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.

Examples illustrating the use of renormalization techniques for singularly perturbed differential equations

With nine examples, we seek to illustrate the utility of the Renormalization Group approach as a unification of other asymptotic and perturbation methods.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

Plasma-enabled, catalyst-free growth of carbon nanotubes on mechanically-written Si features with arbitrary shape

Simple, rapid, catalyst-free synthesis of complex patterns of long, vertically aligned multiwalled carbon nanotubes, strictly confined within mechanically-written features on a Si(1 0 0) surface is reported. It is shown that dense arrays of the nanotubes can nucleate and fully fill the features when the low-temperature microwave plasma is in a direct contact with the surface. This eliminates additional nanofabrication steps and inevitable contact losses in applications associated with carbon nanotube patterns. Using metal catalyst has long been considered essential for the nucleation and growth of surface-supported carbon nanotubes (CNTs) [1] and [2]. Only very recently, the possibility of CNT growth using non-metallic (e.g., oxide [3] and SiC [4]) catalysts or artificially created carbon-enriched surface layers [5] has been demonstrated. However, successful integration of carbon nanostructures into Si-based nanodevice platforms requires catalyst-free growth, as the catalyst nanoparticles introduce contact losses, and their catalytic activity is very difficult to control during the growth [6]. Furthermore, in many applications in microfluidics, biological and molecular filters, electronic, sensor, and energy conversion nanodevices, the CNTs need to be arranged in specific complex patterns [7] and [8]. These patterns need to contain the basic features (e.g., lines and dots) written using simple procedures and fully filled with dense arrays of high-quality, straight, yet separated nanotubes. In this paper, we report on a completely metal or oxide catalyst-free plasma-based approach for the direct and rapid growth of dense arrays of long vertically-aligned multi-walled carbon nanotubes arranged into complex patterns made of various combinations of basic features on a Si(1 0 0) surface written using simple mechanical techniques. The process was conducted in a plasma environment [9] and [10] produced by a microwave discharge which typically generates the low-temperature plasmas at the discharge power below 1 kW [11]. Our process starts from mechanical writing (scribing) a pattern of arbitrary features on pre-treated Si(1 0 0) wafers. Before and after the mechanical feature writing, the Si(1 0 0) substrates were cleaned in an aqueous solution of hydrofluoric acid for 2 min to remove any possible contaminations (such as oil traces which could decompose to free carbon at elevated temperatures) from the substrate surface. A piece of another silicon wafer cleaned in the same way as the substrate, or a diamond scriber were used to produce the growth patterns by a simple arbitrary mechanical writing, i.e., by making linear scratches or dot punctures on the Si wafer surface. The results were the same in both cases, i.e., when scratching the surface by Si or a diamond scriber. The procedure for preparation of the substrates did not involve any possibility of external metallic contaminations on the substrate surface. After the preparation, the substrates were loaded into an ASTeX model 5200 chemical vapour deposition (CVD) reactor, which was very carefully conditioned to remove any residue contamination. The samples were heated to at least 800 °C to remove any oxide that could have formed during the sample loading [12]. After loading the substrates into the reactor chamber, N2 gas was supplied into the chamber at the pressure of 7 Torr to ignite and sustain the discharge at the total power of 200 W. Then, a mixture of CH4 and 60% of N2 gases were supplied at 20 Torr, and the discharge power was increased to 700 W (power density of approximately 1.49 W/cm3). During the process, the microwave plasma was in a direct contact with the substrate. During the plasma exposure, no external heating source was used, and the substrate temperature (∼850 °C) was maintained merely due to the plasma heating. The features were exposed to a microwave plasma for 3–5 min. A photograph of the reactor and the plasma discharge is shown in Fig. 1a and b.

Data collection techniques

The objective of this chapter is to provide an overview of traffic data collection that can and should be used for the calibration and validation of traffic simulation models. There are big differences in availability of data from different sources. Some types of data such as loop detector data are widely available and used. Some can be measured with additional effort, for example, travel time data from GPS probe vehicles. Some types such as trajectory data are available only in rare situations such as research projects.

