Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

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.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Analysis of electromagnetic forces in high voltage superconducting fault current limiters with saturated core

This paper presents a three-dimensional numerical analysis of the electromagnetic forces within a high voltage superconducting Fault Current Limiter (FCL) with a saturated core under short-circuit conditions. The effects of electrodynamics forces in power transformer coils under short-circuit conditions have been reported widely. However, the coil arrangement in an FCL with saturated core differs significantly from existing reactive devices. The boundary element method is employed to perform an electromagnetic force analysis on an FCL. The analysis focuses on axial and radial forces of the AC coil. The results are compared to those of a power transformer and important design considerations are highlighted.

Design and implementation of wideband baluns for Archimedean spiral antennas

The demand for high-speed data services for portable device has become a driving force for development of advanced broadband access technologies. Despite recent advances in broadband wireless technologies, there remain a number of critical issues to be resolved. One of the major concerns is the implementation of compact antennas that can operate in a wide frequency band. Spiral antenna has been used extensively for broadband applications due to its planar structure, wide bandwidth characteristics and circular polarisation. However, the practical implementation of spiral antennas is challenged by its high input characteristic impedance, relatively low gain and the need for balanced feeding structures. Further development of wideband balanced feeding structures for spiral antennas with matching impedance capabilities remain a need. This thesis proposes three wideband feeding systems for spiral antennas which are compatible with wideband array antenna geometries. First, a novel tapered geometry is proposed for a symmetric coplanar waveguide (CPW) to coplanar strip line (CPS) wideband balun. This balun can achieve the unbalanced to balanced transformation while matching the high input impedance of the antenna to a reference impedance of 50 . The discontinuity between CPW and CPS is accommodated by using a radial stub and bond wires. The bandwidth of the balun is improved by appropriately tapering the CPW line instead of using a stepped impedance transformer. Next, the tapered design is applied to an asymmetric CPW to propose a novel asymmetric CPW to CPS wideband balun. The use of asymmetric CPW does away with the discontinuities between CPW and CPS without having to use a radial stub or bond wires. Finally, a tapered microstrip line to parallel striplines balun is proposed. The balun consists of two sections. One section is the parallel striplines which are connected to the antenna, with the impedance of balanced line equal to the antenna input impedance. The other section consists of a microstrip line where the width of the ground plane is gradually reduced to eventually resemble a parallel stripline. The taper accomplishes the mode and impedance transformation. This balun has significantly improved bandwidth characteristics. Characteristics of proposed feeding structures are measured in a back-to-back configuration and compared to simulated results. The simulated and measured results show the tapered microstrip to parallel striplines balun to have more than three octaves of bandwidth. The tapered microstrip line to parallel striplines balun is integrated with a single Archimedean spiral antenna and with an array of spiral antennas. The performance of the integrated structures is simulated with the aid of electromagnetic simulation software, and results are compared to measurements. The back-to-back microstrip to parallel strip balun has a return loss of better than 10 dB over a wide bandwidth from 1.75 to 15 GHz. The performance of the microstrip to parallel strip balun was validated with the spiral antennas. The results show the balun to be an effective mean of feeding network with a low profile and wide bandwidth (2.5 to 15 GHz) for balanced spiral antennas.

Volume estimation from multiplanar 2D ultrasound images using a remote electromagnetic position and orientation sensor

A system is described for calculating volume from a sequence of multiplanar 2D ultrasound images. Ultrasound images are captured using a video digitising card (Hauppauge Win/TV card) installed in a personal computer, and regions of interest transformed into 3D space using position and orientation data obtained from an electromagnetic device (Polbemus, Fastrak). The accuracy of the system was assessed by scanning 10 water filled balloons (13-141 ml), 10 kidneys (147  200 ml) and 16 fetal livers (8  37 ml) in water using an Acuson 128XP/10 (5 MHz curvilinear probe). Volume was calculated using the ellipsoid, planimetry, tetrahedral and ray tracing methods and compared with the actual volume measured by weighing (balloons) and water displacement (kidneys and livers). The mean percentage error for the ray tracing method was 0.9 ± 2.4%, 2.7 ± 2.3%, 6.6 ± 5.4% for balloons, kidneys and livers, respectively. So far the system has been used clinically to scan fetal livers and lungs, neonate brain ventricles and adult prostate glands.

Application of high voltage, high frequency pulsed electromagnetic field on cortical bone tissue

