Reading
When I have time, I find pleasure in attempting to reduce the multitude of things that I know nothing about. In this spirit, I am currently reading a fascinating trio of papers by my great hero G. I. Taylor:
G. I. Taylor, The dynamics of thin sheets of fluid. I. Water bells, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 253, 289-295 (1959).
G. I. Taylor, The dynamics of thin sheets of fluid. II. Waves on fluid sheets, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 253, 296-312 (1959).
G. I. Taylor, The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 253, 313-321 (1959).
Previously, I tried to gain a cursory understanding of current algebras, bosonization, Wess-Zumino-Witten models and the like from some classic papers of the early 1980s:
A. M. Polyakov and P. B. Wiegmann, Theory of nonabelian Goldstone bosons in two dimensions, Physics Letters B 131, 121-126 (1983).
V. G. Knizhnik and A. B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nuclear Physics B 247, 83-103 (1984).
E. Witten, Non-Abelian Bosonization in Two Dimensions, Communications in Mathematical Physics 92, 455-472 (1984).
Prior to that I attempted to read some wonderful papers of Keith Moffatt's on vorticity and topology in fluid dynamics, as well as the two original papers on the integral expression for the Hopf invariant:
H. K. Moffatt, The degree of knottedness of tangled vortex lines, Journal of Fluid Mechanics 35, 117-129 (1969).
H. K. Moffatt and R. L. Ricca, Helicity and the Călugăreanu Invariant, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 439, 411-429 (1992).
H. K. Moffatt and A. Tsinober, Helicity in Laminar and Turbulent Flow, Annual Reviews of Fluid Mechanics 24, 281-312 (1992).
J. H. C. Whitehead, An expression of Hopf's invariant as an integral, Proceedings of the National Academy of Sciences of the United States of America 33, 117-123 (1947).
N. E. Steenrod, Cohomology invariants of mappings, Proceedings of the National Academy of Sciences of the United States of America 33, 124-128 (1947).
A little further back I attempted to read some of the original papers on Whitham's fascinating variational theory of non-linear dispersive waves, and an earlier paper of Fritz Ursell's on long water waves, also about nonlinearity and dispersion:
G. B. Whitham, A general approach to linear and non-linear dispersive waves using a Lagrangian, Journal of Fluid Mechanics 22, 273-283 (1965).
G. B. Whitham, Variational methods and applications to water waves, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 299, 6-25 (1967).
M. J. Lighthill, Some special cases treated by the Whitham theory, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 299, 28-53 (1967).
F. Ursell, The long-wave paradox in the theory of gravity waves, Mathematical Proceedings of the Cambridge Philosophical Society 49, 685-694 (1953).
Earlier still I made some inroads on a set of papers loosely themed around topology:
N. S. Manton, Topology in the Weinberg-Salam model, Physical Review D 28, 2019-2026 (1983).
E. Witten, Global aspects of current algebra, Nuclear Physics B 223, 422-432 (1983).
M. Hindmarsh, Where Are the Hedgehogs in Quenched Nematics?, Physical Review Letters 75, 2502-2505 (1995).
as well as an interesting paper of John and Valentina's that was brought to my attention by Bryan:
V. Riva and J. Cardy, Scale and conformal invariance in field theory: a physical counterexample, Physics Letters B 622, 339-342 (2005).
This current programme was initialised, in late June and early July, when I firsted started to learn about the generation of waves by wind, taking as my main source of inspiration the beautiful papers by John Miles, Brooke Benjamin, and James Lighthill:
J. W. Miles, On the generation of surface waves by shear flows, Journal of Fluid Mechanics 3, 185-204 (1957).
T. B. Benjamin, Shearing flow over a wavy boundary, Journal of Fluid Mechanics 6, 161-205 (1959).
M. J. Lighthill, Physical interpretation of the mathematical theory of wave generation by wind, Journal of Fluid Mechanics 14, 385-398 (1962).