11 Luglio, 2016 16:30

Lezioni Leonardesche

DIAGONAL FLOWS, JOININGS AND ARITHMETIC

Elon Lindenstrauss, Hebrew University of Jerusalem

Aula Chisini, via Saldini 50

abstract

abstract

Arithmetic quotients of algebraic groups such as the space of unit volume lattices in R^n can be studied fruitfully from many directions and contain deep and subtle arithmetic information. Homogeneous dynamics studies these spaces by considering the action of a subgroup of the algebraic group on such a quotient. Of particular interest is the action of multiparameter diagonal groups: these display remarkable rigidity properties that are absent in the context of one parameter diagonalizable group actions.

One aspect of this rigidity is joining rigidity: under suitable conditions, knowing that an orbit of a multiparameter diagonalizable group in a product of two arithmetic quotients is equidistributed in each one of these quotients individually implies joint equidistribution.

I would explain this phenomena as well as some arithmetic consequences.

1 Luglio, 2016 14:30

MOX Seminar

Understanding prion diseases: can we use data-driven statistical and computational models for differential and personalized diagnosis, prognosis, monitoring and treatment?

Alberto Bizzi, M.D. Professionista di Eccellenza, Neuroradiology Unit, Fondazione IRCCS Istituto NeurologicoCarlo B

Aula Seminari "Saleri" VI Piano MOX -Dipartimento di Matematica, POLITECNICO DI MILANO

abstract

abstract

Prion diseases or transmissible spongiform encephalopathies (TSEs) are a family of rare progressive neurodegenerative disorders caused by prions, a type of protein that can trigger normal proteins in the brain to fold abnormally. Prion diseases can affect sporadically both humans and animals, and are sometimes transmitted to humans by infected meat products. One of the most studied human prion desease is Creutzfeldt-Jakob disease (CJD) that accounts for more than 90% of all cases of sporadic prion diseases; it is commonly categorised into twelve subtypes that can be distinguished according to leading clinical signs, histological lesions, and molecular traits of the pathogenic prion protein. Prognosis, survival rate and therapy are different among sCJD subtypes. An accurate and timely classification of the subtype depends on careful clinical examination and early performance and interpretation of diagnostic tests, including electroencephalography, quantitative assessment of the surrogate markers 14-3-3, tau, and of the prion protein in the CSF, and Magnetic Resonance diffusion imaging. In clinical practice signal hyperintensity in the cortex and/or in the striatum on magnetic resonance (MR) diffusion-weighted images (DWI) is a marker of sCJD. MR diagnostic accuracy is greater than 90%, but the biophysical mechanisms underpinning the signal abnormality are unknown. The aim of this seminar is to illustrate the clinical, pathological and MR diffusion imaging biomarkers of sporadic CJD and make a call for development of new powerful data-driven statistical and computational models of prion disease that may open new avenues for understanding the complexity of clinical phenotypes. Mathematical models offer innovation potential by underpinning support systems for clinical and drug-development applications. They may enable “precision Medicine” by providing differential and personalized diagnosis, fine-grained staging, and personalised prognosis.

contact: simone.vantini@polimi.it

30 Giugno, 2016 11:30

MOX Seminar

Statistical assessment and calibration of numerical models with functional response

Nicholas Tarabelloni, Lab MOX - Dipartimento di Matematica, Politecnico di Milano

Aula Seminari "Saleri" VI Piano MOX -Dipartimento di Matematica, POLITECNICO DI MILANO

abstract

abstract

Thanks to the rise in computational resources that are increasingly becoming available, numerical models of all fields are experiencing a growth of complexity and realism. This is especially the case for mathematical models dealing with biomedical phenomena, whose goal is to describe the behaviour of physiological processes of human beings. To this aim, it is now possible to combine them with diverse and complex data coming from real experiments, hospital collections and surveys in order to enhance the modelling. This is of extreme importance for the development of a personalised medicine practice able to instruct clinicians and recommend treatments for targeted patients.
Within this context, we will focus on the problem of assessing the quality and calibrating numerical models producing functional observations, i.e. quantity of interest that can naturally be thought as continuously depending on some variable (e.g. time). To this aim, we will present a general statistical framework based on depth measures and spatial quantiles for multi-dimensional data which is able to naturally and non-parametrically exploit a whole collection of real measurements, to drive the calibration towards multiple possible goals and finally to enhance the agreement between simulated data and real data. We will show an application to the calibration of ODE and PDE based numerical models for the simulation of physiological ECG traces to a dataset of hospital recordings.

contact: christian.vergara@polimi.it

23 Giugno, 2016 12:00

MOX Seminar

Simulation and control of moving-contact-line problems

Ivan Fumagalli, N.A.

