76 lines
1.8 KiB
TeX
Executable File
76 lines
1.8 KiB
TeX
Executable File
\documentclass[a4paper, 11pt]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[
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a4paper,
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headheight = 20pt,
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margin = 1in,
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tmargin = \dimexpr 1in - 10pt \relax
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]{geometry}
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\usepackage{fancyhdr} % for headers and footers
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\usepackage{graphicx} % for including figures
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\usepackage{booktabs} % for professional tables
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\setlength{\headheight}{14pt}
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\fancypagestyle{plain}{
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\fancyhf{}
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\fancyhead[L]{\sffamily Radboud University Nijmegen}
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\fancyhead[R]{\sffamily Superconductivity (NWI-NM117), Q3+Q4}
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\fancyfoot[R]{\sffamily\bfseries\thepage}
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\renewcommand{\headrulewidth}{0.5pt}
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\renewcommand{\footrulewidth}{0.5pt}
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}
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\pagestyle{fancy}
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\usepackage{siunitx}
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\usepackage{hyperref}
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\usepackage{float}
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\usepackage{mathtools}
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\newcommand{\pfrac}[2]{\frac{\partial #1}{\partial #2}}
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\title{Superconductivity - Assignment 2}
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\author{
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Kees van Kempen (s4853628)\\
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\texttt{k.vankempen@student.science.ru.nl}
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}
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\AtBeginDocument{\maketitle}
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% Start from 4
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\setcounter{section}{3}
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\begin{document}
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\section{Temperature dependence in Landau model}
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In the Landau model, free energy is given as function of order parameter $\psi$ and temperature $T$ as
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\[
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\mathcal{F} = a(T - T_c) \psi^2 + \frac{\beta}{2}\psi^4.
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\]
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To find the equilibrium value with respect to the order parameter $\psi_0(T)$,
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we need to equate the derivatives with respect to both $T$ and $\psi(T)$ to zero.
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\[
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0 = \frac{\delta\mathcal{F}}{\delta\psi} = \frac{\partial \mathcal{F}}{\partial \psi} - \nabla \cdot \frac{\partial \mathcal{F}}{\partial (\nabla \psi)}
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\]
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Now we seek the Q = TdS, C = dQ/dT = T dS/dT
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For the entropy, we know
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\[
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S = -\pfrac{}
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\]
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\section{Type-I superconducting foil}
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\section{Type II superconductors and the vortex lattice}
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\section{Currents inside type-II superconducting cylinder}
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\bibliographystyle{vancouver}
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\bibliography{references.bib}
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%\appendix
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\end{document}
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