Over the last few decades, electric and electromagnetic fields have achieved important role as stimulator and therapeutic facility in biology and medicine. In particular, low magnitude, low frequency, pulsed electromagnetic field has shown significant positive effect on bone fracture healing and some bone diseases treatment. Nevertheless, to date, little attention has been paid to investigate the possible effect of high frequency, high magnitude pulsed electromagnetic field (pulse power) on functional behaviour and biomechanical properties of bone tissue. Bone is a dynamic, complex organ, which is made of bone materials (consisting of organic components, inorganic mineral and water) known as extracellular matrix, and bone cells (live part). The cells give the bone the capability of self-repairing by adapting itself to its mechanical environment. The specific bone material composite comprising of collagen matrix reinforced with mineral apatite provides the bone with particular biomechanical properties in an anisotropic, inhomogeneous structure. This project hypothesized to investigate the possible effect of pulse power signals on cortical bone characteristics through evaluating the fundamental mechanical properties of bone material. A positive buck-boost converter was applied to generate adjustable high voltage, high frequency pulses up to 500 V and 10 kHz. Bone shows distinctive characteristics in different loading mode. Thus, functional behaviour of bone in response to pulse power excitation were elucidated by using three different conventional mechanical tests applying three-point bending load in elastic region, tensile and compressive loading until failure. Flexural stiffness, tensile and compressive strength, hysteresis and total fracture energy were determined as measure of main bone characteristics. To assess bone structure variation due to pulse power excitation in deeper aspect, a supplementary fractographic study was also conducted using scanning electron micrograph from tensile fracture surfaces. Furthermore, a non-destructive ultrasonic technique was applied for determination and comparison of bone elasticity before and after pulse power stimulation. This method provided the ability to evaluate the stiffness of millimetre-sized bone samples in three orthogonal directions. According to the results of non-destructive bending test, the flexural elasticity of cortical bone samples appeared to remain unchanged due to pulse power excitation. Similar results were observed in the bone stiffness for all three orthogonal directions obtained from ultrasonic technique and in the bone stiffness from the compression test. From tensile tests, no significant changes were found in tensile strength and total strain energy absorption of the bone samples exposed to pulse power compared with those of the control samples. Also, the apparent microstructure of the fracture surfaces of PP-exposed samples (including porosity and microcracks diffusion) showed no significant variation due to pulse power stimulation. Nevertheless, the compressive strength and toughness of millimetre-sized samples appeared to increase when the samples were exposed to 66 hours high power pulsed electromagnetic field through screws with small contact cross-section (increasing the pulsed electric field intensity) compare to the control samples. This can show the different load-bearing characteristics of cortical bone tissue in response to pulse power excitation and effectiveness of this type of stimulation on smaller-sized samples. These overall results may address that although, the pulse power stimulation can influence the arrangement or the quality of the collagen network causing the bone strength and toughness augmentation, it apparently did not affect the mineral phase of the cortical bone material. The results also confirmed that the indirect application of high power pulsed electromagnetic field at 500 V and 10 kHz through capacitive coupling method, was athermal and did not damage the bone tissue construction.

Cold and heat waves in the United States

Extreme cold and heat waves, characterised by a number of cold or hot days in succession, place a strain on people’s cardiovascular and respiratory systems. The increase in deaths due to these waves may be greater than that predicted by extreme temperatures alone. We examined cold and heat waves in 99 US cities for 14 years (1987–2000) and investigated how the risk of death depended on the temperature threshold used to define a wave, and a wave’s timing, duration and intensity. We defined cold and heat waves using temperatures above and below cold and heat thresholds for two or more days. We tried five cold thresholds using the first to fifth percentiles of temperature, and five heat thresholds using the ninety-fifth to ninety-ninth percentiles. The extra wave effects were estimated using a two-stage model to ensure that their effects were estimated after removing the general effects of temperature. The increases in deaths associated with cold waves were generally small and not statistically significant, and there was even evidence of a decreased risk during the coldest waves. Heat waves generally increased the risk of death, particularly for the hottest heat threshold. Cold waves of a colder intensity or longer duration were not more dangerous. Cold waves earlier in the cool season were more dangerous, as were heat waves earlier in the warm season. In general there was no increased risk of death during cold waves above the known increased risk associated with cold temperatures. Cold or heat waves earlier in the cool or warm season may be more dangerous because of a build up in the susceptible pool or a lack of preparedness for cold or hot temperatures.

Are plasmons responsible for the Raman signal enhancement observed with gold nanoparticle sensors?

The electromagnetic enhancement that occurs in surface enhanced Raman scattering (SERS) substrates containing gold nanoparticles (NPs) is believed to arise through the generation of localised surface plasmons. We present results that show no SERS signals are obtained when 25 nm diameter gold NPs layered quartz substrates exposed to 2-aminopyridine are illuminated with plasmon resonant 532 nm radiation, but SERS signals are observed when the same samples are illuminated with non-resonant 785 nm radiation.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Accuracy of FEM and BEM for electromagnetic flux calculations in high power applications

The development and design of electric high power devices with electromagnetic computer-aided engineering (EM-CAE) software such as the Finite Element Method (FEM) and Boundary Element Method (BEM) has been widely adopted. This paper presents the analysis of a Fault Current Limiter (FCL), which acts as a high-voltage surge protector for power grids. A prototype FCL was built. The magnetic flux in the core and the resulting electromagnetic forces in the winding of the FCL were analyzed using both FEM and BEM. An experiment on the prototype was conducted in a laboratory. The data obtained from the experiment is compared to the numerical solutions to determine the suitability and accuracy of the two methods.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Privacy of RFID - models and protocols

Radio Frequency Identification is a wireless identification method that utilizes the reception of electromagnetic radio waves. This research has proposed a novel model to allow for an in-depth security analysis of current protocols and developed new flexible protocols that can be adapted to offer either stronger security or better efficiency.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.