Evaluation of the path integral for flow through random porous media.

@article{Westbroek2018EvaluationOT,
  title={Evaluation of the path integral for flow through random porous media.},
  author={Marise J. E. Westbroek and Gil-Arnaud Coche and Peter R. King and Dimitri D. Vvedensky},
  journal={Physical review. E},
  year={2018},
  volume={97 4-1},
  pages={
          042119
        }
}
We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three… 

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