13 Giugno, 2012 

Seminari di Cultura Matematica

The orientation of Greek temples: the case of the older Parthenon in Athens
Evento in collaborazione con il congresso Nexus - Architecture and Mathematics

Robert Hannah, Università dell Otago, Nuova Zelanda

Aula Castiglioni, Edificio PK, Campus Bovisa Durando.
ATTENZIONE ORARIO ANTICIPATO ALLE 17

13 Giugno, 2012 16:30

Lezioni Leonardesche

LARGE DEVIATION THEORY. A GENERAL SURVEY WITH SOME RECENT UNUSUAL APPLICATIONS

S.R.S. VARADHAN, Courant Institute of Mathematical Sciences – New York University

Università di Milano, Dipartimento di Matematica, Via Saldini

12 Giugno, 2012 21:00

Lezioni Leonardesche

Mathematical models for simulation and optimal design

Alfio Quarteroni, MOX - Politecnico di Milano

Politecnico di Milano - Campus Bovisa Durando - Aula De Carli - via Durando 10

8 Giugno, 2012 14:00 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Unicità, non unicità e proprietà del supporto di soluzioni dell'equazione dei mezzi porosi con densità variabile su varietà Riemanniane a simmetria sferica.

Fabio Punzo, Università di Roma La Sapienza

Aula seminari III piano

abstract

abstract

Il seminario riguarda l'equazione dei mezzi porosi con densità variabile su varietà Riemanniane M complete non compatte a simmetria sferica; tale classe di varietà Riemanniane comprende, ad esempio, lo spazio iperbolico. Daremo condizioni per l'unicità e la non unicità di soluzioni limitate, in dipendenza del comportamento all'infinito della densità e della funzione di Green dell'operatore di
Laplace-Beltrami su M. Inoltre, nel caso M sia lo spazio iperbolico e il dato iniziale abbia supporto compatto, vedremo quando il supporto
di una qualunque soluzione limitata si mantiene limitato, oppure diventa illimitato ad un certo tempo.

8 Giugno, 2012 11:00 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Modeling Fracture within Local Max-Ent Meshfree Approximation Schemes

Anna Pandolfi, Politecnico di Milano - Structural Engineering Department

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

The numerical simulation of complex physical phenomena calls for efficient and robust algorithms which can be used in concurrent calculations. For standard static and dynamic problems, the priority of the finite element method is out of discussion, and alternative approaches are far from threatening the finite element leadership. This supremacy may not be true, however, when rather difficult problems are tackled. An example of excruciating problems is the propagation of fractures. In such cases, major complications derive from the necessity to track the evolution of boundaries. In view of subsiding numerical difficulties related to the spatial discretization of volumes, alternative algorithms, in some cases based on brilliant concepts, have been proposed. Meshfree methods represent a particular class of numerical
algorithms that do not rely on the definition of a grid, but, in contrast, use the actual geometry of the simulated object for calculations.

I will present the static version of a meshfree method, recently developed for the analysis of the dynamics of solids and fluids, in view of the simulation of explicit crack propagation in brittle materials. The method relies on the discretization of the system into a finite number of particles, representative of the surrounding material. In the spirit of element erosion procedures, the propagation of cracks is modelled by removing material particles upon the attainment of a fracture criterion. The failure criterion adopted here is based on energetic arguments and relies on a small crack-neighbourhood construction for capturing the local degeneration of the material. The study has been developed in collaboration with Michael Ortiz and Bo Li, Caltech (USA).

7 Giugno, 2012 14:15 in punto

Sezione di Geometria, Algebra e loro applicazioni

La superficie di Fano della cubica liscia e la sua funzione normale.

Gian Pietro Pirola, Università di Pavia

aula seminari terzo piano

abstract

abstract

La superficie di Fano delle rette del cubico solido e stata utilizzata da Clemens e Griffiths
per provare la non razionalita di ogni cubica liscia dello spazio proiettivo di dimensione 4.
La superficie di Fano e una superficie irregolare estremamente interessante.
Discutero il legame tra la sua geometria, il ciclo definito nella sua varieta di Albanese
e la funzione normale da esso definita.
I nuovi risultati sono stati ottenuti in collaborazione con A.Collino e J.C. Naranjo.

7 Giugno, 2012 11:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Finite-amplitude thermal convection in fast rotating spherical shell

Ferran Garcia Gonzalez, Universitat Politecnica de Catalunya - Spain

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

The study of thermal convection in rotating spherical geometry is fundamental to explain many geophysical and astrophysical phenomena such as the generation of the magnetic fields, or the differential rotation observed in the atmospheres of the major planets. The difficulties associated with the expe- rimental studies enhance the importance of the three-dimensional numerical simulations, such as those presented in this talk.

