Related papers: Generalized elastica problems under area constrain…
We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking…
Let $(M^n,g)$ be simply connected, complete, with non-positive sectional curvatures, and $\Sigma$ a 2-dimensional closed integral current (or flat chain mod 2) with compact support in $M$. Let $S$ be an area minimising integral 3-current…
We prove short-time existence for the negative $L^2$-gradient flow of the $p$-elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caused by the energy's invariance under curve…
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them…
"It is still not known if the radial cavitating minimizers obtained by Ball [J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. Lond. A 306 (1982) 557--611] (and subsequently by many…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
In this paper, we propose a discrete version of O'Hara's knot energy defined on polygons embedded in the Euclid space. It is shown that values of the discrete energy of polygons inscribing the curve which has bounded O'Hara's energy…
If $E$ is a minimal elliptic curve defined over $\ZZ$, we obtain a bound $C$, depending only on the global Tamagawa number of $E$, such that for any point $P\in E(\QQ)$, $nP$ is integral for at most one value of $n>C$. As a corollary, we…
We show how to explicitly compute the homogenized curvature energy appearing in the isotropic $\Gamma$-limit for flat and for curved initial configuration Cosserat shell models, when a parental three-dimensional minimization problem on…
When one slightly pushes a thin elastic sheet at its center into a hollow cylinder, the sheet forms (to a high degree of approximation) a developable cone, or "d-cone" for short. Here we investigate one particular aspect of d-cones, namely…
We show optimal Lipschitz regularity for very weak solutions of the (measure-valued) elliptic PDE $-\mathrm{div}(A(x) \nabla u) = Q \; \mathcal{H}^{n-1} \llcorner \Gamma$ in a smooth domain $\Omega \subset \mathbb{R}^n$. Here $\Gamma$ is a…
Partial localization is the phenomenon of self-aggregation of mass into high-density structures that are thin in one direction and extended in the others. We give a detailed study of an energy functional that arises in a simplified model…
We present a simple discrete formula for the elastic energy of a bilayer. The formula is convenient for rapidly computing equilibrium configurations of actuated bilayers of general initial shapes. We use maps of principal curvatures and…
In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\int \sqrt{1+K_\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points…
Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the…
It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the…
We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…
This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove $\Gamma$-convergence to the continuous model.…
The energy of extended classical objects, such as vortices, depends on their shape. In particular, we show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. We…