Hands-on table-top science

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1 Hands-on table-top science Harry L. Swinney University of Texas fluid convection bacterial colony chemical pattern daffodil 5 cm A special thanks to the students and postdocs at U. Texas who did this work

Antenna (gravity waves) ITER: international

2 BIG Science cost: ~$ me: ~decade scien+sts: 1000s LHC: Large Hadron Collider to search for Higgs particle 4,3 km LISA: 3 satellites LISA: Laser Interferometer Space Antenna (gravity waves) ITER: international tokamak (fusion power) to detect gravity waves

3 Hands-on table-top science cost: ~$1000 +me: ~year(s) scien+sts: ~few Inexpensive instrumentation webcam $60 Arduino $30 Inexpensive computation 1 TB disk memory 1 TB $100

4 Rip a garbage bag and look at its edge

5 n=6 30 mm x waves within waves within waves x 3.2 x a fractal: same structure on different length scales x Sharon, Roman, Marder, Shin, Swinney. Nature 419 (2002) x 3.2 1

$Britain: D=1.25 Lewis Fry Richardson, 1927 3 1 2 3 log 10 [G(km)] Mandelbrot, How long is the coast of Britain? Science 155 (1967). Mandelbrot coined fractal in 1975$

6 Richardson effect: coastline length L = MG 1-D where G = measurement scale and D = noninteger dimension G=200 km G=50 km RICHARDSON S GRAPH 4 log 10 [L(km)] coast of Britain: D=1.25 Lewis Fry Richardson, log 10 [G(km)] Mandelbrot, How long is the coast of Britain? Science 155 (1967). Mandelbrot coined fractal in 1975

7 Similar buckling in thin sheets Compare torn garbage bag to leaves & flowers side garbage bag beet leaf Sharon et al. American Scientist 92 (2004); Physical Review E 75 (2007) daffodil violet flower

8 Transitions in systems driven away from thermodynamic equilibrium T COLD Example: fluid in a box T HOT For ΔT = T HOT T COLD small, the fluid conducts heat but remains at rest. But for ΔT larger than (ΔT) c an ordered convection pattern emerges.

9 Onset of convection T COLD T HOT For ΔT = T HOT T COLD small, the fluid conducts heat but remains at rest. But for ΔT > (ΔT) c an ordered convection pattern emerges.

10 Can the emergence of a pattern be predicted? Consider a fluid between two parallel plates: speed V V = 0 How large does V have to be for the flow to change? Lord Kelvin, Lord Rayleigh, Sommerfeld, Hopf and others attempted to predict the answer but failed.

11 Fluid between cylinders with the inner one rotating Ω = rotation frequency Reynolds number R aω(b a) G.I. Taylor R= Cambridge University viscosity υ

12 Emergence of a pattern: R > R c Taylor (1923) Pattern: a stack of donut-shaped vortices vortex pair Photo: Andereck, Liu, Swinney J Fluid Mech. (1985)

13 Emergence of Taylor vortex pattern G. I. Taylor, Proc. Royal Society (1923) f inner cylinder EXPERIMENT THEORY f outer cylinder This was the first test of a prediction of the onset of order. All [previous] attempts to calculate the speed at which any type of flow would become unstable have failed.

$phase space attractor: fractal dimension D Re =$ 131 Re = 715 Dimension D of phase space attractor

Rev. A (1987)< 1200 1700 chaos 2500 onset

14 Higher instabilities leading to chaos strange phase space attractor: fractal dimension D Re = 131 Re = 715 Dimension D of phase space attractor Re = 1950 Re = 2800 D Brandstater & Swinney, Phys. Rev. A (1987)< chaos 2500 onset Reynolds number Brandstater & Swinney, Phys. Rev. A (1987)

15 Alan Turing: How does a zebra get its stripes?

16 Turing Chemical patterns patterns Philosophical Transactions Royal Society (London), (1952) Philosophical Transactions Royal Society London (1952)

