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Volumn 371, Issue 1990, 2013, Pages

Two-particle anomalous diffusion: Probability density functions and self-similar stochastic processes

Author keywords

Anomalous diffusion; Fractional Brownian motion; Generalized grey Brownian motion; L vy stable density; M Wright function; Self similar stochastic processes

Indexed keywords

BROWNIAN MOVEMENT; PROBABILITY DENSITY FUNCTION; ROUTERS;

EID: 84875907213     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2012.0154     Document Type: Article
Times cited : (18)

References (26)
  • 2
    • 0026188308 scopus 로고
    • The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows
    • doi:10.1017/S0022112091002847
    • Komori S, Hunt JCR, Kanzaki T, Murakami Y. 1991 The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows. J. Fluid Mech. 228, 629-659. (doi:10.1017/S0022112091002847)
    • (1991) J. Fluid Mech. , vol.228 , pp. 629-659
    • Komori, S.1    Jcr, H.2    Kanzaki, T.3    Murakami, Y.4
  • 3
    • 0034965966 scopus 로고    scopus 로고
    • Turbulent relative dispersion
    • doi:10.1146/annurev.fluid.33.1.289
    • Sawford B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289-317. (doi:10.1146/annurev.fluid.33.1.289)
    • (2001) Annu. Rev. Fluid Mech. , vol.33 , pp. 289-317
    • Sawford, B.1
  • 4
    • 65049084831 scopus 로고    scopus 로고
    • Fractional calculus. Models and numerical methods. Series on Complexity
    • Boston, MA: World Scientific
    • Baleanu D, Diethelm K, Scalas E, Trujillo JJ. 2012 Fractional calculus. Models and numerical methods. Series on Complexity, Nonlinearity and Chaos, vol. 3. Boston, MA: World Scientific.
    • (2012) Nonlinearity and Chaos , vol.3
    • Baleanu, D.1    Diethelm, K.2    Scalas, E.3    Trujillo, J.J.4
  • 5
    • 77953517665 scopus 로고    scopus 로고
    • On the bound of the Lyapunov exponents for the fractional differential systems
    • doi:10.1063/1.3314277
    • Li C, Gong Z, Qian D, Chen YQ. 2010 On the bound of the Lyapunov exponents for the fractional differential systems. Chaos 20, 013127. (doi:10.1063/1.3314277)
    • (2010) Chaos , vol.20 , pp. 013127
    • Li, C.1    Gong, Z.2    Qian, D.3    Chen, Y.Q.4
  • 6
    • 59649085150 scopus 로고    scopus 로고
    • Solving the fractional order Bloch equation
    • doi:10.1002/cmr.a.20129
    • Magin R, Feng X, Baleanu D. 2009 Solving the fractional order Bloch equation. Concepts Mag. Res. A 34, 16-23. (doi:10.1002/cmr.a.20129)
    • (2009) Concepts Mag. Res. A , vol.34 , pp. 16-23
    • Magin, R.1    Feng, X.2    Baleanu, D.3
  • 9
    • 13444255257 scopus 로고    scopus 로고
    • Mellin transform and subordination laws in fractional diffusion processes
    • Mainardi F, Pagnini G, Gorenflo R. 2003 Mellin transform and subordination laws in fractional diffusion processes. Fract. Calc. Appl. Anal. 6, 441-459.
    • (2003) Fract. Calc. Appl. Anal. , vol.6 , pp. 441-459
    • Mainardi, F.1    Pagnini, G.2    Gorenflo, R.3
  • 10
    • 30644469531 scopus 로고    scopus 로고
    • Mellin convolution for subordinated stable processes
    • doi:10.1007/s10958-006-0008-y
    • Mainardi F, Pagnini G, Gorenflo R. 2006 Mellin convolution for subordinated stable processes. J. Math. Sci. 132, 637-642. (doi:10.1007/s10958- 006-0008-y)
    • (2006) J. Math. Sci. , vol.132 , pp. 637-642
    • Mainardi, F.1    Pagnini, G.2    Gorenflo, R.3
  • 11
    • 79953682830 scopus 로고    scopus 로고
    • Subordination pathways to fractional diffusion
    • doi:10.1140/epjst/e2011-01386-2
    • Gorenflo R, Mainardi F. 2011 Subordination pathways to fractional diffusion. Eur. Phys. J. Spec. Top. 193, 119-132. (doi:10.1140/epjst/e2011- 01386-2)
    • (2011) Eur. Phys. J. Spec. Top. , vol.193 , pp. 119-132
    • Gorenflo, R.1    Mainardi, F.2
  • 12
    • 84862678505 scopus 로고    scopus 로고
    • Parametric subordination in fractional diffusion processes
    • (eds SC Lim, J Klafter, R Metzler), ch. 10. Singapore: World Scientific
    • Gorenflo R, Mainardi F. 2012 Parametric subordination in fractional diffusion processes. In Fractional dynamics, recent advances (eds SC Lim, J Klafter, R Metzler), ch. 10, pp. 227-261. Singapore:World Scientific.
    • (2012) Fractional Dynamics, Recent Advances , pp. 227-261
    • Gorenflo, R.1    Mainardi, F.2
  • 14
    • 52349086501 scopus 로고    scopus 로고
    • Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
    • 10.1088/1751-28113/41/28/285003
