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Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $\mu(I)$ rheology is considered. The model is obtained from an asymptotic…
We investigate the geometric properties of percolation clusters, by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo…
Propagation of a fluid-driven crack in an impermeable linear elastic medium under axis-symmetric conditions is investigated in the present work. The fluid exerting the pressure inside the crack is an incompressible Newtonian one and its…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numerical outcomes useful, e.g., for energy management. Depending…
Drawing a direct analogy with the well-studied vibration or elastic modes, we introduce an object's fracture modes, which constitute its preferred or most natural ways of breaking. We formulate a sparsified eigenvalue problem, which we…
We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters.…
A three-dimensional Multiphysics Lattice Discrete Particle Model (M-LDPM) framework is formulated to investigate the fracture permeability behavior of shale. The framework features a dual lattice system mimicking the mesostructure of the…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of…
In fractured poroelastic media under high differential stress, the shearing of fractures and faults and the corresponding propagation of wing cracks can be induced by fluid injection. Focusing on low-pressure stimulation with fluid…
The fracturing-flooding technology is a new process for the development of low-permeability oil reservoirs, achieving a series of successful applications in oilfield production. However, existing numerical simulation methods for pressure…
In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our…
In this work we demonstrate the ability of the Minimal Spanning Tree to duplicate the information contained within a percolation analysis for a point dataset. We show how to construct the percolation properties from the Minimal Spanning…
We applied a hybrid-dimensional flow model to pressure transients recorded during pumping experiments conducted at the Reiche Zeche underground research laboratory to study the normal opening behavior of fractures due to fluid injection.…
We present a variational reduced-order model for three-dimensional coplanar propagation of sharp cracks in heterogeneous perfectly brittle solids under mixed-mode I+II+III loading. The approach connects the variational fracture formulation…
We present a minimal non-Hermitian model where a topologically nontrivial complex energy spectrum is induced by inter-particle interactions. Our model consists of a one-dimensional chain with a dynamical non-Hermitian gauge field with…
Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three dimensional cubic lattice. Individual clusters of given size are shown to present a fractal…