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Non-equilibrium systems External flux self-organization d ~ characteristic size ( D   1/2 ~ characteristic size electro convection …… ocean currents.

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Presentation on theme: "Non-equilibrium systems External flux self-organization d ~ characteristic size ( D   1/2 ~ characteristic size electro convection …… ocean currents."— Presentation transcript:

1 Non-equilibrium systems External flux self-organization d ~ characteristic size ( D   1/2 ~ characteristic size electro convection …… ocean currents

2 Desert vegetation patterns

3 Chemical Turing patterns (Swinney) Striped & hexagonal patterns Labyrinthine pattern Experimental cell

4 Animal coats & Turing patterns Simulated by RD equations Zebra & leopard

5 Spiral patterns in  range (CO oxidation on Pt, Imbihl & Ertl, 1995) Polycrystalline surface 110 surface STM image of Pt(110) – (1x2) showing the corrugated-iron structure; the inset shows a line scan across that structure K. Swamy, E. Bertel and I. Vilfan Surface Science, 425 L369 (1999)

6 Dewetting pattern J.Klein et al, PRL (2001) I.Leizerson & S.G.Lipson

7 Patterns of crystal growth The crystal growth sequence on an (001) cleavage plane in a BaSO4 solution Pina et al, Nature 395, 483 (1998)

8 Colloidal assembly G. Subramania et al, Phys. Rev. B (2001) J.E.G. Wijnhoven and W.L. Vos, Science 281, 802 (1998)

9 Nanoscale deposition pattern STM image of a periodic array of Fe islands nucleated on the dislocation network of a Cu bilayer on Pt(111)

10 Nanocluster arrays on interfaces STM images of In nanoclusters on Si(111) J.-L.Li et al, PRL (2002)

11 Molecular self-assembly on interfaces Rows of pentacene on Cu(110) produced by a substrate-mediated repulsion S.Lucas et al, PRL (2002)

12 Devil’s Causeway Rayleigh–Bénard convection

13 Rayleigh–Bénard convection rolls,squares, hexagons, etc. Spiral defect chaos

14 Patterns of vibrating sand (Swinney)

15 Development of Turing pattern Activator excited locally Long-range inhibitor excited Activator suppressed at neighboring locations Periodic pattern starts to develop

16 activators & inhibitors convectionbuoyancyheat transfer optical cavityrefractive indexlight intensity solid filmelastic stresssurface tension neuronmembrane potentialionic conductance epidemicsinfectious agentimmunity Taylor columncentrifugal forceviscosity

17 Crystals & patterns Equilibrium systemsNon-equilibrium systems Short-range repulsion Long-range attraction Short-range activator Long-range inhibitor CrystalTuring pattern Evolution to equilibrium Frozen defects Non-potential effects: Dynamic regimes are possible

18 Hexagonal & striped Turing patterns 0-hex  -hex stripe

19 Double triplet: quasicrystal

20 Two-wavelength Turing patterns L. Yang, M. Dolnik, A.M.Zhabotinsky, and I.R.Epstein, PRL (2002) A two-layer system with different diffusivities

21 Two-wavelength superposition patterns A two-layer system with strongly different diffusivities L. Yang, M. Dolnik, A.M.Zhabotinsky, and I.R.Epstein, PRL (2002)

22 Resonant superlattice patterns G. Dewel et al, 2001

23 Superlattice patterns: convection in vibrated layer W. Pesch et al, PRL (2000)

24 Rayleigh–Bénard convection: complex patterns Nucleation of hexagons in a defect core Rolls, up- and down- hexagons Experiments of V.Steinberg

25 Two-frequency forced parametric waves H.Arbell and J.Fineberg, PRE (2002)

26 Dynamics of spots in the plane C.P.Schenk,M.Or-Guil,M.Bode,and H.-G.Purwins, Phys.Rev.Lett.78,3781 (1997)

27 Spirals and labyrinth patterns in BZ reaction Action of incoherent light: A spiral wave forms in the upper half of the same reactor, which is in the dark A labyrinthine standing-wave pattern forms in the lower half of the reactor, which is illuminated with light pulsed at twice the natural frequency of the reaction

28 Chemical waves in the BZ reaction. Top: target patterns in a thin film of reagent (1.5 mm). Bottom: spiral waves in reagent similar to above except less acidic. Both sequences from left to right are at 60 s intervals. Reprinted with permission from: Winfree, A. T. Prog. Theor. Chem. 1978, 4, 1.

29 Spiral wave patterns in CGLE Frustrated pattern Turbulent pattern P. G. Kevrekidis, A. R. Bishop, and K. Ø. Rasmussen Phys. Rev. E 65, (2002)

30 Spiral wave and its break-up M. Baer, M. OrGuil, PRL (1999)

31 Instability of a reaction front

32 Boundary dynamics: c n = c n (v) + f(  ) ( Meron et al) Labirynthine pattern develops from a single stripe when the inhibitor is fast Spiral turbulence develops from a single stripe when the inhibitor is slow

33 3D instabilities in surface growth Snowflakes Dendritic patterns in electrodeposition Bacterial colony Multiple-exposure photograph of a dendrite advancing downwards Huang and Glicksman Acta Metall (1981)


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