CA18232 Heating up networks - analysis meets applications workshop

Mat-Dyn-Net Workshop: Heating up Networks - Analysis Meets Applications, Kaiserslautern (Germany), October 05-07, 2022

This workshop's aim is to bring together researchers from real world applications, analysis, and numerics. The meeting will take place at the Fraunhofer Institute for Industrial Mathematics (see https://www.itwm.fraunhofer.de/en.html). The Fraunhofer Institute is a research facility which works closely with partners in industry. Researchers from the Fraunhofer Institute will participate in the meeting
as well. In particular the group working on energy transport networks is close to the subject of our cost action (see https://www.itwm.fraunhofer.de/en/departments/tv/energy-transport-networks-and-model-reduction.html). Moreover, the meeting aims at providing a platform for discussions in a wide range of topics related to the Action Mat-Dyn-Net. Therefore, it will be open to all working groups. Participation is possible online as well as in person.

The program will include 30 min talks, collective discussions on problems and applications, and spare time for scientific interactions in smaller groups. If you want to give a talk at the workshop, please fill in this Form by 30 September 2022

Program

09:30-10:00   Zimmer 09:30:00-10:00      Aybar
10:00-10:30 Post 10:00-10:30 Beckermann
10:30-11:00 Coffee   break 10:30-11:00 Coffee break
11:00-11:30 Nicola De Nitti 11:00-11:30 Bifulco
11:30-12:00 Borsche 11:30-12:00 Mugnolo
12:00-12:30 Täufer 12:00-12:30 Eimer
15:00-15:10 Opening 12:30-15:00 Lunch/Open discussion   12:30 Closing
15:10-15:40 Bock 15:00-15:30  Coffee   break  after 12:30 Lunch/Open   discussion
15:40-16:10 Coffee   break   15:30-16:30 Open discussion
16:10-16:40 Pistol
16:40-17:10 Schillinger
17:10-17:40  Manea

Social events

Wednesday

18:30 Dinner at Sommerhaus https://www.restaurant-sommerhaus.com/

Thursday

16:30-18:30 Walk to the Humbergturm https://www.humberg-kaiserslautern.de/ and then to the Bremer Hof

18:30 Dinner at the Bremer Hof https://bremerhof-kl.de/

List of abstracts

Thomas Schillinger
schillinger@uni-mannheim.de
University of Mannheim
Control Strategies for Serial Networks under Uncertain Demand

We present a stochastic optimal control problem for a serial network. The dynamics of the network are governed by transport equations with a special emphasis on the nonlinear damping function. The demand profile at the network sink is modeled by a stochastic differential equation. An explicit optimal inflow into the network is determined and numerical simulations are presented to show the effects for different choices of the nonlinear damping.

Nicola De Nitti
nico.den@outlook.com
FAU Erlangen-Nürnberg
Control of advection-diffusion equations on networks and singular limits
We consider advection-diffusion equations posed on a tree with suitable transmission conditions at the junctions. We prove that the system is null-controllable using a control which is localized on the exterior nodes. Moreover, we study the asymptotic behavior of the cost of the null-controllability as the diffusivity parameter vanishes: we show that it decays for a sufficiently large time and explodes for short times. These results have been obtained in collaboration with J. A. Bárcena-Petisco, M. Cavalcante, G. M. Coclite, and E. Zuazua.

Delio Mugnolo
delio.mugnolo@fernuni-hagen.de
FernUniversität in Hagen
Parabolic Equations, Spectral and Torsion Geometry of Graphs
I will review the interplay between long-time behavior of diffusion equations on networks and elementary spectral theoretical properties. Several estimates - both classical and recently discovered ones - will be reviewed. In particular, we will discuss the interplay with the modern theory of landscape functions.

Mats-Erik Pistol
mats-erik.pistol@ftf.lth.se
Lund University
Generating isospectral but not isomorphic quantum graphs
There are few know examples of isospectral but not isomorphic quantum graphs. In order to rectify this situation we have used computer algebra to find all sets of isospectral but non-isomorphic equilateral connected quantum graphs with at most nine vertices. This includes thirteen isospectral triplets and one isospectral set of four. One of the isospectral triplets involves a loop where we could prove isospectrality. We will present several different combinatorial methods to generate arbitrarily large sets of isospectral graphs. The talk is based on: https://arxiv.org/abs/2104.12885 but will also include new results.

