On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Communication Architecture Design for Real-Time Networked Control Systems

Networked control over data networks has received increasing attention in recent years. Among many problems in networked control systems (NCSs) is the need to reduce control latency and jitter and to deal with packet dropouts. This paper introduces our recent progress on a queuing communication architecture for real-time NCS applications, and simple strategies for dealing with packet dropouts. Case studies for a middle-scale process or multiple small-scale processes are presented for TCP/IP based real-time NCSs. Variations of network architecture design are modelled, simulated, and analysed for evaluation of control latency and jitter performance. It is shown that a simple bandwidth upgrade or adding hierarchy does not necessarily bring benefits for performance improvement of control latency and jitter. A co-design of network and control is necessary to maximise the real-time control performance of NCSs

Accelerated computation of cyclic steady state for simulated-moving-bed processes

Industrial applications of the simulated-moving-bed (SMB) chromatographic technology have brought an emergent demand to improve the SMB process operation for higher efficiency and better robustness. Improved process modelling and more-efficient model computation will pave a path to meet this demand. However, the SMB unit operation exhibits complex dynamics, leading to challenges in SMB process modelling and model computation. One of the significant problems is how to quickly obtain the steady state of an SMB process model, as process metrics at the steady state are critical for process design and real-time control. The conventional computation method, which solves the process model cycle by cycle and takes the solution only when a cyclic steady state is reached after a certain number of switching, is computationally expensive. Adopting the concept of quasi-envelope (QE), this work treats the SMB operation as a pseudo-oscillatory process because of its large number of continuous switching. Then, an innovative QE computation scheme is developed to quickly obtain the steady state solution of an SMB model for any arbitrary initial condition. The QE computation scheme allows larger steps to be taken for predicting the slow change of the starting state within each switching. Incorporating with the wavelet-based technique, this scheme is demonstrated to be effective and efficient for an SMB sugar separation process. Moreover, investigations are also carried out on when the computation scheme should be activated and how the convergence of the scheme is affected by a variable stepsize.

A versatile and reliable two-component system for tissue-specific gene induction in Arabidopsis

Developmental progression and differentiation of distinct cell types depend on the regulation of gene expression in space and time. Tools that allow spatial and temporal control of gene expression are crucial for the accurate elucidation of gene function. Most systems to manipulate gene expression allow control of only one factor, space or time, and currently available systems that control both temporal and spatial expression of genes have their limitations. We have developed a versatile two-component system that overcomes these limitations, providing reliable, conditional gene activation in restricted tissues or cell types. This system allows conditional tissue-specific ectopic gene expression and provides a tool for conditional cell type- or tissue-specific complementation of mutants. The chimeric transcription factor XVE, in conjunction with Gateway recombination cloning technology, was used to generate a tractable system that can efficiently and faithfully activate target genes in a variety of cell types. Six promoters/enhancers, each with different tissue specificities (including vascular tissue, trichomes, root, and reproductive cell types), were used in activation constructs to generate different expression patterns of XVE. Conditional transactivation of reporter genes was achieved in a predictable, tissue-specific pattern of expression, following the insertion of the activator or the responder T-DNA in a wide variety of positions in the genome. Expression patterns were faithfully replicated in independent transgenic plant lines. Results demonstrate that we can also induce mutant phenotypes using conditional ectopic gene expression. One of these mutant phenotypes could not have been identified using noninducible ectopic gene expression approaches.

Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Raman spectroscopy of stercorite H(NH4)Na(PO4)•4H2O – a cave mineral from Petrogale Cave, Madura, Eucla, Western Australia

Raman spectroscopy complimented with infrared spectroscopy has been used to characterise the mineral stercorite H(NH4)Na(PO4)·4H2O. The mineral stercorite originated from the Petrogale Cave, Madura, Eucla, Western Australia. This cave is one of many caves in the Nullarbor Plain in the South of Western Australia. These caves have been in existence for eons of time and have been dated at more than 550 million years old. The mineral is formed by the reaction of bat guano chemicals on calcite substrates. A single Raman band at 920 cm−1 defines the presence of phosphate in the mineral. Antisymmetric stretching bands are observed in the infrared spectrum at 1052, 1097, 1135 and 1173 cm−1. Raman spectroscopy shows the mineral is based upon the phosphate anion and not the hydrogen phosphate anion. Raman and infrared bands are found and assigned to PO43−, H2O, OH and NH stretching vibrations. The detection of stercorite by Raman spectroscopy shows that the mineral can be readily determined; as such the application of a portable Raman spectrometer in a ‘cave’ situation enables the detection of minerals, some of which may remain to be identified.

