Mauro Rustici

Dynamics of pattern formation in biomimetic systems

This paper is an attempt to conceptualize pattern formation in self-organizing systems and, in particular, to understand how structures, oscillations or waves arise in a steady and homogenous environment, a phenomenon called symmetry breaking. The route followed to develop these ideas was to couple chemical oscillations produced by Belousov-Zhabotinsky reaction with confined reaction environments, the latter being an essential requirement for any process of Life. Special focus was placed on systems showing organic or lipidic compartments, which represent more reliable biomimetic matrices.

Effect of temperature in a closed unstirred Belousov–Zhabotinsky system

Complex periodic and aperiodic behaviours are reported in an unstirred Belousov-Zhabotinsky oscillatory reaction performed at temperatures varying between 0°C and 8°C. A route to chaos following a Ruelle-Takens-Newhouse (RTN) scenario is identified. Thus, temperature effects on the coupling between chemical kinetics, diffusion and convection, seem to be responsible for the observed RTN scenario. In this Letter we demonstrate that the temperature is a bifurcation parameter for the sequence period-1 → quasiperiodicity → chaos.

Chemical Control of Hydrodynamic Instabilities in Partially Miscible Two-Layer Systems.

Hydrodynamic instabilities at the interface between two partially miscible liquids impact numerous applications, including CO2 sequestration in saline aquifers. We introduce here a new laboratory-scale model system on which buoyancy- and Marangoni-driven convective instabilities of such partially miscible two-layer systems can easily be studied. This system consists of the stratification of a pure alkyl formate on top of a denser aqueous solution in the gravitational field. A rich spectrum of convective dynamics is obtained upon partial dissolution of the ester into the water followed by its hydrolysis. The properties of the convective patterns are controlled by the miscibility of the ester in water, the feedback of the dissolved species on its own miscibility, as well as the reactivity of given chemicals in the aqueous solution with the solubilized ester.

Effect of medium viscosity in a closed unstirred Belousov–Zhabotinsky system

Abstract Complex periodic and aperiodic behaviors are reported in an unstirred Belousov–Zhabotinsky oscillatory reaction containing different concentrations of polyethylene-glycol. A route from chaos following an inverse Ruelle–Takens–Newhouse (RTN) scenario is identified. Thus, hydrodynamic effects, being mainly convective, seem to be responsible for the observed RTN scenario. We demonstrate that the medium viscosity, namely the polyethylene-glycol concentration, is a bifurcation parameter for the sequence chaos → quasi-periodicity → period-1.

Evidence of a chaotic transient in a closed unstirred cerium catalyzed Belousov-Zhabotinsky system

Abstract Aperiodic oscillations in a cerium catalyzed Belousov-Zhabotinsky reaction were experimentally observed in a closed system. This phenomenon was noted by a simple spectrophotometric measure which enabled us to prove the dependence of the initial conditions as being the major signature of chaos.

Bifurcations in spiral tip dynamics induced by natural convection in the Belousov–Zhabotinsky reaction

The transition to spatial-temporal complexity exhibited by spiral waves under the effect of gravitational field in the Belousov-Zhabotinsky reaction is numerically studied on the basis of spiral tip dynamics. Successive transformations in tip trajectories are characterized as a function of the hydrodynamical parameter and attributed to a Ruelle-Takens-Newhouse scenario to chaos. The analysis describes the emergence of complexity in terms of the interplay between the evolution of the velocity field and concentration waves. In particular, (i) by mapping the tip motion in relation to some hydrodynamical pseudopotentials, the general mechanism by which the velocity field affects the tip trajectory is pointed out, and, (ii) by comparing the dynamical evolutions of local and mean properties associated with the inhomogeneous structures and to the velocity field, a surprising correlation is found. The results suggest that the reaction-diffusion-convection (RDC) coupling addresses the system to some general regimes, whose nature is imposed by the hydrodynamical contribution. More generally, RDC coupling would be formalized as the phenomenon that governs the system and drives it to chaos.

