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.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

Asymptotic minimax robust and misspecified Lorden quickest change detection for dependent stochastic processes

The quick detection of an abrupt unknown change in the conditional distribution of a dependent stochastic process has numerous applications. In this paper, we pose a minimax robust quickest change detection problem for cases where there is uncertainty about the post-change conditional distribution. Our minimax robust formulation is based on the popular Lorden criteria of optimal quickest change detection. Under a condition on the set of possible post-change distributions, we show that the widely known cumulative sum (CUSUM) rule is asymptotically minimax robust under our Lorden minimax robust formulation as a false alarm constraint becomes more strict. We also establish general asymptotic bounds on the detection delay of misspecified CUSUM rules (i.e. CUSUM rules that are designed with post- change distributions that differ from those of the observed sequence). We exploit these bounds to compare the delay performance of asymptotically minimax robust, asymptotically optimal, and other misspecified CUSUM rules. In simulation examples, we illustrate that asymptotically minimax robust CUSUM rules can provide better detection delay performance at greatly reduced computation effort compared to competing generalised likelihood ratio procedures.

p-type doping of ZnO by means of high-density inductively coupled plasmas

A custom-designed inductively coupled plasma assisted radio-frequency magnetron sputtering deposition system has been used to fabricate N-doped p-type ZnO (ZnO:N) thin films on glass substrates from a sintered ZnO target in a reactive Ar + N2 gas mixture. X-ray diffraction and scanning electron microscopy analyses show that the ZnO:N films feature a hexagonal crystal structure with a preferential (002) crystallographic orientation and grow as vertical columnar structures. Hall effect and X-ray photoelectron spectroscopy analyses show that N-doped ZnO thin films are p-type with a hole concentration of 3.32 × 1018 cm- 3 and mobility of 1.31 cm2 V- 1 s- 1. The current-voltage measurement of the two-layer structured ZnO p-n homojunction clearly reveals the rectifying ability of the p-n junction. The achievement of p-type ZnO:N thin films is attributed to the high dissociation ability of the high-density inductively coupled plasma source and effective plasma-surface interactions during the growth process.

Aluminum-assisted crystallization and p-type doping of polycrystalline Si

Aluminum-doped p-type polycrystalline silicon thin films have been synthesized on glass substrates using an aluminum target in a reactive SiH 4+Ar+H2 gas mixture at a low substrate temperature of 300∈°C through inductively coupled plasma-assisted RF magnetron sputtering. In this process, it is possible to simultaneously co-deposit Si-Al in one layer for crystallization of amorphous silicon, in contrast to the conventional techniques where alternating metal and amorphous Si layers are deposited. The effect of aluminum target power on the structural and electrical properties of polycrystalline Si films is analyzed by X-ray diffraction, Raman spectroscopy, scanning electron microscopy and Hall-effect analysis. It is shown that at an aluminum target power of 100 W, the polycrystalline Si film features a high crystalline fraction of 91%, a vertically aligned columnar structure, a sheet resistance of 20.2 kΩ/□ and a hole concentration of 6.3×1018 cm-3. The underlying mechanism for achieving the semiconductor-quality polycrystalline silicon thin films at a low substrate temperature of 300∈°C is proposed.

Diffusivity of adatoms on plasma-exposed surfaces determined from the ionization energy approximation and ionic polarizability

Microscopic surface diffusivity theory based on atomic ionization energy concept is developed to explain the variations of the atomic and displacement polarizations with respect to the surface diffusion activation energy of adatoms in the process of self-assembly of quantum dots on plasma-exposed surfaces. These polarizations are derived classically, while the atomic polarization is quantized to obtain the microscopic atomic polarizability. The surface diffusivity equation is derived as a function of the ionization energy. The results of this work can be used to fine-tune the delivery rates of different adatoms onto nanostructure growth surfaces and optimize the low-temperature plasma based nanoscale synthesis processes.

Heating mechanism of self-interaction of surface polaritons at n-type semiconductor-metal interface

The influence of electron heating in the high-frequency surface polariton (SP) field on the dispersion properties of the SPs considered is investigated. High frequency SPs propagate at the interface between an n-type semiconductor with finite electron pressure, and a metal. The nonlinear dispersion relation for the SPs is derived and investigated.

Self-interaction of surface polaritons at the narrow-gap n-type semiconductor metal interface

The non-linear self-interaction of the potential surface polaritons (SP) which is due to the free carriers dispersion law where nonparabolicity is studied. The SP propagate at the interface between n-type semiconductor and a metal. The self interaction of the SP is shown to be different in semiconductors with normal and inverse zone structures. The results of the SP field envelope evolution are given. The obtained nonlinear frequency shift has been compared with shifts which are due to another self-interaction mechanisms. This comparison shows that the nonlinear self-interaction mechanism, which is due to free carriers spectrum nonparabolicity, is especially significant in narrow-gap semiconductor materials.

