Busse balloons - from the reversible Gray-Scott model ... - Eurandom

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$Continuous-time random walks, fractional calculus and ... - Eurandom$

Introduction Rise of Patterns The Busse balloon Conclusions and ongoing research The Eckhaus band: nonsymmetric case (C > 0) Let A be the amplitude of the emerging pattern. The evolution of A is now described by the Complex GLE : Aτ = (α1 + iα2)Aξξ + (β1 + iβ2)A + (γ1 + iγ2)|A| 2 A. Spatially periodic patterns appear at a Turing-Hopf bifurcation and are now travelling: i(kc x+ωc t) A(ξ, τ) = Re The Turing-Hopf bifurcation is subcritical if the so-called Landau coefficient satisfies 1 + α2γ2 α1γ2 > 0. Sjors van der Stelt Busse balloons
Introduction Rise of Patterns The Busse balloon Conclusions and ongoing research Super- vs. subcritical bifurcation k A Figure: Schematic picture of supercritical bifurcation (left) and subcritical bifurcation (right). Sjors van der Stelt Busse balloons k A
Page 1 and 2: Introduction Rise of Patterns The B
Page 3 and 4: The Model Introduction Rise of Patt
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Page 7 and 8: Birth of patterns Introduction Rise
Page 9: Introduction Rise of Patterns The B
Page 13 and 14: Busse balloon Introduction Rise of
Page 21 and 22: Conclusions Introduction Rise of Pa
Page 23 and 24: Conclusions Introduction Rise of Pa
Page 25 and 26: Ongoing research Introduction Rise

Busse balloons - from the reversible Gray-Scott model ... - Eurandom

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