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.

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.

Mechanism of dehydroxylation temperature decrease and high temperature phase transition of coal-bearing strata kaolinite intercalated by potassium acetate

The thermal decomposition and dehydroxylation process of coal-bearing strata kaolinite–potassium acetate intercalation complex (CSKK) has been studied using X-ray diffraction (XRD), infrared spectroscopy (IR), thermal analysis, mass spectrometric analysis and infrared emission spectroscopy. The XRD results showed that the potassium acetate (KAc) have been successfully intercalated into coal-bearing strata kaolinite with an obvious basal distance increase of the first basal peak, and the positive correlation was found between the concentration of intercalation regent KAc and the degree of intercalation. As the temperature of the system is raised, the formation of KHCO3, KCO3 and KAlSiO4, which is derived from the thermal decomposition or phase transition of CSKK, is observed in sequence. The IR results showed that new bands appeared, the position and intensities shift can also be found when the concentration of intercalation agent is raised. The thermal analysis and mass spectrometric analysis results revealed that CSKK is stable below 300 °C, and the thermal decomposition products (H2O and CO2) were further proved by the mass spectrometric analysis. A comparison of thermal analysis results of original coal-bearing strata kaolinite and its intercalation complex gives new discovery that not only a new mass loss peak is observed at 285 °C, but also the temperature of dehydroxylation and dehydration of coal bearing strata kaolinite is decreased about 100 °C. This is explained on the basis of the interlayer space of the kaolinite increased obviously after being intercalated by KAc, which led to the interlayer hydrogen bonds weakened, enables the dehydroxylation from kaolinite surface more easily. Furthermore, the possible structural model for CSKK has been proposed, with further analysis required in order to prove the most possible structures.

A high frequency current source converter with adjustable magnitude to drive high power piezoelectric transducers

A general electrical model of a piezoelectric transducer for ultrasound applications consists of a capacitor in parallel with RLC legs. A high power voltage source converter can however generate significant voltage stress across the transducer that creates high leakage currents. One solution is to reduce the voltage stress across the piezoelectric transducer by using an LC filter, however a main drawback is changing the piezoelectric resonant frequency and its characteristics. Thereby it reduces the efficiency of energy conversion through the transducer. This paper proposes that a high frequency current source converter is a suitable topology to drive high power piezoelectric transducers efficiently.

Ion transport in small-molecule electrolytes based on LiI/3-hydroxypropionitrile with high salt contents

Abnormal “polymer-in-salt” conduction behavior is observed in a solid electrolyte composed of lithium iodide (LiI) and 3-hydroxypropionitrile (HPN). Based on comprehensive investigations by X-ray diffraction (XRD) and Raman and infrared spectroscopy, this abnormal conduction behavior is attributed to the formation of new ionic associates [Lim +In−]· · ·N C (m> n) and the reinforced hydrogen bonding of I· · ·HO in the electrolyte at high LiI concentrations.

Power electronic converters for high power ultrasound transducers

Piezoelectric transducers convert electrical energy to mechanical energy and play a great role in ultrasound systems. Ultrasound power transducer performance is strongly related to the applied electrical excitation. To have a suitable excitation for maximum energy conversion, it is required to analyze the effects of input signal waveform, medium and input signal distortion on the characteristic of a high power ultrasound system (including ultrasound transducer). In this research, different input voltage signals are generated using a single-phase power inverter and a linear power amplifier to excite a high power ultrasound transducer in different medium (water and oil) in order to study the characteristic of the system. We have also considered and analyzed the effect of power converter output voltage distortions on the performance of the high power ultrasound transducer using a passive filter.

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.

Improving the efficiency of high power piezoelectric transducers for industrial applications

Most high-power ultrasound applications are driven by two-level inverters. However, the broad spectral content of the two-level pulse results in undesired harmonics that can decrease the performance of the system significantly. On the other hand, it is crucial to excite the piezoelectric devices at their main resonant frequency in order to have maximum energy conversion. Therefore a high-quality, low-distorted power signal is needed to excite the high-power piezoelectric transducer at its resonant frequency. This study proposes an efficient approach to develop the performance of high-power ultrasonic applications using multilevel inverters along with a frequency estimation algorithm. In this method, the resonant frequencies are estimated based on relative minimums of the piezoelectric impedance frequency response. The algorithm follows the resonant frequency variation and adapts the multilevel inverter reference frequency to drive an ultrasound transducer at high power. Extensive simulation and experimental results indicate the effectiveness of the proposed approach.

