This paper employs the molecular-dynamics method to generate random-dot patterns for light guides designed for backlight systems. The proposed approach combines various numerical techniques and is designed to optimize the dot-density distribution in order to satisfy the uniform luminance requirements demanded by liquid-crystal displays. In the proposed algorithm, the total domain is divided into a prescribed number of cells whose dot densities can be individually adjusted in order to fine tune the luminance conditions in accordance with the light source position and type. In addition, a variable truncation distance is implemented in each cell according to the dot density of that cell. This variable r-cut technique localizes the repulsive force effects acting within each cell in order that a high-dot-density gradient can be achieved in the overall dot distribution. Finally, an average force control technique is developed to ensure the uniformity of the dot distribution as it passes across the cell boundaries. Several illustrative examples are provided to demonstrate the robustness of the proposed molecular-dynamics dot-generation algorithm.

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This paper investigates the morphological stability of epitaxial films growing heteroepitaxially on ultra-thin substrates. The misfitting strain model is incorporated into the quasi-static mechanical equilibrium system. The interfacial evolution equation between the vapour and film phases is used to solve the film evolution. The perturbation method of normal modes is used to derive the analytical form of the normal-mode growth rate. Additionally, this paper investigates the dynamic behaviour of the vapour–film interface. The results of the study show that a decrease in substrate thickness tends to stabilize the system regardless of whether the stiffness ratio, ρ (i.e. the ratio of film stiffness to substrate stiffness) is less than, equal to or greater than unity. Furthermore, it is found that the effects of a finite substrate thickness on the stability behaviour of the system are quite profound, and that this is particularly true when the film thickness is close to hc with values of stiffness ratio greater than unity.

The low-energy electronic states and energy gaps of carbon nanocones in an electric field are studied using a single-S-band tight-binding model. The analysis considers five perfect carbon nanocones with disclination angles of 60°, 120°, 180°, 240° and 300°, respectively. The numerical results reveal that the low-energy electronic states and energy gaps of a carbon nanocones are highly sensitive to its geometric shape (i.e. the disclination angle and height), and to the direction and magnitude of an electric field. The electric field causes a strong modulation of the state energies and energy gaps of the nanocones, changes their Fermi levels, and induces zero-gap transitions. The energy-gap modulation effect becomes particularly pronounced at higher strength of the applied electric field, and is strongly related to the geometric structure of the nanocone. Many theoretical [5][6][7][8][9][10] and experimental studies [11][12][13][14] of the geometric and electronic properties of carbon nanocones or nanotube tips have been revealed over the past decade. In general, the results have shown that the electronic structure, e.g. the electronic states, energy gaps and density of states, are highly sensitive to the symmetry of the edge sites at the open apex and to the curvature effect. However, relatively few studies have investigated the effect of an electric field on the electronic structures of carbon nanocones. It is known that an electric field can significantly affect the electronic properties of

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