The spatial cosmic matter distribution on scales of a few up to more than a hundred megaparsec displays a salient and pervasive foam-like pattern. Revealed through the painstaking efforts of redshift survey campaigns, it has completely revised our view of the matter distribution on these cosmological scales. The web-like spatial arrangement of galaxies and mass into elongated filaments, sheet-like walls and dense compact clusters, the existence of large near-empty void regions and the hierarchical nature of this mass distribution – marked by substructure over a wide range of scales and densities – are three major characteristics we have come to know as the cosmic web.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abazajian, K., et al. (The SDSS collaboration): Astron. J. 126, 2081 (2003)
Abramov, O., McEwen, A.S.: Int. J. Rem. Sens. 25, 669 (2004)
Aikio, J., Mähönen, P.: Astrophys. J. 497, 534 (1998)
Alliez, P., Cohen-Steiner, D., Yvinec, M., Desbrun, M.: ACM Trans. Graph. 24, 517 (2005)
Alliez, P., Ucelli, G., Gotsman, M., Attene, M.: Recent Advances in Remeshing of Surfaces. Report of the AIM@SHAPE EU network (2005)
Amenta, N., Bern, M., Kamvysselis, M.: Siggraph ’98, 415 (1998)
Amenta, N., Bern, M.: Discrete and Comp. Geometry 22, 481 (1999)
Arad, I., Dekel, A., Klypin, A.: Mon. Not. R. Astron. Soc. 353, 15 (2004)
Aragón-Calvo, M.A.: Morphology and Dynamics of the Cosmic Web, Ph.D. thesis, Groningen University (2007)
Aragón-Calvo, M.A., Jones, B.J.T.: van de Weygaert, R.: van der Hulst, J.M.: Mon. Not. R. Astron. Soc., subm. Astron. Astrophys., (2007)
Arbabi-Bidgoli, S., Müller, V.: Mon. Not. R. Astron. Soc. 332, 20 (2002)
Arnol’d, V.I.: The Theory of Singularities and Its Applications. Cambridge University Press, Cambridge (1991)
Ascasibar, Y., Binney, J.: Mon. Not. R. Astron. Soc. 356, 872 (2005)
Babul, A., Starkman, G.D.: Astrophys. J. 401, 28 (1992)
Baccelli, F., Zuyev, S.: Oper. Res. 47, 619 (1999)
Balbus, S.A., Hawley, J.F.: Revs. Mod. Phys. 70, 1 (1998)
Bertschinger, E.: Astrophys. J. 323, L103 (1987)
Barrow, J.D., Bhavsar, S.P., Sonoda, D.H.: Mon. Not. R. Astron. Soc. 216, 17 (1985)
Basilakos, S., Plionis, M., Rowan-Robinson, M.: Mon. Not. R. Astron. Soc. 323, 47 (2001)
Bennett, C.L., et al.: Astrophys. J. Suppl. 148, 1 (2003)
Bentley, J.L.: Comm. ACM 18, 509 (1975)
Bentley, J.L., Friedmann, J.H.: IEEE Trans. Comput. C-27, 97 (1978)
Bernardeau, F.: Astrophys. J. 390, L61 (1992)
Bernardeau, F.: Astrophys. J. 433, 1 (1994)
Bernardeau, F., Kofman, L.: Astrophys. J. 443, 479 (1995)
Bernardeau, F., Juszkiewicz, R., Dekel, A., Bouchet, F. R.: Mon. Not.R. Astron. Soc. 274, 20 (1995)
Bernardeau, F., van de Weygaert, R.: Mon. Not. R. Astron. Soc. 279, 693 (1996)
Bernardeau, F., van de Weygaert, R., Hivon, E., PBouchet, F.: Mon. Not. R. Astron. Soc. 290, 566 (1997)
Bernardeau, F., Colombi, S., Gaztanaga, E., Scoccimarro, R.: Phys. Rep. 367, 1 (2002)
Beucher, S., Lantuejoul, C. In: Proc. Intern. Workshop on Image Processing, CCETT/IRISA, Rennes (1979)
Beucher, S., Meyer, F.: The morphological approach to segmentation, the watershed transformation. In: Dougherty, E. (ed.) Mathematical Morphology in Image Processing. M. Dekker Inc., New York (1993)
