相关论文: The Euler-Bernoulli limit of thin brittle lineariz…

Motivated by recent interest in elastic problems in which the target space is non-Euclidean, we study a limit where local rest distances within an elastic body are incompatible, yet close to, distances within the ambient space.…

A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose…

We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we…

We prove a relation between the scaling $h^\beta$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates…

Gravity and general relativity are considered as an Effective Field Theory at low energies and macroscopic distances. The effective action of the conformal anomaly of light or massless quantum fields has significant effects on macroscopic…

Braneworld models typically predict gravity to grow stronger at short distances. In this paper, we consider braneworlds with two types of additional curvature couplings, a Gauss-Bonnet term in the bulk, and an Einstein-Hilbert (EH) term on…

We compute the 4D low energy effective gauge coupling at one-loop order in the compact Randall-Sundrum scenario with bulk gauge fields and charged matter, within controlled approximations. While such computations are subtle, they can be…

We investigate a discrete version of the M\"obius energy, that is of geometric interest in its own right and is defined on equilateral polygons with $n$ segments. We show that the $\Gamma$-limit regarding $L^{q}$ or $W^{1,q}$ convergence,…

This work is devoted to study the asymptotic behavior of critical points $\{(u_\varepsilon,v_\varepsilon)\}_{\varepsilon>0}$ of the Ambrosio-Tortorelli functional. Under a uniform energy bound assumption, the usual $\Gamma$-convergence…

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area…

We study in a Brill-Hartle type of approximation the back reaction of a superposition of linear gravitational waves on the mean gravitational field up to second order in the wave amplitudes. The background field is taken as an…

We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When $\Lambda>0$ the energy…

We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…

We investigate gravitational collapse of a spherically symmetric thin shell in the Einstein-Gauss-Bonnet (EGB) gravity. Under the recently proposed 4D limit, we find that the collapsing shell will be bounced back at a small radius, without…

Weak gravity conjecture can be formulated as a statement that gravity must be the weakest force, compared to the other interactions in low energy effective field theory (EFT). Several arguments in favor of this statement were presented from…

We prove a ${\Gamma}$-convergence result for the $p$-Dirichlet energy functional defined on maps from a smooth bounded domain $\Omega \subseteq \mathbb{R}^{n+k}$ to $\mathscr{N}$, a $(k-2)$-connected and smooth closed Riemannian manifold…

The theory of gauge-fixed Maxwell equations in linear isotropic dielectrics is developed using a generalisation of the standard $R_\xi$ gauge-fixing term. In static space-times, the theory can be quantised using the Gupta-Bleuler method,…

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show…

We consider the well-known minimizing-movement approach to the definition of a solution of gradient-flow type equations by means of an implicit Euler scheme depending on an energy and a dissipation term. We perturb the energy by considering…

In this paper, we apply classical energy principles to Euler elasticae, i.e., closed C^2 curves in the plane supplied with the Euler functional U (the integral of the square of the curvature along the curve). We study the critical points of…