# 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…

## 4 Citations

### Pressure statistics from the path integral for Darcy flow through random porous media

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

The path integral for classical statistical dynamics is used to determine the properties of one-dimensional Darcy flow through a porous medium with a correlated stochastic permeability for several…

### Pressure and flow statistics of Darcy flow from simulated annealing

- EngineeringJournal of Physics A: Mathematical and Theoretical
- 2020

The pressure and flow statistics of Darcy flow through a random permeable medium are expressed in a form suitable for evaluation by the method of simulated annealing and are in excellent agreement with the more conventional finite-volume calculations.

### Path integral Monte Carlo method for the quantum anharmonic oscillator

- PhysicsEuropean Journal of Physics
- 2020

The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes a quadratic term and a quartic term whose…

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