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IAENG Transactions on Engineering Technologies pp 155–165Cite as

Ballistic Behaviour in Bounded Velocity Transport

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 247))

Abstract

Stochastic models of bounded velocity transport are revisited. It is proven that these models exhibit short-time propagative (as opposed to diffusive) behavior for a large class of initial conditions. Numerical simulations also show that this propagative effect is different from the damped propagation predicted by common hyperbolic models. A fit of the density profiles is finally presented and a geometrical generalization of Fick’s law is also proposed.

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Notes

  1. 1.

    This last condition is sufficient but not necessary for the extrema at \(\pm\,{{x}^*}(t)\) to be maxima. The necessary and sufficient condition is \(D^* = - 3 \gamma ^* - \gamma ^{*3} \varvec{\Phi }^{\prime \prime }\left( \gamma ^* \right) <0\).

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Acknowledgments

Part of this work was funded by the ANR Grant 09-BLAN-0364-01.

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Authors and Affiliations

  1. LERMA, UMR 8112, UPMC, Paris, France

    F. Debbasch, D. Espaze & V. Foulonneau

Authors
  1. F. Debbasch
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  2. D. Espaze
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  3. V. Foulonneau
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Corresponding author

Correspondence to F. Debbasch .

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Editors and Affiliations

  1. Computer & Communication Dean of Engineering College, Catholic University of DaeGu Engineering College, DaeGu, Korea, Republic of (South Korea)

    Haeng Kon Kim

  2. Unit 1, 1/F, International Association of Engineers, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. College of Engineering, California State Polytechnic University, Pomona, California, USA

    Mahyar A. Amouzegar

  4. Abt. Linguistische Datenverarbeitung, Universität Trier Inst.Computerlinguistik, Trier, Germany

    Burghard B. Rieger

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Debbasch, F., Espaze, D., Foulonneau, V. (2014). Ballistic Behaviour in Bounded Velocity Transport. In: Kim, H., Ao, SI., Amouzegar, M., Rieger, B. (eds) IAENG Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 247. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6818-5_12

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  • DOI: https://doi.org/10.1007/978-94-007-6818-5_12

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6817-8

  • Online ISBN: 978-94-007-6818-5

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