118,069 research outputs found
Renormalized solutions to the continuity equation with an integrable damping term
No full textWe consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511–547, 1989) proved that, when the damping term is bounded in space and time, the equation is well posed in the class of distributional solutions and the solution is transported by suitable characteristics of the vector field. In this paper, we prove existence and uniqueness of renormalized solutions in the case of an integrable damping term, employing a new logarithmic estimate inspired by analogous ideas of Ambrosio et al. (Rendiconti del Seminario Fisico Matematico di Padova 114:29–50, 2005), Crippa and De Lellis (J Reine Angew Math 616:15–46, 2008) in the Lagrangian case
Oscillatory solutions to transport equations
No full textWe show that there is no topological vector space X\subset
L^\infty\cap L^1_{\loc} (\rn{}\times \rn{n})
which embeds compactly in L^1_{\loc}, contains BV_{\loc}\cap L^\infty
and enjoys the following closure property: If f\in X^n (\rn{}\times \rn{n})
has bounded divergence and u_0\in X (\rn{n}), then there exists u\in X
(\rn{}\times \rn{n}) which solves
in the sense of distributions. X (\rn{n}) is defined as the set
of functions u_0\in L^\infty (\rn{n}) such that
belongs to X (\rn{}\times \rn{n}).
Our proof relies on an example of N.~Depauw showing an ill--posed transport equation whose vector field is ``almost ''
La chiesa di San Giuseppe a Torino e i rapporti con Roma: le feste di canonizzazione di S. Camillo de Lellis e i dipinti di Gaspare Serenari
No full textLa chiesa di San Giuseppe di Torino ha goduto di una assai limitata fortuna negli studi sugli edifici di culto torinesi in età moderna, nonostante numerose pubblicazioni scientifiche e convegni dell’ultimo decennio si siano occupati delle manifestazioni architettoniche e artistiche a Torino tra Sei e Settecento. Il contributo verte su una prima ricostruzione delle principali vicende connesse alla costruzione della chiesa, a partire dagli anni intorno al 1678-80, fase di insediamento dei padri Ministri degli Infermi in Torino per volontà della Seconda Madama Reale, Giovanna Battista di Savoia-Nemours, alla sua decorazione e al suo arredo tra la fine del XVII e la prima metà del XVIII secolo, polarizzando l’attenzione sulla scelta effettuata da parte della stessa committenza interna all’ordine di avvalersi del pittore Gaspare Serenari, largamente attivo in Roma e particolarmente gradito ai camilliani, per la commissione dei teleri con fatti della vita del santo fondatore che rappresentano un unicum non solo nella città di Torino, ma per l’intero territorio sabaudo, inviati in occasione della canonizzazione di Camillo de Lellis nel 1746. La vicenda sarà posta a confronto con le scelte artistiche effettuate nella medesima fase dagli esponenti di altri ordini religiosi e congregazioni fondati in età moderna presenti nel territorio del capoluogo sabaudo con particolare attenzione ai padri di San Filippo Neri, realtà già a più riprese studiata dalla autrice
San Camillo de Lellis e i Camilliani fra l’Abruzzo e Roma
No full textSaggi relativi a San Camillo de Lellis e alla storia dell'ordine dei Ministri degli Infermi in Abruzz
Virtual prototyping of medieval weapons for historical reconstruction of siege scenarios starting from topography and archaeological investigations
No full textChronicles of sieges to castles or fortresses, using “machinae”, can often be found in historical sources. Moreover, archaeological excavations of castles or fortresses has brought to light rocks or projectiles whose carving suggests a military usage. Nevertheless, chronicles and discoveries alone, are seldom enough to propose a faithful reconstruction of these machines. Therefore, the aim of this research is the development of methodologies for reconstructing virtual scenarios of sieges, starting from the scarce information available. In order to achieve it, a procedure for the virtual reconstruction of the siege machine has been set up, focusing on typology and dimensions of the machines, also investigating possible fire positions according to topography. The entire procedure has been developed using the siege of Cervara di Roma’s Rocca as a case study. Late medieval chronicles (end of 13th Century) report the siege brought by the papal army in order to restore the jurisdiction on the Cervara’s stronghold, following the insurrection of a group of vassals headed by a monk named Pelagio. The discovery, in the area of the Rocca, of a stone that could have been used as a projectile confirms what reported. The proposed methodology is composed of two parts. The first one is connected to the study of the “internal ballistics”, to understand the performances and to build virtual models of siege machines. The second part is the study of the “external ballistics”, then to the positioning and shooting ability of possible machines, analysing the topography of the area. In this paper, we present the feasibility of this methodology through the preliminary results achieved correlating internal and external ballistics
Regularity of area minimizing currents I: Gradient L p estimates
No full textIn a series of papers, including the present one, we give a new, shorter proof of Almgren’s partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement on the regularity assumption for the latter. This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approximations with Lipschitz multiple valued graphs. Our new a priori estimate is a higher integrability type result, which has a counterpart in the theory of Dir-minimizing multiple valued functions and plays a key role in estimating the accuracy of the Lipschitz approximations
Exponential self-similar mixing and loss of regularity for continuity equations
No full textWe consider the mixing behaviour of the solutions of the continuity equation associated with a divergence-free velocity eld. In this announcement we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity elds, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity eld exhibiting instantaneous loss of any fractional Sobolev regularity
Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions
No full textAutonomous Take Off System: Development and Experimental Validation
No full textThis paper describes the design and validation process of an innovative Autonomous Take Off system, developed by the Italian Aerospace Research Center (CIRA) in the framework of the Italian national funded project TECVOL (Technologies for the Autonomous Flight). The autonomous take-off module is part of the autonomous Guidance, Navigation and Control prototype worked out by CIRA in the same project, where significant research effort has been devoted to achievement of high automation during all the flight phases, from take off to landing. The developed automated system allows take off, navigation through three-dimensional waypoints and landing of an aircraft without human intervention, also in presence of environmental disturbances and/or subsystem failures. In aerospace research and development activities not only functional requirements play an important role in the project, also process requirements and system engineering methods are fundamental for project success. In particular, the autonomous take off system development and validation process has been designed in order to be highly reliable but with a substantial reduction of needed time and costs. In the paper the process of design and validation applied to the proposed system development is examined in details, while providing also a description of the automatic take off system
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