Stress tensors, Riemannian metrics and the alternative descriptions in elasticity

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Stability Analysis of a Rigid Body with Attached Geometrically Nonlinear Rod by the Energy-Momentum Method

This paper applies the energy-momentum method to the problem of nonlinear stability of relative equilibria of a rigid body with attached flexible appendage in a uniformly rotating state. The appendage is modeled as a geometrically exact rod which allows for finite bending, shearing and twist in three dimensions. Application of the energy-momentum method to this example depends crucially on a special choice of variables in terms of which the second variation block diagonalizes into blocks associated with rigid body modes and internal vibration modes respectively. The analysis yields a nonlinear stability result which states that relative equilibria are nonlinearly stable provided that; (i) the angular velocity is bounded above by the square root of the minimum eigenvalue of an associated linear operator and, (ii) the whole assemblage is rotating about the minimum axis of inertia

Two Particle-Hole Excitations in Charged Current Quasielastic Antineutrino--Nucleus Scattering

We evaluate the quasielastic and multinucleon contributions to the antineutrino nucleus scattering cross section and compare our results with the recent MiniBooNE data. We use a local Fermi gas model that includes RPA correlations and gets the multinucleon part from a systematic many body expansion of the $W$ boson selfenergy in the nuclear medium. The same model had been quite successful for the neutrino cross section and contains no new parameters. We have also analysed the relevance of 2p2h events for the antineutrino energy reconstruction.Comment: 6 pages, 4 figure

Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system