


ESSIM 2012



The Modelling Week — PROJECTS

[P1] 
Optimizing a complex hydroelectric cascade in an electricity market.
posted posted Juni 12, 2012 by ECMI Dresden
Instructor: Marta Margarida Braz Pascoal (Coimbra)
In hydroelectric power stations it is possible to manage the storage of water in reservoirs and to release water downstream, thus producing energy.
While this might not be worthwhile from an energy point of view, the profit resulting from this process depends on the price of energy at times of
energy consumption and energy production.
Having the possibility of pumping water upstream at times when the energy price is low, the energy stored may then be made available at a later time
when prices are higher.
The goal of this study is to provide guidance in decisionmaking aimed at maximizing the profit, when dealing with a branched model for hydroelectric
power station interacting in a cascade arrangement with the possibility of pumping water from one reservoir to two reservoirs.
Mathematical background: hydroelectric power, branched cascade, mathematical modelling, optimisation, optimal control

[P2] 
Parameter estimation in production processes.
posted posted Juni 12, 2012 by ECMI Dresden
Instructor: Kshitij Kulshreshtha (Paderborn)
For numerous applications the estimation of parameters like material constants or concentrations is of
significant importance to ensure the quality of the outcome. Within this project, the students become
acquainted with the modern mathematical techniques for the estimation of parameters in stationary and
instationary processes.
This will require the application of algorithmic differentiation and nonlinear optimisation.
Furthermore, real world applications often suffer from uncertainty, for example due to measurement errors.
Therefore the approaches above will be extended to analyse the resulting uncertainty in the estimated parameters.
Mathematical background:
Inverse Problems, Parameter Estimation, Algorithmic Differentiation,
Nonlinear Optimization, Uncertainty, Robustness

[P3] 
Modelling of a Storage Water Heater.
posted posted Juni 12, 2012 by ECMI Dresden
Instructor: Joachim Krenciszek (Kaiserslautern)
In many households the hot water comes from a storage water heater (tanktype). As the water is heated at a relatively slow rate, the question arises how long it will take to heat fresh water in the tank when the hot water supplies are running short.
Further, what would an optimal heating pipe look like that minimizes the time used for the heating process?
Mathematical background:
heat conduction, convection, fluid dynamics, optimal design

[P4] 
Mathematics of the eye: modeling corneal curvature.
posted posted Juni 12, 2012 by ECMI Dresden
Instructor: Łukasz Płociniczak
(Wrocław)
Sight is the most crucial sense that we posses since it enables us to perceive the world very accurately.
With the advance of medical technology treating various eye diseases becomes more adequate and successful.
This would not be possible without proper mathematical models of biomechanics of eye and its constituents.
Due to its responsibility in maintaining refractive power (about twothirds of the whole sight mechanism) one of the most important parts of the human eye is the cornea. It is situated in the frontal part of the eyeball. Since it must refract light with good efficiency it is very transparent and resistant to mechanical damage. Mathematical description of cornea is very important from the point of view of ophthalmologists because many seeing disorders originate in some distortions in corneal geometry.
The aim of this problem is to propose a model for corneal curvature since it is one of the most important measured properties of the cornea itself. From the distribution of curvature one can then make some diagnosis like determining astigmatism.
Changes of corneal curvature caused by surgery should also be taken into account in the proposed model.
Mathematical background:
ODEs, elementary differential geometry, PDEs

[P5] 
Phantom footballs and impossible freekicks:
modelling the flight of modern soccer balls.
posted Juni 12, 2012 by ECMI Dresden
Instructor: Timothy Reis (Oxford)
As can be remembered from the 2010 FIFA World Cup, apparent uncertainties in the trajectory of soccer balls at high velocities have led to some criticism of the ball manufacturers, most notably by the professional players. The manufactures, on the otherhand, maintain their claim that the 'Jabulani' ball (which is made from eight thermally bonded panels and features Adidas's socalled 'grip and grove' technology) is the most aerodynamically advanced ball to date. Indeed, this is not the first time there have been contradictory reports between players and manufacturers: the 2006 World Cup ball ('Teamgeist') also received criticism; and over the years there have been a number of moments in soccer which have been dubbed 'impossible' (perhaps most notably, Roberto Carlos 1997).
So who has the science to support their claim: the players, the journalists or the manufactures?
The aim of this project is to develop a mathematical model to understand and predict the flight of various soccer balls and to ultimately decide if the choice of ball really makes that much difference.
Mathematical background:
Newton's laws, fluid mechanics, asymptotic approximations

[P6] 
Model the effect on health of contamination from airborne source(s).
posted Juni 18, 2012 by ECMI Dresden
Instructor: Christopher Coles (Glasgow)
The project includes estimating the received dosage and also the identification of the likely
source(s). This currently is topical as there has been an outbreak of Legionnaires disease in
Edinburgh (resulting in several fatalities).
Mathematical background: Ideally the short course on Airborne Pollution of ESSIM 2012.
PDEs.

[P7] 
Optimal heating of an indoor swimming pool.
posted Juni 22, 2012 by ECMI Dresden
Instructor: Monika Wolfmayr (Linz)
Modelling the heating of an object is an important task in many applicational problems.
Moreover, a matter of particular interest is to find the optimal heating of an object such that
it has a desired temperature distribution after some given time. In order to formulate such
optimal control problems and to solve them, one needs to consider e.g. the formulation of the
cost functional as well as the corresponding timedependent PDE constraints. In this project, the
students have to formulate the mathematical model of heating an indoor swimming pool. More
precisely, the swimming pool is located under a glass dome and the heat sources are situated at the
boundary of the glass dome. The task of the project is on the one hand to model this heating process
and on the other hand to determine the optimal heating of the glass dome such that the desired
temperature distribution is attained after a given time, i.e., to formulate the corresponding
optimal control problem and to solve it numerically.
Mathematical background: parabolic PDEs, optimal control problems, solving PDEs numerically, MATLAB programming

[P8] 
What are the effects of anatomical changes in the human arterial system?
posted Juni 25, 2012 by ECMI Dresden
Instructor: Alexandra Moura (Lisbon)
What are the consequences of amputating a leg on the human circulatory system? Or what are the effects of genetical anatomical differences in the cerebral vasculature? To answer these questions there is the need for robust mathematical models and numerical methods, in order to perform numerical simulations in large arterial networks. Here, 1D reduced mathematical models will be used to study blood flow and arterial pressure propagation in the arterial system. Precisely, 1D models are derived from 3D fluidstructure interaction (FSI) models through an averaging and simplifying procedure, resulting in an hyperbolic system of PDEs. Despite having a lower level of accuracy compared to the full 3D FSI model, they are able to capture very effectively the wave propagation nature of blood flow in arteries, and due to their low computational cost, they can be used to represent large arterial trees.
Mathematical background: hyperbolic PDEs, Finite Element Method, boundary and compatibility conditions, wave propagation, blood flow in arteries

[P9] 
How do we go from medical images to computational haemodynamic simulations?
posted Juni 25, 2012 by ECMI Dresden
Instructor: Alberto Gambaruto (Lisbon)
Numerical simulations of blood flow have been shown to be important to understand and predict cardiovascular disease formation, but how can one go about it? MR and CT images are routinely available, and from these one can reconstruct the anatomical geometry, that can then be used for numerical simulations. How do you put everything together? How do you rebuild a 3D geometry from medical images especially for complex, bent, bifurcating geometries? An approach to this nontrivial problem is to use radial basis functions (RBFs) that interpolate the information smoothly once the vessels have been identified. The result is an analytic function that defines your geometry in 3D. This function is then sampled in order to create a mesh or collocation points to solve the NavierStokes equations to simulate the blood flow. The approach is simple and elegant, but requires some care to avoid pitfalls.
Mathematical background: radial basis functions, reconstruction of geometry, medical image processing, arterial vessels, haemodynamics

[P10] 
Morphogenesis and Dynamics of Multicellular Systems.
posted Juni 28, 2012 by ECMI Dresden
Instructor: Fabian Rost (Dresden)
Pattern formation in multicellular biological systems often involves a combination of diffusible signals and cellcell interactions. These phenomena shall be first studied as separated modules and then in combination. The existing multiscale modeling framework "Morpheus" facilitates these studies. We will consider a particular example that involves cell migration, cellcell interactions and diffusible signals and where cell shape plays an explicit role.
Mathematical background: dynamical system, reactiondiffusion system, PDE, chemotaxis equation, cellular Potts model

