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This paper applies the density functional theory to confined liquid crystals comprising ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The restricted orientation model proposed by Rickayzen [Mol. Phys. 95, 393 (1998)] is extended to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the Percus-Yevick DCF for hard spheres; the anisotropy is introduced by means of the closest approach parameter. The average number density and orientational order parameter profiles of a HGO fluid confined in between planar walls are obtained using a hard needle-wall potential to represent the particle-wall interactions. For short and long needle lengths, the homeotropic and planar anchoring are observed, respectively. For the bulk isotropic phase the calculated density and order parameter profiles are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 69, 61705 (2004)]. However, for the bulk nematic phase the theory gives the correct density profile between the walls. The correct order parameters are obtained close to the walls whereas for the region in the middle of the walls, the agreement is less satisfactory.

The density profiles of a hard Gaussian overlap (HGO) fluid confined in between hard walls and in contact with a hard wall are studied using the density functional theory. The hyper-netted chain (HNC) approximation is used to find the coupled integral equations for the density profiles. The restricted orientation model (ROM) is used. The required homogeneous direct correlation function (DCF) is obtained by solving Ornstein–Zernike (OZ) integral equation numerically, using the Precus–Yevick (PY) approximation and the procedure mentioned by Letz and Latz [Phys. Rev.E60, 5865 (1999)]. We also obtained the DCF of hard ellipsoidal (HE) fluid by using the modified closest approach introduced by Rickayzen [Mol. Phys.68, 903 (1989)]. For both HGO and HE, we calculate the density profiles of molecules parallel and perpendicular to the walls and we compare the results. The calculations are performed for various values of packing fractions of the fluid and various molecular elongations. For moderate elongations, k≤3, the results for HGO and HE are almost the same, especially for the density profile of the molecules parallel to the walls but for k=5 there are some discrepancies between the results, in particular for the density profiles of the molecules perpendicular to the walls.

A numerical analysis and experimental study of the temperature distribution and thermal lensing in six types and sizes of standard and composite Nd:YVO 4 crystals with consideration of the temperature dependence of the thermal conductivity tensor is presented. In the first step to test the model, numerical results at 1064 nm and 1342 nm laser wavelengths are compared with previous experimental results in the literature. In these cases there was good agreement between them in comparison with constant thermal conductivity. In the second step, a diode end pumped Nd:YVO 4 laser is constructed with three types of crystals. Single and double-end diffusion bounded crystals have shown equal efficiencies while standard crystal have lower efficiency. A comparison between theoretical and experimental results is done again and a perfect match between them is observed.