Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

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.

A review of the Ustilago-Sporisorium-Macalpinomyces complex

The fungal genera Ustilago, Sporisorium and Macalpinomyces represent an unresolved complex. Taxa within the complex often possess characters that occur in more than one genus, creating uncertainty for species placement. Previous studies have indicated that the genera cannot be separated by morphology alone. Here we chronologically review the history of the Ustilago-Sporisorium-Macalpinomyces complex, argue for its resolution and suggest methods to accomplish a stable taxonomy. A combined molecular and morphological approach is required to identify synapomorphic characters that underpin a new classification. Ustilago, Sporisorium and Macalpinomyces require explicit re-description and new genera, based on monophyletic groups, are needed to accommodate taxa that no longer fit the emended descriptions. A resolved classification will end the taxonomic confusion that surrounds generic placement of these smut fungi.

Thermogravimetric analysis, PXRD, EDX and XPS study of chrysocolla (Cu,Al)2H2Si2O5(OH)4·nH2O : structural implications

Selected chrysocolla mineral samples from different origins have been studied by using PXRD, SEM, EDX and XPS. The XRD patterns show that the chrysocolla mineral samples are non-diffracting and no other phases are present in the minerals, thus showing the chrysocolla samples are pure. SEM analyses show the chrysocolla surfaces are featureless. EDX analyses enable the formulae of the chrysocolla samples to be calculated. The thermal decomposition of the mineral chrysocolla has been studied using a combination of thermogravimetric analysis and derivative thermogravimetric analysis. Five thermal decomposition mass loss steps are observed for the chrysocolla from Arizona (a) at 125 ◦C with the loss of water, (b) at 340 ◦C with the loss of hydroxyl units, (c) at 468.5 ◦C with a further loss of hydroxyls, (d) at 821 ◦C with oxygen loss and (e) at 895 ◦C with a further loss of oxygen. The thermal analysis of the chrysocolla from Congo shows mass losses at 125, 275.3, 805.6 and 877.4 ◦C and for the Nevada chrysocolla, mass loss steps at 268, 333, 463, 786.0 and 817.7 ◦C are observed. The thermal analysis of spertiniite is very different from that of chrysocolla and thermally decomposes at around 160 ◦C. XPS shows that there are two different copper species present, one which is bonded to oxygen and one to a hydroxyl unit. The O 1s is broad and very symmetrical suggesting two O species of equal number. The bond energy of 102.9 eV for the Si 2p suggests that it is in the form of a silicate. The bond energy is much higher for silicas around ∼103.5 eV. The reported value for silica gel has Si 2p at 103.4 eV. The combination of TG, PXRD, EDX and XPS adds to our fundamental knowledge of the structure of chrysocolla.

Decoration of titania nanofibres with anatase nanoparticles as efficient photocatalysts for decomposing pesticides and phenols

Using a series of partial phase transitions, an effective photocatalyst with fibril morphology was prepared. The catalytic activities of these materials were tested against phenol and herbicide in water. Both H-titanate and TiO2-(B) fibres decorated with anatase nanocrystals were studied. It was found that anatase coated TiO2-(B) fibres prepared by a 45 h hydrothermal treatment followed by calcination were not only superior photocatalysts but could also be readily separated from the slurry after photocatalytic reactions due to its fibril morphology.

Process for forming alumino-silicate derivatives

A process for the preparation of an amorphous alumino-silicate derivative which involves reacting a solid corresponding starting material with MOH where M is alkali metal or ammonium cation. The solid corresponding starting material may be selected from montmorillonite, kaolin, natural zeolite (e.g., clinoliptolite/heulandite) as well as illite, palygorskite and saponite and additional reactant MX wherein X is halide may be utilized in conjunction with MOH. The invention also includes alumino-silicate derivatives of the general formula M.sub.p Al.sub.q Si.sub.2 O.sub.r (OH).sub.s X.sub.t.uH.sub.2 O as well as alumino-silicate derivatives of the general formula M.sub.p Al.sub.q Si.sub.2 O.sub.r (OH).sub.s.uH.sub.2 O.

