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Related Concept Videos

Elastic Collisions: Introduction01:00

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
Types of Collisions - II01:19

Types of Collisions - II

When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...
Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Types Of Collisions - I01:04

Types Of Collisions - I

When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...
Impact01:30

Impact

Impact occurs when two bodies collide, leading to the application of impulsive forces between them. Analyzing impact mechanics involves considering two colliding particles moving along a line known as the line of impact, which passes through their centers and is perpendicular to the contact plane.
When particles with different initial velocities collide, they induce deformation by applying equal and opposite impulses. At the point of maximum deformation, the particles move together with...

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Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
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Collision statistics in sheared inelastic hard spheres.

Marcus N Bannerman1, Thomas E Green, Paul Grassia

  • 1School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, Sackville Street, Manchester M60 1QD, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary

Sheared inelastic hard-sphere systems exhibit anisotropic velocity distributions, especially at lower densities. Collisions become more correlated and glancing as systems become more inelastic.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Understanding the behavior of granular materials under shear is crucial in various scientific and engineering fields.
  • Previous studies have explored elastic hard-sphere systems, but the dynamics of inelastic systems under shear require further investigation.

Purpose of the Study:

  • To investigate the dynamics of sheared inelastic hard-sphere systems.
  • To analyze key system properties such as velocity distribution, granular temperature, and collision characteristics.

Main Methods:

  • Employed nonequilibrium molecular-dynamics simulations with Lees-Edwards boundary conditions.
  • Utilized direct simulation Monte Carlo methods for comparison.
  • Monitored one-particle velocity distribution, granular temperature, stress tensor, and collision statistics.

Main Results:

  • Observed an anisotropic Gaussian velocity distribution with slight overpopulation in high-velocity tails.
  • Found velocity distribution anisotropy increases with lower densities and coefficients of restitution.
  • Noted that glancing collisions dominate over head-on collisions in more inelastic systems, leading to correlated particle collisions.

Conclusions:

  • The compressibility factor of sheared inelastic hard-sphere systems closely resembles that of elastic systems.
  • Particle collisions become strongly correlated in highly inelastic systems.
  • Simulation data shows good agreement with the Enskog equation kinetic model for high-density, weakly inelastic systems.