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This paper is devoted to the mechanics of fractal materials. A continuum framework accounting for the topological and metric properties of fractal domains in heterogeneous media is developed. The kinematics of deformations is elucidated and…
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…
This work theoretically analyzes the sound absorption properties of a chirped multi-layer porous material including transmission, in particular showing the broadband unidirectional absorption properties of the system. Using the combination…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
Geological settings with reservoir characteristics include fractures with different material and geometrical properties. Hence, numerical simulations in applied geophysics demands for computational frameworks which efficiently allow to…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the Discrete Fracture Network (DFN) model. A Darcy problem is solved to compute the…
In this work, the projection-based embedded discrete fracture model (pEDFM) for corner-point grid (CPG) geometry is developed for simulation of flow and heat transfer in fractured porous media. Unlike classical embedded discrete fracture…
Fractures play a critical role in governing fluid flow within subsurface energy systems, including oil and gas production, geologic carbon sequestration, and underground hydrogen storage. This study investigated the impact of pore-scale…
The close packing density of log-normal and bimodal distributed, surface-adsorbed particles or discs in 2D is studied by numerical simulation. For small spread in particle size, the system orders in a polycrystalline structure of hexagonal…
We use the fractional integrals in order to describe dynamical processes in the fractal media. We consider the "fractional" continuous medium model for the fractal media and derive the fractional generalization of the equations of balance…
We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model,…
This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
An exact analytical analysis of anomalous diffusion on a fractal mesh is presented. The fractal mesh structure is a direct product of two fractal sets which belong to a main branch of backbones and side branch of fingers. The fractal sets…
The present work deals with the numerical resolution of coupled 3D-2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model,…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
Flow in fractured porous media is modeled frequently by discrete fracture-matrix approaches where fractures are treated as dimensionally reduced manifolds. Generalizing earlier work we focus on two-phase flow in time-dependent fracture…
In this paper we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows to understand many experiments of thin film deposition. In the first…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…