Hybrid (discrete/continuous) systems exhibit both discrete state and continuous state dynamics which interact to such a significant extent that they cannot be decoupled and must be analyzed simultaneously. We present an overview of the work that has been done in the modeling, simulation, sensitivity analysis, and optimization of hybrid systems, paying particular attention to the interaction between discrete and continuous dynamics. A concise intuitive framework for hybrid system modeling is presented, together with discussions on robust state event location, transfer functions of the continuous state at discontinuities, parametric sensitivity analysis of hybrid systems, and challenges in optimization.
Traditional models of single-file diffusion in zeolites assume that adsorbate diffusion mechanisms at high and dilute pore loadings are identical. Atomistic models of single file systems, in contrast, have shown that clusters of adsorbed molecules can diffuse via concerted motions that are not available to individual adsorbates. We report molecular dynamics simulations of CF 4 clusters in AlPO 4 -5 and Xe clusters in AlPO 4 -31. We have used these simulations to characterize the diffusion and dissociation mechanisms and rates of these clusters as a function of temperature and cluster size. We have also used our MD results to parametrize coarse-grained models of adsorbed cluster dynamics. Using kinetic Monte Carlo simulations of our coarse-grained models, we have simulated pores containing hundreds of interacting clusters on microsecond time scales. These simulations offer the first opportunity to examine single-file diffusion in models that accurately account for the existence of concerted cluster diffusion. Our simulations show that concerted cluster motions make large contributions to single-file mobilities. The deviations of the computed single-file mobilities from the well-known result for hard sphere diffusion are discussed, as are the implications of using the latter model to interpret experimental measurements of single-file diffusion.
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