Understanding how things break and slide is of paramount importance to describe the dynamics of a broad range of physical systems. This includes day-to-day problems such as the breaking of a glass of wine or the sliding of skis on snow, but also engineerin ...
We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper ...
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local PDE and some aver ...
Solid particulate additives are sometimes used to promote the uniform growth of multiple hydraulic fractures in horizontal oil and gas wells. The principle is that solid particulates block, accumulate, and form larger porous plugging zones preferentially a ...
We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...
