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Volumn 8, Issue 2, 2013, Pages 17-27

Continuous time random walks with reactions forcing and trapping

Author keywords

Fokker Planck equation; Fractional diffusion; Random walk; Reaction diffusion; Stochastic process

Indexed keywords

CONTINUOUS TIME RANDOM WALKS; EXTERNAL FORCE FIELD; FRACTIONAL DIFFUSION; FRACTIONAL FOKKER-PLANCK EQUATION; FRACTIONAL REACTIONS; MEAN SQUARE DISPLACEMENT; RANDOM WALK; REACTION DIFFUSION;

EID: 84876937493     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20138202     Document Type: Article
Times cited : (74)

References (46)
  • 1
    • 1442289165 scopus 로고
    • Die mittlere energie rotierender elektrischer dipole im strahlungsfeld
    • A. D. Fokker. Die mittlere energie rotierender elektrischer dipole im strahlungsfeld. Annalen der Physik, vol. 348, no. 5, (1914), pp. 810-820.
    • (1914) Annalen der Physik , vol.348 , Issue.5 , pp. 810-820
    • Fokker, A.D.1
  • 3
    • 0004140926 scopus 로고    scopus 로고
    • The Fokker-Planck equation: Methods of solution and applications
    • Springer Verlag
    • H. Risken. The Fokker-Planck equation: Methods of solution and applications. Second Edition., vol. 18. Springer Verlag, 1996.
    • (1996) Second Edition , vol.18
    • Risken, H.1
  • 4
    • 0000078998 scopus 로고    scopus 로고
    • From continuous time random walks to the fractional Fokker-Planck equation
    • E. Barkai, R. Metzler, J. Klafter. From continuous time random walks to the fractional Fokker-Planck equation. Phys. Rev. E, vol. 61, no. 1, (2000), p. 132.
    • (2000) Phys. Rev. e , vol.61 , Issue.1 , pp. 132
    • Barkai, E.1    Metzler, R.2    Klafter, J.3
  • 5
    • 33749485301 scopus 로고    scopus 로고
    • Field-induced dispersion in subdiffusion
    • I. M. Sokolov, J. Klafter. Field-induced dispersion in subdiffusion. Phys. Rev. Lett., vol. 97, no. 14, (2006), p. 140602.
    • (2006) Phys. Rev. Lett , vol.97 , Issue.14 , pp. 140602
    • Sokolov, I.M.1    Klafter, J.2
  • 6
    • 56849094437 scopus 로고    scopus 로고
    • Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: The case of a time-dependent force
    • M. Magdziarz, A. Weron, J. Klafter. Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: The case of a time-dependent force. Phys. Rev. Lett., vol. 101, no. 21, (2008), p. 210601.
    • (2008) Phys. Rev. Lett , vol.101 , Issue.21 , pp. 210601
    • Magdziarz, M.1    Weron, A.2    Klafter, J.3
  • 7
    • 77958134564 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces
    • B. I. Henry, T. A. M. Langlands, P. Straka. Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces. Phys. Rev. Lett., vol. 105, no. 17, (2010), p. 170602.
    • (2010) Phys. Rev. Lett , vol.105 , Issue.17 , pp. 170602
    • Henry, B.I.1    Langlands, T.A.M.2    Straka, P.3
  • 8
    • 41549141851 scopus 로고    scopus 로고
    • Modeling of subdiffusion in space-time-dependent force fields beyond the fractional Fokker-Planck equation
    • A. Weron, M. Magdziarz, K. Weron. Modeling of subdiffusion in space-time-dependent force fields beyond the fractional Fokker-Planck equation. Phys. Rev. E, vol. 77, no. 3, (2008), p. 036704.
    • (2008) Phys. Rev. e , vol.77 , Issue.3 , pp. 036704
    • Weron, A.1    Magdziarz, M.2    Weron, K.3
  • 9
    • 78651327329 scopus 로고    scopus 로고
    • Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion
    • M. G. Hahn, K. Kobayashi, S. Umarov. Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion. Proc. Amer. Math. Soc., (2011), pp. 691-705.
