Basic ideas and tools for projection-based model reduction of parametric partial differential equations

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition and error estimation is introduced. Several tools for geometry parametrizations, such as free form deformation, radial basis function interpolation and inverse distance weighting interpolation are explained. The empirical interpolation method is introduced as a general tool to deal with non-affine parameter dependency and non-linear problems. The discrete and matrix versions of the empirical interpolation are considered as well. Active subspaces properties are discussed to reduce high-dimensional parameter spaces as a pre-processing step. Several examples illustrate the methodologies

Semi-continuous Chlorella vulgaris Cultivation Using Anaerobic Digestate Liquid Fraction Pre-treated by Ultrasonic Cavitation to Improve Carbon Dioxide Solubilization

Nutrients-enriched effluents such as digestate can represent a suitable and economically appealing substrate for microalgae growth since they combine the effluent treatment with biomass production. Then, microalgae biomass can be exploited to produce several bio-based compounds. However, the use of digestate for microalgae cultivation can be challenging due to its high levels of ammonia nitrogen and its low C/N ratio. For this reason, an ultrasonic cavitation (UC) process combined with carbon dioxide (CO2) insufflation was tested on digestate, in order to obtain a faster solubilization of the CO2 in the medium and thus an increase in the C/N ratio. The test was carried out growing Chlorella vulgaris on both digestate (mixotrophic condition) and BG-11 medium (autotrophic condition) in 1 L photobioreactors. For the first 14 days of the experiment the reactors were maintained in batch conditions to acclimatize microalgae. Then, they were switched to semi-continuous for 32 days. The reactors were fed three times a week, with an HRT (Hydraulic Retention Time) of 10.5 d as weekly average. Regarding the test on digestate, both UC pre-treated and untreated conditions reached the highest biomass production at the end of the batch (4.8 and 4.1 g L-1 respectively) and a complete ammonium (NH4+) removal after 9 days. The switch to semi-continuous caused an increase in NH4+ concentration and a consistent decrease in biomass concentration. Biomass production reached the steady-state, with a concentration of 1.9 and 1.2 g L-1 for the UC pre-treated and untreated digestate, respectively (+55.6 % biomass production obtained with UC pre-treated digestate). Moreover, an NH4+ removal of 93.5 % and 92.3 % was reached for UC pre-treated and untreated conditions, respectively

Amyloid and allorecognition in the colonial ascidian Botryllus schlosseri.

Allorecognition, i.e., the ability of intraspecific nonself recognition is widely distributed among colonial, sessile marine organisms in the form of colony specificity. In the cosmopolitan compound ascidian Botryllus schlosseri, colony specificity is controlled by a highly polymorphic Fu/HC locus: two colonies sharing at least one alleleat the Fu/HC locus can fuse into a chimeric colony; if no alleles are shared, a typical inflammatory reaction occurs, with the recruitment of a specific hemocyte type, the cytotoxic morula cells (MCs), inside the tips of the ampullae (the blind termini ofthe tunic vasculature) extending towards the alien colony, their extravasation in the tunic and their final degranulation. As a consequence of allorecognition, necrotic, melanic spots (points of rejection; PORs) form along the contact border, due to the release, by MCs, of their granular content, mainly represented by quinones, polyphenols and the enzyme phenoloxidase (PO), upon the perception of the allogeneic humoral factors diffusing from the alien colony through the partially fused tunics. It is remarkable that the deposition of melanin and the cell death is confined to the immediate outside of the ampullar tips, suggesting that the diffusion of PO and the products of its activity are, in some way, prevented in order to limit cytotoxicity to the immediate neighbourhood of the contact region. In this context, we looked for factors released by MCs that could limit the spreading of cytotoxicity and melanisation. We found that MCs share with vertebrate melanocytes similar packaging of melanin precursors, entrapped in a 3Dscaffold of amyloid fibrils. They contribute to form the electron dense content of MC granules that, after stimulation, flake off and is released in the surrounding medium. Released amyloid fibrils limit the diffusion of the produced melanin. The search for genes and factor controlling both melanogenesis and amyloidogenesis, revealed an evolutionary conserved machinery involved in the processes and an unexpected cross talk between the two Botryllus immunocyte types, i.e., phagocytes and MCs. Furthermore, this work confirms the physiological role of amyloid in tunicate immunity

Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: Overview and perspectives

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments

SURVEY METHODS FOR SEISMIC VULNERABILITY ASSESSMENT OF HISTORICAL MASONRY BUILDINGS

On 20th and 29th of May 2012, two powerful earthquakes struck northern Italy. The epicentres were recorded respectively in Finale Emilia (magnitude 5.9 Ml) and Medolla (magnitude 5.8 Ml) in the province of Modena, though the earthquake was formed by a series of seismic shakes located in the district of the Emilian Po Valley, mainly in the provinces of Modena, Ferrara, Mantova, Reggio Emilia, Bologna and Rovigo. Many monuments in the city of Mantova were hit by the earthquake and, among these, Palazzo Ducale with the well-known Castello di San Giorgio which host the noteworthy "Camera degli Sposi". This building, the most famous of the city, was so damaged that it was closed for more than one year after the earthquake. The emblem of the Palace and Mantova itself, the previously cited "Camera degli Sposi" realized by Andrea Mantegna, was damaged and all the economic and social life of the city was deeply affected. Immediately after the earthquake, the Soprintendenza per i Beni Architettonici e Paesaggistici of Brescia, Cremona and Mantova establish an agreement with the University Iuav of Venice, requiring an analysis and assessment of the damage in order to proceed with the development of an intervention project. This activity turned out to be very important not only from the point of view of the recovery of the architectural and artistic heritage but also because the city's economy is based primarily on tourism. The closure of one of the most important monuments of Mantova has led to a significant and alarming decline in the government income

An opproisal of the energy crdck zero (ECo) test in the evaluation of tempered martensite embrittlement (TME)

Tempered martensite embrittlement (TME) was investigated in an electroslag remelted (ESR) aeronautical grade SAE 4340 steel. The Charpy - Vimpact, plane strarn fracture toughness (K1") and energy crack zero (ECo) tests were employed to evaluate the reduced toughness of 300"C ascompared with 200"C-tempered specimens after fracture in the temperature range from - 70'C to + 150"C. The ECo and Charpy - V results werecomparable. The K1. test, however, failed to detect TME, even though a fatigue precracked specimen was used as in the ECo test. Thisdiscrepancy between the two tests is attributed to the different rnfluence of a microtough zone a few pm thick at the crack tip. Caution is thereforeadvised in the conversion of ECo values to their K6 equivalents