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Published byΙδουμα Γούναρης Modified over 5 years ago
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The Complex Ginzburg-Landau equation II (also real case)
Amplitude-Phase representation Real Gle (mostly 1D) Stability of plane waves, BFN instability Phase equation Phase and amplitude chaos
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AmpPhase1: amplitude-phase representation 1
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AmpPhase2: amplitude-phase representation 2
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GLe1Potential: Overview over all solutions: Potential
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GLe2AllStatSol: All static solutions
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GLe3: quasiperiodic solutions, localized saddle point
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GLe4: Eckhaus with potential
Simulations!
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Solutions 1: Plane waves and their stability
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Solutions 2: Eckhaus instability BFN instability
Simulations!
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ConvAbsStab: Convectice vs absolute intsability
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I. Aronson, L. Aronson, LK, A. Weber PRA 1992)
Fig. 1 of Review: convective versus absolute Eckhaus I. Aronson, L. Aronson, LK, A. Weber PRA 1992)
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Phase diagram for 1D CGLe (b= )
N 1D phase diagram A I= Absolute stability boundary
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PhaseEq1
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PhaseEq2
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Simulations of phase Chaos in 1D H. Chate, 1994
Phase chaos simulations (Chate)
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Beyond phase chaos (and coexistenct):
“amplitude chaos” (or defect chaos) 1D: nonzero rate of “phase slips” (A=0 at some x,t) 2D: nonzero density of zeros of A (topological point defects) Beyond phase chaos 3D: further restrictions for persistent defect lines
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From Vortex to Spiral
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Spiral in 3D representation
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Spiral breakup
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EI = conv. instab., AI=abs. Instab., BFN= Benjamin-Feir-Newell
line, OR=monotonic/oscillatory interaction (bound states). L=limit of phase turbulence, T-limit of defect turbulence (Chate & Manneville, 1996)
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Spiral-filament chaos in 3D
Snapshots at different times =50, c=-0.5 Spiral-filament chaos in 3D Aranson, Bishop, LK (1998) For more details: Aronson & LK, Rev. Mod. Phys. 74, 99 (2002)
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