ENG

  • Corso di Studi in Ingegneria Matematica, nuovo progetto di doppia laurea con EPFL
    Double degree Master Program between Politecnico di Milano and EPFL

Laboratory of Modeling and Scientific Computing
MOX
Laboratorio di Modellistica
e
Calcolo Scientifico
Laboratory of Mathematics Education and Scientific Experimentation
EFFEDIESSE
Laboratorio di Formazione
Matematica e di
Sperimentazione Didattica
differential equations at polimi
differential equations
at polimi
Quantitative Finance LAB
Laboratorio di
Finanza Quantitativa
Game Theory And Computation (Group)
Game Theory And Computation
(Group)


Prossimi Eventi

  • mag
    26
    gio
    2016
    Seminario
    26-05-2016, ore 14:00 precise Normal bundles of rational curves and applications
    Riccardo Re

    • SEMINARIO
    • Normal bundles of rational curves and applications
    • Riccardo Re, Università di Catania
    • Giovedì 26 maggio 2016 alle ore 14:00 precise, Aula Seminari del terzo piano
    • Abstract
      We introduce a new technique to effectively compute the normal bundle of a parametrized rational curve in a projective space. As an application we show how to construct counterexamples to the question, dating from the ’80s, whether the Hilbert space of rational curves with a given splitting type of the normal bundle is irreducible. If time permits, we will apply our results to monomial curves and give a formula for their Castelnuovo-Mumford regularity.

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • mag
    27
    ven
    2016
    Seminario
    27-05-2016, ore 10:00 Fractured rock multiphase flow: insights from a new generation of numeric models
    Stephan K. Matthai

    • SEMINARIO
    • Fractured rock multiphase flow: insights from a new generation of numeric models
    • Stephan K. Matthai, University of Melbourne, Australia (Chair of Reservoir Engineering)
    • Venerdì 27 maggio 2016 alle ore 10:00, Aula Seminari Saleri VI Piano Mox-Dipartimento di Matematica, Politecnico di Milano
    • Abstract
      Understanding multiphase fluid flow in Naturally Fractured Reservoirs (NFRs) is important because much of the world’s remaining oil reserves reside in rocks the flow through which is fracture dominated [1,2]. Geologically realistic models of NFRs are rare, probably due the multidisciplinary nature of the subject matter1. In stead, “effective” or “dual continua” models are abundant [e.g, 3,4]. Their averaging of fracture permeability and block size makes it
      impossible to compare simulated saturation patterns with observations on the real system. Yet, such comparisons are important because, in contrast to experiments, observability of a well-matched realistic numerical model is complete and one can incrementally turn component physics off until the behaviour of interest vanishes. This allows elimination of ambiguities in cause and effect chains. The physics underpinning multiphase flow in NFRs are reasonably well understood [5-7].Governing partial differential equations were presented already in the nineteen sixties [8] and
      have been modified relatively little since then. Computation and analysis of fracture-matrix ensemble behaviour, however, remain challenging due to scale-dependent nonlinear constitutive relationships, the couplings among the variables, order of magnitude variations in key material properties, and the scale-variant heterogeneity of the fractured porous matrix system. These nonlinear couplings imply that the knowledge of the component physics is
      insufficient to predict characteristic NFR states and responses. While these could in theory be revealed in the laboratory, experimental setup and monitoring appear too challenging [9]. This presentation is underpinned by computational results obtained on discrete fracture and matrix models (DFMs), discretized with unstructured grids, and flow simulated with a hybrid finite-element (FEM) – finite volume method (FVM) [10]. Using operator splitting, the fluid
      pressure equation is solved with the FEM and the hyperbolic transport equation including gravitational terms with the FVM [11]. Both methods are used in concert to compute nonlinear capillary diffusion in parallel with gravitational segregation of water and oil in zones of mixed saturation. All equations are solved with a parallelized algebraic multigrid method [12,13]. A decisive feature of the simulation approach is the treatment of the finite volumes at
      fracture-matrix interfaces [14,15]. New methods support saturation discontinuities and counter-current imbibition can therefore be modeled accurately using a Newton’s-method based implementation of the semi-analytical method proposed by VanDuijn and DeNeef [16]. All these methods are implemented in the CSMP++ application programmer interface [17,18]
      which will be introduced in the course of this presentation.
      Several simulation examples will be used to compare the behaviour of the DFMs with conventional dual continua simulations [19-21]. The results show that – beyond benchmarking and the demonstration of numerical methods on simple flow geometries – the decisive step necessary to gain the insights needed for accurate NFR prediction is the application of stateof-the-art simulation methods to relevant realistic non-trivial models. Once the controls on
      their behaviour have been clarified this way, simplifications can be made by elimination of non-influential features and processes. Idealised models only serve the purpose of component algorithm testing. Where analytic calculations can be applied, sophisticated numerical simulations are not needed.

