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In this chapter, we focus on advanced Monte Carlo and molecular dynamics techniques to study vapour-liquid phase equilibria, cross-over behaviour of critical properties and solid-liquid phase transition under confinement. The state of the art in the field is demonstrated by reviewing selected results of our recent computer simulations. We present Monte Carlo studies of cross-over behaviour of critical properties, in different geometries, from 3D to 2D. In the second part of the chapter, we list various issues pertaining to the study of solid-liquid transitions under confinement in the context of lubrication at the nanoscale. We also provide recent molecular dynamics results which provide more clarity in understanding the effect of surface texture on the solid structure of confined fluids. We end the chapter with an introduction to analysis and techniques to evaluate liquid-solid phase transitions and structure formation in cylindrical pores.

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