### Seminari

### Prossimi Seminari

- Nonintrusive reduced order models using physics informed neural networks

Jan S. Hesthaven, Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, CH

giovedì 29 ottobre 2020 alle ore 14:00 precise, Online seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1979&t=763724

### Seminari Passati

- A new approach to quantum mechanics

Yakir Aharonov, Chapman University

martedì 18 giugno 2019 alle ore 16:00 precise, Sala Consiglio, 7 piano, Edificio La Nave, Via Ponzio 31-33ABSTRACTIn my talk, I will discuss a reformulation of quantum mechanics in which each quantum system at any time is described by two Hilbert space vectors rather than one. One of the vectors propagates from past boundary condition towards the present and the other propagates back to the present from a future boundary condition. I will show that this reformulation uncovers a host of fascinating new physical phenomena and new mathematics. Examples of the former, i.e. new physical phenomena, are Weak Measurements and Weak Values. Examples of the latter, i.e. new mathematics, are superoscillations. Both examples will be described in detail within this talk. - ON A MATHEMATICAL THEORY OF REPEATED QUANTUM MEASUREMENTS

Vojkan Jaksic, McGill University

giovedì 13 giugno 2019 alle ore 14:30 precise, Aula Seminari III pianoABSTRACTThe statistics of the (finite alphabet) outcomes of repeated quantum measurements is studied by methods of thermodynamic formalism. Viewed as one-dimensional spin systems with long range interactions, repeated quantum measurements exhibit very rich (and sometimes very singular) thermodynamic behaviour. We will describe general thermodynamical formalism of these systems and illustrate its unexpected features on a number of examples. - Multiphase flow in heterogeneous geologic media

Stephan K. Matthai, Chair of Reservoir Engineering, Department of Infrastructure Engineering, The University of Melbourn

giovedì 13 giugno 2019 alle ore 14:00, Aula consiglio VII piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTHeterogeneous permeability, porosity, capillary pressure and mechanical properties are key characteristics of sedimentary and volcanic rocks with sufficient interconnected pores to permit fluid flow. In many cases, heterogeneities are nested, for instance, where mm-scale laminations define the internal structure of bed-forms that combine into facies associations and facies distributions on the km scale. Where such rocks have experienced an overprint by deformation or reactive fluid flow, initial heterogeneities might have been amplified even further. Thus, fracturing can impart long-range spatial correlations on the permeability structure, strongly amplifying permeability anisotropy, even without a noticeable increase in the porosity.

This presentation examines the impact of such nested heterogeneities on flow, (reactive) transport, and multiphase fluid displacement in natural heterogeneous porous media. The emphasis will be on intermediate scale features (~0.1 - 500-m in size) that are difficult to investigate in the laboratory or in the subsurface because flow patterns cannot be resolved by geophysical imaging techniques. The investigative method used here are field-data based hybrid FEM-FVM numeric simulations where an operator splitting technique is employed, solving elliptic-parabolic equations (fluid pressure, temperature, chemical diffusion) with the FEM and the hyperbolic ones (multiphase flow and tracer transport) with the FVM.

The presentation will illustrate the behaviour of the heterogeneous systems and the numeric methods used to model them, proceeding from tracer transport, to gas injection and water flooding of naturally fractured reservoirs to maximise hydrocarbon recovery. The presentation will conclude with a general discussion of the impact of heterogeneity, addressing questions such as: given the nested nature of geologic heterogeneity, is the spreading of gas plumes ergodic? – or – in view of the impact of heterogeneity on sweep, how can gas storage or hydrocarbon recovery be maximised?