Beyer, T., Schaller, G., Deutsch, A., Meyer-Hermann, M.: Comput. Phys. Commun. 172, 86 (2005)
Beyer, T., Meyer-Hermann, M.: WSEAS Trans. Syst. 5, 1100 (2006)
Böhringer, H., Schuecker, P., Guzzo, L., Collins, C.A., Voges, W., Schindler, S., Neumann, D.M., Cruddace, R.G., De Grandi, S., Chincarini, G., Edge, A.C., MacGillivray, H.T., Shaver, P.: Astron. Astrophys., 369, 826 (2001)
Boissonnat, J.-D., Yvinec, M., Bronniman, H.: Algorithmic Geometry. Cambridge University Press, Cambridge (1998)
Boissonnat, J.-D., Cohen-Steiner, D., Mourain, B., Rote, G., Vegter, G.: Meshing of surfaces. In: Boissonnat, J.-D., Teillaud, M. (eds.) Effective Computational Geometry for Curves and Surfaces. Springer-Verlag, Berlin (2006)
Boots, B.N.: Metallography 17, 411 (1984)
Borgani, S., Guzzo, L.: Nature 409, 39 (2001)
Bradač M., Schneider, P., Lombardi, M., Steinmetz, M., Koopmans, L.V.E., Navarro, J.F.: Astron. Astrophys. 423, 797 (2004)
Branchini, E., Teodoro, L., Frenk, C.S., Schmoldt, I., Efstathiou, G., White, S.D.M., Saunders, W., Sutherland, W., Rowan-Robinson, M., Keeble, O., Tadros, H., Maddox, S., Oliver, S.: Mon. Not. R. Astron. Soc. 308, 1 (1999)
Braun, J., Sambridge, M.: Nature 376, 660 (1995)
Brown, G.S.: New Zealand Forestry Service Research Notes 38, 1 (1965)
Buhmann, M.D.: Approximation and interpolation with radial functions. In: Dyn, N., Leviatan, D., Levin, D., Pinkus, A. (eds.) Multivariate Approximation and Applications, vol. 25, Cambridge University Press, Cambridge (2001)
Cappellari, M., Copin, Y.: Mon. Not. R. Astron. Soc. 342, 345 (2003)
Cheng, S.-W., Dey, T.K., Ramos, E., Ray, T.: Sampling and meshing a surface with guaranteed topology and geometry. In: Proc. 20th Sympos. Comput. Geom. (2004)
Chiang, L.-Y., Coles, P.: Mon. Not. R. Astron. Soc. 311, 809 (2000)
Chincarini, G., Rood, H.J.: Nature 257, 294 (1975)
Chiu, S.N., van de Weygaert, R., Stoyan, D.: Journ. Appl. Prob. 28, 356 (1996)
Christ, N.H., Friedberg, R., Lee, T.D.: Nucl. Phys. B202, 89 (1982)
Christ, N.H., Friedberg, R., Lee, T.D.: Nucl. Phys. B210, 310 (1982)
Christ, N.H., Friedberg, R., Lee, T.D.: Nucl. Phys. B210, 337 (1982)
Colberg, J.M., Krughoff, K.S., Connolly, A.J.: Mon. Not. R. Astron. Soc. 359, 272 (2005)
Colberg, J.M., Sheth, R.K., Diaferio, A., Gao, L., Yoshida, N.: Mon. Not. R. Astron. Soc. 360, 216 (2005)
Colberg, J.M.: Mon. Not. R. Astron. Soc. 375, 337 (2007)
Colberg, J.M., Pearce, F., Brunino, R., Foster, C., Platen, E., Basilakos, S., Fairall, A., Feldman, H., Gottlöber, S., Hahn, O., Hoyle, F., Müller, V., Nelson, L., Neyrinck, M., Plionis, M., Porciani, C., Shandarin, S., Vogeley, M., van de Weygaert, R.: Mon. Not. R. Astron. Soc., (2008)
Coles, P., Chiang, L.-Y.: Nature 406, 376 (2000)
Colless, M., et al.: astro-ph/0306581 (2003)
Colombi, S., Pogosyan, D., Souradeep, T.: Phys. Rev. Let. 85, 5515 (2000)
Cressie, N.: Statistics for Spatial Data, rev. ed., John Wiley & Sons, Chichester (1993)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 2nd ed., Springer-Verlag, Heidelberg (2000)
