Related papers: Second-order prestress stability and third-order r…
We prove that every three-dimensional polyhedron is uniquely determined by its dihedral angles and edge lengths, even if nonconvex or self-intersecting, under two plausible sufficient conditions: (i) the polyhedron has only convex faces and…
Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted.…
In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…
We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on…
In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method,…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth…
We derive and test a new heuristic theory for third-order structure functions that resolve the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally in rotating…
A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to the chosen norm is an isometric copy. We investigate global…
We study rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature like quantities for polyhedral surfaces are introduced. Many of them are shown to determine the polyhedral metric…
Photoelasticity is employed to investigate the stress state near stiff rectangular and rhombohedral inclusions embedded in a 'soft' elastic plate. Results show that the singular stress field predicted by the linear elastic solution for the…
We measure the local contact forces at both the top and bottom boundaries of three-dimensional face-centered-cubic and hexagonal-close-packed granular crystals in response to an external force applied to a small area at the top surface.…
We develop a reduced-order model for thin plates made of hard magnetorheological elastomers (hard-MREs), which are materials composed of hard-magnetic particles embedded in a polymeric matrix. First, we propose a new magnetic potential, as…
We consider a relaxed notion of energy of non-parametric codimension one surfaces that takes account of area, mean curvature, and Gauss curvature. It is given by the best value obtained by approximation with inscribed polyhedral surfaces.…
Gradient polyconvex materials are nonsimple materials where we do not assume smoothness of the elastic strain but instead regularity of minors of the strain is required. This allows for a larger class of admissible deformations than in the…
The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions…
The paper gathers and unifies mechanical stability conditions for all symmetry classes of 3D and 2D materials under arbitrary load. The methodology is based on the spectral decomposition of the fourth-order stiffness tensors mapped to…
We have numerically implemented a perturbation series for the scattered electromagnetic fields above rough surfaces, due to Greffet, allowing us to evaluate the local density of states to second order in the surface profile function. We…