The seminar takes place twice a year.
For more information, please contact the organizers: Svetlana Dubinkina (VU), Frits Veerman (LU), and Yves van Gennip (TU Delft).
A database of earlier years' seminar (including the former VU-UvA dynamical analysis seminar) can be found here.
Upcoming events
One-day VU/Leiden/Delft seminar on Dynamical systems: modelling, analysis and computation
April 3, 2023, 10:00-17:00 at the VU Amsterdam, room NU-4B43
Register here: https://forms.gle/dHZecjhUpnqkMDBz8
10:00 - walk in and coffee
10:30-11:30 Peter van Heijster (U. Wageningen) “Transition from Turing instability to large periodic solutions in a reaction-diffusion system”
11:30-12:00 PhD students Q&A
12:00-13:00 lunch
13:00-14:00 Olga Mula (TU/e) “Optimal State and Parameter Estimation Algorithms and Applications to Biomedical Problems”
14:00-14:30 coffee break
14:30-15:30 Olga Lukina (U. Leiden) ““Dynamical and ergodic properties of a family of interval exchange transformations”
15:30-16:00 PhD students Q&A
16:00-17:00 Chris Bick (VU) “Chaos in symmetric phase oscillator networks”
17:00: drinks
Peter van Heijster (U. Wageningen) “Transition from Turing instability to large periodic solutions in a reaction-diffusion system”
Abstract: Analytically tracking patterns emerging from a Turing small amplitude instability to large amplitude patterns remains a challenge as no general theory is available. In this talk, we consider a three-component reaction-diffusion system and develop an analytical understanding of periodic patterns emerging from a Turing instability using spatial geometric singular perturbation theory. The system has a single singularly perturbed component known as a fast variable. We show analytically that after the initial Turing instability, spatially periodic patterns evolve into a small amplitude spike in the fast variable whose amplitude grows as one moves away from onset. This is followed by a secondary transition where the spike in the fast variable widens, its periodic pattern develops two sharp transitions between two flat states and the amplitudes of the other variables grow. The final type of transition we uncover analytically is where the flat states of the fast variable develop structure in the periodic pattern. Numerically, we show that the structure allows the periodic patterns to undergo a succession of Turing instabilities repeating the transition processes described above. This leads to the development of more complicated periodic patterns and snaking-like behavior.
This is joint work with Christopher Brown, Gianne Derks and David J.B. Lloyd from the University of Surrey in the UK
Olga Mula (TU/e) “Optimal State and Parameter Estimation Algorithms and Applications to Biomedical Problems”
Abstract: In this talk, I will present an overview of recent works aiming at solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a notion of optimal performance in terms of the smallest possible reconstruction error that any reconstruction algorithm can achieve, I will present practical numerical algorithms based on nonlinear reduced models for which we can prove that they can deliver a performance close to optimal. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic notions of accuracy quantification. I will illustrate the performance of the approach on simple benchmark examples, and we will also discuss applications of the methodology to biomedical problems which are challenging due to shape variability.
Olga Lukina (U. Leiden) “Dynamical and ergodic properties of a family of interval exchange transformations”
Abstract: In the talk, we investigate the dynamics of a family of interval exchange transformations with infinite number of intervals, called the rotated odometers. These systems naturally arise as first return maps of parallel flows on translation surfaces of infinite genus. To study the dynamics of a rotated odometer, we embed it into a dynamical system on a Cantor set, given by the Vershik map on an eventually periodic Bratteli diagram. We then study the number of ergodic measures, and the spectrum of the Koopman operator using the associated substitution matrices. This is joint work with Henk Bruin.
Chris Bick (VU) “Chaos in symmetric phase oscillator networks”
Abstract: The collective dynamics of coupled oscillatory systems, such as synchronization, are essential for the functioning of a variety of systems, ranging from coupled neurons to power grid dynamics. Here, we explore the emergence of chaotic collective dynamics in a minimal system of four symmetric coupled phase oscillators. Specifically, we discuss how chaotic dynamics emerge depending on the complexity of the interaction between the oscillators subject to the constraints due to the symmetry of the system.
