From 1c6219f7af0fc2899fe440007439d1284ed2c877 Mon Sep 17 00:00:00 2001 From: Suter Andreas Date: Tue, 19 Aug 2014 16:23:39 +0200 Subject: [PATCH] changed temperature depends of the gap functions, added comments and amended the documentation --- src/external/libGapIntegrals/GapIntegrals.pdf | Bin 77600 -> 172409 bytes src/external/libGapIntegrals/GapIntegrals.tex | 198 ++++++++++ .../libGapIntegrals/PSI-Logo_narrow.jpg | Bin 0 -> 50014 bytes .../libGapIntegrals/TGapIntegrals.cpp | 349 ++++++++++++++++-- src/external/libGapIntegrals/TGapIntegrals.h | 91 ++++- 5 files changed, 600 insertions(+), 38 deletions(-) create mode 100644 src/external/libGapIntegrals/GapIntegrals.tex create mode 100644 src/external/libGapIntegrals/PSI-Logo_narrow.jpg diff --git a/src/external/libGapIntegrals/GapIntegrals.pdf b/src/external/libGapIntegrals/GapIntegrals.pdf index 861126122de11ce5592ab6b035a0c703018da5fb..80214db8af2137acc143913dfcfdbede9f725e4d 100644 GIT binary patch literal 172409 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00000000..57f8bf4d --- /dev/null +++ b/src/external/libGapIntegrals/GapIntegrals.tex @@ -0,0 +1,198 @@ +\documentclass[twoside]{article} + +\usepackage[english]{babel} +%\usepackage{a4} +\usepackage{amssymb,amsmath,bm} +\usepackage{graphicx,tabularx} +\usepackage{fancyhdr} +\usepackage{array} +\usepackage{float} +\usepackage{hyperref} +\usepackage{xspace} +\usepackage{rotating} +\usepackage{dcolumn} +\usepackage{geometry} + +\geometry{a4paper,left=20mm,right=20mm,top=20mm,bottom=20mm} + +% \setlength{\topmargin}{10mm} +% \setlength{\topmargin}{-13mm} +% % \setlength{\oddsidemargin}{0.5cm} +% % \setlength{\evensidemargin}{0cm} +% \setlength{\oddsidemargin}{1cm} +% \setlength{\evensidemargin}{1cm} +% \setlength{\textwidth}{15cm} +\setlength{\textheight}{23.8cm} + +\pagestyle{fancyplain} +\addtolength{\headwidth}{0.6cm} +\fancyhead{}% +\fancyhead[RE,LO]{\bf \textsc{GapIntegrals}}% +\fancyhead[LE,RO]{\thepage} +\cfoot{--- B.M.~Wojek / A.~Suter -- \today~ ---} +\rfoot{\includegraphics[width=2cm]{PSI-Logo_narrow.jpg}} + +\DeclareMathAlphabet{\bi}{OML}{cmm}{b}{it} + +\newcommand{\mean}[1]{\langle #1 \rangle} +\newcommand{\lem}{LE-$\mu$SR\xspace} +\newcommand{\lemhead}{LE-$\bm{\mu}$SR\xspace} +\newcommand{\musr}{$\mu$SR\xspace} +\newcommand{\musrhead}{$\bm{\mu}$SR\xspace} +\newcommand{\trimsp}{\textsc{trim.sp}\xspace} +\newcommand{\musrfithead}{MUSRFIT\xspace} +\newcommand{\musrfit}{\textsc{musrfit}\xspace} +\newcommand{\gapint}{\textsc{GapIntegrals}\xspace} +\newcommand{\YBCO}{YBa$_{2}$Cu$_{3}$O$_{7-\delta}$\xspace} +\newcommand{\YBCOhead}{YBa$_{\bm{2}}$Cu$_{\bm{3}}$O$_{\bm{7-\delta}}$\xspace} + +\newcolumntype{d}[1]{D{.}{.}{#1}} +\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}} + +\begin{document} +% Header info -------------------------------------------------- +\thispagestyle{empty} +\noindent +\begin{tabular}{@{\hspace{-0.2cm}}l@{\hspace{6cm}}r} +\noindent\includegraphics[width=3.4cm]{PSI-Logo_narrow.jpg} & + {\Huge\sf Memorandum} +\end{tabular} +% +\vskip 1cm +% +\begin{tabular}{@{\hspace{-0.5cm}}ll@{\hspace{4cm}}ll} +Date: & September 19, 2009 / August 19, 2014 & & \\[3ex] +From: & B.M.~Wojek / Modified by A. Suter & \\ +E-Mail: & \verb?bastian.wojek@psi.ch? / \verb?andreas.suter@psi.ch? && +\end{tabular} +% +\vskip 0.3cm +\noindent\hrulefill +\vskip 1cm +% +\section*{\musrfithead plug-in for the calculation of the temperature dependence of $\bm{1/\lambda^2}$ for various gap symmetries}% + +This memo is intended to give a short summary of the background on which the \gapint plug-in for \musrfit \cite{musrfit} has been developped. The aim of this implementation is the efficient calculation of integrals of the form +\begin{equation}\label{int} + I(T) = 1 + \frac{1}{\pi}\int_0^{2\pi}\int_{\Delta(\varphi,T)}^{\infty}\left(\frac{\partial f}{\partial E}\right) \frac{E}{\sqrt{E^2-\Delta^2(\varphi,T)}}\mathrm{d}E\mathrm{d}\varphi\,, +\end{equation} +where $f = (1+\exp(E/k_{\mathrm B}T))^{-1}$, like they appear e.g. in the theoretical temperature dependence of $1/\lambda^2$~\cite{Manzano}. +In order not to do too many unnecessary function calls during the final numerical evaluation we simplify the integral (\ref{int}) as far as possible analytically. The derivative of $f$ is given by +\begin{equation}\label{derivative} +\frac{\partial f}{\partial E} = -\frac{1}{k_{\mathrm B}T}\frac{\exp(E/k_{\mathrm B}T)}{\left(1+\exp(E/k_{\mathrm B}T)\right)^2} = -\frac{1}{4k_{\mathrm B}T} \frac{1}{\cosh^2\left(E/2k_{\mathrm B}T\right)}. +\end{equation} +Using (\ref{derivative}) and