Delaunay, B. N.: Bull. Acad. Sci. USSR: Clase Sci. Mat. 7, 793 (1934)
Dey, T., Edelsbrunner, H., Guha, S.: Computational topology. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds.) Advances in Discrete and Computational Geometry. Contemporary Mathematics, AMS, Providence (1998)
Dey, T.K.: Curve and surface reconstruction. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry. 2nd ed., CRC Press LLC, Boca Raton (2004)
Dinh, H.Q., Turk, G., Slabaugh, G.: IEEE Trans. Pattern Anal. Mach. Intell. 24, 1358 (2002)
Dirichlet, G.L.: Journal für die Reine und Angwandte Mathematik 40, 209 (1850)
Dubinski, J., da Costa, L.N., Goldwirth, D.S., Lecar, M., Piran, T.: Astrophys. J. 410, 458 (1993)
Ebeling, H., Wiedenmann, G.: Phys. Rev. E 47, 704 (1993)
Edelsbrunner, H., Kirkpatrick, D., Seidel, R.: IEEE Trans. Inform. Theory IT-29, 551, 193
Edelsbrunner, H., Mücke, E.P.: ACM Trans. Graph. 13, 43
Edelsbrunner, H., Shah, N.R.: Algorithmica 15, 223 (1996)
Edelsbrunner, H., Facello, M., Liang, J.: Discrete Appl. Math. 88, 83 (1998)
Edelsbrunner, H., Letscher, D., Zomorodian, A.: Discrete Comput. Geom. 28, 511
Einasto, J., Joeveer, M., Saar, E., Nature 283, 47 (1980)
El-Ad, H., Piran, T., da Costa, L.N.: Astrophys. J. 462, L13 (1996)
El-Ad, H., Piran, T.: Astrophys. J. 491, 421 (1997)
Eldering, B.: Topology of galaxy models, M.Sc. thesis, Groningen University (2006)
Español, P.: Phys. Rev. E. 57, 2930 (1998)
Euler, L.: Letter dated 1759 October 27 from Euler to Lagrange, Opera Postuma 2, 559 (1862)
De Fabritiis, G., Coveney, P.V.: arXiv:cond-mat/0301378 (2003)
Fairall, A.P.: Voids in the 6dF Galaxy Survey. In: van de Weygaert, R., Vogeley, M., Sheth, R., Peebles, P.J.E., Hoyle, F. (eds.) Cosmic Voids: Much Ado About Nothing, Edita (2008)
Fischer, R.A., Miles, R.E.: Math. Biosci. 18, 335 (1973)
Fisher, K. B., Huchra, J. P., Strauss, M. A., Davis, M., Yahil, A., Schlegel, D.: Astrophys. J. Suppl. 100, 69 (1995)
Flekkøy, E.G., Coveney, P.V.: De Fabritiis, G.: Phys. Rev. E. 62, 2140 (2000)
Florack, L.M.J., ter Haar Romeny, B.M., Koenderink, J.J., Viergever, M.A.: Image Vision Comput. 10, 376 (1992)
Fortune, S.: Voronoi diagrams and delaunay trinagulations. In: Du, D.-Z., Hwang, F. (eds.) Computing in Euclidian Geometry. Lecture Notes Series on Computing vol. 1, World Scientific, Singapore (1992)
Frangi, A.F., Niessen, W.J., Vincken, K.L., Viergever, M.A.: Multiscale vessel enhancement filtering. In: Medical Image Computing and Computer-Assisted Interventation – MICCAI’98. Lecture Notes in Computer Science, vol. 1496, Springer-Verlag, Berlin, Heidelberg (1998)
Friedman, J.H., Bentley, J.L., Finkel, R.A.: ACM Trans. Math. Softw. 3, 209 (1977)
Fukugita, M., Peebles, P.J.E.: Astrophys. J. 616, 643 (2004)
Gaztañaga, E.: Astrophys. J. 398, L17 (1992)
Geller, M., Huchra, J. P.: Nature 246, 897 (1989)
Gerald, C. F., Wheatley, P.O.: Applied Numerical Analysis. Addison Wesley, Reading (1999)
Gilbert, E.N.: Ann. Math. Stat. 33, 958 (1962)
Gingold, R.A., Monaghan, J.J.: Mon. Not. R. Astron. Soc. 181, 375 (1977)
Gnedin, N.Y.: Astrophys. J. Suppl. 97, 231 (1995)
Gold, C.M., Remmele, P.R., Roos, T.: Voronoi methods in GIS. In: Lecture Notes in Computer Science, vol. 1340, p. 21. Springer-Verlag, Berlin (1997)
