Universality in active chaos

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).     

Why are chaotic attractors rare in multistable systems?

We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.     

Poincaré recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors

We study Poincaré recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is no longer supported solely by unstable periodic orbits of finite length inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincaré first return times from a Poissonian. Consequently, by taking into account the contribution of these special recurrent trajectories, a corrected estimate of the measure is obtained. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size, and only unstable periodic orbits of finite length can be detected.     

Chaotic advection,diffusion, and reactions in open flows

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.     

Formation of XeCl− in the gas phase

Ion cyclotron resonance has been used to detect the formation of XeCl^? at pressure 10^?4 torr from the ion-molecule reaction of COCl^? and Xe. The dissociation energy of XeCl^? into Xe and Cl^? is estimated to be less than 10 kcal/mole. The results suggest that other negative ions similar to XeCl^? may be detected by mass spectrometric techniques.     

The structure of castanaguyone a biisocoumarin plant product

The fruit extract of the Mexican shrub $\text{Zanthoxylum}$$\text{fagara}$ Sarg. has afforded castanaguyone $\text{1}$; it is the first biisocoumarin encountered in nature.     

Bifurcations of Umbilic Points and Related Principal Cycles

The simplest patterns of qualitative changes on the configurations of lines of principal curvature around umbilic points on surfaces whose immersions into ³ depend smoothly on a real parameter (codimension one umbilic bifurcations) are described in this paper.Global effects, due to umbilic bifurcations, on these configurations such as the appearance and annihilation of periodic principal lines, called also principal cycles, are also studied here.     

Phase locking control in the Circle Map

The phase-locking between two oscillators occurs when the ratio of their frequencies becomes locked in a ratio p/q of integer numbers over some finite domain of parameters values. Due to it, oscillators with some kind of nonlinear coupling may synchronize for certain set of parameters. This phenomenon can be better understood and studied with the use of a well-known paradigm, the Circle Map, and the definition of the winding number. Two diagrams related to this map are especially useful: the ‘Arnold tongues’ and the ‘devil’s staircase’. The synchronization that occurs in this map is described by the ‘Farey Series’. This property is the starting point for the development of control algorithms capable of locking the system under the action of an external excitation into a desired winding number. In this work, we discuss the main characteristics of the phase-locking phenomenon and consider three control algorithms designed to drive and keep the Circle Map into a desired winding number.     

The chemistry of acetone at extreme conditions by density functional molecular dynamics simulations

Density functional molecular dynamics simulations have been performed in the NVT ensemble (moles (N), volume (V) and temperature (T)) on a system formed by ten acetone molecules at a temperature of 2000 K and density ρ = 1.322 g cm(-3). These conditions resemble closely those realized at the interface of an acetone vapor bubble in the early stages of supercompression experiments and result in an average pressure of 5 GPa. Two relevant reactive events occur during the simulation: the condensation of two acetone molecules to give hexane-2,5-dione and dihydrogen and the isomerization to the enolic propen-2-ol form. The mechanisms of these events are discussed in detail.