This Master's thesis presents the development of correlations in an orientational (director) field within the nematic liquid crystal shell. Firstly we introduce Frank's deformation free energy and within the one-constant approximation determine the director field. Then we introduce elastic multipole coefficients (monopoles ${q}_t$, dipoles $\mathbf{p}_t$ and quadrupoles $\mathbf{Q}_t$) that are used for the characterisation of weakly deformed director fields orientated mainly along one specific direction with small transverse components. A relation between the correlation function and the probability function of orientation of director field on a sphere is presented. Methodologically, we write a computer algorithm that evolves in time the nematic director field as dictated by nematic quasidynamics, on the geometry of a sphere. Correlation function is shown to have a Gaussian-function spatial dependence and it increases with increasing time of nematic quasidynamics. The timescale is determined with time scale $\tau = r_p^2 \Gamma / K$. If nematic experiences quasidynamics in a spherical shell with larger finite width the correlation of the director field increases. After that, we calculate elastic multipole coefficients for small deformations of uniform director field and study the connection between elastic deformation and correlation function of the director field. An increase in the deformation of the director field causes a decrease of correlation and an increase of elastic multipole coefficients. Conversely, time propagation towards homogeneous field increases the correlation of the director field and reduces the elastic multipoles. Dipole and quadrupole moments converge to 0 after long times, whereas the monopoles converge to finite value that agrees with the final orientation of the uniform director field and is dependant on the random initial deformation. This work contributes to understanding of correlations in elastic nematic fields.
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