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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Published on: December 4, 2017

Stochastic dynamics of a rod bouncing upon a vibrating surface.

H S Wright¹, Michael R Swift, P J King

¹School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 7, 2007

Summary

A vibrating surface causes a bouncing rod to transition from predictable to chaotic motion. Impact times and angles follow specific statistical distributions, with energy favoring vertical movement.

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Area of Science:

Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

Understanding the complex dynamics of bouncing objects is crucial in various fields, from granular physics to mechanical engineering.
Previous studies have explored simple object collisions, but the behavior of elongated objects under vibration remains less understood.

Purpose of the Study:

To investigate the transition from periodic to stochastic dynamics of a rod bouncing on a vibrating surface.
To characterize the statistical distributions of impact times, angles, and energy components.
To determine the influence of parameters like acceleration, rod length, and frequency on these dynamics.

Main Methods:

Comparison of experimental results with computer simulations.
Utilizing a stainless-steel rod bouncing on a metal-coated glass surface.
Varying the dimensionless acceleration parameter (Gamma), rod length, and vibration frequency.

Main Results:

A transition from periodic to stochastic dynamics was observed as Gamma increased above unity.
Impact time statistics showed approximate Gaussian tails, while impact angle distributions exhibited near-exponential tails.
Energy statistics, including translational and rotational components, approximated Boltzmann distributions in their tails.
Strong correlations were found between translational and rotational energy, with vertical translational energy dominating.

Conclusions:

The study reveals a clear transition to stochastic behavior in a bouncing rod system under vertical vibration.
The observed statistical distributions provide a quantitative description of the chaotic dynamics.
Energy distribution highlights the dominance of vertical motion and strong coupling between translational and rotational components.