A general solution in the Newtonian limit of f(R)- gravity

We show that any analytic $f(R)$-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only $f(R)=R$ allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.Comment: 5 page

Axially symmetric solutions in f(R)-gravity

Axially symmetric solutions for f (R)-gravity can be derived starting from exact spherically sym- metric solutions achieved by Noether symmetries. The method takes advantage of a complex coordi- nate transformation previously developed by Newman and Janis in General Relativity. An example is worked out to show the general validity of the approach. The physical properties of the solution are also considered.Comment: 13 pages, 1 figure, to appear in Classical and Quantum Gravity 201

Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is required. Examples of exact solutions are given.Comment: 17 pages, to appear in Class. Quant. Gra

Geological and geophysical characterization of the southeastern side of the High Agri Valley (southern Apennines, Italy)

Abstract. In the frame of a national project funded by Eni S.p.A. and developed by three institutes of the National Research Council (the Institute of Methodologies for Environmental Analysis, the Institute of Research for Hydrogeological Protection and the Institute for Electromagnetic Sensing of the Environment), a multidisciplinary approach based on the integration of satellite, aero-photogrammetric and in situ geophysical techniques was applied to investigate an area located in the Montemurro territory in the southeastern sector of the High Agri Valley (Basilicata Region, southern Italy). This paper reports the results obtained by the joint analysis of in situ geophysical surveys, aerial photos interpretation, morphotectonic investigation, geological field survey and borehole data. The joint analysis of different data allowed us (1) to show the shallow geological and structural setting, (2) to detect the geometry of the different lithological units and their mechanical and dynamical properties, (3) to image a previously unmapped fault beneath suspected scarps/warps and (4) to characterize the geometry of an active landslide affecting the study area

Corrigendum to "Geological and geophysical characterization of the southeastern side of the High Agri Valley (southern Apennines, Italy)" published in Nat. Hazards Earth Syst. Sci., 15, 315–323, 2015

No abstract available

The Cauchy problem of f(R) gravity

The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy problem is not well-formulated.Comment: 16 latex pages, to appear in Class. Quantum Grav; typographical errors corrected, new references adde

Modified-Source Gravity and Cosmological Structure Formation

One way to account for the acceleration of the universe is to modify general relativity, rather than introducing dark energy. Typically, such modifications introduce new degrees of freedom. It is interesting to consider models with no new degrees of freedom, but with a modified dependence on the conventional energy-momentum tensor; the Palatini formulation of $f(R)$ theories is one example. Such theories offer an interesting testing ground for investigations of cosmological modified gravity. In this paper we study the evolution of structure in these ``modified-source gravity'' theories. In the linear regime, density perturbations exhibit scale dependent runaway growth at late times and, in particular, a mode of a given wavenumber goes nonlinear at a higher redshift than in the standard $\Lambda$CDM model. We discuss the implications of this behavior and why there are reasons to expect that the growth will be cut off in the nonlinear regime. Assuming that this holds in a full nonlinear analysis, we briefly describe how upcoming measurements may probe the differences between the modified theory and the standard $\Lambda$CDM model.Comment: 22 pages, 6 figures, uses iopart styl

Spherical symmetry in f(R)f(R)-gravity

Spherical symmetry in $f(R)$ gravity is discussed in details considering also the relations with the weak field limit. Exact solutions are obtained for constant Ricci curvature scalar and for Ricci scalar depending on the radial coordinate. In particular, we discuss how to obtain results which can be consistently compared with General Relativity giving the well known post-Newtonian and post-Minkowskian limits. Furthermore, we implement a perturbation approach to obtain solutions up to the first order starting from spherically symmetric backgrounds. Exact solutions are given for several classes of $f(R)$ theories in both $R =$ constant and $R = R(r)$.Comment: 13 page

The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: From Laminar to Turbulent Flows

We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases

Geological and geophysical characterization of the southeastern side of the High Agri Valley (southern Apennines, Italy)

In the frame of a national project funded by Eni S.p.A. and developed by three institutes of the National Research Council (the Institute of Methodologies for Environmental Analysis, the Institute of Research for Hydrogeological Protection and the Institute for Electromagnetic Sensing of the Environment), a multidisciplinary approach based on the integration of satellite, aero-photogrammetric and in situ geophysical techniques was applied to investigate an area located in the Montemurro territory in the southeastern sector of the High Agri Valley (Basilicata Region, southern Italy). This paper reports the results obtained by the joint analysis of in situ geophysical surveys, aerial photos interpretation, morphotectonic investigation, geological field survey and borehole data. The joint analysis of different data allowed us (1) to show the shallow geological and structural setting, (2) to detect the geometry of the different lithological units and their mechanical and dynamical properties, (3) to image a previously unmapped fault beneath suspected scarps/warps and (4) to characterize the geometry of an active landslide affecting the study area