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 ...
Permeability measurements of engineering textiles exhibit large variability as no standardization method currently exists; numerical permeability prediction is thus an attractive alternative. It has all advantages of virtual material characterization, incl ...
In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
Efficient numerical simulations of coupled multi-component systems can be particularly challenging. This is mostly due to the complexity of their solutions, as mutual interactions may cause emergent behaviors, including synchronization and instabilities. V ...
Machine learning has paved the way for the real-time monitoring of complex infrastructure and industrial systems. However, purely data-driven methods have not been able to learn the underlying dynamics and generalize them to operating conditions that have ...
This work studies the nearshore hydrodynamics of a shallow turbulent flow entering a laterally unconfined quiescent ambient with a sloping bottom boundary. Examples of such flow are neutrally buoyant ebb tidal jets and hyperpycnal river plumes entering ope ...
Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These ...
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...
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 ...
To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equ ...
