**Homepage Ko van der Weele**

**Research Themes**

**Granular
Dynamics
**

(a)

(b)

(c)

(d) Birds of a feather. . . : flocking as a phase transition (paper 87)

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

at the 59th Annual Meeting of the

Division of Fluid Dynamics of the APS,

November 24-26, 2006, in Tampa Bay,

Florida.

See also publications 62, 63, 66.

Picture by Michel Versluis,

Univ. of Twente, The Netherlands.

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

(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)

(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)

(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)