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The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Probing ergodicity in granular matter.

Fabien Paillusson1, Daan Frenkel

  • 1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Physical Review Letters
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

Granular systems change volume when tapped. This study reveals non-ergodicity in granular systems, showing their behavior is not captured by single long trajectories, challenging previous assumptions.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Granular systems exhibit volume changes upon external stimuli like tapping.
  • Previous research often assumed ergodicity, studying single system trajectories.
  • Understanding granular system dynamics is crucial for various applications.

Purpose of the Study:

  • To investigate the statistical properties of volume changes in granular systems subjected to tapping.
  • To develop methods for assessing convergence and identifying invariant properties of granular systems.
  • To test the compatibility of granular system behavior with Edwards' canonical assumption.

Main Methods:

  • Preparing an ensemble of granular systems using a macroscopic protocol.
  • Tracking volume changes as a function of the number of taps.
  • Developing a novel method to assess convergence of ensemble volume histograms.
  • Comparing ensemble histograms with single-trajectory histograms to quantify non-ergodicity.
  • Utilizing the overlapping histogram method to test Edwards' canonical assumption.

Main Results:

  • A new method was devised to assess convergence properties of ensemble volume histograms.
  • An approximate invariant histogram for granular systems was introduced.
  • Non-ergodicity was observed and quantified by comparing ensemble and single-trajectory histograms.
  • The study found incompatibility between the observed granular system histograms and Edwards' canonical assumption.

Conclusions:

  • Granular systems exhibit non-ergodic behavior, meaning single long trajectories do not represent the ensemble average.
  • The developed methods provide new tools for analyzing granular system dynamics and convergence.
  • The findings challenge the applicability of Edwards' canonical assumption to these granular systems, suggesting a need for revised theoretical frameworks.