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Gravitational Field of Fractal Distribution of Particles

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Abstract

In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of the Gauss’s law, we consider the simple examples of the fields of homogeneous fractal distribution. The examples of gravitational moments for fractal distribution are considered.

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References

  • H.D. Bale P.W. Schmidt (1984) Phys. Rev. Lett. 53 596–599 Occurrence Handle10.1103/PhysRevLett.53.596 Occurrence Handle1984PhRvL..53..596B

    Article  ADS  Google Scholar 

  • R.M. Christensen (1979) Mechanics of Composite Materials Wiley New York

    Google Scholar 

  • P.H. Coleman L. Pietronero (1992) Phys. Rep. 213 311–389 Occurrence Handle10.1016/0370-1573(92)90112-D Occurrence Handle1992PhR...213..311C

    Article  ADS  Google Scholar 

  • J.C. Collins (1984) Renormalization Cambridge University Press Cambridge

    Google Scholar 

  • J. Feder (1988) Fractals Plenum Press New York

    Google Scholar 

  • J. Fricke (Eds) (1985) Aerogels Springer Berlin

    Google Scholar 

  • A. Gabrielli F. Sylos Labini S. Pellegrini (1999) Europhys. Lett. 46 127–133 Occurrence Handle10.1209/epl/i1999-00235-7 Occurrence Handle1999EL.....46..127G

    Article  ADS  Google Scholar 

  • A. Gabrielli F. Sylos Labini M. Joyce L. Pietronero (2004) Statistical Physics of Cosmic Structures Springer New York

    Google Scholar 

  • R.B. Larson (1981) Month. Not. RAS. 194 809 Occurrence Handle1981MNRAS.194..809L

    ADS  Google Scholar 

  • A. Le Mehaute R.R. Nigmatullin L. Nivanen (1998) Fleches du Temps et Geometric Fractale Hermes Paris

    Google Scholar 

  • R. Nigmatullin (1986) Phys Stat Solidi B 133 425–430

    Google Scholar 

  • P. Pfeifer D. Avnir (1983) J. Chem Phys. 79 3558–3565 Occurrence Handle1983JChPh..79.3558P Occurrence Handle85d:80010a

    ADS  MathSciNet  Google Scholar 

  • L. Pietronero A. Gabrielli F. Sylos Labini (2002) Physica A. 306 395–401 Occurrence Handle10.1016/S0378-4371(02)00517-4 Occurrence Handle2002PhyA..306..395P

    Article  ADS  Google Scholar 

  • F.Y. Ren J.R. Liang X.T. Wang W.Y. Miu (2003) Chaos, Solitons and Fractals 16 107–117 Occurrence Handle10.1016/S0960-0779(02)00211-4 Occurrence Handle2003k:28006

    Article  MathSciNet  Google Scholar 

  • S.G. Samko A.A. Kilbas O.I. Marichev (1993) Fractional Integrals and Derivatives Theory and Applications Gordon and Breach New York

    Google Scholar 

  • Scalo J.M. (1987). In: D.J. Hollenbach and H. A. Thronson (eds), Interstellar Processes, D. Reidel, Dordrecht, pp. 349–392.

  • D.W. Schaefer K.D. Keefer (1984a) Phys. Rev. Lett. 53 1383–1386 Occurrence Handle10.1103/PhysRevLett.53.1383 Occurrence Handle1984PhRvL..53.1383S

    Article  ADS  Google Scholar 

  • D.W. Schaefer J.E. Martin P. Wiltzius D.S. Cannell (1984b) Phys. Rev. Lett. 52 2371–2374 Occurrence Handle10.1103/PhysRevLett.52.2371 Occurrence Handle1984PhRvL..52.2371S

    Article  ADS  Google Scholar 

  • F. Sylos Labini A. Gabrielli (2004) Physica A. 338 44–49 Occurrence Handle2004PhyA..338...44S

    ADS  Google Scholar 

  • F. Sylos Labini M. Montuori L. Pietronero (1998) Phys. Rep. 293 61–226 Occurrence Handle1998PhR...293...61S

    ADS  Google Scholar 

  • V.E. Tarasov (2004) Chaos. 14 123–127 Occurrence Handle10.1063/1.1633491 Occurrence Handle2004Chaos..14..123T

    Article  ADS  Google Scholar 

  • V.E. Tarasov (2005a) Phys. Rev. E. 71 011102 Occurrence Handle10.1103/PhysRevE.71.011102 Occurrence Handle2005PhRvE..71a1102T Occurrence Handle2005m:82088

    Article  ADS  MathSciNet  Google Scholar 

  • V.E. Tarasov (2005b) J. Phys. A. 38 5929–5943 Occurrence Handle2005JPhA...38.5929T Occurrence Handle2006c:37017

    ADS  MathSciNet  Google Scholar 

  • V.E. Tarasov (2005c) J. Phys. Conf. Ser. 7 17–33 Occurrence Handle10.1088/1742-6596/7/1/002

    Article  Google Scholar 

  • V.E. Tarasov (2005d) Phys. Lett. A. 336 167–174 Occurrence Handle10.1016/j.physleta.2005.01.024 Occurrence Handle2005PhLA..336..167T

    Article  ADS  Google Scholar 

  • V.E. Tarasov (2005e) Phys. Lett. A. 341 467–472 Occurrence Handle10.1016/j.physleta.2005.05.022 Occurrence Handle2005PhLA..341..467T

    Article  ADS  Google Scholar 

  • V.E. Tarasov (2005f) Ann Phys. 318 286–307 Occurrence Handle2005AnPhy.318..286T Occurrence Handle2005m:76176

    ADS  MathSciNet  Google Scholar 

  • V.E. Tarasov (2005g) Chaos. 15 023102 Occurrence Handle10.1063/1.1886325 Occurrence Handle2150219

    Article  MathSciNet  Google Scholar 

  • V.E. Tarasov G.M. Zaslavsky (2005) Physica. A. 354 249–261 Occurrence Handle10.1016/j.physa.2005.02.047 Occurrence Handle2005PhyA..354..249T

    Article  ADS  Google Scholar 

  • G.M. Zaslavsky (1998) Physics of Chaos in Hamiltonian Dynamics Imperial College Press London

    Google Scholar 

  • G.M. Zaslavsky (2002) Phys. Rep. 371 461–580 Occurrence Handle10.1016/S0370-1573(02)00331-9 Occurrence Handle2002PhR...371..461Z Occurrence Handle0999.82053 Occurrence Handle2003i:70030

    Article  ADS  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119992

    Vasily E. Tarasov

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  1. Vasily E. Tarasov
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Correspondence to Vasily E. Tarasov.

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Tarasov, V.E. Gravitational Field of Fractal Distribution of Particles. Celestial Mech Dyn Astr 94, 1–15 (2006). https://doi.org/10.1007/s10569-005-1152-2

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  • DOI: https://doi.org/10.1007/s10569-005-1152-2

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