Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature

In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. Based upon a Taylor expansion around $R = 0$ for both functions $f^1(R)$ and $f^2(R)$, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the time perturbation is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. We conclude that the Starobinsky model for inflation complemented with a generalized preheating mechanism is not experimentally constrained by observations. The geodetic precession effects of the model are also shown to be of no relevance for the constraints.Comment: 17 pages, 4 figure

The variational theory of fracture: diffuse cohesive energy and elastic-plastic rupture

This communication anticipates some results of a work in progress [1], addressed to explore the efficiency of the diffuse cohesive energy model for describing the phenomena of fracture and yielding. A first local model is partially successful, but fails to reproduce the strain softening regime. A more robust non-local model, obtained by adding an energy term depending on the deformation gradient, describes many typical features of the inelastic response observed in experiments, including strain localization and necking. Fracture occurs as the result of extreme strain localization. The model predicts different fracture modes, brittle and ductile, depending on the analytical form of the cohesive energy function

Constraining spacetime torsion with the Moon and Mercury

We report a search for new gravitational physics phenomena based on Einstein-Cartan theory of General Relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth and Cabi, we analyze the motion of test bodies in the presence of torsion, and in particular we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general may differ from geodesics when torsion is present. We derive the equations of motion of a test body in a spherically symmetric field, and the equations of motion of a satellite in the gravitational field of the Sun and the Earth. We calculate the secular variations of the longitudes of the node and of the pericenter of the satellite. The computed secular variations show how the corrections to the perihelion advance and to the orbital de Sitter effect depend on the torsion parameters. All computations are performed under the assumptions of weak field and slow motion. To test our predictions, we use the measurements of the Moon geodetic precession from lunar laser ranging data, and the measurements of Mercury's perihelion advance from planetary radar ranging data. These measurements are then used to constrain suitable linear combinations of the torsion parameters

Gamma-convergence of discrete functionals with non convex perturbation for image classification

The purpose of this report is to show the theoretical soundness of a variation- al method proposed in image processing for supervised classification. Based on works developed for phase transitions in fluid mechanics, the classification is obtained by minimizing a sequence of functionals. The method provides an image composed of homogeneous regions with regular boundaries, a region being defined as a set of pixels belonging to the same class. In this paper, we show the gamma-convergence of the sequence of functionals which differ from the ones proposed in fluid mechanics in the sense that the perturbation term is not quadratic but has a finite asymptote at infinity, corresponding to an edge preserving regularization term in image processing

A DIFFUSE COHESIVE ENERGY APPROACH TO FRACTURE AND PLASTICITY: THE ONE-DIMENSIONAL CASE

Abstract. In the fracture model presented in this paper, the basic assumption is that the energy is the sum of two terms, elastic and cohesive, depending on the elastic and inelastic part of the deformation, respectively. Two variants are examined, a local model, and a non-local model obtained by adding a gradient term to the cohesive energy. While the local model only applies to materials which obey Drucker's postulate and only predicts catastrophic failure, the non-local model describes the softening regime, and predicts two collapse mechanisms, one for brittle and one for ductile fracture. In its non-local version, the model has two main advantages over the models existing in the literature. The first is that the basic elements of the theory (yield function, hardening rule, evolution laws) are not assumed, but are determined as necessary conditions for the existence of solutions in incremental energy minimization. This reduces to a minimum the number of the independent assumptions required to construct the model. The second advantage is that, with appropriate choices of the analytical shape of the cohesive energy, it becomes possible to reproduce, with surprising accuracy, a big variety of observed experimental responses. In all cases, the model provides a description of the entire evolution, from the initial elastic regime to final rupture

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B (GPB) complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters