Modelling Problems

Project

Uncertainty quantification of chemical kinetic reaction rate coefficients

Instructor

Éva Valkó, ELTE Eötvös University, Budapest

Summary

In chemical kinetics a reaction rate coefficient (also called rate constant), k, quantifies the rate of a chemical reaction. Chemical kinetics databases for many elementary gas-phase reactions provide the recommended values of the Arrhenius parameters, the temperature range of their validity and the uncertainty of rate coefficient k defined by uncertainty parameter f. In the combustion data collections and evaluations, the uncertainty parameter f is either considered to be temperature independent, or it is defined at a few temperatures or in a few temperature intervals. The goal of this project is to calculate automatically temperature dependent uncertainty limits of rate coefficient of elementary reactions in such a way that these limits are consistent with the original description of the rate coefficient.

Mathematical Background

Numerical Analysis, Matlab programming, Statistics


Project

How to exploit losses - Heating by magnetic induction

Instructor

Sabine Zaglmayr, CST GmbH, a Dassault Systèmes Company, Darmstadt

Summary

Magnetic induction enables efficient, contactless, and controllable heat generation in electrically conducting materials by time-varying magnetic fields. This phenomenon is exploited in the hardening of metallic devices by industrial manufacturers as well as in daily-life applications as induction cookers. Questions like how the input frequency or the used materials influence the heating process arise and should be answered by mathematical modeling and numerical simulation.

Mathematical Background

Mathematical Background: PDEs, FEM


Project

The monitoring problem in Smart Grids

Instructor

Stefania Tomasiello, University of Salerno, Fisciano

Summary

Smart grids (SGs) represent a new paradigm where information and operational technologies applied to the electric grid are merged to provide customers with sustainable options and improved security. In SGs, issues such as grid efficiency improvement, flexible load supply and optimal network regulation are managed by acquiring and processing the available set of information describing the actual SG operation state. The underlying computing process is complex and time-consuming, since it requires the periodic estimation of the power system state, the analysis of the massive data streams generated by the grid sensors and the repetitive solution of large–scale optimization problems, which are complex, non-linear, and NPhard problems. Moreover, in order to provide the grid operators with updated information to better understand and reduce the impact of system uncertainties associated with load and generation variations (e.g. in solar and wind power sources), the required computation times should be fast enough. Recently, the Multi-Agent System (MAS) approach has been recognized as a promising technique for power grid planning, design and operation, and in particular for control issues. A MAS involves different kind of intelligent agents which interact both with each other and their environment to achieve some goals. Agents communicate with neighbors and with centralized controller if necessary, gather data from environment and may be able to perform some computations.
Here we are concerned with an agent based monitoring of SGs with assessment of optimal settings obtained through approximate Optimal Power Flow (OPF) solutions. The primary goal of a generic OPF problem is to minimize the total production costs of the entire system to serve the load demand while maintaining the security of the system operation.The consideration behind the proposed approach is that large historical operation dataset are usually available in SGs and employed to extract useful information; besides, such datasets are also expected to grow over and over because of the pervasive deployment of SGs sensors. The proposed approach combines the MAS technology with the approximation properties of Fuzzy transform (F-Transform). F-transform is a fuzzy approximation technique, stating a functional dependency through a linear combination of basic functions. F-transforms are used in order to address two issues: first to reduce the storage need, by compressing the historical datasets, and second to provide agents with fast and reliable actions to get accurate OPF solutions, by a similarity search throughout the compressed historical dataset.
It should be pointed out that in the SG context, the large volume of the datasets makes data collection, storage and processing a very complex and demanding task. Hence, effective tools aimed at reducing the size and the cardinality of SGs data may be very beneficial. Besides, the solution of OPF problems in SG often requires the compliance with strictly time constraints. In such a context, an approximate solution, through fast computation, is often more useful than a high quality one, implying a higher computational cost. The proposed approach is based on an important property: F–transform preserves similarity. More precisely, under certain conditions, it can be proved that the minimum Euclidean distance in the transformed domain corresponds to the minimum Euclidean distance in the original domain. Then search operations in the transformed domain provide not only fast but also reliable results. The proposed method has been tested on small and large power networks.


