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.

Hybrid model for motorway travel time estimation considering increased detector spacing

Travel time estimation and prediction on motorways has long been a topic of research. Prediction modeling generally assumes that the estimation is perfect. No matter how good is the prediction modeling- the errors in estimation can significantly deteriorate the accuracy and reliability of the prediction. Models have been proposed to estimate travel time from loop detector data. Generally, detectors are closely spaced (say 500m) and travel time can be estimated accurately. However, detectors are not always perfect, and even during normal running conditions few detectors malfunction, resulting in increase in the spacing between the functional detectors. Under such conditions, error in the travel time estimation is significantly large and generally unacceptable. This research evaluates the in-practice travel time estimation model during different traffic conditions. It is observed that the existing models fail to accurately estimate travel time during large detector spacing and congestion shoulder periods. Addressing this issue, an innovative Hybrid model that only considers loop data for travel time estimation is proposed. The model is tested using simulation and is validated with real Bluetooth data from Pacific Motorway Brisbane. Results indicate that during non free flow conditions and larger detector spacing Hybrid model provides significant improvement in the accuracy of travel time estimation.

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.

The influence of Monte Carlo source parameters on detector design and dose perturbation in small field dosimetry

To obtain accurate Monte Carlo simulations of small radiation fields, it is important model the initial source parameters (electron energy and spot size) accurately. However recent studies have shown that small field dosimetry correction factors are insensitive to these parameters. The aim of this work is to extend this concept to test if these parameters affect dose perturbations in general, which is important for detector design and calculating perturbation correction factors. The EGSnrc C++ user code cavity was used for all simulations. Varying amounts of air between 0 and 2 mm were deliberately introduced upstream to a diode and the dose perturbation caused by the air was quantified. These simulations were then repeated using a range of initial electron energies (5.5 to 7.0 MeV) and electron spot sizes (0.7 to 2.2 FWHM). The resultant dose perturbations were large. For example 2 mm of air caused a dose reduction of up to 31% when simulated with a 6 mm field size. However these values did not vary by more than 2 % when simulated across the full range of source parameters tested. If a detector is modified by the introduction of air, one can be confident that the response of the detector will be the same across all similar linear accelerators and the Monte Carlo modelling of each machine is not required.

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.

CTCombine : rotating and combining CT data with an accurate detector model to simulate radiotherapy portal imaging at non-zero beam angles

Established Monte Carlo user codes BEAMnrc and DOSXYZnrc permit the accurate and straightforward simulation of radiotherapy experiments and treatments delivered from multiple beam angles. However, when an electronic portal imaging detector (EPID) is included in these simulations, treatment delivery from non-zero beam angles becomes problematic. This study introduces CTCombine, a purpose-built code for rotating selected CT data volumes, converting CT numbers to mass densities, combining the results with model EPIDs and writing output in a form which can easily be read and used by the dose calculation code DOSXYZnrc...

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.

Half-wave cycloconverter-based photovoltaic microinverter topology with phase-shift power modulation

A grid-connected microinverter with a reduced number of power conversion stages and fewer passive components is proposed. A high-frequency transformer and a series-resonant tank are used to interface the full-bridge inverter to the half-wave cycloconverter. All power switches are switched with zero-voltage switching. Phase-shift power modulation is used to control the output power of the inverter. A steady-state analysis of the proposed topology is presented to determine the average output power of the inverter. Analysis of soft switching of the full-bridge and the half-wave cycloconverter is presented with respect to voltage gain, quality factor, and phase shift of the inverter. Simulation and experimental results are presented to validate the operation of the proposed topology.

Pulsed dc- and sine-wave-excited cold atmospheric plasma plumes: A comparative analysis

Cold atmospheric-pressure plasma plumes are generated in the ambient air by a single-electrode plasma jet device powered by pulsed dc and ac sine-wave excitation sources. Comprehensive comparisons of the plasma characteristics, including electrical properties, optical emission spectra, gas temperatures, plasma dynamics, and bacterial inactivation ability of the two plasmas are carried out. It is shown that the dc pulse excited plasma features a much larger discharge current and stronger optical emission than the sine-wave excited plasma. The gas temperature in the former discharge remains very close to the room temperature across the entire plume length; the sine-wave driven discharge also shows a uniform temperature profile, which is 20-30 degrees higher than the room temperature. The dc pulse excited plasma also shows a better performance in the inactivation of gram-positive staphylococcus aureus bacteria. These results suggest that the pulsed dc electric field is more effective for the generation of nonequilibrium atmospheric pressure plasma plumes for advanced plasma health care applications.

A model of a large-area planar plasma producer based on surface wave propagation in a plasma-metal structure with a dielectric sheath

A theoretical model of a large-area planar plasma producer based on surface wave (SW) propagation in a plasma-metal structure with a dielectric sheath is presented. The SW which produces and sustains the microwave gas discharge in the planar structure propagates along an external magnetic field and possesses an eigenfrequency within the range between electron cyclotron and electron plasma frequencies. The spatial distributions of the produced plasma density, electromagnetic fields, energy flow density, phase velocity and reverse skin depth of the SW are obtained analytically and numerically.

The effect of near-sheath dusts on a surface-wave-sustained gas discharge

The effect of near-sheath dusts on the rf power loss in a surface-wave-sustained gas discharge is studied. The planar plasma is bounded by a dielectric and consists of an inhomogeneous near-wall transition layer (sheath), a dusty plasma layer and an outer dust-free plasma. The discharge is maintained by high-frequency axially symmetrical surface waves. The surface-wave power loss from the most relevant dissipative mechanisms in typical discharge plasmas is analysed.

Nonresonant power transfer in plasma-surface interactions via two-surface wave decay

The excitation of pairs of electron surface waves via nonresonant decay of plasma waves incident onto a solid surface is studied in the context of controlling the interaction of pulsed electromagnetic radiation with plasma-exposed solid surfaces. The role of the plasma-exposed surfaces in nonlinear heating of the plasma edge and related power transfer is discussed. It is shown that the maximum efficiency of the power transfer at solid surfaces with dielectric permittivity εd <3 corresponds to the resonant two-surface wave decay. On the other hand, for solids with εd >3 the maximum power transfer efficiency is achieved through nonresonant excitation of the quasistatic surface waves. In this case the plasma waves generated by external radiation dissipate their energy into the plasma periphery most effectively.

Parameters and equilibrium profiles for large-area surface-wave sustained plasmas

The equilibrium profiles of the plasma parameters of large-area if discharges in a finite-length metal-shielded dielectric cylinder are computed using a two-dimensional fluid code. The rf power is coupled to the plasma through edge-localized surface waves traveling in the azimuthal direction along the plasma edge. It is shown that self-consistent accounting for axial plasma diffusion and radial nonuniformity of the electron temperature can explain the frequently reported deviations of experimentally measured radial density profiles from that of the conventional linear diffusion models. The simulation results are in a good agreement with existing experimental data obtained from surface-wave sustained large-diameter plasmas. © 2002 The American Physical Society.

Two-surface wave decay : controlling power transfer in plasma-surface interactions

Controlled interaction of high-power pulsed electromagnetic radiation with plasma-exposed solid surfaces is a major challenge in applications spanning from electron beam accelerators in microwave electronics to pulsed laser ablation-assisted synthesis of nanomaterials. It is shown that the efficiency of such interaction can be potentially improved via an additional channel of wave power dissipation due to nonlinear excitation of two counterpropagating surface waves, resonant excitations of the plasma-solid system.Physics.