In order to obtain the evolution equations, the Boussinesq approximation is applied to the mass, momentum and energy conservation equations, which are rewritten in terms of toroidal and poloidal potentials. Together with the temperature field, they are expanded in spherical harmonics over the sphere, and in the radial direction a collocation method is used.

In our own time evolution codes we apply the IMEX-BDF formulae with an explicit treatment of the nonlinear terms of the equations. The use of matrix- free methods allows the implicit treatment of the Coriolis term, and makes the implementation of a step and order control easier. The results show that the use of high order methods, especially those with time-step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.

At low Prandtl number (ratio between the thermal diffusive and the viscous time scales), and with non-slip boundary conditions, the nonlinear dynamics is explored by means of temporal evolutions. Far away from the stable flows (periodic orbits, tori, and connecting orbits), the physical properties of the tur- bulent solutions are studied. Using parameters as close as possible to those of the Earth’s outer core, the numerical simulations are compared with laboratory experiments and realistic measurements.

6 Giugno, 2012 12:15

Seminari di Cultura Matematica

Modellare l'incertezza nell'analisi del rischio

Enrico Zio, Politecnico di Milano

Aula B.2.1, Edificio 14 (la Nave) via Bonardi, 9, Politecnico di Milano

The study of thermal convection in rotating spherical geometry is fundamental to explain many geophysical and astrophysical phenomena such as the generation of the magnetic fields, or the differential rotation observed in the atmospheres of the major planets. The difficulties associated with the expe- rimental studies enhance the importance of the three-dimensional numerical simulations, such as those presented in this talk.

In order to obtain the evolution equations, the Boussinesq approximation is applied to the mass, momentum and energy conservation equations, which are rewritten in terms of toroidal and poloidal potentials. Together with the temperature field, they are expanded in spherical harmonics over the sphere, and in the radial direction a collocation method is used.

In our own time evolution codes we apply the IMEX-BDF formulae with an explicit treatment of the nonlinear terms of the equations. The use of matrix- free methods allows the implicit treatment of the Coriolis term, and makes the implementation of a step and order control easier. The results show that the use of high order methods, especially those with time-step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.

At low Prandtl number (ratio between the thermal diffusive and the viscous time scales), and with non-slip boundary conditions, the nonlinear dynamics is explored by means of temporal evolutions. Far away from the stable flows (periodic orbits, tori, and connecting orbits), the physical properties of the tur- bulent solutions are studied. Using parameters as close as possible to those of the Earth’s outer core, the numerical simulations are compared with laboratory experiments and realistic measurements.

5 Giugno, 2012 12:00

Seminari di Cultura Matematica

When long memory meets the Kalman Filter: A Comparative study

Paolo Santucci de Magistris, Department of Economics and Business - Aarhus - Denmark

Aula Seminari III piano

abstract

abstract

The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework,
which directly tackles measurement errors and random level shifts. Missing values and several alternative sources of misspecification are also considered. It emerges that the state space methodology provides a valuable alternative for the estimation of the long memory models, under different data generating processes, which are common in financial and economic series. Two empirical applications highlight the practical
usefulness of the proposed state space methods.

1 Giugno, 2012 17:00

Seminario Matematico e Fisico di Milano

GEOMETRY OF HETEROTIC STRING COMPACTIFICATIONS

XENIA DE LA OSSA, University of Oxford

Università di Milano, Dipartimento di Matematica, Via Saldini

abstract

abstract

I will discuss the geometry of heterotic string compactifications with fluxes. The compactifications on 6 dimensional manifolds which preserve N=1 supersymmetry in 4 dimensions must be complex conformally balanced manifolds which admit a now-where vanishing holomorphic (3,0)-form, together with a holomorphic vector bundle on the manifold which must admit a
Hermitian Yang-Mills connection. The flux, which can be viewed as a torsion, is the obstruction to the manifold being Kahler. I will describe how these compactifications are connected to the more traditional compactifications on Calabi-Yau manifolds through geometric transitions like flops and conifold transitions. For instance, one can construct solutions by flopping rational curves in a Calabi-Yau manifold in such a way that the resulting manifold is no longer Kahler. Time permitting, I will discuss open problems, for example the understanding of the the moduli space of heterotic
compactifications and the related problem of determining the massless
spectrum in the effective 4 dimensional supersymmetric field theory. The study of these compactifications is interesting on its own right both in string theory, in order to understand more generally the degrees of freedom of these theories, and also in mathematics. For example, the connectedness between the solutions is related to problems in mathematics, for instance
Reid s fantasy, that complex manifolds with trivial canonical bundle are all connected through geometric transitions.