100 Pagine Di Calcolo Numerico Pdf Viewer
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Prossimi Seminari
Monegato, Fondamenti di Calcolo Numerico, CLUT (Torino) A. Quarteroni, R. Vendi o cerca 'Metodi e algoritmi per il calcolo numerico' su Libri Polito. Giovanni Monegato. Complementi di matematica e fondamenti di fisica. Monegato - 100 Pagine Di Elementi Di Calcolo Numerico. 100 Pagine Di Elementi Di Calcolo Numerico. Calcolo Numerico Corso di Laurea in Ingegneria Elettronica Appello del 19 gennaio 2015 Problema 1 Siano M = F(2;3) e x = 1 6.Determinare rd(x) e verificare che l’errore relativo commessoapprossimando x con rd(x) non supera, in valore assoluto, la precisione di macchina. Problema 2 Siano. Final fantasy 8 pc itag.
- Entropy-Transport distances between measures and metric measure spaces
Nicolò De Ponti, Università degli Studi di Pavia
martedì 11 febbraio 2020 alle ore 15:15, Aula seminari 3° piano - Semistatic and sparse variance-optimal hedging
Paolo Di Tella, Technische Universitat - Dresden
martedì 11 febbraio 2020 alle ore 10:30 precise, Aula Seminari MOX VI Piano - Modeling and simulation of thermo-poroelastic processes in fractured geothermal reservoirs
Eirik Keilegavlen, Department of Mathematics, University of Bergen, Norway
giovedì 20 febbraio 2020 alle ore 11:30, Aula Saleri - VI piano
Seminari Passati
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- La matematica per vivere meglio
Alfio Quarteroni, MOX - Politecnico di Milano
giovedì 7 febbraio 2013 alle ore 19:00, Museo nazionale della Scienza e della Tecnica - AuditoriumABSTRACTLa matematica oggi permea ogni ambito del sapere. Usiamo, inconsapevolmente, algoritmi matematici quando inviamo immagini dai nostri telefoni cellulari, o quando i motori di ricerca ci dispensano risposte a qualsiasi tipo di richiesta, pescando in tempi infinitesimali fra le migliaia di miliardi di pagine nella rete.
I modelli matematici forniscono una rappresentazione esemplificativa e funzionante di sistemi reali (fisici, biologici, economici o sociali). Essi vengono usati quotidianamente per formulare previsioni meteorologiche su scala continentale, regionale o locale; per prevedere e mitigare il rischio derivante da terremoti, inondazioni, o processi di inquinamento ambientale; per capire meglio come funziona il nostro corpo, come prevedere l insorgere di malattie e come curarle; perfino come farci vivere meglio il nostro tempo libero e aiutare gli atleti a migliorare le loro performance agonistiche.
Questa presentazione mostrerà come questo sia possibile attraverso significativi esempi di grande impatto applicativo.
In collaborazione con il Museo Nazionale della Scienza e della Tecnologia Leonardo da Vinci. - Reduced basis methods in the context of hierarchical model reduction
Kathrin Smetana, Institute of Computational and Applied Mathematics, University of Munster
giovedì 7 febbraio 2013 alle ore 11:00, Aula Seminari - III pianoABSTRACTMany phenomena in fluid dynamics have dominant spatial directions along which the essential dynamics occur. Nevertheless, the processes in the transverse directions are often too relevant for the whole problem to be neglected. For such situations we present a new problem adapted version of the hierarchical model reduction approach. The hierarchical model reduction approach (see [PerErnVen10] and references therein) uses a truncated tensor product decomposition of the solution and hierarchically reduces the full problem to a small lower dimensional system in the dominant directions, coupled by the transverse dynamics. In previous approaches [PerErnVen10] these transverse dynamics are approximated by a reduction
space constructed from a priori chosen basis functions such as trigonometric or Legendre polynomials. We present the hierarchical model reduction-reduced basis approach [OhlSme10] where the reduction space is constructed a posteriori from solutions (snapshots) of appropriate reduced parametrized problems in the transverse directions. Numerical experiments demonstrate that the hierarchical model reduction-reduced basis approach converges exponentially fast with respect to the model order for problems with smooth solutions but also for some test cases where the source term belongs to $C^{0}( Omega)$ only. Run-time experiments verify a linear scaling of the proposed method in the number of degrees of freedom used for the computations in the dominant direction.
contatto: simona.perotto@polimi.it - Gradient estimates for porous medium and fast diffusion equations via FBSDE approach
Ying Hu, IRMAR - Université de Rennes 1
mercoledì 6 febbraio 2013 alle ore 11:00 precise, Aula 3014 del Dipartimento di Matematica e Applicazioni dell Università di Milano-BicoccaABSTRACTIn this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques and Forward and Backward Stochastic Differential Equations (FBSDEs). - Highly Efficient Secondary Migration Of Petroleum As A Colloidal Dispersion
J. Stainforth, Geological/Geochemical consultant
mercoledì 6 febbraio 2013 alle ore 09:30 precise, Aula Consiglio VII piano Dipartimento di Matematica Politecnico di MilanoABSTRACTThe problem of secondary migration is as old as the petroleum industry itself, yet no consensus has been reached on the mechanism. Here, I review existing mechanisms and propose a new one.
