentCommand{\date}{m}
{
	\tl_if_empty:nTF {#1}
		{ \bool_gset_false:N \g__asmejour_date_bool }
    	{ \tl_gset:Nn \g__asmejour_date_tl { #1 } }
}

\RenewDocumentCommand{\thanks}{m}{\relax}%% disabling this standard command, as it is inconsistent with this format
\ExplSyntaxOff

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\endinput
%%
%% End of file `asmejour.cls'.

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