Head of Dept: Prof. Giulio Magli
Vice-Head of Dept: Prof. Gabriele Grillo
Department Manager: Dr.ssa Franca Di Censo

### Seminars

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### Upcoming seminars

• Strategic Use of Seller Information in Private-Value First-Price Auctions
Shmuel Zamir, The Hebrew University
lunedì 22 ottobre 2018 alle ore 11:00, Politecnico di Milano, Dipartimento di Matematica, Sala del Consiglio 7° piano
• Modelli statistici per comprendere dai dati la complessità del reale
Alessandra Menafoglio, Dipartimento di Matematica, Politecnico di Milano
mercoledì 24 ottobre 2018 alle ore 15:00, Aula B.2.4
• Material constitutive modeling and parameter calibration: towards identification of representative material properties
lunedì 29 ottobre 2018 alle ore 14:00, aula Saleri VI piano
• Predator-prey model with competition, the emergence of territoriality
Alessandro Zilio, Université Paris Diderot
martedì 30 ottobre 2018 alle ore 15:15, Aula seminari 3° piano
• An overview of some mathematical and computational problems in Network Science
Michele Benzi, Scuola Normale Superiore, Pisa
giovedì 22 novembre 2018 alle ore 14:00,  Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
• BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES
Shigefumi Mori, Kyoto University Institute of Advanced Study
lunedì 26 novembre 2018 alle ore 16:30, Aula Chisini, Diparimento di Matematica, Via C. Saldini 50

### Past Seminars

• Elastic waves in soft tissues: inverse analysis, experiments, simulations, validation
Michel Destrade, Chair of Applied Mathematics at NUI Galway
giovedì 18 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
Biological soft tissues and soft gels are difficult to study and model mathematically. Bioengineers often see them as engineering materials and try to evaluate their mechanical properties with standard testing protocols, such as tensile testing, simple shear, torsion, etc. These processes are destructive for tissues, as a sample is taken out of the body and placed in a device. The resulting measured parameters and models are expected to be very different from their in vivo counterparts. To test soft tissues properly, non¬-destructively, and non¬-invasively, we can rely on elastic waves. We can study the influence of pre¬stress on their speed and obtain the nonlinear elastic parameter by inverse analysis. This idea forms the basis of the theory of acousto-¬elasticity, which can be dated back to early works of Brillouin, and has been used successfully in the past for “hard” elastic solids such as rocks and metals. With this talk, we will explore the extension of acousto-¬elasticity to “soft” elastic solids, which can be subjected to large deformations in service. We will look at theoretical, numerical, experimental, and even clinical results, generated in particular on gels, brain, breast, and skin.

