28 Aprile, 2015 14:15

MOX Seminar

- Attenzione!: NUOVA DATA 28-04-2015 - Reduced basis methods: principles, algorithms, applications

Alfio Quarteroni, EPFL e Politecnico di Milano (on leave)

Sala Consiglio, VII piano

abstract

abstract

Projection-based reduced-order models (ROMs) provide efficient strategies to tackle parametrized partial differential equations, multi-query problems (control and inverse problems, for instance), and yield real-time simulations. Essential ingredients are the regularity and low dimensionality of solution manifolds, the use of Offline/Online computational stratagems, the availability of a posteriori error estimates,and the use of low-dimensional approximation spaces. In this talk I will recall the mathematical concepts behind Reduced Basis methods (a special family of ROM), provide both algebraic and geometrical interpretation,and address a few meaningful examples.

contact: paola.antonietti@polimi.it

22 Aprile, 2015 12:15

Seminari di Cultura Matematica

SEMINARIO RINVIATO
Arte rupestre mondiale: un patrimonio universale. La cooperazione culturale nel secolo XXI e il ruolo di UNESCO

Nuria Sanz, UNESCO, Messico

aula Rogers, edificio 11, Campus Bonardi

Projection-based reduced-order models (ROMs) provide efficient strategies to tackle parametrized partial differential equations, multi-query problems (control and inverse problems, for instance), and yield real-time simulations. Essential ingredients are the regularity and low dimensionality of solution manifolds, the use of Offline/Online computational stratagems, the availability of a posteriori error estimates,and the use of low-dimensional approximation spaces. In this talk I will recall the mathematical concepts behind Reduced Basis methods (a special family of ROM), provide both algebraic and geometrical interpretation,and address a few meaningful examples.

contact: paola.antonietti@polimi.it

22 Aprile, 2015 14:30 in punto

Dipartimento di Matematica del Politecnico di Milano

A Note on Comparative Ambiguity Aversion and Justifiability

Pierpaolo Battigalli, Unversità Luigi Bocconi

Aula Fausto Saleri

abstract

abstract

21 Aprile, 2015 11:00

MOX Seminar

An asymptotic derivation of the Saint-Venant-Exner model with gravitational effects and energy balance

Gladys Narbona Reina, Universita' di Siviglia

Aula Seminari III Piano presso Edificio La Nave Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

A Saint-Venant-Exner model is deduced from an asymptotic analysis of the Navier-Stokes equations. The model is defined in terms of the mass transference between the static and the moving sediment layers. One of the improvements of this deduction is that the derived model accounts with an associated energy balance, a property that the classical SVE models do not have. Moreover, the model contains a modification to be incorporated to the gravitational term in order to take into account arbitrary sloping beds. Several numerical test will be presented in order to show such differences.

contact: luca.bonaventura@polimi.it

15 Aprile, 2015 12:15

Seminari di Cultura Matematica

Alla scoperta dei ‘big data’ nel DNA

Stefano Ceri, Politecnico di Milano

aula B21, edificio 14, Campus Bonardi

A Saint-Venant-Exner model is deduced from an asymptotic analysis of the Navier-Stokes equations. The model is defined in terms of the mass transference between the static and the moving sediment layers. One of the improvements of this deduction is that the derived model accounts with an associated energy balance, a property that the classical SVE models do not have. Moreover, the model contains a modification to be incorporated to the gravitational term in order to take into account arbitrary sloping beds. Several numerical test will be presented in order to show such differences.

contact: luca.bonaventura@polimi.it

14 Aprile, 2015 11:30

MOX Seminar

Modeling and simulation of the influence of microbubbles on macroscale processes

Daniel Fuster, Universite' Pierre et Marie Curie, Paris

Aula Saleri - 6° piano - Dipartimento di Matematica

abstract

abstract

The collective response of small bubbles to external pressure changes is
a topic of interest in various processes such the elaboration of new
contrast agents, lithotripsy, systems involving wave propagation and
underwater explosions.
Modeling the influence of the smallest scales (of the order of microns
and below) on large scales is crucial to unveil the intrinsic
interaction mechanisms between pressure waves and the response of
bubbles.

In this talk I will present some recent advances on the modeling and
simulation of complex systems containing bubbles. Based on
volume-averaged equations, a subgrid model is added to account for a
bubble, or multiple bubbles, within each computational cell. The model
converges to the solution of ensemble-averaged bubbly flow equations for
weak oscillations and monodisperse systems. In the other extreme, it also
converges to the theoretical solution for a single oscillating bubble,
and captures the bubble radius evolution and the pressure disturbance
induced in the liquid. Compared to previous models based on volume and
phase averaging, the new model extends the range of void fractions that
can be reliably simulated and, for low enough void fractions,reproduces
the results of the polydisperse phase-averaged model with much smaller
computational expense. The new numerical results allow us to gain new
insight into the effect of direct bubble-bubble interactions as well as !
polydispersity in the response of bubble clusters.