From the earliest days, the favored mechanism has been migration of petroleum in its own, separate phase. This hypothesis immediately presented problems: droplets have inadequate buoyancy to overcome capillary entry pressures of pore throats, so that they have to coalesce (how? a Catch-22) into long, continuous phase segments called slugs or stringers to overcome these entry pressures. But, there was a lack of supporting observations, such as:
- Petroleum stringers of the necessary length (10s of meters) and thickness (meters);
- Stringers waiting for take-off on top of source rocks or at permeability boundaries;
- Residual petroleum saturations (in the wake of stringers), according to capillarity theory;
- Differences in the ease or migration for different petroleum types, on account of their
widely different capillary entry pressures and viscosities.
The opposite end-member model of migration in water solution was found to be inadequate, because of the low solubilities and diffusion rates of petroleum. Flowing water had to be
invoked, but compactional and artesian flows are generally too slow to account for the volumes
of migrated petroleum. Also, wholesale convection of pore water in carrier beds is usually denied
by stratified water chemistry. The next step was to call upon migration of petroleum in water
in higher concentrations in the form of colloids or emulsions, but the problem was the large
soap-hydrocarbon ratios that seem to be required. The attractive feature of this hypothesis was
that microdroplets could pass through pore-throats without capillary impediment, and this was supported by experiments half a century ago.
In spite of the difficulties posed by migration of petroleum in its own, continuous phase, this
hypothesis became regarded as “well-established” by the mainstream petroleum media in the late
1970’s and 1980’s, (e.g. Berg, 1975; Schowalter, 1979; England et al., 1987). Yet, there were
actually no new data to support this claim! The only problem that proponents of this hypothesis
seemed to have was its use of the computationally slow Darcy’s law. So, they introduced faster
computational approaches, such as invasion percolation that make even less well-supported
assumptions, e.g., treating viscous forces as negligible!
In view of the problems of petroleum migration in either water solution, or in continuous separate phase, one finally returns to the metastable region of colloidal dispersions. Solutes tend to cluster in supersaturated, metastable solutions, and this should be particularly true for hydrophobic petroleum with its large interfacial tension with water. These colloidal clusters are
smaller than the pore throats of typical carrier beds, so they are not subject to capillary
resistance and migrate at velocities proportional to their radius r squared (according to Stoke’s Law).
Implications of the proposed hypothesis:
1) Cluster formation occurs in the metastable region between solution and exsolution and does not require solubilizers or emulsifiers.
2) There are no capillary constraints. Thus, the ratio of viscous to capillary forces (the Capillary Number) is essentially infinite.
3) The Stokesian flux of petroleum clusters Jsc, through pore throats that are large enough to
allow their passage without capillary restraint, can be compared with the separate phase Darcy flux Jdo through the same rock. To a first approximation, the ratio of these fluxes is
proportional to the ratio of the kinematic viscosities of petroleum and water: Water is generally less viscous than petroleum and the flux of petroleum in clusters is (much) faster than the Darcy flow of a continuous, separate phase.
4) The mechanism works similarly for all types of petroleum, because the constraining viscosity is that of water rather than highly variable petroleum.
5) The ranges of velocity and flux of petroleum are very great. The radii r of clusters and
microdroplets varies by about three orders of magnitude, so the velocities vary by about
six orders of magnitude (~ cm/yr to ~10 km/yr!)
6) The mechanism is self-adjusting. If the migration of clusters or droplets lags behind the
petroleum influxes anywhere in the migration network, the supersaturation of petroleum in the pore water increases. This causes the clusters to enlarge and speed up (with the square of their size), and v.v.
7) The mass flow rates are balanced throughout the migration system, so petroleum does not
accumulate anywhere except in the trap; mass continuity is satisfied automatically.
8) Brownian motion of clusters plays an important role, by (a) assisting their movement through pore throats and preventing their sticking to pore walls, and (b) creating a zone of supersaturation of clusters (~ 1 m thick) at the top of carrier beds (aided by gravity).
9) In spite of the all-important role of clusters and microdroplets in this mechanism, their
volume fractions in the pores are relatively small (generally ~ 0.001 or less).
10) Losses of petroleum into water solution are very small compared with the total quantities
of petroleum migrated, so the mechanism is very highly efficient (~100%): virtually no residual petroleum remains remains along migration pathways.
