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Relationship Between Non-Markovian- and Drift-Fokker-Planck Equation

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Traffic and Granular Flow’05

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Summary

Based on the stochastic description of transport phenomena the relationship between a non-Markovian evolution equation and the Fokker-Planck equation with drift is investigated. Memory is included by direct coupling between initial and current values of probability density. We present the result for three different initial distributions.

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References

  1. R. Mahnke, J. Kaupužs and I. Lubashevsky: Probabilistic description of traffic flow, Phys. Rep., 408, 1–130, 2005.

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  2. T. D. Frank, Nonlinear Fokker-Planck Equations, Springer-Verlag, Berlin, 2005.

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Author information

Authors and Affiliations

  1. Fachbereich Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099, Halle/Saale, Germany

    Knud Zabrocki & Steffen Trimper

  2. Dept. of Physics, Ural State University, 620083, Ekaterinburg, Russia

    Svetlana Tatur

  3. Institut für Physik, Universität Rostock, D-18051, Rostock, Germany

    Reinhard Mahnke

Authors
  1. Knud Zabrocki
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  2. Svetlana Tatur
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  3. Steffen Trimper
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  4. Reinhard Mahnke
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937, Köln, Germany

    Andreas Schadschneider

  2. Campus Virchow Klinikum Centrum für Unfall- und Wiederherstellungschirurgie, Charité, Augustenburger Platz 1, 13353, Berlin, Germany

    Thorsten Pöschel

  3. Institut für Verkehrsforschung, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Rutherfordstr. 2, 12489, Berlin, Germany

    Reinhart Kühne

  4. Physik von Transport und Verkehr, Universität Duisburg-Essen, Lotharstr. 1, 47048, Duisburg, Germany

    Michael Schreckenberg

  5. Theoretische Physik, Universität Duisburg-Essen, Lotharstr. 1, 47048, Duisburg, Germany

    Dietrich E. Wolf

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© 2007 Springer-Verlag Berlin Heidelberg

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Zabrocki, K., Tatur, S., Trimper, S., Mahnke, R. (2007). Relationship Between Non-Markovian- and Drift-Fokker-Planck Equation. In: Schadschneider, A., Pöschel, T., Kühne, R., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow’05. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47641-2_60

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