Goodman, J. E., O’Rourke, J. (eds.): Handbook of Discrete and Computational Geometry, 2nd ed., Chapman & Hall/CRC Press, Boca Raton (1980)
Gor, V., Shapiro, B.E., Jönsson, H., Heisler, M., Reddy, G.V., Meyerowitz, E.M., Mjolsness, E.: A Software Architecture for Developmental Modelling in Plants: The Computable Plant Project. In: Bioinformatics of Genome Regulation and Structure II, Springer, U.S. (2006)
Gott, J.R. III, Dickinson, M., Melott, A.L.: Astrophys. J. 306, 341 (1986)
Gregory, S.A., Thompson, L.A.: Astrophys. J. 222, 784 (1978)
Hardy, R.L.: J. Geophys. Res. 76 (1905)
Hayashino, T. et al.: Astron. J. 128, 2073 (2004)
Heath Jones, D. et al.: Mon. Not. R. Astron. Soc. 355, 747 (2004)
Hoffman, Y., Ribak, E.: Astrophys. J. 380, L5 (1991)
Hoyle, F., Vogeley, M.: Astrophys. J. 566, 641 (2002)
Hoyle, F., Vogeley, M.: Astrophys. J. 580, 663 (2002)
Icke, V., van de Weygaert, R.: Astron. Astrophys. 184, 16 (1987)
Illiev, I.T., Ciardi, B., Alvarez, M.A., Maselli, A., Ferrara, A., Gnedin, N.Y., Mellema, G., Nakamoto, M.L., Norman, M.L., Razoumov, A.O., Rijkhorst, E.-J., Ritzerveld, J., Shapiro, P.R., Susa, H., Umemura, M., Whalen, D.J.: Mon. Not. R. Astron. Soc. 371, 1057 (2006)
Iske, A.: Scattered data modelling using radial basis functions. In: Iske, A., Quak, E., Floater, M.S. (eds.) Tutorials on Multiresolution in Geometric Modelling, Mathematics and Visualization, p. 287, Springer-Verlag, Heidelberg (2002)
Jarrett, T.: Publ. Astr. Soc. Australia, 21, 396 (2004)
Jones, B.J.T., Martínez, V.J., Saar, E., Trimble, V.: Rev. Mod. Phys. 76, 1211 (2005)
Juszkiewicz, R., Weinberg, D.H., Amsterdamski, P., Chodorowski, M., Bouchet, F.: Astrophys. J. 442, 39 (1995)
Kaiser, N.: Statistics of gravitational lensing 2: Weak lenses. In: Martinez, V.J., Portilla, M., Saez, D. (eds.) New Insights into the Universe. Lect. Notes Phys. 408, 279. Springer-Verlag, Berlin, Heidelberg, New York (1992)
Kaiser, N., Squires, G.: Astrophys. J. 404, 441 (1993)
Kansal, A.R., Torquato, S., Harsh, G.R., Chiocca, E.A., Deisboeck, T.S.: J. Theor. Biol. 203, 367
Katz, N., Weinberg, D.H., Hernquist, L.: Astrophys. J. Suppl. 105, 19 (1996)
Kauffmann, G., Fairall, A.P.: Mon. Not. R. Astron. Soc. 248, 313 (1991)
Kauffmann, G., Colberg, J.M., Diaferio, A., White, S.D.M.: Mon. Not. R. Astron. Soc. 303, 188 (1999)
Kendall, D.G.: Stat. Sci. 4, 87 (1989)
Kiang, T.: Z. Astrophys. 64, 433 (1966)
Kim, R. S. J., Kepner, J.V., Postman, M., Strauss, M.A., Bahcall, N.A., Gunn, J.E., Lupton, R.H., Annis, J., Nichol, R.C., Castander, F.J., Brinkmann, J., Brunner, R.J., Connolly, A., Csabai, I., Hindsley, R.B., Izević Ž., Vogeley, M.S., York, D.G.: Astron. J. 123, 20 (2002)
Kimia, B.B., Leymarie, F.F., Symmetry-based representations of 3D data. In: Proc. 2001 Intern. Conf. on Image Processing 2, 581 (2001)
Kirshner, R.P., Oemler, A., Schechter, P.L., Shectman, S.A.: Astrophys. J. 248, L57 (1981)
Kirshner, R.P., Oemler, A., Schechter, P.L., Shectman, S.A.: Astrophys. J. 314, 493 (1987)
Koumoutsakos, P.: Ann. Rev. Fluid Mech. 37, 457 (2005)
