Formation of Concentric Rings Around Sources |
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| Authors: | B P Harlamov |
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| Institution: | (1) Institute of Problems of Mechanical Engineering, RAS, Germany;(2) Institute of Mathematical Geology, RANS, 199178, Bol'shoi pr. (v. o), 61, St. Petersburg, Russia |
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| Abstract: | Zones of increased concentration formed by a solvent flowing from a source are considered. A matehmatical model for forming such zones is proposed. It takes into account that such a zone is composed of a set of independent particles. Hence the distribution of a substance around the source can be explained by movement of an individual particle. In the model this movement is a continuous semi-Markov process with terminal stopping at some random point in space. Parameters of the process depend on the velocity field of the flow. Forward and backward partial differential equations for the distribution density of a random stopping point of the process are derived. The forward equation is investigated for the centrally symmetric case. Solutions of the equation demonstrate either a maximum or a local minimum at the source location. In the latter case a concentric ring around the source is formed. If different substances vary in their absorption rates, they can form separable concentration zones as a family of concentric rings. |
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| Keywords: | continuous semi-Markov process absorption terminal stopping partial elliptical differential equation concentration zone |
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