Contact: pasquale.ciarletta@polimi.it
• La freccia del tempo: una direzione per lo studio della termodinamica
Giovanni Valente, Dipartimento di Matematica, Politecnico di Milano
mercoledì 17 ottobre 2018 alle ore 14:45 precise, Sala Consiglio VII piano
ABSTRACT
Ovunque nel mondo fisico che ci circonda osserviamo fenomeni irreversibili, che accadono in una direzione temporale ma non in quella opposta. Tale asimmetria è proprio ciò che ci permette di distinguere il passato dal futuro. Tuttavia, le leggi che governano la dinamica dei costituenti microscopici della materia risultano simmetriche rispetto alla direzione del tempo, e come tali appaiono in conflitto con l’irreversibilità osservata a livello macroscopico. Si pone così il problema filosofico della freccia del tempo. In questa presentazione, inseguiremo la freccia del tempo attraverso lo sviluppo di teorie fisiche come la termodinamica e la meccanica statistica.
• On the error bound in the normal approximation for Jack measures
Louis H. Y. Chen, National University of Singapore
venerdì 12 ottobre 2018 alle ore 14:00 precise, Aula Seminari III piano
ABSTRACT
The one?parameter family of Jack_? measures on partitions of n is an important discrete analog of Dyson’s ? ensembles of random matrix theory.  Except for ? = ½, 1, 2, which have group theoretic interpretations, the Jack_ ? measure is difficult to analyze. In the case ? = 1, the Jack measure agrees with the Plancherel measure on the irreducible representations of the
symmetric group S_n, parametrized by the partitions of n.  The normal approximation for the
character ratio evaluated at the transposition (12) under the Plancherel measure has been well
studied, notably by Fulman (2005, 2006) and Shao and Su (2006).  A generalization of the
character ratio under the Jack_ ? measure has also been studied by Fulman (2004, 2006) and
Fulman and Goldstein (2011).  In this talk, we present results on both uniform and non?uniform
error bounds on the normal approximation for the Jack_ ? measure for ? > 0.   Our results
improve those in the literature and come very close to solving a conjecture of Fulman (2004).
Our proofs use Stein’s method and zero?bias coupling. This talk is based on joint work with Le
Van Thanh.
• Statistical modeling and monitoring of product and process quality in Additive Manufacturing: opportunities and challenges
Bianca Maria Colosimo, Dipartimento di Meccanica, Politecnico di Milano
giovedì 11 ottobre 2018 alle ore 14:00,  Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
Additive Manufacturing (AM), commonly known as three-dimensional printing, is widely recognized as a disruptive technology, and has the potential to fundamentally change the nature of future manufacturing. Building products layer-by-layer, AM represents a paradigm shift in manufacturing with many industrial applications. It enables production of huge varieties of customized products with considerable geometric complexity, and the same time, with extended capabilities and functional performances.
Despite tremendous enthusiasm, AM faces major research challenges for widespread adoption of this innovative technology. Specifically, addressing the unique challenges associated with quality engineering of AM processes is crucial to the eventual success of AM. This talk presents an overview of quality-related issues for AM processes and products, focusing on opportunities and challenges in quality inspection, monitoring, control.

Contact: piercesare.secchi@polimi.it
• Caputo Evolution Equations with time-nonlocal initial condition
Lorenzo Toniazzi, University of Warwick
martedì 9 ottobre 2018 alle ore 15:15, Aula Seminari 3° piano
ABSTRACT
Consider the Caputo evolution equation (EE) $\partial_t^\beta u =\Delta u$ with initial condition $\phi$ on $\{0\}\times\mathbb R^d$, $\beta\in(0,1)$. As it is well known, the solution reads $u(t,x)=\mathbf E_x[\phi(B_{E_t})]$. Here $B_t$ is a Brownian motion and the independent time-change $E_t$ is an inverse $\beta$-stable subordinator. The fractional kinetic $B_{E_t}$ is a popular model for subdiffusion \cite{Meerschaert2012}, with remarkable universality properties \cite{BC11,Hai18}.\
We substitute the Caputo fractional derivative $\partial_t^\beta$ with the Marchaud derivative. This results in a natural extension of the Caputo EE featuring a \emph{time-nonlocal initial condition} $\phi$ on $(-\infty,0]\times\mathbb R^d$. We derive the new stochastic representation for the solution, namely $u(t,x)=\mathbf E_x[\phi(-W_t,B_{E_t})]$. This stochastic representation has a pleasing interpretation due to the non-obvious presence of $W_t$, elucidating the notion of time-nonlocal initial conditions. Here $W_t$ denotes the waiting/trapping time of the fractional kinetic $B_{E_t}$. We discuss classical-wellposedness \cite{T18}, and time permitting weak-wellposedness \cite{DYZ17,DTZ18} for the respective extensions of Caputo-type EEs (such as in \cite{chen,HKT17}).

Bibliography:

Barlow, \u Cern\’y (2011). Probability theory and related fields, 149.3-4: 639-673.

Chen, Kim, Kumagai, Wang (2017). arXiv:1708.05863.

Du, Toniazzi, Zhou (2018). Preprint. Submitted in Sept. 2018.

Du, Yang, Zhou (2017). Discrete and continuous dynamical systems series B, Vol 22, n. 2.