Contatto: paolo.zunino@polimi.it - 'Strange' rational maps and spectra of graphs and groups

Rostislav Grigorchuk, Texas A&M University

giovedì 13 giugno 2019 alle ore 16:30 precise, 'Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, Via Cozzi 55ABSTRACTI will present a few results concerning spectral theory of

graphs and groups that are based on the use of multidimentional rational

maps and self-similar groups. It will be explained how these maps

appear, how they help to compute the spectrum, and why they are

``strange'' (or better to say, non typical). As part of the story there

will be a short survey on spectra of infinite graphs and groups with

some old and new results belonging to the speaker and his collaborators

(L.Bartholdi, A.Dudko, D.Lenz, T.Nagnibeda, B.Simanek, A.Zuk). The

relation to the random Schrodinger operator will be mentioned at the end

of the talk if time permits. - Symmetry preservation for fourth order eigenvalue optimization problems

Francesca Colasuonno, Università degli Studi di Torino

mercoledì 12 giugno 2019 alle ore 15:15, Aula seminari 3° pianoABSTRACTIn this talk, we will discuss some recent results on two eigenvalue optimization problems governed by the biharmonic operator, under Dirichlet or Navier boundary conditions. From a physical point of view, in two dimensions our problem corresponds to building a plate, of prescribed shape and mass, out of materials with different densities --varying in a certain range of values-- in such a way to minimize the lowest frequency of the body. This problem is also referred to as composite plate problem. Both for the clamped plate (i.e., Dirichlet b.c.) and for the hinged plate (i.e., Navier b.c.), we will prove the existence of an optimal configuration and give an explicit representation of the minimizing densities in terms of sublevel sets of their corresponding first eigenfunctions. Finally, we will discuss symmetry preservation properties of the optimal configurations, in the presence of some symmetry and convexity of the domain. The tools used differ depending on the boundary conditions: while the hinged plate problem inherits the maximum principles for second order elliptic systems, allowing us to exploit the moving plane method to get symmetry preservation in more general domains, the situation is more complicated for the clamped plate problem, where we will use the polarization technique and the properties of the Green's function to deal with radial symmetry preservation in a ball.

This talk is based on two joint papers with Eugenio Vecchi (Trento). - Nonparametric methods for complex spatial domains: density estimation and hypothesis testing

Federico Ferraccioli, Università degli Studi di Padova

martedì 11 giugno 2019 alle ore 14:15, Aula consiglio VII piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTI will present different nonparametric methods for data distributed over complex spatial domains. First I will consider the problem of density estimation. Specifically I will propose a nonparametric penalized likelihood approach for data distributed over planar domains with complex geometries. The model formulation is based on a regularization with differential operators, and it is made computationally tractable by means of finite elements. In this setting, I will describe a permutation procedure for one and two samples hypothesis testing. Then I will consider hypothesis testing procedures in the case of spatial regression models with differential regularization. In particular, I will propose a test based on sign-flipping. I will present the performances of the proposed methods via simulation studies and application to real data.

Contatto: laura.sangalli@polimi.it

- Superoscillations and approximation of generalized functions

Daniele Struppa, Chapman University

lunedì 10 giugno 2019 alle ore 15:15 precise, Sala Consiglio, 7 piano, Edificio La Nave, Via Ponzio 31-33ABSTRACTThis talk offers an introductory look at how superoscillatory sequences can be utilized to approximate generalized functions. After an introduction to superoscillations, I will briefly discuss how such sequences can be used to approximate tempered distributions, and will then focus on their role in the context of the theory of hyperfunctions. The talk will be based on a series of papers jointly coauthored with F.Colombo, I.Sabadini, and A.Yger. - On the quasistatic limit for a debonding model in dimension one; a vanishing inertia and viscosity approach

Filippo Riva, SISSA

giovedì 6 giugno 2019 alle ore 15:15, Aula seminari 3° pianoABSTRACTIn the theory of linearly elastic fracture mechanics one-dimensional debonding models, or peeling tests, provide a simplified but still meaningful version of crack growth models based on Griffith's

criterion. They are both described by the wave equation in a time-dependent domain coupled with suitable energy balances and irreversibility conditions.Unlike the general framework, peeling tests allow to deal with a

natural issue of great interest arising in fracture mechanics. It can be stated as follows: although all these models are dynamic by nature, the evolution process is often assumed to be quasistatic (namely the

body is at equilibrium at every time) since inertial effects can be neglected if the speed of external loading is very slow with respect to the one of internal oscillations. Despite this assumption seems to

be reasonable, its mathematical proof is really far from being achieved.In this talk we validate the quasistatic assumption in a particular damped debonding model, showing that dynamic evolutions converge to the quasistatic one as inertia and viscosity go to zero. We also highlight how the presence of viscosity is crucial to get this kind of convergence.