[P11] 
Risky "risk reduction"? Serosorting, strategic positioning and the spread of HIV amongst men who
have sex with men.
posted Juni 29, 2012 by ECMI Dresden
Instructor: Daniel Simpson (Trondheim)
HIV infections are on the rise again, both in Europe and more widely across the world. In order to formulate appropriate policy responses, it is important to have a good model for the spread of a realistic HIV epidemic. In this project, we will look at how mathematical models can influence policy, education and, hopefully, community behaviour.
In particular, it is necessary to closely examine the means of infection: HIV is not the flu! It is known that amongst populations of men who have sex with men (MSMs), the practices of serosorting and strategic positioning  which are, respectively, selecting sexual partners and selecting sex acts based on disclosed serostatus  are commonly used as "risk reduction" strategies. This begs two questions: when, if ever, does serosorting reduce the risk of HIV infection, and how does serosorting affect the spread of a HIV epidemic.
Mathematical background: : Epidemic modelling. Possible choices of models include ODEs and stochastic simulation of network models. It's up to you!

[P12] 
Maximal tipping angles of nonempty bottles
posted Juni 29, 2012 by ECMI Dresden
Instructor: Martin Schopf and Lars Ludwig (Dresden)
Imagine a bottle that is filled with air and water and placed on an even surface that is inclined by a
certain angle.
Depending on the geometry and material of the bottle, the amount of water inside and the inclination
angle the bottle might tip.
The aim of this project is to model the above setting and to determine the maximal inclination angle and
the corresponding fill quantity for various existing bottles.
Note that for a general geometry of the bottle it is not possible to model this problem in 2D due to the
horizontal surface of the water.
What is the angle maximizing geometry of a radially symmetric bottle that is half full (under reasonable
restrictions)?
Mathematical background: : reconstruction of geometry, nonlinear optimization, optimal
design

[P13] 
Tank size optimization
posted July 02, 2012 by ECMI Dresden
Instructor: Miika Tolonen (Lappeenranta)
Many branches of process industry mean transport of material between a network or chain of storage tanks, processing vessels, intermediate containers etc. The material flow may be liquid, suspension, chips, powder etc. An example of such process is pulp mill. The material transport is carried out by pumps. These material flows are subject to various irregularities due to errors, faults, service breaks etc. This means that the flow volumes in the intermediate pipes are random processes meaning that the level of liquid in the tanks are varying in a stochastic manner. In the design of the process plant the sizes of the vessels must include safety margins to avoid overflow, that could lead into serious results. The task in this project is to build a simulation model to study the random variation of the liquid levels in the intermediate tanks to be used in the design of tank dimensions. Specific stochastic simulation approach is needed.
Students are asked to study a much simplified version of such process, a 4tanks baby model.
Mathematical background: : random processes, stochastic processes.

[P14] 
Efficient management of a dairy farm
posted July 04, 2012 by ECMI Dresden
Instructor: Aureli Alabert (Barcelona)
A typical dairy farm hosts a certain number of cows, that are supposed to produce
as much milk as possible, intended to be sold. For the cows to produce milk, they
have to get pregnant and give birth. There is a typical curve of milk production after
giving birth, but there are several parameters that are random and depend on each
particular animal. The success rate of insemination is also varied and may even depend
on the ability of the farmer to detect the fertile period of each cow. Diseases
affect the production too, among other factors. Every week the farmer must
decide if it sends the less profitable cow to the slaughterhouse, obtaining some
revenue for the meat, and replaces it with a young new cow. This decision is usually
taken on intuitive grounds, and therefore an economic model is sought to help optimise
the overall profit of the farm. A simple model for the life and reproduction cycle of a
cow is needed to start with; the model can be then progressively enhanced with new elements.
Mathematical background: : Probability, programming skills.


Contact
Chair:
Prof. Dr. Stefan Siegmund
ECMI coordinator
of Technische Universität Dresden
Contact Person
Dr. Antje Noack
Technische Universität Dresden
Dep. of Mathematics
Institute of Algebra
Phone: +49 351 46332149
Fax: +49 351 46334235
antje.noack@tudresden.de
Mail to:
TU Dresden
Institute of Algebra
01062 Dresden
Germany
Bulk mail to:
TU Dresden
Helmholtzstraße 10
01069 Dresden
Germany