High-pressure Raman spectroscopic and other structural studies of hydrotalcites containing intercalated dicarboxylic acid anions

The results of pressure-tuning Raman spectroscopic, X-ray powder diffraction and solid-state 13C-NMR studies of selected dicarboxylate anions intercalated in a Mg-Al layered double hydroxide (talcite) lattice are reported. The pressure dependences of the vibrational modes are linear for pressures up to 4.6 GPa indicating that no phase transitions occur. The interlayer spacings show that the oxalate, malonate and succinate dianions are oriented perpendicular to the layers, but the glutarate and adipate are tilted. The solid-state 13C-NMR spectra of these materials show full chemical shift anisotropy and, therefore, the anions are not mobile at room temperature.

Natural convection in attics subject to instantaneous and ramp cooling boundary conditions

A fundamental study of the fluid dynamics inside an attic shaped triangular enclosure with cold upper walls and adiabatic horizontal bottom wall is reported in this study. The transient behaviour of the attic fluid which is relevant to our daily life is examined based on a scaling analysis. The transient phenomenon begins with the instantaneous cooling and the cooling with linear decreases of temperature up to some specific time (ramp time) and then maintain constant of the upper sloped walls. It is shown that both inclined walls develop a thermal boundary layer whose thicknesses increase towards steady-state or quasi-steady values. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the cooling-down of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

Timeliness and Clinical Impact of Hospital-Initiated Medication Reviews

Background: Medication-related problems often occur in the immediate post-discharge period. To reduce medication misadventure the Commonwealth Government funds home medicines reviews (HMRs). HMRs are initiated when general practitioners refer consenting patients to their community pharmacists, who then engage accredited pharmacists to review patients' medicines in their homes. Aim: To determine if hospital-initiated medication reviews (HIMRs) can be implemented in a more timely manner than HMRs; and to assess the impact of a bespoke referral form with comorbidity-specific questions on the quality of reports. Method: Eligible medical inpatients at risk of medication misadventure were referred by the hospital liaison pharmacist to participating accredited pharmacists post-discharge from hospital. Social, demographic and laboratory data were collected from medical records and during interviews with consenting patients. Issues raised in the HIMR reports were categorised: intervention/action, information given or recommendation, and assigned a rank of clinical significance. Results: HIMRs were conducted within 11.6 6.6 days postdischarge. 36 HIMR reports were evaluated and 1442 issues identified - information given (n = 1204), recommendations made (n = 88) and actions taken (n = 150). The majority of issues raised (89%) had a minor clinical impact. The bespoke referral form prompted approximately half of the issues raised. Conclusion: HIMRs can be facilitated in a more timely manner than post-discharge HMRs. There was an associated positive clinical impact of issues raised in the HIMR reports.

High frequency of BRAF mutations in nevi

To evaluate the timing of mutations in BRAF (v-raf murine sarcoma viral oncogene homolog B1) during melanocytic neoplasia, we carried out mutation analysis on microdissected melanoma and nevi samples. We observed mutations resulting in the V599E amino-acid substitution in 41 of 60 (68%) melanoma metastases, 4 of 5 (80%) primary melanomas and, unexpectedly, in 63 of 77 (82%) nevi. These data suggest that mutational activation of the RAS/RAF/MAPK pathway in nevi is a critical step in the initiation of melanocytic neoplasia but alone is insufficient for melanoma tumorigenesis.

Vibrational spectroscopy of synthetic stercorite H(NH4)Na(PO4)•4H2O – a comparison with the natural cave mineral

In order to mimic the chemical reactions in cave systems, the analogue of the mineral stercorite H(NH4)Na(PO4)•4H2O has been synthesised. X-ray diffraction of the stercorite analogue matches the stercorite reference pattern. A comparison is made with the vibrational spectra of synthetic stercorite analogue and the natural Cave mineral. The mineral in nature is formed by the reaction of bat guano chemicals on calcite substrates. A single Raman band at 920 cm-1 (Cave) and 922 cm-1 (synthesised) defines the presence of hydrogen phosphate in the mineral. In the synthetic stercorite analogue, additional bands are observed and are attributed to the dihydrogen and phosphate anions. The vibrational spectra of synthetic stercorite only partly match that of the natural stercorite. It is suggested that natural stercorite is more pure than that of synthesised stercorite. Antisymmetric stretching bands are observed in the infrared spectrum at 1052, 1097, 1135 and 1173 cm-1. Raman spectroscopy shows the stercorite mineral is based upon the hydrogen phosphate anion and not the phosphate anion. Raman and infrared bands are found and assigned to PO43-, H2O, OH and NH stretching vibrations. Raman spectroscopy shows the synthetic analogue is similar to the natural mineral. A mechanism for the formation of stercorite is provided.