Lachieze-Rey, M., da Costa, L.N., Maurogordata, S.: Astrophys. J. 399, 10 (1992)
Lagrange, J.L.: Oeuvres de Lagrange 1, 151 (1762)
Lancaster, P., Salkauskas, K.: Math. Comput. 37, 141 (1981)
de Lapparent, V., Geller, M.J., Huchra, J.P.: Astrophys. J. 302, L1 (1986)
de Lapparent, V., Geller, M.J., Huchra, J.P.: Astrophys. J. 369, 273 (1991)
Lawson, C.L.: Software for C1 surface interpolation. In: Rice, J.R. (eds.) Mathematical Software III, vol. 3, Academic Press, New York (1977)
Leymarie, F.F., Kimia, B.B.: Computation of the shock scaffold for unorganized point clouds in 3D. In: Proc. 2003 Comp. Soc. Conf. on Computer Vision and Pattern Recognition 1, I-821 (2003)
Li, G.-L., Mao, S., Jing, Y.P., Kang, X., Bartelmann, M.: Astrophys. J. 652, 43 (2006)
Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P.V., Subramaniam, S.: Proteins: Struct. Funct. Genet. 33, 1 (1998)
Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P.V., Subramaniam, S.: Proteins: Struct. Funct. Genet. 33, 18 (1998)
Liang, J., Edelsbrunner, H., Woodward, C.: Protein Sci. 7, 1884 (1998)
Lodha, S.K., Franke, R.: Scattered Data Techniques for Surfaces. In: Proc. Dagstuhl Conf. Scientific Visualization, IEEE Computer Society Press, 182 (1999)
Lombardi, M., Schneider, P.: Astron. Astrophys. 373, 359 (2001)
Lombardi, M., Schneider, P.: Astron. Astrophys. 392, 1153 (2002)
Lombardi, M., Schneider, P.: Astron. Astrophys. 407, 385 (2003)
Lopes, P.A.A., de Carvalho, R.R., Gal, R.R., Djorgovski, S.G., Odewahn, S.C., Mahabal, A.A., Brunner, R.J.: Astron. J. 128, 1017 (2004)
Lucy, L.B.: Astron. J. 82, 1013 (1977)
Luo, R., Vishniac, E.: Astrophys. J. Suppl. 96, 429 (1995)
Maddox, S.J., Efstathiou, G., Sutherland, W.J., Loveday, J.: Mon. Not. R. Astron. Soc. 242, 43 (1990)
Maddox, S.J., Efstathiou, G., Sutherland, W.J., Loveday, J.: Mon. Not. R. Astron. Soc. 243, 692 (1990)
Maddox, S.J., Efstathiou, G., Sutherland, W.J.: Mon. Not. R. Astron. Soc. 246, 433 (1990)
Marinoni, C., Davis, M., Newman, J.A., Coil, A.L.: Astrophys. J. 580, 122 (2002)
Martínez, V., Saar, E.: Statistics of the Galaxy Distribution. Chapman & Hall/CRC Press, Boca Raton (2002)
Martínez, V., Starck, J.-L., Saar, E., Donoho, D.L., Reynolds, S.C., de la Cruz, P., Paredes, S.: Astrophys. J. 634, 744 (2005)
Mavripilis, D.J.: Ann. Rev. Fluid Mech. 29, 473 (1997)
Mecke, K.R., Buchert, T., Wagner, H.: Astron. Astrophys. 288, 697 (1994)
Meijering, J.L.: Philips Res. Rep. 8, 270 (1953)
Mellier, Y.: Ann. Rev. Astron. Astrophys. 37, 127 (1999)
Metropolis, N., Ulam, S.: J. Am. Stat. Assoc. 44, 247 (1949)
Meyer, F., Beucher, S.: J. Visual Comm. Image Rep. 1, 21 (1990)
Miles, R.E.: Math. Biosci. 6, 85 (1970)
Miles, R.E.: Adv. Appl. Prob. (Suppl.) 4, 243 (1972)
Miles, R.E.: A synopsis of ‘Poisson Flats in Euclidian Spaces’. In: Harding, E.F., Kendall, D.G. (eds.) Stochastic Geometry, p. 202. John Wiley, New York (1974)
Miles, R.E., Maillardet, R.J.: J. Appl. Prob. 19A, 97 (1982)
Miller, W.: Class. Quant. Grav. 14, L199 (1997)
Mitra, S.K., Sicuranza, G.L.: Nonlinear Image Processing. Academic Press Inc., U.S. (2000)
Molchanov, S.A., Surfailis, D., Woyczynski, W.A.: Ann. Appl. Prob. 7, 200 (1997)
