14,531 research outputs found
The emergence of coherence in complex networks of heterogeneous dynamical systems
We present a general theory for the onset of coherence in collections of
heterogeneous maps interacting via a complex connection network. Our method
allows the dynamics of the individual uncoupled systems to be either chaotic or
periodic, and applies generally to networks for which the number of connections
per node is large. We find that the critical coupling strength at which a
transition to synchrony takes place depends separately on the dynamics of the
individual uncoupled systems and on the largest eigenvalue of the adjacency
matrix of the coupling network. Our theory directly generalizes the Kuramoto
model of equal strength, all-to-all coupled phase oscillators to the case of
oscillators with more realistic dynamics coupled via a large heterogeneous
network.Comment: 4 pages, 1 figure. Published versio
Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
We analyze a large system of globally coupled phase oscillators whose natural
frequencies are bimodally distributed. The dynamics of this system has been the
subject of long-standing interest. In 1984 Kuramoto proposed several
conjectures about its behavior; ten years later, Crawford obtained the first
analytical results by means of a local center manifold calculation.
Nevertheless, many questions have remained open, especially about the
possibility of global bifurcations. Here we derive the system's complete
stability diagram for the special case where the bimodal distribution consists
of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott
and Antonsen, we show that in this case the infinite-dimensional problem
reduces exactly to a flow in four dimensions. Depending on the parameters and
initial conditions, the long-term dynamics evolves to one of three states:
incoherence, where all the oscillators are desynchronized; partial synchrony,
where a macroscopic group of phase-locked oscillators coexists with a sea of
desynchronized ones; and a standing wave state, where two counter-rotating
groups of phase-locked oscillators emerge. Analytical results are presented for
the bifurcation boundaries between these states. Similar results are also
obtained for the case in which the bimodal distribution is given by the sum of
two Gaussians.Comment: 28 pages, 7 figures; submitted to Phys. Rev. E Added comment
Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
The onset of synchronization in networks of networks is investigated.
Specifically, we consider networks of interacting phase oscillators in which
the set of oscillators is composed of several distinct populations. The
oscillators in a given population are heterogeneous in that their natural
frequencies are drawn from a given distribution, and each population has its
own such distribution. The coupling among the oscillators is global, however,
we permit the coupling strengths between the members of different populations
to be separately specified. We determine the critical condition for the onset
of coherent collective behavior, and develop the illustrative case in which the
oscillator frequencies are drawn from a set of (possibly different)
Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in
which the collective dynamics of several interacting populations of oscillators
(such as excitatory and inhibitory neurons and glia) are of interest.Comment: The original was replaced with a version that has been accepted to
Phys. Rev. E. The new version has the same content, but the title, abstract,
and the introductory text have been revise
Elastohydrodynamic study of actin filaments using fluorescence microscopy
We probed the bending of actin subject to external forcing and viscous drag.
Single actin filaments were moved perpendicular to their long axis in an
oscillatory way by means of an optically tweezed latex bead attached to one end
of the filaments. Shapes of these polymers were observed by epifluorescence
microscopy. They were found to be in agreement with predictions of semiflexible
polymer theory and slender-body hydrodynamics. A persistence length of m could be extracted.Comment: RevTex, 4 pages, 5 eps figs, submitted to PR
Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized Dynamics
The bifurcation and chaotic behaviour of unidirectionally coupled
deterministic ratchets is studied as a function of the driving force amplitude
() and frequency (). A classification of the various types of
bifurcations likely to be encountered in this system was done by examining the
stability of the steady state in linear response as well as constructing a
two-parameter phase diagram in the () plane. Numerical explorations
revealed varieties of bifurcation sequences including quasiperiodic route to
chaos. Besides, the familiar period-doubling and crises route to chaos
exhibited by the one-dimensional ratchet were also found. In addition, the
coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of
bifurcations. Chaotic behaviour is characterized by using the sensitivity to
initial condition as well as the Lyapunov exponent spectrum; while a perusal of
the phase space projected in the Poincar cross-section confirms some
of the striking features.Comment: 7 pages; 8 figure
Classical diffusion in double-delta-kicked particles
We investigate the classical chaotic diffusion of atoms subjected to {\em
pairs} of closely spaced pulses (`kicks) from standing waves of light (the
-KP). Recent experimental studies with cold atoms implied an
underlying classical diffusion of type very different from the well-known
paradigm of Hamiltonian chaos, the Standard Map.
