Diffusion of particles bouncing on a one-dimensional periodically corrugated floor

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Abstract

We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume64
Issue number3
DOIs
Publication statusPublished - 2001 Jan 1
Externally publishedYes

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Diffusion Coefficient
diffusion coefficient
Transport Processes
Extended Systems
sustaining
Energy
Mechanical Systems
Irregular
Horizontal
Vertical
Motion
energy
Class

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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abstract = "We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy.",
author = "Takahisa Harayama",
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AB - We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy.

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