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A correlated random walk for the transport and sedimentation of particles. (English) Zbl 0658.60096

[For the entire collection see Zbl 0654.00009.]
The author considers a two-dimensional model for the transport and sedimentation of particles in a tank of fluid where the fluid enters the left hand end and exits from the other end. The particular model used is a continuous time random walk on the discrete state space \(\{0,1,...,K+1\}\times \{0,...,H\}\). The bottom of the tank is the set of states \(\{\) (x,H):\(x=0,...,K\}\) which are absorbing and correspond to sedimentation in the tank. Likewise, the set of states \(\{(K+1, y):y=0,...,H\}\) are absorbing and correspond to particle departure from the tank.
A large number of particles are started in state (0,0) and move independently according to a bivariate Markov process having positive rates only for transitions of the type \((x,y)\to (x+1, y)\), (x, y\(+1)\) or \((x+1, y+1)\), if \(x\leq K\) and for (K, y)\(\to (K+1, y)\). This model allows dependence of the x and y components of jumps - earlier work of the author assumed independence.
The forward equations are solved and used to find the probability of eventual sedimentaion or exit. A modification is considered in which exit occurs through a pipe at the end of the tank.
Reviewer: A.Pakes

MSC:

60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60G50 Sums of independent random variables; random walks

Citations:

Zbl 0654.00009