Three-Dimensional Autonomous Pacemaker in the Photosensitive Belousov-Zhabotinsky medium

In experiments with the photosensitive Belousov-Zhabotinsky reaction (PBZR) we found a stable three-dimensional organizing center that periodically emits trigger waves of chemical concentration. The experiments are performed in a parameter regime with negative line tension using an open gel reactor to maintain stationary non-equilibrium conditions. The observed periodic wave source is formed by a scroll ring stabilized due to its interaction with a no-flux boundary. Sufficiently far from the boundary, the scroll ring expands and undergoes the negative line tension instability before it finally develops into scroll wave turbulence. Our experimental results are reproduced by numerical integration of the modified Oregonator model for the PBZR. Stationary and breathing self-organized pacemakers have been found in these numerical simulations. In the latter case, both the radius of the scroll ring and the distance of its filament plane to the no-flux boundary after some transient undergo undamped stable limit cycle oscillations. So far, in contrary to their stationary counterpart, the numerically predicted breathing autonomous pacemaker has not been observed in the chemical experiment

Massive Binary Black Holes in the Cosmic Landscape

Binary black holes occupy a special place in our quest for understanding the evolution of galaxies along cosmic history. If massive black holes grow at the center of (pre-)galactic structures that experience a sequence of merger episodes, then dual black holes form as inescapable outcome of galaxy assembly. But, if the black holes reach coalescence, then they become the loudest sources of gravitational waves ever in the universe. Nature seems to provide a pathway for the formation of these exotic binaries, and a number of key questions need to be addressed: How do massive black holes pair in a merger? Depending on the properties of the underlying galaxies, do black holes always form a close Keplerian binary? If a binary forms, does hardening proceed down to the domain controlled by gravitational wave back reaction? What is the role played by gas and/or stars in braking the black holes, and on which timescale does coalescence occur? Can the black holes accrete on flight and shine during their pathway to coalescence? N-Body/hydrodynamical codes have proven to be vital tools for studying their evolution, and progress in this field is expected to grow rapidly in the effort to describe, in full realism, the physics of stars and gas around the black holes, starting from the cosmological large scale of a merger. If detected in the new window provided by the upcoming gravitational wave experiments, binary black holes will provide a deep view into the process of hierarchical clustering which is at the heart of the current paradigm of galaxy formation. They will also be exquisite probes for testing General Relativity, as the theory of gravity. The waveforms emitted during the inspiral, coalescence and ring-down phase carry in their shape the sign of a dynamically evolving space-time and the proof of the existence of an horizon.Comment: Invited Review to appear on Advanced Science Letters (ASL), Special Issue on Computational Astrophysics, edited by Lucio Maye

Dynamical mechanism of atrial fibrillation: a topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure

Dynamics of poles with position-dependent strengths and its optical analogues

The dynamics of point vortices is generalized in two ways: first by making the strengths complex, which allows for sources and sinks in superposition with the usual vortices, second by making them functions of position. These generalizations lead to a rich dynamical system, which is nonlinear and yet has conservation laws coming from a Hamiltonian-like formalism. We then discover that in this system the motion of a pair mimics the behavior of rays in geometric optics. We describe several exact solutions with optical analogues, notably Snell's law and the law of reflection off a mirror, and perform numerical experiments illustrating some striking behavior.Comment: 10 page

Spiral Waves in Media with Complex Excitable Dynamics

The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken symmetry and complex temporal dynamics. The main structural features of such waves, synchronization defect lines, are demonstrated to be similar to those of spiral waves in systems with complex-oscillatory dynamics.Comment: to appear in International Journal of Bifurcation and Chao

Birth of massive black hole binaries

If massive black holes (BHs) are ubiquitous in galaxies and galaxies experience multiple mergers during their cosmic assembly, then BH binaries should be common albeit temporary features of most galactic bulges. Observationally, the paucity of active BH pairs points toward binary lifetimes far shorter than the Hubble time, indicating rapid inspiral of the BHs down to the domain where gravitational waves lead to their coalescence. Here, we review a series of studies on the dynamics of massive BHs in gas-rich galaxy mergers that underscore the vital role played by a cool, gaseous component in promoting the rapid formation of the BH binary. The BH binary is found to reside at the center of a massive self-gravitating nuclear disc resulting from the collision of the two gaseous discs present in the mother galaxies. Hardening by gravitational torques against gas in this grand disc is found to continue down to sub-parsec scales. The eccentricity decreases with time to zero and when the binary is circular, accretion sets in around the two BHs. When this occurs, each BH is endowed with it own small-size (< 0.01 pc) accretion disc comprising a few percent of the BH mass. Double AGN activity is expected to occur on an estimated timescale of < 1 Myr. The double nuclear point-like sources that may appear have typical separation of < 10 pc, and are likely to be embedded in the still ongoing starburst. We note that a potential threat of binary stalling, in a gaseous environment, may come from radiation and/or mechanical energy injections by the BHs. Only short-lived or sub-Eddington accretion episodes can guarantee the persistence of a dense cool gas structure around the binary necessary for continuing BH inspiral.Comment: To appear in "2007 STScI Spring Symposium: Black Holes", eds. M. Livio & A. M. Koekemoer, Cambridge University Press, 25 pages, 12 figure