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Related Concept Videos

Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...
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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

Entropy maximization in the force network ensemble for granular solids.

Brian P Tighe1, Adrianne R T van Eerd, Thijs J H Vlugt

  • 1Instituut-Lorentz, Universiteit Leiden, Leiden, The Netherlands.

Physical Review Letters
|July 23, 2008
PubMed
Summary

Researchers resolved the force distribution tail issue in granular media. A conserved tiling area in 2D systems leads to a Gaussian tail for local pressures, matching numerical simulations.

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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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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Published on: September 29, 2019

Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • The force distribution tail in granular media remains a persistent challenge, with ongoing debate regarding its mathematical form (e.g., exponential vs. Gaussian).
  • Understanding granular material behavior is critical in various fields, from engineering to geophysics.

Purpose of the Study:

  • To definitively resolve the nature of the force distribution tail in two-dimensional granular systems.
  • To identify the key physical principles governing local stress distribution in granular media.

Main Methods:

  • Developed a theoretical framework based on the force network ensemble in two dimensions.
  • Utilized the principle of conservation of total area of a reciprocal tiling, derived from local force balance.
  • Employed maximum entropy principles, incorporating constraints of tiling area and total pressure.

Main Results:

  • Demonstrated that the conservation of reciprocal tiling area is fundamental for predicting local stress distributions.
  • Showed that maximizing entropy under these constraints yields a local pressure distribution with a predominantly Gaussian tail.
  • Validated these findings through numerical simulations, observing excellent agreement with and without friction and across different contact networks.

Conclusions:

  • The study resolves the long-standing question of the force distribution tail in 2D granular media, establishing it as generically Gaussian.
  • Highlights the critical role of geometric constraints (conserved tiling area) and statistical principles (maximum entropy) in determining granular material behavior.
  • Provides a robust theoretical model applicable to various frictional and non-frictional granular systems.