相关论文: Korn inequalities for shells with zero Gaussian cu…

The predominant structural protein in vertebrates is collagen, which plays a key role in extracellular matrix and connective tissue mechanics. Despite its prevalence and physical importance in biology, the mechanical properties of molecular…

The Penrose inequality has so far been proven in cases of spherical symmetry and in cases of zero extrinsic curvature. The next simplest case worth exploring would be non-spherical, non-rotating black holes with non-zero extrinsic…

The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous…

We study the Korn-Poincar\'e inequality: \|u\|_{W^{1,2}(S^h)} < C_h \|D(u)\|_{L^2(S^h)}, in domains S^h that are shells of small thickness of order h, around an arbitrary smooth and closed hypersurface S in R^n. By D(u) we denote the…

In this paper we prove a rigidity result for the equality case of the Penrose inequality on $3$-dimensional asymptotically flat manifolds with nonnegative scalar curvature and corners. Our result also has deep connections with the equality…

We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space $\mathbb R^{n+1}$, $n\geq 3$. In…

From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to…

A general framework is developed to study the deformation and stress response in F{\"o}ppl-von K{\'a}rm{\'a}n shallow shells for a given distribution of defects, such as dislocations, disclinations, and interstitials, and metric anomalies,…

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show…

For two-dimensional topological insulators, the integer and intrinsic (without external magnetic field) quantum Hall effect is described by the gauge anomalous (2+1)-dimensional [2+1d] Chern-Simons (CS) response for the background gauge…

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…

We study circular shells in a (2+1)-dimensional background within the framework of Einstein-Born-Infeld theory. For shells around black holes we analyze the mechanical stability under perturbations preserving the symmetry. Shells around…

In the framework of the geometrically nonlinear 6-parameter resultant shell theory we give a characterization of the shells without drilling rotations. These are shells for which the strain energy function $W$ is invariant under the…

Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large…

Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…

We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky(ST). The simulation starts from the…

In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…

In this paper we derive the linear elastic Cosserat shell model incorporating effects up to order $O(h^5)$ in the shell thickness $h$ as a particular case of the recently introduced geometrically nonlinear elastic Cosserat shell model. The…

We first establish a family of sharp Caffarelli-Kohn-Nirenberg type inequalities on the Euclidean spaces and then extend them to the setting of Cartan-Hadamard manifolds with the same best constant. The quantitative version of these…