    • (2011) Proc. Amer. Math. Soc. , pp. 691-705
    • Hahn, M.G.1    Kobayashi, K.2    Umarov, S.3
  • 10
    • 84863638780 scopus 로고    scopus 로고
    • Subdiffusion in a time-dependent force field
    • V. P. Shkilev. Subdiffusion in a time-dependent force field. J. Exp. Theor. Phys., vol. 114, (2012), p. 830.
    • (2012) J. Exp. Theor. Phys , vol.114 , pp. 830
    • Shkilev, V.P.1
  • 11
    • 0343526808 scopus 로고    scopus 로고
    • Fractional reaction-diffusion
    • B. I. Henry, S. L. Wearne. Fractional reaction-diffusion. Physica A, vol. 276, no. 3, (2000), pp. 448-455.
    • (2000) Physica A , vol.276 , Issue.3 , pp. 448-455
    • Henry, B.I.1    Wearne, S.L.2
  • 12
    • 33748775171 scopus 로고    scopus 로고
    • Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations
    • B. I. Henry, T. A. M. Langlands, S. L. Wearne. Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations. Phys. Rev. E, vol. 74, no. 3, (2006), p. 031116.
    • (2006) Phys. Rev. e , vol.74 , Issue.3 , pp. 031116
    • Henry, B.I.1    Langlands, T.A.M.2    Wearne, S.L.3
  • 13
    • 33644697057 scopus 로고    scopus 로고
    • Reaction-subdiffusion equations
    • I. M. Sokolov, M. G. W. Schmidt, F. Sagués. Reaction-subdiffusion equations. Phys. Rev. E, vol. 73, no. 3, (2006), p. 031102.
    • (2006) Phys. Rev. e , vol.73 , Issue.3 , pp. 031102
    • Sokolov, I.M.1    Schmidt, M.G.W.2    Sagués, F.3
  • 14
    • 40549123984 scopus 로고    scopus 로고
    • Anomalous subdiffusion with multi-species linear reaction dynamics
    • T. A. M. Langlands, B. I. Henry, S. L. Wearne. Anomalous subdiffusion with multi-species linear reaction dynamics. Phys. Rev. E, vol. 77, no. 2, (2008), p. 021111.
    • (2008) Phys. Rev. e , vol.77 , Issue.2 , pp. 021111
    • Langlands, T.A.M.1    Henry, B.I.2    Wearne, S.L.3
  • 15
    • 75349084049 scopus 로고    scopus 로고
    • Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts
    • S. Fedotov. Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts. Phys. Rev. E, vol. 81, no. 1, (2010), p. 011117.
    • (2010) Phys. Rev. e , vol.81 , Issue.1 , pp. 011117
    • Fedotov, S.1
  • 16
    • 77949713010 scopus 로고    scopus 로고
    • Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks
    • E. Abad, S. B. Yuste, K. Lindenberg. Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks. Phys. Rev. E, vol. 81, no. 3, (2010), p. 031115.
    • (2010) Phys. Rev. e , vol.81 , Issue.3 , pp. 031115
    • Abad, E.1    Yuste, S.B.2    Lindenberg, K.3
  • 17
    • 27744586782 scopus 로고    scopus 로고
    • Weak ergodicity breaking in the continuous-time random walk
    • G. Bel, E. Barkai. Weak ergodicity breaking in the continuous-time random walk. Phys. Rev. Lett., vol. 94, no. 24, (2005), p. 240602.
    • (2005) Phys. Rev. Lett , vol.94 , Issue.24 , pp. 240602
    • Bel, G.1    Barkai, E.2
  • 18
    • 70350763863 scopus 로고    scopus 로고
    • Fractional Brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics
    • M. Magdziarz, A. Weron, K. Burnecki, J. Klafter. Fractional Brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics. Phys. Rev. Lett., vol. 103, (2009), p. 180602.
    • (2009) Phys. Rev. Lett , vol.103 , pp. 180602
    • Magdziarz, M.1    Weron, A.2    Burnecki, K.3    Klafter, J.4
  • 19
    • 59349102367 scopus 로고    scopus 로고
    • Ergodic properties of fractional Brownian-Langevin motion
    • W. Deng, E. Barkai. Ergodic properties of fractional Brownian-Langevin motion. Phys. Rev. E, vol. 79, no. 1, (2009), p. 011112.