Hairer, Iyer, Koralov, Novikov, Pajor-Gyulai (2018). The Annals of Probability, 46(2), 897-955.

Hern\’andez-Hern\’andez, Kolokoltsov, Toniazzi (2017). Chaos, Solitons \& Fractals, 102, 184-196.

Meerschaert, Sikorskii (2012). De Gruyter Studies in Mathematics, Book 43.

Toniazzi (2018). To appear in: Journal of Mathematical Analysis and Applications. arXiv:1805.02464.
• Computational Prediction of Blood Damage
Marek Behr, Chair for Computational Analysis of Technical Systems Faculty of Mechanical Engineering, RWTH Aachen
lunedì 1 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
Modeling and computational analysis play an increasingly important role in bioengineering, particularly in the design of implantable ventricular assist devices (VAD) and other blood-handling devices. Numerical simulation of blood flow and associated physiological phenomena has the potential to shorten the design cycle and give the designers important insights into causes of blood damage and suboptimal performance. A set of modeling techniques is presented which are based on stabilized space-time finite element formulation of the Navier-Stokes equations. Alternate methods that represent the rotating components in an averaged sense using a rotating frame of reference will be discussed. In order to obtain quantitative hemolysis prediction, cumulative tensor-based measures of strain experienced by individual blood cells must be developed; red blood cells under shear can be modeled as deforming droplets, and their deformation tracked throughout the flow volume. The methods are applied to a simplified rotary blood pump, which is currently a subject of an inter-laboratory round-robin study.

Contact: luca.dede@polimi.it
• Space-Time Adaptive THMC Simulation with Hybrid FEM-FVM Methods Applied to CO2 Geo-Sequestration
Stephan Matthai, Peter Cook Centre for CCS, The University of Melbourne at Parkville, VIC 3010, Australia
giovedì 27 settembre 2018 alle ore 14:00, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
Modelling the highly localised plume spreading during CO2 geo-sequestration using conventional synchronous time-driven simulation (TDS) has been impeded by the stringent Courant-Fredrich-Levy (CFL) condition, which leads to an excessive number of time steps and consequently long computing times. To overcome this problem, we present an asynchronous discrete event simulation (DES) scheme based on local time stepping criteria, specifically developed for the CSMP++ CO2 geo-sequestration simulator. The proposed DES method is applied to a complex and heterogeneous heuristic CO2 storage model, where it proves that DES is able to concentrate the computational effort on the active regions where fast CO2 flow occurs. As a result, the execution time for the modelling of a 5-year injection is significantly reduced from over 91 days (estimated for TDS) to only 0.5 days. This dramatic speedup facilitates the modelling of CO2 injection and long-term plume spreading behaviours at the scales of field storage sites. The benefits of the new method scale with the level of refinement of geologic detail and include a distinct increase in the level of physical realism of the simulations because fast and slow events are equally well resolved in contrast with TDS implicit schemes which are robust, but fail to resolve the events captured by the new asynchronous scheme.

Contact: paolo.zunino@polimi.it
• Coupled problems in Environmental and medical applications
Hiroshi Suito, Mathematical Science Group, Advanced Institute for Materials Research, Tohoku University, Japan
martedì 18 settembre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
Fluid–structure interaction (FSI) problems arise under various circumstances including environmental and medical applications. This talk firstly presents numerical simulations for motions of aquatic plants interacting with surrounding fluids using immersed boundary method (IBM) with finite-difference approximation on fixed meshes. We also present simulations for blood flows in aorta solved on finite-element meshes moving with the vessel wall. Aortic aneurysms and aortic coarctations are considered here. Geometrical characteristics such as curvature and torsion help us to understand the essential difference for morphologies among patients. The latter problem is followed by a machine learning approach by which wall shear stress and oscillatory shear index distributions are estimated using geometrical characteristics of the vessels.

Contact: alfio.quarteroni@polimi.it