Drops and Fingers in a Tempered Ginzburg-Landau set-up

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We introduce gradient-tempered Ginzburg-Landau, GL, free energy functional J=∫(G(ux)−W(u))dx, where W(u)=λ2(2u2−u4) is the bulk energy endowed with a stiffness coefficient a2(u) which vanishes both at the phases and on the interface: a2(u)=|u||1−u2|, [Formula presented]<β,γ≤1. It induces compact drops and interphase transitions within a finite domain. The assumed interface energy G=1+a2ux2−1, tempers the divergence of gradients in the ultra-violet limit. Consequently, when λ2, the bulk energy strength parameter crosses a critical value, depending on their amplitude, the forming drops may develop at their edges sharp jumps and turn into fingers across which the energy remains finite. In the Tempered Allen-Cahn, ut=−[Formula presented]J equation, the resulting flux-saturating diffusion delays the resolution of initial discontinuities and if 1≤γ, it blocks excitation's spread beyond its initial span. A number of explicit spherical solutions is also presented.

Original languageEnglish
Article number132956
JournalPhysica D: Nonlinear Phenomena
StatePublished - Nov 2021


  • Drops
  • Fingers
  • Tempered Ginzburg–Landau


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