Related papers: Loopless non-trapping invasion percolation model f…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the discrete fracture-matrix approach. The…
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In…
We present a detailed study of a two-dimensional minimal lattice model for the description of mud cracking in the limit of extremely thin layers. In this model each bond of the lattice is assigned to a (quenched) breaking threshold.…
We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of a tensile or shear…
The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…
Many geo-engineering applications, e.g., enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack…
We extend our previous model, avalanche-burst invasion percolation (AIP) by introducing long-range correlations between sites described by fractional Brownian statistics. In our previous models with independent, random site strengths, we…
This paper presents the coupled model of a hydraulic fracturing and proppant transport. The former is described in terms of enhanced pseudo-3D model that considers height growth across two symmetric stress barriers, while the latter is…
Understanding and controlling fracture propagation is one of the most challenging engineering problems, especially in the oil and gas sector, groundwater hydrology and geothermal energy applications. Predicting the fracture orientation…
We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show…
There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight…
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
Drilling is a requisite operation for many industries to reach a targeted subsurface zone. Loss of circulation is a common problem that often causes interruptions to the drilling process and a reduction in efficiency. In this work, a…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…
A model function relating effective stress to fracture permeability is developed from Hooke's law, implemented in the tensorial form of Darcy's law, and used to evaluate discharge rates and pressure distributions at regional scales. The…
We formulate the problem of probabilistic predictions of global failure in the simplest possible model based on site percolation and on one of the simplest model of time-dependent rupture, a hierarchical fiber bundle model. We show that…