In this talk, we will present an extension of the discrete potential theory and discrete function theory to rectangular lattices. As usual in the discrete theories, construction of discrete operators is strongly influenced by a definition of discrete geometric setting. For providing consistent constructions, a detailed discussion on the discrete geometric setting will be presented in the beginning of the talk. After that, the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice and its numerical analysis will be discussed. By using the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, the discrete potential theory is then constructed for interior and exterior settings. Several discrete interior and exterior boundary value problems are then solved. Moreover, discrete transmission problems are introduced and several numerical examples of these problems are discussed. In the last part of the talk, we present discrete function theory on rectangular lattices based on the discrete Cauchy-Riemann operators. Discrete analogues of Borel-Pompeiu formulae, Cauchy formulae, and Teodorescu transform are constructed for interior and exterior settings within the discrete function theory.
Isogeometric Analysis (IGA) is a successful simulation framework originally proposed by T.J.R. Hughes et al. in 2005, with the aim of bridging Computational Mechanics and Computer Aided Design. In addition to this, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per degree-of-freedom and an enhanced robustness with respect to standard finite elements in many applications, ranging from solids and structures to fluids, as well as to different kinds of coupled problems, also opening the door to the approximation in primal form of higher-order partial differential equations.
After a concise introduction of the basic isogeometric concepts, this lecture aims at presenting an overview of some recent advances with a special focus on coupled problems where the characteristics of IGA seem to be of great advantage, including the simulation of fluid-structure interaction in different contexts (e.g., biomedical problems), studies on the effects of mechanically-induced stresses on prostate cancer growth, thermo-mechanical simulations for additive manufacturing processes, electro-mechanical simulations for biological tissues, and the use of phase-field modeling for fracture and topology optimization problems or for predicting the polarization evolution in elastic ferroelectric materials.
Contatto:
paola.antonietti@polimi.it
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
Partendo da una derivazione elementare della legge di gravitazione universale di Newton, si tratterà il problema dei due corpi (Sole-Pianeta) da un punto di vista matematico, mostrando come ricavare le tre leggi di Keplero. Successivamente si imposterà il problema dei tre corpi mostrando come ricavare la celebre soluzione triangolare di Lagrange. Da un punto di vista didattico si illustreranno alcune proposte di argomenti, come ad esempio le coordinate polari, che potrebbero aiutare l'introduzione della tematica in classe.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
In the context of regression with functional data, one of the most popular semiparametric models is the functional single-index model. For this model, which involves a scalar response and a single functional covariate, Novo, Aneiros, and Vieu (2019, Journal of Nonparametric Statistics) proposed an automatic estimation procedure capable of adapting to the local characteristics of the data. However, the studied methodology remains restrictive as it assumes the functional covariate is fully observed. In this ongoing work, we compare different reconstruction methods for the functional covariate, such as those developed by Kneip and Liebl (2020, The Annals of Statistics) and Palummo et al. (2024, Environmental and Ecological Statistics), and evaluate their impact on model estimation through simulations and applications to real-world datasets.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
Computational modeling and simulation of the electrical activity of the heart is an emerging and interdisciplinary field, which is establishing as a fundamental tool in cardiac electrophysiology practice. However, the employment of cardiac simulations in the clinical practice is still challenging and limited by the high computational power and expertise needed for the development of cardiac models. The talk will focus on the available strategies to overcome such limitations providing specific examples of cardiac electrophysiology simulations in clinical cardiology. In particular, scar-related arrhythmia ablation guided\aided by computational models is one of the most promising applications in this context. The talk will present a recent unpublished study assessing the performance of computational models in identifying deceleration zones and reentry circuits to aid clinicians in ablation planning.
