Lie Group Classifications and Stability of Exact Solutions for Multidimensional Landau-Lifshitz Equations

In this paper, based on classical Lie group method, we study multi-dimensional Landau-Lifshitz equation, and get its infinitesimal generator, symmetry group and new solutions. In particular, we build the connection between new exact solutions and old exact solutions. At the same time, we also prove that the initial boundary value condition of the three-dimensional Landau-Lifshitz equation admits a unique solution and discuss the stability of the solution.

Cu single-atom electrocatalyst on nitrogen-containing graphdiyne for CO_(2)electroreduction to CH4

Developing Cu single-atom catalysts(SACs)with well-defined active sites is highly desirable for producing CH4 in the electrochemical CO_(2)reduction reaction and understanding the structure-property relationship.Herein,a new graphdiyne analogue with uniformly distributed N2-bidentate(note that N2-bidentate site=N^N-bidentate site;N2¹dinitrogen gas in this work)sites are synthesized.Due to the strong interaction between Cu and the N2-bidentate site,a Cu SAC with isolated undercoordinated Cu-N2 sites(Cu1.0/N2-GDY)is obtained,with the Cu loading of 1.0 wt%.Cu1.0/N2-GDY exhibits the highest Faradaic efficiency(FE)of 80.6%for CH4 in electrocatalytic reduction of CO_(2)at-0.96 V vs.RHE,and the partial current density of CH4 is 160 mA cm^(-2).The selectivity for CH4 is maintained above 70%when the total current density is 100 to 300 mA cm^(-2).More remarkably,the Cu1.0/N2-GDY achieves a mass activity of 53.2 A/mgCu toward CH4 under-1.18 V vs.RHE.In situ electrochemical spectroscopic studies reveal that undercoordinated Cu-N2 sites are more favorable in generating key*COOH and*CHO intermediate than Cu nanoparticle counterparts.This work provides an effective pathway to produce SACs with undercoordinated Metal-N2 sites toward efficient electrocatalysis.

Lie Symmetry Reductions and Exact Solutions of a Multidimensional Double Dispersion Equation

In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solutions and travelling wave solutions of the multidimensional double dispersion equation are derived from the reduction equations.

Significantly enhanced oxygen reduction activity of Cu/CuN_xC_y co-decorated ketjenblack catalyst for Al–air batteries

Highly efficient and non-precious catalysts are imperative for oxygen reduction reaction（ORR） to replace Pt/C. Anchoring efficient active species to carbon supports is a promising and scalable strategy. Here we synthesize Cu nanoparticles and noncrystalline CuNxCy species co-decorated ketjenblack（KB） carbon catalyst（denoted as Cu-N-KB-acid） by a facile and scalable method using copper sulfate, melamine, and KB as raw materials. An initial one-pot hydrothermal treatment is designed before pyrolysis process to achieve the good distribution of Cu and melamine on KB via a possible chelation effect. Owing to the synergistic effect of Cu and CuNxCy on KB, this composite catalyst displays excellent ORR catalytic activity in alkaline solution, which is comparable to the commercial 20% Pt/C. When used as a catalyst in a home-made Al-air battery, it shows a stable discharge voltage of 1.47 V at a discharge density of 50 mA cm-2, a little higher than that of Pt/C（1.45 V）.

Phosphorous-doped carbon nanotube/reduced graphene oxide aerogel cathode enabled by pseudocapacitance for high energy and power zinc-ion hybrid capacitors

The design and development of energy storage device with high energy/power density has become a research hotspot.Zinc-ion hybrid capacitors(ZHCs)are considered as one of the most promising candidates.However,the application of ZHCs is hindered by their low energy density at high power density due to the unsatisfactory cathode material.In this study,a novel 3D phosphorus-doped carbon nanotube/reduced graphene oxide(P-CNT/rGO)aerogel cathode is synthesized through a synergistic modification strategy of CNT insertion and P doping modification combined with 3D porous design.The as-obtained P-CNT/rGO aerogel cathode manifests significantly increased surface aera,expanded interlayer spacing,and enhanced pseudocapacitance behavior,thus leading to significantly enhanced specific capacitance and superb ions transport performance.The as-assembled ZHC based on P-CNT/rGO cathode delivers a superior energy density of 42.2 Wh/kg at an extreme-high power density of 80 kW/kg and excellent cycle life.In-depth kinetic analyses are undertaken to prove the enhanced pseudocapacitance behavior and exceptional power output capability of ZHCs.Furthermore,the reaction mechanism of physical and chemical adsorption/desorption of electrolyte ions on the P-CNT/rGO cathode is revealed by systematic ex-situ characterizations.This work can provide a valuable reference for developing advanced graphene-based cathode for high energy/power density ZHCs.

Upgrade of three municipal wastewater treatment lagoons using a high surface area media

Abstract Lagoon-based municipal wastewater treatment plants （WWTPs） are facing difficulties meeting the needs of rapid population growth as well as the more stringent requirements of discharge permits. Three municipal WWTPs were modified using a high surface area media with upgraded fine-bubble aeration systems. Performance data collected showed very promising results in terms of five-day biochemical oxygen demand （BOD5）, ammonia （NH3） and total suspended solids （TSS） removal. Two-year average ammonia effluents were 4.1 mg. L-1 for Columbia WWTP, 4 mg. L-1 for Larchmont WWTP and 2.1 mg. L-1 for Laurelville WWTE respectively. Two- year average BOD5 effluents were 6.8, 4.9 and 2.7 mg.Ll, and TSS effluents were 15.0, 9.6 and 7.5 mg.L-L The systems also showed low fecal coliform （FC） levels in their effluents.