      References
      1Physicists and applied mathematicians rarely have enough earth-science background to understand the
      heterogeneity and scale-variance of geological media; earth scientists lack the computational skills to build computer models.

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • mag
    31
    mar
    2016
    Seminario
    31-05-2016, ore 12:30 precise Models of dynamic trading with price impact
    Marko Hans Weber

    • SEMINARIO
    • Models of dynamic trading with price impact
    • Marko Hans Weber, Associate at JP Morgan in London
    • Martedì 31 maggio 2016 alle ore 12:30 precise, Aula Consiglio – VII Piano del Dipartimento di Matematica – Politecnico di Milano

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • giu
    01
    mer
    2016
    Seminario
    01-06-2016, ore 12:15 I repentini cambiamenti globali nella società umana
    Fiorenzo Galli

    • SEMINARIO
    • I repentini cambiamenti globali nella società umana
    • Fiorenzo Galli, Direttore Generale del Museo della Scienza e della Tecnologia di Milano
    • Mercoledì 1 giugno 2016 alle ore 12:15, Aula B21, ed. 14 (Nave), Campus Bonardi, via Bonardi 9, Milano

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • giu
    01
    mer
    2016
    Seminario
    01-06-2016, ore 14:30 Inference on covariance operators via concentration inequalities
    Adam Kashlak

    • SEMINARIO
    • Inference on covariance operators via concentration inequalities
    • Adam Kashlak , Cambridge University (PhD student of Faculty of Mathematics)
    • Mercoledì 1 giugno 2016 alle ore 14:30, Aula Seminari “Saleri” VI Piano Edificio 14, MOX-Dipartimento di Matematica, Politecnico di Milano
    • Abstract
      Inference on covariance operators is an important part of functional data analysis. Panaretos, Kraus, and Maddocks (2010) compare covariance operators for Gaussian process data. Pigoli, Aston, Dryden, and Secch.

      (2014) consider a variety of metrics over the space of covariance operators. In this talk, we propose a novel approach to the analysis of covariance operators making use of concentration inequalities. First, non-asymptotic confidence sets are constructed for such operators.
      Then, subsequent applications including a k sample test for equality of covariance, a functional data classifier, and an expectation-maximization style clustering algorithm are derived and tested on both simulated and phoneme data.

      contact: piercesare.secchi@polimi.it

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • giu
    01
    mer
    2016
    Seminario
    01-06-2016, ore 16:15 precise Poincare inequalities and the p-laplacian
    Scott Rodney

    • SEMINARIO
    • Poincare inequalities and the p-laplacian
    • Scott Rodney, Cape Breton University, Canada
    • Mercoledì 1 giugno 2016 alle ore 16:15 precise, Aula seminari 3° piano
    • Abstract
      In this talk I will explore a necessary and sufficient condition for the validity of a Poincar\’e – type inequality. This work will be presented in the context of the degenerate Sobolev spaces $W^{1,p}_Q(\Omega)$ and the Degenerate $p$-Laplacian given by $\Delta_p u = \text{Div} Q(x) \nabla u$ where $Q(x)$ is a non-negative definite $L^1_{\text{loc}}$ matrix valued function.

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • giu
    16
    gio
    2016
    Seminario
    16-06-2016, ore 10:30 Comparison of numerical methods for reactive transport modeling in porous media
    Thibault Faney

    • SEMINARIO
    • Comparison of numerical methods for reactive transport modeling in porous media
    • Thibault Faney , IFPEN, Parigi (Francia)
    • Giovedì 16 giugno 2016 alle ore 10:30, Sala Consiglio al VII Piano presso Dipartimento di Matematica, Politecnico di Milano
    • 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


    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • giu
    17
    ven
    2016
    Seminario
    17-06-2016, ore 15:00 A geometric approach to confidence regions and bands for functional parameters
    Matthew Reimher

    • SEMINARIO
    • A geometric approach to confidence regions and bands for functional parameters
    • Matthew Reimher, Department of Statistics at Penn State University.
    • Venerdì 17 giugno 2016 alle ore 15:00, Aula Seminari
    • 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

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568
  • giu
    22
    mer
    2016
    Seminario
    22-06-2016, ore 10:30 A two-phase solid\fluid model for dense granular flows including dilatancy effects
    Enrique Fernandez Nieto

    • SEMINARIO
    • A two-phase solid\fluid model for dense granular flows including dilatancy effects
    • Enrique Fernandez Nieto , IMUS – Universidad de Sevilla (Spagna)
    • Mercoledì 22 giugno 2016 alle ore 10:30, Aula Seminari “Saleri al VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano
    • 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

    Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568