Abstract
As galaxy redshift surveys probe deeper into the universe, they uncover ever more dramatic structures in the large-scale distribution of galaxies. In particular, the CfA2 and SSRS2 surveys to an apparent magnitude limit of 15.5 exhibit an impressive complex of sheets, filaments, and clusters. The formation of the large-scale structure in the universe results from the gravitational amplification of the primordial small perturbations of density. The primordial density perturbations are thought to be random fields originated as quantum fluctuations at the very early stage. Thus the understanding of the formation of the large-scale structure may reveal important information about the early universe and the laws of fundamental physics. One of the major obstacles to understanding the formation of the large-scale structure is the complexity of the evolution of the density inhomogeneities at the nonlinear stage when the observable structures form. One way of addressing this problem is to run three-dimensional numerical simulations. Here we review another approach based on the approximate analytic model of the nonlinear gravitational instability utilizing Burgers’ equation of the nonlinear diffusion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arnol’d, V.I., Shandarin, S.F., Zel’dovich, Ya.B. 1982, Astrophys. Fluid Dyn., 20, 111.
Beacom, J.F., Dominik, K.G., Melott, A.L., Perkins, S., and Shandarin, S.F. 1991, Astrophys. J., 372, 351.
Burgers, J.M. 1974, The Non-linear Diffusion Equation ( Dordrecht: Reidel).
da Costa, L.N., Geller, M.J., Pellegrini, P.S., Latham, D.W., Fairall, A.P., Marzke, R.O., Willmer, C.N.A., Huchra, J.P., Calderon, J.H., and Kurtz, M.J. 1994, Astrophys. J. Lett., 424, Ll.
Doroshkevich, A.G., Kotok, E.V., Novikov, I.D., Polyudov, A.N., Shandarin, S.F., and Sigov Yu.S. 1980, Mon. Not. R. astr. Soc., 192 321.
Geller, M., and Huchra, J. 1989, Science, 246, 897.
Gurbatov, S.N., Saichev, A.I., and Shandarin, S.F. 1985. Soy. Phys. Doklady, 30, 921.
Gurbatov, S.N., Saichev A.I., and Shandarin, S.F. 1989, Mon. Not. R. astr. Soc., 236 385.
Klypin, A.A., and Shandarin, S.F. 1983, Mon. Not. R. astr. Soc., 204 891.
Kofman, L.A., Pogosyan, D.Yu., and Shandarin S.F. 1990, Mon. Not. R. astr. Soc., 242, 200.
Kofman, L., Pogosyan, D., Shandarin, S.F., and Melott, A.L. 1992, Astrophys. J., 393, 437.
Kotok, E.V., and Shandarin, S.F. 1987, Soy. Astr., 64, 1144.
Linde, A.D. 1990, Particle Physics and Inflationary Cosmology ( Harwood, New York).
Melott, A.L., and Shandarin, S.F. 1993, Astrophys. J., 410, 469.
Melott, A.L., Shandarin, S.F., and Weinberg, D.H. 1994, Astrophys. J., 428, 28.
Nusser, A., and Dekel, A. 1990, Astrophys. J., 362, 14.
Oort, J. 1983, Ann. Rev. Astron. Astrophys., 21, 373.
Peebles, P.J.E. 1980, The Large-scale Structure of the Universe ( Princeton: Princeton University Press).
Salmi, V., and Coles, P. 1995, Physics Reports, 262, 1.
Salmi, V., Sathyaprakash, B.S., and Shandarin, S.F. 1994, Astrophys. J., 431, 20.
Shandarin, S.F., Doroshkevich, A.G., and Zel’dovich, Ya.B. 1983, Soy. Phys. Usp., 26, 46.
Shandarin S.F., and Zel’dovich, Ya.B. 1989, Rev. Mod. Phys., 61, 185.
Shandarin, S.F., Melott, A.L., McDavitt, K., Pauls, J., and Tinker, J. 1995, Phys. Rev. Lett., 75, 7.
Weinberg, D., and Gunn, J. 1989, Astrophys. J. Lett., 352, L25.
Weinberg, D., and Gunn, J. 1990, Mon. Not. R. astr. Soc., 247, 260.
White, M., Scott, D., and Silk, J. 1994 Ann. Rev. Astron. Astrophys., 32, 319.
Zel’dovich, Ya.B. 1970, Astron. Astrophys., 5 84.
Zel’dovich, Ya.B., and Novikov, I.D. 1983, The Structure and Evolution of the Universe (Chicago/London: University of Chicago Press).
Zel’dovich, Ya.B., Mamaev, A.V., and Shandarin, S.F. 1983 Soy. Phys. Usp., 26, 77.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Shandarin, S.F. (1997). Three-Dimensional Burgers’ Equation as a Model for the Large-Scale Structure Formation in the Universe. In: Molchanov, S.A., Woyczynski, W.A. (eds) Stochastic Models in Geosystems. The IMA Volumes in Mathematics and its Applications, vol 85. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8500-4_18
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8500-4_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8502-8
Online ISBN: 978-1-4613-8500-4
eBook Packages: Springer Book Archive