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Numerical Studies on the Approximation of Horizontal Diffusion using Sigma Coordinate System
Jong Wook Lee,Michael D. Teubner,John B. Nixon,Yong-Sik Cho 대한토목학회 2006 KSCE journal of civil engineering Vol.10 No.2
In this paper, horizontal diffusion using sigma coordinates was examined numerically. To transform the horizontal diffusion equation, the chain rule was applied twice resulting in extra terms that are cumbersome to treat computationally. Two published direct modifications to the transformed equation were chosen, and numerical solutions using these modified equations are compared to those using the fully transformed equation. Our numerical studies have shown that only the fully transformed equation produces realistic solutions.
Kim, Jayeong,Glier, Tomke E.,Grimm-Lebsanft, Benjamin,Buchenau, Sö,ren,Teubner, Melissa,Biebl, Florian,Kim, Nam-Jung,Kim, Heehun,Yi, Gyu-Chul,Rü,bhausen, Michael,Yoon, Seokhyun American Chemical Society 2019 The Journal of Physical Chemistry Part C Vol.123 No.40
<P>We studied surface-enhanced Raman spectroscopy (SERS) in 4-mercaptopyridine (4-Mpy) deposited on zinc oxide (ZnO) nanostructures, by using resonance Raman scattering covering a range of incident photon energies from 1.7 to 5.7 eV. We investigated all primary routes of the energy-specific resonances that are associated with the electronic transitions between the ZnO valence band (VB) to the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) to the ZnO conduction band (CB), respectively. Two resonances at 5.55 and 5.15 eV in the ultraviolet (UV) spectral range can be associated with transitions into the CB and most importantly into an excitonic-related state below the ZnO CB, respectively. The energy difference between the UV resonances is 0.4 eV corresponding to the excitonic binding energy as a result of excitonic quantum confinement in the 10-20 nm thick ZnO nanowalls. The observed excitonic SERS resonance enhancement of the ring-breathing mode of 4-Mpy is about 15 times stronger than for the VB resonance observed at 2.43 eV and free of luminescence background. Hence, we outline new pathways of improving the detectability of molecules by chemical SERS due to tuning of the quantum confinement in the excitonic resonance enhancement.</P> [FIG OMISSION]</BR>