Comparison of two suspension control strategies for multi-axle heavy truck

Two simple and effective control strategies for a multi-axle heavy truck, modified skyhook damping (MSD) control and proportional-integration-derivative (PID) control, were implemented into functional virtual prototype (FVP) model and compared in terms of road friendliness and ride comfort. A four-axle heavy truck-road coupling system model was established using FVP technology and validated through a ride comfort test. Then appropriate passive air suspensions were chosen to replace the rear tandem suspensions of the original truck model for preliminary optimization. The mechanical properties and time lag of dampers were taken into account in simulations of MSD and PID semi-active dampers implemented using MATLAB/Simulink. Through co-simulations with Adams and MATLAB, the effects of semi-active MSD and PID control were analyzed and compared, and control parameters which afforded the best comprehensive performance for each control strategy were chosen. Simulation results indicate that compared with the passive air suspension truck, semi-active MSD control improves both ride comfort and road-friendliness markedly, with optimization ratios of RMS vertical acceleration and RMS tyre force ranging from 10.1% to 44.8%. However, semi-active PID control only reduces vertical vibration of the driver’s seat by 11.1%, 11.1% and 10.9% on A, B and C level roads respectively. Both strategies are robust to the variation of road level.

Language affects length of stay in emergency departments in Queensland public hospitals

BACKGROUND: A long length of stay (LOS) in the emergency department (ED) associated with overcrowding has been found to adversely affect the quality of ED care. The objective of this study is to determine whether patients who speak a language other than English at home have a longer LOS in EDs compared to those whose speak only English at home. METHODS: A secondary data analysis of a Queensland state-wide hospital EDs dataset (Emergency Department Information System) was conducted for the period, 1 January 2008 to 31 December 2010. RESULTS: The interpreter requirement was the highest among Vietnamese speakers (23.1%) followed by Chinese (19.8%) and Arabic speakers (18.7%). There were significant differences in the distributions of the departure statuses among the language groups (Chi-squared=3236.88, P<0.001). Compared with English speakers, the Beta coeffi cient for the LOS in the EDs measured in minutes was among Vietnamese, 26.3 (95%CI: 22.1–30.5); Arabic, 10.3 (95%CI: 7.3–13.2); Spanish, 9.4 (95%CI: 7.1–11.7); Chinese, 8.6 (95%CI: 2.6–14.6); Hindi, 4.0 (95%CI: 2.2–5.7); Italian, 3.5 (95%CI: 1.6–5.4); and German, 2.7 (95%CI: 1.0–4.4). The fi nal regression model explained 17% of the variability in LOS. CONCLUSION: There is a close relationship between the language spoken at home and the LOS at EDs, indicating that language could be an important predictor of prolonged LOS in EDs and improving language services might reduce LOS and ease overcrowding in EDs in Queensland's public hospitals.

Rock, paper, scissors : reflective practice for design process in the novice landscape architect

We describe a pedagogical approach that addresses challenges in design education for novices. These include an inability to frame new problems and limited-to-no design capability or domain knowledge. Such challenges can reduce student engagement with design practice, cause derivative design solutions as well as the inappropriate simplification of design assignments and assessment criteria by educators. We argue that a curriculum that develops the student’s design process will enable them to deal with the uncertain and dynamic situations that characterise design. We describe how this may be achieved and explain our pedagogical approach in terms of methods from Reflective Practice and theories of abstraction and creativity. We present a landscape architecture unit, recently taught, as an example. It constitutes design exercises that require little domain or design expertise to support the development of conceptual thinking and a design rationale. We show how this approach (a) leveraged the novice’s existing spatial and thinking skills while (b) retaining contextually-rich design situations. Examples of the design exercises taught are described along with samples of student work. The assessment rationale is also presented and explained. Finally, we conclude by reflecting on how this approach relates to innovation, sustainability and other disciplines.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Connecting across continents : collaborative learning in a Web 2.0 world

Purpose – The article aims to review a university course, offered to students in both Australia and Germany, to encourage them to learn about designing, implementing, marketing and evaluating information programs and services in order to build active and engaged communities. The concepts and processes of Web 2.0 technologies come together in the learning activities, with students establishing their own personal learning networks (PLNs). Design/methodology/approach – The case study examines the principles of learning and teaching that underpin the course and presents the students' own experiences of the challenges they faced as they explored the interactive, participative and collaborative dimensions of the web. Findings – The online format of the course and the philosophy of learning through play provided students with a safe and supportive environment for them to move outside of their comfort zones, to be creative, to experiment and to develop their professional personas. Reflection on learning was a key component that stressed the value of reflective practice in assisting library and information science (LIS) professionals to adapt confidently to the rapidly changing work environment. Originality/value – This study provides insights into the opportunities for LIS courses to work across geographical boundaries, to allow students to critically appraise library practice in different contexts and to become active participants in wider professional networks.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.