No abstract

We introduce a new approach to evaluate transition rates for rare events in complex many-particle systems. Building on a path-integral representation of transition probabilities for Markov processes, the rate is first expressed in terms of a free energy in the transition-path ensemble. We then define an auxiliary process where a suitably defined reaction variable is dynamically decoupled from all the others, whose dynamics is left unchanged. For this system the transition rates coincide with those of a unidimensional process whose only coordinate is the reaction variable. The free-energy difference between the auxiliary and the physical transition-path ensembles is finally evaluated using standard techniques. The efficiency of this method is deemed to be optimal because the physical and auxiliary dynamics differ by one degree of freedom only at any system size. Our method is demonstrated numerically on a simple model of Lennard-Jones particles ruled by the overdamped Langevin equation.

Abstract.1 The solvent extraction of cerium(III) from its sulfuric solution with di-(2-ethylhexyl) phosphoric acid diluted by kerosene was investigated. Initially, a survey was conducted in order to identify the conditions influencing the solvent extraction process. Extractant concentration in the organic phase, organic phase to aqueous phase ratio, temperature, pH, and contact time were identified as important factors. Among these factors, the temperature and contact time were found less effective in comparison to other factors. Thus, a contact time of ten minutes for the two phases at room temperature of 298 K was chosen for all experiments. Design expert software was employed for designing the experiments, investigating the effects of the factors on the solvent extraction, statistical analysis, and obtaining the optimal values of the factors. It was established that the factors influencing the solvent extraction, except extractant concentration and organic phase to aqueous phase ratio, were independent and have no interaction on each other.

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