Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Planning of distribution networks for medium voltage and low voltage

Determination of the placement and rating of transformers and feeders are the main objective of the basic distribution network planning. The bus voltage and the feeder current are two constraints which should be maintained within their standard range. The distribution network planning is hardened when the planning area is located far from the sources of power generation and the infrastructure. This is mainly as a consequence of the voltage drop, line loss and system reliability. Long distance to supply loads causes a significant amount of voltage drop across the distribution lines. Capacitors and Voltage Regulators (VRs) can be installed to decrease the voltage drop. This long distance also increases the probability of occurrence of a failure. This high probability leads the network reliability to be low. Cross-Connections (CC) and Distributed Generators (DGs) are devices which can be employed for improving system reliability. Another main factor which should be considered in planning of distribution networks (in both rural and urban areas) is load growth. For supporting this factor, transformers and feeders are conventionally upgraded which applies a large cost. Installation of DGs and capacitors in a distribution network can alleviate this issue while the other benefits are gained. In this research, a comprehensive planning is presented for the distribution networks. Since the distribution network is composed of low and medium voltage networks, both are included in this procedure. However, the main focus of this research is on the medium voltage network planning. The main objective is to minimize the investment cost, the line loss, and the reliability indices for a study timeframe and to support load growth. The investment cost is related to the distribution network elements such as the transformers, feeders, capacitors, VRs, CCs, and DGs. The voltage drop and the feeder current as the constraints are maintained within their standard range. In addition to minimizing the reliability and line loss costs, the planned network should support a continual growth of loads, which is an essential concern in planning distribution networks. In this thesis, a novel segmentation-based strategy is proposed for including this factor. Using this strategy, the computation time is significantly reduced compared with the exhaustive search method as the accuracy is still acceptable. In addition to being applicable for considering the load growth, this strategy is appropriate for inclusion of practical load characteristic (dynamic), as demonstrated in this thesis. The allocation and sizing problem has a discrete nature with several local minima. This highlights the importance of selecting a proper optimization method. Modified discrete particle swarm optimization as a heuristic method is introduced in this research to solve this complex planning problem. Discrete nonlinear programming and genetic algorithm as an analytical and a heuristic method respectively are also applied to this problem to evaluate the proposed optimization method.

Performance load testing and structural adequacy evaluation of road bridge decks

Many ageing road bridges, particularly timber bridges, require urgent improvement due to the demand imposed by the recent version of the Australian bridge loading code, AS 5100. As traffic volume plays a key role in the decision of budget allocations for bridge refurbishment/ replacement, many bridges in low volume traffic network remain in poor condition with axle load and/ or speed restrictions, thus disadvantaging many rural communities. This thesis examines an economical and environmentally sensible option of incorporating disused flat rail wagons (FRW) in the construction of bridges in low volume, high axle load road network. The constructability, economy and structural adequacy of the FRW road bridge is reported in the thesis with particular focus of a demonstration bridge commissioned in regional Queensland. The demonstration bridge comprises of a reinforced concrete slab (RCS) pavement resting on two FRWs with custom designed connection brackets at regular intervals along the span of the bridge. The FRW-RC bridge deck assembly is supported on elastomeric rubber pads resting on the abutment. As this type of bridge replacement technology is new and its structural design is not covered in the design standards, the in-service structural performance of the FRW bridge subjected to the high axle loadings prescribed in AS 5100 is examined through performance load testing. Both the static and the moving load tests are carried out using a fully laden commonly available three-axle tandem truck. The bridge deck is extensively strain gauged and displacement at several key locations is measured using linear variable displacement transducers (LVDTs). A high speed camera is used in the performance test and the digital image data are analysed using proprietary software to capture the locations of the wheel positions on the bridge span accurately. The wheel location is thus synchronised with the displacement and strain time series to infer the structural response of the FRW bridge. Field test data are used to calibrate a grillage model, developed for further analysis of the FRW bridge to various sets of high axle loads stipulated in the bridge design standard. Bridge behaviour predicted by the grillage model has exemplified that the live load stresses of the FRW bridge is significantly lower than the yield strength of steel and the deflections are well below the serviceability limit state set out in AS 5100. Based on the results reported in this thesis, it is concluded that the disused FRWs are competent to resist high axle loading prescribed in AS 5100 and are a viable alternative structural solution of bridge deck in the context of the low volume road networks.

Adaptive and optimal under frequency load shedding

Power systems in many countries are stressed towards their stability limit. If these stable systems experience any unexpected serious contingencies, or disturbances, there is a significant risk of instability, which may lead to wide-spread blackout. Frequency is a reliable indicator for such instability condition exists on the power system; therefore under-frequency load shedding technique is used to stable the power system by curtail some load. In this paper, the SFR-UFLS model redeveloped to generate optimal load shedding method is that optimally shed load following one single particular contingency event. The proposed optimal load shedding scheme is then tested on the 39-bus New England test system to show the performance against random load shedding scheme.

