Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

A geometric construction of travelling wave solutions to the Keller–Segel model

We study a version of the Keller–Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.

Comparing methods for modelling spreading cell fronts

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performace of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made.

Acoustic emission condition monitoring : an application for wind turbine fault detection

Low speed rotating machines which are the most critical components in drive train of wind turbines are often menaced by several technical and environmental defects. These factors contribute to mount the economic requirement for Health Monitoring and Condition Monitoring of the systems. When a defect is happened in such system result in reduced energy loss rates from related process and due to it Condition Monitoring techniques that detecting energy loss are very difficult if not possible to use. However, in the case of Acoustic Emission (AE) technique this issue is partly overcome and is well suited for detecting very small energy release rates. Acoustic Emission (AE) as a technique is more than 50 years old and in this new technology the sounds associated with the failure of materials were detected. Acoustic wave is a non-stationary signal which can discover elastic stress waves in a failure component, capable of online monitoring, and is very sensitive to the fault diagnosis. In this paper the history and background of discovering and developing AE is discussed, different ages of developing AE which include Age of Enlightenment (1950-1967), Golden Age of AE (1967-1980), Period of Transition (1980-Present). In the next section the application of AE condition monitoring in machinery process and various systems that applied AE technique in their health monitoring is discussed. In the end an experimental result is proposed by QUT test rig which an outer race bearing fault was simulated to depict the sensitivity of AE for detecting incipient faults in low speed high frequency machine.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Outdoor flight testing of a pole inspection UAV incorporating high-speed vision

We present a pole inspection system for outdoor environments comprising a high-speed camera on a vertical take-off and landing (VTOL) aerial platform. The pole inspection task requires a vehicle to fly close to a structure while maintaining a fixed stand-off distance from it. Typical GPS errors make GPS-based navigation unsuitable for this task however. When flying outdoors a vehicle is also affected by aerodynamics disturbances such as wind gusts, so the onboard controller must be robust to these disturbances in order to maintain the stand-off distance. Two problems must therefor be addressed: fast and accurate state estimation without GPS, and the design of a robust controller. We resolve these problems by a) performing visual + inertial relative state estimation and b) using a robust line tracker and a nested controller design. Our state estimation exploits high-speed camera images (100Hz) and 70Hz IMU data fused in an Extended Kalman Filter (EKF). We demonstrate results from outdoor experiments for pole-relative hovering, and pole circumnavigation where the operator provides only yaw commands. Lastly, we show results for image-based 3D reconstruction and texture mapping of a pole to demonstrate the usefulness for inspection tasks.

Damage evaluation based on a wave energy flow map using multiple PZT sensors

A new wave energy flow (WEF) map concept was proposed in this work. Based on it, an improved technique incorporating the laser scanning method and Betti’s reciprocal theorem was developed to evaluate the shape and size of damage as well as to realize visualization of wave propagation. In this technique, a simple signal processing algorithm was proposed to construct the WEF map when waves propagate through an inspection region, and multiple lead zirconate titanate (PZT) sensors were employed to improve inspection reliability. Various damages in aluminum and carbon fiber reinforced plastic laminated plates were experimentally and numerically evaluated to validate this technique. The results show that it can effectively evaluate the shape and size of damage from wave field variations around the damage in the WEF map.

Wind speed perception and risk

Background How accurately do people perceive extreme wind speeds and how does that perception affect the perceived risk? Prior research on human–wind interaction has focused on comfort levels in urban settings or knock-down thresholds. No systematic experimental research has attempted to assess people's ability to estimate extreme wind speeds and perceptions of their associated risks. Method We exposed 76 people to 10, 20, 30, 40, 50, and 60 mph (4.5, 8.9, 13.4, 17.9, 22.3, and 26.8 m/s) winds in randomized orders and asked them to estimate wind speed and the corresponding risk they felt. Results Multilevel modeling showed that people were accurate at lower wind speeds but overestimated wind speeds at higher levels. Wind speed perceptions mediated the direct relationship between actual wind speeds and perceptions of risk (i.e., the greater the perceived wind speed, the greater the perceived risk). The number of tropical cyclones people had experienced moderated the strength of the actual–perceived wind speed relationship; consequently, mediation was stronger for people who had experienced fewer storms. Conclusion These findings provide a clearer understanding of wind and risk perception, which can aid development of public policy solutions toward communicating the severity and risks associated with natural disasters.