Previous talks
On Tuesday 25 October, 15:00h - 17:00h, the joint VU/Delft/Leiden seminar series took place at TU Delft, in Lecture Hall Chip (36.HB.01.600) in the EEMCS building at Mekelweg 4 (building 36, first floor). For a campus map with building numbers: https://iamap.tudelft.nl
You are all cordially invited to join, and enjoy the following programme:
15:00 - 15:45: Silke Glas (Universiteit Twente)
15:45 - 16:15: Coffee/tea break with an opportunity to meet your colleagues from other universities
16:15 - 17:00: Palina Salanevich (Universiteit Utrecht)
After the talks we will go for drinks to /Pub (in the basement of building 36). Everyone is welcome to join.
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Wednesday November 23, 15:00 - 17:00, at Leiden University.
Silke Glas (Universiteit Twente)
Title: Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds
Abstract: In the beginning of this talk, I will introduce the concept of model order reduction and provide a short overview of the field. I will particularly talk about so-called classical linear-subspace reduced order models (ROMs) and explain the necessary steps to arrive at such a model. In the second part of the talk, we consider problems, where classical linear-subspace ROMs of low dimension might yield inaccurate results. This could be the case for certain transport-dominated problems. Thus, the reduced space needs to be extended to more general nonlinear manifolds. Moreover, as we are dealing with Hamiltonian systems, it is crucial that the underlying physical so-called symplectic structure is preserved in the reduced model. To the best of our knowledge, existing literature addresses either model reduction on manifolds or symplectic model reduction for Hamiltonian systems, but not their combination. We bridge the two aforementioned approaches by providing a novel projection technique called symplectic manifold Galerkin. We derive analytical results such as stability, energy-preservation and a rigorous a-posteriori error bound. Moreover, we construct a weakly symplectic convolutional autoencoder in order to computationally approximate the nonlinear symplectic trial manifold. We numerically demonstrate the ability of the method to outperform structure-preserving linear subspace ROMs results for a linear wave equation, which is known to not be well-approximated by linear-subspace ROMs.
Palina Salanevich (Universiteit Utrecht)
Title: Phase retrieval with time-frequency structured measurements
Abstract: Phase retrieval is a non-convex inverse problem that arises in many practical applications, such as diffraction imaging, audio processing, and many more. In phase retrieval, we seek to recover a signal from the intensities of its linear measurements with respect to an ensemble of vectors, called the measurement frame. Even though this problem has been studied for a long time, until recently very little was known about how to achieve stable and efficient reconstruction, and the existing reconstruction methods lacked rigorous mathematical understanding. Nowadays, the case when the measurements are taken with respect to independent random Gaussian vectors is sufficiently well studied. At the same time, very little is known about the case when the measurement frame has structure that is relevant for applications. The main reason for this is that geometric properties of structured frames are not yet fully understood. In the talk, we are going to focus on phase retrieval with Gabor frames. In these frames, the measurement vectors follow time-frequency structure that naturally appears in imaging and acoustics applications. We will discuss which geometric properties of the frames ensure injectivity and stability of the placeless measurement map. We will also construct an efficient and robust phase retrieval algorithm that uses a close to optimal number of time-frequency structured measurements, and show reconstruction and robustness guarantees for its performance.
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On Wednesday 23 November, 15:00h - 17:00h, the joint VU/Delft/Leiden seminar series took place at Leiden University, Huygens Laboratory room 226, Niels Bohrweg 2.
15:00 - 15:45: Kateryna Marynets (TU Delft)
15:45 - 16:15: Coffee/tea break with an opportunity to meet your colleagues from other universities.
16:15 - 17:00: Jose Mujica (VU)
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Tuesday 20 September, 15:00h - 17:00h, we start again our joint VU/Delft/Leiden seminar series. The next installment will take place at
VU Amsterdam, De Boelelaan 1111, 9th floor.
