Probabilistic Approach to Pattern Selection

Details Probabilistic Approach to Pattern Selection Probabilistic Approach to Pattern Selection

2001-04-02

arxiv.org/abs/cond-mat/0104024v1

Physica A 291 (2001) 255-274

Physics

Condensed Matter

LaTex, 22 pages

Scientific paper

10.1016/S0378-4371(00)00517-3

The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the probability distribution of patterns. Then the most probable pattern naturally corresponds to the largest probability weight. This approach provides the ordering principle for the multiplicity of solutions explaining why some of them are more preferable than other. The approach is applied to solving the problem of turbulent photon filamentation in resonant media.

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