Fault diagnosis of low speed bearing based on acoustic emission signal and multi-class relevance vector machine

This study presents an acoustic emission (AE) based fault diagnosis for low speed bearing using multi-class relevance vector machine (RVM). A low speed test rig was developed to simulate the various defects with shaft speeds as low as 10 rpm under several loading conditions. The data was acquired using anAEsensor with the test bearing operating at a constant loading (5 kN) andwith a speed range from20 to 80 rpm. This study is aimed at finding a reliable method/tool for low speed machines fault diagnosis based on AE signal. In the present study, component analysis was performed to extract the bearing feature and to reduce the dimensionality of original data feature. The result shows that multi-class RVM offers a promising approach for fault diagnosis of low speed machines.

Fault detection of slow speed rolling element bearing with noise removal techniques

Rolling Element Bearings (REBs) are vital components in rotating machineries for providing rotating motion. In slow speed rotating machines, bearings are normally subjected to heavy static loads and a catastrophic failure can cause enormous disruption to production and human safety. Due to its low operating speed the impact energy generated by the rotating elements on the defective components is not sufficient to produce a detectable vibration response. This is further aggravated by the inability of general measuring instruments to detect and process the weak signals at the initiation of the defect accurately. Furthermore, the weak signals are often corrupted by background noise. This is a serious problem faced by maintenance engineers today and the inability to detect an incipient failure of the machine can significantly increases the risk of functional failure and costly downtime. This paper presents the application of noise removal techniques for enhancing the detection capability for slow speed REB condition monitoring. Blind deconvolution (BD) and adaptive line enhancer (ALE) are compared to evaluate their performance in enhancing the source signal with consequential removal of background noise. In the experimental study, incipient defects were seeded on a number of roller bearings and the signals were acquired using acoustic emission (AE) sensor. Kurtosis and modified peak ratio (mPR) were used to determine the detectability of signal corrupted by noise.

Time- vs. frequency-domain identification of parametric radiation force models for marine structures at zero speed

The dynamics describing the motion response of a marine structure in waves can be represented within a linear framework by the Cummins Equation. This equation contains a convolution term that represents the component of the radiation forces associated with fluid memory effects. Several methods have been proposed in the literature for the identification of parametric models to approximate and replace this convolution term. This replacement can facilitate the model implementation in simulators and the analysis of motion control designs. Some of the reported identification methods consider the problem in the time domain while other methods consider the problem in the frequency domain. This paper compares the application of these identification methods. The comparison is based not only on the quality of the estimated models, but also on the ease of implementation, ease of use, and the flexibility of the identification method to incorporate prior information related to the model being identified. To illustrate the main points arising from the comparison, a particular example based on the coupled vertical motion of a modern containership vessel is presented.

Robust speed tracking control of synchronous motors using immersion and invariance

This paper presents a novel control strategy for velocity tracking of Permanent Magnet Synchronous Machines (PMSM). The model of the machine is considered within the port-Hamiltonian framework and a control is designed using concepts of immersion and invariance (I&I) recently developed in the literature. The proposed controller ensures internal stability and output regulation, and it forces integral action on non-passive outputs.

Damping structure selection in nonlinear ship manoeuvring models

This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data.

Electromechanical wave in power systems : theory and applications

The continuum model is a key paradigm describing the behavior of electromechanical transients in power systems. In the past two decades, much research work has been done on applying the continuum model to analyze the electromechanical wave in power systems. In this work, the uniform and non-uniform continuum models are first briefly described, and some explanations borrowing concepts and tools from other fields are given. Then, the existing approaches of investigating the resulting wave equations are summarized. An application named the zero reflection controller based on the idea of the wave equations is next presented.

Modeling and analysis of a novel variable-speed cage induction generator

This paper introduces a novel cage induction generator and presents a mathematical model, through which its behavior can be accurately predicted. The proposed generator system employs a three-phase cage induction machine and generates single-phase and constant-frequency electricity at varying rotor speeds without an intermediate inverter stage. The technique uses any one of the three stator phases of the machine as the excitation winding and the remaining two phases, which are connected in series, as the power winding. The two-series-connected-and-one-isolated (TSCAOI) phase winding configuration magnetically decouples the two sets of windings, enabling independent control. Electricity is generated through the power winding at both sub- and super-synchronous speeds with appropriate excitation to the isolated single winding at any frequency of generation. A dynamic mathematical model, which accurately predicts the behavior of the proposed generator, is also presented and implemented in MATLAB/Simulink. Experimental results of a 2-kW prototype generator under various operating conditions are presented, together with theoretical results, to demonstrate the viability of the TSCAOI power generation. The proposed generator is simple and capable of both storage and retrieval of energy through its excitation winding and is expected to be suitable for applications, such as small wind turbines and microhydro systems.