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2 results

  • Crack detection using electrostatic measurements

  • Martin Brühl, Martin Hanke, Michael Pidcock
  • Journal:
    ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 3 / May 2001
    Published online by Cambridge University Press:
    15 April 2002, pp. 595-605
    Print publication:
    May 2001

  • In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation of our algorithm more computationally demanding.

  • A note on the inverse problem for reducible Markov chains

  • A. O. Pittenger
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 3 / September 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 621-625
    Print publication:
    September 1977

  • Suppose a physical process is modelled by a Markov chain with transition probability on S 1 ∪ S 2, S 1 denoting the transient states and S 2 a set of absorbing states.

    If v denotes the output distribution on S 2, the question arises as to what input distributions (of raw materials) on S 1 produce v. In this note we give an alternative to the formulation of Ray and Margo [2] and reduce the problem to one system of linear inequalities. An application to random walk is given and the equiprobability case examined in detail.