Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the emergence of patterns of order
HTML articles powered by AMS MathViewer

by J. M. Burgers PDF
Bull. Amer. Math. Soc. 69 (1963), 1-25
References
    1. W. Shockley and others, Imperfections in nearly perfect crystals, Wiley, New York, 1952.
  • H. G. van Bueren, Imperfections in crystals, Series in Physics, North-Holland Publishing Co., Amsterdam, 1960. MR 0127337
  • 3. W. T. Read, Dislocations in crystals, McGraw-Hill, New York, 1953.
  • F. R. Eirich (ed.), Rheology: theory and applications. Vol. 1, Academic Press, Inc., New York, 1956. MR 0092444
  • 5. A. Verma, Crystal growth and dislocations, Butterworth, London, 1953. 6. W. Dekeyser et S. Amelinckx, Les dislocations et la croissance des cristaux, Masson, Paris, 1955. 7. M. L. Kronberg, Plastic deformation of single crystals of sapphire: Basal slip and twinning, Acta Metallurgica 5 (1957), 507-524. 8. S. Amelinckx, W. Bontinck, W. Dekeyser and F. Seitz, On the formation and properties of helical dislocations, Philos. Mag. 2 (1957), 355-378. 9. W. Bontinck, Climb phenomena in synthetic fluorite crystals, Philos. Mag. 2 (1957), 561-567. 10. W. C. Dash, Generation of prismatic dislocation loops in silicon crystals, Phys. Rev. Lett. 1 (1958), 400-402. 11. Henri Bénard, Les tourbillons cellulaires dans une nappe liquide transportant de la chaleur en régime permanent, Annales de Chimie et de Physique (7e série) 23 (1901), 62-144. 12. Henri Bénard, Les tourbillons cellulaires dans une nappe liquide, Revue Générale des Sciences 11 (1900), 1261-1271, 1309-1328. 13. K. Chandra, Instability of fluids heated from below, Proc. Roy. Soc. London. Ser. A 164 (1938), 231-242. 14. H. Jeffreys, Some cases of instability in fluid motion, Proc. Roy. Soc. London. Ser. A 118 (1928), 195-208.
  • W. H. Reid and D. L. Harris, Some further results on the Bénard problem, Phys. Fluids 1 (1958), 102–110. MR 128235, DOI 10.1063/1.1705871
  • Jeremi Wasiutyński, Studies in hydrodynamics and structure of stars and planets, Astrophys. Norvegica 4, Jacob Dybwad, Oslo, 1946. MR 0019426
  • 17. D. C. Christopherson, Note on the vibration of membranes, Quart. J. Math. 11 (1940), 63-65. 18. F. A. Vening Meinesz, A remarkable feature of the earth’s topography; origin of continents and oceans, Proc. Roy. Netherl. Acad. Sciences, Ser. B 54 (1951), 212-228; Convection currents in the earth and the origin of the continents, ibid. 55 (1952), 527-553. 19. G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Philos. Trans. Roy. Soc. London, Ser. A 223 (1923), 289-343. 20. A. R. Low and D. Brunt, Instability of viscous fluid motion, Nature 115 (1925), 299-301. 21. A. R. Low, On the criterion for stability of a layer of viscous fluid heated from below, Proc. Roy. Soc. London Ser. A 125 (1929), 180-195.
  • H. Görtler, Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden, Nachr. Ges. Wiss. Göttingen. Fachgruppe I. N.F. 2 (1940), 1–26 (German). MR 3757
  • 23. H. B. Squire, On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls, Proc. Roy. Soc. London, Ser. A 142 (1933), 621-628. 24. F. R. Hama, J. D. Long and J. C. Hogarthy, On transition from laminar to turbulent flow, Technical Note BN-81, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, August, 1956. 25. J. R. Weske, Experimental study of detail phenomena of transition in boundary layers, Technical Note BN-91, ibidem, February, 1957. 26. S. Goldstein, Modern developments in fluid dynamics, Oxford Univ. Press, Oxford, Vol. I, 1938, pp. 210-214. 27. A. A. Townsend, The eddy viscosity in turbulent shear flow, Philos. Mag. 41 (1950), 890-906. 28. A. A. Townsend, The structure of the turbulent boundary layer, Proc. Cambridge Philos. Soc. 47, (1950), 375-395.
  • A. A. Townsend, The structure of turbulent shear flow, Cambridge University Press, New York, 1956. MR 0078813
  • J. M. Burgers, Some considerations on turbulent flow with shear. I, II, Nederl. Akad. Wetensch. Proc. Ser. B. 56 (1953), 125–136, 137–147. MR 0055123
  • 31. E. A. Milne, Relativity, gravitation and world structure, Oxford Univ. Press, Oxford, 1935.
  • J. M. Burgers, Further statistical problems connected with the solution of a simple non-linear partial differential equation, Nederl. Akad. Wetensch. Proc. Ser. B. 57 (1954), 159–169. MR 0062324
  • Eberhard Hopf, The partial differential equation $u_t+uu_x=\mu u_{xx}$, Comm. Pure Appl. Math. 3 (1950), 201–230. MR 47234, DOI 10.1002/cpa.3160030302
  • 34. J. D. Cole, a private communication (1949).
  • J. M. Burgers, Correlation problems in a one-dimensional model of turbulence. I, Nederl. Akad. Wetensch., Proc. 53 (1950), 247–260. MR 35581
  • 36. A. N. Whitehead, Science and the modern world, Macmillan, New York, 1925. 37. A. N. Whitehead, Process and reality, Cambridge Univ. Press, Cambridge, 1929. 38. A. N. Whitehead, Adventures of ideas, ibidem 1933.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 69 (1963), 1-25
  • DOI: https://doi.org/10.1090/S0002-9904-1963-10832-0
  • MathSciNet review: 0143359