Evaluation of resonant damping techniques for Z-source current-type inverter

For the renewable energy sources whose outputs vary continuously, a Z-source current-type inverter has been proposed as a possible buck-boost alternative for grid-interfacing. With a unique X-shaped LC network connected between its dc power source and inverter topology, Z-source current-type inverter is however expected to suffer from compounded resonant complications in addition to those associated with its second-order output filter. To improve its damping performance, this paper proposes the careful integration of Posicast or three-step compensators before the inverter pulse-width modulator for damping triggered resonant oscillations. In total, two compensators are needed for wave-shaping the inverter boost factor and modulation ratio, and they can conveniently be implemented using first-in first-out stacks and embedded timers of modern digital signal processors widely used in motion control applications. Both techniques are found to damp resonance of ac filter well, but for cases of transiting from current-buck to boost state, three-step technique is less effective due to the sudden intermediate discharging interval introduced by its non-monotonic stepping (unlike the monotonic stepping of Posicast damping). These findings have been confirmed both in simulations and experiments using an implemented laboratory prototype.

A linear-elastic model of anisotropic tumour growth

This paper examines the effect of anisotropic growth on the evolution of mechanical stresses in a linear-elastic model of a growing, avascular tumour. This represents an important improvement on previous linear-elastic models of tissue growth since it has been shown recently that spatially-varying isotropic growth of linear-elastic tissues does not afford the necessary stress-relaxation for a steady-state stress distribution upon reaching a nutrient-regulated equilibrium size. Time-dependent numerical solutions are developed using a Lax-Wendroff scheme, which show the evolution of the tissue stress distributions over a period of growth until a steady-state is reached. These results are compared with the steady-state solutions predicted by the model equations, and key parameters influencing these steady-state distributions are identified. Recommendations for further extensions and applications of this model are proposed.

Contactless and replaceable modularized battery energy storage system for electric vehicles

A novel replaceable, modularized energy storage system with wireless interface is proposed for a battery operated electric vehicle (EV). The operation of the proposed system is explained and analyzed with an equivalent circuit and an averaged state-space model. A non-linear feedback linearization based controller is developed and implemented to regulate the DC link voltage by modulating the phase shift ratio. The working and control of the proposed system is verified through simulation and some preliminary results are presented.

Surface reconstruction of wheat leaf morphology from three-dimensional scanned data

Realistic virtual models of leaf surfaces are important for a number of applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be sufficiently smooth to facilitate the use of the mathematical equations that govern the motion of the droplet. While an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat leaves that tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.

Non-invasive techniques for imaging in-vivo human corneal sub basal nerve mapping and migration rate in diabetic neuropathy

Purpose Corneal confocal microscopy (CCM) is a rapid non-invasive ophthalmic technique, which has been shown to diagnose and stratify the severity of diabetic neuropathy. Current morphometric techniques assess individual static images of the subbasal nerve plexus; this work explores the potential for non-invasive assessment of the wide-field morphology and dynamic changes of this plexus in vivo. Methods In this pilot study, laser scanning CCM was used to acquire maps (using a dynamic fixation target and semi-automated tiling software) of the central corneal sub-basal nerve plexus in 4 diabetic patients with and 6 without neuropathy and in 2 control subjects. Nerve migration was measured in an additional 7 diabetic patients with neuropathy, 4 without neuropathy and in 2 control subjects by repeating a modified version of the mapping procedure within 2-8 weeks, thus facilitating re-identification of distinctive nerve landmarks in the 2 montages. The rate of nerve movement was determined from these data and normalised to a weekly rate (µm/week), using customised software. Results Wide-field corneal nerve fibre length correlated significantly with the Neuropathy Disability Score (r = -0.58, p < 0.05), vibration perception (r = -0.66, p < 0.05) and peroneal conduction velocity (r = 0.67, p < 0.05). Central corneal nerve fibre length did not correlate with any of these measures of neuropathy (p > 0.05 for all). The rate of corneal nerve migration was 14.3 ± 1.1 µm/week in diabetic patients with neuropathy, 19.7 ± 13.3µm/week in diabetic patients without neuropathy, and 24.4 ± 9.8µm/week in control subjects; however, these differences were not significantly different (p = 0.543). Conclusions Our data demonstrate that it is possible to capture wide-field images of the corneal nerve plexus, and to quantify the rate of corneal nerve migration by repeating this procedure over a number of weeks. Further studies on larger sample sizes are required to determine the utility of this approach for the diagnosis and monitoring of diabetic neuropathy.

