The post-processed Galerkin method applied to non-linear shell vibrations

We present the results of a computational study of the post-processed Galerkin methods put forward by Garcia-Archilla et al. applied to the non-linear von Karman equations governing the dynamic response of a thin cylindrical panel periodically forced by a transverse point load. We spatially discretize the shell using finite differences to produce a large system of ordinary differential equations (ODEs). By analogy with spectral non-linear Galerkin methods we split this large system into a 'slowly' contracting subsystem and a 'quickly' contracting subsystem. We then compare the accuracy and efficiency of (i) ignoring the dynamics of the 'quick' system (analogous to a traditional spectral Galerkin truncation and sometimes referred to as 'subspace dynamics' in the finite element community when applied to numerical eigenvectors), (ii) slaving the dynamics of the quick system to the slow system during numerical integration (analogous to a non-linear Galerkin method), and (iii) ignoring the influence of the dynamics of the quick system on the evolution of the slow system until we require some output, when we 'lift' the variables from the slow system to the quick using the same slaving rule as in (ii). This corresponds to the post-processing of Garcia-Archilla et al. We find that method (iii) produces essentially the same accuracy as method (ii) but requires only the computational power of method (i) and is thus more efficient than either. In contrast with spectral methods, this type of finite-difference technique can be applied to irregularly shaped domains. We feel that post-processing of this form is a valuable method that can be implemented in computational schemes for a wide variety of partial differential equations (PDEs) of practical importance.

Compliant shell mechanisms.

This paper describes a class of lightweight structures known as compliant shell mechanisms. These are novel reconfigurable solutions for advanced structures, such as morphing shells and deployable membranes. They have local, discrete corrugations, which articulate and deform to achieve dramatic changes in the overall shape of the shell. The unique kinematics are considered by highlighting examples and by performing analysis using established and novel concepts, and favourable predictions of shape compared with laboratory models are demonstrated.

Photovoltaic measurements in carbon nanotube - Amorphous silicon core/shell nanowire

Carbon nanotube is one of the promising materials for exploring new concepts in solar energy conversion and photon detection. Here, we report the first experimental realization of a single core/shell nanowire photovoltaic device (2-4μm) based on carbon nanotube and amorphous silicon. Specifically, a multi-walled carbon nanotube (MWNTs) was utilized as the metallic core, on which n-type and intrinsic amorphous silicon layers were coated. A Schottky junction was formed by sputtering a transparent conducting indium-tin-oxide layer to wrap the outer shell of the device. The single coaxial nanowire device showed typical diode ratifying properties with turn-on voltage around 1V and a rectification ratio of 104 when biased at ±2V. Under illumination, it gave an open circuit voltage of ∼0.26V. Our study has shown a simple and useful platform for gaining insight into nanowire charge transport and collection properties. Fundamental studies of such nanowire device are important for improving the efficiency of future nanowire solar cells or photo detectors. © 2012 IEEE.

Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Elastic properties of crystalline-amorphous core-shell silicon nanowires

The pressure behavior of Raman frequencies and line widths of crystalline core-amorphous shell silicon nanowires (SiNWs) with two different core-to-shell ratio thicknesses was studied at pressures up to 8 GPa. The obtained isothermal compressibility (bulk modulus) of SiNWs with a core-to-shell ratio of about 1.8 is ∼20% higher (lower) than reported values for bulk Si. For SiNWs with smaller core-to-shell ratios, a plastic deformation of the shell was observed together with a strain relaxation. A significant increase in the full width at half-maximum of the Raman LTO-peak due to phonon decay was used to determine the critical pressure at which LTO-phonons decay into LO + TA phonons. Our results reveal that this critical pressure in strained core-shell SiNWs (∼4 GPa) is different from the reported value for bulk Si (∼7 GPa), whereas no change is observed for relaxed core-shell SiNWs. © 2013 American Chemical Society.

Carrier lifetime and mobility enhancement in nearly defect-free core-shell nanowires measured using time-resolved terahertz spectroscopy.

We have used transient terahertz photoconductivity measurements to assess the efficacy of two-temperature growth and core-shell encapsulation techniques on the electronic properties of GaAs nanowires. We demonstrate that two-temperature growth of the GaAs core leads to an almost doubling in charge-carrier mobility and a tripling of carrier lifetime. In addition, overcoating the GaAs core with a larger-bandgap material is shown to reduce the density of surface traps by 82%, thereby enhancing the charge conductivity.

Defect-free GaAs/AlGaAs Core-shell nanowires on Si substrates

We report straight and vertically aligned defect-free GaAs nanowires grown on Si(111) substrates by metal-organic chemical vapor deposition. By deposition of thin GaAs buffer layers on Si substrates, these nanowires could be grown on the buffer layers with much less stringent conditions as otherwise imposed by epitaxy of III-V compounds on Si. Also, crystal-defect-free GaAs nanowires were grown by using either a two-temperature growth mode consisting of a short initial nucleation step under higher temperature followed by subsequent growth under lower temperature or a rapid growth rate mode with high source flow rate. These two growth modes not only eliminated planar crystallographic defects but also significantly reduced tapering. Core-shell GaAs-AlGaAs nanowires grown by the two-temperature growth mode showed improved optical properties with strong photoluminescence and long carrier life times. © 2011 American Chemical Society.

Structural and optical characterization of vertical GaAs/GaP core-shell nanowires grown on Si substrates

GaAs nanowires were grown on Si (111) substrates. By coating a thin GaAs buffer layer on Si surface and using a two-temperature growth, the morphology and crystal structure of GaAs nanowires were dramatically improved. The strained GaAs/GaP core-shell nanowires, based on the improved GaAs nanowires with a shell thickness of 25 nm, showed a significant shift in emission energy of 260 meV from the unstrained GaAs nanowires. © 2010 IEEE.

The rhythm of fountains: The length and time scales of rise height fluctuations at low and high Froude numbers

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 ≤ Fr 0 ≤ 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr 0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Strtop, based on experimental measures of the fountain top, defined such that Strtop = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- Fr 0 fountains we find Strtop ≈ 0. 9. © 2013 Cambridge University Press.