ECMI Modelling Week 2015


Project 1. Modelling drying in paper production

The paper industry produces several types of paper sheets. Among those, we can find regular paper sheets or impregnated paper with resin which is widely used for decorative surface finishing panels. These products are produced through the process of drying a primary paper film, which goes through a series of dryers. For the quality of paper to be acceptable and fitting the required quality parameters, the temperature inside the dryers, as well as the percentage of water/resin in the paper are important to know (and control) during the drying process. In this project, we aim at developing and simulating a partial differential equations model for the drying of paper soaked in water or resin inside a drying tunnel.

Instructor: Gonçalo Pena (CMUC, University of Coimbra)

Mathematical background: Numerical methods, partial differential equations, ordinary differential equations and programming skills (C++, Matlab)

Project 2. Estimating the amount of wood

In January I bought a new house which has a nice open fireplace creating a cosy warm atmosphere. For the next winter season, I have to buy logs for heating. Since I doubt to find time to cut the wood in the forest myself, I will get the mauled wood, i.e. the logs, delivered. The dealer will deliver me the logs in one of the two alternative ways:

  • Either a truck will dump the loose logs on a pile.
  • Or the logs are transported in a barred box of a given size.

To quantify the amount of wood delivered, there are different units in use

    solid cubic meter: volume of one cubic meter measured without the space between the woodblocks.
    stere: volume of one cubic meter of regularly stacked logs including the space between the woodblocks.
    loose cubic meter: volume of one cubic meter of randomly piled logs, again including the space in-between.

The payment is mostly according to the amount of wood measured in steres.

Image Project2

Figure 1. Left: One stere of wood. Right: Barred box used for transporting logs; Source: wikipedia.de

As a rule of thumb, the following conversion formulas are often used:
                  1 loose cubic meter = 0.7 stere
                                        1 stere = 0.7 solid cubic meter
Can you confirm them?
Can you measure the amount of wood in an arbitrary pile of wood?

Instructor:  Thomas Götz (Mathematical Institute, University Koblenz)

Mathematical background:  --

Project 3. Optimal solution for a KAMIKAZE RANGER

The aim of this project is to compute an optimal solution for a “KAMIKAZE RANGER”.

Given is a KAMIKAZE RANGER (pendulum, see also the picture) with some given length and some mass (also including the passengers). The pendulum is driven by an engine which has a bounded angular momentum. The aim is now to reach some given movement of the pendulum (i.e. the deflection and the angular velocity) on a given time scale (0,T), such that the costs to run the engine are minimized.

To do:

  • Derive a model which includes all the given data
  • Obtain a (numerical) scheme/approach to solve the derived model
  • Implement the scheme/approach
  • Solve the problem for some given data of your choice
  • Compute the acceleration forces for the passengers (to be sure that the forces are acceptable)
  • Analyze the existence / uniqueness of solution for the model
  • Analyze the derived scheme/approach

Image Project3

Instructor:  Martin Neumueller (Johannes Kepler University)

Mathematical background:  Ordinary differential equations, Numerical methods for ordinary differential equations, (Discrete) Optimization with constraints, Basics in numerical analysis, Use of mathematical tools and software

Project 4. Shape analysis of a rotating axisymmetric drop

Surface tension is a property of fluids that makes them take a shape that minimizes their surface area. Making devices measuring surface tension is a huge industry. For this purpose, a drop of a given fluid is being rotated which leads to its elongation—it obtains almost cylindrical form. Then, a photo of the drop is taken. The latter is digitalized and, thus, a set of points that describes the experimental profile is obtained. On the other hand, taking into account the forces that act on the drop, its shape could be computed if the surface tension is known. The mathematical model is a three-dimensional nonlinear system of ordinary differential equations. Software that is used to control the measuring devices finds the value of the surface tension for which the theoretical and experimental profiles coincide.

  1. Students will get acquainted with the mathematical modeling of the shape of a drop that is subjected to rotation.
  2. Given experimental data (a drop’s image) they will have to find the drop’s surface tension.

Instructor:  Tihomir Ivanov (Sofia University, Faculty of Mathematics and Informatics; Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)

Mathematical background:  ODEs, Numerical Methods, Programming (preferably, in MATLAB or Mathematica)

Project 5. Patient-specific blood flow modelling

Medical images allow us to obtain good representations of blood vessels, even in pathological cases. However concerning the dynamics of the blood itself, medical images can only give us some sparse velocity measurements. Medical doctors would make a good use of accurate blood flow simulations in predicting either the evolution of certain pathologies, or the effect of some therapies. Our project consists in finding a model which allows to reconstruct the blood flow in the complete domain by using the information obtained from the velocity measurements.

