Homepage Ko van der Weele

Research Themes

Granular Dynamics

> Clustering cars, beads, and birds

(a) "Cluster's last stand": Collapse of a granular cluster
Clustering cars: traffic jam formation
Competitive clustering: David vs. Goliath
(d) Birds of a feather. . . : flocking as a phase transition (paper 87)

> Complex Matter Project

> "Bouncing beads outwit Feynman": Granular realization of a Brownian motor (paper 79)

> Inverse Chladni patterning: New surprises in a classic demonstration experiment

> Faraday heaping: The self-assembling interplay of air & sand

> Granular Leidenfrost effect & beyond: The collective dynamics of "boiling particles"

> Meteor impact on a laboratory scale: Dinosaurs beware!

> Granular roll waves on a chute: How many will survive in the end? (paper 89)

Fluid Dynamics

> Physics of the Granite Sphere Fountain (paper 88)

> Solitary water waves: Exploring the limits of the KdV soliton

> Leaping Shampoo (3-minute movie, 31 MB)

 Winning entry in the Gallery of Fluid Motion
 at the 59th Annual Meeting of the
Division of Fluid Dynamics of the APS,
 November 24-26, 2006, in Tampa Bay,

 See also
publications 62, 63, 66.

 Picture by Michel Versluis,
 Univ. of Twente, The Netherlands.

Free Field Physics: questions inspired by phenomena from daily life

>> How on earth can a solid granite sphere be levitated by a thin film of water?! (paper 88)

>> In the relativistic paradox of the barn and the pole, is the pole caught after all? Or not? (paper 64)

>> When a horse accelerates, why does it first walk, then trot and finally break into a gallop? (paper 33)

>> Throw a ball straight up in the air. What do you think: does the way down take just as long as the way up? (paper 27)

>> How efficiently do you chew? A mathematical description of the grinding of food particles (paper 6)

Nonlinear Dynamics

> The Route to Chaos via period-doubling bifurcations:
(a) in 1D maps with a maximum of order z > 1, yielding (among other things) the Feigenbaum numbers δ(z) and α(z) and an analytical relation between them! (publications 3, 4, 7)
(b) in anti-symmetric maps, where the sequence of period doublings is enriched by an intermediate symmetry-breaking bifurcation (publication 20)
(c) in 2D maps with a Jacobian between 1 and 0, showing the not-too-smooth crossover from conservative (Hamiltonian) to purely dissipative behavior (publications 1, 2, 5, 7)

> The Route to Chaos via intermittency:
(a) including a proof that the length of the intermittent phase in 1D maps cannot be arbitrarily short (papers 10, 11, 13, 15)
(b) and a scaling law for the width of the periodic windows as function of their period (paper 14)

> Resonances and bifurcations in 2D maps
(a) The 1:3 resonance (and the associated loss of stability via the "squeeze effect") in area-preserving maps (publications 7, 8, 9)
(b) The birth of twin periodic orbits (Poincare-Birkhoff chains) in non-twist maps (publications 7, 9, 12, 18)
(c) On the occurrence of "Rimmer type" saddle-node bifurcations (and the associated birth of repellors and attractors) in maps with time-reversal symmetry (paper 17)

Coupled Nonlinear Oscillators

> The complex dynamics of two coupled, parametrically driven pendulums (papers 23, 25, 26, 27, 28)
(a) Generalization to 4 parametrically driven pendulums: the locomotion of four-legged animals (papers 30, 33, 34)
(b) Reduction to 1 parametrically driven pendulum: resonances, routes to chaos & the stable dance of the inverted pendulum (papers 16, 19, 20)

> The spring pendulum: a fascinating example of two coupled oscillators (paper 24)

> Discrete breathers (localized oscillatory modes) in an array of coupled nonlinear oscillators: unfolding the homoclinic tangle (papers 31, 32)

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