Langevin equation ferrofluids

The complex susceptibility of a ferrofluid in a weak applied field may be written directly from Eqs. (109) and (110) and the Langevin equations (98) and (99) [taking note of Eq. (102)] using the shift theorem for one-sided Eourier transforms, Eq. (30). Thus... 

Here the ratio Xri/xb represents the coupling between the magnetic and mechanical motions arising from the nonseparable namre of the Langevin equations, Lqs. (121) and (122). Thus the correction to the solid-state result imposed by the fluid is once again of the order 10 Hence we may conclude, despite the iionseparability of the equations of motion, that the Neel relaxation time of the ferrofluid particle should still be accurately represented in the IHD and VLD limits by the solid-state relaxation time formulae, Eqs. (87) and (90). Furthermore, Eq. (122) should be closely approximated by the solid-state relaxation equation... 

In order to discuss the Langevin equation for a single domain ferrofluid particle we first consider Gilbert s equation for the dynamic behavior of the particle s magnetization vector M in the presence of thermal agitation, which is Eq. (1.12),... 

Equation (5.4) is the Langevin equation of the problem. This equation is now analogous to the equation of motion of a polar molecule under the influence of an electric field [52]. The quantity that directly corresponds to the dipole moment of the polar molecule p. in the Debye theory is the magnetic moment vM of an individual ferrofluid particle, not the magnetization M which is the magnetic moment per unit volume. Equation... 

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