We analyze the dynamics of the Sun-Earth-Moon system in the context of a particular class of theories of gravity where curvature and matter are nonminimally coupled (NMC). These theories can potentially violate the Equivalence Principle as they give origin to a fifth force and a extra non-Newtonian force that may imply that Earth and Moon fall differently towards the Sun. We show, through a detailed analysis, that consistency with the bound on Weak Equivalence Principle arising from 48 years of Lunar Laser Ranging data, for a range of parameters of the NMC gravity theory, can be achieved via the implementation of a suitable screening mechanism.

In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established. The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches. The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations.

We compute the Euler equations of a functional useful for simultaneous video inpainting and motion estimation, which was obtained in [17] as the relaxation of a modified version of the functional proposed in [16]. The functional is defined on vectorial functions of bounded variations, therefore we also get the Euler equations holding on the singular sets of minimizers, highlighting in particular the conditions on the jump sets. Such conditions are expressed by means of traces of geometrically meaningful vector fields and characterized as pointwise limits of averages on cylinders with axes parallel to the unit normals to the jump sets.

We consider a nonminimally coupled curvature-matter gravity theory at the Solar System scale. Both a fifth force of Yukawa type and a further non-Newtonian extra force that arises from the nonminimal coupling are present in the solar interior and in the solar atmosphere up to interplanetary space. The extra force depends on the spatial gradient of space-time curvature R. The conditions under which the effects of such forces can be screened by the chameleon mechanism and be made consistent with Cassini measurement of parametrized post-Newtonian parameter gamma are examined. Constraints from spectroscopic observations of the solar atmosphere are also taken into account. This consistency analysis requires a specific study of the Sun's dynamical contribution to the arising forces at all its layers.

We consider a variational model analyzed in March and Riey (Inverse Probl Imag 11(6): 997-1025, 2017) for simultaneous video inpainting and motion estimation. The model has applications in the field of recovery of missing data in archive film materials. A gray-value video content is reconstructed in a spatiotemporal region where the video data is lost. A variational method for motion compensated video inpainting is used, which is based on the simultaneous estimation of apparent motion in the video data. Apparent motion is mathematically described by a vector field of velocity, denoted optical flow, which is estimated through gray-value variations of the video data. The functional to be minimized is defined on a space of vector valued functions of bounded variation and the relaxation method of the Calculus of Variations is used. We introduce in the functional analyzed in March and Riey(Inverse Probl Imag 11(6): 997-1025, 2017) a suitable positive weight, and we show that diagonal minimizing sequences of the functional converge, up to subsequences as the weight tends to infinity, to minimizers of an appropriate limit functional. Such a limit functional is the relaxed version of a functional, modified with suitable improvements, proposed by Lauze and Nielsen (2004) and which permits an accurate joint reconstruction both of the optical flow and of the video content.

We examine the constraints on the Yukawa regime from the nonminimally coupled curvature-matter gravity theory arising from deep underwater ocean experiments. We consider the geophysical experiment of Zumberge et al. [Phys. Rev. Lett. 67, 3051 (1991)] for searching deviations of Newton's inverse square law in ocean. In the context of nonminimally coupled curvature-matter theory of gravity the results of Zumberge et al. can be used to obtain an upper bound both on the strength a and range lambda of the Yukawa potential arising from the nonrelativistic limit of the nonminimally coupled theory. The existence of an upper bound on lambda is related to the presence of an extra force, specific of the nonminimally coupled theory, which depends on lambda and on the gradient of mass density, and has an effect in the ocean because of compressibility of seawater. These results can be achieved after a suitable treatment of the conversion of pressure to depth in the ocean by resorting to the equation of state of seawater and taking into account the effect of the extra force on hydrostatic equilibrium. If the sole Yukawa interaction were present, the experiment would yield only a bound on alpha, while, in the presence of the extra force we find an upper bound on the range: lambda(max )= 57.4 km. In the interval 1 m < lambda < lambda(max) the upper bound on alpha is consistent with the constraint alpha < 0.002 found in [Phys. Rev. Lett. 67, 3051 (1991)].

We study a variational problem for simultaneous video inpainting and motion estimation. We consider a functional proposed by Lauze and Nielsen [25] and we study, by means of the relaxation method of the Calculus of Variations, a slightly modified version of this functional. The domain of the relaxed functional is constituted of functions of bounded variation and we compute a representation formula of the relaxed functional. The representation formula shows the role of discontinuities of the various functions involved in the variational model. The present study clarifies the variational properties of the functional proposed in [25] for motion compensated video inpainting.

The effects of a nonminimally coupled curvature-matter 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 $R$. This work expands upon previous results, extending the framework developed there to compute corrections up to order $O\left(1\slash c^4\right)$ of the 00 component of the metric tensor. It is shown that additional contributions arise due to both the non-linear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including exponential contributions that cannot be expressed as an expansion in powers of $1/r$. Some possible experimental implications are assessed with application to perihelion precession.

The effects of a nonminimally coupled curvature-matter model of gravity on planetary orbits are computed. The parameters of the model are then constrained by the observation of Mercury orbit.

