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A theoretical framework describing the carbon nanotubes interaction, involving two distinct approaches, is presented. Based on the results obtained practical applications using carbon nanotubes are further proposed. First a classical approach is employed for different geometrical configurations, such as parallel or concentric carbon nanotubes. For all the cases analytical expressions for the systems potential energies are derived. The results obtained using the classical approach are used to propose a few practical applications. These applications include a non-contact device for profiling surfaces and a custom telescopic double wall carbon nanotube for nanolithography applications. It is expected that such devices can be effectively used with major advantages. Next the interaction between nanotubes is considered using a quantum electrodynamics approach suitable for dispersing and absorbing media. Each carbon nanotube is characterized by its individual full dielectric response. The method also allows taking into account the full carbon nanotube cylindrical geometry by imposing the appropriate boundary conditions at the nanotubes surfaces. It is found that at small nanotube separations, similar to their equilibrium distances, the interaction is dominated by the collective excitations in the electron energy loss spectra originating from interband transitions. Furthermore, it is shown that the collective surface excitations and their chirality dependent characteristics play a profound role in the interaction strength in double wall carbon nanotube systems. The obtained results are in good agreement with experimental measurements on determining the chirality of individual double wall carbon nanotubes

yes / This work outlines a novel approach for determining thermal contact resistance (TCR) in micromoulding. The proposed technique aims to produce TCR predictions with known confidence values and combines experimental evidence (temperature fields and contact angle measurements) with various mathematical modelling procedures (parametric representation of surfaces, finite element analysis and stochastic processes). Here, emphasis is made on the mathematical aspects of the project. In particular, we focus on the description of the parametric surface representation technique based on the use of partial differential equations, known as the PDE method, which will be responsible for characterizing and compressing micro features in either moulds or surface tools. / EPSRC