Effects of non-ionic micelles on transient chaos in an unstirred Belousov–Zhabotinsky reaction

The behaviour of the Ce(IV)-catalyzed Belousov-Zhabotinsky (BZ) system has been monitored at 20.0 degrees C in unstirred batch conditions in the absence and presence of different amounts of the non-ionic micelle-forming surfactants hexaethylene glycol monodecyl ether (C10E6) and hexaethylene glycol monotetradecyl ether (C14E6). The influence of the non-ionic surfactants on both the kinetics of the oxidation of malonic acid (MA) by Ce(IV) species and the behaviour of the BZ reaction in stirred batch conditions has also been studied over a wide surfactant concentration range. The experimental results have shown that, in unstirred batch conditions, at surfactant concentrations below the critical micelle concentration (c.m.c.) no significant change in the dynamics of the Belousov-Zhabotinsky system occurs. Beyond this critical concentration the presence of micelles forces the BZ system to undergo a chaos-->quasi-periodicity-->period-1 transition. Thus, the surfactant concentration has been considered as a bifurcation parameter for a Ruelle-Takens-Newhouse (RTN) scenario. Addition of increasing amounts of non-ionic surfactants has no significant effect on the kinetics of the reaction between MA and Ce(IV), but it influences the oscillatory parameters of the stirred BZ system. At surfactant concentrations below the c.m.c. all the oscillatory parameters are practically unaffected by the presence of surfactant, while beyond this critical value the induction period is the same as in aqueous solution but both the oscillation period and the duration of the rising portion of the oscillatory cycle decrease. In all cases, the experimental trends have been ascribed to the enhancement in the medium viscosity due to the presence of micelles.

Onset of chaotic dynamics in a ball mill: Attractors merging and crisis induced intermittency

In mechanical treatment carried out by ball milling, powder particles are subjected to repeated high-energy mechanical loads which induce heavy plastic deformations together with fracturing and cold-welding events. Owing to the continuous defect accumulation and interface renewal, both structural and chemical transformations occur. The nature and the rate of such transformations have been shown to depend on variables, such as impact velocity and collision frequency that depend, in turn, on the whole dynamics of the system. The characterization of the ball dynamics under different impact conditions is then to be considered a necessary step in order to gain a satisfactory control of the experimental set up. In this paper we investigate the motion of a ball in a milling device. Since the ball motion is governed by impulsive forces acting during each collision, no analytical expression for the complete ball trajectory can be obtained. In addition, mechanical systems exhibiting impacts are strongly nonlinear due to sudden changes of velocities at the instant of impact. Many different types of periodic and chaotic impact motions exist indeed even for simple systems with external periodic excitation forces. We present results of the analysis on the ball trajectory, obtained from a suitable numerical model, under growing degree of impact elasticity. A route to high dimensional chaos is obtained. Crisis and attractors merging are also found. (c) 2002 American Institute of Physics.

Hyperchaotic qualities of the ball motion in a ball milling device.

Ball collisions in milling devices are governed by complex dynamics ruled by impredictable impulsive forces. In this paper, nonlinear dynamics techniques are employed to analyze the time series describing the trajectory of a milling ball in an empty container obtained from a numerical model. The attractor underlying the system dynamics was reconstructed by the time delay method. In order to characterize the system dynamics the calculation of the spectrum of Lyapunov exponents was performed. Six Lyapunov exponents, divided into two terns with opposite sign, were obtained. The detection of the positive tern demonstrates the occurrence of the hyperchaotic qualities of the ball motion. A fractal Lyapunov dimension, equal to 5.62, was also obtained confirming the strange features of the attractor. (c) 1999 American Institute of Physics.

Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Direct numerical simulations of the transition process from periodic to chaotic dynamics are presented for two variable Oregonator-diffusion model coupled with convection. Numerical solutions to the corresponding reaction-diffusion-convection system of equations show that natural convection can change in a qualitative way, the evolution of concentration distribution, as compared with convectionless conditions. The numerical experiments reveal distinct bifurcations as the Grashof number is increased. A transition to chaos similar to Ruelle-Takens-Newhouse scenario is observed. Numerical results are in agreement with the experiments.