# Elevator pitches — donderdag 14 april

Voorzitter: *Ruben Hoeksma (Universiteit Twente) Waaier 2, do 11:15-11:45*

Masterstudenten en promovendi presenteren hun onderzoek via posters en lichten deze toe in een presentatie van twee minuten.

**Delays at signalised intersections with exhaustive traffic control**

*Marko Boon (Technische Universiteit Eindhoven) Waaier 2, do 11:15-11:18*

In this paper we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under Heavy Traffic (HT) conditions, using theory on polling models. Furthermore, we derive the Light Traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behaviour for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful and simple to implement.

**Minimizing the Waiting Time of Emergency Surgery**

*Theresia van Essen (Universiteit Twente) Waaier 2, do 11:18-11:21*

Hospitals aim to deliver high quality of care. One aspect in this context is to schedule emergency surgeries as quick as possible. Postponing these surgeries may increase a patient’s risk of complications and morbidity. Reserving capacity in the Operating Rooms (ORs) for emergency surgeries can be done in two ways: (1) dedicating an entire OR to emergency surgeries or (2) scheduling the emergency surgeries in one of the elective ORs. Previous literature has shown that the second option is the best one in terms of waiting time, staff overtime, and OR utilization. In this situation, emergency patients are operated once an ongoing elective surgery is finished. These moments in time are denoted by “break-in-moments” (BIMs). By spreading the BIMs as evenly as possible over the day, the waiting time of the emergency surgeries can be reduced even further. We discuss the problem of spreading these BIMs and we treat several solution methods for the off-line and on-line version of this problem.

**Persistence of noncompact Normally Hyperbolic Invariant Manifolds**

*Jaap Eldering (Universiteit Utrecht) Waaier 2, do 11:21-11:24*

Within dynamical systems, normally hyperbolic invariant manifolds (NHIMs) are a generalization to hyperbolic fixed points. The fixed point is replaced by a whole invariant manifold with corresponding generalized hyperbolicity criteria. Similar to a hyperbolic fixed point, a NHIM has (un)stable manifolds and persists under small perturbations. These structures play an important role in studying local and global nonlinear behavior, such as in bifurcation analysis and dimensional reduction. The classical theorems by Fenichel and by Hirsch, Pugh and Shub on persistence of NHIMs assume compactness of the invariant manifold. We will formulate a persistence theorem for general noncompact NHIMs. To properly generalize to arbitrary manifolds, e.g. with non-trivial normal bundle, we require the concept of a Riemannian manifold of *bounded geometry*. We illustrate why the perturbed manifold has only finite smoothness and, using examples, we show some of the issues specific to the noncompact setting and how bounded geometry comes into play.

**Model Based Control – Improving efficiency on Wastewater Treatment Plants**

*Maartje van de Vrugt (Universiteit Twente) Waaier 2, do 11:24-11:27*

Wastewater treatment plants in the Netherlands are forced by a new Dutch law to increase their efficiency with 2% each year until 2020. In many treatment plants the wastewater is cleaned by a biological process that consumes oxygen. This process accounts for about 60% of the energy consumption of the plant. In collaboration with Witteveen+Bos we have developed a new mechanism for the oxygen supply, referred to as Model Based Control, that is based on a model that predicts the pollution level of the wastewater. In a pilot study in treatment plant Westpoort the efficiency increase was shown to be substantial.

The pollution level in the wastewater was predicted with an adaptive model. To this end, a moving average filter was applied to the input signals to increase the correlation coefficient between prediction and measurements. Using adaptive control techniques an unsupervised adaptive oxygen supply mechanism was developed. Simulation results for Westpoort show that the new mechanism increases efficiency by 9%.

**A decomposition result for representations on ***L*^{p}**-spaces**

*Jan Rozendaal (Universiteit Leiden) Waaier 2, do 11:28-11:31*

In representation theory one is often interested in decomposing a representation of a group on some space into a sum of irreducible representations. In the case of groups acting unitarily on Hilbert spaces, results of this form have been found. Less is known about actions on Banach spaces, let alone on ordered Banach spaces or Banach lattices. Moreover, representations are usually decomposed into direct sums of irreducible representations. Sometimes one cannot hope to find such a direct sum decomposition, and one wishes to consider a type of direct integral. Such a concept exists for Hilbert spaces, but for Banach spaces there is no widely accepted theory.

In my thesis, I prove a decomposition result for group actions on certain specific Banach lattices, *L** ^{p}*-spaces of

*p*-integrable functions. These spaces carry a pointwise ordering which behaves nicely with respect to the norm, and we would like to decompose such a space in a manner which respects this ordering. Hence our goal is to decompose a representation on these ordered Banach spaces in an order irreducible manner.

I use the theory of so-called Banach bundles to consider an “integral” of Banach spaces, thereby providing a possible alternative to the direct integral concept for Banach spaces. Combining this with results on integral decompositions of invariant measures, we have the tools necessary to decompose a representation of a group on such an *L** ^{p}*-space intorepresentations which are order irreducible.

