Seminars

A series of seminars has been organised to promote discussions and scientific interaction on topics inherent to the project.

Regularization models and koopmon trajectories in mixed quantum-classical dynamics

Speaker

Cesare Tronci (University Of Surrey, UK)

Schedule 

July the 15th, 2025

Venue

Politecnico di Bari (Italy)

Abstract

How does a classical particle interact with a quantum particle? Since the early days in quantum mechanics, this question has represented one of the most outstanding problems in physics. In computational chemistry, this question emerges naturally when approximating nuclei as classical, while retaining quantum electrons, to alleviate the computational costs of fully quantum molecular simulations. Here, we present a new mixed quantum-classical (MQC) model based on the theory of Koopman wavefunctions. While conventional MQC models often suffer from consistency issues such as the violation of Heisenberg's principle, we overcome these difficulties by blending Koopman's classical mechanics on Hilbert spaces with methods in symplectic geometry. The resulting continuum model enjoys both a variational and a Hamiltonian structure. However, its formidable nonlinear character calls for suitable closures. Here, we apply a regularization technique on the underlying action principle. This step allows for a singular solution ansatz which introduces the trajectories of computational particles —the koopmons—  sampling the Lagrangian classical paths in phase space. In the case of Tully's benchmark problems from molecular dynamics, the method reproduces the results of fully quantum simulations with levels of accuracy that are not achieved by standard MQC methods. In addition, the koopmon method is computationally advantageous over fully quantum hydrodynamic approaches, which are also considered in our study. As a further step, we probe the limits of the method by considering the Rabi problem in both the ultrastrong and the deep strong coupling regimes, where MQC treatments appear hardly applicable. In this case, the method succeeds in reproducing parts of the fully quantum results.

Γ-expansion of the Cahn-Hilliard functional with Dirichlet boundary conditions  

Speaker

Leonard Kreutz (Technische Universität München)

Schedule 

June the 25th, 2025

Venue

Politecnico di Bari (Italy)

Abstract

In this talk, we present the second-order asymptotic development of the Cahn-Hilliard functional under Dirichlet boundary conditions via Γ-convergence. We begin by reviewing results from the literature on the asymptotic expansion of the Cahn-Hilliard functional. Subsequently, we discuss our ongoing research focused on the Cahn-Hilliard functional with Dirichlet boundary conditions. In particular, we examine the case where no interior interfaces are present and highlight several open questions for future investigation. This seminar is based on work in collaboration with Irene Fonseca and Giovanni Leoni. 

More on Modelling, simulation and optimisation of power plants based on renewable energies

Speaker

Ingenuin Gasser (Universität Hamburg)

Schedule 

June the 25th, 2025

Venue

Politecnico di Bari (Italy)

Abstract

The presentation refers to the mathematical modelling of power plants based on renewable resources ranging  from established applications such as parabolic trough power plants to osmotic pressure driven energy conversion technologies. The complexity of such  applications requires a substantial mathematical modelling effort to finally end up with reasonable models, which can be simulated fast and robust and which allow optimisation approaches. All applications involve fluid dynamic or thermo-fluid dynamic models which have to be significantly reduced under the restriction of keeping the most relevant chemical and physical effects. Mathematically these models are nonlinear systems of PDE’s od mixed elliptic-hyperbolic type.  

In view of the underlying application we discuss which quantities are reasonable to be optimized, e.g. the power output of the power plant with respect to operational or system parameters.

On the wave equation in time-dependent domains and the problem of dynamic debonding 

Speaker

Giuliano Lazzaroni (Università degli Studi di Firenze)

Schedule 

May the 26th, 2025

Venue

Politecnico di Bari (Italy)

Abstract

In models for dynamic debonding, the wave equation is set on a time-dependent domain and is coupled with a Griffith criterion for the evolution of such domain. This problem can be seen as a simplified version of dynamic fracture, at least in dimension one, where solutions can be determined in closed form. In dimension two the problem is more complex due to the shape of the debonding front, which may affect wave propagation. In the talk I will present some abstract results for the wave equation in time-dependent domains, bringing to a definition of dynamic energy release rate and to a formulation of the coupled problem in a general setting. I will also show how such problem can be solved assuming that solutions are radial. Finally I will mention some work in progress on the cohesive case. From joint works with G. Dal Maso, R. Molinarolo, L. Nardini, F. Riva, F. Solombrino. 

