Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Formation and electron field emission of graphene films grown by hot filament chemical vapor deposition

Graphene films with different structures were catalytically grown on the silicon substrate pre-deposited with a gold film by hot filament chemical vapor deposition under different conditions, where methane, hydrogen and nitrogen were used as the reactive gases. The morphological and compositional properties of graphene films were studied using advanced instruments including field emission scanning electron microscopy, micro-Raman spectroscopy and X-ray photoelectron spectroscopy. The results indicate that the structure and composition of graphene films are changed with the variation of the growth conditions. According to the theory related to thermodynamics, the formation of graphene films was theoretically analyzed and the results indicate that the formation of graphene films is related to the fast incorporation and precipitation of carbon. The electron field emission (EFE) properties of graphene films were studied in a high vacuum system of ∼10-6 Pa and the EFE results show that the turn-on field is in a range of 5.2-5.64 V μm-1 and the maximum current density is about 63 μ A cm-2 at the field of 7.7 V μm-1. These results are important to control the structure of graphene films and have the potential applications of graphene in various nanodevices.

Carbon nanorods and graphene-like nanosheets by hot filament CVD : growth mechanisms and electron field emission

Carbon nanorods and graphene-like nanosheets are catalytically synthesized in a hot filament chemical vapor deposition system with and without plasma enhancement, with gold used as a catalyst. The morphological and structural properties of the carbon nanorods and nanosheets are investigated by field-emission scanning electron microscopy, transmission electron microscopy and micro-Raman spectroscopy. It is found that carbon nanorods are formed when a CH4 + H2 + N2 plasma is present while carbon nanosheets are formed in a methane environment without a plasma. The formation of carbon nanorods and carbon nanosheets are analyzed. The results suggest that the formation of carbon nanorods is primarily a precipitation process while the formation of carbon nanosheets is a complex process involving surface-catalysis, surface diffusion and precipitation influenced by the Gibbs–Thomson effect. The electron field emission properties of the carbon nanorods and graphene-like nanosheets are measured under high-vacuum; it is found that the carbon nanosheets have a lower field emission turn-on than the carbon nanorods. These results are important to improve the understanding of formation mechanisms of carbon nanomaterials and contribute to eventual applications of these structures in nanodevices.

Enhanced electron field emission from plasma-nitrogenated carbon nanotips

Nitrogenated carbon nanotips (NCNTPs) are synthesized by plasma-enhanced hot filament chemical vapor deposition from the hydrogen, methane, and nitrogen gas mixtures with different flow rate ratios of hydrogen to nitrogen. The morphological, structural, compositional, and electron field emission (EFE) properties of the NCNTPs were investigated by field emissionscanning electron microscopy, Raman spectroscopy, x ray photoelectron spectroscopy, and EFE high-vacuum system. It is shown that the NCNTPs deposited at an intermediate flow rate ratio of hydrogen to nitrogen feature the best size/shape and pattern uniformity, the highest nanotip density, the highest nitrogen concentration, as well as the best electron field emission performance. Several factors that come into play along with the nitrogen incorporation, such as the combined effect of the plasma sputtering and etching, the transition of sp 3carbon clusters to sp 2carbon clusters, the increase of the size of the sp 2 clusters, as well as the reduction of the work function, have been examined to interpret these experimental findings. Our results are highly relevant to the development of the next generation electron field emitters, flat panel displays, atomic force microscope probes, and several other advanced applications.

Structure- and composition-dependent electron field emission from nitrogenated carbon nanotips

The electron field emission (EFE) properties of nitrogenated carbon nanotips (NCNTPs) were studied under high-vacuum conditions. The NCNTPs were prepared in a plasma-assisted hot filament chemical vapor deposition system using CH4 and N2 as the carbon and nitrogen sources, respectively. The work functions of NCNTPs were measured using x-ray photoelectron spectroscopy. The morphological and structural properties of NCNTPs were studied by field emission scanning electron microscopy, micro-Raman spectroscopy, and x-ray photoelectron spectroscopy. The field enhancement factors of NCNTPs were calculated using relevant EFE models based on the Fowler-Nordheim approximation. Analytical characterization and modeling results were used to establish the relations between the EFE properties of NCNTPs and their morphology, structure, and composition. It is shown that the EFE properties of NCNTPs can be enhanced by the reduction of oxygen termination on the surface as well as by increasing the ratio of the NCNTP height to the radius of curvature at its top. These results also suggest that a significant amount of electrons is emitted from other surface areas besides the NCNTP tops, contrary to the common belief. The outcomes of this study advance our knowledge on the electron emission properties of carbonnanomaterials and contribute to the development of the next-generation of advanced applications in the fields of micro- and opto-electronics.

