1,114 research outputs found
Insights into collective cell behaviour from populations of coupled chemical oscillators.
Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Here, we show how experiments with coupled chemical oscillators can provide insights into collective behaviour in cellular systems. Two methods of coupling the oscillators are described: exchange of chemical species with the surrounding solution and computer-controlled illumination of a light-sensitive catalyst. The collective behaviour observed includes synchronisation, dynamical quorum sensing (a density dependent transition to population-wide oscillations), and chimera states, where oscillators spontaneously split into coherent and incoherent groups. At the core of the different types of behaviour lies an intracellular autocatalytic signal and an intercellular communication mechanism that influences the autocatalytic growth
Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication
Domains containing spiral waves form on a stationary background in a photosensitive Belousov-Zhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns
Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication
Domains containing spiral waves form on a stationary background in a photosensitive Belousov-Zhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns
The Christiansen Effect in Saturn's narrow dusty rings and the spectral identification of clumps in the F ring
Stellar occultations by Saturn's rings observed with the Visual and Infrared
Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveal that dusty
features such as the F ring and the ringlets in the Encke and the Laplace Gaps
have distinctive infrared transmission spectra. These spectra show a narrow
optical depth minimum at wavelengths around 2.87 microns. This minimum is
likely due to the Christiansen Effect, a reduction in the extinction of small
particles when their (complex) refractive index is close to that of the
surrounding medium. Simple Mie-scattering models demonstrate that the strength
of this opacity dip is sensitive to the size distribution of particles between
1 and 100 microns across. Furthermore, the spatial resolution of the
occultation data is sufficient to reveal variations in the transmission spectra
within and among these rings. For example, in both the Encke Gap ringlets and F
ring, the opacity dip weakens with increasing local optical depth, which is
consistent with the larger particles being concentrated near the cores of these
rings. The strength of the opacity dip varies most dramatically within the F
ring; certain compact regions of enhanced optical depth lack an opacity dip and
therefore appear to have a greatly reduced fraction of grains in the few-micron
size range.Such spectrally-identifiable structures probably represent a subset
of the compact optically-thick clumps observed by other Cassini instruments.
These variations in the ring's particle size distribution can provide new
insights into the processes of grain aggregation, disruption and transport
within dusty rings. For example, the unusual spectral properties of the F-ring
clumps could perhaps be ascribed to small grains adhering onto the surface of
larger particles in regions of anomalously low velocity dispersion.Comment: 42 pages, 15 figures, accepted for publication in Icarus. A few small
typographical errors fixed to match correction in proof
Experimental observation of extreme multistability in an electronic system of two coupled R\"{o}ssler oscillators
We report the first experimental observation of extreme multistability in a
controlled laboratory investigation. Extreme multistability arises when
infinitely many attractors coexist for the same set of system parameters. The
behavior was predicted earlier on theoretical grounds, supported by numerical
studies of models of two coupled identical or nearly identical systems. We
construct and couple two analog circuits based on a modified coupled
R\"{o}ssler system and demonstrate the occurrence of extreme multistability
through a controlled switching to different attractor states purely through a
change in initial conditions for a fixed set of system parameters. Numerical
studies of the coupled model equations are in agreement with our experimental
findings.Comment: to be published in Phys. Rev.
On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation
In a recent paper Goriely considers the one--dimensional scalar
reaction--diffusion equation with a polynomial reaction
term and conjectures the existence of a relation between a global
resonance of the hamiltonian system and the asymptotic
speed of propagation of fronts of the reaction diffusion equation. Based on
this conjecture an explicit expression for the speed of the front is given. We
give a counterexample to this conjecture and conclude that additional
restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation
The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case () as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004
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