Yufeng Nie — Page 2

arXiv2016

Maximum-norm error analysis of compact difference schemes for the backward fractional Feynman-Kac equation

The fractional Feynman-Kac equations describe the distribution of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the discretized schemes for fractional substantial derivatives proposed recently, we construct compact finite difference schemes for the backward fractional Feynman-Kac equation, which has q-th (q=1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. In the case q=1, the numerical stability and convergence of the difference scheme in the discrete L-infinity norm are proved strictly, where a new inner product is defined for the theoretical analysis. Finally, numerical examples are provided to verify the effectiveness and accuracy of the algorithms.

math.NA↗

arXiv2015

Wafer-scale CVD Growth of Monolayer Hexagonal Boron Nitride with Large Domain Size by Cu Foil Enclosure Approach

Chemical vapor deposition synthesis of large domain hexagonal boron nitride (h-BN) with uniform thickness on Cu foils is of great challenge, originating from the extremely high nucleation densities and the reverse hydrogen etching competition reaction. We report herein the successful growth of wafer-scale high-quality h-BN monolayer film with the largest single crystalline domain sizes up to 72 micrometer in edge length using a folded Cu enclosure approach. The highly-confined growth space with this facile and unique approach enables the drastic decrease of nucleation centers together with the effective suppression of hydrogen etching reaction. It is revealed, for the first time, that the orientations of as-grown h-BN monolayers are strongly correlated with the crystalline facets of growth substrates, with the Cu (111) being the best substrate for growing high-quality single crystalline h-BN monolayer, consistent with the density functional theory calculations. The present study offers a practical pathway for growing high-quality h-BN films and deepens the fundamental understanding of h-BN growth process.

cond-mat.mtrl-sci↗