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.

Effect of depithing on the safety and environmental aspects of bagasse stockpiling

Large scale sugarcane bagasse storage in uncovered stockpiles has the potential to result in adverse impacts on the environment and surrounding communities through hazards associated with nuisance dust, groundwater seepage, spontaneous combustion and generation of contaminated leachates. Managing these hazards will assist in improved health and safety outcomes for factory staff and reduced potential environmental impacts on surrounding communities. Removal of the smaller fibres (pith) from bagasse prior to stockpiling reduced the dust number of bagasse by 50% and modelling suggests peak ground level PM10 dust emissions would reduce by 70%. Depithed bagasse has much lower water holding capacity (~43%) than whole bagasse. This experimental and modelling study investigated the physical properties of depithed and whole bagasse. Dust dispersion modelling was undertaken to determine the likely effects associated with storage of whole and depithed sugarcane bagasse.

Numerical solutions of stochastic differential equations – implementation and stability issues

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.

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 novel winding structure in planar inductors to decrease overall capacitive couplings

This paper analyses effects of winding structure on capacitive coupling reduction appearing in the planar magnetic elements at high frequencies. Capacitive coupling appears between the conductive layers of the planar transformers resulting in high current spikes and consequently high power dissipation. With finite element analysis, the equivalent capacitive coupling of magnetic elements is calculated for different structures of planar windings. Finally, a new winding structure with minimum capacitive coupling is introduced for the planar magnetic elements, which is verified by simulation and experiments.

On robust face recognition via sparse encoding : the good, the bad, and the ugly

In the field of face recognition, Sparse Representation (SR) has received considerable attention during the past few years. Most of the relevant literature focuses on holistic descriptors in closed-set identification applications. The underlying assumption in SR-based methods is that each class in the gallery has sufficient samples and the query lies on the subspace spanned by the gallery of the same class. Unfortunately, such assumption is easily violated in the more challenging face verification scenario, where an algorithm is required to determine if two faces (where one or both have not been seen before) belong to the same person. In this paper, we first discuss why previous attempts with SR might not be applicable to verification problems. We then propose an alternative approach to face verification via SR. Specifically, we propose to use explicit SR encoding on local image patches rather than the entire face. The obtained sparse signals are pooled via averaging to form multiple region descriptors, which are then concatenated to form an overall face descriptor. Due to the deliberate loss spatial relations within each region (caused by averaging), the resulting descriptor is robust to misalignment & various image deformations. Within the proposed framework, we evaluate several SR encoding techniques: l1-minimisation, Sparse Autoencoder Neural Network (SANN), and an implicit probabilistic technique based on Gaussian Mixture Models. Thorough experiments on AR, FERET, exYaleB, BANCA and ChokePoint datasets show that the proposed local SR approach obtains considerably better and more robust performance than several previous state-of-the-art holistic SR methods, in both verification and closed-set identification problems. The experiments also show that l1-minimisation based encoding has a considerably higher computational than the other techniques, but leads to higher recognition rates.

Design and modeling of collaboration architecture for security

Threats against computer networks evolve very fast and require more and more complex measures. We argue that teams respectively groups with a common purpose for intrusion detection and prevention improve the measures against rapid propagating attacks similar to the concept of teams solving complex tasks known from field of work sociology. Collaboration in this sense is not easy task especially for heterarchical environments. We propose CIMD (collaborative intrusion and malware detection) as a security overlay framework to enable cooperative intrusion detection approaches. Objectives and associated interests are used to create detection groups for exchange of security-related data. In this work, we contribute a tree-oriented data model for device representation in the scope of security. We introduce an algorithm for the formation of detection groups, show realization strategies for the system and conduct vulnerability analysis. We evaluate the benefit of CIMD by simulation and probabilistic analysis.

Regression and hypothesis tests for multivariate GNSS state time series

A satellite based observation system can continuously or repeatedly generate a user state vector time series that may contain useful information. One typical example is the collection of International GNSS Services (IGS) station daily and weekly combined solutions. Another example is the epoch-by-epoch kinematic position time series of a receiver derived by a GPS real time kinematic (RTK) technique. Although some multivariate analysis techniques have been adopted to assess the noise characteristics of multivariate state time series, statistic testings are limited to univariate time series. After review of frequently used hypotheses test statistics in univariate analysis of GNSS state time series, the paper presents a number of T-squared multivariate analysis statistics for use in the analysis of multivariate GNSS state time series. These T-squared test statistics have taken the correlation between coordinate components into account, which is neglected in univariate analysis. Numerical analysis was conducted with the multi-year time series of an IGS station to schematically demonstrate the results from the multivariate hypothesis testing in comparison with the univariate hypothesis testing results. The results have demonstrated that, in general, the testing for multivariate mean shifts and outliers tends to reject less data samples than the testing for univariate mean shifts and outliers under the same confidence level. It is noted that neither univariate nor multivariate data analysis methods are intended to replace physical analysis. Instead, these should be treated as complementary statistical methods for a prior or posteriori investigations. Physical analysis is necessary subsequently to refine and interpret the results.

