
Mathematical Modeling and SystemTheoretic Analysis
MiniSymposium: Mathematical Modeling and SystemTheoretic Analysis
Date and Time: February 13, 2019, 10:00  17:30
Location: MF 1112, Floor 4, Metaforum, Eindhoven University of Technology, The Netherlands
Registration 
Introduction 
Program 
Abstracts 
Flyer 
Organization Committee 
Location
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).
It is our great pleasure to announce our three renowned and internationally recognized keynote speakers:
Peter Markowich,
Volker Mehrmann
and MarieTherese Wolfram along with several experts both from abroad and within Netherlands.
The morning session will be dedicated to continuum modeling for various application fields such as Biological Transportation Networks, SocioEconomic Sciences, Multiphysics Systems and etc.
The afternoon session will be dedicated to portHamiltonian systems, including the general perspectives and the emerging trends in the modeling and numerical fields.
The program also offers sufficient time for networking and discussions.
Program
10:00  10:05 Wil Schilders (Introduction)
10:05  11:00 Peter Markowich (Keynote Speaker)
11:00  11:40 MarieTherese 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.
 MarieTherese Wolfram, University of Warwick and University of Munich
Title: Applied PDE in the socioeconomic 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 meanfield 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
microscopicreversibility 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 closetoequilibrium,
linearfrictionoperator context of Onsager's. I will describe how the largedeviation theory of fluctuations allows one to make a much more general statement, where microscopic
reversibility is onetoone 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).
Afternoon Session
 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 portHamiltonian (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 spacetime 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 portHamiltonian modeling of multiphysics systems
In this talk we will provide a brief summary of the essentials of portHamiltonian 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 powerconserving interconnection. Finally
we will formulate and address the problem of portHamiltonian structure preserving model reduction.
 Tudor Ionescu, Politehnica University of Bucharest
Title: Moment matchingbased model order reduction for nonlinear portHamiltonian/gradient systems
PortHamiltonian 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 timedomain 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 portHamiltonian or gradient structure and matches the moments of the given nonlinear portHamiltonian system. In
other words, from the family of models that achieve moment matching, we select the reduced order model that inherits the portHamiltonian/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 portHamiltonian/gradient structure of the
given system.
 Hans Zwart, University of Twente
Title: Descriptor portHamiltonian models
The existence and uniqueness theory for portHamiltonian systems described by a linear partial differential equation on a onedimensional 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
portHamiltonian partial differential equations with algebraic constraints. We link our results to some wellknown results in PDE and operator theory.
 Siep Weiland, Eindhoven University of Technology
Title: Are thermodynamical systems portHamiltonian?
PortHamiltonian 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 portHamiltonian 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
