Related papers: Fracture network characterization with deep genera…

Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We…

Fracture networks are ubiquitous in nature, spanning scales from millimeter-sized cracks in botanical peels to hundred-kilometer-long lineae on planetary satellites. The propagation of a crack is a complex, nonlinear phenomenon governed by…

The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…

In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on porous medium fluid mass and velocity. To achieve this task,…

Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…

A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field formulation of the Darcy law for the description of the hydraulic head on the fractures and uses a cost…

In this work, we investigate a novel approach for the simulation of two-dimensional, brittle, quasi-static fracture problems based on a shape optimization approach. In contrast to the commonly-used phase-field approach, this proposed…

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a…

In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci. U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a…

Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called…

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,…

This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…

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…

Crack micro-geometries and tribological properties pose an important impact on the elastic characteristics of fractured rocks. Numerical simulation as a promising way for this issue still faces some challenges. With the rapid development of…

Basic principles of statistical inference are commonly violated in network data analysis. Under the current approach, it is often impossible to identify a model that accommodates known empirical behaviors, possesses crucial inferential…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

Heat transfer in fractured media is governed by the interplay between advective transport along rough-walled fractures and conductive transport, both within the fractures and in the surrounding low-permeability matrix. Flow localization…

We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be…

For bone segmentation, the classical geodesic active contour model is usually limited by its indiscriminate feature extraction, and then struggles to handle the phenomena of edge obstruction, edge leakage and bone fracture. Thus, we propose…