doing the substitution $E'^2 = E^2-\Delta^2(\varphi,T)$, equation (\ref{int}) can be written as +\begin{equation} +\begin{split} +I(T) & = 1 - \frac{1}{4\pi k_{\mathrm B}T}\int_0^{2\pi}\int_{\Delta(\varphi,T)}^{\infty}\frac{1}{\cosh^2\left(E/2k_{\mathrm B}T\right)}\frac{E}{\sqrt{E^2-\Delta^2(\varphi,T)}}\mathrm{d}E\mathrm{d}\varphi \\ +& = 1 - \frac{1}{4\pi k_{\mathrm B}T}\int_0^{2\pi}\int_{0}^{\infty}\frac{1}{\cosh^2\left(\sqrt{E'^2+\Delta^2(\varphi,T)}/2k_{\mathrm B}T\right)}\mathrm{d}E'\mathrm{d}\varphi\,. +\end{split} +\end{equation} +Since a numerical integration should be performed and the function to be integrated is exponentially approaching zero for $E'\rightarrow\infty$ the infinite $E'$ integration limit can be replaced by a cutoff energy $E_{\mathrm c}$ which has to be chosen big enough: +\begin{equation} +I(T) \simeq \tilde{I}(T) \equiv 1 - \frac{1}{4\pi k_{\mathrm B}T}\int_0^{2\pi}\int_{0}^{E_{\mathrm c}}\frac{1}{\cosh^2\left(\sqrt{E'^2+\Delta^2(\varphi,T)}/2k_{\mathrm B}T\right)}\mathrm{d}E'\mathrm{d}\varphi\,. +\end{equation} +In the case that $\Delta^2(\varphi,T)$ is periodic in $\varphi$ with a period of $\pi/2$ (valid for all gap symmetries implemented at the moment), it is enough to limit the $\varphi$-integration to one period and to multiply the result by $4$: +\begin{equation} +\tilde{I}(T) = 1 - \frac{1}{\pi k_{\mathrm B}T}\int_0^{\pi/2}\int_{0}^{E_{\mathrm c}}\frac{1}{\cosh^2\left(\sqrt{E'^2+\Delta^2(\varphi,T)}/2k_{\mathrm B}T\right)}\mathrm{d}E'\mathrm{d}\varphi\,. +\end{equation} +For the numerical integration we use algorithms of the \textsc{Cuba} library \cite{cuba} which require to have a Riemann integral over the unit square. Therefore, we have to scale the integrand by the upper limits of the integrations. Note that $E_{\mathrm c}$ and $\pi/2$ (or in general the upper limit of the $\varphi$ integration) are now treated as dimensionless scaling factors. +\begin{equation} +\tilde{I}(T) = 1 - \frac{E_{\mathrm c}}{2k_{\mathrm B}T}\int_0^{1_{\varphi}}\int_{0}^{1_{E}}\frac{1}{\cosh^2\left(\sqrt{(E_{\mathrm c}E)^2+\Delta^2\left(\frac{\pi}{2}\varphi,T\right)}/2k_{\mathrm B}T\right)}\mathrm{d}E\mathrm{d}\varphi +\end{equation} + +\subsection*{Implemented gap functions and function calls from MUSRFIT} +At the moment the calculation of $\tilde{I}(T)$ is implemented for various gap functions all using the approximate \textsc{BCS} temperature dependence~\cite{Prozorov} +\begin{equation}\label{eq:gapT} + \Delta(\varphi,T) \simeq \Delta(\varphi,0)\,\tanh\left[\frac{\pi k_{\rm B} T_{\rm c}}{\Delta_0}\sqrt{a_{\rm G} \left(\frac{T_{\rm c}}{T}-1\right)}\right] +\end{equation} +\noindent with $\Delta_0$ as given below, and $a_{\rm G}$ depends on the pairing state: + +\begin{description} + \item [\textit{s}-wave:] $a_{\rm G}=1$ \qquad with $\Delta_0 = 1.76\, k_{\rm B} T_c$ + \item [\textit{d}-wave:] $a_{\rm G}=4/3$ \quad with $\Delta_0 = 2.14\, k_{\rm B} T_c$ +\end{description} + +\noindent Eq.(\ref{eq:gapT}) replaces the \emph{previously} used approximation~\cite{Manzano}: +\begin{equation} +\Delta(\varphi,T) \simeq \Delta(\varphi)\tanh\left(1.82\left(1.018\left(\frac{T_{\mathrm c}}{T}-1\right)\right)^{0.51}\right)\,. +\end{equation} +The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi)$: + +\begin{description} + \item[\textit{s}-wave gap:] + \begin{equation} + \Delta(\varphi) = \Delta_0 + \end{equation} + \musrfit theory line: \verb?userFcn libGapIntegrals TGapSWave 1 2 [3]?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$, if $a_{\rm G}$ is not given, $a_{\rm G} = 1$) + \item[\textit{d}-wave gap \cite{Deutscher}:] + \begin{equation} + \Delta(\varphi) = \Delta_0\cos\left(2\varphi\right) + \end{equation} + \musrfit theory line: \verb?userFcn libGapIntegrals TGapDWave 1 2 [3]?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$, if $a_{\rm G}$ is not given, $a_{\rm G} = 4/3$) + \item[non-monotonic \textit{d}-wave gap \cite{Matsui}:] + \begin{equation} + \Delta(\varphi) = \Delta_0\left[a \cos\left(2\varphi\right) + (1-a)\cos\left(6\varphi\right)\right] + \end{equation} + \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave1 1 2 3 [4]?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[a_{\rm G}~(1)]$, if $a_{\rm G}$ is not given, $a_{\rm G} = 4/3$) + \item[non-monotonic \textit{d}-wave gap \cite{Eremin}:] + \begin{equation} + \Delta(\varphi) = \Delta_0\left[\frac{2}{3} \sqrt{\frac{a}{3}}\cos\left(2\varphi\right) / \left( 1 + a\cos^2\left(2\varphi\right)\right)^{\frac{3}{2}}\right],\,a>1/2 + \end{equation} + \musrfit theory line: \verb?userFcn libGapIntegrals TGapNonMonDWave2 1 2 3 [4]?