To be more precise, I prove that for any locally compact Polish transformation group (*G,X*) and any finite *G*-invariant measure *μ *on *X*, the action of *G *on *L** ^{p}*(

*X, μ*) induced by that on

*X*can be decomposed into band-irreducible representations for any . This is done by constructing an isometric lattice isomorphism between the space

*L*

*(*

^{p}*X, μ*) and a space of

*p*-integrable sections of a certain Banach bundle having spaces

*L*

*(*

^{p}*X, λ*), for

*λ*ranging over the ergodic measures on

*X*, as fibers. As far as the author is aware of, such a result has not yet appeared in the literature.

**Differentiaalvergelijkingen begrijpen**

*Joke Zwarteveen-Roosenbrand (Universiteit Twente / ELAN), Waaier 2, do 11:32-11:35*

The concept of differential equations (DEs) is essential in university science. The Dutch government introduced a new subject, Mathematics D, in the existing mathematics curriculum of the secondary education in recent years. Mathematics D aims to prepare for university science education. The concept of DEs’ introduction is a principal part of this preparation. A key objective on this topic, according to the Dutch government’s mathematics innovation committee, is analyzing (the solutions of) dynamic systems. Therefore the mostly used textbooks describe how to solve some types of DEs using algebraic methods and focus on the behavior of DEs, like equilibrium. In these cases the DEs are given, but the concept of a DE as a model of dynamic phenomena is not highlighted. This is not only the case in the Netherlands. However, research outcomes show that students have great difficulties in analyzing dynamic systems when they don’t know how to model those systems. So conceptual understanding of the concept of DEs needs the knowledge of setting up a DE. Therefore instructions are designed to promote understanding of the concept of DEs by means of setting up DEs. The poster shows the cyclic design research process of improving the design of the instructions as well as measuring the effects of the instructions. So the research question of my PhD research is: What are the characteristics of teaching the concept of DEs in line with students’ thinking processes?

**Invariant Measures of Random Walks in the Quarter-plane**

*Yanting Chen (Universiteit Twente) Waaier 2, do 11:35-11:38*

We consider the invariant measure of homogeneous random walks in the quarterplane. In previous research, it is revealed that there are some random walks for which the invariant measure is of geometric product form. We consider the class of measures that can be expressed as a linear combination of geometric product forms. First, it is shown that no finite linear combination of terms can be the invariant measure of an ergodic random walk. Second, it is shown that the only class of countable linear combinations are of the form in which terms occur in pairs. This completely characterizes the class of series of geometric terms that can be the invariant measure of a random walk in the quarter-plane.

**Model Checking Stochastic Systems using Rare Event Simulation**

*Daniël Reijsbergen (University of Twente) Waaier 2, do 11:39-11:42*

We are interested in estimating system failure probabilities in highly dependable systems, such as a telecommunications network or a nuclear power plant. Examples of probabilities of interest could be system failure before some time bound, or the long run fraction of time that the system is down. Often, the models have state spaces that are too large for iterative methods (such as the Gauss-Seidel method). Stochastic simulation is then typically used as the alternative. Obviously, in a highly dependable system, system failure is a *rare event*, so we need to apply *efficient *simulation techniques. We use Importance Sampling, i.e. we simulate under a new distribution which oversamples occurrence of the rare event. The focus of our research is to find simulation distributions that perform well for a given model setting.

**Immersed boundary method for pulsatile flow in cerebral aneurysms**

*Julia Mikhal (Universiteit Twente) Waaier 2, do 11:42-11:45*

We present a numerical method for simulation of blood flow inside the human brain. The focus is on cerebral aneurysms that may form on some vessels. The precise blood flow and the forces on the vessel wall are computed. This contributes to our understanding of possible long-term rupture of aneurysms from an analysis of the short-time pulsatile flow. The computational model is based on the incompressible Navier-Stokes equations in 3D. Flow in complex aneurysm geometries is represented with the use of a volume-penalizing Immersed Boundary (IB) method. The main feature of our IB method is the so-called masking function which equals “0” inside the flow domain while in solid parts it takes the value “1”. This technique allows a fast and relatively simple definition of any geometry. The flow inside the defined geometry is simulated on the basis of a skew-symmetric finite-volume discretization and explicit time-stepping. We compute the blood flow at various physiologically relevant flow speeds and for several types of pulsatile forcing of the flow. The model aneurysm consists of a curved vessel with a spherical cavity attached to it. Time-dependent flow and the evolution of the forces on the vessel wall are analyzed for a basic sinusoidal forcing and a parameterized realistic cardiac cycle. For relatively slow flows the flow forcing pattern dominates the forces on the walls. Upon increasing the flow-speed we observe a lively unsteady flow with more and more vortical structures arising inside the curved vessel and in the spherical cavity of the aneurysm. At these faster flows the pulsatile forcing pattern is less pronounced and the flow is dominated by its intrinsic Navier-Stokes unsteadiness. The simulations confirm that, within a physiologically relevant range of flow speeds, strong transitions in flow behavior and in force levels develop inside the aneurysm cavity, which may contribute to the long-term risk of aneurysm rupture.