High-sensitivity fiber Bragg grating temperature sensor at high temperature [一种高温下高灵敏光纤光栅温度传感器的制作方法]

A method of making full use of the durable strain which fiber Bragg grating (FBG) can undertake is presented, which hugely improves the sensitivities of FBG temperature sensors at high temperature. When a sensor is manufactured at room temperature, its FBG should be given a pre-relaxing length according to the temperature it is asked to measure; once the temperature rise to the asked one, its FBG starts to be stretched and it starts to work with high sensitivity. The relationship between the pre-relaxing length and the working temperature is analyzed. In experiments, when the pre-relaxing lengths are 0.2mm、0.5mm、0.6mm, the working temperatures rise 25℃、50℃、61℃, respectively, and the sensitivities are almost the same (675pm/℃). The facts that the experimental results agree well with the theoretical analyses verify this method’s validity.

The application of fiber Bragg grating sensor to high precision temperature measurement [基于光纤光栅的高精度测温传感器研究]

Basing on the character that Fiber Bragg Grating (FBG) is sensitive to both temperature and strain, by using Al and Fe-Ni alloy’s bimetal structure, we successfully design and manufacture a high accuracy FBG temperature sensor for earthquake premonition. Furthermore, we analyze the accuracy of the FBG sensors with enhanced sensitivity for the first time, and get its accuracy is up to ±0.05℃ with highest resolution ever in all FBG temperature sensors (0.0014℃/pm). This work experimentally proves the feasibility of using FBG in the earthquake premonition monitoring, and builds the foundation for the application of optic technology in earthquake premonition monitoring.

Collective sampling and analysis of high order tensors for chatroom communications

This work investigates the accuracy and efficiency tradeoffs between centralized and collective (distributed) algorithms for (i) sampling, and (ii) n-way data analysis techniques in multidimensional stream data, such as Internet chatroom communications. Its contributions are threefold. First, we use the Kolmogorov-Smirnov goodness-of-fit test to show that statistical differences between real data obtained by collective sampling in time dimension from multiple servers and that of obtained from a single server are insignificant. Second, we show using the real data that collective data analysis of 3-way data arrays (users x keywords x time) known as high order tensors is more efficient than centralized algorithms with respect to both space and computational cost. Furthermore, we show that this gain is obtained without loss of accuracy. Third, we examine the sensitivity of collective constructions and analysis of high order data tensors to the choice of server selection and sampling window size. We construct 4-way tensors (users x keywords x time x servers) and analyze them to show the impact of server and window size selections on the results.

Using ‘think aloud’ as a strategy for improving clinical reasoning in high fidelity case-based simulation for undergraduate nursing students.

Theme Paper for Curriculum innovation and enhancement theme AIM: This paper reports on a research project that trialled an educational strategy implemented in an undergraduate nursing curriculum. The project aimed to explore the effectiveness of ‘think aloud’ as a strategy for improving clinical reasoning for students in simulated clinical settings. BACKGROUND: Nurses are required to apply and utilise critical thinking skills to enable clinical reasoning and problem solving in the clinical setting (Lasater, 2007). Nursing students are expected to develop and display clinical reasoning skills in practice, but may struggle articulating reasons behind decisions about patient care. The ‘think aloud’ approach is an innovative learning/teaching method which can create an environment suitable for developing clinical reasoning skills in students (Banning, 2008, Lee and Ryan-Wenger, 1997). This project used the ‘think aloud’ strategy within a simulation context to provide a safe learning environment in which third year students were assisted to uncover cognitive approaches to assist in making effective patient care decisions, and improve their confidence, clinical reasoning and active critical reflection about their practice. MEHODS: In semester 2 2011 at QUT, third year nursing students undertook high fidelity simulation (some for the first time), commencing in September of 2011. There were two cohorts for strategy implementation (group 1= used think aloud as a strategy within the simulation, group 2= no specific strategy outside of nursing assessment frameworks used by all students) in relation to problem solving patient needs. The think aloud strategy was described to students in their pre-simulation briefing and allowed time for clarification of this strategy. All other aspects of the simulations remained the same, (resources, suggested nursing assessment frameworks, simulation session duration, size of simulation teams, preparatory materials). Ethics approval has been obtained for this project. RESULTS: Results of a qualitative analysis (in progress- will be completed by March 2012) of student and facilitator reports on students’ ability to meet the learning objectives of solving patient problems using clinical reasoning and experience with the ‘think aloud’ method will be presented. A comparison of clinical reasoning learning outcomes between the two groups will determine the effect on clinical reasoning for students responding to patient problems. CONCLUSIONS: In an environment of increasingly constrained clinical placement opportunities, exploration of alternate strategies to improve critical thinking skills and develop clinical reasoning and problem solving for nursing students is imperative in preparing nurses to respond to changing patient needs.

Fast exact nearest neighbour matching in high dimensions using d-D Sort

Data structures such as k-D trees and hierarchical k-means trees perform very well in approximate k nearest neighbour matching, but are only marginally more effective than linear search when performing exact matching in high-dimensional image descriptor data. This paper presents several improvements to linear search that allows it to outperform existing methods and recommends two approaches to exact matching. The first method reduces the number of operations by evaluating the distance measure in order of significance of the query dimensions and terminating when the partial distance exceeds the search threshold. This method does not require preprocessing and significantly outperforms existing methods. The second method improves query speed further by presorting the data using a data structure called d-D sort. The order information is used as a priority queue to reduce the time taken to find the exact match and to restrict the range of data searched. Construction of the d-D sort structure is very simple to implement, does not require any parameter tuning, and requires significantly less time than the best-performing tree structure, and data can be added to the structure relatively efficiently.

Combustion products of bulk aluminum rods burning in high pressure oxygen

Characterization of the combustion products released during the burning of commonly used engineering metallic materials may aid in material selection and risk assessment for the design of oxygen systems. The characterization of combustion products in regards to size distribution and morphology gives useful information for systems addressing fire detection. Aluminum rods (3.2-mm diameter cylinders) were vertically mounted inside a combustion chamber and ignited in pressurized oxygen by resistively heating an aluminum/palladium igniter wire attached to the bottom of the test sample. This paper describes the experimental work conducted to establish the particle size distribution and morphology of the resultant combustion products collected after the burning was completed and subsequently analyzed. In general, the combustion products consisted of a re-solidified oxidized slag and many small hollow spheres of size ranging from about 500 nm to 1000 µm in diameter, surfaced with quenched dendritic and grain-like structures. The combustion products were characterized using optical and scanning electron microscopy.

Zircon chronochemistry of high heat-producing granites in Queensland and Europe

High heat-producing granites (HHPGs) are reservoir rocks for enhanced geothermal systems (EGS), yet the origins of their anomalous chemistry remain poorly understood. To gain a better understanding of the characteristic distribution of elemental depletions and enrichments (focussing on U, Th & K) within granite suites of different heritage and tectonic setting, and the processes that lead to these enrichments, we are undertaking a systematic accessory-mineral chronochemical study of two suites of S- and I-type granites in northern Queensland, as well as two archetypal HHPGs in Cornwall, England (S-type) and Soultz-sous- Forêts, France (I-type). Novel zircon LA-ICP-MS chronochemical methods will later be underpinned by a systematic petrographic, scanning electron microscope (SEM), and electron microprobe (EPMA) study of all the REE-Y-Th-U-rich accessory minerals to fully characterise how the composition, textural distributions and associations change with rock chemistry between and among the suites. Preliminary results indicate that zircons with inherited ages do not have anomalously high U (>1000 ppm) & Th (>400 ppm) values (Ahrens, 1965). Instead, enrichment in these HPE is seen in zircons dated to around the time of magmatic emplacement. These results indicate that enrichment arose primarily through fractional crystallisation of the granitic magmas. Our results support the suggestion that a source pre-enriched in the HPEs does not appear to be fundamental for the formation of all HHPGs. Instead fractional crystallisation processes, and the accessory minerals formed in magmas of differing initial compositions, are the key controls on the levels of enrichment observed (e.g. Champion & Chappell, 1992; Chappell & Hine, 2006). One implication is that the most fractionated granites may not be the most enriched in the HPEs and therefore prospective to future EGS development.