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $a~(1)$, $[a_{\rm G}~(1)]$, if $a_{\rm G}$ is not given, $a_{\rm G} = 4/3$) + \item[anisotropic \textit{s}-wave gap \cite{AnisotropicSWave}:] + \begin{equation} + \Delta(\varphi) = \Delta_0\left[1+a\cos\left(4\varphi\right)\right]\,,\,0\leqslant a\leqslant1 + \end{equation} + \musrfit theory line: \verb?userFcn libGapIntegrals TGapAnSWave 1 2 3 [4]?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $a~(1)$, $[a_{\rm G}~(1)]$, if $a_{\rm G}$ is not given, $a_{\rm G} = 1$) +\end{description} + +\noindent It is also possible to calculate a power law temperature dependence (in the two fluid approximation $n=4$) and the dirty \textit{s}-wave expression. +Obviously for this no integration is needed. +\begin{description} + \item[Power law return function:] + \begin{equation} + \frac{\lambda(0)^2}{\lambda(T)^2} = 1-\left(\frac{T}{T_{\mathrm c}}\right)^n + \end{equation} + \musrfit theory line: \verb?userFcn libGapIntegrals TGapPowerLaw 1 2?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $n~(1)$) + \item[dirty \textit{s}-wave \cite{Tinkham}:] + \begin{equation} + \frac{\lambda(0)^2}{\lambda(T)^2} = \frac{\Delta(T)}{\Delta_0}\,\tanh\left[\frac{\Delta(T)}{2 k_{\rm B} T}\right] + \end{equation} + with $\Delta(T)$ given by Eq.(\ref{eq:gapT}).\\ + \musrfit theory line: \verb?userFcn libGapIntegrals TGapDirtySWave 1 2 [3]?\\ + (Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[a_{\rm G}~(1)]$, if $a_{\rm G}$ is not given, $a_{\rm G} = 1$) +\end{description} + +\noindent Currently there are two gap functions to be found in the code which are \emph{not} documented here: +\verb?TGapCosSqDWave? and \verb?TGapSinSqDWave?. For details for these gap functions (superfluid density along the \textit{a}/\textit{b}-axis +within the semi-classical model assuming a cylindrical Fermi surface and a mixed $d_{x^2-y^2} + s$ symmetry of the superconducting order parameter +(effectively: $d_{x^2-y^2}$ with shifted nodes and \textit{a}-\textit{b}-anisotropy)) see the source code. + +\subsection*{License} +The \gapint library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation \cite{GPL}; either version 2 of the License, or (at your option) any later version. + +\bibliographystyle{plain} +\begin{thebibliography}{1} + +\bibitem{musrfit} A.~Suter, \textit{\musrfit User Manual}, https://wiki.intranet.psi.ch/MUSR/MusrFit +\bibitem{cuba} T.~Hahn, \textit{Cuba -- a library for multidimensional numerical integration}, Comput.~Phys.~Commun.~\textbf{168}~(2005)~78-95, http://www.feynarts.de/cuba/ +\bibitem{Prozorov} R.~Prozorov and R.W.~Giannetta, \textit{Magnetic penetration depth in unconventional superconductors}, Supercond.\ Sci.\ Technol.\ \textbf{19}~(2006)~R41-R67, and Erratum in Supercond.\ Sci.\ Technol.\ \textbf{21}~(2008)~082003. +\bibitem{Manzano} A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205 +\bibitem{Deutscher} G.~Deutscher, \textit{Andreev-Saint-James reflections: A probe of cuprate superconductors}, Rev.~Mod.~Phys.~\textbf{77}~(2005)~109-135 +\bibitem{Matsui} H.~Matsui~\textit{et al.}, \textit{Direct Observation of a Nonmonotonic $d_{x^2-y^2}$-Wave Superconducting Gap in the Electron-Doped High-T$_{\mathrm c}$ Superconductor Pr$_{0.89}$LaCe$_{0.11}$CuO$_4$}, Phys.~Rev.~Lett.~\textbf{95}~(2005)~017003 +\bibitem{Eremin} I.~Eremin, E.~Tsoncheva, and A.V.~Chubukov, \textit{Signature of the nonmonotonic $d$-wave gap in electron-doped cuprates}, Phys.~Rev.~B~\textbf{77}~(2008)~024508 +\bibitem{AnisotropicSWave} ?? +\bibitem{Tinkham} M.~Tinkham, \textit{Introduction to Superconductivity} $2^{\rm nd}$ ed. (Dover Publications, New York, 2004). +\bibitem{GPL} http://www.gnu.org/licenses/old-licenses/gpl-2.0.html + +\end{thebibliography} + + +\end{document} diff --git a/src/external/libGapIntegrals/PSI-Logo_narrow.jpg b/src/external/libGapIntegrals/PSI-Logo_narrow.jpg new file mode 100644 index 0000000000000000000000000000000000000000..9bda1610d63b6cbae528f0a42d52ea949a3abab2 GIT binary patch literal 50014 zcmeFYWmH>Vw>O#^6$+FV*P_KK?$F`{D-JkjFyzuy6jfLnk&|J4TY zAN24M;r#~$_wL-i{jUb#Cjh{`JGX8V+<)@;(Y;6a?g0R|@7%q2i{So)hmS~~KBJNF zCL?Du@xtOLD5;pm4UCKvlT%XbC#R+b#PmGj3B`3IqvI1Stb(s~3>}lkHbq3`UBju_ zg>>~TJ&@J4Y%hdA#w#dVS-aiLMfIPI{3jd#`FrQ~t-CihT%@;d7=3u>-oIM>XU(nK zH?!+l<}4iwRF5zTx_*p*{q@e#-&w%pJGXA0?+z(I4$$`HpJV<1|Np;Ofd|`D#FLuY zS7I9wLVFPP`5@St>wG3}r>z)wvXG*O(O}&q zG`D)&!?Uwtl22xfD~RytL$-!reyi=de)GxTfA_d41Y$%LcwukJ3tme)aA-Gkt3)TC zb9>GV%qAC1BMA!CdNoSzbv6WyRye@qG_IvIk&gCGd;@!6Ei48zP;MrWP-)*`d^CN9 z+vk~!