17 Turing pattern hexagonal pattern (in a thin gel layer) close-up Turing wavelength λ = 2π Dτ Colors: chloride concentration in the chlorite-iodide-malonic acid reaction Ouyang & Swinney, Nature (1991) 0.2 mm

18 Shake sand shake vertically light LIGHT Experiments and simulations: Goldman, Shattuck, Rericha, et al. LOUDSPEAKER

19 Pattern formed in a shaken granular layer Pattern forms when the vertical acceleration is greater than 2.6 x gravitational acceleration Goldman, Shattuck, Moon, Swift, Swinney Phys. Rev. Lett. 90 (2002) close up snapshot 1000 x (particle diameter)

20 Numerical simulations of Newton s laws Assume the particles are hard spherical balls that obey Newton s laws in each collision Linear momentum and angular momentum are conserved in collisions, but some energy is lost. Between collisions the particles move on parabolic paths

21 Compare experiment and computation EXPERIMENT 60,000 spheres d = 0.55 mm diameter layer: 100d x 100d x 6d acceleration = 3g f = 15 Hz f = 25 Hz Bizon, Shattuck, Swift, McCormick, Swinney Physical Review Letters (1998) COMPUTATION

22 Oscillon: localized oscillating structure 365 µm balls snapshot Umbanhowar, Melo, Swinney Nature (1996)

23 Jupiter s Great Red Spot discovered by Robert Hooke (1664) Voyager 2 (1979) 86 cm dia. rotating tank persistent dominant vortex t = 6 sec Sommeria, Meyers, Swinney Nature 331 (1988)

24 Gulf Stream Sea surface temperature ( o C) NEW YORK

25 Surface air temperature: Deviation from average at a latitude 80 o +10 o C 60 o 40 o o 0 o -20 o -40 o -60 o Rahmstorph, Nature (2005)

26 Internal gravity waves in the oceans: generated by tidal flow over topography sin θ = ω/n where AL ENT TIN E CONSLOP CONTINENTAL SHELF θ θ Garrett, Science (2003) Internal gravity waves transport much of the energy in the oceans through mixing: drive ocean currents which affect climate

27 Tidal flow on a laboratory model slope Tidal flow on a laboratory model slope

28 Tracer particle motion reveals boundary current MOVIE 6 cm image window: z x

29 Resonance: intense boundary current when topographic slope = internal wave slope 10 z (cm) 8 6 (V/V 0 ) 2 (V 0 = tidal amplitude) ω=0.91 rad/s, N=1.55 rad/s, A=0.1 cm x (cm)

30 Resonant boundary current at critical frequency where topographic and internal wave slopes are equal ( V / V0) 2 Zhang, King, Swinney Phys. Rev. Lett. (2008)

31 Strong shear at resonance leads to mixing 5 mm H.P. Zhang, King, & Swinney Phys. Rev. Lett. (2008) Rodenborn et al., Physics of Fluids (2011) King et al., J. Geophysical Research (2012)

Table-top experiments reveal surface of vibrating layer of water Systems forced away from thermodynamic equilibrium spontaneously form diverse universal dynamics/patterns at critical parameter values.

32 Table-top experiments reveal surface of vibrating layer of water Systems forced away from thermodynamic equilibrium spontaneously form diverse universal dynamics/patterns at critical parameter values. wal k Turing pattern TURING stick.another example - LEVY FLIGHTS, LEVY WALKS Lévy distributions P(x) ~ x -µ Solomon, Weeks, Swinney, Phys. Rev. Lett. 71 (1993) Unlike equilibrium systems, there is no general theory, no extremum principle far from equilibrium

33 Hands-on Table-top Science FLEXIBILITY --- freed of the constraint of big machines and big research teams, let nature speak and guide the research

Hepeng Zhang Ben King Bruce Rodenborn

Hepeng Zhang Ben King Bruce Rodenborn International School of Physics "Enrico Fermi" - Course CLXXVI Complex materials in physics and biology, 9 June - 9 July 010 Nonlinear dynamics of waves and transport in the atmosphere and oceans: Internal