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@@ -113,7 +111,7 @@ pre {
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<script src="https://intranet.psi.ch/pub/System/ChecklistPlugin/itemstatechange.js" language="javascript" type="text/javascript"></script><script src="https://intranet.psi.ch/pub/System/TimeTablePlugin/timetabletooltips.js" language="javascript" type="text/javascript"></script><link rel="stylesheet" href="../pub/System/FootNotePlugin/styles.css" type="text/css" media="all" /><!--FOOTNOTEPLUGIN_LINKCSS-->
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<div class="patternContent"><div class="foswikiTopic">
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<a name="TopIc"></a>
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<h1><a name="libFitPofB"></a> libFitPofB </h1>
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@@ -169,7 +169,7 @@ Assuming an array of <img alt="N" class="mmpImage" src="../pub/MUSR/LibFitPofB/_
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<p style="text-align:center">
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<img alt="\frac{\partial^2}{\partial z^2}B_i(z) = \frac{1}{\lambda_i^2}B_i(z)" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_dfd02951094e1cb98f48e3f6d4562f38.png" title="London-eq" />
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</p>
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for each layer <img alt="i" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_c465118a8d86d5f25bba37cc1dcb38a0.png" title="i" /> taking into account the boundary conditions<a name="FootNote1text"></a><span class="FootNoteTextLink" title="F. London, Superfluids: Macroscopic Theory of Superconductivity, Dover (1961), p. 34"><a href="#FootNote1note" class="foswikiCurrentTopicLink">(1)</a></span>
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for each layer <img alt="i" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_c465118a8d86d5f25bba37cc1dcb38a0.png" title="i" /> taking into account the boundary conditions<a name="FootNote1text"></a><span class="FootNoteTextLink" title="F. London, Superfluids: Macroscopic Theory of Superconductivity, Dover (1961), p. 34"><a href="#FootNote1note" class="foswikiCurrentTopicLink">(1)</a></span>
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<p style="text-align:center">
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<img alt="B_1(0) = B_N(d) = \mu_0H" class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_432d7664e0756ded77e7423dd256c122.png" title="cond1" />
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</p>
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@@ -275,11 +275,11 @@ When investigating superconductors in the mixed state by means of conventional &
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<img alt="B(\mathbf{r}) = \langle B \rangle \sum\limits_{\mathbf{K}}B_{\mathbf{K}}\exp(-\imath\mathbf{K}\mathbf{r})," class="mmpImage" src="../pub/MUSR/LibFitPofB/_MathModePlugin_c25933e91d56089992506f463d71de8f.png" title="spatialB" />
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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 href="#FootNote2note" class="foswikiCurrentTopicLink">(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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<dt> London model with Gaussian cutoff<a name="FootNote2text"></a><span class="FootNoteTextLink" title="E.H. Brandt, <a href="http://dx.doi.org/10.1007/BF00683568" target="_top">J. Low Temp. Phys. <strong>73</strong>, 355 (1988)</a>."><a href="#FootNote2note" class="foswikiCurrentTopicLink">(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 <em>et al.</em>, <a href="http://dx.doi.org/10.1103/PhysRevB.52.10569" target="_top">Phys. Rev. B <strong>52</strong>, 10569 (1995)</a>."><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 Réotier and E.H. Brandt, <a href="http://dx.doi.org/10.1103/PhysRevB.55.11107" target="_top">Phys. Rev. B <strong>55</strong>, 11107 (1997)</a>."><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></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 href="#FootNote5note" class="foswikiCurrentTopicLink">(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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Apart from the mentioned analytical models the <strong>numerical Ginzburg-Landau model</strong> <a name="FootNote5text"></a><span class="FootNoteTextLink" title="E.H. Brandt, <a href="http://dx.doi.org/10.1103/PhysRevB.68.054506" target="_top">Phys. Rev. B <strong>68</strong>, 054506 (2003)</a>."><a href="#FootNote5note" class="foswikiCurrentTopicLink">(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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<p></p>
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<font color="#ff0000">Concerning the applicability (e.g. field regions) of each of the mentioned models please refer to the original publications!</font>
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<p></p>
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@@ -414,7 +414,7 @@ An example XML file looks as follows:
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</div>
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</div>
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<div class="clear"> </div>
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</div><div id="patternBottomBar"><div id="patternBottomBarContents"><div id="patternWebBottomBar">Ideas, requests, problems regarding <a href="https://intranet.psi.ch/Main/WebHome">PSI Wiki</a>? <a href="mailto:psi.intranet@psi.ch?subject=PSI%20Wiki%20Feedback%20on%20MUSR.LibFitPofB">Send feedback</a></div></div></div>
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@@ -445,17 +445,15 @@ An example XML file looks as follows:
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</tr>
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