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<div class="patternContent"><div class="foswikiTopic">
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<span id="TopIc"></span>
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<h1 id="libFitPofB"> libFitPofB </h1>
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<div id="foswikiTOC" class="foswikiToc"> <ul>
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<div class="foswikiToc" id="foswikiTOC"> <ul>
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<li> <a href="LibFitPofB.html#libFitPofB"> libFitPofB </a>
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</li> <li> <a href="LibFitPofB.html#A_1_Introduction"> 1 Introduction </a>
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</li> <li> <a href="LibFitPofB.html#A_2_LE_45SR"> 2 LE-μSR </a> <ul>
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@@ -148,7 +148,7 @@ where <img alt="\gamma_{\mu} = 2\pi\times 135.54~\mathrm{MHz/T}" class="
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At the moment the only available implementations deal with field distributions measured in local isotropic superconductors, either by means of <a href="http://lmu.web.psi.ch/lem/">low-energy μSR</a> in the Meissner state or by conventional μSR in the mixed state. In the following the basic usage of the library in <code>musrfit</code> is explained—the calculations by themselves are only outlined. For further information please refer to the original literature and/or the source code of the implementation.
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<p></p>
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<hr />
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<strong><span class='foswikiBlackFG'>Remark 1:</span></strong> In order to supply certain information needed for the calculations but not suited to be stored in the <code>musrfit</code> msr files an XML configuration file in the working directory is used. For details, see <a href="#XmlFile" class="foswikiCurrentTopicLink">below</a>.
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<strong><span class='foswikiBlackFG'>Remark 1:</span></strong> In order to supply certain information needed for the calculations but not suited to be stored in the <code>musrfit</code> msr files an XML configuration file in the working directory is used. For details, see <a class="foswikiCurrentTopicLink" href="#XmlFile">below</a>.
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<p></p>
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<strong><span class='foswikiBlackFG'>Remark 2:</span></strong> The implementations in this library heavily rely on <code><a href="http://www.fftw.org/">FFTW3</a></code>. In principle, it always checks what is the best way to do efficient Fourier transforms for a given machine before the transforms are actually done. If repeatedly Fourier transforms of the same (sizable) length should be done, it might be worth storing the once obtained information in an external file and just load it the next time this information is needed (<a href="http://fftw.org/fftw3_doc/Wisdom.html">"wisdom handling"</a>). In case this feature shall be used, a valid wisdom file has to be specified in the <a class="foswikiCurrentTopicLink" href="#XmlFile">XML file</a>.
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@@ -262,7 +262,7 @@ The optional parameters are: <ol>
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Notes
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<p></p>
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<a name="FootNote1note"></a><span class="FootNoteLabel"><a class="foswikiCurrentWebHomeLink" href="LibFitPofB.html#FootNote1text"> <strong>1</strong> </a></span>: <span class="FootNote">F. London, Superfluids: Macroscopic Theory of Superconductivity, Dover (1961), p. 34</span>
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<a name="FootNote1note"></a><span class="FootNoteLabel"><a href="#FootNote1text"><b>1</b></a></span>: <span class="FootNote">F. London, Superfluids: Macroscopic Theory of Superconductivity, Dover (1961), p. 34</span>
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@@ -277,8 +277,8 @@ When investigating superconductors in the mixed state by means of conventional &
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</p>
