A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.     

Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.     

Interference effects in 157 nm laser ablated cones in polycarbonate and application to spatial coherence measurement

Conical structures formed in 157 nm laser-ablated polycarbonate exhibit a well-defined fringe structure with a period of a few 100 nm surrounding the cone base. Experiments and modelling studies of the interference produced by these micro-conical mirrors are shown to provide a means of measuring the spatial coherence of the highly multi-mode 157 nm laser.     

A Two-Layer Model for Superposed Electrified Maxwell Fluids in Presence of Heat Transfer

Based on a modified-Darcy-Maxwell model, two-dimensional, incompressible and heat transfer flow of two bounded layers, through electrified Maxwell fluids in porous media is performed. The driving force for the instability under an electric field, is an electrostatic force exerted on the free charges accumulated at the dividing interface. Normal mode analysis is considered to study the linear stability of the disturbances layers. The solutions of thelinearized equations of motion with the boundary conditions lead to an implicit dispersion relation between the growth rate and wave number. These equations are parameterized by Weber number, Reynolds number, Marangoni number, dimensionless conductivities, and dimensionless electric potentials. The case of long waves interfacial stability has been studied. The stability criteria are performed theoretically in which stability diagrams are obtained. Inthe limiting cases, some previously published results can be considered as particular cases of our results. It is found that the Reynolds number plays a destabilizing role in the stability criteria, while the damping influence is observed for the increasing of Marangoni number and Maxwell relaxation time.     

Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

The effect of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane is analyzed using linear and non-linear stability analysis in the long wave limit. The principle aim of this study is to illustrate the influence of electric field on the non-linear stability of a thin liquid layer flow down incline substrate when the plane is porous. The driving force for the instability under an electric field is an electrostatic force exerted on the free charges accumulated at the dividing interface. The coupled non-linear evolution equations for the local film thickness and the interfacial charge for two-dimensional disturbances are derived to analyze the effect of long-wave instabilities. The method of multiple scales is applied to obtain approximate solutions and analyze the stability criteria. Numerical simulations of this system of non-linear evolution equations are performed. It is found that the permeability parameter as well as the inclination of the plane plays a destabilizing role in the stability criteria, while the damping influence is observed for increasing of the electrical conductivity in both linear and non-linear behavior.     

Tualang Honey: A Decade of Neurological Research

Tualang honey has been shown to protect against neurodegeneration, leading to improved memory/learning as well as mood. In addition, studies have also demonstrated its anti-inflammatory and antioxidant properties. However, a substantial part of this research lacks systematization, and there seems to be a tendency to start anew with every study. This review presents a decade of research on Tualang honey with a particular interest in the underlying mechanisms related to its effects on the central nervous system. A total of 28 original articles published between 2011 and 2020 addressing the central nervous system (CNS) effects of Tualang honey were analysed. We identified five main categories, namely nootropic, antinociceptive, stress-relieving, antidepressant, and anxiolytic effects of Tualang honey, and proposed the underlying mechanisms. The findings from this review may potentially be beneficial towards developing new therapeutic roles for Tualang honey and help in determining how best to benefit from this brain supplement.     

Oxide semiconductors for solar to chemical energy conversion: nanotechnology approach

The present work considers the application of oxide semiconductors in the conversion of solar energy into the chemical energy required for water purification (removal of microbial cells and toxic organic compounds from water) and the generation of solar hydrogen fuel by photoelectrochemical water splitting. The first part of this work considers the concept of solar energy conversion by oxide semiconductors and the key performance-related properties, including electronic structure, charge transport, flat band potential and surface properties, which are responsible to the reactivity and photoreactivity of oxides with water. The performance of oxide systems for solar energy conversion is briefly considered in terms of an electronic factor. The progress of research in the formation of systems with high performance is considered in terms of specific aspects of nanotechnology, leading to the formation of systems with high performance. The nanotechnology approach in the development of high-performance photocatalysts is considered in terms of the effect of surface energy associated with the formation of nanostructured system on the formation of surface structures that exhibit outstanding properties. The unresolved problems that should be tackled in better understanding of the effect of nanostructures on properties and performance of oxide semiconductors in solar energy conversion are discussed. This part is summarised by a list of unresolved problems of crucial importance in the formation of systems with enhanced performance. This work also formulates the questions that must be addressed in order to overcome the hurdles in the formation of oxide semiconductors with high performance in water purification and the generation of solar fuel. The research strategy in the development of oxide systems with high performance, including photocatalysts for solar water purification and photoelectrodes for photoelectrochemical water splitting, is considered. The considerations are focused on the systems based on titanium dioxide of different defect disorder as well as its solid solutions and composites.     

金属圆柱腔体中使用非均一背景增强微波断层成像

针对基于圆柱金属腔体的微波断层成像系统,提出了一种利用非均一背景增强系统获取目标信息能力的方法.该方法通过在腔体内放置已知物体构成非均一背景,这样不但能利用背景的先验信息,而且可以增加等效辐射源对目标进行探测.首先,利用矩量法计算圆柱金属腔体内非均一背景的格林函数和离散积分算子,并对离散积分算子进行奇异值谱和条件数分析,在理论上证明该方法的可行性;然后,利用基于有限元的对比源逆成像法对均一背景、有耗非均一背景和无耗非均一背景三种情况进行仿真研究;最后对仿真结果进行了误差分析和比较.仿真结果表明,该方法可以提高反演收敛速度和结果准确度,有耗非均一背景略优于无耗非均一背景.该方法可以在不改变硬件系统和算法的情况下得到更准确的反演结果,可应用于医学成像与工业无损探测.