Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save com- putational time, we rely on reduced basis techniques as a reliable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems, and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. Finally, we test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations, in its linear and nonlinear version, describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale as well as physical meaning

The role of Internal Solitary Waves on deep-water sedimentary processes. The case of up-slope migrating sediment waves off the Messina Strait

Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary “current” that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities

Analisi del fenomeno di blocco atmosferico osservato a Trieste tra agosto 2003 ed agosto 2018

Il blocco atmosferico \ue8 una configurazione dell'atmosfera particolarmente stabile, caratterizzata dalla persistenza di alta pressione (anticiclone di blocco) che interrompe la propagazione delle perturbazioni atlantiche provenienti da ovest. L'analisi matematica mostra che generalmente un blocco pu\uf2 essere ottenuto dalla sovrapposizione di un opportuno usso medio zonale e un'onda di Rossby e che ha un decorso di circa 15 giorni, periodo ben pi\uf9 alto dei tipici pochi giorni di alternanza "bel tempo-brutto tempo"

Prostorna raspodjela fizikalnih, kemijskih i bioloških oceanografskih karakteristika, fitoplanktona, hranjivih tvari i otopljene obojane organske materije (CDOM) u Bokokotorskom zaljevu na Jadranu

The temporal variations of temperature, salinity, fluorescence, dissolved oxygen concentration, Coloured Dissolved Organic Matter (CDOM) and of chemical (nutrients, chlorophyll a) and biological (phytoplankton composition) parameters in the Boka Kotorska Bay were observed during two periods. CDOM regulates the penetration of UV light into the sea and therefore plays an important role in many hydrological and biogeochemical processes in the sea surface layer including primary productivity. In the framework ADRICOSM-STAR it was possible to investigate the Boka Kotorska Bay during May and June 2008 in order to increase an understanding of optical and chemical characteristics and their evolution during these periods. In both periods station KO (located furthest from the open sea) presented different physical, chemical and biological characteristics with respect to the other stations inside the Boka Kotorska Bay. A positive correlation was found between CDOM and chlorophyll a (R = 0.7, P < 0.001, n = 15) and this implies that in this area, similarly to the open sea, the primary source of CDOM should be the biological production from phytoplankton. This is probably due to the fact that the rivers entering the Boka Kotorska Bay are not severely impacted by man.U Bokokotorskom zaljevu su mjerene vremenske promjene temperature, saliniteta, fluorescencije, koncentracije otopljenog kisika, obojene otopljene organske materije (CDOM) i kemijskih (hranjive soli, klorofila) i bioloških (sastav fitoplanktona) parametara tijekom dva razdoblja (svibanj i lipanj 2008. godine). CDOM određuje prodiranje UV svjetlosnih zraka u more i stoga igra vrlo važnu ulogu u mnogim hidrološkim i biogeokemijskim procesima u površinskom sloju mora koji uključuje primarnu produkciju. Unutar ADRICOSM-STAR projekta, bilo je moguće istražiti Bokokotorski zaljev tijekom svibnja i lipnja 2008. godine radi povećanja razumijevanja optičkih i kemijskih karakteristika i njihovog razvoja kroz ova razdoblja. Zbog dotoka krških rijeka i smanjenja razmjene s otvorenim morem, u oba razdoblja postaja KO (smještena najdalje od otvorenog mora) je pokazala različite fizikalne, kemijske i biolo{ke karakteristike u odnosu na postaje unutar Bokokotorskog zaljeva. Pronađena je pozitivna korelacija izme|u CDOM i klorofila a (R = 0.7, P < 0.001, n = 15) {to upućuje na to da bi u ovom području, slično otvorenom moru, primarni izvor CDOM trebao biti biološka produkcija od fitoplanktona. To je vjerojatno zbog toga što dotoci rijeka u Bokokotorskom zaljevu nisu ozbiljnije ugroženi ljudskim djelovanjem

Bottom current-controlled quaternary sedimentation at the foot of the Malta Escarpment (Ionian Basin, Mediterranean)