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where <img alt="\mathbf{r}=(x,y)" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_e47f33589d28eaa3f9baccb7a80fdbaa.png" title="r" />, <img alt="\mathbf{K}" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_e6688a12ee4e821abc31b4c1dd511539.png" title="K" /> are the reciprocal lattice vectors of a two-dimensional vortex lattice and the <img alt="B_{\mathbf{K}}" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_8fa3ac8f18b7bc49eb89163d6528684c.png" title="Bk" /> are the Fourier coefficients depending on the magnetic penetration depth <img alt="\lambda" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_28f3ed750a4819b4256c2f9be649f594.png" title="lambda" /> and the superconducting coherence length <img alt="\xi" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_e8414d477977d226317c020980b7d34f.png" title="xi" />. The <img alt="B_{\mathbf{K}}" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_8fa3ac8f18b7bc49eb89163d6528684c.png" title="Bk" /> for some specific models are as follows: <dl>
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<dt> London model with Gaussian cutoff<a name="FootNote2text"></a><span class="FootNoteTextLink" title="E.H. Brandt, [[http://dx.doi.org/10.1007/BF00683568][J. Low Temp. Phys. *73*, 355 (1988)]]."><a class="foswikiCurrentTopicLink" href="#FootNote2note">(2)</a></span> </dt><dd> <p style="text-align:center"><img alt="B_{\mathbf{K}} = \frac{\exp\left({-K^2\xi^2/2}\right)}{1 + K^2\lambda^2}" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_469d5d1b83125e4915e2f073d8150b12.png" title="BkLondon" /></p>
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</dd> <dt> Modified London model<a name="FootNote3text"></a><span class="FootNoteTextLink" title="T.M. Riseman _et al._, [[http://dx.doi.org/10.1103/PhysRevB.52.10569][Phys. Rev. B *52*, 10569 (1995)]]."><a href="#FootNote3note" class="foswikiCurrentTopicLink">(3)</a></span> </dt><dd> <p style="text-align:center"><img alt="B_{\mathbf{K}} = \frac{\exp\left({-K^2\xi^2/2(1-b)}\right)}{1 + K^2\lambda^2/(1-b)}," class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_b6719fad8e30208538b34bc94040b7a5.png" title="BkML" /></p> where <img alt="b = \langle B \rangle/\mu_0H_{\mathrm{c}2}." class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_039b3b38df7c6f284089c14f1efdf643.png" title="b" />
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</dd> <dt> Analytical Ginzburg-Landau model<a name="FootNote4text"></a><span class="FootNoteTextLink" title="A. Yaouanc, P. Dalmas de R&eacute;otier and E.H. Brandt, [[http://dx.doi.org/10.1103/PhysRevB.55.11107][Phys. Rev. B *55*, 11107 (1997)]]."><a href="#FootNote4note" class="foswikiCurrentTopicLink">(4)</a></span> </dt><dd> <p style="text-align:center"><img alt="B_{\mathbf{K}} = \frac{f_{\infty}K_1\left(\frac{\xi_v}{\lambda}\sqrt{f_{\infty}^2+\lambda^2K^2}\right)}{K_1\left(\frac{\xi_v}{\lambda}f_{\infty}\right)\sqrt{f_{\infty}^2+\lambda^2K^2}}," class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_3146cb17887e3a20cc2078f103605af5.png" title="BkAGL" /></p> where <img alt="f_{\infty} = 1 - b^4,~\xi_v = \xi\left(\sqrt{2}-{3\xi}/\left({4\lambda}\right)\right)\sqrt{(1+b^4)(1-2b(1-b)^2)}" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_e0b0e98f9a3974249b42b6910523c8a4.png" title="f_inf_and_xi_v" /> and <img alt="K_1" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_3cee3cc69dbe918398ec39a72a465014.png" title="K1" /> is a modified Bessel function.
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</dd> <dt> Modified London model<a name="FootNote3text"></a><span class="FootNoteTextLink" title="T.M. Riseman _et al._, [[http://dx.doi.org/10.1103/PhysRevB.52.10569][Phys. Rev. B *52*, 10569 (1995)]]."><a class="foswikiCurrentTopicLink" href="#FootNote3note">(3)</a></span> </dt><dd> <p style="text-align:center"><img alt="B_{\mathbf{K}} = \frac{\exp\left({-K^2\xi^2/2(1-b)}\right)}{1 + K^2\lambda^2/(1-b)}," class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_b6719fad8e30208538b34bc94040b7a5.png" title="BkML" /></p> where <img alt="b = \langle B \rangle/\mu_0H_{\mathrm{c}2}." class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_039b3b38df7c6f284089c14f1efdf643.png" title="b" />
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</dd> <dt> Analytical Ginzburg-Landau model<a name="FootNote4text"></a><span class="FootNoteTextLink" title="A. Yaouanc, P. Dalmas de R&eacute;otier and E.H. Brandt, [[http://dx.doi.org/10.1103/PhysRevB.55.11107][Phys. Rev. B *55*, 11107 (1997)]]."><a class="foswikiCurrentTopicLink" href="#FootNote4note">(4)</a></span> </dt><dd> <p style="text-align:center"><img alt="B_{\mathbf{K}} = \frac{f_{\infty}K_1\left(\frac{\xi_v}{\lambda}\sqrt{f_{\infty}^2+\lambda^2K^2}\right)}{K_1\left(\frac{\xi_v}{\lambda}f_{\infty}\right)\sqrt{f_{\infty}^2+\lambda^2K^2}}," class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_3146cb17887e3a20cc2078f103605af5.png" title="BkAGL" /></p> where <img alt="f_{\infty} = 1 - b^4,~\xi_v = \xi\left(\sqrt{2}-{3\xi}/\left({4\lambda}\right)\right)\sqrt{(1+b^4)(1-2b(1-b)^2)}" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_e0b0e98f9a3974249b42b6910523c8a4.png" title="f_inf_and_xi_v" /> and <img alt="K_1" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_3cee3cc69dbe918398ec39a72a465014.png" title="K1" /> is a modified Bessel function.
