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1 results

  • A stochastic model of particle shattering

  • William S. Griffith, Richard J. Kryscio, Peter Purdue
  • Journal:
    Advances in Applied Probability / Volume 16 / Issue 1 / March 1984
    Published online by Cambridge University Press:
    01 July 2016, pp. 70-87
    Print publication:
    March 1984

  • Motivated by the problem of solid catalytic particle attrition during chemical reactions we formulate a continuous-time Markov model to describe the shattering of a particle when it is assumed that particles can be classified into a small number of types by size. We then obtain a recursive expression for the joint probability generating function of the count of the different types of particle at time t and derive a system of differential equations for the mean number of particle counts and a system of matrix differential equations for the covariance matrix of the particle counts. Solutions to these differential equations are presented in an important special case.