Møller, J.: Adv. Appl. Prob. 21, 37 (1989)
Møller, J.: Lectures on Random Voronoi Tessellations. In: Lecture Notes in Statistics, p. 87. Springer-Verlag, New York (1994)
Monaghan, J.J.: Ann. Rev. Astron. Astrophys. 30, 543 (1992)
Mücke, E.P.: Shapes and Implementations in three-dimensional geometry, Ph.D. thesis, University of Illinois Urbana-Champaign (1993)
Neyrinck, M. C., Gnedin, N. Y., Hamilton, A. J. S.: Astrophys. J. 356, 1222 (2005)
Novikov, D., Colombi, S., Doré, O.: Mon. Not. R. Astron. Soc. 366, 1201 (2006)
Nusser, A., Dekel, A., Bertschinger, E., Blumenthal, G. R.: Astrophys. J. 379, 6 (1991)
Okabe, A., Boots, B., Sugihara, K., Chiu, S. N.: Spatial tessellations: concepts and applications of Voronoi diagrams, 2nd ed., John Wiley & Sons, Chichester, Toronto (2000)
Ord, J.K.: Math. Scientist 3, 23 (1978)
Patiri, S.G., Betancort-Rijo, J.E., Prada, F., Klypin, A., Gottlöber, S.: Mon. Not. R. Astron. Soc. 369, 335 (2006)
Patiri, S.G., Prada, F., Holtzman, J., Klypin, A., Betancort-Rijo, J.E.: Mon. Not. R. Astron. Soc. 372, 1710 (2006)
Peacock, J.A., Dodds, S.J.: Mon. Not. R. Astron. Soc. 267, 1020 (1994)
Peebles, P.J.E.: The Large-Scale Structure of the Universe. Princeton University Press, Princeton, NJ (1980)
Pelupessy, F.I., Schaap, W.E., van de Weygaert, R.: Astron. Astrophys. 403, 389 (2003)
Pen, Ue.-Li.: Astrophys. J. Suppl. 115, 19 (1998)
Pimbblet, K.A.: Mon. Not. R. Astron. Soc. 358, 256 (2005)
Platen, E.: Segmenting the Universe, M.Sc. thesis, Groningen University (2005)
Platen, E., van de Weygaert, R., Jones, B.J.T.: Mon. Not. R. astr. Soc., 387, 128 (2008)
Plionis, M., Basilakos, S.: Mon. Not. R. Astron. Soc. 330, 399 (2002)
Powell, M.J.D.: The theory of radial basis function approximation in 1990. In: Light, W.A. (ed.) Advances in Numerical Analysis II: Wavelets, Subdivision, and Radial Functions, p. 105. Oxford University Press, Oxford (1992)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes. Cambridge University Press, Cambridge, U.K. (1992)
Ramella, M., Boschin, W., Fadda, D., Nonino, M.: Astron. Astrophys. 368, 776 (2001)
Refregier, Y.: Ann. Rev. Astron. Astrophys. 41, 645 (2003)
Regge, T.: Nuovo Cimentto A 19, 558
Regös, E., Geller, M.J.: Astrophys. J. 373, 14 (1991)
Reiprich, T.H., Böhringer, H.: Astron. Nachr. 320, 296 (1999)
Ripley, B.D.: Spatial Statistics, Wiley & Sons, Chichester (1981)
Ritzerveld, J.: The simplicity of transport, Ph.D. thesis, Leiden University (2007)
Ritzerveld, J., Icke, V.: Phys. Rev. E. 74, 026704 (2006) 331, 386, 394
Ritzerveld, J., Pawlik, A., Schaye, J.: in prep. (2007)
Rojas, R.R., Vogeley, M.S., Hoyle, F., Brinkmann, J.: Astrophys. J. 624, 571 (2005)
Romano-Díaz, E.: Probing Cosmic Velocity Flows in the Local Universe, Ph.D. thesis, Groningen University (2007)
Romano-Díaz (2004)
Rybicki, G.B., Press, W.H.: Astrophys. J. 398, 169 (1992)
Ryden, B.S., Gramann, M.: Astrophys. J. 383, 33 (1991)
Sambridge, M., Braun, J., McQueen, H.: Geophys. J. Int. 122, 837 (1995)
Sahni, V., Sathyaprakash, B.S., Shandarin, S.F.: Astrophys. J. 495, 5 (1998)
Sato, Y., Nakajima, D., Atsumi, H., Koller, T., Gerig, G., Yoshida, S., Kikinis, R.: IEEE Medical Image Analysis, vol. 2, p. 143 (1998)
