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I have done graduation in Mechanical Engineering and due to my interest in Mathematics, I have completed my MS in Mathematical Physics. Now I am planning to do a Ph.D. I want to do this on some mathematical applications either in Engineering or Physics, but I can't decide the topic. Can anyone in this field suggest me any Books or Research papers for motivation and insight? Thanks in advance.

Vikrant Verma
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  • A bit biased, but Fluid Dynamics has everything you're looking for – caverac Jul 26 '19 at 11:52
  • How about mathematical aspects of quantum mechanics? – Wuestenfux Jul 26 '19 at 12:08
  • If your interested in delving deeper into continuum mechanics, read for example "On the Roots of Continuum Mechanics in Differential Geometry – A Review" Paul Steinmann. (Most physicists don't much bother with CM because they either believe (a) it is just engineering maths and (b) that although General Relativity, is a continuum mechanics type theory, it will be ultimately found to be fundamentally quantised in nature in the final analysis. Definitive experimental evidence for hypothesis (b) is currently weak and this currently fashionable view may turn out to be wrong in the final analysis.) – James Arathoon Jul 26 '19 at 13:44
  • My final year project was on the General theory of relativity and in my country, India more consideration for Ph.D. is given to students with a similar topic as there projects. According to your suggestion, I think that "Continuum Mechanics in Differential Geometry" matches my project topic. I want to ask one more thing, some people say that the research should be done on current topics so, Can you explain the scope if I continue my study on this topic.@JamesArathoon – Vikrant Verma Jul 26 '19 at 14:10
  • The scope you can set depends firstly on whether you are studying for a PhD in a physics department or a mathematics department; and secondly whether you are working with a group of people including your supervisor, with existing research interests and infrastructure, or want to fly solo, with greater flexibility on your research topic, by choosing a supervisor that doesn't have a big group of post doc's and students to constantly raise funds for. – James Arathoon Jul 26 '19 at 14:51
  • For further ideas on actual topic scope take a look at "On the History of Unified Field Theories" https://link.springer.com/article/10.12942/lrr-2004-2 – James Arathoon Jul 26 '19 at 15:10
  • Sir can you suggest me some good research Institute where there is active research going on this topic.@JamesArathoon – Vikrant Verma Jul 26 '19 at 15:22
  • I would recommend mathematical researchers who are conservatively concentrating on 3D space + 1D Time Models (or the Minkowski's Space-time approach), with a willingness to take the results of the MOND research program seriously. That narrows things down by over 95%. For example Prof. John Moffat (the mathematical physicist at University of Toronto, Canada). I met him a few years ago, he is semi-retired now, but perhaps you could write to him for advice. Another free and original thinking mathematical physicist you could try and write to is Prof Joao Magueijo of Imperial College, London. – James Arathoon Jul 26 '19 at 17:41

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