Physics – Condensed Matter – Statistical Mechanics
Scientific paper
Nov 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006smpr.confe...9b&link_type=abstract
Proceedings of the International conference on Statistical Mechanics of Plasticity and Related Instabilities. August 29-Septembe
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
In this paper we develop a kinetic theory for interacting dislocation systems. Dislocations interact via a long range 1/r-type force so that the system will be spatially inhomogeneous. A new kinetic equation is obtained using the time-dependent projection operator formalism of Willis and Picard. An exact equation for the time evolution of the one-particle probability density is obtained, which can be approximated as a closed Markovian equation in the approximation that the time scale of fluctuations is much shorter than the relaxation and dynamical time scales. The core of the distribution of dislocation velocity fluctuations is found to be Gaussian, while the high-velocity tail decays algebraically. A well-defined non-vanishing self-consistent mean field can be isolated for which we recover precisely the same expression as Groma obtained by a truncation of the BBGKY hierarchy of dislocation distribution functions. PACS: 61.72.Bb, 61.72.Lk
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