Turing Instability in a Boundary-fed System

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review

Center or Limit Cycle: Renormalization Group as a Probe

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers

Diclofenac Prolongs Repolarization in Ventricular Muscle with Impaired Repolarization Reserve

Background: The aim of the present work was to characterize the electrophysiological effects of the non-steroidal anti- inflammatory drug diclofenac and to study the possible proarrhythmic potency of the drug in ventricular muscle. Methods: Ion currents were recorded using voltage clamp technique in canine single ventricular cells and action potentials were obtained from canine ventricular preparations using microelectrodes. The proarrhythmic potency of the drug was investigated in an anaesthetized rabbit proarrhythmia model. Results: Action potentials were slightly lengthened in ventricular muscle but were shortened in Purkinje fibers by diclofenac (20 mM). The maximum upstroke velocity was decreased in both preparations. Larger repolarization prolongation was observed when repolarization reserve was impaired by previous BaCl 2 application. Diclofenac (3 mg/kg) did not prolong while dofetilide (25 mg/kg) significantly lengthened the QT c interval in anaesthetized rabbits. The addition of diclofenac following reduction of repolarization reserve by dofetilide further prolonged QT c . Diclofenac alone did not induce Torsades de Pointes ventricular tachycardia (TdP) while TdP incidence following dofetilide was 20%. However, the combination of diclofenac and dofetilide significantly increased TdP incidence (62%). In single ventricular cells diclofenac (30 mM) decreased the amplitude of rapid (I Kr ) and slow (I Ks ) delayed rectifier currents thereby attenuating repolarization reserve. L-type calcium current (I Ca ) was slightly diminished, but the transient outward (I to ) and inward rectifier (I K1 ) potassium currents were not influenced. Conclusions: Diclofenac at therapeutic concentrations and even at high dose does not prolong repolarization markedly and does not increase the risk of arrhythmia in normal heart. However, high dose diclofenac treatment may lengthen repolarization and enhance proarrhythmic risk in hearts with reduced repolarization reserve

Scenarios of domain pattern formation in a reaction-diffusion system

We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as a result of Turing instability. In the stable homogeneous system with the fast inhibitor one can excite both localized and extended patterns by applying a localized stimulus. Depending on the parameters and the excitation level of the system stripes, spots, wriggled stripes, or labyrinthine patterns form. The labyrinthine patterns may be both connected and disconnected. In the the stable homogeneous system with the slow inhibitor one can excite self-replicating spots, breathing patterns, autowaves and turbulence. The parameter regions in which different types of patterns are realized are explained on the basis of the asymptotic theory of instabilities for patterns with sharp interfaces developed by us in Phys. Rev. E. 53, 3101 (1996). The dynamics of the patterns observed in our simulations is very similar to that of the patterns forming in the ferrocyanide-iodate-sulfite reaction.Comment: 15 pages (REVTeX), 15 figures (postscript and gif), submitted to Phys. Rev.

The soft and the hard pomerons in hadron elastic scattering at small t

We consider simple-pole descriptions of soft elastic scattering for pp, pbar p, pi+ p, pi- p, K+ p and K- p. We work at t and s small enough for rescatterings to be neglected, and allow for the presence of a hard pomeron. After building and discussing an exhaustive dataset, we show that simple poles provide an excellent description of the data in the region - 0.5 GeV^2 < t < -0.1 GeV^2, 6 GeV<sqrt(s)< 63 GeV. We show that new form factors have to be used, and get information on the trajectories of the soft and hard pomerons.Comment: 27 pages, 9 figures, LaTeX. A few typos fixed, and references correcte