### Seminari

### Prossimi Seminari

**Dealing with unreliable computing platforms at extreme scale**

Luc Giraud, INRIA (Inria Bordeaux – Sud-Ouest)

mercoledì 23 gennaio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Poroelasticity: Discretizations and fast solvers based on geometric multigrid methods**

Francisco José Gaspar Lorenz, Department of Applied Mathematics -Zaragoza University – Spain

giovedì 31 gennaio 2019 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Application of Polyconvexity and multivariable convexity of energy potentials in nonlinear solid mechanics**

Javier Bonet, University of Greenwich

giovedì 14 febbraio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**Illuminazione, visione e opere d’arte: il punto di vista del fisico**

Farini Alessandro, Istituto Nazionale di Ottica, CNR, Firenze

mercoledì 21 novembre 2018 alle ore 15:00, Sala Consiglio VII pianoABSTRACTQuale è il legame tra le onde elettromagnetiche appartenenti a quella parte dello spettro che chiamiamo visibile e la nostra visione? L’interpretazione che il nostro occhio e il nostro cervello forniscono della realtà circostante è così complessa che è necessario tenere conto di tantissimi fattori per comprendere ad esempio perché vediamo alcuni colori o percepiamo il contrasto in un certo modo. Uno degli esempi più affascinanti è sicuramente quello delle opere pittoriche, dove spesso ci rendiamo conto che l’artista dimostra una comprensione, almeno

implicita, del funzionamento della nostra percezione veramente interessante. Questi aspetti saranno mostrati con alcuni esperimenti dal vivo che vogliono rendere più chiari i concetti espressi.**Mixed finite elements for next-generation atmospheric models**

Tommaso Benacchio , MOX, Politecnico di Milano

martedì 20 novembre 2018 alle ore 10:30, aula Saleri VI pianoABSTRACTThe terrestrial atmosphere provides the arena for physical processes on multiple spatial and temporal scales. Numerical methods used to solve the governing hyperbolic models must simulate features of meteorological interest accurately while handling efficiently fast and less significant wavelike phenomena. Tight production constraints in operational numerical weather prediction (NWP) drive the development of scalable dynamical cores to keep up with computing architectures that increasingly rely on massively parallel systems for performance.

While spectral transform and grid-point models have traditionally held sway in operational NWP and climate prediction, finite element methods have been gaining ground in recent years, due to their straightforward accuracy-tuning capabilities and flexibility towards unstructured grid arrangements in a context of deteriorating parallel performance of legacy codes. The seminar will present a mixed finite element-based dynamical core for the solution of the nonhydrostatic compressible equations under gravity. The mimetic spatial discretization reproduces continuous vector identities at the discrete level and ensures desirable properties such as pointwise mass conservation. Placement of the thermodynamic variable in a horizontally discontinuous, vertically continuous function space was recently shown to remove spurious buoyancy modes. Time discretization is handled by an iterative semi-implicit method. The numerical scheme is coded in object-oriented Fortran within a novel co-des!

igned software framework using PSyClone, a Python-based domain-specific compiler. The new paradigm enables a clear separation of the scientific routines from the computational infrastructure, greatly facilitating portability across platforms and performance optimization.

Results on two- and three-dimensional benchmarks of nonhydrostatic dynamics with idealized orography closely match those of existing models. Scaling scores will also be presented that highlight the model’s computational performance.

**What about nutrient kinetics in a (gliomatous) brain**

Angelique Perrillat , Université de Poitiers

martedì 20 novembre 2018 alle ore 14:00, aula Saleri VI pianoABSTRACTThe brain is an organ with high energy needs. While it represents only 2% of the body

weight it grabs at least 20% of its total energy needs. The consumed energy can come from many

forms such as glutamate, glucose, oxygen and also lactate. Moreover energy is necessary to support

neural activity. But because energy management in healthy and tumoral cells can be difficult to

observe and explain experimentally, we use mathematical modeling to help to describe and

understand cells energy changes. We present here a time-delayed system and two fast-slow systems

describing the local mechanisms of interest. We will also compare simulations with MRS and

litterature data and discuss our results.

