Augmented Fokker-Planck equation

In Section I.B we discuss how to devise a general MFPKE to describe complex liquids. A three-body model will be presented as a description of a system in which at least two significant additional sets of solvent degrees of freedom are introduced. In Section I.C we show the relation between some of the previously cited approaches and particular cases of our model. In particular, augmented Fokker-Planck equations (AFPE) of Stillman and Freed are seen to be directly related to the MFPK formal-... 

Planar models are also important for comparing our work to some of the previous theoretical studies along the same lines, for example, the planar augmented Fokker-Planck equation described by Stillman and Freed (see next section) and the itinerant oscillator model of Coffey and Evans. 

In Section II, Gilbert s equation describing the Neel relaxation is augmented by a random field term, representing thermal fluctuations. The underlying Fokker-Planck equation is then constructed from this augmented equation. The time constant in this equation is the Neel relaxation time... 

In this section we summarize the approach used by previous authors [8, 16-19] to find expressions for the relaxation times of single domain ferromagnetic and ferrofluid particles. We begin with the Fokker-Planck equation obtained from Gilbert s equation, in spherical polar coordinates, augmented by a random field term, that is, with Brown s equation. We then expand the probability density of orientations of M, that is. 

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