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

Improving ultrasound excitation systems using a flexible power supply with adjustable voltage and frequency to drive piezoelectric transducers

The ability of a piezoelectric transducer in energy conversion is rapidly expanding in several applications. Some of the industrial applications for which a high power ultrasound transducer can be used are surface cleaning, water treatment, plastic welding and food sterilization. Also, a high power ultrasound transducer plays a great role in biomedical applications such as diagnostic and therapeutic applications. An ultrasound transducer is usually applied to convert electrical energy to mechanical energy and vice versa. In some high power ultrasound system, ultrasound transducers are applied as a transmitter, as a receiver or both. As a transmitter, it converts electrical energy to mechanical energy while a receiver converts mechanical energy to electrical energy as a sensor for control system. Once a piezoelectric transducer is excited by electrical signal, piezoelectric material starts to vibrate and generates ultrasound waves. A portion of the ultrasound waves which passes through the medium will be sensed by the receiver and converted to electrical energy. To drive an ultrasound transducer, an excitation signal should be properly designed otherwise undesired signal (low quality) can deteriorate the performance of the transducer (energy conversion) and increase power consumption in the system. For instance, some portion of generated power may be delivered in unwanted frequency which is not acceptable for some applications especially for biomedical applications. To achieve better performance of the transducer, along with the quality of the excitation signal, the characteristics of the high power ultrasound transducer should be taken into consideration as well. In this regard, several simulation and experimental tests are carried out in this research to model high power ultrasound transducers and systems. During these experiments, high power ultrasound transducers are excited by several excitation signals with different amplitudes and frequencies, using a network analyser, a signal generator, a high power amplifier and a multilevel converter. Also, to analyse the behaviour of the ultrasound system, the voltage ratio of the system is measured in different tests. The voltage across transmitter is measured as an input voltage then divided by the output voltage which is measured across receiver. The results of the transducer characteristics and the ultrasound system behaviour are discussed in chapter 4 and 5 of this thesis. Each piezoelectric transducer has several resonance frequencies in which its impedance has lower magnitude as compared to non-resonance frequencies. Among these resonance frequencies, just at one of those frequencies, the magnitude of the impedance is minimum. This resonance frequency is known as the main resonance frequency of the transducer. To attain higher efficiency and deliver more power to the ultrasound system, the transducer is usually excited at the main resonance frequency. Therefore, it is important to find out this frequency and other resonance frequencies. Hereof, a frequency detection method is proposed in this research which is discussed in chapter 2. An extended electrical model of the ultrasound transducer with multiple resonance frequencies consists of several RLC legs in parallel with a capacitor. Each RLC leg represents one of the resonance frequencies of the ultrasound transducer. At resonance frequency the inductor reactance and capacitor reactance cancel out each other and the resistor of this leg represents power conversion of the system at that frequency. This concept is shown in simulation and test results presented in chapter 4. To excite a high power ultrasound transducer, a high power signal is required. Multilevel converters are usually applied to generate a high power signal but the drawback of this signal is low quality in comparison with a sinusoidal signal. In some applications like ultrasound, it is extensively important to generate a high quality signal. Several control and modulation techniques are introduced in different papers to control the output voltage of the multilevel converters. One of those techniques is harmonic elimination technique. In this technique, switching angles are chosen in such way to reduce harmonic contents in the output side. It is undeniable that increasing the number of the switching angles results in more harmonic reduction. But to have more switching angles, more output voltage levels are required which increase the number of components and cost of the converter. To improve the quality of the output voltage signal with no more components, a new harmonic elimination technique is proposed in this research. Based on this new technique, more variables (DC voltage levels and switching angles) are chosen to eliminate more low order harmonics compared to conventional harmonic elimination techniques. In conventional harmonic elimination method, DC voltage levels are same and only switching angles are calculated to eliminate harmonics. Therefore, the number of eliminated harmonic is limited by the number of switching cycles. In the proposed modulation technique, the switching angles and the DC voltage levels are calculated off-line to eliminate more harmonics. Therefore, the DC voltage levels are not equal and should be regulated. To achieve this aim, a DC/DC converter is applied to adjust the DC link voltages with several capacitors. The effect of the new harmonic elimination technique on the output quality of several single phase multilevel converters is explained in chapter 3 and 6 of this thesis. According to the electrical model of high power ultrasound transducer, this device can be modelled as parallel combinations of RLC legs with a main capacitor. The impedance diagram of the transducer in frequency domain shows it has capacitive characteristics in almost all frequencies. Therefore, using a voltage source converter to drive a high power ultrasound transducer can create significant leakage current through the transducer. It happens due to significant voltage stress (dv/dt) across the transducer. To remedy this problem, LC filters are applied in some applications. For some applications such as ultrasound, using a LC filter can deteriorate the performance of the transducer by changing its characteristics and displacing the resonance frequency of the transducer. For such a case a current source converter could be a suitable choice to overcome this problem. In this regard, a current source converter is implemented and applied to excite the high power ultrasound transducer. To control the output current and voltage, a hysteresis control and unipolar modulation are used respectively. The results of this test are explained in chapter 7.