    • (2009) Phys. Rev. e , vol.79 , Issue.1 , pp. 011112
    • Deng, W.1    Barkai, E.2
  • 20
    • 79955601345 scopus 로고    scopus 로고
    • Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking
    • A. Weigel, B. Simon, M. Tamkun, D. Krapf. Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking. Proc. Natl. Acad. Sci., vol. 108, no. 16, (2011), pp. 6438-6443.
    • (2011) Proc. Natl. Acad. Sci , vol.108 , Issue.16 , pp. 6438-6443
    • Weigel, A.1    Simon, B.2    Tamkun, M.3    Krapf, D.4
  • 21
    • 77952038458 scopus 로고    scopus 로고
    • Fractional chemotaxis diffusion equations
    • T. A. M. Langlands, B. I. Henry. Fractional chemotaxis diffusion equations. Phys. Rev. E, vol. 81, no. 5, (2010), p. 051102.
    • (2010) Phys. Rev. e , vol.81 , Issue.5 , pp. 051102
    • Langlands, T.A.M.1    Henry, B.I.2
  • 22
    • 79952532158 scopus 로고    scopus 로고
    • Subdiffusion chemotaxis, and anomalous aggregation
    • S. Fedotov. Subdiffusion, chemotaxis, and anomalous aggregation. Phys. Rev. E, vol. 83, no. 2, (2011), p. 021110.
    • (2011) Phys. Rev. e , vol.83 , Issue.2 , pp. 021110
    • Fedotov, S.1
  • 23
    • 80051595373 scopus 로고    scopus 로고
    • Anomalous is ubiquitous
    • I. Eliazar, J. Klafter. Anomalous is ubiquitous. Ann. Phys., vol. 326, no. 9, (2011), pp. 2517-2531.
    • (2011) Ann. Phys , vol.326 , Issue.9 , pp. 2517-2531
    • Eliazar, I.1    Klafter, J.2
  • 24
    • 21244494104 scopus 로고    scopus 로고
    • Detection of non-Brownian diffusion in the cell membrane in single molecule tracking
    • K. Ritchie, X. Y. Shan, J. Kondo, K. Iwasawa, T. Fujiwara, A. Kusumi. Detection of non-Brownian diffusion in the cell membrane in single molecule tracking. Biophysical journal, vol. 88, no. 3, (2005), p. 2266.
    • (2005) Biophysical Journal , vol.88 , Issue.3 , pp. 2266
    • Ritchie, K.1    Shan, X.Y.2    Kondo, J.3    Iwasawa, K.4    Fujiwara, T.5    Kusumi, A.6
  • 25
    • 80051622926 scopus 로고    scopus 로고
    • The diffusional properties of dendrites depend on the density of dendritic spines
    • F. Santamaria, S. Wils, E. De Schutter, G. Augustine. The diffusional properties of dendrites depend on the density of dendritic spines. European Journal of Neuroscience, vol. 34, no. 4, (2011), pp. 561-568.
    • (2011) European Journal of Neuroscience , vol.34 , Issue.4 , pp. 561-568
    • Santamaria, F.1    Wils, S.2    De Schutter, E.3    Augustine, G.4
  • 26
    • 0030050141 scopus 로고    scopus 로고
    • Anomalous diffusion due to binding: A monte carlo study
    • M. Saxton. Anomalous diffusion due to binding: a monte carlo study. Biophysical journal, vol. 70, no. 3, (1996), pp. 1250-1262.
    • (1996) Biophysical Journal , vol.70 , Issue.3 , pp. 1250-1262
    • Saxton, M.1
  • 27
    • 77952294035 scopus 로고    scopus 로고
    • Elucidating anomalous protein diffusion in living cells with fluorescence correlation spectroscopy-facts and pitfalls
    • N. Malchus, M. Weiss. Elucidating anomalous protein diffusion in living cells with fluorescence correlation spectroscopy-facts and pitfalls. J. Fluoresc., vol. 20, (2010), pp. 19-26.
