
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; slides)
11:00  11:40 MarieTherese Wolfram (Keynote Speaker; slides)
11:40  12:10 Mark Peletier (slides)
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; slides)
14:15  14:45 Arjan van der Schaft (slides)
14:45  15:00 Coffee Break
15:00  15:20 Tudor Ionescu (slides)
15:20  15:40 Hans Zwart (slides)
15:40  16:00 Siep Weiland (slides)
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 Universit?t 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
