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Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
Fractured metal fragments with rough and irregular surfaces are often found at crime scenes. Current forensic practice visually inspects the complex jagged trajectory of fractured surfaces to recognize a ``match'' using comparative…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations.…
Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions.…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $<x^2 > \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation…
An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe…
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures. A fundamental step in any typical iterative inversion method, is the numerical solution of the underlying direct…
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…
The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require…
This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
Miscible tracer dispersion measurements in transparent model fractures with different types of wall roughness are reported. The nature (Fickian or not) of dispersion is determined by studying variations of the mixing front as a function of…