9 research outputs found
Clustering, Chaos and Crisis in a Bailout Embedding Map
We study the dynamics of inertial particles in two dimensional incompressible
flows. The particle dynamics is modelled by four dimensional dissipative
bailout embedding maps of the base flow which is represented by 2-d area
preserving maps. The phase diagram of the embedded map is rich and interesting
both in the aerosol regime, where the density of the particle is larger than
that of the base flow, as well as the bubble regime, where the particle density
is less than that of the base flow. The embedding map shows three types of
dynamic behaviour, periodic orbits, chaotic structures and mixed regions. Thus,
the embedding map can target periodic orbits as well as chaotic structures in
both the aerosol and bubble regimes at certain values of the dissipation
parameter. The bifurcation diagram of the 4-d map is useful for the
identification of regimes where such structures can be found. An attractor
merging and widening crisis is seen for a special region for the aerosols. At
the crisis, two period-10 attractors merge and widen simultaneously into a
single chaotic attractor. Crisis induced intermittency is seen at some points
in the phase diagram. The characteristic times before bursts at the crisis show
power law behaviour as functions of the dissipation parameter. Although the
bifurcation diagram for the bubbles looks similar to that of aerosols, no such
crisis regime is seen for the bubbles. Our results can have implications for
the dynamics of impurities in diverse application contexts.Comment: 16 pages, 9 figures, submitted for publicatio
Transport and diffusion in the embedding map
We study the transport properties of passive inertial particles in a
incompressible flows. Here the particle dynamics is represented by the
dissipative embedding map of area-preserving standard map which models
the incompressible flow. The system is a model for impurity dynamics in a fluid
and is characterized by two parameters, the inertia parameter , and the
dissipation parameter . We obtain the statistical characterisers of
transport for this system in these dynamical regimes. These are, the recurrence
time statistics, the diffusion constant, and the distribution of jump lengths.
The recurrence time distribution shows a power law tail in the dynamical
regimes where there is preferential concentration of particles in sticky
regions of the phase space, and an exponential decay in mixing regimes. The
diffusion constant shows behaviour of three types - normal, subdiffusive and
superdiffusive, depending on the parameter regimes. Phase diagrams of the
system are constructed to differentiate different types of diffusion behaviour,
as well as the behaviour of the absolute drift. We correlate the dynamical
regimes seen for the system at different parameter values with the transport
properties observed at these regimes, and in the behaviour of the transients.
This system also shows the existence of a crisis and unstable dimension
variability at certain parameter values. The signature of the unstable
dimension variability is seen in the statistical characterisers of transport.
We discuss the implications of our results for realistic systems.Comment: 28 pages, 14 figures, To Appear in Phys. Rev. E; Vol. 79 (2009
Stuck in traffic: Patterns of powder adhesion
The adhesion of fine particles to surfaces is important for applications ranging from drug delivery to fouling of solar cells. In this letter, we show that powder adhesion can occur in unexpected patterns, concentrating particular grain types in some locations and clearing them from others, and we propose a straightforward traffic model that appears to reproduce many of the behaviors seen. The model predicts different patterns depending on inter-particle cohesion, and we find in both experiment and model that adhesion occurs in three distinct stages