Saunders, W., Sutherland, W.J., Maddox, S.J., Keeble, O., Oliver, S.J., Rowan-Robinson, M., McMahon, R.G., Efstathiou, G.P., Tadros, H., White, S.D.M., Frenk, C.S., Carramiñana, A., Hawkins, M.R.S.: Mon. Not. R. Astron. Soc. 317, 55 (2000)
Schaap, W.E.: The Delaunay Tessellation Field Estimator, Ph.D. thesis, Groningen University (2007)
Schaap, W.E., van de Weygaert, R.: Astron. Astrophys. 363, L29 (2000)
Schaap, W.E., van de Weygaert, R.: Astron. Astrophys., subm. (2007)
Schaback, R., Wendland, H.: Characterization and construction of radial basis functions. In: Dyn, N., Leviatan, D., Levin, D., Pinkus, A. (eds.) Multivariate Approximation and Applications, p. 1. Cambridge University Press, Cambridge (2001)
Schaller, G., Meyer-Hermann, M.: Comput. Phys. Commun. 162, 9 (2004)
Schaller, G., Meyer-Hermann, M.: Phys. Rev. E. 71, 051910.1 (2005)
Schmalzing, J., Buchert, T., Melott, A.L., Sahni, V., Sathyaprakash, B.S., Shandarin, S.F.: Astrophys. J. 526, 568
Schmidt, J.D., Ryden, B.S., Melott, A.L.: Astrophys. J. 546, 609
Schoenberg, I.J.: Quart. Appl. Math. 4, 45 (1946)
Schoenberg, I.J.: Quart. Appl. Math. 4, 112 (1946)
Serrano, M., Español, P.: Phys. Rev. E. 64, 046115 (2001)
Serrano, M., De Fabritiis, G., Español, P., Flekkøy, E.G., Coveney, P.V.: J. Phys. A. Math. Gen. 35, 1605 (2002)
Shandarin, S.F., Sheth, J.V., Sahni, V.: Mon. Not. R. Astron. Soc. 353, 162 (2004)
Shandarin, S., Feldman, H.A., Heitmann, K., Habib, S.: Mon. Not. R. Astron. Soc. 376, 1629 (2006)
Sharma, S., Steinmetz, M.: Mon. Not. R. Astron. Soc. 373, 1293 (2006)
Shepard, D.: A two-dimensional interpolation function for irregularly spaced points. In: ACM National Conference, 517 (1968)
Sheth, J.V., Sahni, V., Sathyaprakash, B.S., Shandarin, S.F.: Mon. Not. R. Astron. Soc. 343, 22 (2003)
Sheth, R. K., van de Weygaert, R.: Mon. Not. R. Astron. Soc. 350, 517 (2004)
Shewchuk, J.R.: Comp. Geom. Theor. Appl. 22, 21 (2002)
Sibson, R.: Math. Proc. Cambridge Phil. Soc. 87, 151 (1980)
Sibson, R.: A brief description of natural neighbor interpolation. In: Barnett, V. (ed.) Interpreting Multi-Variate Data, p. 21. Wiley, Chichester (1981)
Sloan, S.W.: Adv. Eng. Software 9, 34 (1987)
Smoot, G.F., et al.: Astrophys. J. 396, L1 (1992)
Soneira, R.M., Peebles, P.J.E.: Astrophys. J. 211, 1 (1977)
Sousbie, T., Pichon, C., Courtois, H., Colombi, S., Novikov, D.:astroph/0602628 (2006)
Spergel, D.N., et al.: Astrophys. J. Suppl. 170, 377 (2007)
Springel, V., Yoshida, N., White, S.D.M.: New Astron. 6, 79 (2001)
Springel, V.: Mon. Not. R. Astron. Soc. 364, 1105 (2005)
Springel, V., White, S.D.M., Jenkins, A., Frenk, C.S., Yoshida, N., Gao, L., Navarro, J., Thacker, R., Croton, D., Helly, J., Peacock, J.A., Cole, S., Thomas, P., Couchman, H., Evrard, A., Colberg, J.M., Pearce, F.: Nature 435, 629 (2005)
Stoica, R.S., Martínez, V.J., Mateu, J., Saar, E.: Astron. Astrophys. 434, 423 (2005)
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications, 1st ed., John Wiley, New York (1987)
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications, 2nd ed., John Wiley, New York (1995)