Influence of ventilation and filtration on indoor particle concentrations in urban office buildings

This study aimed to quantify the efficiency of deep bag and electrostatic filters, and assess the influence of ventilation systems using these filters on indoor fine (<2.5 µm) and ultrafine particle concentrations in commercial office buildings. Measurements and modelling were conducted for different indoor and outdoor particle source scenarios at three office buildings in Brisbane, Australia. Overall, the in-situ efficiency, measured for particles in size ranges 6 to 3000 nm, of the deep bag filters ranged from 26.3 to 46.9% for the three buildings, while the in-situ efficiency of the electrostatic filter in one building was 60.2%. The highest PN and PM2.5 concentrations in one of the office buildings (up to 131% and 31% higher than the other two buildings, respectively) were due to the proximity of the building’s HVAC air intakes to a nearby bus-only roadway, as well as its higher outdoor ventilation rate. The lowest PN and PM2.5 concentrations (up to 57% and 24% lower than the other two buildings, respectively) were measured in a building that utilised both outdoor and mixing air filters in its HVAC system. Indoor PN concentrations were strongly influenced by outdoor levels and were significantly higher during rush-hours (up to 41%) and nucleation events (up to 57%), compared to working-hours, for all three buildings. This is the first time that the influence of new particle formation on indoor particle concentrations has been identified and quantified. A dynamic model for indoor PN concentration, which performed adequately in this study also revealed that using mixing/outdoor air filters can significantly reduce indoor particle concentration in buildings where indoor air was strongly influenced by outdoor particle levels. This work provides a scientific basis for the selection and location of appropriate filters and outdoor air intakes, during the design of new, or upgrade of existing, building HVAC systems. The results also serve to provide a better understanding of indoor particle dynamics and behaviours under different ventilation and particle source scenarios, and highlight effective methods to reduce exposure to particles in commercial office buildings.

