>>13231187>>13231193They aren't truly used.
>Basic crystallographyDo you recognise terms like "FCC" or "CC". They are homologous to symmetry groups and that is where the connection ends, textbooks do not talk about Group theory, the repeating patterns were spotted by the eye from early images. There are basically some papers opining about it, but nothing consequential.
>Advanced crystallographyThe problem is the cutting edge of the field deals with organic crystals in amorpous thermoplastic matrices. There are no symmetries or repeating structures to compute, it it largely statistical models.
>ThermodynamicsJust, no. I have read all the papers (and one thesis) trying to reformulate thermodynamics with differential forms, they all have 1-4 self-citations and are of little consequence. Without getting into too much detail the problem is that we don't actually have a problem with the postulates (entropy is a smooth, monotonously increasing hypersurface etc). Modern problems in the field are far removed from the ideal models that the DG generalise (nicely though; no more fucking around with pages of Maxwell relations), it deals with non-ideal complex systems where due to some non-ideal phases the hypersurface of the energies is not even continuous in most modern models. So neither calculus nor smooth differtial geometry applies and that is why DG reformulations have found no applications and you don't see it outside of Mathematical Physics textbooks with simple first year level case studies. I don't think the work is useless, it is just not usable.
>>13231193>Would it make sense to model heat as a vector field?Yes, a vector field is not an object exclusive to DG though (it is usually taught in multivariable and tensor calculus already)
