Linearly constrained evolutions of critical points and an application to cohesive fractures

We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material

The AGILE Mission

AGILE is an Italian Space Agency mission dedicated to observing the gamma-ray Universe. The AGILE's very innovative instrumentation for the first time combines a gamma-ray imager (sensitive in the energy range 30 MeV-50 GeV), a hard X-ray imager (sensitive in the range 18-60 keV), a calorimeter (sensitive in the range 350 keV-100 MeV), and an anticoincidence system. AGILE was successfully launched on 2007 April 23 from the Indian base of Sriharikota and was inserted in an equatorial orbit with very low particle background. Aims. AGILE provides crucial data for the study of active galactic nuclei, gamma-ray bursts, pulsars, unidentified gamma-ray sources, galactic compact objects, supernova remnants, TeV sources, and fundamental physics by microsecond timing. Methods. An optimal sky angular positioning (reaching 0.1 degrees in gamma- rays and 1-2 arcmin in hard X-rays) and very large fields of view (2.5 sr and 1 sr, respectively) are obtained by the use of Silicon detectors integrated in a very compact instrument. Results. AGILE surveyed the gamma- ray sky and detected many Galactic and extragalactic sources during the first months of observations. Particular emphasis is given to multifrequency observation programs of extragalactic and galactic objects. Conclusions. AGILE is a successful high-energy gamma-ray mission that reached its nominal scientific performance. The AGILE Cycle-1 pointing program started on 2007 December 1, and is open to the international community through a Guest Observer Program

Anisotropic Mesh Adaptation for Crack Detection In Brittle Materials

The quasistatic brittle fracture model proposed by G. Francfort and J.-J. Marigo can be Γ-approximated at each time evolution step by the Ambrosio-Tortorelli functional. In this paper, we focus on a modification of this functional which includes additional constraints via penalty terms to enforce the irreversibility of the fracture as well as the applied displacement field. Secondly, we build on this variational model an adapted discretization to numerically compute the time-evolving minimizing solution. We present the derivation of a novel a posteriori error estimator driving the anisotropic adaptive procedure. The main properties of these automatically generated meshes are to be very fine and strongly anisotropic in a very thin neighborhood of the crack, but only far away from the crack tip, while they show a highly isotropic behavior in a neighborhood of the crack tip instead. As a consequence of these properties, the resulting discretizations follow very closely the propagation of the fracture, which is not significantly influenced by the discretization itself, delivering a physically sound prediction of the crack path, with a reasonable computational effort. In fact, we provide numerical tests which assess the balance between accuracy and complexity of the algorithm. We compare our results with isotropic mesh adaptation and we highlight the remarkable improvements both in terms of accuracy and computational cost with respect to simulations in the pertinent most recent literature

I modelli quali-quantitativi a supporto della progettazione e gestione delle reti fognarie

Oggetto del lavoro è la valutazione della robustezza di due codici di calcolo commerciali (InfoWorks, sviluppato da Wallingford Ltd e MOUSE, sviluppato dal Danish Hydraulic Institute) nella simulazione del sistema drenante di un piccolo bacino di 1,15 ettari sito in prossimità della città di Bologna, sul quale sono stati, in precedenza, raccolti sia dati di portata, sia dati di concentrazione dei principali costituenti di qualità. La superficie del bacino, completamente asfaltata, è adibita ad area di transito e di sosta di mezzi pesanti e le acque drenate sono raccolte in una vasca di prima pioggia prima di essere immesse in una vasca di laminazione e successivamente inviate al ricettore finale. Per circa 8 mesi sono stati campionati con continuità sia dati di pioggia sia dati di qualità nella vasca. Tali dati sono stati utilizzati per calibrare i modelli attraverso una procedura di prova e correggi per entrambi gli aspetti di quantità e di qualità dell’acqua. È stata condotta infine un’analisi di sensitività per i principali parametri dei modelli implementati nei due software

Biological transportation networks: Modeling and simulation

We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations