Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

The effect of Yb addition in bi2sr2ca 1-xybxcu2oy partial melted thick films

To study the phase relations in the Bi-2212 and Yb2O3 system, Bi2Sr2Ca1-xYbxCu 2Oy thick films are prepared by partial melt processing via an intermediate reaction between Bi-2212 and Yb2O3. When Bi-2212 and Yb2O3 are partially melted and then slowly cooled, solid solutions of Bi2Sr2Ca 1-xYbxCu2Oy, form by reactions between liquid and solid phases which contain Yb. Following these reactions, Ca is partially replaced in Bi-2212 matrix and participates in the formation of secondary phases, such as Bi-free, (Ca, Sr)Ox and CaO. Variation of the Bi-2212-Yb2O3 ratios and processing parameters changes the balance between the phases and leads to different Yb:Ca ratios in the Bi-2212 matrix of processed thick films. When the partial melting process is optimized for each sample to minimize the growth of secondary phases, x = 0.42-0.46 for the samples prepared at pO2 = 0.01 atm, x = 0.24-0.29 for the samples prepared at pO2 = 0.21 atm, x = 0.18-0.23 for the samples prepared at pO2 = 0.99 atm are obtained regardless to the starting compositions. It is found that superconducting properties of Bi 2Sr2Ca1-xYbxCu2O y thick films strongly depend on the processing conditions, because the conditions result in different Yb content in the Bi-2212 matrix and the volume fraction of the secondary phases. The highest Tc(0) of 77, 90 and 91 K were obtained for the samples processed at 0.01, 0.21 and 0.99 atm of O2, respectively.

Magnetic flux analysis in superconducting Fault Current Limiters under short-circuit conditions

In order to obtain a more compact Superconducting Fault Current limiter (SFCL), a special geometry of core and AC coil is required. This results in a unique magnetic flux pattern which differs from those associated with conventional round core arrangements. In this paper the magnetic flux density within a Fault Current Limiter (FCL) is described. Both experimental and analytical approaches are considered. A small scale prototype of an FCL was constructed in order to conduct the experiments. This prototype comprises a single phase. The analysis covers both the steady state and the short-circuit condition. Simulation results were obtained using commercial software based on the Finite Element Method (FEM). The magnetic flux saturating the cores, leakage magnetic flux giving rise to electromagnetic forces and leakage magnetic flux flowing in the enclosing tank are computed.

Saturated core high-temperature superconducting fault current limiters as an alternative to conventional series reactors in a distribution grid

Series reactors are used in distribution grids to reduce the short-circuit fault level. Some of the disadvantages of the application of these devices are the voltage drop produced across the reactor and the steep front rise of the transient recovery voltage (TRV), which generally exceeds the rating of the associated circuit breaker. Simulations were performed to compare the characteristics of a saturated core High-Temperature Superconducting Fault Current Limiter (HTS FCL) and a series reactor. The design of the HTS FCL was optimized using the evolutionary algorithm. The resulting Pareto frontier curve of optimum solution is presented in this paper. The results show that the steady-state impedance of an HTS FCL is significantly lower than that of a series reactor for the same level of fault current limiting. Tests performed on a prototype 11 kV HTS FCL confirm the theoretical results. The respective transient recovery voltages (TRV) of the HTS FCL and an air core reactor of comparable fault current limiting capability are also determined. The results show that the saturated core HTS FCL has a significantly lower effect on the rate of rise of the circuit breaker TRV as compared to the air core reactor. The simulations results are validated with shortcircuit test results.

Use of brain computer interface to drive : preliminary results

This paper reports on the implementation of a non-invasive electroencephalography-based brain-computer interface to control functions of a car in a driving simulator. The system is comprised of a Cleveland Medical Devices BioRadio 150 physiological signal recorder, a MATLAB-based BCI and an OKTAL SCANeR advanced driving experience simulator. The system utilizes steady-state visual-evoked potentials for the BCI paradigm, elicited by frequency-modulated high-power LEDs and recorded with the electrode placement of Oz-Fz with Fz as ground. A three-class online brain-computer interface was developed and interfaced with an advanced driving simulator to control functions of the car, including acceleration and steering. The findings are mainly exploratory but provide an indication of the feasibility and challenges of brain-controlled on-road cars for the future, in addition to a safe, simulated BCI driving environment to use as a foundation for research into overcoming these challenges.

Assessment of real-time networks and timing for process bus applications

Widespread adoption by electricity utilities of Non-Conventional Instrument Transformers, such as optical or capacitive transducers, has been limited due to the lack of a standardised interface and multi-vendor interoperability. Low power analogue interfaces are being replaced by IEC 61850 9 2 and IEC 61869 9 digital interfaces that use Ethernet networks for communication. These ‘process bus’ connections achieve significant cost savings by simplifying connections between switchyard and control rooms; however the in-service performance when these standards are employed is largely unknown. The performance of real-time Ethernet networks and time synchronisation was assessed using a scale model of a substation automation system. The test bed was constructed from commercially available timing and protection equipment supplied by a range of vendors. Test protocols have been developed to thoroughly evaluate the performance of Ethernet networks and network based time synchronisation. The suitability of IEEE Std 1588 Precision Time Protocol (PTP) as a synchronising system for sampled values was tested in the steady state and under transient conditions. Similarly, the performance of hardened Ethernet switches designed for substation use was assessed under a range of network operating conditions. This paper presents test methods that use a precision Ethernet capture card to accurately measure PTP and network performance. These methods can be used for product selection and to assess ongoing system performance as substations age. Key findings on the behaviour of multi-function process bus networks are presented. System level tests were performed using a Real Time Digital Simulator and transformer protection relay with sampled value and Generic Object Oriented Substation Events (GOOSE) capability. These include the interactions between sampled values, PTP and GOOSE messages. Our research has demonstrated that several protocols can be used on a shared process bus, even with very high network loads. This should provide confidence that this technology is suitable for transmission substations.

On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity ( KE) and macrodispersivity ( αE) for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of KE and αE on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal KE and αE are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical KE and αE are found to be reduced slightly when the density factor ( γ ) is less than 0.01, whereas significant decreases occur when γ exceeds 0.01. Of note, the variation of KE and αE is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

Cold-formed steel columns subject to local buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing losses of properties and lives in fires. However, the structural behaviour of thin-walled cold-formed steel columns under fire conditions is not well understood despite the increasing use of light gauge steels in building construction. Cold-formed steel columns are often subject to local buckling effects. Therefore a series of laboratory tests of lipped and unlipped channel columns made of varying steel thicknesses and grades was undertaken at uniform elevated temperatures up to 700°C under steady state conditions. Finite element models of the tested columns were also developed, and their elastic buckling and nonlinear analysis results were compared with test results at elevated temperatures. Effects of the degradation of mechanical properties of steel with temperature were included in the finite element analyses. The use of accurately measured yield stress, elasticity modulus and stress-strain curves at elevated temperatures provided a good comparison of the ultimate loads and load-deflection curves from tests and finite element analyses. The commonly used effective width design rules and the direct strength method at ambient temperature were then used to predict the ultimate loads at elevated temperatures by using the reduced mechanical properties. By comparing these predicted ultimate loads with those from tests and finite element analyses, the accuracy of using this design approach was evaluated.

Review of current fire design rules for cold-formed steel wall systems

Light gauge steel frame wall systems are commonly used in industrial and commercial buildings, and there is a need for simple fire design rules to predict their load capacities and fire resistance ratings. During fire events, the light gauge steel frame wall studs are subjected to non-uniform temperature distributions that cause thermal bowing, neutral axis shift and magnification effects and thus resulting in a combined axial compression and bending action on the studs. In this research, a series of full-scale fire tests was conducted first to evaluate the performance of light gauge steel frame wall systems with eight different wall configurations under standard fire conditions. Finite element models of light gauge steel frame walls were then developed, analysed under transient and steady-state conditions and validated using full-scale fire tests. Using the results from fire tests and finite element analyses, a detailed investigation was undertaken into the prediction of axial compression strength and failure times of light gauge steel frame wall studs in standard fires using the available fire design rules based on Australian, American and European standards. The results from both fire tests and finite element analyses were used to investigate the ability of these fire design rules to include the complex effects of non-uniform temperature distributions and their accuracy in predicting the axial compression strength of wall studs and the failure times. Suitable modifications were then proposed to the fire design rules. This article presents the details of this investigation on the fire design rules of light gauge steel frame walls and the results.