Variational models for image segmentation, e.g. Mumford-Shah variational model [47] and Chan-Vese model [21,59], generally involve a regularization term that penalizes the length of the boundaries of the segmentation. In practice often the length term is replaced by a weighted length, i.e., some portions of the set of boundaries are penalized more than other portions, thus unbalancing the geometric term of the segmentation functional. In the present paper we consider a class of variational models in the framework of ?-convergence theory. We propose a family of functionals defined on vector valued functions that involve a multiple well potential of the type arising in diffuse-interface models of phase transitions. A potential with equally distanced wells makes it possible to retrieve the penalization of the true (i.e., not weighted) length of the boundaries as the ?-convergence parameter tends to zero. We explore the differences and the similarities of behavior of models in the proposed class, followed by some numerical experiments. © 2014 Elsevier Inc. All rights reserved.

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We consider a variational model for image segmentation proposed in Sandberg et al. (2010) [12]. In such a model the image domain is partitioned into a finite collection of subsets denoted as phases. The segmentation is unsupervised, i.e., the model finds automatically an optimal number of phases, which are not required to be connected subsets. Unsupervised segmentation is obtained by minimizing a functional of the Mumford-Shah type (Mumford and Shah, 1989 [1]), but modifying the geometric part of the Mumford-Shah energy with the introduction of a suitable scale term. The results of computer experiments discussed in [12] show that the resulting variational model has several properties which are relevant for applications. In this paper we investigate the theoretical properties of the model. We study the existence of minimizers of the corresponding functional, first looking for a weak solution in a class of phases constituted by sets of finite perimeter. Then we find various regularity properties of such minimizers, particularly we study the structure of triple junctions by determining their optimal angles.

We consider the regularization of linear inverse problems by means of the minimization of a functional formed by a term of discrepancy to data and a Mumford-Shah functional term. The discrepancy term penalizes the L 2 distance between a datum and a version of the unknown function which is filtered by means of a non-invertible linear operator. Depending on the type of the involved operator, the resulting variational problem has had several applications: image deblurring, or inverse source problems in the case of compact operators, and image inpainting in the case of suitable local operators, as well as the modeling of propagation of fracture. We present counterexamples showing that, despite this regularization, the problem is actually in general ill-posed. We provide, however, existence results of minimizers in a reasonable class of smooth functions out of piecewise Lipschitz discontinuity sets in two dimensions. The compactness arguments we developed to derive the existence results stem from geometrical and regularity properties of domains, interpolation inequalities, and classical compactness arguments in Sobolev spaces.

In the fracture model presented in this paper, the basic assumption is that the energy is the sum of two terms, one elastic and one cohesive, depending on the elastic and inelastic part of the deformation, respectively. Two variants are examined: a local model, and a nonlocal 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 nonlocal model describes the softening regime and predicts two collapse mechanisms, one for brittle fracture and one for ductile fracture. In its nonlocal version, the model has two main advantages over the models existing in the literature. The first is that the basic elements of the theory (the yield function, hardening rule, and 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 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 large 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.

We extend the analysis of Chiba et al. [Phys. Rev. D 75, 124014 (2007)] of Solar System constraints on f(R) gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize f(R) theories by replacing the action functional of general relativity with a more general form involving two functions f1(R) and f2(R) of the Ricci scalar curvature R. While the function f1(R) is a nonlinear term in the action, analogous to f(R) gravity, the function f2(R) yields a NMC between the matter Lagrangian density Lm and the scalar curvature. The developed method allows for obtaining constraints on the admissible classes of functions f1(R) and f2(R), by requiring that predictions of NMC gravity are compatible with Solar System tests of gravity. Then we consider a NMC model which accounts for the observed accelerated expansion of the Universe and we show that such a model cannot be constrained by the present method.

We report a search for new gravitational physics phenomena based on Riemann-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 consider the motion of a test body in a spherically symmetric field, and the motion of a satellite in the gravitational field of the Sun and the Earth. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general differ from geodesics when torsion is present. We derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of celestial mechanics. 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's 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.

Many real life problems can be represented by an ordered sequence of digital images. At a given pixel a specific time course is observed which is morphologically related to the time courses at neighbor pixels. Useful information can be usually extracted from a set of such observations if we are able to classify pixels in groups, according to some features of interest for the final user. Moreover parameters with a physical meaning can be extracted from the time courses. In a continuous setting we can formalize the problem by assuming to observe a noisy version of a positive real function defined on a bounded set T ×\Omega ‚ R×R2, parameterized by a vector of unknown functions defined on R2 with discontinuities along regular curves in \Omega which separate regions with different features. Suitable regularity conditions on the parameters are also assumed in order to take into account the physical constraints. The problem consists in estimating the parameter functions, segmenting \Omega in subsets with regular boundaries and assigning to each subset a label according to the values that the parameters assume on the subset. A global model is proposed which allows to address all of the above subproblems in the same framework. A variational approach is then adopted to compute the solution and an algorithm has been developed. Some numerical results obtained by using the proposed method to solve a dynamic Magnetic Resonance imaging problem are reported.

l'attività seminariale è sostenuta dai ricercatori e collaboratori dell'IAC ed è rivolta ai ricercatori dell'area romana, essendo finalizzata alla promozione degli interessi di ricerca coltivati in istituto e alla disseminazione dei risultati conseguiti.