We review advances in the last few years on the study of the Faraday instability onset on thermotropic liquid crystals of nematic and smectic A types under external magnetic fields which have been investigated with a linear stability theory. Especially, we show that thermal phase transition effects on nematics of finite thickness samples produce an enhanced response to the instability as a function of the frequency of Shaker's movement. The linear stability theory has successfully been used before to study dynamical processes on surfaces of complex fluids. Consequently, in Section 1, we show its extension to the study of the instability in the nematics, which set the theoretical framework for its further application to smectics or other anisotropic fluids such as lyotropic liquid crystals. We present the dispersion relationships of both liquids and its dependence on interfacial elastic parameters governing the surface elastic responses to external perturbations, to the sample size and their bulk viscosities. Finally, we point out the importance of following both experimental and theoretical analysis of various effects that needs to be incorporated into this model for the quantitative understanding of the hydrodynamics behavior of surface phenomena in liquid crystals.

In this chapter, we review the experimental and theoretical modeling of structural and dynamical properties of colloidal magnetic fluids at equilibrium. Presently, several prototype experimental systems are very well characterized. We survey the different models, which help to reach a comprehensive knowledge of these complex magnetic fluids. One prime example is the ongoing investigation of the realistic interparticle potentials that drive the formation of the different phase states observed experimentally. Further, a stochastic equation approach for the description of tracer diffusion, viscoelasticity, and dielectric relaxation at equilibrium in colloidal ferrofluids is discussed.