Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

4 Issues per year


CiteScore 2017: 0.67

SCImago Journal Rank (SJR) 2017: 0.417
Source Normalized Impact per Paper (SNIP) 2017: 0.860

Mathematical Citation Quotient (MCQ) 2017: 0.25

Online
ISSN
1569-3961
See all formats and pricing
More options …
Volume 24, Issue 2

Issues

Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging

Karl K. SabelfeldORCID iD: http://orcid.org/0000-0003-3698-7540 / Anastasiya Kireeva
  • Russian Academy of Sciences, Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, Russia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-04-06 | DOI: https://doi.org/10.1515/mcma-2018-0007

Abstract

Exact representations for the probability density of the life time and survival probability for a sphere and a disc are derived for a general drift-diffusion-reaction process. Based on these new formulas, we suggest an extremely efficient stochastic simulation algorithm for solving transient cathodoluminescence (CL) problems without any mesh in space and time. The method can be applied to a broad class of drift-diffusion-reaction problems where the time behavior of the absorbed material is of interest. The important advantage of the method suggested is the ability to incorporate local inclusions like dislocations, point defects and other singular folds and complicated structures. General Robin boundary conditions on the boundary are treated in a probabilistic way. The method is tested against exact solutions for a series of examples with bounded and unbounded domains. An application to the dislocation imaging problem, which includes thousand threading dislocations, is given.

Keywords: Life time; cathodoluminescence transients; random walk on spheres; dislocation imaging

MSC 2010: 65C05; 65C40; 65Z05

References

  • [1]

    J. Crank, The Mathematics of Diffusion, 2nd ed., Clarendon Press, Oxford, 1975. Google Scholar

  • [2]

    A. Friedman, Partial Differential Equations of Parabolic Type, Dover Publications, Mineola, 2008. Google Scholar

  • [3]

    W. Liu, J. F. Carlin, N. Grandjean, B. Deveaud and G. Jacopin, Exciton dynamics at a single dislocation in GaN probed by picosecond time-resolved cathodoluminescence, Appl. Phys. Lett. 109 (2016), no. 4, Article ID 042101. Web of ScienceGoogle Scholar

  • [4]

    A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC, Boca Raton, 2002. Google Scholar

  • [5]

    A. P. Prudnikov, J. F. Brychkov and O. I. Marichev, Integrals and Series, Nauka, Moscow, 1981. Google Scholar

  • [6]

    K. K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems, Springer, Berlin, 1991. Google Scholar

  • [7]

    K. K. Sabelfeld, Random walk on spheres method for solving drift-diffusion problems, Monte Carlo Methods Appl. 22 (2016), no. 4, 265–281. Web of ScienceGoogle Scholar

  • [8]

    K. K. Sabelfeld, A meshfree floating random walk method for solving diffusion imaging problems, Statist. Probab. Lett. 121 (2017), 6–11. CrossrefGoogle Scholar

  • [9]

    K. K. Sabelfeld, Random walk on spheres method for solving transient drift-diffusion-reaction problems, Monte Carlo Methods Appl. 23 (2017), no. 3, 189–212. Google Scholar

  • [10]

    K. K. Sabelfeld, V. Kaganer, C. Pfüller and O. Brandt, Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0001), J. Phys. D. 50 (2017), Article ID 405101. Web of ScienceGoogle Scholar

  • [11]

    K. K. Sabelfeld and A. E. Kireeva, Supercomputer simulation of the cathodoluminescence transients in the vicinity of threading dislocations, ‘Parallel Computational Technologies–PCT’2018, to appear. Google Scholar

  • [12]

    K. K. Sabelfeld, A. Kireeva, V. M. Kaganer, C. Pfüller and O. Brandt, Drift and diffusion of excitons at threading dislocations in GaN(0001), preprint (2018); to appear in Phys. Rev. Appl.

  • [13]

    K. K. Sabelfeld and N. A. Simonov, Stochastic Methods for Boundary Value Problems. Numerics for High-dimensional PDEs and Applications, De Gruyter, Berlin, 2016. Google Scholar

  • [14]

    A. Singer, Z. Schuss and D. Holcmann, Narrow escape, part II: The circular disc, J. Stat. Phys. 122 (2006), no. 3, 465–489. CrossrefGoogle Scholar

About the article

Received: 2017-11-01

Accepted: 2018-03-14

Published Online: 2018-04-06

Published in Print: 2018-06-01


Funding Source: Russian Science Foundation

Award identifier / Grant number: N 14-11-00083

Support of the Russian Science Foundation under Grant N 14-11-00083 is kindly acknowledged.


Citation Information: Monte Carlo Methods and Applications, Volume 24, Issue 2, Pages 79–92, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2018-0007.

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in