Lyapunov exponents of one-dimensional, binary stochastic cellular automata

In this paper the stability of elementary cellular automata (ECAs) upon introduction of stochasticity, in the form of an update probability for each cell, is assessed. To do this, Lyapunov exponents, which quantify the rate of divergence between two nearby trajectories in phase space, were used. Furthermore, the number of negative Lyapunov exponents was tracked, in order to gain a more profound insight into the interference between the stability and the update probability, and an upper bound on the Lyapunov exponents of stochastic cellular automata (SCAs) was established

Cellular automata approach to hybrid surface and diffusion controlled reactions

\u3cp\u3eCellular automata are frequently used to model chemical reactions and processes. In this paper, a direct relation is established between chemical kinetic models for surface and diffusion controlled reactions and cellular automata parameters. The considered particles are allowed to have growing/shrinking sizes, caused by the difference in the volume of the consumed reactant and the formed reaction product. From the moment a minimum diffusion layer thickness is obtained, the cellular automata approach can be applied to study the diffusion (ash layer) controlled model for both cases. In order to be able to also describe the reaction before this minimum diffusion layer thickness is formed, chemical reaction controlled and diffusion controlled models are combined here. Applying this hybrid model, a closed-form relation is found between the cellular automata parameters (particle size, reaction probability) and the fundamental kinetics of surface (β\u3csub\u3e1\u3c/sub\u3e) and diffusion (β\u3csub\u3e2\u3c/sub\u3e) controlled reactions.\u3c/p\u3

Mathematical Modeling and Use of Magnetic Resonance Imaging (MRI) for Oil Migration in Chocolate Confectionery Systems

Oil migration is a common problem in chocolate confectionery products leading to quality defects, particularly fat bloom. Several factors such as contact area, ratio of the two fat phases, type of the fat, solid fat content, presence of non-fat solid particles, particle size, viscosity, structure, concentration gradient of triacylglycerols (TAGs), and storage temperature have all effect on migration rate. Mechanism of oil migration has still not been clearly understood, but possible mechanisms have been suggested and studied in the literature. Diffusion mechanism was demonstrated and modeled in many studies. Although there are so many methods to monitor and quantify migration, magnetic resonance imaging (MRI) is among the most promising techniques as being non-destructive. This review covers the literature related to basics of migration, mechanisms, and monitoring and modeling migration in chocolate through MRI and also includes a brief description about chocolate, chocolate processing, and fundamental concepts in MRI