Pre-Poisson submanifolds

This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson structures.Comment: Proceedings of the conference "Poisson 2006". 14 page

Products of multisymplectic manifolds and homotopy moment maps

Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an L-infinity-embedding of the L-infinity-algebra of observables of the individual factors into the observables of the product, and that homotopy moment maps for the individual factors induce a homotopy moment map for the product. As a by-product, we associate to every multisymplectic form a curved L-infinity-algebra, whose curvature is the multisymplectic form itself.Comment: 27 pages. Version to be published in Journal of Lie Theor

Spin(7)-manifolds in compactifications to four dimensions

We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold $\mathcal{M}_{8}$ equipped with a particular set of tensors $\mathfrak{S}$ that allow to naturally embed in $\mathcal{M}_{8}$ a family of $G_{2}$-structure seven-dimensional manifolds as the leaves of a codimension-one foliation. Under a different set of assumptions, $\mathfrak{S}$ allows to make $\mathcal{M}_{8}$ into a principal $S^{1}$ bundle, which is equipped with a topological $Spin(7)$-structure if the base is equipped with a topological $G_{2}$-structure. We also show that $\mathfrak{S}$ can be naturally used to describe regular as well as a singular elliptic fibrations on $\mathcal{M}_{8}$, which may be relevant for F-theory applications, and prove several mathematical results concerning the relation between topological $G_{2}$-structures in seven dimensions and topological $Spin(7)$-structures in eight dimensions.Comment: 50 pages. We have included Proposition 6.4 about elliptic fibrations in relation to a pair of vector fields. We have also included Remark 5.13, thanks to an internal communication by Dominic Joyce. Discussion about the relation of singular foliations and D7-branes include

Deformations of Lagrangian submanifolds in log-symplectic manifolds

This paper is devoted to deformations of Lagrangian submanifolds contained in the singular locus of a log-symplectic manifold. We prove a normal form result for the log-symplectic structure around such a Lagrangian, which we use to extract algebraic and geometric information about the Lagrangian deformations. We show that the deformation problem is governed by a DGLA, we discuss whether the Lagrangian admits deformations not contained in the singular locus, and we give precise criteria for unobstructedness of first order deformations. We also address equivalences of deformations, showing that the gauge equivalence relation of the DGLA corresponds with the geometric notion of equivalence by Hamiltonian isotopies. We discuss the corresponding moduli space, and we prove a rigidity statement for the more flexible equivalence relation by Poisson isotopies

Deformations of symplectic foliations

We develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result of this paper is that each symplectic foliation has an attached $L_\infty$-algebra controlling its deformation problem. Indeed, viewing symplectic foliations as regular Poisson structures, we establish a one-to-one correspondence between the small deformations of a given symplectic foliation and the Maurer-Cartan elements of the associated $L_\infty$-algebra. Using this, we show that infinitesimal deformations of symplectic foliations can be obstructed. Further, we relate symplectic foliations with foliations on one side and with (arbitrary) Poisson structures on the other, showing that obstructed infinitesimal deformations of the former may give rise to unobstructed infinitesimal deformations of the latter

A method for the location of noise-polluted area

This paper deals with the working out of a method suitable to locate the critical areas from an acoustic point of view inside the pertinence zones of the roads. We have applied our method to about one thousand kilometres of major roads managed by ANAS in Lombardia. The procedure is based on the coupling of a Geographic Information System (GIS) with an acoustics simulation model. In order to characterize the noise sources in the prediction software, it has been necessary to estimate in every significant section of the streets the day and night average fluxes of vehicles, the vehicle typology and their average velocity. This study started from a statistical analysis of the experimental data obtained by sound measurements and by counting the vehicle fluxes. As a result, we have obtained on a GIS the acoustics map of the whole Lombardia road network with information on where the noise limits classes are exceeded

Errors evaluation in the estimate of the noise from the road traffic

Specific algorithms together with noise data acquired during a measurement campaign, consisting of approximately 80 one-hour records, were utilized to model the noise levels of a road network. Experimental measurements were used to evaluate the reliability of the model by analyzing the differences between the measured values and the estimated ones. We think that these differences have to be especially ascribed to an imperfect representation of the combined effects of the attenuation due to acoustic wave diffraction and the attenuation produced by the ground effect

The (Evolving) vineyard\u2019s age structure in the valencian community, Spain. A new demographic approach for rural development and landscape analysis

Vineyards have assumed a key role as rural landmarks in recent decades. Investigating vineyard dynamics and contexts may reveal various economic, cultural, and environmental aspects of rural landscapes, which can be linked to land-use changes and major soil degradation processes, including soil erosion. As a contribution to rural landscape studies, the purpose of this work is to investigate the spatial distribution of vineyard plots in the Valencian community, located in the eastern area of the Iberian Peninsula, focusing on the final product, the type of vineyard and how long each vineyard has been settled over time. The work provides a comprehensive analysis of a wine-growing landscape, considering strategic (spatial) assets in present and past times. Vineyards were interpreted as a distinctive landmarks that give value to local economies, basic knowledge of how long different types of wine plots have been present in the Valencian community is useful when estimating their degree of sustainability and formulating suggestions, policies, and strategies to prevent processes of landscape degradation at various spatial scales