Ginzburg-Landau Equation and Vortex(<Special Topics>Pattern Dynamics)

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  • ギンツブルグ・ランダウ方程式とボルテクス(<特集>パターンダイナミクス)
  • 特集 パターンダイナミクス
  • トクシュウ パターンダイナミクス

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I describe recent studies on Ginzburg-Landau equation and behavior of vortices under singular perturbation situation. Each vortex carries a quantized energy of amountπ log (1/ε) +0(1). The behavior of the vortices can be described in terms of ODE with the aid of a finite dimensional Potential function, which is called the renormalized energy. Examples of vortex motion in the case of disk with Neumann boundary condition are explained and the total dynamics are solved.

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