1,355,478 research outputs found
Porcelio de' Pandoni, 'De sestertio et talento'. Edizione critica e traduzione italiana a cura di N. Rozza. Introduzione, traduzione inglese e commento a cura di A. Burnett (pp. 85-155, 185-202)
No full textPorcelio de' Pandoni's De sestertio et talento is a work of extraordinary interest for the history of Humanistic and Renaissance antiquarianism. This short work was written in the middle of the fifteenth century, and it throws new light on a little-known aspect of the vast and varied humanist learning. Moreover, to the best of our knowledge, it is the first treatise ever written about numismatics.
Although its origins are not entirely clear, it was completed in Milan. In a prefatory letter, in fact, Pandoni offers the work to the powerful secretary of Francesco Sforza, Cicco Simonetta. In fact, as Andrew Burnett speculates, it is possible that the letter of dedication contains statements that are only partially accurate and that the treatise was originally written in Rome, the city in which Pandoni was trained and in whose cultural milieu he had had close ties to the Colonna family, and in particular to Cardinal Prospero Colonna, a well-known patron with strong interests in antiquities. If so, it was re-purposed, a typical practice of Pandoni, and, in his dedication, he placed the interest, the fascination and the antiquarian and numismatic curiosity that had brought about the writing of the short treatise, in a Milan context.
A critical edition is offered here for the first time (by Nicoletta Rozza), accompanied by a full commentary (by Andrew Burnett), and with a double translation, into both Italian and English
Comparison between reduced basis and stochastic collocation methods for elliptic problems
No full textThe stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005–1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411–2442, 2008a; SIAM J Numer Anal 46(5):2309–2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118–1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289–294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229–275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41–44):3187–3206, 2009; Arch Comput Methods Eng 17:435–454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O(1) to moderate dimensions O(10) and to high dimensions O(100) . The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs
Non-Intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: a Comparison and Perspectives
No full textIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones
Reduced order methods for modeling and computational reduction
No full textThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems
Shape optimization for viscous flows by reduced basis methods and free-form deformation
No full textIn this paper, we further develop an approach previously introduced in Lassila and Rozza, 2010, for shape optimization that combines a suitable low-dimensional parametrization of the geometry (yielding a geometrical reduction) with reduced basis methods (yielding a reduction of computational complexity). More precisely, free-form deformation techniques are considered for the geometry description and its parametrization, whereas reduced basis methods are used upon a FE discretization to solve systems of parametrized partial differential equations. This allows an efficient flow field computation and cost functional evaluation during the iterative optimization procedure, resulting in effective computational savings with respect to usual shape optimization strategies. This approach is very general and can be applied to a broad variety of problems. In this paper, we apply it to find the optimal shape of aorto-coronaric bypass anastomoses based on vorticity minimization in the down-field region. Blood flows in the coronary arteries are modeled using Stokes equations; afterwards, results have been verified in feedback using Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd
Storie di viaggi di manoscritti, di libri, di miti e di alberi
No full textIl gruppo di ricerca, costituito da Antonietta Iacono, Antonella Ambrosio, Mariafrancesca Cozzolino, Mariantonietta Paladini, Chiara Renda e Nicoletta Rozza, si propone di presentare i risultati di un’indagine su manoscritti di classici approdati per vie diverse a Napoli e nelle biblioteche umanistiche e rinascimentali del Regno di Napoli, soprattutto nelle raccolte dei principi Trastamara, per offire un esempio di connessione tra trasmissione/ricezione dei classici e civiltà materiale, con particolare attenzione per la diffusione degli agrumi nel territorio del Regno di Napoli, e la creazione della moda aristocratica del giardino piantato ad agrumi. In particolare, il focus di questa indagine parte dalla diffusione a Napoli di una letteratura agronomica specialistica (ad esempio, Virgilio, Columella, Palladio, Geoponica) e coinvolge però anche la letteratura de agricultura coeva, tra cui spicca, ad esempio, il poema De hortis Hesperidum di Giovanni Gioviano Pontano (grande rappresentante dell’Umanesimo aragonese in latino, e primo ministro di Ferrante I d’Aragona, re di Napoli, indicato da tutta la letteratura de re rustica successiva come l’inventore dell’equiparazione tra agrumi e poma Hesperidum). Il poema pontaniano fu modello di una ricchissima letteratura botanica in cui genuini interessi scientifici si intrecciarono con l’amore per la poesia etiologica, il gusto per l’allegoria mitologica, ed ancora con passioni artistiche e culto dei giardini
Metrologia monetaria e cultura antiquaria nel De sestertio et talento di Porcelio de’ Pandoni (XV secolo), N. Rozza – A. Burnett eds. 2022
No full textMetrologia monetaria nell'opera numismatica di Porcelio de' Pandoni, umanista napoletano vissuto nel XV secol
Giambattista Vico, 'De nostri temporis studiorum ratione', a cura di Giovanni Polara e Nicoletta Rozza, Roma, Edizioni di Storia e Letteratura (Opere di Giambattista Vico 3), 2022.
No full textModel Order Reduction in Fluid Dynamics: Challenges and Perspectives
No full textThis chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references
A weighted empirical interpolation method: a priori convergence analysis and applications
No full textWe extend the classical empirical interpolation method [1] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the
recent work [13]. We apply our method to geometric Brownian motion, exponential Karhunen-Loeve expansion and reduced basis approximation of non-ane stochastic elliptic equations. We demonstrate its improved accuracy and eciency over the empirical interpolation method, as well as sparse grid stochastic collocation method
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