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</dd></dl>
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Apart from the mentioned analytical models the <strong>numerical Ginzburg-Landau model</strong> <a name="FootNote5text"></a><span class="FootNoteTextLink" title="E.H. Brandt, [[http://dx.doi.org/10.1103/PhysRevB.68.054506][Phys. Rev. B *68*, 054506 (2003)]]."><a class="foswikiCurrentTopicLink" href="#FootNote5note">(5)</a></span> is available. In this case <img alt="B(\mathbf{r})" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_373e9bf1fc97e2c6aacf93bcc090402c.png" title="BofR" /> is obtained by an iterative minimization of the free energy of the vortex lattice.
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Notes
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<a name="FootNote2note"></a><span class="FootNoteLabel"><a class="foswikiCurrentWebHomeLink" href="LibFitPofB.html#FootNote2text"> <strong>2</strong> </a></span>: <span class="FootNote">E.H. Brandt, <a href="http://dx.doi.org/10.1007/BF00683568">J. Low Temp. Phys. <strong>73</strong>, 355 (1988)</a>.</span>
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<a name="FootNote2note"></a><span class="FootNoteLabel"><a href="#FootNote2text"><b>2</b></a></span>: <span class="FootNote">E.H. Brandt, <a href="http://dx.doi.org/10.1007/BF00683568">J. Low Temp. Phys. <strong>73</strong>, 355 (1988)</a>.</span>
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<a name="FootNote3note"></a><span class="FootNoteLabel"><a class="foswikiCurrentWebHomeLink" href="LibFitPofB.html#FootNote3text"> <strong>3</strong> </a></span>: <span class="FootNote">T.M. Riseman <em>et al.</em>, <a href="http://dx.doi.org/10.1103/PhysRevB.52.10569">Phys. Rev. B <strong>52</strong>, 10569 (1995)</a>.</span>
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<a name="FootNote3note"></a><span class="FootNoteLabel"><a href="#FootNote3text"><b>3</b></a></span>: <span class="FootNote">T.M. Riseman <em>et al.</em>, <a href="http://dx.doi.org/10.1103/PhysRevB.52.10569">Phys. Rev. B <strong>52</strong>, 10569 (1995)</a>.</span>
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<p></p>
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<a name="FootNote4note"></a><span class="FootNoteLabel"><a class="foswikiCurrentWebHomeLink" href="LibFitPofB.html#FootNote4text"> <strong>4</strong> </a></span>: <span class="FootNote">A. Yaouanc, P. Dalmas de Réotier and E.H. Brandt, <a href="http://dx.doi.org/10.1103/PhysRevB.55.11107">Phys. Rev. B <strong>55</strong>, 11107 (1997)</a>.</span>
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<a name="FootNote4note"></a><span class="FootNoteLabel"><a href="#FootNote4text"><b>4</b></a></span>: <span class="FootNote">A. Yaouanc, P. Dalmas de Réotier and E.H. Brandt, <a href="http://dx.doi.org/10.1103/PhysRevB.55.11107">Phys. Rev. B <strong>55</strong>, 11107 (1997)</a>.</span>
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<a name="FootNote5note"></a><span class="FootNoteLabel"><a class="foswikiCurrentWebHomeLink" href="LibFitPofB.html#FootNote5text"> <strong>5</strong> </a></span>: <span class="FootNote">E.H. Brandt, <a href="http://dx.doi.org/10.1103/PhysRevB.68.054506">Phys. Rev. B <strong>68</strong>, 054506 (2003)</a>.</span>
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<a name="FootNote5note"></a><span class="FootNoteLabel"><a href="#FootNote5text"><b>5</b></a></span>: <span class="FootNote">E.H. Brandt, <a href="http://dx.doi.org/10.1103/PhysRevB.68.054506">Phys. Rev. B <strong>68</strong>, 054506 (2003)</a>.</span>
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@@ -409,12 +409,12 @@ An example XML file looks as follows:
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<div class="patternInfo">This topic: MUSR<span class='foswikiSeparator'> > </span><a href="WebHome.html" class="foswikiCurrentWebHomeLink">WebHome</a> > <a href="MusrFit.html">MusrFit</a> > <a href="BmwLibs.html">BmwLibs</a><span class='foswikiSeparator'> > </span>LibFitPofB <br />
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<div class="patternInfo">This topic: MUSR<span class='foswikiSeparator'> > </span><a class="foswikiCurrentWebHomeLink" href="WebHome.html">WebHome</a> > <a href="MusrFit.html">MusrFit</a> > <a href="BmwLibs.html">BmwLibs</a><span class='foswikiSeparator'> > </span>LibFitPofB <br />
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Topic revision: <span class='patternRevInfo'>03 Jul 2015, suter_a</span></div>
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