Job Eindhoven University of Technology (TU/e) - PhD student Analysis of dislocation models-a generalized gradient flow approach

Project description:
Permanent, plastic deformation in metals is the result of the collective motion of a large number of dislocations. These are curve-like defects in the atomic lattice of the metal, which move in response to applied stresses. In this project we will connect two different descriptions of this phenomenon. At the fine scale the dislocations are represented individually; at a coarse scale, only by continuum densities. The former is more accurate, the latter is more convenient, but current models at the coarse scale are phenomenological in nature: the exact connection with fine-scale models is unclear.

We will use the theory of generalized gradient flows to make a rigorous connection between the fine-scale, discrete-dislocation formulation and the coarse-scale, continuum plasticity formulation. This system is itself a model for a large class of problems, where the emergence of coarse-scale features and slow dynamics from fine-scale behavior cannot be understood via classical averaging techniques due to the complex spatial-temporal behavior. By focusing on dislocations we expect to develop methods that will be applicable to a wide range of complex systems.

Typical techniques that we will use are variational calculus, including methods such as energy minimization, weak and Gamma-convergence, and PDE theory.

This work is done as a project in the Complexity program of NWO, 'Correlating fluctuations across the scales' in close collaboration with Dr. Ron Peerlings, Dr. Markus Hütter, and Prof. Marc Geers, Department of Mechanical Engineering. A companion PhD student from the Department of Mechanical Engineering will be working on related questions, especially on the way the GENERIC framework of non-equilibrium thermodynamics and coarse-graining techniques can be used to obtain the dynamics of dislocation-mediated plasticity. Note that both PhD students share largely the same objectives only the methodologies to reach these objectives are different.

As a PhD Student you will fulfill the following tasks:

perform scientific research;

present results on international conferences;

publish results in scientific journals;

do a small amount of teaching.

Requirements:

We are looking for a candidate who meets the following requirements:

an MSc. Degree in Mathematics

strong affinity with partial differential equations

good communication and writing skills in English

Appointment and salary:
We offer:

a full-time temporary appointment for a period of 4 years, with an intermediate evaluation after 10 months;

a gross salary of € 2,042 per month in the first year, increasing up to € 2,612 per month in the fourth year;

support for your personal development and career planning;

a broad package of fringe benefits (e.g. excellent technical infrastructure, child care, savings schemes, and excellent sports facilities).

Information: 

More information about CASA can be found at: http://www.win.tue.nl/casa

Information about the position: dr. Adrian Muntean, e-mail: a.muntean@tue.nl; tel. +31(0)40-2472702

Information about the employment conditions: Ms. C.M. van Dam, HR advisor, e-mail: pzwin@tue.nl; tel. +31(0)40-2472735

Please do NOT send your application to one of the above e-mail addresses, but use the APPLY NOW button hereunder!

Application:
The application should consist of the following parts:

An explanation of your interest in the proposed research field

a detailed curriculum vitae;

a complete list of the courses you have attended and corresponding grades, references, and all other information that might be relevant to your application.

2 letters of recommendation