114 research outputs found
Runaway electrification of friable self-replicating granular matter
We establish that the nonlinear dynamics of collisions between particles
favors the charging of a insulating, friable, self-replicating granular
material that undergoes nucleation, growth, and fission processes; we
demonstrate with a minimal dynamical model that secondary nucleation produces a
positive feedback in an electrification mechanism that leads to runaway
charging. We discuss ice as an example of such a self-replicating granular
material: We confirm with laboratory experiments in which we grow ice from the
vapor phase in situ within an environmental scanning electron microscope that
charging causes fast-growing and easily breakable palm-like structures to form,
which when broken off may form secondary nuclei. We propose that thunderstorms,
both terrestrial and on other planets, and lightning in the solar nebula are
instances of such runaway charging arising from this nonlinear dynamics in
self-replicating granular matter
Three-frequency resonances in dynamical systems
We investigate numerically and experimentally dynamical systems having three
interacting frequencies: a discrete mapping (a circle map), an exactly solvable
model (a system of coupled ordinary differential equations), and an
experimental device (an electronic oscillator). We compare the hierarchies of
three-frequency resonances we find in each of these systems. All three show
similar qualitative behaviour, suggesting the existence of generic features in
the parameter-space organization of three-frequency resonances.Comment: See home page http://lec.ugr.es/~julya
Crystal growth as an excitable medium
Crystal growth has been widely studied for many years, and, since the
pioneering work of Burton, Cabrera and Frank, spirals and target patterns on
the crystal surface have been understood as forms of tangential crystal growth
mediated by defects and by two-dimensional nucleation. Similar spirals and
target patterns are ubiquitous in physical systems describable as excitable
media. Here, we demonstrate that this is not merely a superficial resemblance,
that the physics of crystal growth can be set within the framework of an
excitable medium, and that appreciating this correspondence may prove useful to
both fields. Apart from solid crystals, we discuss how our model applies to the
biomaterial nacre, formed by layer growth of a biological liquid crystal
Brinicles as a case of inverse chemical gardens
Brinicles are hollow tubes of ice from centimetres to metres in length that
form under floating sea ice in the polar oceans when dense, cold brine drains
downwards from sea ice into sea water close to its freezing point. When this
extremely cold brine leaves the ice it freezes the water it comes into contact
with; a hollow tube of ice --- a brinicle --- growing downwards around the
plume of descending brine. We show that brinicles can be understood as a form
of the self-assembled tubular precipitation structures termed chemical gardens,
plant-like structures formed on placing together a soluble metal salt, often in
the form of a seed crystal, and an aqueous solution of one of many anions,
often silicate. On one hand, in the case of classical chemical gardens, an
osmotic pressure difference across a semipermeable precipitation membrane that
filters solutions by rejecting the solute leads to an inflow of water and to
its rupture. The internal solution, generally being lighter than the external
solution, flows up through the break, and as it does so a tube grows upwards by
precipitation around the jet of internal solution. Such chemical-garden tubes
can grow to many centimetres in length. In the case of brinicles, on the other
hand, in floating sea ice we have porous ice in a mushy layer that filters out
water, by freezing it, and allows concentrated brine through. Again there is an
osmotic pressure difference leading to a continuing ingress of sea water in a
siphon pump mechanism that is sustained as long as the ice continues to freeze.
Since the brine that is pumped out is denser than the sea water, and descends
rather rises, a brinicle is a downwards growing tube of ice; an inverse
chemical garden
Exploding Chemical Gardens: A Phase-Change Clock Reaction.
Chemical gardens and clock reactions are two of the best-known demonstration reactions in chemistry. Until now these have been separate categories. We have discovered that a chemical garden confined to two dimensions is a clock reaction involving a phase change, so that after a reproducible and controllable induction period it explodes
Bailout Embeddings, Targeting of KAM Orbits, and the Control of Hamiltonian Chaos
We present a novel technique, which we term bailout embedding, that can be
used to target orbits having particular properties out of all orbits in a flow
or map. We explicitly construct a bailout embedding for Hamiltonian systems so
as to target KAM orbits. We show how the bailout dynamics is able to lock onto
extremely small KAM islands in an ergodic sea.Comment: 3 figures, 9 subpanel
Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems
We show that, even in the most favorable case, the motion of a small
spherical tracer suspended in a fluid of the same density may differ from the
corresponding motion of an ideal passive particle. We demonstrate furthermore
how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya
Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow
We introduce and study the first model of an experimentally realizable
three-dimensional time-dependent nonturbulent fluid flow to display the
phenomenon of global diffusion of passive-scalar particles at arbitrarily small
values of the nonintegrable perturbation. This type of chaotic advection,
termed {\it resonance-induced diffusion\/}, is generic for a large class of
flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys.
Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/,
or on paper by reques
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
We apply results from nonlinear dynamics to an old problem in acoustical
physics: the mechanism of the perception of the pitch of sounds, especially the
sounds known as complex tones that are important for music and speech
intelligibility
Emergent global oscillations in heterogeneous excitable media: The example of pancreatic beta cells
Using the standard van der Pol-FitzHugh-Nagumo excitable medium model I
demonstrate a novel generic mechanism, diversity, that provokes the emergence
of global oscillations from individually quiescent elements in heterogeneous
excitable media. This mechanism may be operating in the mammalian pancreas,
where excitable beta cells, quiescent when isolated, are found to oscillate
when coupled despite the absence of a pacemaker region.Comment: See home page http://lec.ugr.es/~julya
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