<;w8bu1&HMSa@X(UKri1119N=j#Tj_fVH)LY$aogtB6l 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zJ=I_-P0AkYy4dZcn3P)V_HaOMQkqukbEzoT`E+sDjOP||gV#@cUyN|=m?WW|C`1zVsY|XCEEr)kx*G3%VM`~%O dBebWXyTb&NLtscc_on|pr}%&GU;KVf{0GEE5#j&< literal 0 HcmV?d00001 diff --git a/src/external/libGapIntegrals/TGapIntegrals.cpp b/src/external/libGapIntegrals/TGapIntegrals.cpp index 448556d3..6a3545f8 100644 --- a/src/external/libGapIntegrals/TGapIntegrals.cpp +++ b/src/external/libGapIntegrals/TGapIntegrals.cpp @@ -2,13 +2,13 @@ TGapIntegrals.cpp - Author: Bastian M. Wojek + Author: Bastian M. Wojek / Andreas Suter ***************************************************************************/ /*************************************************************************** * Copyright (C) 2009 by Bastian M. Wojek * - * bastian.wojek@psi.ch * + * bastian.wojek@psi.ch / andreas.suter@psi.ch * * * * This program is free software; you can redistribute it and/or modify * * it under the terms of the GNU General Public License as published by * @@ -64,8 +64,10 @@ ClassImp(TLambdaInvPowerLaw) ClassImp(TFilmMagnetizationDWave) -// s wave gap integral - +//-------------------------------------------------------------------- +/** + *

s wave gap integral + */ TGapSWave::TGapSWave() { TGapIntegral *gapint = new TGapIntegral(); fGapIntegral = gapint; @@ -78,6 +80,10 @@ TGapSWave::TGapSWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapDWave::TGapDWave() { TDWaveGapIntegralCuhre *gapint = new TDWaveGapIntegralCuhre(); fGapIntegral = gapint; @@ -90,6 +96,10 @@ TGapDWave::TGapDWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapCosSqDWave::TGapCosSqDWave() { TCosSqDWaveGapIntegralCuhre *gapint = new TCosSqDWaveGapIntegralCuhre(); fGapIntegral = gapint; @@ -102,6 +112,10 @@ TGapCosSqDWave::TGapCosSqDWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapSinSqDWave::TGapSinSqDWave() { TSinSqDWaveGapIntegralCuhre *gapint = new TSinSqDWaveGapIntegralCuhre(); fGapIntegral = gapint; @@ -114,6 +128,10 @@ TGapSinSqDWave::TGapSinSqDWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapAnSWave::TGapAnSWave() { TAnSWaveGapIntegralCuhre *gapint = new TAnSWaveGapIntegralCuhre(); fGapIntegral = gapint; @@ -126,6 +144,10 @@ TGapAnSWave::TGapAnSWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapNonMonDWave1::TGapNonMonDWave1() { TNonMonDWave1GapIntegralCuhre *gapint = new TNonMonDWave1GapIntegralCuhre(); fGapIntegral = gapint; @@ -138,6 +160,10 @@ TGapNonMonDWave1::TGapNonMonDWave1() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapNonMonDWave2::TGapNonMonDWave2() { TNonMonDWave2GapIntegralCuhre *gapint = new TNonMonDWave2GapIntegralCuhre(); fGapIntegral = gapint; @@ -150,46 +176,90 @@ TGapNonMonDWave2::TGapNonMonDWave2() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaSWave::TLambdaSWave() { fLambdaInvSq = new TGapSWave(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaDWave::TLambdaDWave() { fLambdaInvSq = new TGapDWave(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaAnSWave::TLambdaAnSWave() { fLambdaInvSq = new TGapAnSWave(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaNonMonDWave1::TLambdaNonMonDWave1() { fLambdaInvSq = new TGapNonMonDWave1(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaNonMonDWave2::TLambdaNonMonDWave2() { fLambdaInvSq = new TGapNonMonDWave2(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvSWave::TLambdaInvSWave() { fLambdaInvSq = new TGapSWave(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvDWave::TLambdaInvDWave() { fLambdaInvSq = new TGapDWave(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvAnSWave::TLambdaInvAnSWave() { fLambdaInvSq = new TGapAnSWave(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvNonMonDWave1::TLambdaInvNonMonDWave1() { fLambdaInvSq = new TGapNonMonDWave1(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvNonMonDWave2::TLambdaInvNonMonDWave2() { fLambdaInvSq = new TGapNonMonDWave2(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapSWave::~TGapSWave() { delete fGapIntegral; fGapIntegral = 0; @@ -201,6 +271,10 @@ TGapSWave::~TGapSWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapDWave::~TGapDWave() { delete fGapIntegral; fGapIntegral = 0; @@ -212,6 +286,10 @@ TGapDWave::~TGapDWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapCosSqDWave::~TGapCosSqDWave() { delete fGapIntegral; fGapIntegral = 0; @@ -223,6 +301,10 @@ TGapCosSqDWave::~TGapCosSqDWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapSinSqDWave::~TGapSinSqDWave() { delete fGapIntegral; fGapIntegral = 0; @@ -234,6 +316,10 @@ TGapSinSqDWave::~TGapSinSqDWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapAnSWave::~TGapAnSWave() { delete fGapIntegral; fGapIntegral = 0; @@ -245,6 +331,10 @@ TGapAnSWave::~TGapAnSWave() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapNonMonDWave1::~TGapNonMonDWave1() { delete fGapIntegral; fGapIntegral = 0; @@ -256,6 +346,10 @@ TGapNonMonDWave1::~TGapNonMonDWave1() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TGapNonMonDWave2::~TGapNonMonDWave2() { delete fGapIntegral; fGapIntegral = 0; @@ -267,60 +361,110 @@ TGapNonMonDWave2::~TGapNonMonDWave2() { fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaSWave::~TLambdaSWave() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaDWave::~TLambdaDWave() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaAnSWave::~TLambdaAnSWave() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaNonMonDWave1::~TLambdaNonMonDWave1() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaNonMonDWave2::~TLambdaNonMonDWave2() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvSWave::~TLambdaInvSWave() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvDWave::~TLambdaInvDWave() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvAnSWave::~TLambdaInvAnSWave() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvNonMonDWave1::~TLambdaInvNonMonDWave1() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

+ */ TLambdaInvNonMonDWave2::~TLambdaInvNonMonDWave2() { delete fLambdaInvSq; fLambdaInvSq = 0; } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TGapIntegral. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (9). + */ double TGapSWave::operator()(double t, const vector &par) const { - assert(par.size() == 2); // two parameters: Tc, Delta(0) + assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] + // see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + double aa = 1.0; + if (par.size() == 3) + aa = par[2]; if (t<=0.0) return 1.0; @@ -364,8 +508,8 @@ double TGapSWave::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral, T & Delta(T) - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K - intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aa*(par[0]/t-1.0)))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K fGapIntegral->SetParameters(intPar); ds = 1.0-1.0/intPar[0]*fGapIntegral->IntegrateFunc(0.0, 2.0*(t+intPar[1])); @@ -384,9 +528,19 @@ double TGapSWave::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TDWaveGapIntegralCuhre. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (10). + */ double TGapDWave::operator()(double t, const vector &par) const { - assert(par.size() == 2); // two parameters: Tc, Delta(0) + assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] + // see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67 + // and Erratum Supercond. Sci. Technol. 21 (2008) 082003 + double aa = 4.0/3.0; + if (par.size() == 3) + aa = par[2]; if (t<=0.0) return 1.0; @@ -429,9 +583,8 @@ double TGapDWave::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral, T & Delta(T) - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K - //intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); - intPar.push_back(par[1]*tanh(TMath::Pi()*0.08617384436*par[0]/par[1]*sqrt(4.0/3.0*(par[0]/t-1.0)))); + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aa*(par[0]/t-1.0)))); // tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration @@ -456,9 +609,21 @@ double TGapDWave::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TCosSqDWaveGapIntegralCuhre. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (??). + */ double TGapCosSqDWave::operator()(double t, const vector &par) const { - assert(par.size() == 3); // three parameters: Tc, DeltaD(0), DeltaS(0) + assert((par.size() == 3) || (par.size() == 5)); // three or five parameters: Tc (K), DeltaD(0) (meV), DeltaS(0) (meV), [aD (1), aS (1)] + + double aD = 4.0/3.0; + double aS = 1.0; + if (par.size() == 5) { + aD = par[3]; + aS = par[4]; + } if (t<=0.0) return 1.0; @@ -501,12 +666,11 @@ double TGapCosSqDWave::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral, T & Delta(T) - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K -// intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); - intPar.push_back(par[1]*tanh(TMath::Pi()*0.08617384436*par[0]/par[1]*sqrt(4.0/3.0*(par[0]/t-1.0)))); // DeltaD(T) + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K intPar.push_back(1.