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Giornata di seminari in occasione del pensionamento di Andrea Gavioli

Mercoledì 13 febbraio, nell'Aula M1.2 del Dipartimento FIM dell'Università degli Studi di Modena e Reggio Emilia, si svolgerà una giornata di seminari in occasione del pensionamento del prof. Andrea Gavioli. Gli argomenti delle conferenze riguarderanno aree di ricerca che il prof. Andrea Gavioli ha contribuito a sviluppare.

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Programma:

  • 09:30 - Apertura dei lavori.

  • 09:45 - Seminario: The role of terrain analysis in catchment hydrologic modeling.

    Relatore: prof. Stefano Orlandini (Università di Modena e Reggio Emilia)

    Abstract: Terrain analysis is the analysis and interpretation of topographic features. Such features include elevation, slope, aspect, plan and profile curvature, drainage area, and specific drainage area. The intention is to build mathematical abstraction of surface terrain in order to delineate or stratify landscapes and create an understanding of relationships between hydrological, geomorphological, and ecological processes and physical terrain features. The roots of terrain analysis date back to 1870, when James Clerk Maxwell presented a paper on the mathematical description of hills and dales to the London, Edinburgh and Dublin philosophical magazine and journal of science. It was only with Freeze and Harlan’s (1969) blueprint for a physically-based, digitally-simulated hydrologic response model, however, that terrain analysis become an essential component of catchment hydrologic modeling. The more recent step forward was made by Gallant and Hutchinson (2011), who provided the hydrologic community with a new differential equation for specific drainage area that helps catchment hydrology to better find a recognized position among the areas of continuum mechanics. In the present seminar, the role of terrain analysis in catchment hydrologic modeling is illustrated and directions for future research are discussed. Special emphasis is given to the contribution given by UNIMORE, and to the importance of a collaborative effort between Mathematicians and Civil and Environmental Engineers for the solution of real societal problems.

  • 10:45 - Seminario: Approccio geometrico-analitico a funzionali di curvatura.

    Relatore: prof. Domenico Mucci (Università di Parma)

    Abstract: Svariati fenomeni (corde vibranti, segmentazione di segnali) coinvolgono energie del secondo ordine, che in particolare dipendono dalla curvatura. Il caso di curve in codimensione maggiore di uno presenta fenomeni interessanti, che vengono analizzati da un punto di vista geometrico/analitico. Usando (come strumento) le correnti cartesiane, è possibile determinare una rappresentazione in BV dell'inviluppo semicontinuo di funzionali molto naturali. Nel caso "elastico" di crescite più che lineari, vengono inoltre osservati fenomeni diversi dal caso "plastico".
    I risultati che presenterò sono stati ottenuti in collaborazione con Emilio Acerbi, dell'Università di Parma.

  • 11:45 - Seminario: Approximate curvatures of a varifold.

    Relatore: prof. Gian Paolo Leonardi (Università di Trento)

    Abstract: Varifolds, i.e. Radon measures on the Grassmannian bundle of unoriented tangent d-planes of a Riemannian n-manifold M, represent a variational generalization of unoriented, d-dimensional submanifolds of M. By a suitable extension of classical variation operators, we introduce a notion of approximate second fundamental form that is well-defined for a generic varifold. Rectifiability, compactness, and convergence results are proved, showing in particular the consistency and stability of approximate curvatures with respect to varifold convergence. If restricted to the case of "discrete varifolds", this theory provides a general framework for extracting key features from discrete geometric data. Some numerical tests on point clouds (evaluation of curvatures and geometric flows, also in presence of noise and singularities) will be shown. We shall finally discuss some future perspectives and open problems.
    This is a joint research with Blanche Buet (Univ. Paris XI - Orsay) and Simon Masnou (Univ. Lyon 1).

  • 12:45 Chiusura dei lavori.

[Ultimo aggiornamento: 28/01/2019 14:30:37]