Dragos Manea
dmanea28@gmail.com
"Simion Stoilow" Mathematical Institute of the Romanian Academy
Non-local non-linear convection-diffusion on metric trees
This talk is concerned with a particle motion model on metric trees, driven by two non-local kernels, corresponding to the diffusion and convection behaviour, respectively. The convection part also contains a power-like non-linear term.\\ In this setting, we introduce a family of kernels, that localize the motion as the shrinking parameter $\varepsilon$ tends to 0, and we prove that the corresponding solutions converge weakly in $L^2$ to the weak solutions of a local convection-diffusion equation. \\ Since the diffusion-only case is known in the literature, we focus ourselves on finding an appropriate construction for the convection kernel, for the non-local equation to properly approximate the local one.\\ The transfer of the convergence through the non-linear term relies on a compactness result which resembles the norms of Sobolev-Slobodeckij spaces.

Wolfgang Bock
bock@mathematik.uni-kl.de
TU Kaiserslautern
The analysis behind epidemiological network models
In this talk I will sketch how Bollobas-Janson-Riordan graphs can be used to analytically deduce epidemiological relevant observables in a network model. The use of these random graphs gives rise to models having features which can not be modelled by standard mechanistic models. We show simulations to deduce the epidemic threshold in such models and how inhomogeneities are influencing it.

Olaf Post
olaf.post@uni-trier.de
Universität Trier
Examples of generalised norm resolvent convergence
This talk is a contiuation of the talk by Sebastian Zimmer. We give many examples illustrating the different concepts of generalised norm resolvent convergent. We also include a thick network model converging towards a metric graph.

Zimmer Sebastian
zimmerse@uni-trier.de
Universität Trier
Generalised norm resolvent convergence: comparison of different concepts
We show that the two concepts of "generalised norm resolvent convergence" introduced by Weidmann and the concept of "Quasi-unitary-equivalent-convergence" are equivalent. We also focus on the convergence speed and provide conditions under which the convergence speed is the same for both concepts.

Patrizio Bifulco
patrizio.bifulco@fernuni-hagen.de
FernUniversität in Hagen
Single and Attractive: Uniqueness and Stability of Economic Equilibria under Monotonicity Assumptions
In this talk we present a new theorem providing sufficient conditions for uniqueness and attractivity (respectively stability) in a certain class of models. We briefly discuss the uniqueness in this theorem and present how Perron-Frobenius theory for irreducible matrices plays a role there. To illustrate the applicability of our theorem, we characterize the general equilibrium properties of two simplified but commonly used quantitative trade models afterwards. This talk is based on a working paper in collaboration with Jochen Glück (University of Wuppertal), Oliver Krebs (ETH Zürich) and Bohdan Kukharskyy (City University of New York), see arXiv:2209.02635.

Paul Beckermann
paulbeckermann@online.de
TU Kaiserslautern
Invariance Properties of Laplacians on Metric Graphs
We investigate the semigroups corresponding to Laplacians on metric graphs concerning certain invariance properties, in particular reality, positivity and L^\infty-contractivity. Using form methods, we derive necessary and sufficient conditions depending on the quasi-Weierstraß normal form of the coupling boundary conditions.

Raul Borsche
borsche@mathematik.uni-kl.de
TU Kaiserslautern
Kinetic coupling conditions for hyperbolic equations on networks
In networks of hyperbolic conservation laws coupling conditions play a key role. In this talk we consider kinetic models to derive coupling conditions for the associated macroscopic equations. On the kinetic level the coupling conditions are often found easily. By using an asymptotic analysis near the nodes of the network, the problem can be formulated using kinetic half-space problems and macroscopic conditions are derived. This technique can be applied to several types of networks.

Ilknur Kusbeyzi Aybar
ikusbeyzi@yeditepe.edu.tr
Yeditepe University
Estimating oscillations in mathematical neuron models using a hybrid approach
In this study, we propose a hybrid approach to examine to what extent the mathematical neuron models characterize the experimental data in terms of electrical activities, transition to oscillatory phases, oscillation frequencies, and other dynamical states.

Matthias Täufer
matthias.taeufer@fernuni-hagen.de
FernUniversität in Hagen
Toolbox for controlling heat on domains (alternative title: Step 1: Dissipativity. Step 2: Unique Continuation. Step 3: Profit!)
We review the so-called Lebeau-Robbiano strategy (and subsequent works, among others by Miller) for controlling the heat equation on domains which reduce proofs of controllability to proofs of certain ingredients and comment on challenges when generalising this to metric graphs, modelling networks. Based in parts on joint work with Ivica Nakic, Martin Tautenhahn and Ivan Veselic.

Matthias Eimer
matthias.eimer@itwm.fraunhofer.de
Modeling of district heating networks
In this talk we look at the modeling of district heating networks. The dynamical behavior of water in the pipes is described by the incompressible Euler equations. Conservation of the involved quantities determines the coupling at each node of the network. For that system, we show unique existence of a solution. In the end we show some numerical simulations on real networks and optimization results from our work group.

For travel information please see: https://www.itwm.fraunhofer.de/en/contact.html and find “How to Reach the Fraunhofer ITWM” at the bottom of the page.