Enhanced dissipation for time-dependent shear flows

Speaker

Johannes Benthaus (University of Surrey, UK) 

Schedule 

May the 12th, 2025

Venue

Politecnico di Bari (Italy)

Abstract

Enhanced dissipation—an acceleration of dissipation compared to classical diffusion—is commonly observed in physical processes such as laboratory mixing and pollutant dispersion in oceanic flows. These phenomena are often modelled by advection-diffusion equations, where a passive scalar diffuses while being transported by an underlying velocity field. The transport can induce mixing, creating larger gradients for the diffusion to act on. This interplay gives rise to the enhanced dissipation phenomenon.

In this talk, we discuss the quantification of enhanced dissipation by deriving decay rates for the solution's energy. A primary analytical difficulty arises from the non-self-adjoint nature of the associated operator. A prominent strategy to obtain explicit decay rates is the hypocoercivity method, which we briefly introduce.

While stationary velocity fields are relatively well-understood, the physically important scenario of time-dependent (nonautonomous) flows has received less attention. Lately however, this case has gained increased interest, and we present a recent result modifying hypocoercivity techniques to analyse flows decomposing into a space-time product. In this setting, we demonstrate decay rates exceeding those established for autonomous flows.

Additionally, we discuss an illustrative example for which numerical simulations suggest the existence of a richer decay structure than what might be accessible via standard hypocoercivity methods. This open problem highlights the potential need for new approaches to fully characterise enhanced dissipation in this class of flows.

Macroscopic second order traffic models in presence of obstacles and heterogeneity of the road

Speaker

Prof.ssa Carlotta Donadello (Université de Franche-Comté, Besançon, Francia) 

Schedule 

April the 11th, 2025

Venue

Politecnico di Bari (Italy)

Abstract

We briefly recall the classical ARZ second order model for vehicular traffic, and we describe how it can be modified to take into account the presence of obstacles and heterogeneity of the road.

Then, we present some results on the theoretical and numerical investigation of the resulting systems of PDEs.

Our approach exploits recent advances on scalar conservation laws with point wise constrained or discontinuous flux, but the particular structure of the system asks for specific technical solutions and some relevant questions remain open.

Compensated Compactness for Scalar Conservation Laws

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

March the 19th, 2025

Venue

Université Marie et Louis Pasteur, Besançon (France)

Abstract

Compensated Compactness is a useful measure theory tool based on the compression effects of nonlinear equations. It works only in the nonlinear case and applies in several convergence problems.

The lectures will be organized as follows

1. Motivation

2. Compensated compactness 

3. Young measures

4. Murat Lemma

5. Div-Curl Lemma

6. Proof of Compensated Compactness 

7. Global Existence of Bounded Solutions

8. Long Time Behavior of Periodic Solutions

9. Diffusive-Dispersive Limits

Measure valued solutions for an optimal harvesting problem 

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

March the 14th, 2025

Venue

Queen's University (Canada)

Abstract

In this lecture we consider a model for the harvesting of marine resources. Since the cost functionals have linear growth with respect to the pointwise intensity of fishing effort, optimal solutions are in general measure-valued. For the control problem, we prove the existence of optimal strategies. 

Those results were obtained in collaboration with A. Bressan, G. Devillanova, M. Garavello, W. Shen, S. F. Solimini, L. V. Spinolo.

Vanishing viscosity versus Rosenau approximation for scalar conservation laws: the fractional case

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

March the 14th, 2025

Venue

Queen's University (Canada)

Abstract

In this talk we consider approximations of scalar conservation laws by adding nonlocal diffusive operators. In particular, we  consider solutions associated to  fractional Laplacian and fractional Rosenau perturbations and show that, for any t>0, the mutual L1 distance  of their profiles is  negligible as compared to their common distance to the underlying inviscid entropy solution. We provide explicit examples showing that our rates are optimal in the  supercritical and critical cases,  in one space dimension and for  strictly  convex fluxes. For subcritical equations, our rates are not optimal but they remain explicit.

Those results were obtained in collaboration with N. Alibaud, M. Dalery, and C. Donadello.

Vanishing viscosity versus Rosenau approximation for scalar conservation laws: the fractional case

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

January the 28th, 2025

Venue

University of Oslo (Norway)

Abstract

In this talk we consider approximations of scalar conservation laws by adding nonlocal diffusive operators. In particular, we  consider solutions associated to  fractional Laplacian and fractional Rosenau perturbations and show that, for any t>0, the mutual L1 distance  of their profiles is  negligible as compared to their common distance to the underlying inviscid entropy solution. We provide explicit examples showing that our rates are optimal in the  supercritical and critical cases,  in one space dimension and for  strictly  convex fluxes. For subcritical equations, our rates are not optimal but they remain explicit.

Those results were obtained in collaboration with N. Alibaud, M. Dalery, and C. Donadello.