    • Mura A, Pagnini G. 2008 Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A Math. Theor. 41, 285003. (10.1088/1751-8113/41/28/285003)
    • (2008) J. Phys. A Math. Theor. , vol.41 , pp. 285003
    • Mura, A.1    Pagnini, G.2
  • 15
    • 61949156991 scopus 로고    scopus 로고
    • A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics
    • doi:10.1080/10652460802567517
    • Mura A, Mainardi F. 2009 A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Integr. Transform Spec. Funct. 20, 185-198. (doi:10.1080/10652460802567517)
    • (2009) Integr. Transform Spec. Funct. , vol.20 , pp. 185-198
    • Mura, A.1    Mainardi, F.2
  • 16
    • 84862661240 scopus 로고    scopus 로고
    • Erdélyi-Kober fractional diffusion
    • doi:10.2478/s13540-012-0008-1
    • Pagnini G. 2012 Erdélyi-Kober fractional diffusion. Fract. Calc. Appl. Anal. 15, 117-127. (doi:10.2478/s13540-012-0008-1)
    • (2012) Fract. Calc. Appl. Anal. , vol.15 , pp. 117-127
    • Pagnini, G.1
  • 17
    • 84869015438 scopus 로고    scopus 로고
    • Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion
    • Pagnini G, Mura A, Mainardi F. 2012 Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Int. J. Stoch. Anal. 2012, 427383.
    • (2012) Int. J. Stoch. Anal. , vol.2012 , pp. 427383
    • Pagnini, G.1    Mura, A.2    Mainardi, F.3
  • 18
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi F, Luchko Yu, Pagnini G. 2001 The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4, 153-192.
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 153-192
    • Mainardi, F.1    Yu, L.2    Pagnini, G.3
  • 19
    • 13444255257 scopus 로고    scopus 로고
    • Mellin transform and subordination laws in fractional diffusion processes
    • Mainardi F, Pagnini G, Gorenflo R. 2013 Mellin transform and subordination laws in fractional diffusion processes. Fract. Calc. Appl. Anal. 6, 441-459.
    • (2013) Fract. Calc. Appl. Anal. , vol.6 , pp. 441-459
    • Mainardi, F.1    Pagnini, G.2    Gorenflo, R.3
  • 20
    • 30644469531 scopus 로고    scopus 로고
    • Mellin convolution for subordinated stable processes
    • Mainardi F, Pagnini G, Gorenflo R. 2006 Mellin convolution for subordinated stable processes. J. Math. Sci. 132, 637-642.
    • (2006) J. Math. Sci. , vol.132 , pp. 637-642
    • Mainardi, F.1    Pagnini, G.2    Gorenflo, R.3
  • 21
    • 0347248330 scopus 로고
    • Grey noise
    • (eds S Albeverio, G Casati, U Cattaneo, D Merlini, R Moresi). Teaneck NJ:World Scientific
    • Schneider WR. 1990 Grey noise. In Stochastic processes, physics and geometry (eds S Albeverio, G Casati, U Cattaneo, D Merlini, R Moresi), pp. 676-681. Teaneck, NJ:World Scientific.
    • (1990) Stochastic Processes, Physics and Geometry , pp. 676-681
    • Schneider, W.R.1
  • 22
    • 1942435439 scopus 로고
    • Grey noise
    • (eds S Albeverio, JE Fenstad, H Holden, T Lindstrøm). Cambridge UK: Cambridge University Press
    • Schneider WR. 1992 Grey noise. In Ideas and methods in mathematical analysis, stochastics, and applications, vol. 1 (eds S Albeverio, JE Fenstad, H Holden, T Lindstrøm), pp. 261-282. Cambridge, UK: Cambridge University Press.
    • (1992) Ideas and Methods in Mathematical Analysis, Stochastics, and Applications , vol.1 , pp. 261-282
    • Schneider, W.R.1
  • 23
    • 78650789902 scopus 로고    scopus 로고
    • The M-Wright function in time-fractional diffusion processes: A tutorial survey
    • doi:10.1155/2010/104505
    • Mainardi F, Mura A, Pagnini G. 2010 The M-Wright function in time-fractional diffusion processes: a tutorial survey. Int. J. Differ. Equ. 2010, 104505. (doi:10.1155/2010/104505)
    • (2010) Int. J. Differ. Equ. , vol.2010 , pp. 104505
    • Mainardi, F.1    Mura, A.2    Pagnini, G.3
  • 24
    • 0018974861 scopus 로고
    • A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence
    • doi:10.1017/S0022112080001152
    • Durbin PA. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279-302. (doi:10.1017/S0022112080001152)
    • (1980) J. Fluid Mech. , vol.100 , pp. 279-302
    • Durbin, P.A.1
  • 25
    • 0025200131 scopus 로고
    • A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance
    • doi:10.1017/S0022112090001239
    • Thomson DJ. 1990 A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance. J. Fluid Mech. 210, 113-153. (doi:10.1017/ S0022112090001239)
    • (1990) J. Fluid Mech. , vol.210 , pp. 113-153
    • Thomson, D.J.1


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