Idealised simulation of downburst winds

Convectively driven downburst winds pose a threat to structures and communities in many regions of Australia not subject to tropical cyclones. Extreme value analysis shows that for return periods of interest to engineering design these events produce higher gust wind speeds than synoptic scale windstorms. Despite this, comparatively little is known of the near ground wind structure of these potentially hazardous windstorms. With this in mind, a series of idealised three-dimensional numerical simulations were undertaken to investigate convective storm wind fields. A dry, non-hydrostatic, sub-cloud model with parameterisation of the microphysics was used. Simulations were run with a uniform 20 m horizontal grid resolution and a variable vertical resolution increasing from 1 m. A systematic grid resolution study showed further refinement did not alter the morphological structure of the outflow. Simulations were performed for stationary downbursts in a quiescent air field, stationary downbursts embedded within environmental boundary layer winds, and also translating downbursts embedded within environmental boundary layer winds.

Loading of a very tall building in a simulated downburst wind field

Thunderstorm downbursts are important for wind engineers as they have been shown to produce the design wind speeds for mid to high return periods in many regions of Australia [1]. In structural design codes (e.g. AS/NZS1170.02-02) an atmospheric boundary layer (ABL) is assumed, and a vertical profile is interpolated from recorded 10 m wind speeds. The ABL assumption is however inaccurate when considering the complex structure of a thunderstorm outflow, and its effects on engineered structures. Several researchers have shown that the downburst, close to its point of divergence is better represented by an impinging wall jet profile than the traditional ABL. Physical modelling is the generally accepted approach to estimate wind loads on structures and it is therefore important to physically model the thunderstorm downburst so that its effects on engineered structures may be studied. An advancement on the simple impinging jet theory, addressed here is the addition of a pulsing mechanism to the jet which allows not only the divergent characteristics of a downburst to be produced, but also it allows the associated leading ring vortex to be developed. The ring vortex modelling is considered very important for structural design as it is within the horizontal vortex that the largest velocities occur [2]. This paper discusses the flow field produced by a pulsed wall jet, and also discusses the induced pressures that this type of flow has on a scaled tall building.

Influence of jet inclination on structural loading in an experimentally simulated microburst

Steady and pulsed flow stationary impinging jets have been employed to simulate the wind field produced by a thunderstorm microburst. The effect on the low level wind field due to jet inclination with respect to the impingement surface has been studied. A single point velocity time history has been compared to the full-scale Andrews AFB microburst for model validation. It was found that for steady flow, jet inclination increased the radial extent of high winds but did not increase the magnitude of these winds when compared to the perpendicular impingement case. It was found that for inclined pulsed flow the design wind conditions could increase compared to perpendicular impingement. It was found that the location of peak winds was affected by varying the outlet conditions.

Enhancement of electron field emission of vertically aligned carbon nanotubes by nitrogen plasma treatment

The electron field emission (EFE) characteristics from vertically aligned carbon nanotubes (VACNTs) without and with treatment by the nitrogen plasma are investigated. The VACNTs with the plasma treatment showed a significant improvement in the EFE property compared to the untreated VACNTs. The morphological, structural, and compositional properties of the VACNTs are extensively examined by scanning electron microscopy, transmission electron microscopy, Raman spectroscopy, and energy dispersive X-ray spectroscopy. It is shown that the significant EFE improvement of the VACNTs after the nitrogen plasma treatment is closely related to the variation of the morphological and structural properties of the VACNTs. The high current density (299.6 μA/cm2) achieved at a low applied field (3.50 V/μm) suggests that the VACNTs after nitrogen plasma treatment can serve as effective electron field emission sources for numerous applications.