Related papers: How curvature flows: scaling laws and global geome…
We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble,…
The reliability of any day-to-day material is critically dictated by its properties. One factor which governs the behaviour of a material, under a given condition, is the microstructure. Despite the absence of any phase transformation, a…
The incorporation of particle inertia into the usual mean field theory for particle aggregation and fragmentation in fluid flows is still an unsolved problem. We therefore suggest an alternative approach that is based on the dynamics of…
Geologic shear fractures such as faults and slip surfaces involve marked friction along the discontinuities as they are subjected to significant confining pressures. This friction plays a critical role in the growth of these shear…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of…
We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By…
We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
By means of Molecular Dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in 2 dimensions: a single ball confined to moving along an inclined line consisting of balls. The global…
Gravity-driven flows of granular matter are involved in a wide variety of situations, ranging from industrial processes to geophysical phenomena, such as avalanches or landslides. These flows are characterized by the coexistence of solid…
We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage…
This paper discusses a continuum approach to track the evolution of permeability in granular rocks by accounting for the combined effect of porosity changes, grain breakage and cement bond damage. To account for such a broad range of…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
Impact-induced fragmentation is a fundamental dissipative process in geosciences, yet its stochastic nature makes predicting debris evolution a persistent challenge. Here, we introduce a discrete element framework to resolve fragmentation…
This article introduces a new geophysical theory, in the form of a single simple partial integro-differential equation, to explain how frictional abrasion alone of a stone on a planar beach can lead to the oval shapes observed empirically.…
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…
Mean curvature flow is the most natural evolution equation in extrinsic geometry, and shares many features with Hamilton's Ricci flow from intrinsic geometry. In this lecture series, I will provide an introduction to the mean curvature flow…
In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution $N(t)$ of the number $N$ of static balance points of the abrading particle. Static balance points correspond to the critical points…
Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of…