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::Pi()); // upper limit of phi-integration - intPar.push_back(par[2]*tanh(TMath::Pi()*0.08617384436*par[0]/par[2]*sqrt((par[0]/t-1.0)))); // DeltaS(T) + intPar.push_back(par[2]*tanh(0.2707214816*par[0]/par[2]*sqrt(aS*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K // double xl[] = {0.0, 0.0}; // lower bound E, phi // double xu[] = {4.0*(t+intPar[1]), 0.5*PI}; // upper bound E, phi @@ -529,9 +693,21 @@ double TGapCosSqDWave::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TSinSqDWaveGapIntegralCuhre. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (??). + */ double TGapSinSqDWave::operator()(double t, const vector &par) const { - assert(par.size() == 3); // two parameters: Tc, Delta(0), s-weight + assert((par.size() == 3) || (par.size() == 5)); // three or five parameters: Tc (K), DeltaD(0) (meV), DeltaS(0) (meV), [aD (1), aS (1)] + + double aD = 4.0/3.0; + double aS = 1.0; + if (par.size() == 5) { + aD = par[3]; + aS = par[4]; + } if (t<=0.0) return 1.0; @@ -574,12 +750,11 @@ double TGapSinSqDWave::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral, T & Delta(T) - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K -// intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); - intPar.push_back(par[1]*tanh(TMath::Pi()*0.08617384436*par[0]/par[1]*sqrt(4.0/3.0*(par[0]/t-1.0)))); + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K intPar.push_back(1.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::Pi()); // upper limit of phi-integration - intPar.push_back(par[2]*tanh(TMath::Pi()*0.08617384436*par[0]/par[2]*sqrt((par[0]/t-1.0)))); // DeltaS(T) + intPar.push_back(par[2]*tanh(0.2707214816*par[0]/par[2]*sqrt(aS*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K // double xl[] = {0.0, 0.0}; // lower bound E, phi // double xu[] = {4.0*(t+intPar[1]), 0.5*PI}; // upper bound E, phi @@ -602,9 +777,19 @@ double TGapSinSqDWave::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TAnSWaveGapIntegralCuhre (anisotropic s-wave). + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (13). + */ double TGapAnSWave::operator()(double t, const vector &par) const { - assert(par.size() == 3); // three parameters: Tc, Delta(0), a + assert((par.size() == 3) || (par.size() == 4)); // three or four parameters: Tc (K), Delta(0) (meV), a (1), [aS_Gap (1)] + + double aS = 1.0; + if (par.size() == 4) { + aS = par[3]; + } if (t<=0.0) return 1.0; @@ -647,8 +832,8 @@ double TGapAnSWave::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral, T & Delta(T) - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K - intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aS*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K intPar.push_back(par[2]); intPar.push_back(4.0*(t+(1.0+par[2])*intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration @@ -674,9 +859,19 @@ double TGapAnSWave::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TNonMonDWave1GapIntegralCuhre. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (11). + */ double TGapNonMonDWave1::operator()(double t, const vector &par) const { - assert(par.size() == 3); // two parameters: Tc, Delta(0), a + assert((par.size() == 3) || (par.size() == 4)); // three or four parameters: Tc (K), Delta(0) (meV), a (1), [aD_Gap (1)] + + double aD = 4.0/3.0; + if (par.size() == 4) { + aD = par[3]; + } if (t<=0.0) return 1.0; @@ -719,8 +914,8 @@ double TGapNonMonDWave1::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral: 2 k_B T, Delta(T), a, E_c, phi_c - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K - intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K intPar.push_back(par[2]); intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration @@ -743,9 +938,19 @@ double TGapNonMonDWave1::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

prepare the needed parameters for the integration carried out in TNonMonDWave2GapIntegralCuhre. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (11). + */ double TGapNonMonDWave2::operator()(double t, const vector &par) const { - assert(par.size() == 3); // two parameters: Tc, Delta(0), a + assert((par.size() == 3) || (par.size() == 4)); // three parameters: Tc (K), Delta(0) (meV), a (1), [aD_Gap (1)] + + double aD = 4.0/3.0; + if (par.size() == 4) { + aD = par[3]; + } if (t<=0.0) return 1.0; @@ -788,8 +993,8 @@ double TGapNonMonDWave2::operator()(double t, const vector &par) const { double ds; vector intPar; // parameters for the integral: 2 k_B T, Delta(T), a, E_c, phi_c - intPar.push_back(2.0*0.08617384436*t); // 2 kB T, kB in meV/K - intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); + intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K + intPar.push_back(par[1]*tanh(0.2707214816*par[0]/par[1]*sqrt(aD*(par[0]/t-1.0)))); // DeltaD(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K intPar.push_back(par[2]); intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy intPar.push_back(TMath::PiOver2()); // upper limit of phi-integration @@ -812,9 +1017,14 @@ double TGapNonMonDWave2::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

