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Updated: Jul 3, 2026

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
09:12

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation

Published on: June 28, 2015

Driven fragmentation of granular gases.

Raúl Cruz Hidalgo1, Ignacio Pagonabarraga

  • 1AMADE, Departament de Física, Departament de Enginyeria Mecànica i de la Construcció Industrial, Universitat de Girona, Avenida Montilivi s/n, Girona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 23, 2008
PubMed
Summary

Granular gases fragmenting due to collisions exhibit dynamical scaling. Fragmentation probability determines if grain number diverges (shattering singularity) or grows as a power law.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Granular gases are systems of macroscopic particles interacting via collisions.
  • Understanding their complex dynamics, especially under heating and fragmentation, is crucial.
  • Kinetic theory provides a framework for analyzing particle collisions and system evolution.

Purpose of the Study:

  • To analyze the dynamics of homogeneously heated granular gases undergoing fragmentation.
  • To develop a kinetic model accounting for collision-induced correlations.
  • To investigate the influence of fragmentation probabilities on system kinetics and velocity distributions.

Main Methods:

  • Analytical and numerical studies, including direct simulation Monte Carlo (DSMC) methods.
  • Development of a kinetic model incorporating grain collision correlations.
  • Consideration of a broad family of fragmentation probabilities and homogeneous thermostats.

Main Results:

  • Granular gases evolve into a dynamical scaling regime.
  • Constant fragmentation probability leads to a shattering singularity; vanishing probability results in power-law growth.
  • System kinetics show weak dependence on grain inelasticity and driving, but fragmentation significantly impacts velocity distributions.

Conclusions:

  • Fragmentation is a key factor in granular gas dynamics, influencing both particle number evolution and velocity distributions.
  • The velocity distribution's tail can be exponential or follow a generalized exponential form depending on the thermostat and fragmentation mechanism.
  • The study provides insights into the behavior of driven, fragmenting granular materials.