An in situ high pressure FT-IR study of CO2/H2 interactions with model ZnO/SiO2, Cu/SiO2 and Cu/ZnO/SiO2 methanol synthesis catalysts

In situ FT-IR spectroscopy allows the methanol synthesis reaction to be investigated under actual industrial conditions of 503 K and 10 MPa. On Cu/SiO2 catalyst formate species were initially formed which were subsequently hydrogenated to methanol. During the reaction a steady state concentration of formate species persisted on the copper. Additionally, a small quantity of gaseous methane was produced. In contrast, the reaction of CO2 and H2 on ZnO/SiO2 catalyst only resulted in the formation of zinc formate species: no methanol was detected. The interaction of CO2 and H2 with Cu/ZnO/SiO2 catalyst gave formate species on both copper and zinc oxide. Methanol was again formed by the hydrogenation of copper formate species. Steady-state concentrations of copper formate existed under actual industrial reaction conditions, and copper formate is the pivotal intermediate for methanol synthesis. Collation of these results with previous data on copper-based methanol synthesis catalysts allowed the formulation of a reaction mechanism

Laboratory measurement of hydraulic conductivity functions of two unsaturated sandy soils during drying and wetting processes

The importance of applying unsaturated soil mechanics to geotechnical engineering design has been well understood. However, the consumption of time and the necessity for a specific laboratory testing apparatus when measuring unsaturated soil properties have limited the application of unsaturated soil mechanics theories in practice. Although methods for predicting unsaturated soil properties have been developed, the verification of these methods for a wide range of soil types is required in order to increase the confidence of practicing engineers in using these methods. In this study, a new permeameter was developed to measure the hydraulic conductivity of unsaturated soils using the steady-state method and directly measured suction (negative pore-water pressure) values. The apparatus is instrumented with two tensiometers for the direct measurement of suction during the tests. The apparatus can be used to obtain the hydraulic conductivity function of sandy soil over a low suction range (0-10 kPa). Firstly, the repeatability of the unsaturated hydraulic conductivity measurement, using the new permeameter, was verified by conducting tests on two identical sandy soil specimens and obtaining similar results. The hydraulic conductivity functions of the two sandy soils were then measured during the drying and wetting processes of the soils. A significant hysteresis was observed when the hydraulic conductivity was plotted against the suction. However, the hysteresis effects were not apparent when the conductivity was plotted against the volumetric water content. Furthermore, the measured unsaturated hydraulic conductivity functions were compared with predictions using three different predictive methods that are widely incorporated into numerical software. The results suggest that these predictive methods are capable of capturing the measured behavior with reasonable agreement.

Metrological performances of a diffusion charger particle counter for personal monitoring

Airborne particles have been shown to be associated with a wide range of adverse health effects, which has led to a recent increase in medical research to gain better insight into their health effects. However, accurate evaluation of the exposure-dose-response relationship is highly dependent on the ability to track actual exposure levels of people to airborne particles. This is quite a complex task, particularly in relation to submicrometer and ultrafine particles, which can vary quite significantly in terms of particle surface area and number concentrations. Therefore, suitable monitors that can be worn for measuring personal exposure to these particles are needed. This paper presents an evaluation of the metrological performance of six diffusion charger sensors, NanoTracer (Philips Aerasense) monitors, when measuring particle number and surface area concentrations, as well as particle number distribution mean when compared to reference instruments. Tests in the laboratory (by generating monodisperse and polydisperse aerosols) and in the field (using natural ambient particles) were designed to evaluate the response of these devices under both steady-state and dynamics conditions. Results showed that the NanoTracers performed well when measuring steady state aerosols, however they strongly underestimated actual concentrations during dynamic response testing. The field experiments also showed that, when the majority of the particles were smaller than 20 nm, which occurs during particle formation events in the atmosphere, the NanoTracer underestimated number concentration quite significantly. Even though the NanoTracer can be used for personal monitoring of exposure to ultrafine particles, it also has limitations which need to be considered in order to provide meaningful results.

Unsteady buoyancy driven flows and heat transfer through coupled thermal boundary layers in a partitioned triangular enclosure

A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.