A better understanding of the evolution of bottom current circulation and associated deposits is significant for many applications including paleoclimatology and geological hazard. Besides the large contourite drifts, bottom currents may generate fields of large sediment waves that, depending on their height and velocity of migration, may pose severe risk for infrastructures. Conversely, the time span of their paleoceanographic record is generally relatively short. We use bathymetry data, sub-bottom and seismic reflection profiles and legacy oceanographic data to analyze the sediment waves occurring in a deep environment (from 2400 to 3800 m water depth at the foot of the Malta Escarpment in the Mediterranean Sea) to understand their evolution in time, their significance for paleoceanography, and their relation to present day hydrographic conditions. In the absence of direct stratigraphic information, we use the information from nearby studies and from ODP Site 964 and DSDP Site 374 to constrain the age of the sedimentary successions. We discover that these waves (about 2.5 km in wavelength, 50 m in height, with crest sub-perpendicular to the continental slope trend) have been steadily growing and migrating northward since about 500 ka, although an irregular growth and unsteady migration is distinguishable since about 1800 ka. The waves are generated by predominantly alongslope southward flowing bottom currents compatible with modern hydraulic conditions (mean flow speed of ~5 cm s−1, peaks of 15 cm s−1). The rate of crest migration (~ 2.0–3.2 mm a−1) and the average sedimentation rate (0.64–0.69 mm a−1) are unusually high for deep sea environments away from turbidity currents paths. We infer that the steady development of sediment waves is produced by a drastic increase in sediment input to the Ionian Basin resulting from the tectonic uplift in NE Sicily and Calabria and the onset of a relatively steady, low energy bottom current regime following the Mid-Pleistocene Transition. We attempt to extract information on orbital cyclicity preserved in the seismic record from the power spectra of virtual seismic traces from the well preserved succession of 5 visually discernible, regularly spaced sub-units consisting of alternation of high-amplitude and low-reflectivity packages within the last 500 ka. Peaks in the power spectra can be identified around orbital obliquity and precession periodicities, while eccentricity appears not to be recorded. We discuss the results of seismic cyclicity analysis relative to uncertainties of stratigraphic and petrophysical constraints. The sediment waves along the foot of the Malta escarpment are an excellent candidate for the extraction of a long, continuous and high resolution sedimentary record of the paleo circulation changes and climate cycles in the Mediterranean Sea since about 500 ka.peer-reviewe

Principal Component Analysis of Quantum Correlation

The concept of the quantum correlation matrix for observables leads to the application of PCA (Principal Component Analysis) also for quantum systems in Hilbert space. The consistency of PCA for quantum systems, is illustrated in the case of a qubit system with two Pauli matrices as observables and a density matrix polarized along the third one. As the main application of this theory, it is shown that the principal components are able to generate a class of quantum channels and depolarizing operators mapping density matrices (even pure states) to maximally mixed state

Linear asymptotic stability of geophysical channeled flows in the presence of arbitrary longitude-shaped perturbations

Sufficient conditions for the linear asymptotic stability of large scale wind-driven oceanic flows are derived in the presence of arbitrary longitude-shaped perturbations. Criteria work when both bottom dissipation and lateral diffusion of relative vorticity are simultaneously present. The stability is controlled by the maximum of the shear of the basic flow and by the maximum of its meridional derivative and involves the dissipation-diffusion coefficients

Fondamenti e risultati classici della meccanica dei fluidi geofisici ad uso degli studenti del corso di Laurea in Fisica

Lo scopo fondamentale del testo è quello di fornire agli studenti e ai cultori di Scienze della Terra fondamenti rigorosi, dal punto di vista fisico, di una fenomenologia cui si accede spesso per via elementare ma priva di adeguate spiegazioni. Un esempio tipico è dato dalle mappe di previsione meteorologiche diffuse dai mezzi di informazione, in cui resta misteriosa la struttura ondulatoria dei campi di pressione che determinano le aree cicloniche e anticicloniche. In numerosi modelli di processo, come quello sopra accennato, è possibile disaccoppiare in modo coerente la meccanica dalla termodinamica e generare modelli puramente meccanici, limitandosi a fluidi a densità costante. Il testo si colloca in questo ambito in modo da renderlo più facilmente accessibile alle sopraddette categorie di potenziali lettori. Il lavoro, che è basato su una pluriennale esperienza didattica degli autori, sembra trovare agevolmente spazio nell’esigua letteratura scientifica in lingua italiana sull’argomento