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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA

Alumni

Andreas Hafver

Class of 2013

Bio

Andreas obtained his BSc and MSc degrees in Theoretical Physics from the University of Stellenbosch, South Africa. He is currently back in his hometown of Oslo, Norway, where he is working towards a PhD degree in Computational Physics at the interdisciplinary institute Physics of Geological Processes (PGP).

Andreas is interested in pattern-forming processes in nature, particularly fracture patterns. Intrigued by the fact that complex patterns can result from simple programs, he believes that there are promising prospects of using NKS to study patterns observed in geological contexts.

Project: Fluid Drainage Mediated by Fracturing

Fluid migration through porous solids is commonly considered as a diffusion-like process and modeled using Darcy's law. The efficiency of this mechanism depends on the permeability and size of the solid, and fluid may accumulate if it is generated at a higher rate than diffusion is able to drain. Elevated fluid pressure may trigger fracturing, which in turn can accelerate transport by providing new flow pathways. This feedback mechanism is believed to play an important role in many geological processes, including the migration of oil and gas from source rock to reservoirs.

In this project we propose a simple model where the coupled system is represented by a lattice of nodes connected by bonds. The bonds can be in state 1 or 0, representing fractures or intact solids, respectively. At each time step, fluid is added to every node, and diffusion between the nodes is solved by a finite difference scheme with a Dirichlet condition on the external boundaries. Fractures take up fluid from their environment and fast fluid transport in the fracture network is achieved by redistributing fluid between fractures if a threshold value is exceeded. The states of the bonds are then updated based on the states of the neighboring bonds.

The model shares similarities with invasion-percolation models as well as biological growth models, and is amenable for investigation from a network perspective or within a statistical physics framework.

During the summer school we hope to reproduce fracture patterns observed experimentally in [1], and by calibrating the model we may be able to make quantitative predictions for geological applications.

Favorite Four-Color, Four State Turing Machine

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