In this work, we investigate two issues that are important to computational e ciency and reliability in uid dynamics applications of the lattice Boltzmann equation (LBE): (1) Computational stability and accuracy of di erent lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3Q15, D3Q...

It is known that the Cayley graph ? of a negatively curved (Gromov-hyperbolic) group G has a well-deened boundary at innnity @?. Furthermore, @? is compact and metrizable.

We prove a new isoperimetric inequality which relates the area of a multiply connected curved surface, its Euler characteristic, the length of its boundary, and its Gaussian curvature.

The integrity of phonon transport properties of large graphene (linear and curved) grain boundaries (GBs) is investigated under the influence of structural and dynamical disorder. To do this, density functional tight-binding (DFTB) method is combined with atomistic Green's function technique. The results show that curved GBs have lower thermal conductance than linear GBs. Its magnitude depends ...

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose a quantitative analysis of the robustness of classifiers to universal perturbations, and draw a formal link between the robustness to universal perturbations, and ...

Abstract. The influence of small boundary variations of the domain on optimal controls is investigated in this paper. The domain variations are governed by a small parameter h → 0. In a previous paper we have studied the Neuman control problem. In this paper, the Dirichlet control problem is considered. The optimal solutions are compared between the problems defined in the curved domain Ω and t...

Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert’s Delaunay refinement algorithm to domains with curved boundaries and prove that the same quality bounds ...

We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final ...