19 Ottobre, 2012 14:00

Seminari PhD di Equazioni Differenziali

Some generalizations of the Cahn-Hilliard equation

Alain Miranville, Université de Poitiers

Aula Seminari III piano

17 Ottobre, 2012 15:00

Seminari FDS

5° ciclo di seminari FDS
Archeoastronomia: la scienza delle stelle e delle pietre

Giulio Magli, Politecnico di Milano

Aula De Donato (S01) - Piazza Leonardo Da Vinci, 32 - Milano

abstract

abstract

L'Archeoastronomia studia gli allineamenti astronomici presenti nel progetto degli antichi monumenti, e quindi il rapporto che i loro costruttori avevano con il cielo e le stelle. Si tratta di una scienza giovane che opera con moderni strumenti di rilievo e analisi dati, ma in stretta connessione con l'archeologia. Se usata con le dovute cautele, può fornire nuove, affascinanti informazioni su tanti enigmatici monumenti del passato, quali ad esempio Machu Picchu o le grandi piramidi di Giza.

15 Ottobre, 2012 16:30

Lezioni Leonardesche

SYMMETRY, STATISTICAL MECHANICS AND RANDOM MATRICES

THOMAS SPENCER, Institute for Advanced Study, Princeton

Università di Milano, Dipartimento di Matematica, Via Saldini

abstract

abstract

The theory of random matrices appears in many parts of mathematics such as probability, statistics, quantum chaos, number theory and the spectral theory of random Schrödinger operators. This lecture will give a brief introduction to the history and conjectures of this subject. We show how certain models of statistical mechanics provide a dual representation for spectral problems in random matrix theory. This representation enables one to obtain numerous identities arising from symmetry and to apply new
tools of analysis and phase transitions. Ordered and disordered phases correspond to different spectral types and time evolution of a random matrix Hamiltonian. A particular statistical mechanics model is equivalent to a history dependent random walk which prefers to jump to vertices it has visited in the past. The phase transition for this process is reflected in a change of the long time behavior of the walk.

15 Ottobre, 2012 11:00 oclock

Lezioni Leonardesche

Mesoscopic origins of cell shape changes during tissue morphogenesis

Pierre-François Lenne, Institut de Biologie du Développement de Marseille-Luminy

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

abstract

abstract

Cortical forces drive a variety of cell shape changes and cell movements during tissue morphogenesis [1,2]. While the molecular components underlying these forces have been largely identified, how they assemble and spatially and temporally organize at cell surfaces to promote cell shape changes in developing tissues are open questions. I will present how cortical forces emerge from the dynamics of actomyosin networks in interactions with adhesion complexes during early tissue morphogenesis. I will focus on the elongation of Drosophila melanogaster embryos, which results from polarized cell neighbour exchanges. I will describe the pulsatile nature of force generation and the role of actomyosin flows in this process [3] and show how E-cadherin organizes at cell surfaces to ensure the mechanical stability of the epithelium [4].

1 Rauzi, M., Verant, P., Lecuit, T., Lenne, P.F., 2008. Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis. Nature Cell Biol 10, 1401-U1457.

2 Rauzi, M., Lenne, P.F., 2011. Cortical forces in cell shape changes and tissue morphogenesis. Curr Top Dev Biol 95, 93-144.

3 Rauzi, M., Lenne, P.F., Lecuit, T., 2010. Planar polarized actomyosin contractile flows control epithelial junction remodelling. Nature 468, 1110-1114.

4 Truong Quang, B. A., Markova, O. and Lenne, P.F. 2012. Regulation and control of the fine-grained organization of E-cadherin in an epithelium revealed by quantitative super-resolved microscopy, submitted.

8 Ottobre, 2012 12:15

Sezione di Probabilità Quantistica

Ehrenfest-type theorems for open quantum systems

Carlos Mora, Departamento de Ingeniería Matemática - Universidad de Concepción

Aula seminari III piano

Cortical forces drive a variety of cell shape changes and cell movements during tissue morphogenesis [1,2]. While the molecular components underlying these forces have been largely identified, how they assemble and spatially and temporally organize at cell surfaces to promote cell shape changes in developing tissues are open questions. I will present how cortical forces emerge from the dynamics of actomyosin networks in interactions with adhesion complexes during early tissue morphogenesis. I will focus on the elongation of Drosophila melanogaster embryos, which results from polarized cell neighbour exchanges. I will describe the pulsatile nature of force generation and the role of actomyosin flows in this process [3] and show how E-cadherin organizes at cell surfaces to ensure the mechanical stability of the epithelium [4].

1 Rauzi, M., Verant, P., Lecuit, T., Lenne, P.F., 2008. Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis. Nature Cell Biol 10, 1401-U1457.

2 Rauzi, M., Lenne, P.F., 2011. Cortical forces in cell shape changes and tissue morphogenesis. Curr Top Dev Biol 95, 93-144.

3 Rauzi, M., Lenne, P.F., Lecuit, T., 2010. Planar polarized actomyosin contractile flows control epithelial junction remodelling. Nature 468, 1110-1114.

4 Truong Quang, B. A., Markova, O. and Lenne, P.F. 2012. Regulation and control of the fine-grained organization of E-cadherin in an epithelium revealed by quantitative super-resolved microscopy, submitted.

