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UID:b130deebdcfe04a5e21a3ba1bfd87c07
CATEGORIES:Applied and Computational Math Seminar
CREATED:20240117T132809
SUMMARY:Static currents in type-1 superconductors
LOCATION:Hill 705
DESCRIPTION:<p>In this talk, we describe the classical magneto-static approach to the t
 heory of type-I superconductors. The magnetic field and the current in type
 -I superconductors are related by the London equations and tend to decay ex
 ponentially inside the superconducting material with support of the fields 
 contained primarily in O(λ_L) neighborhood of the superconductor. We presen
 t a Debye source based integral representation for the numerical solution o
 f the London equations, and demonstrate the efficacy of our approach for mo
 derate values of λ_L on complex three dimensional geometries. However, for 
 typical materials λ_L ∼ O(10−7), which makes the PDE and integral equation 
 increasingly difficult to solve in the limit λ_L → 0 due to the presence of
  two different length scales in the problem. We derive a limiting PDE and a
  corresponding integral equation, and show that the solutions of this limit
 ing PDE and integral equations are O(λ_L) accurate as compared to the corre
 sponding solutions of the London equations and the Debye source integral eq
 uations respectively. We demonstrate the effectiveness of this asymptotic a
 pproach both in terms of speed and accuracy through several numerical examp
 les.</p>
CONTACT:Manas Rachh (Flatiron Institute)
DTSTAMP:20260830T202514
DTSTART;TZID=America/New_York:20240131T110000
DTEND;TZID=America/New_York:20240131T120000
SEQUENCE:0
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