Skip to main content
SpringerLink
Log in

Random Diffusion Processes

Continuous Markov Processes

  • Chapter
Principles of Mathematical Geology

  • 203 Accesses

Abstract

Wide application of events in geology closely approximating a diffusion process and in many cases also conforming to a model of a true diffusion process. Fick’s law, continuity equation continuous Markov process. Backward and forward equations of Kolmogorov. Ten partial models of diffusion processes, covering the most typical situations. Analysis of experimental data on the melting of quartz in the gabbronorite melt.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Becker Gw.F.(1897) Some Queries on Rock Differentiation. Am. Journ. Sci., 4th ser., v. III, 13, p. 21–30.

    Google Scholar 

  • Bowen N.L.(1921) Diffusion in silicate melts. Journ. Geol., V. XXIX, p. 295–317.

    Google Scholar 

  • Carnegie Institution Year Book. 84(1985) Baltimore, Port City Press, 198p.

    Google Scholar 

  • Courant R. and Brychkov Yu.A. and Marichev O.I.(1981) Integrals and Series. Moscow, Nauka, 800p. (in Russian).

    Google Scholar 

  • Cramer H.(1975) Mathematical Methods in Statistics. Moscow, Mir, 648p. (in Russian).

    Google Scholar 

  • Ditkin V.A. and Prudinikov A.P.(1965) Handbook of Operational Calculus. Moscow, Vysshaja shkola, 466p. (in Russian).

    Google Scholar 

  • Ditkin V.A(1966) Operational Calculus. Moscow, Vysshaja shkola, 406p. (in Russian).

    Google Scholar 

  • Doob J.L.(1953) Stochastic Processes. New York, Wiley and Sons, 654p.

    Google Scholar 

  • Fick A. (1855) Über Diffusion. Annal en der Physik und Chemie (von J.C. Poggendorf). Bd. XCIV, p. 59–86.

    Google Scholar 

  • Gel’fund I.M. and Shilov G.E.(1958) Generalized functions and operations on them. Fiz. mat. giz. v.II. (in Russian).

    Google Scholar 

  • Graunov O.V.(1988) The Stationary Diffusion Problem in Circular Domain I and II. Math. Geol. v. 21, 8 pp. 938, 939 and 970, 971.

    Google Scholar 

  • Hoff van’t (1887) Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen Zeitschrift für Physikalische Chemie. Bd. I, Hf. 9, p. 481–508.

    Google Scholar 

  • Kharlamov B.P.(1978) On a mathematical model of accumulation of accessory minerals in sedimentary deposits. In the book: Investigations in Mathematical Geology, Leningrad, Nauka, p. 80–89. (in Russian).

    Google Scholar 

  • Konnikov E.G., Epelbaum M.B. and Chekhmir A.C.(1981) Causes of concentration of potassium in endocontact of Chineisky gabbro-norite plut on. Geochimiya, v. 2, p. 257–263 (in Russian).

    Google Scholar 

  • Kushiro I.(1983) Diffusion of Network-Forming Cations in Jadeitic Melts. Carnegie Institution of Washington Year Book 82, Washington, 328p.

    Google Scholar 

  • Ludwig C.(1856) Diffusion zwischen ungleich erwärmten Orten gleich zusammengesetzter Lösungen. Kien Sitz. Ber. XX, Hf. III, 539p.

    Google Scholar 

  • Prudinikov A.P., Brychkov Yu.A. and Marichev O.I.(1981) Integrals and Series. Moscow, Nauka, 800p. (in Russian).

    Google Scholar 

  • Rozanov Yu.A. (1979) Randann Processes. Moscow, Nauka, 184p. (in Russian).

    Google Scholar 

  • Sato H. (1975) Diffusion coronas around quartz xenocrysts in andesite and basalt from Tertiary volcanic region in north eastern Shikoku, Japan. Cont rib. Mineral, and Petrology, 50p.

    Google Scholar 

  • Sobolev S.L.(1954) Equations of Mathematical Physics. Moscow, Gosudarstvennoe izdarel’stvo tekhniko-teoretichesekoi literatury, 444p. (in Russian).

    Google Scholar 

  • Soret Ch. (1880) Influence de la température sur la distribution des sels dans leurs solutions. Cam. rendus, de l’Academie des Sciences. Juillet-Decembre 1880, p.289-291.

    Google Scholar 

  • Ussing N.V.(1912) Geology of the country around Julianehaab. Greenland Meddeleiser on Grønland. XXXVIII, p. 3–376.

    Google Scholar 

  • Vistelius A.B. Graunov O. and Pavlov V.(1989) Main Stages of Zonal Massifs formation: mathematical models of Cammingling, self-cleaning and Preeutectic Stabilization. Abstracts, vol. 3 of 3, p. 304, 305, 28th Int. Geol. Confr., Washington, D.C., USA.

    Google Scholar 

  • Yavorsky B.M. and Detlaf A.A. (1985) Handbook of Physics. Moscow, Nauka, 512p.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematical Geology, St. Petersburg, Russia

    A. B. Vistelius

Authors
  1. A. B. Vistelius
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Vistelius, A.B. (1992). Random Diffusion Processes. In: Principles of Mathematical Geology. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2934-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2934-3_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5303-7

  • Online ISBN: 978-94-011-2934-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation