By Seidel W., Mosler K., Alker M.
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Additional info for A Cautionary Note on Likelihood Ratio Tests in Mixture Models
The idea of a two-ﬂuid model, with coexistent ‘superelectrons’ and normal electrons, was probably not new when Heinz London wrote his doctoral thesis in 1933, but it seems that the ﬁrst published mention was by Casimir and Gorter in 1934. London had searched unsuccessfully for resistive loss when the presumed normal electrons are stimulated by a high-frequency electric ﬁeld in the penetration layer. His frequency of 40 MHz was far too low, but he succeeded in 1940 with 1500 MHz ; by then the two-ﬂuid model was well established as a theoretical concept.
The persistence of the current then depends on phase slippage having a sufﬁciently small probability. We emphasize that the persistent current is an equilibrium state of the system (a minimum in the free energy, maintained by collisions), subject only to the constraint that the phase of C does not change. 5 A3:1 An introduction to superconductivity Flux lines, the mixed state, and type I and type II superconductors We might ask whether a single quantum of ﬂux, for example, could be trapped inside a bulk sample of superconductor.
The situation can be described by an appropriate solution of the Ginsburg – Landau equations. The amplitude of the Ginsburg –Landau wavefunction vanishes along the line, and it rises to its normal value over a distance from the line of order the Ginsburg– Landau coherence length jGL . The phase SðrÞ changes by 2p as the line is encircled, so that one ﬂux quantum is associated with the line. 3). The resulting structure is called a ‘ﬂux line’ or ‘vortex’, the latter name originating from the fact that close to the line the electron velocity is similar to that in a hydrodynamic vortex (proportional to 1=r).
A Cautionary Note on Likelihood Ratio Tests in Mixture Models by Seidel W., Mosler K., Alker M.