Planar radial spots in a three-component FitzHugh-Nagumo system

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

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.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Numerical modelling of load bearing light gauge steel frame wall systems exposed to realistic design fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. Conventionally the fire rating of load bearing wall systems made of Light gauge Steel Frames (LSF) is determined using fire tests based on the standard time-temperature curve in ISO834 [1]. However, modern commercial and residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the fire performance of LSF walls was undertaken using realistic design fire curves developed based on Eurocode parametric [2] and Barnett’s BFD [3] curves using both full scale fire tests and numerical studies. It included LSF walls without cavity insulation, and the recently developed externally insulated composite panel system. This paper presents the details of finite element models developed to simulate the full scale fire tests of LSF wall panels under realistic design fires. Finite element models of LSF walls exposed to realistic design fires were developed, and analysed under both transient and steady state fire conditions using the measured stud time-temperature curves. Transient state analyses were performed to simulate fire test conditions while steady state analyses were performed to obtain the load ratio versus time and failure temperature curves of LSF walls. Details of the developed finite element models and the results including the axial deformation and lateral deflection versus time curves, and the stud failure modes and times are presented in this paper. Comparison with fire test results demonstrate the ability of developed finite element models to predict the performance and fire resistance ratings of LSF walls under realistic design fires.

Design of light gauge steel roofing systems subject to high wind forces

Light gauge steel roofing systems made of thin profiled roof sheeting and battens are used commonly in residential, industrial and commercial buildings. Their critical design load combination is that due to wind uplift forces that occur during high wind events such as tropical cyclones and thunderstorms. However, premature local failures at their screw connections have been a concern for many decades since cyclone Tracy that devastated Darwin in 1974. Extensive research that followed cyclone Tracy on the pull-through and pull-out failures of roof sheeting to batten connections has significantly improved the safety of roof sheeting. However, this has made the batten to rafter/truss connection the weakest, and recent wind damage investigations have shown the failures of these connections and the resulting loss of entire roof structures. Therefore an experimental research program using both small scale and full scale air-box tests is currently under way to investigate the pull-through failures of thin-walled steel battens under high wind uplift forces. Tests have demonstrated that occurrence of pull-through failures in the bottom flanges of steel batttens and the need to develop simple test and design methods as a function of many critical parameters such as steel batten geometry, thickness and grade, screw fastener sizes and other fastening details. This paper presents the details of local failures that occur in light fauge roofing systems, a review of the current design and test methods for steel battens and associated short comings, and the test results obtained to date on pull-through failures of battens from small scale and full scale tests. Finally, it proposes the use of suitable small scale test methods that can be used by both researchers and manufacturers of such screw-fastened light gauge steel batten systems.

Low-pressure planar magnetron discharge for surface deposition and nanofabrication

Current-voltage characteristics of the planar magnetron are studied experimentally and by numerical simulation. Based on the measured current-voltage characteristics, a model of the planar magnetron discharge is developed with the background gas pressure and magnetic field used as parameters. The discharge pressure was varied in a range of 0.7-1.7 Pa, the magnetic field of the magnetron was of 0.033-0.12 T near the cathode surface, the discharge current was from 1 to 25 A, and the magnetic field lines were tangential to the substrate surface in the region of the magnetron discharge ignition. The discharge model describes the motion of energetic secondary electrons that gain energy by passing the cathode sheath across the magnetic field, and the power required to sustain the plasma generation in the bulk. The plasma electrons, in turn, are accelerated in the electric field and ionize effectively the background gas species. The model is based on the assumption about the prevailing Bohm mechanism of electron conductivity across the magnetic field. A criterion of the self-sustained discharge ignition is used to establish the dependence of the discharge voltage on the discharge current. The dependence of the background gas density on the current is also observed from the experiment. The model is consistent with the experimental results. © 2010 American Institute of Physics.

Fire performance and design of load bearing light gauge steel frame wall systems exposed to realistic design fires

This paper presents the fire performance results of light gauge steel frame (LSF) walls lined with single and double plasterboards, and externally insulated with rock fibre insulation as obtained using a finite element analysis based parametric study. A validated numerical model was used to study the influence of various fire curves developed for a range of compartment characteristics. Data from the parametric study was utilized to develop a simplified method to predict the fire resistance ratings of LSF walls exposed to realistic design fire curves. Further, this paper also presents the details of suitable fire design rules based on current cold-formed steel standards and the modifications proposed by previous researchers. Of these the recently developed design rules by Gunalan and Mahendran [1] were investigated to determine their applicability to predict the axial compression strengths and fire resistance ratings (FRR) of LSF walls exposed to realistic design fires. Finally, the stud failure times obtained from fire design rules and finite element studies were compared for LSF walls lined with single and double plasterboards, and externally insulated with rock fibres under realistic design fire curves.

Fire resistance rating of light gauge steel frame walls exposed to realistic design fires : a review and development of time equivalent approach

This paper presents the details of research undertaken on the development of an energy based time equivalent approach for light gauge steel frame (LSF) walls. This research utilized an energy based time equivalent approach to obtain the fire resistance ratings (FRR) of LSF walls exposed to realistic design fires with respect to standard fire exposure [1]. It is based on the equal area concept of fire severity and relates to the amount of energy transferred to the member. The proposed method was used to predict the fire resistance of single and double plasterboard lined and externally insulated LSF walls. The predicted fire resistance ratings were compared with the results from finite element analyses and fire design rules for three different wall configurations. This paper presents the review of the available time equivalent approaches and the development of energy based time equivalent approach for the prediction of fire resistance ratings of LSF walls exposed to realistic design fires.

Standing surface waves in a dust-contaminated large-area planar plasma source

The effect of charged particulates or dusts on surface wave produced microwave discharges is studied. The frequencies of the standing electromagnetic eigenmodes of large-area flat plasmas are calculated. The dusts absorb a significant amount of the plasma electrons and can lead to a modification of the electromagnetic field structure in the discharge by shifting the originally excited operating mode out of resonance. For certain given proportions of dusts, mode conversion is found to be possible. The power loss in the discharge is also increased because of dust-specific dissipations, leading to a decrease of the operating mode quality factor.

Discharge parameters and dominant electron conductivity mechanism in a low-pressure planar magnetron discharge

Parameters of a discharge sustained in a planar magnetron configuration with crossed electric and magnetic fields are studied experimentally and numerically. By comparing the data obtained in the experiment with the results of calculations made using the proposed theoretical model, conclusion was made about the leading role of the turbulence-driven Bohm electron conductivity in the low-pressure operation mode (up to 1 Pa) of the discharge in crossed electric and magnetic fields. A strong dependence of the width of the cathode sputter trench, associated with the ionization region of the magnetron discharge, on the discharge parameters was observed in the experiments. The experimental data were used as input parameters in the discharge model that describes the motion of secondary electrons across the magnetic field in the ionization region and takes into account the classical, near-wall, and Bohm mechanisms of electron conductivity.

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.