Mathematical Modeling and System-Theoretic Analysis
Mini-Symposium: Mathematical Modeling and System-Theoretic
Date and Time: February 13, 2019, 10:00 - 17:30
Location: MF 11-12, Floor 4, Metaforum, Eindhoven
University of Technology, The Netherlands
Registration | Introduction
| Program | Abstracts | Flyer | Organization Committee
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 (email@example.com) or Harshit
It is our great pleasure to announce our three renowned and
internationally recognized keynote speakers: Peter
Mehrmann and Marie-Therese
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, Socio-Economic Sciences, Multi-physics
Systems and etc. The afternoon session will be dedicated to port-Hamiltonian
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.
10:00 - 10:05 Wil Schilders (Introduction)
10:05 - 11:00 Peter Markowich (Keynote Speaker; slides)
11:00 - 11:40 Marie-Therese 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
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.
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.
Peletier, Eindhoven University of Technology
Title: Onsager reciprocity, gradient flows, and large
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
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
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).
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 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
van der Schaft, University of Groningen
Title: A gentle introduction to port-Hamiltonian modeling of
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.
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
- 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.
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.
The campus is on 5 minutes walking distance of the train station
of Eindhoven (exit north side).
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