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Absorption of a randomly accelerated particle: recent results for partially absorbing and inelastic boundaries

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  • Burkhardt, Theodore W.

Abstract

Consider a particle which is randomly accelerated by Gaussian white noise on the half line x>0, with an absorbing boundary at x=0. The nonequilibrium statistics of this system was analyzed exactly by McKean in 1963. Recent results for two other boundary conditions of physical interest will be reviewed. In the case of a partially absorbing boundary, the randomly accelerated particle is absorbed, on arriving at x=0, with probability 1−p and reflected elastically with probability p. In the case of an inelastic boundary, the velocities of the particle just after and before striking the boundary satisfy vf=−rvi, where r is the coefficient of restitution. The absorption of a particle moving between two boundaries and some related results for confined semi-flexible polymers, which have similar statistical properties, will also be discussed.

Suggested Citation

  • Burkhardt, Theodore W., 2002. "Absorption of a randomly accelerated particle: recent results for partially absorbing and inelastic boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 306(C), pages 107-116.
    • Handle: RePEc:eee:phsmap:v:306:y:2002:i:c:p:107-116
    DOI: 10.1016/S0378-4371(02)00490-9
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