## Study Group Mathematics with Industry: Selected Research 2007-2010

**Organizer & Chair: Onno Bokhove (Universiteit Twente)**

Waaier 1, 13:45 – 15:45

## 13:45-14:15

### Understanding the electromagnetic field in an MRI scanner: applications to parallel MRI techniques

*Alessandro Sbrizzi (Imaging Division, University Medical Center Utrecht)*

Magnetic Resonance Imaging (MRI) is a technique for non-invasive inner inspection of the human body. In the last decade, MRI has been subject of extensive research with the main goals of shortening the scanning time and acquiring better resolution images. For these reasons, higher magnetic fields have being employed and parallel imaging techniques (pMRI) have being developed. These new tools require detailed information about the electromagnetic fields in the scanner. In this presentation, an introduction to the mathematical foundation of pMRI is given and a method to acquire the information needed is described. The method is based on a simplification of Maxwell’s equations into a single, scalar, Helmholtz equation. The foundation of this work has been laid during the SWI workshop in 2007.

## 14:15-14:45

### Increasing detection performance of surveillance sensor networks

*Sandra van Wijk (Technische Universiteit Eindhoven, Eindhoven)*

We study a surveillance wireless sensor network (SWSN) comprised of small and low-cost sensors. These are deployed in a region in order to detect objects crossing the field of interest. We address two problems concerning the design and performance of an SWSN: optimal sensor placement and algorithms for object detection in the presence of false alarms. For both problems, we propose explicit decision rules and efficient algorithmic solutions. Further, we provide several numerical examples and present a simulation model that combines our placement and detection methods. The problem was presented to the Study Group Mathematics with Industry in 2008 by Thales.

## 14:45-15:15

### Roll dynamics of ships in large amplitude head waves

*Ed van Daalen ^{1}, M. Gunsing^{1}, Johan Grasman^{2}, and J. Remmert^{3}*

^{1}Maritime Research Institute Netherlands (MARIN), The Netherlands

^{2}Biometris, Wageningen University and Research Centre (WUR), The Netherlands

^{3}Dept. of Maritime Technology, Delft University of Technology, The Netherlands

Some ship types may show large amplitude rolling when sailing in large amplitude head waves. The dynamics of the ship is such that roll is affected by the surface elevation of the encountering waves. If the natural roll period (without forcing) is about half the period of the forcing by the surface elevation, then the stationary solution will have an amplitude that is much larger than for other forcing frequencies. This phenomenon is called parametric resonance. Due to the shape of the hull its heave motion is influenced considerably by the phase of the wave as it passes the ship. Moreover, the waves will also have a direct effect upon the roll dynamics. For these processes a differential equation model is formulated, being a Mathieu type of equation. Furthermore, the waves are of a type that is met in open seas; as a parameterization of these waves the Pierson-Moskowitz spectrum is used. The risk that the roll angle reaches a critical size is characterized by the time of arrival at this value, starting from an arbitrary pattern of the waves and the dynamic state of the vessel in the stationary situation. Large scale Monte Carlo simulations of this process are carried out. The percentiles of the distribution of arrival times give an indication of the risk of extreme roll to which the vessel is exposed. Furthermore, a method is proposed to estimate the maximum roll angle in a stationary sea by just taking into consideration the part of the wave spectrum that relates to the state of parametric resonance. The result is compared with the outcome of the Monte Carlo simulations.

## 15:15-15:45

### Optimal distributed power generation under network load constraints

*Jason Frank ^{1} and Gabriël Bloemhof^{2}*

^{1}Centrum Wiskunde & informatica, Amsterdam

^{2}KEMA Consulting, Arnhem

In modern electrical power networks more and more customers are becoming power producers, mainly because of the development of novel components for decentral power generation (solar panels, small wind turbines and heat pumps). KEMA is interested in the question how much generation of each type (solar panel, small wind turbine or central heating power units) can be inserted into any transmission line in the network, such that under given distributions on the typical production and consumption over time, the maximum loads on the lines and components will not be exceeded. For SWI2010, we developed a linear programming model for maximizing the amount of decentral power generation while respecting the load limitations of the network. We describe a prototype showing that for an example network the maximization problem can be solved efficiently. We also modelled the case were the power consumption and decentral power generation are considered as stochastic variables, which is inherently more complex.