Finally, I will discuss some recent progress on the generalization of the
model to more complex situations and some challenges when modeling the
influence of nanometric bubbles at large scales.

Evento finanziato dalla Fondazione CEN (ref.Prof Pasquale Ciarletta)

contact: pasquale.ciarletta@polimi.it

13 Aprile, 2015 16:45 in punto

Sezione di Finanza Quantitativa

A Jump and Smile Ride: Continuous and Jump Variance Risk Premia in Option Pricing

Giacomo Bormetti, Scuola Normale Superiore Pisa

Aula Saleri

abstract

abstract

Stochastic and time-varying volatility models typically fail to correctly price out-of-the-money (OTM) put options at short maturity. We extend Realized Volatility option pricing models by adding a jump component estimated from high-frequency data and the associated risk premium. The inclusion of jumps provides a rapidly moving volatility factor, which improves on the fitting properties under the physical measure. The change of measure is performed adopting a Stochastic Discount Factor (SDF) with three risk premia: equity, and two variance risk premia related to the continuous and jump components. On the one hand, employing an SDF with multiple risk premia further improve the flexibility under risk neutral dynamics while preserving analytical tractability. On the other hand, it provides new way of separately estimate the continuous and jump variance risk premia by coherently combining high-frequency returns and option data in a multi-factor option pricing model. The empirical analysis illustrates the contribution of the jump factor to the pricing performance of Standard and Poor's 500 index OTM options. Finally, we apply our multi-factor model to estimate the time evolution of the two components of the variance risk premium and test their ability to predict future market returns.

10 Aprile, 2015 15:00

MOX Seminar

Mathematics competitions and classroom practices: Bridging the gap

Igor Kontorovich, Simon Fraser University - Vancouver

Aula Saleri VI Piano MOX Dipartimento di Matematica -Politecnico di Milano

abstract

abstract

On the one hand, the movement of mathematics competitions is a prominent part of the mathematics education community. On the other hand, the movement is considered as self-contained community, the mathematics and practices of which, are far away from the context of a typical classroom. In this talk I will address the contexts of a mathematics competition and a typical classroom in terms of learners, pedagogical goals, organization of the learning setting and mathematical problems. A systematic comparison between the two contexts is used to reduce the gap between the two, which appears as unbridgeable on the first sight.

contact: chiara.andra@polimi.it

1 Aprile, 2015 15:00

MOX Seminar

Progress in Anisotropic Surface Mesh Generation with TetGen

Franco Dassi, Weierstrass Institute, Berlin Germany

Aula Saleri VI Piano MOX -Dipartimento di Matematica Politecnico di Milano

abstract

abstract

A discretization of a computational domain is the starting point in many
different numerical applications. Anisotropic meshes allow to obtain simulation results of similar accuracy with significantly less effort.
TetGen offers an efficient triangular and tetrahedral data structure for robust and efficient local mesh operations. So far, all these features are employed in an isotropic framework. While they can be exploited to get anisotropic triangular or tetrahedral mesh. The key concept is the following: an anisotropic mesh corresponds to an isotropic one in a proper distorted space. Indeed, in this distorted space we may re-use all the routine developed for the isotropic case,but now, the resulting mesh will be anisotropic.
In this talk, we present how we have developed this idea to make TetGen an
anisotropic triangular mesh generator. More in detail, we provide two differentways used to distort the space and get anisotropic triangular meshes.


contact: marco.verani@polimi.it

31 Marzo, 2015 11:00

MOX Seminar

Understanding Bayes spaces

J. J. Egozcue - V. Pawlowsky-Glahn, U. Politecnica de Catalunya, Barcelona, Spain --- Univ. de Girona, Girona, Spain

Aula Saleri VI piano del Dipartimento di Matematica - MOX - Politecnico di Milano

abstract

abstract

Bayes spaces contain equivalence classes of -additive measures. Two measures are equivalent when they are proportional. These measures are represented by densities and vector space operations are dened. Probability measures and density functions are included in these spaces. When the densities are log-square-integrable, they are in a Hilbert space called B2.
Bayes spaces and associated Hilbert spaces B2 have been developed in a theoretical way, but there is still a long way to understand the implications of the theory, as well as to develop potential applications. The talk is aimed at reviewing the theory and giving some examples of distributions for which the B2 distance can be easily obtained. These examples show the variety of distribution supports that can be dealt with the theory. An application to grain size distribution is presented. The goal is to decide whether different populations have different mean distribution.

contact: piercesare.secchi@polimi.it --- laura.sangalli@polimi.it