You are all cordially invited to join, and enjoy the following program:
15:00 - 15:45: Martina Chirilus-Bruckner (Leiden U.)
15:45 - 16:15: Coffee/tea break with an opportunity to meet your colleagues from other universities.
16:15 - 17:00: Vanja Nikolić (U of Nijmegen)
After the talks, we will go for drinks and snacks downstairs
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25. June (TU-Leiden EEMCS building, building 36, pi room, Mekelweg 4)
Programme:
15:00 - 15:45: Tinka Valentijn (United Nations)
15:45 - 16:15: Coffee/tea break with an opportunity to meet your colleagues from other universities
16:15 - 17:00: Martina Chirilus-Bruckner (Universiteit Leiden)
After the talks we will go for dinner. Everyone is welcome to join (at own expense).
Speaker: Tinka Valentijn (United Nations)
Title: Can we assess damage from space?
Abstract: With the increasing availability of data and models, opportunities arise to apply these to new contexts. One such context is the humanitarian sector. Tinka is working as humanitarian data scientist at the United Nations. Before joining the UN, she researched the ability of computer vision models to assess damage to buildings after disasters from satellite imagery. During her talk she will dive into what and how's of these models, with a specific focus on making them usable during humanitarian operations.
Speaker: Martina Chirilus-Bruckner (Universiteit Leiden)
Title: Exotic fronts in a system of reaction-diffusion equations
Abstract: Unraveling the general dynamics of nonlinear PDEs is often a grand challenge. Adopting the classical dynamical systems viewpoint, one can follow the strategy of first concentrating on existence, stability and bifurcations of special solutions and then examine their role for more complicated dynamics. Localized structures such as front solutions, pulses and wavepackets are precisely such special solutions for infinite-dimensional dynamical systems given by PDEs. In this talk we focus on the dynamics of front solutions in a multi-compontent reaction-diffusion system. After an overview of past results we give an exposition of new results on a novel type of traveling front solution featuring heterogeneous (instead of constant) tails. These are encountered when adding spatially varying coefficients to the nonlinear PDE.
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Wednesday 18 May, 15:00h - 17:00h, the joint VU/Delft/Leiden seminar series took place at Leiden University, Huygens Laboratory room 226, Niels Bohrweg 2. You are all cordially invited to join, and enjoy the following programme:
15:00 - 15:45: Fahimeh Mokhtari (VU Amsterdam)
15:45 - 16:15: Coffee/tea break with an opportunity to meet your colleagues from other universities.
16:15 - 17:00: Domenico Lahaye (TU Delft)
After the talks, drinks and snacks will be served at the Foobar, in the Snellius building (Niels Bohrweg 1)
Versal deformation for non-simple singularities (Fahimeh Mokhtari)
In normal form theory for general differential equations or symplectic systems around equilibria, not much attention is usually given to the linear part of the problem.
A typical approach in bifurcation theory is to compute the normal form of a general system with respect to a given organizing center and add versal deformation terms (as first considered by V.I. Arnol'd in 1971). One can then analyze all possible bifurcations in a neighborhood of the organizing center.
While there is nothing wrong with this approach, it does not answer the following question: how does one compute the versal normal form when a given system is in the neighborhood of the organizing center?
In this talk, we address this issue by giving a complete description of a first-order calculation in a three-dimensional irreducible nilpotent case, which is then followed up by an explicit calculation to find the transformation to versal normal form in a particular fluid dynamics problem and in the celestial mechanics L4 problem.
Sustainable Combustion through Modeling and Simulation (Domenico Lahaye)
Heavy industry relies on hydro-carbon fuels (natural gas and coal) as a primary source of energy. The energy density required renders alternatives unavailable at least on short term. The future use of fossil fuels, however, is met by environmental, economical and geo-political challenges. Measures to combat climate change impose ever stringent requirements on pollutant emissions. The World Health Organization calls for urgency in improving air quality. The depletion of proper sources renders the Netherlands critically dependent of foreign import. Data-driven insight to formulate guidelines for sustainable and economical use of hydro-carbon fuels is thus urgently required.
In this talk, we will discuss our work on the numerical simulation of the combustion of Dutch natural gas in large industrial furnaces. The models we develop consist of four components. These component describe the turbulent flow and mixing of the gasseous fuel and combustion air, the chemical reactions and heat release of the combustion, the heat transfer by convection and radiation through the furnace and the pollutant formation.
We will show how efforts in building digital twins of industrial furnaces allowed our industrial partners to eliminate unscheduled plant shutdowns and to find measures to mitigate the formation of undesired nitric-oxides.
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13 April (15:00 - 17:99) at VU Amsterdam, New University Building, De Boelelaan 1111 (9th floor)
A map of the campus can be found here. After the seminar we plan to go for drinks in a downstairs pub. Please note that the drinks are at your own expense.
Programme:
15:00 -- 15:45: Talk by Henk Schuttelaars (TU Delft)
15:45 -- 16:15: Coffee/tea break with an opportunity to meet your colleagues from other universities.
16:15 -- 17:00: Talk by Olfa Jaïbi (TU Delft)
Speaker: Henk Schuttelaars (TU Delft)
Title: Morphodynamic equilibria of double inlet systems
Abstract: Complex bottom patterns are often observed in tidal basins, found in for example the Wadden Sea along the Dutch, German and Danish coast. These patterns consist of branching channel-shoal patterns, that often exhibit cyclic behavior. An idealised morphodynamic model, consisting of a coupled system of nonlinear partial differential equations that describe the water motion, sediment transport and bed evolution, is derived. Using continuation techniques, morphodynamic equilibria are identified and their stability is assessed. In this presentation, I focus on such equilibria for tidal systems that are forced at two inlets connected to the coastal sea.
Speaker: Olfa Jaïbi (TU Delft)
Title: Existence of (novel) localised vegetation patterns in a generalised ecosystem model.
Abstract: One of the effects of climate change is the phenomenon of desertification, a process that occurs in semi-arid and arid areas and causes land degradation as well as vegetation loss. Due to the lack of resources, vegetation self-organises to sustain itself by forming large-scale spatial patterns. In this talk, the underlying mathematical structure of these observed vegetation patterns is studied using a partial differential equations model. The vegetation patterns are analysed using techniques from geometrical singular perturbation theory and numerical simulations. We focus on a two-component reaction-diffusion model for vegetation biomass and soil water content for dryland ecosystem dynamics and prove the existence of `basic' 1-front invasion patterns and 2-front spot/gap patterns which have a direct ecological interpretation and form the building blocks of `novel' multi-front patterns that are exhibited by the model.
16 March (16:00 - 17:00) at the Technische Universiteit Delft, EEMCS/EWI Building 36, Snijderszaal
Speaker: Alef Sterk (Rijksuniversiteit Groningen)
Title: Extremes in dynamical systems: max-stable and max-semistable laws
Abstract: Extreme value theory for chaotic, deterministic dynamical systems is a rapidly expanding area of research. Given a dynamical system and a real-valued observable defined on its state space, extreme value theory studies the limit probabilistic laws for asymptotically large values attained by the observable along orbits of the system. Under suitable mixing conditions the extreme value laws are the same as those for stochastic processes of i.i.d. random variables. Max-stable laws are particularly suitable for probability distributions with regularly varying tails. However, in the context of dynamical systems, where the underlying invariant measure can be irregular, max-semistable laws seem to be more relevant. In this talk I will discuss the classical results for i.i.d. processes, some recently obtained results for dynamical systems, and directions for future research.
16 February: Gianmarco Bet from University of Firenze will give an online talk.
Title: Weakly interacting oscillators on dense random graphs
Abstract: We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence. We establish a Law of Large Numbers for the empirical measure of the system that holds whenever the graph sequence is convergent in the sense of graph limits theory (i.e. it converges to a so-called graphon). The limit is shown to be the solution of a non-linear Fokker-Planck equation weighted by the (possibly random) graphon limit. We also characterize the sequences of graphs, both random and deterministic, for which the associated empirical measure converges to the mean-field limit, i.e., to the solution of the classical McKean-Vlasov equation.
