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Qiang's Research Gallery 1                   Quantized vortices in type-II superconductors          (for details see Qiang's publications)

Our research in this direction has focused on the study of quantized vortex dynamics in superconductors using mezoscale models as typified by the celebrated Ginzburg-Landau model (equations) (for vortices in Bose Einstein condensates, see Gallery 2). Though we have also worked on the microscopic BCS models that can be used to understand the basic structure of superconductors and of the atomic and sub-atomic behavior of these materials, as well as the macroscopic vortex density and critical state models that can be of use for the design of devices. Mezoscale models are of great use in understanding important phenomena in superconductors such as vortex nucleation, motion and interaction, vortex pinning, critical fields and currents, Josephson effects, inhomogeneities and fluctuations, vortex glass and vortex fluid structures, resistivity, etc. Our efforts in superconductivity center on the following aspects: to develop, refine and simplify mezoscale and macroscale models for superconductivity, via rigorous analysis, computation and asymptotic studies to analyze the models to gain further understanding of the properties of these models and of their solutions, and also to determine their validity and usefulness for solving physically interesting problems; to develop, analyze, and implement algorithms for the numerical simulation of solutions of the various models including algorithms that give gauge invariant approximations, those based on artificial bc, and those which are parallelizable to use our algorithms and codes to study superconducting phenomena. Below we present some sample pictures from our numerical simulations and some references.

	Illustration: vortices in type-II superconductors
	3d vortex tubes
	double d-wave vortices
	current drived vortex motion
	vortex lattice melting
	real and imaginary worlds, what if they merge?

Partial list of collaborators: P. Gray, J. Remski, J. Chapman, F.H. Lin, M. Gunzburger, A. Aftalion, L. Ju, W. Bao,
J. Deang, S. Ding, J. Peterson, X. Wu and P. Zhang

Recent survey lectures and papers:

• Tutorials at the Inst of Math. and Appl, 2004.
  
• Tutorials at the IMS, National Univ of Singapore, 2004
  Lecture 1, Lecture 2, Lecture 3
• Recent Talk on Quantized Vortices
  Slide 1, Slide 2, Slide 3, Slide 4, Slide 5, Slide 6, Slide 7, Slide 8, Slide 9, Slide 10
  Slide 11, Slide 12, Slide 13, Slide 14, Slide 15, Slide 16, Slide 17, Slide 18,
  Slide 19, Slide 20 Slide 21, Slide 22, Slide 23.
  
• Q. Du, Diverse vortex dynamics in superfluids, Contemp Math. 329, pp105-117, AMS, 2003.
  
• Q. Du, Numerical approximations of the Ginzburg Landau Models for Superconductivity, J. Mathematical Physics, 46, pp.095109 1-22, 2005
  
• Q. Du, M. Gunzburger and J. Peterson, Analysis and Approximation of the Ginzburg Landau Model of Superconductivity , SIAM Review, 34, pp54-81, 1992
  
• More papers on the subject
  
  

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Contact   Qiang Du  2003-04-08