18 Giugno, 2009 10:30

A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems

Marco Restelli, Ozean Im Erdsystem, Max Planck Institute for Meteorology, Germany

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

abstract

abstract

We consider a novel discontinuous Galerkin method for convection-diffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable. The second is that, when the method uses polynomial approximations of the same degree for both the total flux and the scalar variable, optimal convergence properties are obtained for both variables. The third is that it is possible to postprocess in an element-by-element fashion the solution to obtain an approximation of the scalar variable which converges faster than the original one.

The proposed method is compared with other well established methods concerning the accuracy of the results and the computational cost, both in the diffusion dominated regime and in the convection dominated regime. Our analysis indicates that the hybridizable discontinuous Galerkin formulation is a viable alternative to the more classical approaches; in particular, it shows that the typical benefits of the mixed finite element methods can be obtained at a computational cost comparable to that of the standard primal continuous formulation.

17 Giugno, 2009 16:00

Bayesian non-parametric analysis of diffusions

Gareth O. Roberts, University of Warwick

Aula F. Saleri VI Piano Mox - Dipartimento di Matematica -

abstract

abstract

This presentation will describe recent progress on Bayesian non-parametric analysis of diffusion drift functions given continuous data on a finite time interval. It turns out that Gaussian processes can be used as conjugate priors, and we describe methodology for characterising posterior mean and covariance structure in terms of solutions to differential equations with coefficients given as functions of the observed diffusion local time.

17 Giugno, 2009 17:00

Seminario Matematico e Fisico di Milano

Analysis of the flow associated with the function $n\mapsto\lambda^{n^k}$

Isaac Namioka, University of Washington

Dipartimento di Matematica, Politecnico di Milano, Aula Seminari III piano

abstract

abstract

A flow is a pair $(S,X)$, where $X$ is a compact Hausdorff space and $S$ is a semigroup of continuous
maps of $X$ into itself. In this joint work with Ali Jabbari, we analyze the family of special flows.
Let ${\mathbb{T}}=\{z\in{\mathbb{C}}:|z|=1\}, k\in{\mathbb{N}}$ and $\lambda=e^{2\pi it}$ with $t$ a
fixed irrational real number and let $f\in{{\mathbb{T}}^{\mathbb Z}}$ be defined by $f(n)=\lambda^{n^k}$.
As usual we define the shift operator $U:{\mathbb T}^{\mathbb Z}\rightarrow {\mathbb T}^{\mathbb Z}$
by $Ug(n)=g(n+1)$ for each $g\in{\mathbb T}^{\mathbb Z}$.
Let $X_f$ be the closure of the orbit $\{U^nf:n\in\mathbb N\}$.
Then the flow we are interested is of the form $(\{U^n:n\in\mathbb N\},X_f)$.
Previously the case $k=2$ was treated by us in 1984, and the case $k=4$ was considered by P.Milnes.

11 Giugno, 2009 15:00

Sezione di Probabilità e Statistica Matematica

The mass of sites visited by a random walk on an infinite graph

Lee Gibson, Department of Mathematics, University of Louisville, KY, USA

Aula seminari MOX VI piano

abstract

abstract

We determine the log-asymptotic decay rate of the negative exponential moments of the mass of sites visited by a random walk on an infinite graph which satisfies a two-sided sub-Gaussian estimate on its transition kernel. This provides a new method of proof of the correct decay rate for Cayley graphs of finitely generated groups with polynomial volume growth. This method also extend known results by determining this decay rate for certain graphs with fractal-like structure or with non-Alfors regular volume growth functions.

10 Giugno, 2009 12:15

Seminari di Cultura Matematica

Algebra, geometria e inattese applicazioni

Ciro Ciliberto, Università di Roma Tor Vergata

Aula B 2.1, Via Bonardi 9

We determine the log-asymptotic decay rate of the negative exponential moments of the mass of sites visited by a random walk on an infinite graph which satisfies a two-sided sub-Gaussian estimate on its transition kernel. This provides a new method of proof of the correct decay rate for Cayley graphs of finitely generated groups with polynomial volume growth. This method also extend known results by determining this decay rate for certain graphs with fractal-like structure or with non-Alfors regular volume growth functions.

8 Giugno, 2009 16:30

Lezioni Leonardesche

Homogeneous Dynamics And Number Theory

Gregory Margulis, Yale University

Dipartimento di Matematica, Università di Milano, V. Saldini 50, Aula Chisini

We determine the log-asymptotic decay rate of the negative exponential moments of the mass of sites visited by a random walk on an infinite graph which satisfies a two-sided sub-Gaussian estimate on its transition kernel. This provides a new method of proof of the correct decay rate for Cayley graphs of finitely generated groups with polynomial volume growth. This method also extend known results by determining this decay rate for certain graphs with fractal-like structure or with non-Alfors regular volume growth functions.

8 Giugno, 2009 11:00

Sezione di Probabilità Quantistica

Invariant states for the asymmetric exclusion quantum Markov semigroup

Roberto Quezada, UAM - Mexico City

Aula Seminari III piano

abstract

abstract

We describe the structure of invariant states and projections of the asymmetric exclusion quantum Markov semigroup. (Joint work with J.C. Garcia and L.P. Martinez)

3 Giugno, 2009 12:15

Seminari di Cultura Matematica

Spazi Frattali: paradossi della semplicità

Fabio Cipriani, Politecnico di Milano

Aula B 2.1, Via Bonardi 9

We describe the structure of invariant states and projections of the asymmetric exclusion quantum Markov semigroup. (Joint work with J.C. Garcia and L.P. Martinez)

27 Maggio, 2009 12:15

Seminari di Cultura Matematica

Ludwig Boltzmann, il genio del disordine (con proiezione dell omonimo film di E. Agapito)

Carlo Cercignani, Politecnico di Milano

Aula B 2.1, Via Bonardi 9

We describe the structure of invariant states and projections of the asymmetric exclusion quantum Markov semigroup. (Joint work with J.C. Garcia and L.P. Martinez)

25 Maggio, 2009 14:30

Sezione di Geometria, Algebra e loro applicazioni

Indispensable binomials in semigroup ideals

Ignacio Ojeda Martinez de Castilla, Universidad de Extremadura

Aula interna, III piano

We describe the structure of invariant states and projections of the asymmetric exclusion quantum Markov semigroup. (Joint work with J.C. Garcia and L.P. Martinez)