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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:In this talk, we describe the classical magneto-static approach to the theo
 ry of type-I superconductors. The magnetic field and the current in type-I 
 superconductors are related by the London equations and tend to decay expon
 entially inside the superconducting material with support of the fields con
 tained primarily in O(λ_L) neighborhood of the superconductor. We present a
  Debye source based integral representation for the numerical solution of t
 he London equations, and demonstrate the efficacy of our approach for moder
 ate values of λ_L on complex three dimensional geometries. However, for typ
 ical materials λ_L ∼ O(10−7), which makes the PDE and integral equation inc
 reasingly difficult to solve in the limit λ_L → 0 due to the presence of tw
 o different length scales in the problem. We derive a limiting PDE and a co
 rresponding integral equation, and show that the solutions of this limiting
  PDE and integral equations are O(λ_L) accurate as compared to the correspo
 nding solutions of the London equations and the Debye source integral equat
 ions respectively. We demonstrate the effectiveness of this asymptotic appr
 oach both in terms of speed and accuracy through several numerical examples
 .\n
X-ALT-DESC;FMTTYPE=text/html:<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:20260828T141038
DTSTART;TZID=America/New_York:20240131T110000
DTEND;TZID=America/New_York:20240131T120000
SEQUENCE:0
TRANSP:OPAQUE
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