The kicks in each pair are separated by a small time interval , which together with the kick strength , characterizes the transport.
Phase space for the -KP is partitioned into momentum `cells' partially
separated by momentum-trapping regions where diffusion is slow. We present here
an analytical derivation of the classical diffusion for a -KP
including all important correlations which were used to analyze the
experimental data.
We find a new asymptotic () regime of `hindered' diffusion:
while for the Standard Map the diffusion rate, for , oscillates about the uncorrelated, rate , we find
analytically, that the -KP can equal, but never diffuses faster than,
a random walk rate.
We argue this is due to the destruction of the important classical
`accelerator modes' of the Standard Map.
We analyze the experimental regime , where
quantum localisation lengths are affected by fractal
cell boundaries. We find an approximate asymptotic diffusion rate , in correspondence to a regime in the Standard Map
associated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte
Exploring classically chaotic potentials with a matter wave quantum probe
We study an experimental setup in which a quantum probe, provided by a
quasi-monomode guided atom laser, interacts with a static localized attractive
potential whose characteristic parameters are tunable. In this system,
classical mechanics predicts a transition from a regular to a chaotic behavior
as a result of the coupling between the longitudinal and transverse degrees of
freedom. Our experimental results display a clear signature of this transition.
On the basis of extensive numerical simulations, we discuss the quantum versus
classical physics predictions in this context. This system opens new
possibilities for investigating quantum scattering, provides a new testing
ground for classical and quantum chaos and enables to revisit the
quantum-classical correspondence
Neutrino Signatures and the Neutrino-Driven Wind in Binary Neutron Star Mergers
We present VULCAN/2D multigroup flux-limited-diffusion radiation-hydrodynamics simulations of binary neutron star mergers, using the Shen equation of state, covering âł 100 ms, and starting from azimuthal-averaged two-dimensional slices obtained from three-dimensional smooth-particle-hydrodynamics simulations of Rosswog & Price for 1.4Mâ (baryonic) neutron stars with no initial spins, co-rotating spins, or counter-rotating spins. Snapshots are post-processed at 10 ms intervals with a multiangle neutrino-transport solver. We find polar-enhanced neutrino luminosities, dominated by ÂŻÎœe and âΜΌâ neutrinos at the peak, although Îœe emission may be stronger at late times. We obtain typical peak neutrino energies for Îœe, ÂŻÎœe, and âΜΌâ of âŒ12, âŒ16, and âŒ22 MeV, respectively. The supermassive neutron star (SMNS) formed from the merger has a cooling timescale of ⟠1 s. Charge-current neutrino reactions lead to the formation of a thermally driven bipolar wind with (M·) ⌠10^â3 Mâ s^â1 and baryon-loading in the polar regions, preventing any production of a Îł-ray burst prior to black hole formation. The large budget of rotational free energy suggests that magneto-rotational effects could produce a much-greater polar mass loss. We estimate that ⟠10^â4 Mâ of material with an electron fraction in the range 0.1â0.2 becomes unbound during this SMNS phase as a result of neutrino heating. We present a new formalism to compute the Îœi ÂŻÎœi annihilation rate based on moments of the neutrino-specific intensity computed with our multiangle solver. Cumulative annihilation rates, which decay as âŒt^â1.8, decrease over our 100 ms window from a few Ă1050 to ⌠1049 erg sâ1, equivalent to a few Ă10^54 to âŒ10^53 eâe+ pairs per second
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