DATA: 6 febbraio 2013, ore 9.30-12.30 presso l'Aula Consiglio VII Piano Dipartimento di Matematica Politecnico di Milano
contatto: edie.miglio@polimi.it - Mechanisms of Petroleum Trap-Filling & Compositional Implications
J. Stainforth, Geological/Geochemical consultant
mercoledì 6 febbraio 2013 alle ore 14:00 precise, Aula B5.2 Dipartimento di Matematica Politecnico di MilanoABSTRACTThe problem of compositional grading in petroleum fields has received renewed interest in the last ten years, especially in the context of reservoir compartmentalization, and there are now two rival hypotheses to explain the phenomenon. The old one is gravitational segregation acting on petroleum that was well-mixed by the trap-filling process. The newer one is that the grading merely reflects the filling history of the trap with little mixing in the trap (Stainforth, 2004).
These two hypotheses have become to be regarded as opposite end-members.
In this presentation, I outline the theories behind the hypotheses and then test them against
classic field cases showing strong compositional grading. The petroleum distribution in all these
field cases can be explained entirely by the trap-filling hypothesis coupled with the petroleum system logic of source rock kitchen, reservoir volume and shape. I also show how the same cases can be fitted with a model of molecular clumping (mainly of asphaltenes), as proposed by Mullins and co-workers at Schlumberger, but only by making some rather arbitrary assumptions.
An added difficulty with the latter hypothesis is that the cases presented straddle a complete
spectrum of petroleum from heavy tarry oils to light gas-condensate in which the latter contain
virtually no asphaltene.
Neither of these hypotheses, as it stands, sits easily with the diffusivities of petroleum
compounds. These are generally too low for petroleum fields to have achieved complete
equilibrium between gravity and diffusion in the time since trap-filling began. But they are large
enough that there should generally have been some noticeable mixing in that time, especially in the older fields: curiously, though, there is no indication that older petroleum accumulations are better mixed than younger ones.
Finally, I present a way out to this quandary, which reconciles these two rival hypotheses that appear diametrically opposed to one another. This requires the addition of a new conjecture,
which is very simple, yet seems to eliminate all the difficulties posed by the observations. - La nascita del Calcolo Infinitesimale
Umberto Bottazzini, Università degli Studi di Milano
mercoledì 6 febbraio 2013 alle ore 15:00, Aula Consiglio del Dipartimento di Matematica, edificio Nave - via Bonardi 9ABSTRACTCome determinare i massimi o i minimi di una curva piana? Come determinarne la tangente in un punto? Qual è la generalità dei metodi di volta in volta proposti? Sono i nuovi problemi con cui si cimentano i matematici del Seicento. Da Fermat e Cartesio a Pascal e Huygens, sono molti gli attori della storia culminata, con Leibniz e Newton, nella creazione del calcolo infinitesimale.
Pur nella diversità di motivazioni, metodi e strategie di comunicazione, e nonostante le polemiche sulla priorità dell’invenzione, il calcolo differenziale di Leibniz e i metodi - delle serie infinite, delle fluenti e flussioni, delle prime e ultime ragioni via via elaborati da Newton, hanno rappresentano la nascita dell’analisi matematica e, di fatto, della matematica moderna. - Sedimentary Basins and Petroleum Systems: An Overview of Geologic Processes and Controls
R. di Primio, Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences and Jacobs University Bremen, G
martedì 5 febbraio 2013 alle ore 14:30 precise, Aula Consiglio VII Piano del Dipartimento di Matematica -Politecnico di MilanoABSTRACTSedimentary basins shape large parts of the Earth s surface and contain the majority of fossil and renewable energy resources, as well as groundwater reservoirs. An in-depth understanding and knowledge of the structure, formation and evolution of sedimentary basins is fundamental for fossil energy exploration, as the development of sedimentary basins is one of the main controls on petroleum formation, migration and accumulation. The structure and geometry of the basin along with tectonic elements such as faults play an important role in focusing, providing conduits or barriers to hydrocarbon flow. The numerical reconstruction of the processes ongoing during sedimentary basin evolution is one main goal of modern geosciences. Here geoprocess modelling of geological scenarios based on current geological information is the key. Examples include the simulation of organic matter deposition and preservation, the evolution and characterisation of petroleum systems from generation, through expulsion and migration up to the accumulation of petroleum in reservoirs, as well as its degradation by bacterial alteration.
DATA: 5 febbraio 2013, ore 14.30-17.30 presso Aula Consiglio VII Piano
contatto: edie.miglio@polimi.it - CURVE RAZIONALI IN GEOMETRIA ALGEBRICA
PAOLO CASCINI, Imperial College, London
lunedì 4 febbraio 2013 alle ore 17:00, Dipartimento di Matematica, Università di Milano, Via SaldiniABSTRACTLo scopo di questo seminario è di fornire una introduzione allo studio di curve razionali
su varietà proiettive, sia da un punto di vista algebrico che da un punto di vista analitico.
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Seminari Matematici
Politecnico di Milano
Seminari Matematici
Milano e dintorni
- Matematica applicata
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