Mathematical Modeling and System-Theoretic Analysis

Registration:
Participation is free of charge, but registration is mandatory.
To register, please fill the google form at: http://goo.gl/wTkeX5.
Kindly register by February 4, 2019.
For more information, contact Xingang Cao (x.cao.1@tue.nl) or Harshit Bansal (h.bansal@tue.nl).

Program

10:00 - 10:05 Wil Schilders (Introduction)
10:05 - 11:00 Peter Markowich (Keynote Speaker)
11:00 - 11:40 Marie-Therese Wolfram (Keynote Speaker)
11:40 - 12:10 Mark Peletier
12:10 - 12:35 Discussions
12:35 - 13:25 Lunch

13:25 - 13:30 Wil Schilders (Introduction)
13:30 - 14:15 Volker Mehrmann (Keynote Speaker)
14:15 - 14:45 Arjan van der Schaft
14:45 - 15:00 Coffee Break
15:00 - 15:20 Tudor Ionescu
15:20 - 15:40 Hans Zwart
15:40 - 16:00 Siep Weiland
16:00 - 17:30 Discussions + Drinks

Abstracts:

Morning Session

• Peter Markowich, University of Cambridge and KAUST
  Title: Continuum Modeling of Biological Transportation Networks (Keynote Talk)

  An overview is presented of recent analytical and numerical results for the elliptic - parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transportation networks. The model describes the pressure field using a Darcy type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. We first introduce micro- and mesoscopic models and show how they are connected to the macroscopic PDE system. Then, we provide an overview of analytical results for the PDE model, focusing mainly on the existence of weak and mild solutions and analysis of the steady states. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on finite elements and study the qualitative properties of network structures for various parameter values.

• Marie-Therese Wolfram, University of Warwick and University of Munich
  Title: Applied PDE in the socio-economic sciences - from pedestrians to the ELO rating system (Keynote Talk)

  In recent years nonlinear PDE models have been used to describe opinion formation and knowledge growth in a society, collective dynamics in large pedestrian crowds or the change of ratings in competitor versus competitor games. In this talk we focus on two different classes of such mean-field models. First we discuss Boltzmann type approaches, in which interactions with others lead to the change of an individual characteristic. For example pedestrians change their velocity in case of a potential 'collision', or the rating of players in- or decrease due to wins and loses in a tournament. These simple individual interaction rules lead to complex macroscopic phenomena, such as lane formation of clustering. After discussing the underlying modeling approaches as well as the behavior of solutions in various examples, we continue with PDE models for pedestrian crowds. Here we are particularly interested in segregation dynamics. We shall see that already simple interaction rules, such as side stepping lead to lane formation in bidirectional pedestrian flows.

• Mark Peletier, Eindhoven University of Technology
  Title: Onsager reciprocity, gradient flows, and large deviations

  The second law of thermodynamics states that in a thermodynamically consistent system the 'entropy' is a Lyapunov function, a function that is monotonic along solutions of the corresponding differential equations. When the system can be written as a gradient flow of the entropy, then this statement is strengthened: not only is this functional monotonic, but it drives the dissipative part of the evolution in a precise way, mediated by a 'friction operator'.

  In this lecture I will go one step further. Onsager already pointed out how symmetry properties of linear friction operators arise through an upscaling procedure from a microscopic-reversibility property of the underlying system. Fluctuations figure centrally in his argument, but at that time their theory was not well developed, and more could not be said.

  However, recently we have found that the connection between microscopic reversibility and macroscopic 'symmetry' properties is not at all limited to the close-to-equilibrium, linear-friction-operator context of Onsager's. I will describe how the large-deviation theory of fluctuations allows one to make a much more general statement, where microscopic reversibility is one-to-one coupled to 'symmetry' at the macroscopic level - provided one generalizes the concept of symmetry in an appropriate way.

  This is joint work with Michiel Renger and Alexander Mielke (both WIAS, Berlin).

• Volker Mehrmann, Technische Universität Berlin
  Title: Energy based modeling, simulation and optimization of multiphysics systems (Keynote Talk)

  Coupled systems from different physical domains present a major challenge for simulation and optimization algorithms due to largely different scales or modeling accuracy. An approach to address these challenges is the use of network based energy based modeling via port-Hamiltonian (pH) systems and the use of model hierarchies ranging from very fine grain models to highly reduced surrogate models arising from model reduction or data based modeling.

  This talk presents an overview over recent developments in pH modeling in the context of fluid- and thermodynamics as well as new approaches to integrate constraints in pH modeling. The implications for space-time discretization and model selection are discussed as well and illustrated at several real world applications.

• Arjan van der Schaft, University of Groningen
  Title: A gentle introduction to port-Hamiltonian modeling of multi-physics systems

  In this talk we will provide a brief summary of the essentials of port-Hamiltonian modeling, and its potential for simulation, analysis and control. Basic concepts include the compositional modeling of energy storage and energy dissipation, as well as the geometric notion of a Dirac structure formalizing power-conserving interconnection. Finally we will formulate and address the problem of port-Hamiltonian structure preserving model reduction.

• Tudor Ionescu, Politehnica University of Bucharest
  Title: Moment matching-based model order reduction for nonlinear port-Hamiltonian/gradient systems

  Port-Hamiltonian and gradient systems represent an important class of systems used in modeling, analysis and control. Physical modelling often leads to systems of high dimension, usually difficult to analyze and simulate and unsuitable for control design. In this talk, we use the time-domain approach to nonlinear moment matching, yielding a parametrization of a family of reduced order models achieving moment matching. These models depend on a set of free parameters, useful for enforcing properties such as, e.g., passivity, stability, etc. We characterize the reduced order models that preserve the port-Hamiltonian or gradient structure and matches the moments of the given nonlinear port-Hamiltonian system. In other words, from the family of models that achieve moment matching, we select the reduced order model that inherits the port-Hamiltonian/gradient form, by picking a particular (subset of) member(s), i.e., we obtain a (family of) reduced order model(s) that matches (match) the moments and inherit (inherit) the port-Hamiltonian/gradient structure of the given system.

• Hans Zwart, University of Twente
  Title: Descriptor port-Hamiltonian models

  The existence and uniqueness theory for port-Hamiltonian systems described by a linear partial differential equation on a one-dimensional spatial domain is now very well understood, see for instance the book of Jacob and Zwart. However, this changes when a constraint is added. In this talk we will give some first results on the existence and uniqueness results for port-Hamiltonian partial differential equations with algebraic constraints. We link our results to some well-known results in PDE and operator theory.

• Siep Weiland, Eindhoven University of Technology
  Title: Are thermodynamical systems port-Hamiltonian?

  Port-Hamiltonian systems have found widespread applications in the modelling and control of physical systems. The power conserving properties of interconnected ports lead to a natural structure preservation and compositional framework that is of key importance for the modelling, discretization and control of networked systems. Important examples include systems in electrical engineering, mechanical engineering and fluid dynamics, but not in thermodynamics. This leads to the natural question whether thermal properties of systems can, or cannot be incorporated in the port-Hamiltonian framework.

Organization Committee:
Wil Schilders
Xingang Cao
Harshit Bansal

Location
The campus is on 5 minutes walking distance of the train station of Eindhoven (exit north side).
Accessibility, route and map TU/e Campus