15. December: Nikolaos Sfakianakis (University of St Andrews).
Title: A genuinely hybrid 3-D single- and multi-organ cancer invasion framework and virtual environment
Abstract: The ability to locally degrade the Extracellular Matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a critical step in the tumour metastasis. The tissue invasion involves the coordinated action of the cancer cells, the ECM, the Matrix Degrading Enzymes, and the Epithelial-to-Mesenchymal transition (EMT). In this talk, we present a 2- and 3D mathematical model which describes the transition from an epithelial invasion strategy of the Epithelial-like Cancer cells (ECs) to an individual invasion strategy for the Mesenchymal-like Cancer cells (MCs); this is a genuinely multiscale and hybrid model of PDEs and SDEs. In the second part of the talk we present the most recent extension of our model to a multi-organ (and connected via the circulatory system) conformation of the organism and investigate the principles of cancer metastasis. The material of this presentation is based on joint works with: M. Chaplain, A. Madzvamuse, L. Franssen, T. Williams, A. Wilson, L. Fu, and N. Kolbe
17 November: Claire Postlethwaite (Auckland)
Title: A heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock
Abstract: The well-known game of Rock-Paper-Scissors can be used as a simple model of competition between three species. When modelled in continuous time using differential equations, the resulting system contains a heteroclinic cycle between three equilibrium solutions. The game can be extended in a symmetric fashion by the addition of two further strategies (‘Lizard’ and ‘Spock’): now each strategy is dominant over two of the four other strategies, and is dominated by the remaining two. The differential equation now contains a set of coupled heteroclinic cycles forming a heteroclinic network. In this talk I will discuss how we study the dynamics near this heteroclinic network. In particular, I will show how we are able to identify regions of parameter space in which arbitrarily long periodic sequences of visits are made to the neighbourhoods of the equilibria, and how these regions form a complicated pattern in parameter space.
15 September: Alethea Barbaro (TU Delft)
Title: From particles to continuum: a convection-diffusion model for territorial development
Abstract: Many species demonstrate territoriality, with individuals or groups marking their territories either chemically or visually. In this talk, we will present an agent-based lattice model for territorial development. In this model, there are several groups, and agents from each group put down that group’s territorial markings as they move on the lattice. Agents move away from areas with territorial markings which do not belong to their own group. We will show that this model undergoes a phase transition between well-mixed collective dynamics and distinct territories as parameters are varied. We will then discuss the derivation of a system of coupled convection-diffusion equations from this model. This system exhibits cross-diffusion due to the avoidance of other groups’ markings. We will pinpoint the critical value for the phase transition using linear stability analysis and discuss further analytical and numerical work stemming from this model.
16 June: June 16, Hildeberto Jardón Kojakhmetov (U. Groningen)
12 May: Marten Wortel (University of Pretoria)
14 April: Anna Geyer (TU Delft, Institute of Applied Mathematics).
Stability and persistence of periodic traveling waves
In the first part of my talk, I will present a result on the stability of smooth periodic traveling waves of the Camassa-Holm equation. This equation models the propagation of shallow water waves and has been studied extensively. The problem of spectral stability of periodic waves however was still open. The key to obtaining the spectral stability is that the periodic waves can be characterized by an alternative Hamiltonian structure, different from the standard formulation.
In the second part of my talk, I will focus on the problem of persistence of periodic traveling waves in Hamiltonian PDE (for instance, the Camassa-Holm equation) under perturbations. I will show that the number of traveling waves that persist are controlled by the zeros of certain Abelian integrals. Moreover I will show that one can design the perturbations precisely so that any prescribed number of traveling waves persists.
The first part is joint work with Dmitry Pelinovsky and Fabio Natali, the second part with Armengol Gasull and Víctor Mañosa.