Project

Optical excitation of metallic nanoparticles by light

Instructor

Gerhard Unger, Graz University, Austria

Summary

Light causes on the surface of metallic nanoparticles coherent charge oscillations, so-called surface plasmons. These are responsible that metallic nanoparticles have special optical properties which can hardly be achieved by other optical materials. Surface plasmons enable to amplify, concentrate and manipulate light at the nanoscale with a wide range of applications as in information technology or in biomedicine. In the project we explore models which describe the excitation of metallic nanoparticles by light and which characterize optical properties of nanoparticles. These models are mainly based on Maxwell's equations. For metallic nanoparticles of sizes up to 50 nanometers the optical response can be modeled by the the Poisson equation. For that case we will also implement a numerical scheme (boundary element method) in Octave.


Project

Characterizing outdoor water consumption

Instructor

Conceicao o Amado, Instituto Superior Técnico, University of Lisbon, Lisbon

Summary

Home gardens contribute to an improved air quality, providing home for birds and other animals. In some areas, outdoor water use is an important slice of urban water consumption. Increasing water demand in coastal regions, where the saltwater intrusion problem in the aquifers, which will cause the closure of boreholes used to water gardens, together with climate changes makes it challenge to predict long-term consumption scenarios. An important part of water conservation strategies must go through a better understanding of the outdoor water use. The participants are asked to characterize daily outdoor water demand and develop a model to predict outdoor water. The available data is from residential houses in a coastal and touristic region.

Mathematical Background

Statistics, R (preferred), also Weka, MATLAB, Python programming skills


Project

Modelling of erythrocyte sedimentation

Instructor

Ivana Vojnovic, University of Novi Sad, Novi Sad

Summary

The erythrocyte sedimentation rate (ESR) is a simple blood test frequently used in a clinical medicine. The test measures the rate at which erythrocytes sediment in a sample of blood under the influence of gravity in a period of one hour. Blood is placed in a thin, tall tube and inflamation can cause erythrocytes to climp together. These climps settle to the bottom of the tube. Hence, ESR can reveal inflamatory activity in a body and it helps doctor to diagnose or monitor the progress of inflamatory desease.
The aim of this project is to study sedimentation of erythrocytes properties and to find the mathematical model that describes this process. Numerical simulations are also expected.

Mathematical Background

partial differential equations, numerical analysis


Project

Optimal strategies in crowd evacuation problems

Instructor

Giacomo Albi, University of Verona, Verona

Summary

In recent years the study of pedestrian dynamics, as well as the design of safety strategies for emergency situations has become of paramount importance in modern societies.
In this project we will study the collective motion of a crowd leaving an unknown area under limited visibility. In this scenario we have two main phases first exploration, second evacuation, and their interplay is strongly influenced by the "emotional state" of the crowd: from normal to panic situations. Thus we will concentrate on the design of safety strategies to ease evacuation time, using tools from optimal control theory. In particular we will explore the following issues: (i) leaders-followers dynamics, (ii) obstacle optimization, (iii) emergency signal positioning.
Numerical simulations will validate the proposed modelling framework, comparing different strategies efficiency in various settings.

Mathematical Background

ODE systems, numerical analysis, basics on optimization, MATLAB


Project

How to find a lost airplane?

Instructor

Marek Teuerle, Wrocław University of Science and Technology, Wrocław

Summary

From time to time, it happens that some passenger aircraft is lost over an ocean. A recent example is a Malaysia Airlines Flight 370 that disappeared over the Indian Ocean. In this project students are ask to propose a search strategies that would be beneficial over huge areas with sparse targets. Such a search can be performed collaboratively or individually assuming some equivalent limitation of the total energy in searching machines. The main goal of this project is to distinguish using numerical or/and analytical tools, which of the proposed strategies is the most efficient and decide in what scenario it is better to use a single, multiple or swarm-like search.

Mathematical Background

probability theory, stochastic processes, programming in MATLAB, Python or Julia


Project

Forecasting of Energy Spot Prices

Instructor

Matthias Ehrhardt, Bergische Universität Wuppertal, Wuppertal

Summary

The mathematical forecasting of electricity spot prices is essential for energy trading companies, but also for companies with a significant consumption of electrical power, like aluminium smelters. In this project we will investigate the structure of the electricity spot prices in the german market and design a hierarchy of different mathematical models with increasing complexity, including a concise discussion of hybrid modelling approaches.
Finally, we will calibrate our models using real market data from the European Energy Exchange (EEX) and study their performance against standard approaches implemented in MATLAB.


Contact

Technische Universität Darmstadt

Graduate School CE
Dolivostraße 15
D-64293 Darmstadt

Phone+49 6151/16-24401    or
-24402
Fax+49 6151/16-24404
OfficeS4|10-322

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Open BSc/MSc Theses

Show a list of open BSc/MSc topics at GSC CE.

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