    • (2010) J. Fluoresc , vol.20 , pp. 19-26
    • Malchus, N.1    Weiss, M.2
  • 29
    • 33751019968 scopus 로고    scopus 로고
    • Anomalous diffusion in Purkinje cell dendrites caused by spines
    • F. Santamaria, S. Wils, E. De Schutter, G. J. Augustine. Anomalous diffusion in Purkinje cell dendrites caused by spines. Neuron, vol. 52, no. 4, (2006), pp. 635-648.
    • (2006) Neuron , vol.52 , Issue.4 , pp. 635-648
    • Santamaria, F.1    Wils, S.2    De Schutter, E.3    Augustine, G.J.4
  • 30
    • 80051622926 scopus 로고    scopus 로고
    • The diffusional properties of dendrites depend on the density of dendritic spines
    • F. Santamaria, S. Wils, E. De Schutter, G. J. Augustine. The diffusional properties of dendrites depend on the density of dendritic spines. Eur. J. Neurosci., vol. 34, no. 4, (2011), pp. 561-568.
    • (2011) Eur. J. Neurosci , vol.34 , Issue.4 , pp. 561-568
    • Santamaria, F.1    Wils, S.2    De Schutter, E.3    Augustine, G.J.4
  • 31
    • 41549083671 scopus 로고    scopus 로고
    • Fractional cable models for spiny neuronal dendrites
    • B. I. Henry, T. A. M. Langlands, S. L. Wearne. Fractional cable models for spiny neuronal dendrites. Phys. Rev. Lett., vol. 100, no. 12, (2008), p. 128103.
    • (2008) Phys. Rev. Lett , vol.100 , Issue.12 , pp. 128103
    • Henry, B.I.1    Langlands, T.A.M.2    Wearne, S.L.3
  • 32
    • 70350663279 scopus 로고    scopus 로고
    • Fractional cable equation models for anomalous electrodiffusion in nerve cells: Infinite domain solutions
    • T. A. M. Langlands, B. I. Henry, S. L. Wearne. Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions J. Math. Biol., vol. 59, no. 6, (2009), pp. 761-808.
    • (2009) J. Math. Biol , vol.59 , Issue.6 , pp. 761-808
    • Langlands, T.A.M.1    Henry, B.I.2    Wearne, S.L.3
  • 33
    • 80052706414 scopus 로고    scopus 로고
    • Fractional cable equation models for anomalous electrodiffusion in nerve cells: Finite domain solutions
    • T. A. M. Langlands, B. I. Henry, S. L. Wearne. Fractional cable equation models for anomalous electrodiffusion in nerve cells: Finite domain solutions. SIAM J. Appl. Math., vol. 71, no. 4, (2011), pp. 1168-1203.
    • (2011) SIAM J. Appl. Math , vol.71 , Issue.4 , pp. 1168-1203
    • Langlands, T.A.M.1    Henry, B.I.2    Wearne, S.L.3
  • 34
    • 45849152620 scopus 로고    scopus 로고
    • Fluorescence recovery after photobleaching: The case of anomalous diffusion
    • A. Lubelski, J. Klafter. Fluorescence recovery after photobleaching: the case of anomalous diffusion. Biophys. J., vol. 94, no. 12, (2008), pp. 4646-4653.
    • (2008) Biophys. J , vol.94 , Issue.12 , pp. 4646-4653
    • Lubelski, A.1    Klafter, J.2
  • 35
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique
    • A. Kolmogoroff, I. Petrovsky, N. Piscounoff. Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique. Moscow Univ. Bull. Math, vol. 1, (1937), pp. 1-25.
    • (1937) Moscow Univ. Bull. Math , vol.1 , pp. 1-25
    • Kolmogoroff, A.1    Petrovsky, I.2    Piscounoff, N.3
  • 36
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R. Fisher. The wave of advance of advantageous genes. Ann. Hum. Genet., vol. 7, no. 4, (1937), pp. 355-369.
