{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80868"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80868","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Discrete Stochastic Modeling of Ion Channels","abstract":"Kernel representations are obtained for the concentration and flux away from equilibrium, where the kernel functions have a probabilistic interpretation. This is done in a discrete space model and also in its diffusion limit. In particular, the kernel representation is given for the flux at a boundary for the diffusion model. This requires special attention since one of the kernel functions exhibits a singularity.","abstract_html":"Kernel representations are obtained for the concentration and flux away from equilibrium, where the kernel functions have a probabilistic interpretation. 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