We report experimental evidence of transition scenarios during the chemical evolution in an unstirred closed Belousov−Zhabotinsky (BZ) system. We demonstrate that during its chemical evolution the system spontaneously gives the following sequence of dynamic behavior before reaching equilibrium:  period-1 → quasiperiodicity → chaos → quasiperiodicity → period-1. Two transition scenarios are observed:  at the onset of chaos and at its end. One appears as the mirror image of the other. Our observations support the view that closed chemical systems also are able to show chaotic behavior and the corresponding transition scenarios.

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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. © 1999 American Institute of Physics. ͓S1054-1500͑99͒00101-9͔The synthesis of metastable phases and new materials often requires severe processing conditions. Techniques based on heavy mechanical deformation of solid mixtures have reached a stage of considerable development in the field of materials science. Due to its commercial possibilities and to the unusual physical phenomena involved, powder processing by ball milling still arouses both technological and scientific interest. Energy is transferred from the milling tools to the entrapped powder, which is subject to heavy mechanical loads and undergoes continuous defect accumulation and an ultimate limit of stability is achieved. Diffusion and mass transport phenomena occur through the continuously developed fresh surfaces. The phase transformation and its rate are intimately linked to the energy transfer of the collision event. The efficiency of the transfer depends, in turn, on the degree of elasticity of the collision, which also affects the general features of the milling dynamics. As the elasticity increases, the milling dynamics change from periodic to aperiodic. This behavior can be suitably characterized with the help of nonlinear dynamical analyses. In this paper, a milling system was modeled and the trajectory of a single ball colliding elastically inside the milling container was numerically simulated. Nonlinear dynamics analyses showed that elastic impact conditions determine the occurrence of a hyper-chaotic behavior.

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