Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of...Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by Adomian’s decomposition method (ADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.展开更多
We used scattering-type scanning near-field optical microscopy(s-SNOM)to investigate the plasmonic properties of edges in well-defined graphene nanostructures,including sharp tapers,nanoribbons and nanogaps,which were...We used scattering-type scanning near-field optical microscopy(s-SNOM)to investigate the plasmonic properties of edges in well-defined graphene nanostructures,including sharp tapers,nanoribbons and nanogaps,which were all fabricated via the growth-etching chemical vapor deposition(GECVD)method.The obtained near-field images revealed the localized plasmon modes along the graphene nanoribbon;these modes strongly depended on the size of the graphene pattern,the angle of the tapered graphene and the infrared excitation wavelength.These interesting plasmon modes were verified by numerical simulations and explained by the reflection,and interference of electromagnetic waves at the graphene–SiO_(2) edge.The constructive interference at the graphene nanogap caused by charge accumulation was demonstrated for the first time.Using the infrared nanoimaging technique,greater plasmon broadening was observed in the zigzag edge than in the armchair edge.Our study suggests that graphene edges should be separated by an effective working distance to avoid the overlapping of localized plasmon modes,which is very important for the design of graphene-based plasmonic circuits and devices.展开更多
文摘Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by Adomian’s decomposition method (ADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.
基金support from the National Key Research&Development Program(2015CB932700 and 2016YFA0201902)the National Natural Science Foundation of China(grant No.51290273,91433107,51325205 and 51521091)+6 种基金the Doctoral Fund of the Ministry of Education of China(grant No.20123201120026)ARC(DP140101501 and FT150100450)the Collaborative Innovation Center of Suzhou Nano Science&Technologythe Priority Academic Program Development of Jiangsu Higher Education InstitutionsA*STAR Pharos Programme(grant No.1527000014,with Project No.R-263-000-B91-305)Competitive Research Program(CRP Award No.NRF-CRP15-2015-03)the National Research Foundation,Prime Minister’s Office,Singapore。
文摘We used scattering-type scanning near-field optical microscopy(s-SNOM)to investigate the plasmonic properties of edges in well-defined graphene nanostructures,including sharp tapers,nanoribbons and nanogaps,which were all fabricated via the growth-etching chemical vapor deposition(GECVD)method.The obtained near-field images revealed the localized plasmon modes along the graphene nanoribbon;these modes strongly depended on the size of the graphene pattern,the angle of the tapered graphene and the infrared excitation wavelength.These interesting plasmon modes were verified by numerical simulations and explained by the reflection,and interference of electromagnetic waves at the graphene–SiO_(2) edge.The constructive interference at the graphene nanogap caused by charge accumulation was demonstrated for the first time.Using the infrared nanoimaging technique,greater plasmon broadening was observed in the zigzag edge than in the armchair edge.Our study suggests that graphene edges should be separated by an effective working distance to avoid the overlapping of localized plasmon modes,which is very important for the design of graphene-based plasmonic circuits and devices.