**Bayesian Dynamic Tensor Regression**

Matteo Iacopini , Università Ca’ Foscari di Venezia

giovedì 8 novembre 2018 alle ore 11:30, aula Saleri VI pianoABSTRACTMultidimensional arrays (i.e. tensors) of data are becoming increasingly available and call for suitable econometric tools.

We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well known multivariate models such as SUR, VAR, VECM, panel VAR and matrix regression models as special cases.

For dealing with the over-parametrization and over-fitting issues due to the curse of dimensionality, we exploit a suitable parametrization based on the parallel factor (PARAFAC) decomposition which enables to achieve both parameter parsimony and to incorporate sparsity effects. Our contribution is twofold: first, we provide an extension of multivariate econometric models to account for both tensor-variate response and covariates; second, we show the effectiveness of proposed methodology in defining an autoregressive process for time-varying real economic networks.

Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). We show the efficiency of the MCMC procedure on simulated datasets, with different size of the response and independent variables, proving computational efficiency even with high-dimensions of the parameter space. Finally, we apply the model for studying the temporal evolution of real economic networks.

**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° pianoABSTRACTI will present a series of works in collaboration with Henri Berestycki (PSL), dealing with systems of predators interacting with a single prey. The system is linked to the Lotka-Volterra model of interaction with diffusion, but unlike more classic works, we are interested in studying the case where competition between predators is very strong: in this context, the original domain is partitioned in different sub-territories occupied by different predators. The question that we ask is under which conditions the predators segregate in packs and whether there is a benefit to the hostility between the packs. More specifically, we study the stationary states of the system, the stability of the solutions and the bifurcation diagram, and the asymptotic properties of the system when the intensity of the competition becomes infinite.**Material constitutive modeling and parameter calibration: towards identification of representative material properties**

Vladimir Buljak, Department of Strength of Materials, University of Belgrade

lunedì 29 ottobre 2018 alle ore 14:00, aula Saleri VI pianoABSTRACTNumerical simulations are used with growing popularity in diverse sectors of engineering. The most important applications are those which attempt to replace expensive experiments on real structures that involve material mechanical behavior beyond their elastic limit. Such circumstance makes strong requirement for formulating material constitutive models with appropriate numerical implementation and for defining protocols for their calibration. Both problems are rather challenging when dealing with advanced materials.

In order to describe mechanical behavior of materials through an appropriate constitute model experiments are needed, but the transition from measurable quantities to sought parameters cannot always be directly established. Additional difficulty is encountered when dealing with complex constitutive models which tend to capture most of the physical processes taking place during material deforming, resulting in constitutive models with elevated number of parameters. Calibration of such models on the basis of too simple experiments, risks to identify particular solutions only, managing to fit a single experiment, thus not to be treated as material representative properties. A systematic way of resolving these difficulty is through the application of inverse analysis, centered on the minimization of a discrepancy function designed to quantify the difference between measured quantities and their counter parts, computed as a function of sought material parameters. This approach is!

more and more frequently adopted despite common mathematical difficulties, such as ill-posedness, non-uniqueness of the solution and non-convex function minimization.

Within this lecture some recent research contributions achieved by our team to the methodology of inverse analysis apt for calibration of complex constitutive models will be given. Results are presented with reference to real life engineering problems, related to diverse industrial environments. The first group of problems considers diagnostic analysis of structures based on instrumented indentation test. Results concern the development of reduced basis model for the acceleration of non-linear elasto-plastic simulations. The second group of problems concerns compaction of ceramic powders and the development of phenomenological constitutive models together with protocols for their calibration. The last group of problems, discussed within the lecture, is related to applications of porous ceramics for diesel particulate filters and catalytic substrates. Some innovative modeling techniques regarding thermally induced cracking and crack healing, observed in these materials will b!e shown.

**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**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° pianoABSTRACTIn the framework of a private-value-first-price auction, we consider the seller as a player in a game with the buyers in which he has private information about their realized valuations. We ask whether the seller can benefit by using his private information strategically. We find that in fact, depending upon his information, set of signals, and commitment power the seller may indeed increase his revenue by strategic transmission of his information. For example, in the case of two buyers with values distributed independently and uniformly on [0,1], a seller informed of the private values of the buyers, can achieve a revenue close to 1/2 by sending verifiable messages (compared to 1/3 in the standard auction), and this is the largest revenue that can be obtained with any signalling strategy.