Controlling current and voltage type interfaces in power-hardware-in-the-loop simulations

The usual practice to study a large power system is through digital computer simulation. However, the impact of large scale use of small distributed generators on a power network cannot be evaluated strictly by simulation since many of these components cannot be accurately modelled. Moreover, the network complexity makes the task of practical testing on a physical network nearly impossible. This study discusses the paradigm of interfacing a real-time simulation of a power system to real-life hardware devices. This type of splitting a network into two parts and running a real-time simulation with a physical system in parallel is usually termed as power-hardware-in-the-loop (PHIL) simulation. The hardware part is driven by a voltage source converter that amplifies the signals of the simulator. In this paper, the effects of suitable control strategy on the performance of PHIL and the associated stability aspects are analysed in detail. The analyses are validated through several experimental tests using an real-time digital simulator.

Two-channel waveguide modulator based on surface wave propagating in a semiconductor-metal thin-film structure

The results of theoretical investigations of two-channel waveguide modulator based on Surface Wave (SW) propagation are presented. The structure studied consists of two n-type semiconductor waveguide channels separated from each other by a dielectric gap and coated by a metal. The SW propagates at the semiconductor-metal interface across an external magnetic field which is parallel to the interface. An external dc voltage is applied to the metal surface of one channel to provide a small phase shift between two propagating modes. In a coupled mode approximation, two possible regimes of operation of the structure, namely as a directional coupler and as an electro-optical modulator, are considered. Our results suggest new applications in millimeter and submillimeter wave solid-state electronics and integrated optics.

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.

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.

Development and evaluation of the Ontrack Diabetes Program : an automated, web-based type 2 diabetes self-management and dysphoria intervention

This research was conducted in the area of Clinical and Health Psychology. The study involved the development and evaluation of a novel, web-based program aimed to improve Type 2 diabetes self-management and mood. The program was developed as an original technological intervention aimed to improve access to support for rural and remote communities, and is currently being trialled across Australia with a larger sample size. The researcher aims to continue research into the field of clinical psychology, and in particular is interested in working on further interventions to support those with comorbid physical and mental health conditions.

Functional role for senataxin, defective in ataxia oculomotor apraxia type 2, in transcriptional regulation

Ataxia oculomotor apraxia type 2 (AOA2) is an autosomal recessive neurodegenerative disorder characterized by cerebellar ataxia and oculomotor apraxia. The gene mutated in AOA2, SETX, encodes senataxin, a putative DNA/RNA helicase which shares high homology to the yeast Sen1p protein and has been shown to play a role in the response to oxidative stress. To investigate further the function of senataxin, we identified novel senataxin-interacting proteins, the majority of which are involved in transcription and RNA processing, including RNA polymerase II. Binding of RNA polymerase II to candidate genes was significantly reduced in senataxin deficient cells and this was accompanied by decreased transcription of these genes, suggesting a role for senataxin in the regulation/modulation of transcription. RNA polymerase II-dependent transcription termination was defective in cells depleted of senataxin in keeping with the observed interaction of senataxin with poly(A) binding proteins 1 and 2. Splicing efficiency of specific mRNAs and alternate splice-site selection of both endogenous genes and artificial minigenes were altered in senataxin depleted cells. These data suggest that senataxin, similar to its yeast homolog Sen1p, plays a role in coordinating transcriptional events, in addition to its role in DNA repair.

The impact of diabetic ketoacidosis and age on behavior six months post-diagnosis in children with type 1 diabetes

Objectives: Children with type 1 diabetes mellitus (DM1) may be at increased risk of psychosocial and adjustment difficulties. We examined behavioral outcomes six months post-diagnosis in a group of children with newly diagnosed DM1. Methods: This study formed part of a larger longitudinal project examining pathophysiology and neuropsychological outcomes in diabetic patients with or without diabetic ketoacidosis (DKA). Participants were 61 children (mean age 11.8 years, SD 2.7 years) who presented with a new diagnosis of DM1 at the Royal Children’s Hospital, Melbourne. Twenty-three (11 female) presented in DKA and 38 (14 female) without DKA. Parents completed the behavior assessment system for children, second edition six months post-diagnosis. Results: There was a non-linear relationship between age and behavior. Internalising problems (i.e. anxiety depression, withdrawal) peaked in the transition from childhood to adolescence; children aged 10–13 years had elevated rates relative to the normal population (t = 2.55, P = 0.018). There was a non-significant trend for children under 10 to display internalising problems (P = 0.052), but rates were not elevated in children over 13 (P = 0.538). Externalising problems were not significantly elevated in any age group. Interestingly, children who presented in DKA were at lower risk of internalising problems than children without DKA (t = 3.83, P < 0.001). There was no effect of DKA on externalising behaviors. Conclusions: Children transitioning from childhood to adolescence are at significant risk for developing internalising problems such as anxiety and lowered mood after diagnosis of DM1. Somewhat counter-intuitively, parents of children presenting in DKA reported fewer internalising symptoms than parents of children without DKA. These results highlight the importance of monitoring and supporting psychosocial adjustment in newly diagnosed children even when they seem physically well.