Sukumar, N.: The Natural Element Method in Solid Mechanics, Ph.D. thesis, Northwestern University (1998)
Szapudi, I.: Astrophys. J. 497, 16 (1998)
Tegmark, M., et al.: Astrophys. J. 606, 702 (2004)
Thiessen, A.H.: Mon. Wea. Rev. 39, 1082 (1911)
Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, New York (2002)
Turk, G., O’Brien, J.F.: Shape transformation using variational implicit functions. In: Computer Graphics. Annual Conference Series (SIGGRAPH 1999), 335 (1999)
Turk, G., O’Brien, J.F.: Reconstructing Surfaces Using Anisotropic Basis Functions. In: Proc. Intern. Conference Computer Vision (ICCV), Vancouver, 606 (2001)
Ubertini, S., Succi, S.: Prog. Comp. Fluid Dyn. 5, 85 (2005)
van de Weygaert, R.: The Multidimensional binary tree and its use in astronomy, (minor) M.Sc. Thesis, Leiden University (1987)
van de Weygaert, R.: Voids and the Geometry of Large Scale Structure, Ph.D. thesis, Leiden University (1991)
van de Weygaert, R.: Astron. Astrophys. 283, 361 (1994)
van de Weygaert, R.: Froth across the universe, dynamics and stochastic geometry of the cosmic foam. In: Plionis, M., Cotsakis, S. (eds.) Modern Theoretical and Observational Cosmology, Proc. 2nd Hellenic Cosmology Meeting, ASSL 276, p. 119. Kluwer, Dordrecht (2002)
van de Weygaert, R.: Astron. Astrophys., subm. (2007)
van de Weygaert, R., Astron. Astrophys., subm. (2007)
van de Weygaert, R., van Kampen, E.: Mon. Not. R. Astron. Soc. 263, 481 (1993)
van de Weygaert, R., Bertschinger, E.: Mon. Not. R. Astron. Soc. 281, 84 (1996)
Romano-Díaz, E., van de Weygaert, R.: Mon. Not. R. Astr. Soc., 382, 2 (2007)
Vegter, G.: Computational topology. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, 2nd. ed., p. 719. CRC Press LLC, Boca Raton (2004)
Vegter, G., van de Weygaert, R., Platen, E., Kruithof, N., Eldering, B.: Mon. Not. R. Astron. Soc. in prep. (2007)
Voronoi, G.: J. Reine Angew. Math. 134, 167 (1908)
Watson, D.F., Contouring: A Guide to the Analysis and Display of Spatial Data. Pergamon Press, Oxford (1992)
Wendland, H.: Scattered Data Approximation. Cambridge Mon. Appl. Comput. Math., Cambridge University Press, Cambridge (2005)
White, S.D.M.: Mon. Not. R. Astron. Soc. 186, 145 (1979)
Whitehurst, R.: Mon. Not. R. Astron. Soc. 277, 655 (1995)
Yahil, A., Strauss, M. A., Davis, M., Huchra, J. P.: Astrophys. J. 372, 380 (1991)
Zaroubi, S., Hoffman, Y., Fisher, K.B., Lahav, O.: Astrophys. J. 449, 446 (1995)
Zel’dovich Ya. B.: Astron. Astrophys. 5, 84 (1970)
Zel’dovich Ya.B., Einasto, J., Shandarin, S.F.: Nature 300, 407 (1982)
Zomorodian, A.J.: Topology for Computing, Cambr. Mon. Appl. Comp. Math. (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
van de Weygaert, R., Schaap, W. (2008). The Cosmic Web: Geometric Analysis. In: Martinez, V., Saar, E., Gonzales, E., Pons-Borderia, M. (eds) Data Analysis in Cosmology. Lecture Notes in Physics, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44767-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-44767-2_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23972-7
Online ISBN: 978-3-540-44767-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)