    • (1937) Ann. Hum. Genet , vol.7 , Issue.4 , pp. 355-369
    • Fisher, R.1
  • 38
    • 41349112464 scopus 로고    scopus 로고
    • Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: Application to the theory of neolithic transition
    • M. O. Vlad, J. Ross. Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of neolithic transition. Phys. Rev. E, vol. 66, no. 6, (2002), p. 061908.
    • (2002) Phys. Rev. e , vol.66 , Issue.6 , pp. 061908
    • Vlad, M.O.1    Ross, J.2
  • 39
    • 84875525984 scopus 로고    scopus 로고
    • Pattern formation on networks with reactions: A continuous time random walk approach
    • C. N. Angstmann, I. C. Donnelly, B. I. Henry. Pattern formation on networks with reactions: A continuous time random walk approach. Phys. Rev. E, vol. 87, no. 3, (2012), p. 032804.
    • (2012) Phys. Rev. e , vol.87 , Issue.3 , pp. 032804
    • Angstmann, C.N.1    Donnelly, I.C.2    Henry, B.I.3
  • 40
    • 84859071165 scopus 로고    scopus 로고
    • Subdiffusive master equation with space-dependent anomalous exponent and structural insta-bility
    • S. Fedotov, S. Falconer. Subdiffusive master equation with space-dependent anomalous exponent and structural insta-bility. Phys. Rev. E, vol 85, no. 3, (2012), p. 031132.
    • (2012) Phys. Rev. e , vol.85 , Issue.3 , pp. 031132
    • Fedotov, S.1    Falconer, S.2
  • 41
    • 35949027117 scopus 로고
    • Stochastic transport in a disordered solid. i
    • H. Scher, M. Lax. Stochastic transport in a disordered solid. I. Theory. Phys. Rev. B, vol. 7, (1973), pp. 4491-4502.
    • (1973) Theory. Phys. Rev. B , vol.7 , pp. 4491-4502
    • Scher, H.1    Lax, M.2
  • 42
    • 33846399755 scopus 로고    scopus 로고
    • Kinetic equations for reaction-subdiffusion systems: Derivation and stability analysis
    • A. Yadav, W. Horsthemke. Kinetic equations for reaction-subdiffusion systems: Derivation and stability analysis. Phys. Rev. E, vol. 74, no. 6, (2006), p. 066118.
    • (2006) Phys. Rev. e , vol.74 , Issue.6 , pp. 066118
    • Yadav, A.1    Horsthemke, W.2
  • 43
    • 26444463863 scopus 로고    scopus 로고
    • Fractional diffusion in inhomogeneous media
    • A. V. Chechkin, R. Gorenflo, I. M. Sokolov. Fractional diffusion in inhomogeneous media. J. Phys. A, vol. 38, (2005), p. L679.
    • (2005) J. Phys. A , vol.38
    • Chechkin, A.V.1    Gorenflo, R.2    Sokolov, I.M.3
  • 44
    • 33845247896 scopus 로고    scopus 로고
    • Modelling non-Fickian transport in geological formations as a continuous time random walk
    • B. Berkowitz, A. Cortis, M. Dentz, H. Scher. Modelling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys., vol. 44, (2006), p. RG2003.
    • (2006) Rev. Geophys , vol.44
    • Berkowitz, B.1    Cortis, A.2    Dentz, M.3    Scher, H.4
  • 45
    • 0037311921 scopus 로고    scopus 로고
    • Revisiting the derivation of the fractional diffusion equation
    • E. Scalas, R. Gorenflo, F. Mainardi, M. Raberto. Revisiting the derivation of the fractional diffusion equation. Fractals, vol. 11, (2003), pp. 281-289.
    • (2003) Fractals , vol.11 , pp. 281-289
    • Scalas, E.1    Gorenflo, R.2    Mainardi, F.3    Raberto, M.4
  • 46
    • 33750080668 scopus 로고
    • Definitions of Stieltjes integrals of the Riemann type
    • T. H. Hildebrandt. Definitions of Stieltjes integrals of the Riemann type. The Amer. Math. Monthly, vol. 45, (1938), p. 265.
    • (1938) The Amer. Math. Monthly , vol.45 , pp. 265
    • Hildebrandt, T.H.1


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