13 Giugno, 2005 11:30

Equazioni di Navier-Stokes come limiti singolari di flussi di Jeffreys

Stefania Gatti, Università di Ferrara

Aula Seminari MOX - 6° piano dip. matematica

abstract

abstract

Si considera un modello di tipo Jeffreys che descrive il moto di una soluzione di polimeri viscoelastici con memoria lineare contenuta in un dominio $R^2$. Assunte al bordo condizioni di non-scivolamento (nonslip) e fissati i valori delle concentrazioni, viene studiato il comportamento asintotico. Si dimostra poi che, quando il parametro di riscalamento dei nuclei di memoria, corrispondente al numero di Weissenberg del flusso, tende a zero, il modello converge in un senso opportuno alle equazioni di Navier-Stokes. Questa analisi ha un'immediata interpretazione fisica, in quanto consente di confrontare il comportamento di una soluzione polimerica descritta dal modello di Jeffreys con quella di un fluido Newtoniano. Fissato il numero di Reynolds, se la soluzione è abbastanza diluita, il suo comportamento asintotico è simile a quello di un flusso Newtoniano, mentre se la concentrazione è elevata, la soluzione può ancora comportarsi come un fluido Newtoniano, a patto che il numero di Weissenberg sia sufficientemente piccolo.
Questi risultati sono oggetto di un lavoro in collaborazione con C. Giorgi, V. Pata.

13 Giugno, 2005 14:30

High-Order Element-based Galerkin Methods for Geophysical Fluid Dynamics

Francis X. Giraldo, Naval Research Laboratory, Monterey

Aula Seminari MOX - 6° piano dip. di matematica

abstract

abstract

Seminario congiunto del Dipartimento di Matematica
dell'Universita' degli Studi di Milano Statale
e del MOX-Dipartimento di Matematica del Politecnico
di Milano

For the past thirty years global atmospheric models (hydrostatic primitive
equations) have been based on global methods such as spherical harmonics
(SH). Because the current trend in high-performance computing has moved
towards clustered systems having tens of thousands of processors it is
anticipated that SH will meet their doom due because they may notbe able to take full advantage of such large processor-count systems.
In addition, with the ever increasing computing power it will soon be
possible to run global atmospheric models at sufficiently high resolution
such that the hydrostatic approximation breaks down. At this resolution
the models then need to use the non-hydrostatic equations (i.e., the
Euler equations). This then means that the global and regional models can
be unified into one model. To properly handle fine-scale regions such as
hurricanes, the GFD models then need to be much more similar to CFD models
than in the past. For example, constructing not just globally but also
locally conservative methods becomes important.
In this talk we discuss the types of spatial discretization methods being
developed and implemented for the purposes of constructing: global
hydrostatic atmospheric models, regional non-hydrostatic atmospheric
models, and coastal ocean models.While the role of time-integrators should also be discussed, in this talk
we shall concentrate specifically on spatial discretization methods such
as spectral element and discontinuous Galerkin methods based on both
quadrilaterals and triangles.

NOTA: Il dr. Giraldo sara' ospite del Dipartimento di Matematica
dell'Universita' degli Studi di Milano Statale
e del MOX-Dipartimento di Matematica del Politecnico
di Milano per tutta la settimana dal 13 al 17 giugno.
Chi fosse interessato ad incontrarlo puo` rivolgersi
al prof. L.Pavarino o al dr. L.Bonaventura.

13 Giugno, 2005 17:00

Seminario Matematico e Fisico di Milano

Infinite dimensional tilting theory and its applications

Jan Trlifaj, Univerzita Karlova, Praga (Repubblica Ceca)

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Aula 8

abstract

abstract

Modules (representations) play a key role in the structure theory of associative rings (algebras). Starting from Morita theorem characterizing equivalence of full module categories, we will proceed to Brenner-Butler theorem (1-dimensional case), and the Miyashita theorem (n-dimensional case). In all these theorems, the representing tilting modules are finitely generated. Then we will introduce the recent notion of an infinitely generated tilting module and show its relation to module approximations. Though infinitely generated, the tilting modules are of `finite type', and this fact makes it possible to classify them over particular rings. We will finish by presenting two recent applications of infinitely generated n-tilting modules: (i) for n=1, to describing the structure of Matlis localizations of commutative rings, and (ii) for an arbitrary n, to proving finitistic dimension conjectures for (non-commutative) Iwanaga-Gorenstein rings.

7 Giugno, 2005 14:30

Sezione di Probabilità e Statistica Matematica

Quantum Markov Semigroups/Quantum Dynamical Semigroups/Master Equations - I

Alberto Barchielli, Politecnico di Milano

aula seminari III piano

Modules (representations) play a key role in the structure theory of associative rings (algebras). Starting from Morita theorem characterizing equivalence of full module categories, we will proceed to Brenner-Butler theorem (1-dimensional case), and the Miyashita theorem (n-dimensional case). In all these theorems, the representing tilting modules are finitely generated. Then we will introduce the recent notion of an infinitely generated tilting module and show its relation to module approximations. Though infinitely generated, the tilting modules are of `finite type', and this fact makes it possible to classify them over particular rings. We will finish by presenting two recent applications of infinitely generated n-tilting modules: (i) for n=1, to describing the structure of Matlis localizations of commutative rings, and (ii) for an arbitrary n, to proving finitistic dimension conjectures for (non-commutative) Iwanaga-Gorenstein rings.

6 Giugno, 2005 17:00

Seminario Matematico e Fisico di Milano

Multiscale problems in crystal plasticity

Michael Ortiz, California Institute of Technology, Pasadena (Stati Uniti)

Dipartimento di Matematica - Politecnico di Milano - Via Bonardi 9 - Milano - Aula Seminari III piano

abstract

abstract

The macroscopic plasticity of ductile crystals is the net result of the collective motion of large numbers of crystal lattice defects, most notably, glissile dislocations, with structures forming at multiple length scales. These include the scale of the lattice, where dislocations may be regarded as discrete topological defects: the scale of the mean distance between dislocations, where the dynamics of the dislocation ensemble is of primary interest: and the sub-grain scale, where dislocations form characteristic patterns. The development of mathematical links between the behaviors at all scales, and the characterization of the effective macroscopic behavior of ductile crystals, remains a central and long-standing problem in physical metallurgy. Tools of the calculus of variations such as relaxation and Gamma convergence prove powerful and convenient in forging those links. I plan to review a number of mathematical problems that arise in that context, and some recent results pertaining to those problems, including: the formulation of a geometrical mechanics of discrete dislocations and the passage to the continuum: the effective energetics and dynamics of dislocation ensembles: and the relaxation and optimal scaling properties of single-crystals.

1 Giugno, 2005 12:30

Seminari di Cultura Matematica

Principio di indeterminazione e Analisi di Fourier

E. Laeng, Dip. di Matematica

Aula B.21

The macroscopic plasticity of ductile crystals is the net result of the collective motion of large numbers of crystal lattice defects, most notably, glissile dislocations, with structures forming at multiple length scales. These include the scale of the lattice, where dislocations may be regarded as discrete topological defects: the scale of the mean distance between dislocations, where the dynamics of the dislocation ensemble is of primary interest: and the sub-grain scale, where dislocations form characteristic patterns. The development of mathematical links between the behaviors at all scales, and the characterization of the effective macroscopic behavior of ductile crystals, remains a central and long-standing problem in physical metallurgy. Tools of the calculus of variations such as relaxation and Gamma convergence prove powerful and convenient in forging those links. I plan to review a number of mathematical problems that arise in that context, and some recent results pertaining to those problems, including: the formulation of a geometrical mechanics of discrete dislocations and the passage to the continuum: the effective energetics and dynamics of dislocation ensembles: and the relaxation and optimal scaling properties of single-crystals.

31 Maggio, 2005 14:30

Sezione di Probabilità e Statistica Matematica

Dilatazione classica universale di una evoluzione markoviana a tempo discreto - II

Matteo Gregoratti, Politecnico di Milano

aula seminari III piano

The macroscopic plasticity of ductile crystals is the net result of the collective motion of large numbers of crystal lattice defects, most notably, glissile dislocations, with structures forming at multiple length scales. These include the scale of the lattice, where dislocations may be regarded as discrete topological defects: the scale of the mean distance between dislocations, where the dynamics of the dislocation ensemble is of primary interest: and the sub-grain scale, where dislocations form characteristic patterns. The development of mathematical links between the behaviors at all scales, and the characterization of the effective macroscopic behavior of ductile crystals, remains a central and long-standing problem in physical metallurgy. Tools of the calculus of variations such as relaxation and Gamma convergence prove powerful and convenient in forging those links. I plan to review a number of mathematical problems that arise in that context, and some recent results pertaining to those problems, including: the formulation of a geometrical mechanics of discrete dislocations and the passage to the continuum: the effective energetics and dynamics of dislocation ensembles: and the relaxation and optimal scaling properties of single-crystals.

25 Maggio, 2005 12:30

Seminari di Cultura Matematica

Dal sogno di Richardson all'Earth Simulator: passato, presente e futuro dei modelli matematici per le previsioni del tempo e del clima

L. Bonaventura, Dip. di Matematica

aula T2.2

The macroscopic plasticity of ductile crystals is the net result of the collective motion of large numbers of crystal lattice defects, most notably, glissile dislocations, with structures forming at multiple length scales. These include the scale of the lattice, where dislocations may be regarded as discrete topological defects: the scale of the mean distance between dislocations, where the dynamics of the dislocation ensemble is of primary interest: and the sub-grain scale, where dislocations form characteristic patterns. The development of mathematical links between the behaviors at all scales, and the characterization of the effective macroscopic behavior of ductile crystals, remains a central and long-standing problem in physical metallurgy. Tools of the calculus of variations such as relaxation and Gamma convergence prove powerful and convenient in forging those links. I plan to review a number of mathematical problems that arise in that context, and some recent results pertaining to those problems, including: the formulation of a geometrical mechanics of discrete dislocations and the passage to the continuum: the effective energetics and dynamics of dislocation ensembles: and the relaxation and optimal scaling properties of single-crystals.

24 Maggio, 2005 14:30

Sezione di Probabilità e Statistica Matematica

Dilatazione classica universale di una evoluzione markoviana a tempo discreto - I

Matteo Gregoratti, Politecnico di Milano

aula seminari III piano

The macroscopic plasticity of ductile crystals is the net result of the collective motion of large numbers of crystal lattice defects, most notably, glissile dislocations, with structures forming at multiple length scales. These include the scale of the lattice, where dislocations may be regarded as discrete topological defects: the scale of the mean distance between dislocations, where the dynamics of the dislocation ensemble is of primary interest: and the sub-grain scale, where dislocations form characteristic patterns. The development of mathematical links between the behaviors at all scales, and the characterization of the effective macroscopic behavior of ductile crystals, remains a central and long-standing problem in physical metallurgy. Tools of the calculus of variations such as relaxation and Gamma convergence prove powerful and convenient in forging those links. I plan to review a number of mathematical problems that arise in that context, and some recent results pertaining to those problems, including: the formulation of a geometrical mechanics of discrete dislocations and the passage to the continuum: the effective energetics and dynamics of dislocation ensembles: and the relaxation and optimal scaling properties of single-crystals.

23 Maggio, 2005 14:30

Sezione di Probabilità e Statistica Matematica

1D Finite Volume River Flow Computations

John Wright, Imperial College Londra, MOX

Aula Seminari MOX - 6° piano dip matematica

abstract

abstract

The aim of the project is to implement a numerical method based on finite volume for the simulation of 1D open-channel flow characterized by an irregular bathymetry. The key idea is to reformulate in the classical 1D Saint-Venant equations in such a way that the slope and nonprismaticity effects are included in the momentum flux. From the numerical point of view the a characteristic-based flux predictor is adopted combined with a suitable treatment of the critical sections and wetting fronts. This approach allows to treat a wide variety of real situations