596 research outputs found
Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue
The present study investigates the spatio-temporal variability in the
dynamics of self-sustained supersonic reaction waves propagating through an
excitable medium. The model is an extension of Fickett's detonation model with
a state dependent energy addition term. Stable and pulsating supersonic waves
are predicted. With increasing sensitivity of the reaction rate, the reaction
wave transits from steady propagation to stable limit cycles and eventually to
chaos through the classical Feigenbaum route. The physical pulsation mechanism
is explained by the coherence between internal wave motion and energy release.
The results obtained clarify the physical origin of detonation wave instability
in chemical detonations previously observed experimentally.Comment: 4 pages, 3 figure
Time scales in shear banding of wormlike micelles
Transient stress and birefringence measurements are performed on wormlike micellar solutions that "shear band", i.e. undergo flow-induced coexistence of states of different viscosities along a constant stress "plateau". Three well-defined relaxation times are found after a strain rate step between two banded flow states on the stress plateau. Using the Johnson-Segalman model, we relate these time scales to three qualitatively different stages in the evolution of the bands and the interface between them: band destabilization, reconstruction of the interface, and travel of the fully formed interface. The longest timescale is then used to estimate the magnitude of the (unknown) "gradient" terms that must be added to constitutive relations to explain the history independence of the steady flow and the plateau stress selection
Wide complex tachycardia in an elderly woman due to Ebstein\u27s anomaly with two accessory pathways
Dense packing on uniform lattices
We study the Hard Core Model on the graphs
obtained from Archimedean tilings i.e. configurations in with the nearest neighbor 1's forbidden. Our
particular aim in choosing these graphs is to obtain insight to the geometry of
the densest packings in a uniform discrete set-up. We establish density bounds,
optimal configurations reaching them in all cases, and introduce a
probabilistic cellular automaton that generates the legal configurations. Its
rule involves a parameter which can be naturally characterized as packing
pressure. It can have a critical value but from packing point of view just as
interesting are the noncritical cases. These phenomena are related to the
exponential size of the set of densest packings and more specifically whether
these packings are maximally symmetric, simple laminated or essentially random
packings.Comment: 18 page
Coincidence isometries of a shifted square lattice
We consider the coincidence problem for the square lattice that is translated
by an arbitrary vector. General results are obtained about the set of
coincidence isometries and the coincidence site lattices of a shifted square
lattice by identifying the square lattice with the ring of Gaussian integers.
To illustrate them, we calculate the set of coincidence isometries, as well as
generating functions for the number of coincidence site lattices and
coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool
The Johnson-Segalman model with a diffusion term in Couette flow
We study the Johnson-Segalman (JS) model as a paradigm for some complex
fluids which are observed to phase separate, or ``shear-band'' in flow. We
analyze the behavior of this model in cylindrical Couette flow and demonstrate
the history dependence inherent in the local JS model. We add a simple gradient
term to the stress dynamics and demonstrate how this term breaks the degeneracy
of the local model and prescribes a much smaller (discrete, rather than
continuous) set of banded steady state solutions. We investigate some of the
effects of the curvature of Couette flow on the observable steady state
behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog
Vorticity Banding During the Lamellar-to-Onion Transition in a Lyotropic Surfactant Solution in Shear Flow
We report on the rheology of a lamellar lyotropic surfactant solution
(SDS/dodecane/pentanol/water), and identify a discontinuous transition between
two shear thinning regimes which correspond to the low stress lamellar phase
and the more viscous shear induced multi-lamellar vesicle, or ``onion'' phase.
We study in detail the flow curve, stress as a function of shear rate, during
the transition region, and present evidence that the region consists of a shear
banded phase where the material has macroscopically separated into bands of
lamellae and onions stacked in the vorticity direction. We infer very slow and
irregular transformations from lamellae to onions as the stress is increased
through the two phase region, and identify distinct events consistent with the
nucleation of small fractions of onions that coexist with sheared lamellae.Comment: 10 pages, 10 figure
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