31 Ottobre, 2006 14:30

Sezione di Probabilità e Statistica Matematica

Dilatazioni classiche alla Hudson e Parthasarathy di semigruppi Markoviani

Matteo Gregoratti, Politecnico di Milano

aula seminari III piano

24 Ottobre, 2006 13:30

Sezione di Probabilità e Statistica Matematica

Decomposizione in cicli delle catene di Markov

Franco Fagnola, Politecnico di Milano

aula seminari III piano

23 Ottobre, 2006 14:15

Sezione di Probabilità e Statistica Matematica

Liquid Crystal Elastomers: modeling analysis, and simulation

Antonio De Simone, SISSA-International School for Advanced Studies

Aula Seminari MOX, VI piano Dipartimento, ed. Nave

abstract

abstract

Liquid crystal elastomers (LCEs) are rubbery solids exhibiting many of the partially ordered mesophases (mematc, smectic A, smectic C) of liquid crystals.
The resulting phase transitions are at the root of their many interesting material properties, such as soft elasticity and shape memory effects.

In recent years, the application of modern tools in the calculus of variations (in particular, relaxation of nonconvex energy functionals) has contributed significantly to the understanding of the material properties of LCEs.
I will review some of the recent results justifying this claim.

3 Ottobre, 2006 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

The longtime dynamics of the viscous Cahn-Hilliard equation in a large domain

Ahmed Bonfoh, Abdus Salam International Centre for Theoretical Physics, Mathematics Section

Liquid crystal elastomers (LCEs) are rubbery solids exhibiting many of the partially ordered mesophases (mematc, smectic A, smectic C) of liquid crystals.
The resulting phase transitions are at the root of their many interesting material properties, such as soft elasticity and shape memory effects.

In recent years, the application of modern tools in the calculus of variations (in particular, relaxation of nonconvex energy functionals) has contributed significantly to the understanding of the material properties of LCEs.
I will review some of the recent results justifying this claim.

2 Ottobre, 2006 14:30

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

PLASMA-FEMmE: An adaptive Shallow Water Model on the Sphere

Thomas Heinze,, German Weather Service (DWD)

Aula Seminari MOX, VI piano Dipartimento ed. Nave

abstract

abstract

PLASMA-FEMmE solves on the sphere the shallow water equations, a prototype for partial differential equations in atmospheric modelling, using a semi-implicit semi-Lagrangian time step and linear finite elements. Grid generation is done by the grid generator amatos.

In our talk we present results using statically and dynamically adapted grids and compare them with the predecessor model FEMmE that uses a static uniform grid. Steady state flow regimes and more complex ones, e.g. flow over a mountain, are demonstrated.
The outcome shows the capability of the chosen approach as well as its limits. Grid adaptation can easily be achieved with amatos. No reflexions at the grid interfaces are observed.
The numerical errors are reduced without a considerable enhancement of the computational effort in the steady state test case. In respect to the conservation properties the results are more sophisticated. In contrast to conservation of mass that cannot improved in any investigated test case, this is achieved for conservation of energy. In case of complex flow regimes this statement only holds for static grid adaption. Here, with dynamic grid adaption, all conservation properties fade in the second half of a 15-day simulation period.
Nevertheless it can be concluded that the investigated scheme works out fine within the expectations. With additional research effort and using conservative advection schemes as well as more sophisticated adaption criteria there is hope that the aforementioned problems can be overcome.

26 Settembre, 2006 14:30

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

L'archivio istituzionale di Dipartimento per i preprint in formato digitale

Mariella Testa, Dipartimento di Matematica - Politecnico di Milano

Aula seminari MOX, VI piano

abstract

abstract

Il Dipartimento di Matematica ha attivato una procedura di conservazione e diffusione dei lavori scientifici in formato elettronico, in prosecuzione della storica collana cartacea del Quaderni di Dipartimento.
Oltre a descrivere caratteristiche e utilizzo dell'archivio, in questo seminario si illustrerà come tale iniziativa si inserisca in una ormai vasta attività di pubblicazione elettronica "libera" della comunità scientifica.

22 Settembre, 2006 

Sezione di Geometria, Algebra e loro applicazioni

Constructions of free inverse semigroups

Boris Schein, University of Arkansas

Aula seminari III piano

abstract

abstract

Differents constractions of free inverse semigroups are presented and the advantes and disvantages of all of them are compared.

14 Settembre, 2006 15:00

Sezione di Geometria, Algebra e loro applicazioni

Extending the scalability of FETI-DP: From exact to inexact algorithms

Prof. Axel Klawonn, Universität Duisburg-Essen

Aula Seminari MOX, VI piano Dipartimento,ed. NAVE

abstract

abstract

Dual-primal FETI methods are among the most severely tested domain decomposition
methods for the solution of partial differential equations. With the advent of massively parallel computers with up to 100,000 processors new concepts are necessary to maintain the good scalability of these iterative methods. In this talk, a framework for the algorithmic design of
dual-primal FETI methods will be discussed focusing on the construction of scalable domain decomposition methods on massively parallel machines; preliminary numerical results will also be presented.
This work is based on joint work with Oliver Rheinbach, Essen.
¤Department of Mathematics, University of Duisburg-Essen, Universit¨atsstr. 3, D-
45117 Essen, Germany. E-mail: axel.klawonn@uni-due.de

25 Luglio, 2006 15:00

Sezione di Geometria, Algebra e loro applicazioni

Control Problems for the Lagrangian Averaged Navier-Stokes Equations

Dr. Peter Korn,, Max Planck Institute for Meteorology, Hamburg

Aula Seminari MOX, VI piano ed. Nave, Dipartimento

abstract

abstract

The Lagrangian-Averaged Navier-Stokes equations
(also known as Navier-Stokes-alpha equations), a
regularization of the Navier-Stokes equations, describe the mean motion of a viscous incompressible fluid.
We study time-dependent optimal control problems for the Lagrangian-Averaged Navier-Stokes equations on a three-dimensional periodic domain. The problem of 'turbulence control' via enstrophy reduction and the velocity matching problem are adressed. In both cases external forcing serves as control variable. It is shown that for both control problems optimal controls exist and that the optimal controls can be characterized
by a first-order necessary condition, involving the linearized adjoint Lagrangian-Averaged Navier-Stokes equations.
Numerical methods to compute the optimal controls
are outlined.

21 Giugno, 2006 12:30

Seminari di Cultura Matematica

Un secolo di matematica e di logica

U. Bottazzini, Univ. di Milano

Aula B.21

The Lagrangian-Averaged Navier-Stokes equations
(also known as Navier-Stokes-alpha equations), a
regularization of the Navier-Stokes equations, describe the mean motion of a viscous incompressible fluid.
We study time-dependent optimal control problems for the Lagrangian-Averaged Navier-Stokes equations on a three-dimensional periodic domain. The problem of 'turbulence control' via enstrophy reduction and the velocity matching problem are adressed. In both cases external forcing serves as control variable. It is shown that for both control problems optimal controls exist and that the optimal controls can be characterized
by a first-order necessary condition, involving the linearized adjoint Lagrangian-Averaged Navier-Stokes equations.
Numerical methods to compute the optimal controls
are outlined.