Participants 2014

Shivam Trivedi

Name  

Shivam Trivedi

University

Indian Institute of Technology Kanpur, India

Supervisor

Prof. Dr. Eva Gutheil

Workgroup  

Multiphase Flows and Combustion

Project

Analysis of spray development under different pressure conditions

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The understanding of sprays is very crucial for many industrial processes, such as the design of combustion chambers and fabrication of automotive parts. The goal of this research is to analyze the development of a water spray under different pressure conditions, and specifically to investigate the length at which the spray jet collapses, which is essential for the design of spray combustion chambers.Simulations for different pressure conditions are done using the open source software OpenFOAM. Suitable mathematical models were selected to appropriately describe the development of spray. The results are generated using different turbulence models including the classical k-e and the Launder-Reece-Rodi Reynolds stress models. Further steps are to incorporate the Large Eddy Simulations (LES) to resolve the large length scales. It is found that the numerical simulation is capable of properly retrieving the collapse of the spray jet, and a parameter study is performed to study and verify its occurrence and characteristics in comparison with experimental data.

Canberk İrimağzı
Berke Noyan Karagöz

Name  

Canberk İrimağzı & Berke Noyan Karagöz

University

Koç University, Istanbul

Supervisor

Prof. Dr. Gebhard Böckle

Workgroup  

Computational Arithmetic Geometry

Project

Galois Representations with an Open Image

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One of the central objects in number theory is the absolute Galois group Gal(Q'/Q), the group of automorphisms of the field of algebraic numbers fixing the field of rational numbers. The current trend to study Gal(Q'/Q) is through its linear representations over finitely generated free Zp-modules, where Zp denotes the ring of p-adic integers. These representations are the so-called p-adic Galois representations, which are essentially continuous group homomorphisms ρ:Gal(Q'/Q)-->GL_n(Zp). Such representations naturally occur in geometry as actions of Gal(Q'/Q) on the p^n torsion points of algebraic varieties such as elliptic curves. Still though, Ralph Greenberg indicates that given a prime p and an integer n>3, it is hard to come up with Galois representations with an open image, that is, informally speaking, with a big image. He suggests that if a number field K has a particular type of extension M dependent on a fixed prime p, one can obtain p-adic representations of Gal(M/K) of certain degrees n. Such a field K is called p-rational. Our study is to understand Greenberg's way of constructing Galois representations with 'big images' and to study the questions surrounding p-rationality of number fields along the path he opens. This should lead to experimental and theoretical experiments to further explore p-rationality, as well as to an extension of the range of applicability of Greenberg's results to other groups than GL_n.

Justin Carpentier

Name  

Justin Carpentier

University

Ecole Normale Supérieure de Cachan, France

Supervisor

Prof. Dr. Katja Mombaur

Workgroup  

Optimization in Robotics and Biomechanics

Project

Introducing the rolling contact model of two surfaces in dynamic simulation

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During locomotion, humans naturally exploit the rolling of the foot on the ground in order to minimize the global mechanical energy

consumption. In order to mimic this mechanical property, it is necessary to do some mathematical assumption, mainly by considering that the foot is a rigid manifold rolling on a plane. With such an assumption, my contribution was to find an algebraic solution to the aforementioned contact model, binding the state of human-like avatar with its tangent space. We have now closed solution for the rolling of an egg (ellipsoid form) onto a plane. Moreover, the developed approach might be extended to other exotic surfaces. Finally, the contact model is now exploited to generate feasible human-like locomotion including the rolling of the feet, by means of the optimal control solver MUSCOD developed at IWR of Heidelberg University.

Kush Chandra

Name  

Kush Chandra

University

Amherst College, Amherst MA, United States of America

Supervisor

Prof. Dr. Katja Mombaur

Workgroup  

Optimization in Robotics and Biomechanics

Project

Integration and comparison of rigid-body models

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During his stay in Heidelberg, Kush Chandra worked on the musculoskeletal dynamics software OpenSim. The first focus of his work was the integration of rigid-body models used in the ORB group with the OpenSim pipeline in order to enable a comparison between the dynamics computations. Second, he worked on evaluating the effects of parameter perturbation (e.g. segment masses) on the computed dynamics. His research work was conducted in relation to the Frontier-Orthoses project which aims at building patient-specific multi-body models for computational analysis of pathological gait.

Diana-Patricia Danciu

Name

Diana-Patricia Danciu

University

University of Cambridge, United Kingdom

Supervisor

Prof. Dr. Anna Marciniak-Czochra

Workgroup   

Applied Analysis and Modelling in Biosciences

Project

Modelling stem cell differentiation in leukaemias

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It has been recently suggested by experimental evidence that acute myeloid leukaemias might be caused by multiple clones of malignant cells. However, the different clones may differ with respect to cell properties, such as proliferation and self-renewal, and this fact is not entirely understood. Due to the lack of data regarding the way in which cell properties change after chemotherapy and relapse, mathematical modelling is needed for investigation. Such a mathematical model has been proposed by my supervisor and collaborators, and simulations have been carried out to prove that the model is consistent with patient data. The aim of the project I have worked on was to extend this model to account for space. It involved reaction-diffusion equations coupled to ODEs and I have been running numerical simulations in order to visualize the dynamics of the system. One of the challenging aspects was to find parameters and initial conditions suitable to describe the real-world phenomena. The system can be further investigated through mathematical analysis for additional insights into its dynamics.

Khansa Abdul Waheed Khan

Name

Khansa Abdul Waheed Khan

University

COMSATS Institute of Information Technology, Islamabad, Pakistan

Supervisor

Prof. Dr. Peter Bastian

Workgroup   

Parallel Computing

Project

Distributed and Unified Numerics Environment DUNE

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The Distributed and Unified Numerics Environment (DUNE) is a software framework for the numerical solution of partial differential equations with grid-based methods. The high flexibility and high performance of DUNE is achieved by using generic programming techniques. A prerequisite for working with DUNE is a proficiency in scientific C++ and knowledge about advanced programming concepts like templates.
In my post bachelor program, I researched on learning the high flexibility and performance of DUNE by using the programming techniques that allow to write an algorithm once and parametrise it with the data type. To this end, I successfully completed part of the DUNE course dealing with advanced C++ concepts.

Bhaskar Dubey

Name  

Bhaskar Dubey

University

Supervisor

Prof. Dr. Guido Kanschat

Workgroup  

Mathematical Methods of Simulation

Project

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