Aula Seminari

abstract

abstract

Free surface problems are ubiquitous in fluid dynamics applications: e.g., we can think of waves on a liquid, capillary rising, droplets movement. Simulating such phenomena is a challenging issue from the numerics, analytics, and even modeling point of view, in particular when the contact line (the three-phase interface among the wall, the fluid, and the medium beyond the free surface) is allowed to move. Indeed, different models for a moving contact line are proposed in the literature, but each of them brings some hindrance to the analysis and the discretization of the problem.
In the present talk, a time-dependent free-surface Navier-Stokes problem with moving contact line is addressed. A variational derivation of the contact line model justifies it, and proper spaces are introduced to have it mathematically well-defined. A discussion on its discretization via ALE is then carried on, showing how numerical results and energy estimates drove to the choice of piecewise linear finite elements in both pressure and velocity. A control problem is, then, introduced, having the free-surface problem as a constraint, and an optimization procedure is designed for its solution, based on a two-level Lagrangian approach.

contact: paola.antonietti@polimi.it

22 Giugno, 2016 10:30

MOX Seminar

A two-phase solid/fluid model for dense granular flows including dilatancy effects

Enrique Fernandez Nieto, IMUS - Universidad de Sevilla (Spagna)

Aula Seminari "Saleri" VI Piano MOX -Dipartimento di Matematica, POLITECNICO DI MILANO

abstract

abstract

We present in this talk a two-phase two-thin-layer model for fluidized debris flows that takes into account dilatancy effects. It describes the velocity of both the solid and the fluid phases, the compression/dilatation of the granular media and its interaction with the pore fluid pressure (see [Bouchut et al., 2016]).

The model is derived from a 3D two-phase model proposed by [Jackson, 2000]. This system has 5 unknowns: the solid and fluid velocities, the solid and fluid pressures and the solid volume fraction. As a result, an additional equation inside the mixture is necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been developed on the basis of Jackson’s work [Bouchut et al., 2015]. In particular, in [Pitman-Le, 2005] authors replaced this closure simply by imposing an extra boundary condition at the surface of the flow. When making a shallow expansion, this condition can be considered as a closure condition. However, the corresponding model cannot account for a dissipative energy balance. We present in this talk (see [Bouchut et al., 2016]), an approach to correctly deal with the thermodynamics of Jackson’s model by closing the mixture equations by a weak compressibility relation following [Roux-Radjai, 1998]. This relation implies that the occurrence of dilation or contraction of the granular material in the model depends on whether the solid volume fraction is respectively higher or lower than a critical value. When dilation occurs, the fluid is sucked into the granular material, the pore pressure decreases and the friction force on the granular phase increases. On the contrary, in the case of contraction, the fluid is expelled from the mixture, the pore pressure increases and the friction force diminishes. To account for this transfer of fluid into and out of the mixture, a two-layer model is proposed with a fluid layer on top of the two-phase mixture layer. Mass and momentum conservation are satisfied for the two phases, and mass and momentum are transferred between the two layers. A thin-layer approximation is used to derive average equations. Special attention is paid to the drag friction terms that are responsible for the transfer of momentum between the two phases and for the appearance of an excess pore pressure with respect to the hydrostatic pressure.
Finally, we present several numerical tests by comparing with the models proposed in [Pailha-Pouliquen, 2009] and [Iverson-George, 2014], and with experimental data for the case of uniform flows.

References:
[Bouchut et al., 2015] F. Bouchut, E.D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina, A two-phase shallow debris flow model with energy balance, ESAIM: Math. Modelling Num. Anal., 49, 101-140 (2015).

[Bouchut et al., 2016] F. Bouchut, E. D. Fernandez-Nieto, A. Mangeney, G. Narbona-Reina, A two-phase two-layer model for fluidized granular flows with dilatancy effects, J. Fluid Mech., submitted (2016).

[Iverson-George, 2014] R. M. Iverson and D. L. George. A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis. Proc. R. Soc. A, 470:20130819, (2014).

[Jackson, 2000] R. Jackson, The Dynamics of Fluidized Particles, Cambridges Monographs on Mechanics (2000).

[Pailha-Pouliquen, 2009] M. Pailha and O. Pouliquen. A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech., 633:115–135, (2009)

[Pitman-Le, 2005] E.B. Pitman, L. Le, A two-fluid model for avalanche and debris flows, Phil.Trans. R. Soc. A, 363, 1573-1601 (2005).

[Roux-Radjai, 1998] S. Roux, F. Radjai, Texture-dependent rigid plastic behaviour, Proceedings: Physics of Dry Granular Media, September 1997. (eds. H. J. Herrmann et al.). Kluwer. Carge?se, France, 305-311 (1998).

contatto: luca.bonaventura@polimi.it

17 Giugno, 2016 15:00

MOX Seminar

A Geometric Approach to Confidence Regions and Bands for Functional Parameters

Matthew Reimher, Department of Statistics at Penn State University.