4 Ottobre, 2012 17:00

Seminario Matematico e Fisico di Milano

PHYSICS AND MATHEMATICS WITHOUT COORDINATES

WALTER NOLL, Carnegie Mellon University

Politecnico di Milano, Dipartimento di Matematica, Sala del Consiglio VII piano

abstract

abstract

I will start with a quote from the most famous scientist of the first half of the 20th century:Why were another seven years required for the construction of the general theory of relativity. The main reason is the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.

The following quote is from a far less famous scientist:
The approach of this treatise is conceptual, geometric, and uncompromisingly coordinate-free. In some of the literature tensors are still defined in terms of coordinates and their transformations. To me, this is like looking at shadows dancing on the wall rather than at reality itself.

The first quote is, of course, by Albert Einstein, and is cited in Section 1.2, (entitled spacetime with and without coordinates) of the book Gravitation by Misner, Thorne, and Wheeler. The second quote is by a far less famous scientist, namely me (Walter Noll) in part F of the Introduction to the Book entitled Finite-Dimensional Spaces, Algebra, Geometry, and Analysis.

I will discuss specific examples of coordinate-free treatments of the following topics:

1. Continuum Mechanics

2. Geometry

3. Special Relativity

4. General Relativity

5 Lineons versus Matrices

19 Settembre, 2012 11:00 oclock

Seminario Matematico e Fisico di Milano

Modelling of Single- and Multi-Phase Flow in Porous Media

Nicolas Schwenck, University of Stuttgar, Department of Hydromechanics and Modelling of Hydrosystems

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

abstract

abstract

Possible application areas of flow in porous media are CO2 storage in deep geological formations, gas and water management in fuel cells or hydraulic fracturing to improve the extraction of fossil fuels.
Simulating such practical engineering applications requires the development of conceptual models and efficient numerical methods.
Domains of interest can become quite large so that different aspects dominate different areas on different scales. Multi-scale and
multi-physics approaches including coupling of free- and porous-media flow are presented as well as recent examples.

19 Settembre, 2012 16:00 oclock

Seminario Matematico e Fisico di Milano

Functional average derivative regression

Juhyun Park, Lancaster University, UK

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

abstract

abstract

Single index model is studied in the framework of regression estimation involving functional data. The model combines low sensitivity to dimensional effects together with flexibility and easiness of interpretation. This paper proposes to construct
a functional adaptation of the average derivative method for estimating the functional index involved in the model. The convergence (with rate) of the estimator of the index is also derived based on asymptotic results on nonparametric functional derivatives estimation. In addition, it is shown that the nonlinear regression component of the model can be estimated at the standard univariate rate, being therefore insensitive to the infinite dimensionality of the data. These appealing theoretical features of the functional average derivative method are combined with easiness of implementation as shown through finite sample studies.

11 Settembre, 2012 14:00 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Approssimazioni ellittiche per il trasporto ramificato e il problema di Steiner

Filippo Santambrogio, Parigi Orsay

Aula seminari III piano

abstract

abstract

Il problema del trasporto ramificato si pone come la minimizzazione di un
funzionale concavo fra le misure vettoriali a divergenza fissata.
Presenterò un approssimazione tramite Gamma-convergenza usando funzionali
del tipo ( alpha<1) min eps^{-1} int |v|^ alpha + eps int |Dv|^2 : div v = f, v in H^1( Omega; R^N). Naturalmente gli esponenti giusti non sono né eps e eps^{-1} né alpha per |v|.
L utilità di quest approssimazione, oltre al legame evidente con l
approssimazione di altre energie concentrate su oggetti fini tramite
energie ellittiche, sta soprattutto nei progressi numerici che ha permesso
(ottenuti in collaborazione con E. Oudet, Grenoble). Inoltre, mandando
alpha a 0, è possibile ottenere un approssimazione del problema di
Steiner di connessione di lunghezza minima.

17 Luglio, 2012 14:30 oclock

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Two and three dimensional simulation of flow and particle transport in porous media

Matteo Icardi, Politecnico di Torino

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

abstract

abstract

The simulation of fluid flow and particle transport in porous media finds important
appli cations in many different fields, ranging from environmental and petroleum engineering to filtration and industrial chromatography. Different types of approaches exist and are generally classified by the length- and time-scales involved. Real industrial problems require the treatment of the porous medium as a continuum via the definition of porosity and permeability.
However, these parameters are very difficult to be determined and therefore a strategy to identify
them from pore-scale simulation is investigated here. When particles are characterized by nanoscopic size we are in presence of a so-called colloidal suspensions and also micro-scale forces and phenomena such as particle aggregation and deposition play an important role in determining the overall dispersivity of particles. Two and three dimensional geometries characterized by different degrees of complexity are created and studied using computational fluid dynamics codes. First the flow and particle transport around spherical grains arranged in a regular lattice is investigated. Then the analysis is extended to irregularly arranged spherical grains (of equal and different size) mimicking a realistic porous medium. Eventually geometries constituted by grains of realistic shapes are also considered. The accurate simulation of these systems require the solution of a number of mathematical and numerical challenges, related to multi-scale modelling, computational geometry, mesh processing and discretization techniques. Particular attention is devoted to the choice of adequate mathematical models and numerical strategies for the simulation of dispersed multiphase flows and to the assessment of
two meshing strategies: highly irregular body-fitted meshes versus regular cartesian-based
immersed-boundary approach.