Contatti:
roberto.piersanti@polimi.it
luca.dede@polimi.it
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
We decompose p - integrable functions on the boundary of a bounded simply connected Lipschitz domain U, subset of the complex plane, into the sum of the boundary values of two, uniquely determined holomorphic functions, where one is in the holomorphic Hardy space for U while the other is in the holomorphic Hardy space for the (interior of) the complement of U. Various refinements are presented showing the dependence of the decomposition on the regularity of the domain U, and/or of the boundary function. We discuss a few applications. The main tool is a regularity result for the holomorphic Hardy space of U which can be traced back to Privalov for smooth U but appears to be new for U Lipschitz. This is joint work with S. Bell and N. Wagner.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
In the talk it will be presented a variational characterisation for a class of non-linear evolution equations with constant non-negative Dirichlet boundary conditions on a bounded domain as gradient flows in the space of non-negative measures. The relevant geometry is given by the modified Wasserstein distance introduced by Figalli and Gigli that allows for a change of mass by letting the boundary act as a reservoir. We give a dynamic formulation of this distance as an action minimisation problem for curves of non-negative measures satisfying a continuity equation in the spirit of Benamou-Brenier. Then we characterise solutions to non-linear diffusion equations with Dirichlet boundary conditions as metric gradient flows of internal energy functionals in the sense of curves of maximal slope. The topic has been addressed in a joint work with Matthias Erbar.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
I will discuss how superfluidity manifests itself in the spectrum of the Hamiltonian for a test particle travelling through a Bose Einstein condensate.
In the Bogoliubov-Fröhlich polaron model, a stable polaron with momentum P corresponds to a ground state of the Hamiltonian at fixed total momentum. I will explain a recent result in collaboration with Benjamin Hinrichs, which shows that a ground state exists if the momentum is less than mc, where m is the particle mass and c is the slope at zero momentum of the dispersion relation of the Bogoliubov phonons.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
In this talk we explore F-purity of geometrically vertex decomposable ideals. After a brief overview of some basic concepts in F-singularity theory and geometric vertex decomposition, we present a way to iteratively construct Frobenius splittings for certain geometric vertex decomposable ideals. This technique will be illustrated with examples.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
Given a complete Riemannian manifold (M,g) I will prove that, for any point p in M and for any integer n>2, there exists a family of sets containing p and a family of solutions to the torsion problem that admits at least n maximum points. Moreover the domains are close to be convex (in a suitable sense). The proof relies on similar results in R^d, for d>3.
The talk is based on past and ongoing results involving M. Grossi and A. Enciso.
Alessandro Reali (born in 1977) is Full Professor of Solid and Structural Mechanics at the University of Pavia since 2016. He is currently the Rector’s Delegate for International Research (2019-2025) as well as a member of the Regional Forum for Research & Innovation of Regione Lombardia (2023-2025); moreover, he served as the Dean of the Department of Civil Engineering and Architecture for two terms (2018-2024) and as a member of the Academic Senate (2018-2019). He is specialized in different engineering fields, such as numerical simulation, structural and materials mechanics, biomechanics. During his academic career, he supervised more than 20 PhD students and 15 Postdoctoral fellows. He was the principal investigator of several national and international research projects, including a prestigious ERC grant of the European Research Council. He published about 190 papers on international journals and received more than 16,000 citations with an h-index of 60 (according to Google Scholar). He was also invited to deliver over 100 seminars at internationally renowned institutions, as well as 35 plenary/keynote lectures and more than 40 other invited lectures at international conferences. For his research achievements he received numerous honors and awards, and was appointed, among others, Fellow of the European Academy of Sciences, Knight Commander of the Order of Merit of the Italian Republic, Clarivate/ISI Highly Cited Researcher, Ambassador of the Technical University of Munich - TUM, ECCOMAS Euler medalist, Panetti-Ferrari medalist (Accademia delle Scienze di Torino), IACM Fellows awardee, Fischer Fellow (TUM Institute for Advanced Study), Finzi awardee (Istituto Lombardo – Accademia di Scienze e Lettere), IACM Argyris awardee, ECCOMAS Zienkiewicz awardee, AIMETA Junior awardee.
More information can be found at: www.unipv.it/alereali.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica