Symmetry in engineering, science and mathematics—a study of the fundamentals with a view to developing new cross-disciplinary methodologies and applications—MPhil or PhD project by research

It is well recognized that symmetry underlies the processes and laws of nature. Developing an understanding of symmetry has already helped engineers, scientists and mathematicians to make significant advances in their respective fields. This research project will be characterized by the fact that the study will be undertaken within a Department of Mechanical Engineering and making use of some of the approaches, tools and techniques that are used by engineers, but yet also reaching out to other disciplines.

The aim of the project will be to conduct an in-depth investigation of symmetry fundamentals and applications across engineering, science and mathematics with a view to developing new methodologies and finding new applications of approaches based on symmetry or, simply, new ideas inspired by symmetry. While this will be an &lsquo’in-depth’ project based on the fundamentals of symmetry, it would be unrealistic to expect that it could be fully comprehensive; rather it is the intention to identify some promising leads or themes and pursue these. Some specific examples of engineering applications of symmetry would be in the development of structural components such as trusses or space frames, nanotechnology structures, lattices for use in computational fluid dynamics and finite element analysis, or signal analysis using discrete Fourier transforms. Another engineering example relates to thermodynamics and the development of improved techniques for the classification and quantification of thermodynamic disorder and irreversible processes. At a more fundamental level, some important contributions in the area of a theory of thermodynamics based on the ordering of sets have been proposed and discussed by a number of authors, but have not yet been extended into the engineering field, and this too may be a fertile area for research based on symmetry. The particular theme or themes to be pursued will be identified in conjunction with the research student and the identification process itself is likely to involve some tentative explorations in diverse directions.

The project will be broad in that it will be highly cross-disciplinary and will seek to bring together ideas and knowledge from a diverse range of areas within engineering, science and mathematics, without excluding other areas that could provide useful insights, such as the arts. At the outset of the project no specific deliverables are identified, other than the objective of publishing several peer-reviewed papers each year. Use will be made of the techniques and expertise of engineers, scientists and mathematicians and of the tools and research facilities within the Faculty of Engineering and the Dublin Institute of Technology, as appropriate. For a number of years Prof. Jim McGovern has been researching the topic of symmetry and this has led to a good number of ideas that will be used to seed this research project.

The preferred software application for undertaking the mathematical analyses and for developing new methodologies will be Mathematica, which is particularly well suited to modelling and analysis involving symmetry because of its versatility, its incorporation of a huge mathematical repertoire, its ability to perform calculations symbolically or numerically, as well as the facility for performing calculations to arbitrary precision and for the use of integer variables of arbitrary length.

The project will require a postgraduate student having at least a 2.1 honours degree in Mechanical Engineering or a cognate discipline. This student will need to have very broad engineering, scientific and mathematical interests. He or she will need to be very strong in the area of mathematics and in the use of software (including programming) for analysis, visualisation, simulation and problem solving.

The main resources required, besides desk space and access to the facilities of the Institute, will be two computers (one high-end workstation and one standard PC) and software licences (principally Mathematica). Funding will be required for attending international conferences and visiting other research centres (across disciplines in both cases). Funds will also be required to allow the researcher to undertake specialized training in the use of Mathematica. In addition, some funding will be required for dissemination of the outcomes of the research.

This entry was written on 3 January 2008 at 12:33 a.m. as a private blog.