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
R. Mahnke, J. Kaupužs and I. Lubashevsky: Probabilistic description of traffic flow, Phys. Rep., 408, 1–130, 2005.
T. D. Frank, Nonlinear Fokker-Planck Equations, Springer-Verlag, Berlin, 2005.
S. Trimper and K. Zabrocki: Phys. Lett. A, 331, 423–431, 2004.
M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions Dover Pub. New York, 1972.
K. Zabrocki, R. Mahnke, and S. Trimper, in preparation.
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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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DOI: https://doi.org/10.1007/978-3-540-47641-2_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47640-5
Online ISBN: 978-3-540-47641-2
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