Taguchi optimized synthesis of graphene films by copper catalyzed ethanol decomposition

Taguchi method is for the first time applied to optimize the synthesis of graphene films by copper-catalyzed decomposition of ethanol. In order to find the most appropriate experimental conditions for the realization of thin high-grade films, six experiments suitably designed and performed. The influence of temperature (1000–1070 °C) and synthesis duration (1–30 min) and hydrogen flow (0–100 sccm) on the number of graphene layers and defect density in the graphitic lattice was ranked by monitoring the intensity of the 2D- and D-bands relative to the G-band in the Raman spectra. After critical examination and adjusting of the conditions predicted to give optimal results, a continuous film consisting of 2–4 nearly defect-free graphene layers was obtained.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.