Instructor: Jorge Tiago (CEMAT, IST-ULisboa)

Mathematical background: PDE's, numerical methods, programming skills (Matlab, FreeFEM++)

Project 6. Optimization of an antenna network (alternative to Project 7)

Given a model of antennas, how to optimize, automatically, their position in space in order to maximize the quality of a signal on a given territory?

Instructor:  Stéphane Labbé (Université Joseph Fourier, Grenoble)

Mathematical background:  Optimization, PDE’s, discretization

Project 7. Electrical circuit testing characterization (alternative to Project 6)

Given an electrical circuit in a black box, is it possible to characterize its composition by the analyse of its response to current or tension excitations?

Instructor:  Stéphane Labbé (Université Joseph Fourier, Grenoble)

Mathematical background: ODE’s, inverse problem

Project 8. Parking lot simulations

In many public places, arranging the right capacity and layout of parking places is crucial for smooth customer flow and service. On the other hand, from the customers’ point of view, finding a parking place can be both a time consuming and stressful task. However, its outcome might also be related to the seeker’s attitude. Quite often the success or failure can depend on how much the customer is greedy to find a place possibly closest to the building entrance.
The aim of the project is to exercise a number of simulations (assuming simple parking geometry, cars arriving throughout the day with time-varying frequency, and varying drivers’ greed level) in order to study:

  • How the parking gets filled and emptied through the day?
  • What is the average time to find a parking place depending on the hour of the day?
  • What is the probability that the arriving person will not find a parking within a fixed time from the moment of arrival?

Instructor: Matylda Jablonska-Sabuka (Department of Mathematics, Lappeenranta University of Technology)

Mathematical background:  The skills needed for successful completion of the project is general knowledge of random number generation (sampling from theoretical and empirical distributions), statistical analysis of random events and queuing systems, and good programming skills (preferably Matlab).

 Project 9. Reduce OD matrix dimensions (Railway context)

SISCOG – Sistemas Cognitivos (www.siscog.pt)  is a Portuguese software company that develops products and systems that provide decision support for planning, managing, and dispatching resources in transportation companies. 

The challenge brought by SISCOG is to improve one of the combinatorial optimization algorithms used by ONTIME, the SISCOG’s product that provides decision support to timetable generation.

SISCOG’s product suite

Line planning is a classical optimization problem in the design of a public transportation system. It involves the selection of paths in the railway network on which train lines are operated. The aim is to select a set of lines with corresponding operation frequencies, such that a given travel demand can be satisfied. This demand data is usually given for pairs of origins and destinations in a so-called origin-destination matrix (OD matrix).

To make it easier to work with real and big instances, a possible approach is to reduce the original dimension of the OD matrix, removing certain stations and adapting demand accordingly.

The aim of this project is to propose and implement a method capable of reducing the OD matrix dimension, given a set of constraints that must be met and an optimization criterion that minimizes the cancelled demand and the transferred demand between stations.

Realistic data will be supplied for testing the proposed method.

Instructors: João Gouveia (CMUC, University of Coimbra), Elsa Carvalho (SISCOG)

Mathematical background: Optimization, programming skills

 Project 10. Mathematical modeling of financial data in many dimensions

Financial econometrics is a complex branch of science. In many cases analysis of various financial data through one dimensional models is not enough to better understand complex mechanisms hidden in them. One can say that financial models are inherently multivariate. Thus in order to build models which better describe real systems one has to take into consideration various dependencies among different variables, sometimes we can use those dependencies to build better models. In his project we will try to build some multidimensional models appropriate in modeling especially real financial data sets.

We divide our work into four steps.

  1. Analysis of data sets from financial markets - seasonality and trend detection.
  2. The common analysis of time series – dependencies between real financial data.
  3. Modeling the data sets on the basis of points 1 and 2.
  4. Validating the obtained model and prediction.

Instructor: Janusz Gajda (Hugo Steinhaus Center, Wroclaw University of Technology)

Mathematical background:  Programming skills, basics from probability theory,
time series analysis or econometrics.

 Project 11. Oscillations in gravity-driven fluid exchange

If you take a bottle with water and turn it upside down, the water will of course spill out. But as it spills, air comes in. A little bit of experimentation shows that if the opening in the bottle is narrow enough, the air comes in in bursts, bubble by bubble. This sometimes causes a periodic sound, the characteristic glug-glug of the water coming out. The aim of the project is to derive a model for the process, which should incorporate the diameter of the opening, and some realistic features of the bottle geometry and should explain the periodicity of the motion and its disappearance as the diameter of the opening is increased. The system can be made even (!) more interesting by connecting bottles by a pipe.

Instructor: Michael Grinfeld (University of Strathclyde)

Mathematical background:  Some knowledge of fluid dynamics and experience with MATLAB/MAPLE to simulate dynamical systems will be required. Knowledge of non-smooth dynamical systems and desire to experiment with real bottles, pipes and get splashed in the process is a bonus.