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A Fractional Diffusion Model with Resetting

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

We consider a model that serves as a paradigm for a class of search strategies in which the searcher having explored its environment unsuccessfully for a while, returns to its initial position and begins a new search. The model describes the diffusive motion of a particle, performing a random walk with Lévy distributed jump lengths, which is interrupted at random times when the particle is reset to its initial position. A numerical method is proposed to determine the solutions of this diffusive problem with resetting. The influence of resetting on the solutions is analysed and physical quantities such as the pseudo second moment will be discussed.

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References

  1. Bray, A.J., Majumdar, S.N., Schehr, G.: Persistence and first passage properties in non equilibrium systems. Adv. Phys. 62, 225–361 (2013)

    Article  Google Scholar 

  2. Evans, M.R., Majumbar, S.N.: Diffusion with optimal resetting. J. Phys. A. 44, 435001 (2011)

    Article  Google Scholar 

  3. Evans, M.R., Majumbar, S.N.: Diffusion with stochastic resetting. Phys. Rev. Lett. 106, 160601 (2011)

    Article  Google Scholar 

  4. Evans, M.R., Majumdar, S.N., Mallick, K.: Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics. J. Phys. A: Math. Theor. 46, 185001 (2013)

    Article  MathSciNet  Google Scholar 

  5. Fogedby, H.C.: Lévy flights in quenched random force fields. Phys. Rev. E 58, 1890 (1998)

    Article  MathSciNet  Google Scholar 

  6. Jespersen, S., Metzler, R., Fogedby, H.C.: Lévy flights in external force fields: Langevin and fractional Fokker-Planck equations and their solutions. Phys. Rev. E. 59, 2736 (1999)

    Article  Google Scholar 

  7. Kusmierz, L., Majumdar, S.N., Sabhapandit, S., Schehr, G.: First order transition for the optimal search time of Lévy flights with resetting. Phys. Rev. Lett. 113, 220602 (2014)

    Article  Google Scholar 

  8. Metzler, R., Klafter, J.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)

    Article  MathSciNet  Google Scholar 

  9. Pal, A.: Diffusion in a potential landscape with stochastic resetting. Phys. Rev. E. 91, 012113 (2015)

    Article  Google Scholar 

  10. Sousa, E.: An explicit high order method for fractional advection diffusion equations. J. Comput. Phys. 278, 257–274 (2014)

    Article  MathSciNet  Google Scholar 

  11. Sousa, E., Li, C.: A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative. Appl. Numer. Math. 90, 22–37 (2015)

    Article  MathSciNet  Google Scholar 

  12. Whitehouse, J., Evans, M.R., Majumbar, S.N.: Effect of partial absorption on diffusion with resetting. Phys. Rev. E. 87, 022118 (2013)

    Google Scholar 

  13. Zaslavsky, G.M.: Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461–580 (2002)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal

    Ercília Sousa

  2. Department of Physics, Dalhousie University, Halifax, Canada

    Amal K. Das

Authors
  1. Ercília Sousa
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  2. Amal K. Das
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Corresponding author

Correspondence to Ercília Sousa .

Editor information

Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Sousa, E., Das, A.K. (2019). A Fractional Diffusion Model with Resetting. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_59

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_59

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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