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We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value $N$, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the $n$ particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particle and their time correlation. We generalize previous results for $N=2$ to an arbitrary distribution of entry times and obtain new, exact solutions for $N=3$ for a Poisson distribution and partial results for $Nge 4$.
We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 +- 0.002 and its leading correction to scaling are the same as in t
We give the trade-off curve showing the capacity of a quantum channel as a function of the amount of entanglement used by the sender and receiver for transmitting information. The endpoints of this curve are given by the Holevo-Schumacher-Westmorelan
We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic
In model-based reinforcement learning, planning with an imperfect model of the environment has the potential to harm learning progress. But even when a model is imperfect, it may still contain information that is useful for planning. In this paper, w
We discuss a channel consisting of nodes of a network and lines which connect these nodes and form ways for motion of a substance through the channel. We study stationary flow of substance for channel which arms contain finite number of nodes each an