Superfluid density in the ``two-fluid'' approximation. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (14). + */ double TGapPowerLaw::operator()(double t, const vector &par) const { - assert(par.size() == 2); // two parameters: Tc, N + assert(par.size() == 2); // two parameters: Tc, n if(t<=0.0) return 1.0; @@ -826,22 +1036,35 @@ double TGapPowerLaw::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

Superfluid density for a dirty s-wave superconductor. + * For details see also the Memo GapIntegrals.pdf, especially Eq.(7) and (15). + */ double TGapDirtySWave::operator()(double t, const vector &par) const { - assert(par.size() == 2); // two parameters: Tc, Delta(0) + assert((par.size() == 2) || (par.size() == 3)); // two or three parameters: Tc (K), Delta(0) (meV), [a (1)] + + double a = 1.0; + if (par.size() == 3) { + a = par[2]; + } if (t<=0.0) return 1.0; else if (t >= par[0]) return 0.0; - double deltaT(tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51))); - - return deltaT*tanh(par[1]*deltaT/(2.0*0.08617384436*t)); // Delta(T)/Delta(0)*tanh(Delta(T)/2 kB T), kB in meV/K + double deltaT(tanh(0.2707214816*par[0]/par[1]*sqrt(a*(par[0]/t-1.0)))); // DeltaS(T) : tanh(pi kB Tc / Delta(0) * sqrt()), pi kB = 0.2707214816 meV/K + return deltaT*tanh(par[1]*deltaT/(0.172346648*t)); // Delta(T)/Delta(0)*tanh(Delta(T)/2 kB T), kB in meV/K } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaSWave::operator()(double t, const vector &par) const { assert(par.size() == 2); // two parameters: Tc, Delta0 @@ -856,6 +1079,10 @@ double TLambdaSWave::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaDWave::operator()(double t, const vector &par) const { assert(par.size() == 2); // two parameters: Tc, Delta0 @@ -870,6 +1097,10 @@ double TLambdaDWave::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaAnSWave::operator()(double t, const vector &par) const { assert(par.size() == 3); // three parameters: Tc, Delta0, a @@ -884,6 +1115,10 @@ double TLambdaAnSWave::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaNonMonDWave1::operator()(double t, const vector &par) const { assert(par.size() == 3); // three parameters: Tc, Delta0, a @@ -898,6 +1133,10 @@ double TLambdaNonMonDWave1::operator()(double t, const vector &par) cons } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaNonMonDWave2::operator()(double t, const vector &par) const { assert(par.size() == 3); // three parameters: Tc, Delta0, a @@ -912,6 +1151,10 @@ double TLambdaNonMonDWave2::operator()(double t, const vector &par) cons } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaPowerLaw::operator()(double t, const vector &par) const { assert(par.size() == 2); // two parameters: Tc, N @@ -926,6 +1169,10 @@ double TLambdaPowerLaw::operator()(double t, const vector &par) const { } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaInvSWave::operator()(double t, const vector &par) const { assert(par.size() == 2); // two parameters: Tc, Delta0 @@ -940,6 +1187,10 @@ double TLambdaInvSWave::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaInvDWave::operator()(double t, const vector &par) const { assert(par.size() == 2); // two parameters: Tc, Delta0 @@ -954,6 +1205,10 @@ double TLambdaInvDWave::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaInvAnSWave::operator()(double t, const vector &par) const { assert(par.size() == 3); // three parameters: Tc, Delta0, a @@ -968,6 +1223,10 @@ double TLambdaInvAnSWave::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaInvNonMonDWave1::operator()(double t, const vector &par) const { assert(par.size() == 3); // three parameters: Tc, Delta0, a @@ -982,6 +1241,10 @@ double TLambdaInvNonMonDWave1::operator()(double t, const vector &par) c } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaInvNonMonDWave2::operator()(double t, const vector &par) const { assert(par.size() == 3); // three parameters: Tc, Delta0, a @@ -996,6 +1259,10 @@ double TLambdaInvNonMonDWave2::operator()(double t, const vector &par) c } +//-------------------------------------------------------------------- +/** + *

