30 Settembre, 2008 15:00

Numerical simulation of the subducting lithosphere: Snapshot and time-dependent models

dr. Nicola Tosi, Charles University of Prague

Aula Seminari Fausto Saleri, 6° piano

abstract

abstract

To simulate the convection in the Earth mantle, two complementary approaches are possible. On the one hand one can solve self consistently the full set of equations of thermal convection employing parameters and relationships derived from mineral physics.
Although such models are presently still unable to predict the actual convection pattern in the Earth, they are extremely useful tools to investigate general characteristics of given physical systems. On the other hand, to permit comparison with specific geophysical observables associated with flow, one can consider a more restricted problem. Instead of focusing on the time evolution of mantle flow, assuming to know a priori the temperature anomalies that drive the convection, we can build a snapshot of the present-day flow pattern that successfully predicts the observables and that, in turn, puts important constraints on unknown parameters.
Examples from both such approaches will be presented. In particular, we will focus on numerical models of the evolution of a subducting lithosphere with complex non-linear rheology and on the prediction of the non-hydrostatic geoid associated with the instantaneous flow due to a subducted slab.

26 Settembre, 2008 14:30

Sezione di Probabilità e Statistica Matematica

Optimal Portfolio, Partial Information and Malliavin Calculus

Prof. Giulia Di Nunno, Centro di Matematica Applicata, Università di Oslo

Aula Seminari 3° piano, Dipartimento di Matematica

abstract

abstract

In a market driven by Levy processes, we consider an optimal portfolio problem for a trader who has access to some information in general smaller than the one generated by the market events. In this sense we refer to this trader as having partial information.
For this generally incomplete market and within a non-Markovian setting, we give a characterization for a portfolio maximizing the expected utility of the final wealth.
Techniques of Malliavin calculus are used for the analysis.
(This presentation is based on a joint work with Bernt Øksendal).

12 Settembre, 2008 11:00

Sezione di Probabilità e Statistica Matematica

Pervasive ICT

Prof. Alfonso Fuggetta, Dip. Elettronica e Informazione, Politecnico

Aula Seminari Fausto Saleri, 6° piano

abstract

abstract

12 Settembre, 2008 15:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Another fourth order elliptic equation

Guido Sweers, Università di Colonia, Germania

aula seminari MOX - VI piano

8 Settembre, 2008 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Computer-assisted existence proofs for semilinear elliptic boundary value problems

Michael Plum, Università di Karlsruhe

5 Settembre, 2008 

Sezione di Geometria, Algebra e loro applicazioni

"Connections between words and matrices".

Juhani Karhumaki, Università di Turku-

aula seminari III piano Dipartimento di Matematica

abstract

abstract

There is well known connection between words and integer matrices known already almost hundred years stating that free monoids (finitely or countably generated) can be embedded into the multiplicatice semigroup of matrices. This allows in one hand to conclude simple undecidablity results for matrices, and on the other hand some weak dimension properties for words. These and related results are analyzed in this lecture.

9 Luglio, 2008 16:15

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Robust exponential attractors for singularly perturbed phase-field equations with dynamic boundary conditions

Ciprian G. Gal, University of Missouri, Columbia, MO, USA

aula seminari III piano

There is well known connection between words and integer matrices known already almost hundred years stating that free monoids (finitely or countably generated) can be embedded into the multiplicatice semigroup of matrices. This allows in one hand to conclude simple undecidablity results for matrices, and on the other hand some weak dimension properties for words. These and related results are analyzed in this lecture.

7 Luglio, 2008 11:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Mathematical Models and Methods in Electrocardiology

Prof. Yves Coudiere, Université de Nantes

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

Computing the electrical excitation wave that occurs in the heart is
of great scientific interest, to understand propagation patterns and
also as a base to understand the formation of the electrocardiogram
(ECG). This propagation is modeled by the bidomain system of
reaction-diffusion equations. Analysis results will be presented. A new finite volume method for the bidomain equations is proposed and
analysed. Numerical results on realistic geometries and simulated
ECGs will be shown and discussed.

7 Luglio, 2008 16:15

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

A Three Dimensional Model of Cellular Electrical Activity

dr. Yoichiro Mori, University of British Columbia, Vancouver BC

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

We propose a three dimensional description of cellular electrophysiology which takes into account ionic concentration dynamics. The model consists of a set of partial differential equations satisfied in the intracellular and extracellular domains supplemented with dynamic nonlinear interface conditions at the membrane boundaries. After formulating the model, we perform a systematic reduction of the model to elucidate its relationship with traditional models in electrophysiology.
In so doing, we also uncover the presence of disparate time scales in the model. This "stiffness" poses interesting challenges for the construction of reliable computational schemes. We finally apply this modeling methodology to a problem in cellular cardiac
electrophysiology: electric conduction in cardiac tissue under severely reduced gap-junctional coupling

25 Giugno, 2008 14:30

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

The analysis and applications of an anisotropic sparse grid stochastic collocation technique for PDEs with random input data

dr. Clayton Webster, Sandia National Laboratories, Albuquerque, USA

Aula Seminari Fausto Saleri, VI piano Dipartimento

abstract

abstract

This talk will consist of two parts: In the first part we propose and analyze an anisotropic sparse grid stochastic collocation method for solving partial differential equations with random coefficients and forcing terms (input data of the model). The method consists of a Galerkin approximation in the space variables and a collocation, in probability space, on anisotropic sparse tensor product grids utilizing either Clenshaw-Curtis or Gaussian knots. Even in the presence of nonlinearities, the stochastic collocation approach leads to the solution of uncoupled deterministic problems, similar to sampling-based methods, such as Monte Carlo. This talk includes both a priori and a posteriori approaches to adapt the anisotropy of the sparse grids to each given problem. Our rigorously derived error estimates, for the fully discrete problem, will be described and used to compare the efficiency of the method with several other ensemble-based methods.
These methods have proven to have dramatic impact on several application areas, including statistical mechanics, financial mathematics, bioinformatics, and other fields that must properly predict certain model behaviors. However, in many of these fields it is often the case that not all random input coefficients can be fully realized, and therefore, in the second part of this talk we will provide a mechanism for determining statistical information about the input parameters from, e.g., measurements of output quantities. This parameter identification algorithm couples an adjoint-based deterministic algorithm with the sparse grid stochastic collocation approach discussed in the first part, for tracking statistical quantities of interest from the computational solutions of PDEs driven by random inputs.
Numerical examples illustrate the theoretical results and are used to show that, for moderately large dimensional problems, the sparse grid approach with a properly chosen anisotropy is very efficient and superior to all examined methods, including Monte Carlo.