A spectroscopic comparison of YBCO superconductors synthesised by solid-state and co-precipitation methods

Raman spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM) have been used to compare samples of YBa2Cu3O7 (YBCO) synthesised by the solid-state method and a novel co-precipitation technique. XRD results indicate that YBCO prepared by these two methods are phase pure, however the Raman and SEM results show marked differences between these samples.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Order conditions of stochastic Runge-Kutta methods by B-series

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Agricultural biodiversity, farm level technical efficiency and conservation benefits : an empirical investigation

The issues involved in agricultural biodiversity are important and interesting areas for the application of economic theory. However, very little theoretical and empirical work has been undertaken to understand the benefits of conserving agricultural biodiversity. Accordingly, the main objectives of this PhD thesis are to: (1) Investigate farmers’ valuation of agricultural biodiversity; (2) Identify factors influencing farmers’ demand for agricultural biodiversity; (3) Examine farmers’ demand for biodiversity rich farming systems; (4) Investigate the relationship between agricultural biodiversity and farm level technical efficiency. This PhD thesis investigates these issues by using primary data in small-scale farms, along with secondary data from Sri Lanka. The overall findings of the thesis can be summarized as follows. Firstly, owing to educational and poverty issues of those being interviewed, some policy makers in developed countries question whether non-market valuation techniques such as Choice Experiment (CE) can be applied to developing countries such as Sri Lanka. The CE study in this thesis indicates that carefully designed and pre-tested nonmarket valuation techniques can be applied in developing countries with a high level of reliability. The CE findings support the priori assumption that small-scale farms and their multiple attributes contribute positively and significantly to the utility of farm families in Sri Lanka. Farmers have strong positive attitudes towards increasing agricultural biodiversity in rural areas. This suggests that these attitudes can be the basis on which appropriate policies can be introduced to improve agricultural biodiversity. Secondly, the thesis identifies the factors which influence farmers’ demand for agricultural biodiversity and farmers’ demands on biodiversity rich farming systems. As such they provide important tools for the implementation of policies designed to avoid the loss agricultural biodiversity which is shown to be a major impediment to agricultural growth and sustainable development in a number of developing countries. The results illustrate that certain key household, market and other characteristics (such as agricultural subsidies, percentage of investment of owned money and farm size) are the major determinants of demand for agricultural biodiversity on small-scale farms. The significant household characteristics that determine crop and livestock diversity include household member participation on the farm, off-farm income, shared labour, market price fluctuations and household wealth. Furthermore, it is shown that all the included market characteristics as well as agricultural subsidies are also important determinants of agricultural biodiversity. Thirdly, it is found that when the efficiency of agricultural production is measured in practice, the role of agricultural biodiversity has rarely been investigated in the literature. The results in the final section of the thesis show that crop diversity, livestock diversity and mix farming system are positively related to farm level technical efficiency. In addition to these variables education level, number of separate plots, agricultural extension service, credit access, membership of farm organization and land ownerships are significant and direct policy relevant variables in the inefficiency model. The results of the study therefore have important policy implications for conserving agricultural biodiversity in Sri Lanka.

The effectiveness of energy feedback for conservation and peak demand : a literature review

This paper reviews electricity consumption feedback literature to explore the potential of electricity feedback to affect residential consumers’ electricity usage patterns. The review highlights a substantial amount of literature covering the debate over the effectiveness of different feedback criteria to residential customer acceptance and overall conservation and peak demand reduction. Researchers studying the effects of feedback on everyday energy use have observed substantial variation in effect size, both within and between studies. Although researchers still continue to question the types of feedback that are most effective in encouraging conservation and peak load reduction, some trends have emerged. These include that feedback be received as quickly as possible to the time of consumption; be related to a standard; be clear and meaningful and where possible both direct and indirect feedback be customised to the customer. In general, the literature finds that feedback can reduce electricity consumption in homes by 5 to 20 per cent, but that significant gaps remain in our knowledge of the effectiveness and cost benefit of feedback.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Application of multi-criteria decision making methods to compression ignition engine efficiency and gaseous, particulate and greenhouse gas emissions

Compression ignition (CI) engine design is subject to many constraints which presents a multi-criteria optimisation problem that the engine researcher must solve. In particular, the modern CI engine must not only be efficient, but must also deliver low gaseous, particulate and life cycle greenhouse gas emissions so that its impact on urban air quality, human health, and global warming are minimised. Consequently, this study undertakes a multi-criteria analysis which seeks to identify alternative fuels, injection technologies and combustion strategies that could potentially satisfy these CI engine design constraints. Three datasets are analysed with the Preference Ranking Organization Method for Enrichment Evaluations and Geometrical Analysis for Interactive Aid (PROMETHEE-GAIA) algorithm to explore the impact of 1): an ethanol fumigation system, 2): alternative fuels (20 % biodiesel and synthetic diesel) and alternative injection technologies (mechanical direct injection and common rail injection), and 3): various biodiesel fuels made from 3 feedstocks (i.e. soy, tallow, and canola) tested at several blend percentages (20-100 %) on the resulting emissions and efficiency profile of the various test engines. The results show that moderate ethanol substitutions (~20 % by energy) at moderate load, high percentage soy blends (60-100 %), and alternative fuels (biodiesel and synthetic diesel) provide an efficiency and emissions profile that yields the most “preferred” solutions to this multi-criteria engine design problem. Further research is, however, required to reduce Reactive Oxygen Species (ROS) emissions with alternative fuels, and to deliver technologies that do not significantly reduce the median diameter of particle emissions.

The adoption of e-learning 2.0 in higher education by teachers and students : an investigation using mixed methods approach

This paper describes an approach to investigate the adoption of Web 2.0 in the classroom using a mixed methods study. By using a combination of qualitative or quantitative data collection and analysis techniques, we attempt to synergize the results and provide a more valid understanding of Web 2.0 adoption for learning by both teachers and students. This approach is expected to yield a better holistic view on the adoption issues associated with the e-learning 2.0 concept in current higher education as opposed to single method studies done previously. This paper also presents some early findings of e-learning 2.0 adoption using this research method