+ */ double TLambdaInvPowerLaw::operator()(double t, const vector &par) const { assert(par.size() == 2); // two parameters: Tc, N @@ -1009,12 +1276,20 @@ double TLambdaInvPowerLaw::operator()(double t, const vector &par) const } +//-------------------------------------------------------------------- +/** + *

+ */ TFilmMagnetizationDWave::TFilmMagnetizationDWave() { fLambdaInvSq = new TGapDWave(); fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ TFilmMagnetizationDWave::~TFilmMagnetizationDWave() { delete fLambdaInvSq; @@ -1022,6 +1297,10 @@ TFilmMagnetizationDWave::~TFilmMagnetizationDWave() fPar.clear(); } +//-------------------------------------------------------------------- +/** + *

+ */ double TFilmMagnetizationDWave::operator()(double t, const vector &par) const { assert(par.size() == 4); // four parameters: Tc, Delta0, lambda0, film-thickness diff --git a/src/external/libGapIntegrals/TGapIntegrals.h b/src/external/libGapIntegrals/TGapIntegrals.h index 53835148..603b08a9 100644 --- a/src/external/libGapIntegrals/TGapIntegrals.h +++ b/src/external/libGapIntegrals/TGapIntegrals.h @@ -37,6 +37,10 @@ using namespace std; #include "PUserFcnBase.h" #include "BMWIntegrator.h" +//-------------------------------------------------------------------- +/** + *

+ */ class TGapSWave : public PUserFcnBase { public: @@ -61,6 +65,10 @@ private: ClassDef(TGapSWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapDWave : public PUserFcnBase { public: @@ -85,6 +93,10 @@ private: ClassDef(TGapDWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapCosSqDWave : public PUserFcnBase { public: @@ -109,6 +121,10 @@ private: ClassDef(TGapCosSqDWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapSinSqDWave : public PUserFcnBase { public: @@ -133,7 +149,10 @@ private: ClassDef(TGapSinSqDWave,1) }; - +//-------------------------------------------------------------------- +/** + *

+ */ class TGapAnSWave : public PUserFcnBase { public: @@ -158,6 +177,10 @@ private: ClassDef(TGapAnSWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapNonMonDWave1 : public PUserFcnBase { public: @@ -182,6 +205,10 @@ private: ClassDef(TGapNonMonDWave1,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapNonMonDWave2 : public PUserFcnBase { public: @@ -207,6 +234,10 @@ private: }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapPowerLaw : public PUserFcnBase { public: @@ -224,6 +255,10 @@ private: ClassDef(TGapPowerLaw,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TGapDirtySWave : public PUserFcnBase { public: @@ -242,6 +277,10 @@ private: }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaSWave : public PUserFcnBase { public: @@ -260,6 +299,10 @@ private: ClassDef(TLambdaSWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaDWave : public PUserFcnBase { public: @@ -278,6 +321,10 @@ private: ClassDef(TLambdaDWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaAnSWave : public PUserFcnBase { public: @@ -296,6 +343,10 @@ private: ClassDef(TLambdaAnSWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaNonMonDWave1 : public PUserFcnBase { public: @@ -314,6 +365,10 @@ private: ClassDef(TLambdaNonMonDWave1,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaNonMonDWave2 : public PUserFcnBase { public: @@ -332,7 +387,10 @@ private: ClassDef(TLambdaNonMonDWave2,1) }; - +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaPowerLaw : public PUserFcnBase { public: @@ -350,6 +408,10 @@ private: ClassDef(TLambdaPowerLaw,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaInvSWave : public PUserFcnBase { public: @@ -368,6 +430,10 @@ private: ClassDef(TLambdaInvSWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaInvDWave : public PUserFcnBase { public: @@ -386,6 +452,10 @@ private: ClassDef(TLambdaInvDWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaInvAnSWave : public PUserFcnBase { public: @@ -404,6 +474,10 @@ private: ClassDef(TLambdaInvAnSWave,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaInvNonMonDWave1 : public PUserFcnBase { public: @@ -422,6 +496,10 @@ private: ClassDef(TLambdaInvNonMonDWave1,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaInvNonMonDWave2 : public PUserFcnBase { public: @@ -440,7 +518,10 @@ private: ClassDef(TLambdaInvNonMonDWave2,1) }; - +//-------------------------------------------------------------------- +/** + *

+ */ class TLambdaInvPowerLaw : public PUserFcnBase { public: @@ -458,6 +539,10 @@ private: ClassDef(TLambdaInvPowerLaw,1) }; +//-------------------------------------------------------------------- +/** + *

+ */ class TFilmMagnetizationDWave : public PUserFcnBase { public: