24 Marzo, 2010 12:15

Seminari di Cultura Matematica

Leonardo Sinisgalli, ingegnere e poeta nella civiltà delle macchine

G.I. Bischi, Università di Urbino

Aula B21 (Edificio 14 Nave )

22 Marzo, 2010 14:30 in punto

Seminari di Cultura Matematica

Forza e potenza in meccanica dei continui

Alfredo Marzocchi, Dip. di Matematica e Fisica, Univ. Cattolica del Sacro Cuore, Sede di Brescia

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

abstract

abstract

La formulazione del bilancio della quantita di moto mediante una generalizzazione della legge di d Alembert consente di ricomprendere e dedurre direttamente la forma debole delle equazioni differenziali della meccanica dei continui, in un formato valido anche in ambiente non euclideo,
permettendo campi di sforzo concentrati aventi divergenza misura. Tale impostazione rivela poi come naturale la generalizzazione a materiali di
gradiente elevato, e permette di considerare sottocorpi sfumati .

17 Marzo, 2010 15:00 in punto

Sezione di Fisica Matematica

Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems

Nicola Bellomo, Politecnico di Torino

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

abstract

abstract

This lecture deals with the development of new paradigms based on the mathematical methods of the kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by some biological functions which are able to modify the above laws.
The first part of the presentation technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The second part deals with a critical analysis and with the indication of some research perspective concerning the challenging target of developing a biological-mathematical theory for the living matter.
The sequential steps to achieve the above outlined objectives are as follows:

(i) Integration of the concept of functional subsystems to reduce the complexity of large living systems within the approach of system biology;
(ii) Development of the mathematical kinetic and stochastic game theory for active particles;
(iii) Modelling the immune system as a large complex system;
(iv) Development of a multiscale analysis and modelling from genes to tissues.

References

N. Bellomo, Modelling Complex Living Systems-A Kinetic Theory and Stochastic Game Approach (Birkhauser, Boston, 2008).
N. Bellomo, N.K. Li, and P.K. Maini, On the foundations of cancer modelling: Selected topics, speculations, and perspectives, Mathematical Models and Methods in Applied Sciences, 18 (2008)
593-646.
N. Bellomo, C. Bianca and M. Delitala, Complexity analysis and mathematical tools towards the modelling of living systems, Physics of Life Review, 6 (2009) 144-175.

17 Marzo, 2010 12:15

Seminari di Cultura Matematica

Archeologia cognitiva: la matematica dalla preistoria alle tribù fossili

G. Dimitriatis, Università di Genova

Aula B21 (Edificio 14 Nave )

This lecture deals with the development of new paradigms based on the mathematical methods of the kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by some biological functions which are able to modify the above laws.
The first part of the presentation technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The second part deals with a critical analysis and with the indication of some research perspective concerning the challenging target of developing a biological-mathematical theory for the living matter.
The sequential steps to achieve the above outlined objectives are as follows:

(i) Integration of the concept of functional subsystems to reduce the complexity of large living systems within the approach of system biology;
(ii) Development of the mathematical kinetic and stochastic game theory for active particles;
(iii) Modelling the immune system as a large complex system;
(iv) Development of a multiscale analysis and modelling from genes to tissues.

References

N. Bellomo, Modelling Complex Living Systems-A Kinetic Theory and Stochastic Game Approach (Birkhauser, Boston, 2008).
N. Bellomo, N.K. Li, and P.K. Maini, On the foundations of cancer modelling: Selected topics, speculations, and perspectives, Mathematical Models and Methods in Applied Sciences, 18 (2008)
593-646.
N. Bellomo, C. Bianca and M. Delitala, Complexity analysis and mathematical tools towards the modelling of living systems, Physics of Life Review, 6 (2009) 144-175.

17 Marzo, 2010 15:00 in punto

Seminari di Cultura Matematica

Mean-variance Problems in Credit Risk Models

Claudio Fontana, Università degli Studi di Padova

Aula seminari III piano

This lecture deals with the development of new paradigms based on the mathematical methods of the kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by some biological functions which are able to modify the above laws.
The first part of the presentation technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The second part deals with a critical analysis and with the indication of some research perspective concerning the challenging target of developing a biological-mathematical theory for the living matter.
The sequential steps to achieve the above outlined objectives are as follows:

(i) Integration of the concept of functional subsystems to reduce the complexity of large living systems within the approach of system biology;
(ii) Development of the mathematical kinetic and stochastic game theory for active particles;
(iii) Modelling the immune system as a large complex system;
(iv) Development of a multiscale analysis and modelling from genes to tissues.

References

N. Bellomo, Modelling Complex Living Systems-A Kinetic Theory and Stochastic Game Approach (Birkhauser, Boston, 2008).
N. Bellomo, N.K. Li, and P.K. Maini, On the foundations of cancer modelling: Selected topics, speculations, and perspectives, Mathematical Models and Methods in Applied Sciences, 18 (2008)
593-646.
N. Bellomo, C. Bianca and M. Delitala, Complexity analysis and mathematical tools towards the modelling of living systems, Physics of Life Review, 6 (2009) 144-175.

15 Marzo, 2010 15:00

Sezione di Geometria, Algebra e loro applicazioni

Una survey sui sistemi splicing

Clelia De Felice, Università di Salerno

Aula seminari III piano

abstract

abstract

Abstract
Recombinant DNA (rDNA) is a general term which refers to the DNA resulting from the process of combining a piece of DNA, with another strand of DNA.
In 1987 Tom Head pioneered a language-theoretic approach for studying recombinant DNA. He introduced the splicing systems, abstract models which are a formal counterpart of the DNA
recombination under the action of restriction and ligase enzymes (gene splicing).
In spite of a vast literature on splicing systems,
briefly surveyed here, a few problems related to their computational power are still open.
We intend to evidence how classical techniques and concepts in automata theory are a legitimate tool for investigating some of these problems.

15 Marzo, 2010 11:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Constrained Mixtures Models for Blood Vessels

Luca Cardamone, Sector of Functional Analysis and Applications, SISSA, Trieste

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

abstract

abstract

Research on growth and remodeling of blood vessels focuses on the characterization of the
mechanical behavior of arteries and of their response to altered chemo-mechanical environment
resembling either pathological situations, like hypertension, flow disturbances and Marfan
syndrome, or physiological development and aging
A microstructurally based constitutive models is proposed, accounting for the principal structural constituents of the arterial wall (collagen fibers, elastin and smooth muscles cells) and for
muscle activity. The theory of constrained mixtures is employed to relate the kinematics of the constituents to the motion of the vessel. The growth and remodeling formulation allows the single constituents to be continuously deposited and removed with rates that are function of the stress state of the vessel, of the stress rate over the cardiac cycle as well of the concentration of some chemical agents. The constituents are assumed to be deposited with different prestretches in the in-vivo configuration and this allows the evolution of the unloaded length during the growth and
remodeling process according to the deposition and removal of new constituents. Several results are presented concerning arterial response to quasi-static and dynamic perturbation of the
hemodynamics, aging, and development.

10 Marzo, 2010 12:15

Seminari di Cultura Matematica

Ricordo di Carlo Cercignani. Interventi di Piercesare Secchi e Luigi Galgani e proiezione del film “Ludwig Boltzmann, il genio del disordine” di L.Agapito

Aula B21 (Edificio 14 Nave )

Research on growth and remodeling of blood vessels focuses on the characterization of the
mechanical behavior of arteries and of their response to altered chemo-mechanical environment
resembling either pathological situations, like hypertension, flow disturbances and Marfan
syndrome, or physiological development and aging
A microstructurally based constitutive models is proposed, accounting for the principal structural constituents of the arterial wall (collagen fibers, elastin and smooth muscles cells) and for
muscle activity. The theory of constrained mixtures is employed to relate the kinematics of the constituents to the motion of the vessel. The growth and remodeling formulation allows the single constituents to be continuously deposited and removed with rates that are function of the stress state of the vessel, of the stress rate over the cardiac cycle as well of the concentration of some chemical agents. The constituents are assumed to be deposited with different prestretches in the in-vivo configuration and this allows the evolution of the unloaded length during the growth and
remodeling process according to the deposition and removal of new constituents. Several results are presented concerning arterial response to quasi-static and dynamic perturbation of the
hemodynamics, aging, and development.

9 Marzo, 2010 14:30 in punto

Seminari di Cultura Matematica

Two grid discretization scheme for nonlinear eigenvalues problems

Rachida Chakir, Laboratoire Jacques-Louis Lions, Paris, France

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

abstract

abstract

Many mathematical models in science and engineering give rise to nonlinear eigenvalue problems. Let us mention for instance the Gross-Pitaevskii equation describing the steady-states of Bose-Einstein condensates, or the Hartree-Fock and Kohn-Sham equations used to calculate ground state (electronic structures of molecular systems in quantum chemistry and materials science.

Since solving these problems is quite expensive, we propose new methods to simplify this computation. To understand the effect of this simplification on the accuracy of the result, we need some a priori errors estimates of the discretization for variational approximations of the ground state energy, eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems. These results were used for the implementation and the numerical analysis of
two-grid discretization schemes for nonlinear eigenvalue problem.

5 Marzo, 2010 15:00

Sezione di Probabilità Quantistica

Mourre theory and unitary operators

Claudio Fernandez, Pontifcia Universidad Catolica de Chile

Aula seminari III piano

abstract

abstract

We show how to use a unitary Mourre method to prove the absence of singular continuous spectrum for abstract unitary operators. As in the self-adjoint case, one can also control the possible eigenvalues. Finally, we show how to apply the theory in several specifc examples, including quantum mechanical systems.