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KOH activation is a well-accepted approach to develop microporosity for porous carbons, but its severe etching reactions could inevitably destroy the structural integrity and diminish the heteroatomic surface chemistry of the resultant carbons. Herein, we report a method to prepare well-defined micro-spherical, high-surface-area and high-nitrogen-doping carbons via a mild KOH activation. The key to our synthesis relies in the pre-oxidation of the nitrogen-rich polymeric microspheres from resorcinol, formaldehyde and melamine, which could enrich nitrogen heteroatoms into the resultant carbonized framework, resulting in the carbon easily activated by KOH with low surface etching and high residual of nitrogen heteroatoms. The obtained carbons possess high specific surface area of 2234-3121 m 2 /g, high nitrogen content of 6.1-12.5 wt. % and well-preserved spherical morphology. When used as the electrodes of supercapacitor, these carbon microspheres could deliver high specific capacitance up to 309 F/g, excellent rate performance and high cyclic performance of 96 % after 5000 cycles in H 2 SO 4 electrolyte. Furthermore, it is found that nitrogen functionalities could contribute considerable pseudo-capacitance, basically through Faradic reactions of the nitrogen.

The paper analyses by Taylor series the several fifth-order of accuracy schemes for hyperbolic conservation laws: the classical WENOJS scheme [G.S. Jiang, and C.W.Shu. Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126:202-228, 1996], the WENOM scheme [A.K. Henrick, T.D. Aslam, and J.M. powers. Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J. Comput. Phys. 207:542-567, 2005], the WENOZ scheme [R. Borges, M. Carmona, B. Costa, and W.S. Don. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. J. Comput. Phys. 227:3191-3211, 2008] and the scheme, called WENOε here, [F. Aràndiga, A. Baeza, A.M. Belda, and P. Mulet. Analysis of WENO schemes for full and global accuracy. SIAM J. Numer. Anal., 49:893-915, 2011]. The order of weights of these four schemes agreed to the optimal weights is presented in detail. Then three prerequisites are developed if one intends to improve the WENOJS scheme: the scheme arrives the 5th-order at critical points; the weights of scheme approximate the optimal weights with high-order accuracy when solution is smooth; the scheme shouldn't introduce much oscillations intuitively in the vicinity of discontinuities. According to the prerequisites above, a new WENO scheme (MWENOZ) is devised which is similar to the WENOZ scheme. Finally, the method designed here is demonstrated robustly by applying it to 1D and 2D numerical simulations and its advantage compared with the WENOZ scheme seems more striking in 2D problems.

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