Seminars
MIUR Prin 2022 - Project code 2022M9BKBC
A series of seminars has been organised to promote discussions and scientific interaction on topics inherent to the project.
Nonlinear Peridynamic Models
Speaker
Prof. Giuseppe Maria Coclite (Politecnico di Bari)
Schedule
June the 6th, 2024
Venue
Institute for Mathematics, Julius-Maximilians-Universität in Würzburg (Germany)
Metodi quantitativi nella scienza del clima: contributi dell’analisi teorica
Speaker
Prof. Piermarco Cannarsa (Università di Roma "Tor Vergata")
Schedule
May the 30th, 2024
Venue
Dipartimento di Matematica e Informatica, Università di Palermo
Abstract
Sappiamo che le caratteristiche climatiche della Terra hanno subito variazioni importanti nel corso della storia del pianeta. Anche oggi stiamo assistendo a cambiamenti sempre più rapidi e intensi del clima, generati probabilmente dall’intervento umano per la prima volta nella storia del nostro pianeta. Ma come si può stabilire quale fosse la temperatura terrestre mille, diecimila, centomila anni fa o ancora più indietro nel tempo?
Uno strumento molto utile per lo studio del paleoclima sono le analisi degli strati di ghiaccio più antico - anche se pure questi depositi di storia planetaria si vanno facendo sempre più rari. Come poter dedurre informazioni sulla temperatura dell’intero pianeta da misure che coinvolgono necessariamente solo alcune regioni e solo in alcuni intervalli temporali? A queste domande cercano di rispondere i matematici che studiano il clima. Naturalmente, è necessario avere un modello ben formulato, non eccessivamente complesso perché possa essere studiato teoricamente, ma opportunamente calibrato perché possa cogliere le caratteristiche piu salienti della dinamica del clima.In questa conferenza vedremo come si possono usare a questo scopo i modelli di bilancio energetico, che furono introdotti negli anni ’60 da russi e americani per studiare gli effetti del cosiddetto inverno nucleare. Vedremo come questi modelli ci hanno svelato segreti di un passato molto lontano del nostro pianeta, e come ci aiutano a capire quali impatti possa avere sul clima di domani la variazione di determinati agenti climatici, quali l'irradiazione solare o la quantità di gas serra presenti in atmosfera.
Nonlinear Peridynamic Models
Speaker
Prof. Giuseppe Maria Coclite (Politecnico di Bari)
Schedule
April the 19th, 2024
Venue
Institute of Mathematics, EPFL - École polytechnique fédérale de Lausanne (Switzerland)
Nonlinear Peridynamic Models
Speaker
Prof. Giuseppe Maria Coclite (Politecnico di Bari)
Schedule
April the 4th, 2024
Venue
Università degli Studi di Parma
Nonlocal conservation laws: singular limit and long-time behavior
Speaker
Prof. Giuseppe Maria Coclite (Politecnico di Bari)
Schedule
March the 3rd, 2024
Venue
Queen's University (Canada)
Long-time behavior of scalar conservation laws
Speaker
Prof. Giuseppe Maria Coclite (Politecnico di Bari)
Schedule
February the 2nd, 2024
Venue
University of Oslo (Norway)
Viscous vorticity-current MHD equations in ℝ²
Speaker
Prof. Vincenzo Sciacca (Università degli Studi di Palermo)
Schedule
To be scheduled.
Venue
Politecnico di Bari, DMMM, Aula MAT_01
Abstract
We consider the two dimensional magneto-hydrodynamic (MHD) equations describing the evolution of an incompressible electrically conducting fluid, with velocity u = (u₁, u₂), moving through a magnetic vector field B = (b₁,b₂). The interaction between the fluid velocity and the magnetic field is described by the coupling between the Navier-Stokes equations and the Maxwell’s equations. The fluid vorticity ω and the magnetic current density j are defined, respectively, by ω = ∂₁u₂ −∂₂u₁ and j = ∂₁b₂ −∂₂b₁. In this talk we present results about the well-posedness of the viscous MHD equations in the whole space ℝ², in the vorticity-current formulation, and we analyze the zero viscosity limit problem.
From linear to nonlinear model order reduction: some results and perspectives
Speaker
Dott. Giovanni Stabile (Università degli Studi di Urbino Carlo Bo)
Schedule
January the 17th, 2023 - h14:30
Venue
Politecnico di Bari, DMMM, Aula MAT_01
Abstract
Non-affine parametric dependencies, nonlinearities, and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on Proper Orthogonal Decomposition. Among the possible solutions, there are purely data-driven methods that leverage nonlinear approximation techniques such as autoencoders and their variants to learn a latent representation of the dynamical system, and then evolve it in time with another architecture. Despite their success in many applications where standard linear techniques fail, more has to be done to increase the interpretability of the results, especially outside the training range and not in regimes characterized by an abundance of data. Not to mention that none of the knowledge on the physics of the model is exploited during the predictive phase. In this talk, in order to overcome these weaknesses, I introduce a variant of the nonlinear manifold method introduced in previous works with hyper-reduction achieved through reduced over-collocation and teacher-student training of a reduced decoder. We test the methodology on different problems with increasing complexity.
Nonlinear Peridynamic Models
Speaker
Prof. Giuseppe Maria Coclite (DMMM, Politecnico di Bari)
Schedule
January the 09, 2024
Venue
Università degli Studi di Padova
Modelling, simulation and optimisation of power plants based on renewable energies
Speaker
Prof. Ingenuin Gasser (Department of Mathematics, Universität Hamburg)
Schedule
November the 16th, 2023 - h11:00
Venue
Politecnico di Bari, DMMM, Aula MAT_01
Abstract
The presentation refers to power plants based on renewable resources, from well known applications such as parabolic trough power plants as well as non-standard possible future applications like solar updraft towers, energy towers or pressure retarded osmosis power plants. The complexity of all these applications requires a substantial modelling effort to extract reasonable models, which can be simulated fastly and which are appropriate for optimisation tasks. All applications involve thermo-fluid dynamic models which have do be reduced under the restriction of keeping the most relevant chemical and physical effects. At the end we maximize the power output of the power plant with respect to operational or system parameters.
On the weak solutions to the Navier-Stokes equations: a possible gap related to the energy equality
Speaker
Prof. Paolo Maremonti (Università degli Studi della Campania Luigi Vanvitelli)
Schedule
November the 8th, 2023 - h16:00
Venue
Politecnico di Bari, DMMM, Aula MAT_01
Abstract
It is well known that a weak solution a priori enjoys an energy inequality. We investigate the existence of a Leray-Hopf weak solution enjoying the energy equality. We are unable to fully prove the result. However, we show that if there is a possible gap for the energy equality, then the gap is represented by means of a suitable additional dissipation, given either in terms of “internal energy” or in terms of “kinetic energy”. Both quantities vanish in the case of a further “small regularity” of the weak solution. We are not able to detect a turbulence character for these quantities. Since no uniqueness result is known for a Leray-Hopf weak solution, our result a priori does not work for any Leray-Hopf weak solution.
Nonlinear Peridynamic Models
Speaker
Prof. Giuseppe Maria Coclite (DMMM, Politecnico di Bari)
Schedule
October the 27, 2023
Venue
Università degli Studi di Palermo