


ESSIM 2013



Modelling Week — PROJECTS
[P1]

Modelling of potential depolarization signals in the hippocampus.
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
VoltageSensitive 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)

[P2]

Modelling of humanarm kinematics
posted April 04, 2013 by A. Jurlewicz.
Instructor:
A. Jurlewicz (Wroclaw)
Modelling the kinematics of the humanarm 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
humanarm 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

[P3]

Modeling forest as porous medium. Canopy properties in wind park simulations
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).

[P4]

Atmospheric tomography in adaptive optics
posted April 04, 2013 by Prof. Ewald Lindner.
Instructor:
Daniela Saxenhuber (Linz)
Large groundbased 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 MatrixVector Multiplication (MVM). Instead of using one
big matrixvector 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)

[P5]

Modelling of tumours
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)

[P6]

The Optimal Billiard Shot
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

[P7]

Modelling the trajectory of a skydiver
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
:

[P8]

A dambreak simulation.
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 dambreak 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 breakdam flow in a rectangular
crosssection channel. Next, the simulation of a study case based on real data will be addressed by using the webplatform
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).

[P9]

Efficient parameterdependent simulation of infections in a population model
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 ‘realtime’ 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)

[P10]

Distribution of the coal flow in the millduct system of a power plant
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 millducts 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 millduct
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)


Last update on 20/June/2013 by M. Carretero

Contact
Chair:
Prof. L. L. Bonilla
Director of the Gregorio Millán Institute.
ECMI Coordinator of the University Carlos III and member of the ECMI Council.
Coordinator:
Prof. J. M. Gambi
Gregorio Millán Institute.
University Carlos III of Madrid,
Madrid, Spain
Phone: +34 916249441
Fax: +34 91 6249129
gambi@math.uc3m.es
Mail to:
Escuela Politécnica Superior.
Gregorio Millán Institute.
Universidad Carlos III de Madrid.
28911 Leganés, Madrid, Spain
