posted April 04, 2013 by Prof. P. Fischer.

Instructor:   A. Bouharguane   (Bordeaux)

The goal of the project is to quantitatively analyze the neuronal activity in the hippocampus. To achieve this aim, we will use experimental data called Voltage-Sensitive Dye Imaging (VSDI), which enables to visualize the neuronal dynamic in acute brain slices. We will then develop a numerical method based on the resolution of the optimal transportation problem. It will be used to derive precise information on the velocity fields of neuronal activity in hippocampal circuits by using VSDI data.

Mathematical background : numerical methods and programming skills (MATLAB)

posted April 04, 2013 by A. Jurlewicz.

Instructor:   A. Jurlewicz   (Wroclaw)

Modelling the kinematics of the human-arm is very important, for example, to evaluate the results of medical rehabilitation, to construct artificial limbs, or robot's hands, or to increase the achievements in sport disciplines. The aim of this project is to construct a model of the movements of a human arm. To study its benefits, some typical tests of human-arm kinematics will be carried out, among them, a measurement of the effects of the treatment of physical disabilities by rehabilitation.

Mathematical background : analysis, geometry, optimization, numerical methods

posted April 04, 2013 by Prof. Matti Heiliö.

Instructor:   Oxana Agafonova   (Lappeenranta)

The main idea of the wind park simulations is to build a model of a wind park based on a real geometry of the wind park, compute the case and compare with the wind measurements of that place. There are point clouds based on LIDAR measurements of the forest. As was already said above, the forest will be modeled as a porous medium. Certain information about porous properties of the medium will be provided as an external file. The geometry and finite volume mesh will be built from the point clouds. Let us assume that the properties of the medium will be different in each mesh cell. External data will be read in special software called OpenFOAM. Therefore, it is necessary to be able to compute values of the porous medium properties in each cell center. The coordinates (x, y, z) of cell centers are known. The goal of the project is to find and implement some interpolation scheme suitable for wind park simulations.

Mathematical background : numerical methods and programming skills (C++, MATLAB).

posted April 04, 2013 by Prof. Ewald Lindner.

Instructor:   Daniela Saxenhuber   (Linz)

Large ground-based telescopes rely on adaptive optic systems in order to achieve good image quality. Adaptive optic systems physically correct atmospheric turbulences via deformable mirrors. The optimal shape of the deformable mirrors is determined from wave front measurements of natural and/or laser guide stars. Due to steadily growing telescope sizes, there is a strong increase in the computational load for atmospheric reconstruction with current methods, first and foremost the Matrix-Vector Multiplication (MVM). Instead of using one big matrix-vector system, one can decouple the problem in 3 steps: the reconstruction of the incoming wave fronts, the reconstruction of the turbulent layers (atmospheric tomography), and the computation of the best mirror correction (fitting step). In this project we will focus on atmospheric tomography, and develop cheap (iterative) methods in order to achieve a fast and flexible reconstruction.

Mathematical background : inverse problems, numerical methods, programming skills (MATLAB)

posted April 04, 2013 by Prof. Fabian Spill.

Instructor:   Fabian Spill  (Oxford)

Cancer is one of the major factors of death. Despite huge improvements in various treatment strategies over many decades, the complexity and diversity of the disease makes the understanding and curing of cancer a difficult task. There are also a number of common features of tumours, which can form as the starting point to build mathematical models describing the growth of tumours. Besides studying commonalities, we will look at some specific examples of tumours and develop models to capture their behaviour.

Mathematical background : ODEs, PDEs, stochastic processes (not all of them are required)

posted April 04, 2013 by Prof. Martin Bracke.

Instructor:   Joachim Krenciszek  (Kaiserslautern)

Since the billiard game was invented in the 16th century, people have been fascinated not only by the game itself, but also by the wish to understand and predict the behavior of billiard balls and use this knowledge to improve their game. In almost every school or university text book, examples from the billiard game illustrate many principles of mechanics, but a deeper look into the dynamics reveals the high complexity. The task of this project is to model the billiard game and answer the question of what is the best possible shot in any situation.

Mathematical background : Rigid body dynamics, ODEs, optimization

posted April 23, 2013 by Dr Kshitij Kulshreshtha .

Instructor:   Kshitij Kulshreshtha   (Paderborn)

The goal is to model the trajectory of a skydiver as he falls. Various factors, such as wind, starting velocity, drag due to the diver's posture, and positioning during the skydive, should be taken into account. Modern skydiving equipment contains instruments able to measure the barometric pressure and acceleration four times per second. In principle, emergency instruments should be able to determine the exact height of the diver above the ground by using the recorded data, and in case of emergencies automatically deploy the parachute. Unfortunately, due to changes in the position and posture of the skydiver, as he falls, the measured data is very noisy. The physical model of the skydiver developed in this project should be such that the measured data can be calibrated onto the physical model and the noise can be analysed and cleaned up. After calibration and noise correction, the model should be able to predict the height of the skydiver based on the last few data points up to sufficient accuracy.

Mathematical background :

posted May 27, 2013 by Carlos Parés .

Instructor:   José Manuel González Vida   (Málaga)

The main goal of the project is to simulate the flood produced by a dam-break using real topographic data. These simulations will be based on the discretization of the shallow water system by means of the numerical methods studied in the course ‘Simulation of geophysical flows’. As a first step, the students will have to obtain a Matlab simulation of a simple break-dam flow in a rectangular cross-section channel. Next, the simulation of a study case based on real data will be addressed by using the web-platform HySEA developed by the EDANYA (University of Málaga): a practical session to get started in the use of the platform will be scheduled at the beginning of the week.

Mathematical background : numerical methods and programming skills (C++, MATLAB).

posted June 12, 2013 by Filippo Terragni.

Instructor:   Filippo Terragni   (Madrid)

A large host population, living in a bounded and isolated habitat, is infected by a parasite that very quickly spreads the disease. Propagation of the infection is promoted by a time dependent transmission rate between the organisms, which interact with each other, move within the habitat, and possibly recover. Births and deaths may also affect the group. According to expert biologists, developing a control strategy of the epidemic evolution requires the analysis of the population dynamics for several scenarios, which are associated with different values of some parameters regulating the organisms behavior. Hence, an efficient procedure has to be implemented in order to carry out the task in a reasonably short time, thus preventing the infection to become uncontrolled. Modelling has here a twofold goal. First, a suitable mathematical description of the situation should be found. In addition, a reduced order model for the identified equations is highly needed to simplify the problem and make its solution feasible. The project illustrates, by means of a simple paradigm, how some model reduction techniques can be used to perform a ‘real-time’ control of a system response, which is a common task to various scientific and engineering applications.

Mathematical background : matrix algebra, PDEs, numerical methods, programming skills (MATLAB)

posted June 14, 2013 by Laura Saavedra .

Instructor:   Laura Saavedra   (Madrid)

The efficiency of a Power Plant is affected by the distribution of the pulverized coal within the furnace. The coal, which is pulverized in the mills, is transported and distributed by the primary gas through the mill-ducts to the interior of the furnace. This is done with a double function: dry and enter the coal by different levels for optimizing the combustion in the sense that a complete combustion occurs with homogeneous heat fluxes to the walls. The mill-duct systems of a real Power Plant are very complex and they are not yet well understood. In particular, experimental data concerning the mass flows of coal to the different levels are very difficult to measure. An Eulerian/Lagrangian approach is used due to the low solid–gas volume ratio. The goal of this project is to build a model to predict the trajectories of the coal particles taking into account their turbulent dispersion. The mean variables of the gas flow through the duct system will be given. The students have to implement a scheme to solve the solid phase model in order to obtain the distribution of the coal flow within the furnace.

Mathematical background : ODEs, PDEs, numerical methods and programming skills (FORTRAN, C++, MATLAB)