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lines changed Original file line number Diff line number Diff line change @@ -60,18 +60,22 @@ \section{Model}
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R_N = \frac {λ}{W L} \frac {1}{σ^N} ,
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\end {equation }
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and the function
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- \begin {widetext }
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- \begin {equation }
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- \label {eq:f }
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- f = \re { \left \{ \left (
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- 2 \left [ \sqrt {1 + i ω τ} + \frac {λ}{2} \left ( \frac {1}{r_0} + \frac {1}{r_L} \right ) \right ]
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- e^{\left ( L / λ \right ) \sqrt {1 + i ω τ}}
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- + \frac {λ^2}{r_0 r_L} \frac {
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- \sinh { \left [ \left ( L / λ \right ) \sqrt {1 + i ω τ} \right ] }}
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- {\sqrt {1 + i ω τ}}
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- \right )^{-1} \right \} } .
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- \end {equation }
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- \end {widetext }
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+ \begin {multline }
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+ \label {eq:f }
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+ f = \re \left ( \left \{
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+ \vphantom {
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+ \frac {
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+ \sinh { \left [ \left ( L / λ \right ) \sqrt {1 + i ω τ} \right ] }
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+ }{\sqrt {1 + i ω τ}}
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+ }
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+ 2 \left [ \sqrt {1 + i ω τ} + \frac {λ}{2} \left ( \frac {1}{r_0} + \frac {1}{r_L} \right ) \right ]
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+ e^{\left ( L / λ \right ) \sqrt {1 + i ω τ}}
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+ \right . \right . \\ \left . \left .
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+ + \frac {λ^2}{r_0 r_L} \frac {
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+ \sinh { \left [ \left ( L / λ \right ) \sqrt {1 + i ω τ} \right ] }
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+ }{\sqrt {1 + i ω τ}}
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+ \right \} ^{-1} \right ) .
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+ \end {multline }
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Note that $ f$ is unitless and depends only on the scales $ L / λ$ , $ ω τ$ , and $ λ / r_i$ .
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The parameters $ r_i$ with $ i$ either $ 0 $ for the left contact or $ L$ for the right are
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