Measure valued solutions for an optimal harvesting problem 

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

January the 8th, 2025

Venue

Università degli Studi di Firenze (Italy)

Abstract

In this lecture we consider a model for the harvesting of marine resources. Since the cost functionals have linear growth with respect to the pointwise intensity of fishing effort, optimal solutions are in general measure-valued. For the control problem, we prove the existence of optimal strategies. 

Those results were obtained in collaboration with A. Bressan, G. Devillanova, M. Garavello, W. Shen, S. F. Solimini, L. V. Spinolo.

From PDEs to Scaling Laws: Quantitative Analysis on Turbolent Convection

Speaker

Dr. Camilla Nobili (University of Sussex)

Schedule 

December the 6th, 2024

Venue

Politecnico di Bari (Italy)

Abstract

In this seminar, we will explore the derivation and significance of scaling laws within the context of Rayleigh-Bénard convection, a key problem in fluid dynamics that is essential for understanding geophysical flows in the atmosphere, oceans, and various industrial applications. Scaling laws offer a framework for characterizing how crucial quantities, such as heat transport, behave in extreme parameter regimes that cannot be reached through direct experimental methods.

Our focus will be on the Nusselt number Nu, which quantifies the efficiency of heat transport compared to pure conduction, and its relationship with the Rayleigh number Ra, which measures the thermal driving force of the system. We will review recent developments on rigorous upper bounds for Nu under various boundary conditions in both flat and rough domains.

A key part of this seminar will involve presenting simplifications and refinements of the techniques first introduced by Doering and Constantin in their seminal works from the 1990s. By refining their approach, we not only simplify the proofs but also obtain improved bounds on Nu, which shed light on the fundamental limits of heat transport in convective flows.

Measure valued solutions for an optimal harvesting problem 

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

November the 14th, 2024

Venue

University of Hamburg (Germany)

Abstract

In this lecture we consider a model for the harvesting of marine resources. Since the cost functionals have linear growth with respect to the pointwise intensity of fishing effort, optimal solutions are in general measure-valued. For the control problem, we prove the existence of optimal strategies. 

Those results were obtained in collaboration with A. Bressan, G. Devillanova, M. Garavello, W. Shen, S. F. Solimini, L. V. Spinolo.

Dynamics of wedge disclinations

Speaker

Prof. Marco Morandotti (Politecnico di Torino)

Schedule 

November the 6th, 2024

Venue

Politecnico di Bari (Italy)

Abstract

Disclinations in crystalline materials are point defects that are responsible for rotational kinematic incompatibility [4]. They are characterised by the so-called Frank angle, measuring the severity of the lattice mismatch. The variational setting and semi-discrete modeling of a systems of disclinations has been developed in [3] resorting to the Airy stress function. In this talk, we present recent results on the dynamics of disclinations in a two-dimensional domain. Disclinations move by energy minimization, in a similar fashion as dislocations do [1,2]. We study the well-posedness of the ODE governing the motion of a system of disclinations, with particular attention to the simple, yet illuminating cases of one disclination alone or two disclinations in the domain. An analysis of collision times is performed, and we also show how to account for the possible presence of preferred directions of motion determined by the crystalline structure.  Finally, we show numerical evidence of this dynamics. This is work in collaboration with Pierluigi Cesana (Kyushu University) and Alfio Grillo and Andrea Pastore (Politecnico di Torino).

Mean-field Limit and Optimal Control for a Hybrid Multi-Population Traffic Flow Model

Speaker

Prof. Maria Teresa Chiri (Queen's University)

Schedule 

July the 17th, 2024

Venue

Politecnico di Bari (Italy)

Abstract

Heterogeneous and multi-lane tra!c flow modeling is fundamental to understanding the dynamics and control of complex tra!c systems. In this talk, we consider three populations of vehicles: two classes of human-driven vehicles (cars and trucks) and autonomous vehicles (AV). We first develop a finite-dimensional hybrid system which relies on continuous Bando-Follow-the-Leader dynamics coupled with discrete events motivated by the lane-change maneuvers. Then we rigorously prove that the mean-field limit is given by a system of Vlasov-type PDE with source terms generated by the lane-change maneuvers of the human-driven vehicles. The PDEs are coupled with ODEs for the dynamic of AVs. Using Γ-convergence, we prove the well-posedness of an optimal control problem for the mean-field limit.

This is a Joint work with X. Gong (Amherst College) and B. Piccoli (Rutgers)

Nonlinear Peridynamic Models

Speaker

Prof. Giuseppe Maria Coclite (Politecnico di Bari)

Schedule 

June the 27th, 2024

Venue

Università di Pisa (Italy)

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.

Link to the PDF version of the abstract. 

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