Yumin Cheng

The Error Estimates of the Interpolating Element-Free Galerkin Method for Two-Point Boundary Value Problems

The interpolating moving least-squares (IMLS) method is discussed in detail, and a simpler formula of the shape function of the IMLS method is obtained. Then, based on the IMLS method and the Galerkin weak form, an interpolating element-free Galerkin (IEFG) method for two-point boundary value problems is presented. The IEFG method has high computing speed and precision. Then error analysis of the IEFG method for two-point boundary value problems is presented. The convergence rates of the numerical solution and its derivatives of the IEFG method are presented. The theories show that, if the original solution is sufficiently smooth and the order of the basis functions is big enough, the solution of the IEFG method and its derivatives are convergent to the exact solutions in terms of the maximum radius of the domains of influence of nodes. For the purpose of demonstration, two selected numerical examples are given to confirm the theories.

Diffusion mechanism of platinum nanoclusters on well-aligned carbon nanotubes

Carbon supported platinum (Pt/C) remains among the preferred catalyst materials for use in proton exchange membrane fuel cells; however, its durability must be improved. In this work, we considered well-aligned carbon nanotubes (WACNTs) as a carbon support material and investigated the diffusion mechanism of Pt nanoparticles by using molecular dynamic (MD) simulations, including calculation of the binding energy, aggregation probability, and the diffusion coefficient. Moreover, the use of graphene as a support material is also examined. The trenches in well-aligned carbon nanotubes were found to not only increase the binding energy between the Pt particles and the substrates but also decrease the aggregation probability of Pt particles compared with the graphene substrates. Furthermore, we estimated the Pt mass per substrate area (Pt loading) when there is no occurrence or a reduced occurrence of Pt agglomeration: a value of 0.167 μg cm−2 for WACNTs (24, 24), and a Pt particle diameter of 2.4 nm are suggested.