+ Resolve Article
+ Follow Us
Follow on FacebookFollow on Facebook
Follow on TwitterFollow on Twitter

+ Translate
+ Subscribe to Site Feed
GeoScience Most Shared ContentMost Shared Content

Fractal geometry in an expanding, one-dimensional, Newtonian universe

, : Fractal geometry in an expanding, one-dimensional, Newtonian universe. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 76(3 Pt 2): 036705-036705

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.


PMID: 17930359

DOI: 10.1103/PhysRevE.76.036705

Other references

Fruen, B.R.; Bardy, J.M.; Byrem, T.M.; Strasburg, G.M.; Louis, C.F., 2000: Differential Ca(2+) sensitivity of skeletal and cardiac muscle ryanodine receptors in the presence of calmodulin. Calmodulin (CaM) activates the skeletal muscle ryanodine receptor Ca(2+) release channel (RyR1) in the presence of nanomolar Ca(2+) concentrations. However, the role of CaM activation in the mechanisms that control Ca(2+) release from the sarcopla...

Soberman, R.J., 1950: Use of antipyrine in measurement of total body water in animals. Antipyrine is distributed in the various tissues of animals in close proportion to their water content. The values obtained for total body water by antipyrine and by desiccation in 5 monkeys, 4 dogs, and 4 rabbits agreed well and gave a correlatio...

Hunter, H.A.; Anderson, D.L., 1966: The Ontario oral cytology study at the end of two and one-half years. Journal of the Ontario Dental Association 43(12): 10-14

Caussignac, Y.; David, F., 1982: Humoral growth factor after small intestinal resection in the dog. The serum of dogs with a 50% proximal small bowel resection is capable of growth stimulation in small intestinal epithelioid cells in monolayer culture. This overstimulation by postresection serum is not seen when dogs undergo either a small intes...

Pugh, K.; O'Donnell, I.; Catalan, J., 1993: Suicide and HIV disease. It has been suggested that HIV infection is associated with an increased risk of suicidal behaviour. This paper reviews the literature on suicide in patients with HIV disease and discusses methodological problems encountered in studying the incide...

Hughes, J.L.slie; Siddall, M., E., 2007: A new species of leech from the New York metropolitan area. Placobdella ali, n.sp., a sanguivorous glossiphoniid leech, is described from material collected in Harriman State Park, approximately 50 km north of the island of Manhattan, New York City. The new species resembles Placobdella ornata and could b...

Nehra, A.S.; Hooda, I.S., 2002: Influence of integrated use of organic manures and inorganic fertilizers on wheat yields and soil properties. A field experiment was conducted during winter seasons of 1997-98 and 1998-99 at CCS Haryana Agricultural University, Hisar, Haryana, India, to study the influence of organic manures (no manure, farmyard manure at 15 t, vermicompost at 10 and 15 t...

Nemelka, O.; Occella, C.; Schiazza, L.; Persi, A.; Rampini, E., 1983: Fluocortin butyl in various dermatoses in childhood. Giornale Italiano di Dermatologia E Venereologia 118(1): Vii-Vix

Dammerman, K.W., 1934: On pre-historic Mammals from the Sampoeng Cave, central Java. Treubia Buitenzorg, 14: 477-486

Hancock, J.C.; Hoover, D.B.; Tompkins, J.D., 1999: Role of NK3 receptors in the increased ganglion, blood pressure and heart rate responses to substance P in hypertensive rats. FASEB Journal 13(5 PART 2): A774, March 15