Urban transit quality of service : user perception and behaviour

Despite its potential multiple contributions to sustainable policy objectives, urban transit is generally not widely used by the public in terms of its market share compared to that of automobiles, particularly in affluent societies with low-density urban forms like Australia. Transit service providers need to attract more people to transit by improving transit quality of service. The key to cost-effective transit service improvements lies in accurate evaluation of policy proposals by taking into account their impacts on transit users. If transit providers knew what is more or less important to their customers, they could focus their efforts on optimising customer-oriented service. Policy interventions could also be specified to influence transit users’ travel decisions, with targets of customer satisfaction and broader community welfare. This significance motivates the research into the relationship between urban transit quality of service and its user perception as well as behaviour. This research focused on two dimensions of transit user’s travel behaviour: route choice and access arrival time choice. The study area chosen was a busy urban transit corridor linking Brisbane central business district (CBD) and the St. Lucia campus of The University of Queensland (UQ). This multi-system corridor provided a ‘natural experiment’ for transit users between the CBD and UQ, as they can choose between busway 109 (with grade-separate exclusive right-of-way), ordinary on-street bus 412, and linear fast ferry CityCat on the Brisbane River. The population of interest was set as the attendees to UQ, who travelled from the CBD or from a suburb via the CBD. Two waves of internet-based self-completion questionnaire surveys were conducted to collect data on sampled passengers’ perception of transit service quality and behaviour of using public transit in the study area. The first wave survey is to collect behaviour and attitude data on respondents’ daily transit usage and their direct rating of importance on factors of route-level transit quality of service. A series of statistical analyses is conducted to examine the relationships between transit users’ travel and personal characteristics and their transit usage characteristics. A factor-cluster segmentation procedure is applied to respodents’ importance ratings on service quality variables regarding transit route preference to explore users’ various perspectives to transit quality of service. Based on the perceptions of service quality collected from the second wave survey, a series of quality criteria of the transit routes under study was quantitatively measured, particularly, the travel time reliability in terms of schedule adherence. It was proved that mixed traffic conditions and peak-period effects can affect transit service reliability. Multinomial logit models of transit user’s route choice were estimated using route-level service quality perceptions collected in the second wave survey. Relative importance of service quality factors were derived from choice model’s significant parameter estimates, such as access and egress times, seat availability, and busway system. Interpretations of the parameter estimates were conducted, particularly the equivalent in-vehicle time of access and egress times, and busway in-vehicle time. Market segmentation by trip origin was applied to investigate the difference in magnitude between the parameter estimates of access and egress times. The significant costs of transfer in transit trips were highlighted. These importance ratios were applied back to quality perceptions collected as RP data to compare the satisfaction levels between the service attributes and to generate an action relevance matrix to prioritise attributes for quality improvement. An empirical study on the relationship between average passenger waiting time and transit service characteristics was performed using the service quality perceived. Passenger arrivals for services with long headways (over 15 minutes) were found to be obviously coordinated with scheduled departure times of transit vehicles in order to reduce waiting time. This drove further investigations and modelling innovations in passenger’ access arrival time choice and its relationships with transit service characteristics and average passenger waiting time. Specifically, original contributions were made in formulation of expected waiting time, analysis of the risk-aversion attitude to missing desired service run in the passengers’ access time arrivals’ choice, and extensions of the utility function specification for modelling passenger access arrival distribution, by using complicated expected utility forms and non-linear probability weighting to explicitly accommodate the risk of missing an intended service and passenger’s risk-aversion attitude. Discussions on this research’s contributions to knowledge, its limitations, and recommendations for future research are provided at the concluding section of this thesis.

Turbulent mixing and sediment processes in peri-urban estuariesin South-East Queensland (Australia)

An estuary is formed at the mouth of a river where the tides meet a freshwater flow and it may be classified as a function of the salinity distribution and density stratification. An overview of the broad characteristics of the estuaries of South-East Queensland(Australia) is presented herein, where the small peri-urban estuaries may provide an useful indicator of potential changes which might occur in larger systems with growing urbanisation. Small peri-urban estuaries exhibits many key hydrological features and associated with ecosystem types of larger estuaries, albeit at smaller scales, often with a greater extent of urban development as a proportion of catchment area. We explore the potential for some smaller peri-urban estuaries to be used as natural laboratories to gain some much needed information on the estuarine processes, although any dynamics similarity is presently limited by critical absence of in-depth physical investigation in larger estuarine systems. The absence of the detailed turbulence and sedimentary data hampers the understanding and modelling of the estuarine zones. The interactions between the various stake holders are likely to define the vision for the future of South-East Queensland's peri-urban estuaries. This will require a solid understanding of the bio-physical function and capacity of the peri-urban estuaries. Based upon the knowledge gap, it is recommended that an adaptive trial and error approach be adopted for the future of investigation and management strategies.

Bending properties of Ag nanowires with pre-existing surface defects

Materials used in the engineering always contain imperfections or defects which significantly affect their performances. Based on the large-scale molecular dynamics simulation and the Euler–Bernoulli beam theory, the influence from different pre-existing surface defects on the bending properties of Ag nanowires (NWs) is studied in this paper. It is found that the nonlinear-elastic deformation, as well as the flexural rigidity of the NW is insensitive to different surface defects for the studied defects in this paper. On the contrary, an evident decrease of the yield strength is observed due to the existence of defects. In-depth inspection of the deformation process reveals that, at the onset of plastic deformation, dislocation embryos initiate from the locations of surface defects, and the plastic deformation is dominated by the nucleation and propagation of partial dislocations under the considered temperature. Particularly, the generation of stair-rod partial dislocations and Lomer–Cottrell lock are normally observed for both perfect and defected NWs. The generation of these structures has thwarted attempts of the NW to an early yielding, which leads to the phenomenon that more defects does not necessarily mean a lower critical force.