Abstract
On the real line initially there are infinite number of particles on the positive half-line., each having one of K negative velocities \(v_{1}^{(+)},\ldots,v_{K}^{(+)}\). Similarly, there are infinite number of antiparticles on the negative half-line, each having one of L positive velocities \(v_{1}^{(-)},\ldots,v_{L}^{(-)}\). Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of β(t) – the coordinate of the last collision before t between particle and antiparticle.
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Notes
- 1.
Work of this author was supported by the Russian Foundation of Basic Research (grants 09-01-00761 and 11-01-90421)
References
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Malyshev, V., Manita, A., Zamyatin, A. (2013). Multi-agent Model of the Price Flow Dynamics. In: Kozlov, V., Buslaev, A., Bugaev, A., Yashina, M., Schadschneider, A., Schreckenberg, M. (eds) Traffic and Granular Flow '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39669-4_10
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DOI: https://doi.org/10.1007/978-3-642-39669-4_10
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