Load modelling : induction motors

Modelling the power systems load is a challenge since the load level and composition varies with time. An accurate load model is important because there is a substantial component of load dynamics in the frequency range relevant to system stability. The composition of loads need to be charaterised because the time constants of composite loads affect the damping contributions of the loads to power system oscillations, and their effects vary with the time of the day, depending on the mix of motors loads. This chapter has two main objectives: 1) describe the load modelling in small signal using on-line measurements; and 2) present a new approach to develop models that reflect the load response to large disturbances. Small signal load characterisation based on on-line measurements allows predicting the composition of load with improved accuracy compared with post-mortem or classical load models. Rather than a generic dynamic model for small signal modelling of the load, an explicit induction motor is used so the performance for larger disturbances can be more reliably inferred. The relation between power and frequency/voltage can be explicitly formulated and the contribution of induction motors extracted. One of the main features of this work is the induction motor component can be associated to nominal powers or equivalent motors

Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine : a finite element investigation

Background: In vitro investigations have demonstrated the importance of the ribcage in stabilising the thoracic spine. Surgical alterations of the ribcage may change load-sharing patterns in the thoracic spine. Computer models are used in this study to explore the effect of surgical disruption of the rib-vertebrae connections on ligament load-sharing in the thoracic spine. Methods: A finite element model of a T7-8 motion segment, including the T8 rib, was developed using CT-derived spinal anatomy for the Visible Woman. Both the intact motion segment and the motion segment with four successive stages of destabilization (discectomy and removal of right costovertebral joint, right costotransverse joint and left costovertebral joint) were analysed for a 2000Nmm moment in flexion/extension, lateral bending and axial rotation. Joint rotational moments were compared with existing in vitro data and a detailed investigation of the load sharing between the posterior ligaments carried out. Findings: The simulated motion segment demonstrated acceptable agreement with in vitro data at all stages of destabilization. Under lateral bending and axial rotation, the costovertebral joints were of critical importance in resisting applied moments. In comparison to the intact joint, anterior destabilization increases the total moment contributed by the posterior ligaments. Interpretation: Surgical removal of the costovertebral joints may lead to excessive rotational motion in a spinal joint, increasing the risk of overload and damage to the remaining ligaments. The findings of this study are particularly relevant for surgical procedures involving rib head resection, such as some techniques for scoliosis deformity correction.

A nonlinear PI and backstepping based controller for tractor-steerable trailer influenced by slip

Autonomous guidance of agricultural vehiclesis vital as mechanized farming production becomes more prevalent. It is crucial that tractor-trailers are guided with accuracy in both lateral and longitudinal directions, whilst being affected by large disturbance forces, or slips, owing to uncertain and undulating terrain. Successful research has been concentrated on trajectory control which can provide longitudinal and lateral accuracy if the vehicle moves without sliding, and the trailer is passive. In this paper, the problem of robust trajectory tracking along straight and circular paths of a tractor-steerable trailer is addressed. By utilizing a robust combination of backstepping and nonlinear PI control, a robust, nonlinear controller is proposed. For vehicles subjected to sliding, the proposed controller makes the lateral deviations and the orientation errors of the tractor and trailer converge to a neighborhood near the origin. Simulation results are presented to illustrate that the suggested controller ensures precise trajectory tracking in the presence of slip.

The effect of emotional and attentional load on attentional startle modulation

The interactive effects of emotion and attention on attentional startle modulation were investigated in two experiments. Participants performed a discrimination and counting task with two visual stimuli during which acoustic eyeblink startle-eliciting probes were presented at long lead intervals. In Experiment 1, this task was combined with aversive Pavlovian conditioning. In Group Attend CS+, the attended stimulus was followed by an aversive unconditional stimulus (US) and the ignored stimulus was presented alone whereas the ignored stimulus was paired with the US in Group Attend CS−. In Experiment 2, a non-aversive reaction time task US replaced the aversive US. Regardless of the conditioning manipulation and consistent with a modality non-specific account of attentional startle modulation, startle magnitude was larger during attended than ignored stimuli in both experiments. Blink latency shortening was differentially affected by the conditioning manipulations suggesting additive effects of conditioning and discrimination and counting task on blink startle.

Transit line passenger transmission and productiveness under high load conditions

Deterministic transit capacity analysis applies to planning, design and operational management of urban transit systems. The Transit Capacity and Quality of Service Manual (1) and Vuchic (2, 3) enable transit performance to be quantified and assessed using transit capacity and productive capacity. This paper further defines important productive performance measures of an individual transit service and transit line. Transit work (p-km) captures the transit task performed over distance. Passenger transmission (p-km/h) captures the passenger task delivered by service at speed. Transit productiveness (p-km/h) captures transit work performed over time. These measures are useful to operators in understanding their services’ or systems’ capabilities and passenger quality of service. This paper accounts for variability in utilized demand by passengers along a line and high passenger load conditions where passenger pass-up delay occurs. A hypothetical case study of an individual bus service’s operation demonstrates the usefulness of passenger transmission in comparing existing and growth scenarios. A hypothetical case study of a bus line’s operation during a peak hour window demonstrates the theory’s usefulness in examining the contribution of individual services to line productive performance. Scenarios may be assessed using this theory to benchmark or compare lines and segments, conditions, or consider improvements.