Abstract/Details

Numerical studies of granular gases


2009 2010

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Abstract (summary)

In this dissertation, we study velocity distributions in granular gases. For granular systems at low density, kinetic theory reduces to the Boltzmann equation which is based on the assumption of molecular chaos. At large velocity scales, stationary solutions with power-law tails, f( v) ∼ v–σ, have been derived from the Boltzmann equation for spatially homogeneous granular systems [6]. The behavior of power-law tail is complete generic, holding for arbitrary dimension, arbitrary collision rules, and general collision rates.

We find the non-Maxwellian steady states using event-driven molecular dynamics simulations. Firstly, power-law steady states are observed in driven systems where energy is injected rarely at large velocity scale V . The range of power-law tail shrinks when we increase the heating-dissipation ratio [special characters omitted], where NI and NC are number of injections and number of collisions, respectively. Then a crossover from a power-law to a stretched exponential distribution is developed when the heating-dissipation ratio [special characters omitted] is close to 1.

It is the energy cascade from a few energetic particles to the overwhelming majority of slowly moving particles that causes the non-Maxwellian velocity distributions. Steady states with power-law tail are robust as long as the injection velocity scale V is essentially separated from the typical velocity scale v0. These steady states are shown to exist for a wide range of number densities, different combinations of injection velocities and injection rates. The injection velocity scale V, the typical velocity scale v0, and the injection rate per particle are related by energy balance. This energy balance relation is confirmed by data collapse of velocity distributions for various choices of parameters.

Indexing (details)


Subject
Condensed matter physics;
Theoretical physics
Classification
0611: Condensed matter physics
0753: Theoretical physics
Identifier / keyword
Pure sciences, Boltzmann equation, Granular gas, Periodic boundary conditions, Stretched exponentials
Title
Numerical studies of granular gases
Author
Kang, Wenfeng
Number of pages
103
Publication year
2009
Degree date
2010
School code
0118
Source
DAI-B 71/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109698855
Advisor
Machta, Jonathan
Committee member
Menon, Narayanan; Rey-Bellet, Luc; Svistunov, Boris
University/institution
University of Massachusetts Amherst
Department
Physics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3397714
ProQuest document ID
250890157
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/250890157
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