Aula Seminari "Saleri" VI Piano MOX -Dipartimento di Matematica, POLITECNICO DI MILANO

abstract

abstract

Functional data analysis, FDA, is now a well established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which have received relatively little attention. One of these is the systematic development of techniques for constructing confidence regions for functional parameters. I will present new work that takes a geometric approach to developing, understanding, and visualizing such regions. Simulations and an application to Fractional Anisotropy will also be presented.

contact: piercesare.secchi@polimi.it

16 Giugno, 2016 10:30

MOX Seminar

Comparison of numerical methods for reactive transport modeling in porous media

Thibault Faney, IFPEN, Parigi (Francia)

Sala Consiglio al VII Piano presso Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

Reactive transport numerical models [1] are used to predict temperature and pressure variations, brine and gas phases displacement, and chemical effects of gas-water-rock interactions in porous media. One of the main challenges of these models is to accurately represent the coupling between transport phenomena and mass transfer occurring in sub-surface porous media. In a previous work [2], we have introduced a new mathematical formulation to handle the phase appearance and disappearance issues associated with multi-component, multi-phase flow combined with stoichiometric mass transfer. In this work, we compare our formulation with an implementation of a splitting scheme between flow, transport and chemical reactions [3] on a larger range of benchmark problems associated with complex chemical equilibria. Both formulations are implemented in a three-dimensional multi-phase flow code using the HPC numerical framework Arcane [4]. We discuss the gain in robustness, performance and accuracy for the fully implicit method relative to the more traditional splitting algorithm.

References:
[1] C.I. Steefel et al., Reactive transport modeling: An essential tool and a new research approach for the Earth sciences, Earth and Planetary Science Letters, 240, 539–55, 2005.
[2] T.Faney, A.Michel and Q.L.Nguyen, A mathematical formulation for reactive transport in porous media adapted to CO2 sequestration, SIAM 2015 Computational Geosciences.
[3] C. de Dieuleveult, J.Erhel and M.Kern, A global strategy for solving reactive transport equations, Journal of Computational Physics, 228 6395-6410, 2009.
[4] Grospellier, G. et al., The Arcane Development Framework, POOSC’09, Genova, Italy, 2009

contatto: luca.bonaventura@polimi.it

10 Giugno, 2016 10:00 oclock

Sezione di Geometria, Algebra e loro applicazioni

Un sotto-monoide degli endomorfismi invertibili del monoide libero.

Christian Choffrut, Université de Paris-Diderot - Paris 7

Aula seminari-III piano

abstract

abstract

Motivati dalla sfida di descrivere tutte le soluzioni di una equazione nel
monoide libero, abbiamo studiato il sottomonoide proprio N del monoide
di tutti gli endomorfismi invertibili del monoide libero generati dai morfismi f del seguente tipo: siano a, b due lettere arbitrarie del monoide libero,f mappa a su ba e lascia tutte le altre lettere invarianti, per esempio: f(cabba) = cbabbba.
Dirò rapidamente come questa problematica si inserisce nella teoria delle
equazioni del monoide libero. Ricorderò i risultati anteriori delle letteratura. Presentrò i nostri risultati: una presentazione (“monoid presentation”) di N, una procedura che risolve il problema dell’appartenanza di un morfismo ad N e la soluzione del problema della parola (“word problem”) in N.

8 Giugno, 2016 16:15 oclock

Sezione di Analisi

Multiple Neumann solutions of some second order ODEs with indefinite weight

Maurizio Garrione, Università degli Studi di Milano-Bicocca

Aula seminari 3° piano

abstract

abstract

We consider the Neumann problem associated with the scalar second order ODE u''+q(t)g(u)=0, where q is a sign-changing weight and g is a positive function satisfying sublinear growth assumptions. Through the use of a suitable change of variables, the problem is led back to the study of Neumann solutions for a forced perturbation of an autonomous planar system, which we study by means of a shooting technique. We illustrate results of existence and multiplicity of solutions depending in a quite precise way on mean properties of the weight.

1 Giugno, 2016 12:15

Seminari di Cultura Matematica

I repentini cambiamenti globali nella società umana

Fiorenzo Galli, Direttore Generale del Museo della Scienza e della Tecnologia di Milano

Aula B21, ed. 14 (Nave), Campus Bonardi, via Bonardi 9, Milano

We consider the Neumann problem associated with the scalar second order ODE u''+q(t)g(u)=0, where q is a sign-changing weight and g is a positive function satisfying sublinear growth assumptions. Through the use of a suitable change of variables, the problem is led back to the study of Neumann solutions for a forced perturbation of an autonomous planar system, which we study by means of a shooting technique. We illustrate results of existence and multiplicity of solutions depending in a quite precise way on mean properties of the weight.