Grading : A Workbook of Manual Land Grading Techniques [Revised Edition]

Grading is basic to the work of Landscape Architects concerned with design on the land. Gradients conducive to easy use, rainwater drained away, and land slope contributing to functional and aesthetic use are all essential to the amenity and pleasure of external environments. This workbook has been prepared specifically to support the program of landscape construction for students in Landscape Architecture. It is concerned primarily with the technical design of grading rather than with its aesthetic design. It must be stressed that the two aspects are rarely separate; what is designed should be technically correct and aesthetically pleasing - it needs to look good as well as to function effectively. This revised edition contains amended and new content which has evolved out of student classes and discussion with colleagues. I am pleased to have on record that every delivery of this workbook material has resulted in my own better understanding of grading and the techniques for its calculation and communication.

Simulation study for analysis of online dielectric measurement problems on transformer insulation system

Determining the condition as well as the remaining life of an insulation system is essential for the reliable operation of large oil-filled power transformers. Frequency-domain spectroscopy (FDS) is one of the diagnostic techniques used to identify the dielectric status of a transformer. Currently, this technique can only be implemented on a de-energized transformer. This paper presents an initial investigation into a novel online monitoring method based on FDS dielectric measurements for transformers. The proposed technique specifically aims to address the real operational constraints of online testing. This is achieved by designing an online testing model extending the basic “extended Debye” linear dielectric model and taking unique noise issues only experienced during online measurements into account via simulations. Approaches to signal denoising and potential problems expected to be encountered during online measurements will also be discussed. Using fixed-frequency sinusoidal excitation waveforms will result in a long measurement times. The use of alternatives such as a chirp has been investigated using simulations. The results presented in the paper predict that reliable measurements should be possible during online testing.

The sideways hourglass : establishing the lemniscate as a narrative structure for writing and reading non-linear stories

This thesis is a study in narratology that examines the pre-theoretical ideas that underlie the study of narrative and time. The thesis explores how the lemniscate can be transported from geometry to narrative in order to structure a non-linear story that breaks the rules of causality and chronology by coupling physical movement through space with the backward pull of memory. The findings offer new possibilities for understanding the nexus between shape and story and for recording non-linear narratives that are marked by simultaneity, counterpoint, and reversal.

Pipeline renewal decision support : a case study using LinEAR in a water pipeline network

This paper presents a case study for the application of a Linear Engineering Asset Renewal decision support software tool (LinEAR) at a water distribution network in Australia. This case study examines how the LinEAR can assist water utilities to minimise their total pipeline management cost, to make a long-term budget based on mathematically predicted expenditure, and to present calculated evidence for supporting their expenditure requirements. The outcomes from the study on pipeline renewal decision support demonstrate that LinEAR can help water utilities to improve the decision process and save renewal costs over a long-term by providing an optimum renewal schedules. This software can help organisation to accumulate technical knowledge and prediction future impact of the decision using what-if analysis.

A non-linear interface element model for thin layer high adhesive mortared masonry

A nonlinear interface element modelling method is formulated for the prediction of deformation and failure of high adhesive thin layer polymer mortared masonry exhibiting failure of units and mortar. Plastic flow vectors are explicitly integrated within the implicit finite element framework instead of relying on predictor–corrector like approaches. The method is calibrated using experimental data from uniaxial compression, shear triplet and flexural beam tests. The model is validated using a thin layer mortared masonry shear wall, whose experimental datasets are reported in the literature and is used to examine the behaviour of thin layer mortared masonry under biaxial loading.