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.

Observation of solution-induced corneal staining with fluorescein, rose bengal and lissamine green

Ever since sodium fluorescein (‘fluorescein’ [FL]) was first used to investigate the ocular surface over a century ago, the term ‘staining’ has been taken to mean the presence of ocular surface fluorescence [1]. This term has not been necessarily taken to infer any particular mechanism of causation, and indeed, can be attributed to a variety of possible aetiologies [2]. In recent times, there has been considerable interest in a form of ocular surface fluorescence seen in association with the use of certain combinations of soft contact lenses and multipurpose solutions. The first clinical account of this phenomenon was reported by Jones et al. [3], which was followed by a more formal investigation by the same author in 2002 [4]. Jones et al described this appearance as a ‘classic solution-based toxicity reaction’. Subsequently, this appearance has come to be known as ‘solution-induced corneal staining’ or more recently by the acronym ‘SICS’ [5]. The term SICS is potentially problematic in that from a cell biology point of view, there is an inference that ‘staining’ means the entry of a dye into corneal epithelial cells. Morgan and Maldonado-Codina [2] noted there was no foundation of solid scientific literature underpinning our understanding of the true basic causative mechanisms of this phenomenon; since that time, further work has been published in this field [6] and [7] but questions still remain about the precise aetiology of this phenomenon...

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.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

A Satellite Selection Algorithm for Achieving High Reliability of Ambiguity Resolution with GPS and Beidou Constellations

Reliability of carrier phase ambiguity resolution (AR) of an integer least-squares (ILS) problem depends on ambiguity success rate (ASR), which in practice can be well approximated by the success probability of integer bootstrapping solutions. With the current GPS constellation, sufficiently high ASR of geometry-based model can only be achievable at certain percentage of time. As a result, high reliability of AR cannot be assured by the single constellation. In the event of dual constellations system (DCS), for example, GPS and Beidou, which provide more satellites in view, users can expect significant performance benefits such as AR reliability and high precision positioning solutions. Simply using all the satellites in view for AR and positioning is a straightforward solution, but does not necessarily lead to high reliability as it is hoped. The paper presents an alternative approach that selects a subset of the visible satellites to achieve a higher reliability performance of the AR solutions in a multi-GNSS environment, instead of using all the satellites. Traditionally, satellite selection algorithms are mostly based on the position dilution of precision (PDOP) in order to meet accuracy requirements. In this contribution, some reliability criteria are introduced for GNSS satellite selection, and a novel satellite selection algorithm for reliable ambiguity resolution (SARA) is developed. The SARA algorithm allows receivers to select a subset of satellites for achieving high ASR such as above 0.99. Numerical results from a simulated dual constellation cases show that with the SARA procedure, the percentages of ASR values in excess of 0.99 and the percentages of ratio-test values passing the threshold 3 are both higher than those directly using all satellites in view, particularly in the case of dual-constellation, the percentages of ASRs (>0.99) and ratio-test values (>3) could be as high as 98.0 and 98.5 % respectively, compared to 18.1 and 25.0 % without satellite selection process. It is also worth noting that the implementation of SARA is simple and the computation time is low, which can be applied in most real-time data processing applications.

Organo-LDH synthesized via tricalcium aluminate hydration in the present of Na-dodecylbenzenesulfate aqueous solution and subsequent investigated by near-infrared and mid-infrared

Na-dodecylbenzenesulfate (SDBS), a natural anionic surfactant, has been successfully intercalated into a Ca based LDH host structure during tricalcium aluminate hydration in the presence of SDBS aqueous solution (CaAl-SDBS-LDH). The resulting product was characterized by powder X-ray diffraction (XRD), mid-infrared (MIR) spectroscopy combined with near-infrared (NIR) spectroscopy technique, thermal analysis (TG–DTA) and scan electron microscopy (SEM). The XRD results revealed that the interlayer distance of resultant product was expanded to 30.46 Å. MIR combined with NIR spectra offered an effective method to illustrate this intercalation. The NIR spectra (6000–5500 cm−1) displayed prominent bands to expound SDBS intercalated into hydration product of C3A. And the bands around 8300 cm−1 were assigned to the second overtone of the first fundamental of CH stretching vibrations of SDBS. In addition, thermal analysis showed that the dehydration and dehydroxylation took place at ca. 220 °C and 348 °C, respectively. The SEM results appeared approximately hexagonal platy crystallites morphology for CaAl-SDBS-LDH, with particle size smaller and thinner.

A new approach to prepare ZVI and its application in removal of Cr(VI) from aqueous solution

Zero valent iron (ZVI) was prepared by reducing natural goethite (NG-ZVI) and synthetic goethite (SG-ZVI) in hydrogen at 550 °C. XRD, TEM, FESEM/EDS and specific surface area (SSA) and pore analyser were used to characterize goethites and reduced goethites. Both NG-ZVI and SG-ZVI with a size of nanoscale to several hundreds of nanometers were obtained by reducing goethites at 550 °C. The reductive capacity of the ZVIs was assessed by removal of Cr(VI) at ambient temperature in comparison with that of commercial iron powder (CIP). The effect of contact time, initial concentration and reaction temperature on Cr(VI) removal was investigated. Furthermore, the uptake mechanism was discussed according to isotherms, thermodynamic analysis and the results of XPS. The results showed that SG-ZVI had the best reductive capacity to Cr(VI) and reduced Cr(VI) to Cr(III). The results suggest that hydrogen reduction is a good approach to prepare ZVI and this type of ZVI is potentially useful in remediating heavy metals as a material of permeable reaction barrier.

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

Detection and quantification of tear phospholipids and cholesterol in contact lens deposits : the effect of contact lens material and lens care solution

PURPOSE. To examine the deposition of tear phospholipids and cholesterol onto worn contact lenses and the effect of lens material and lens care solution. METHODS. Lipids were extracted from tears and worn contact lenses using 2:1 chloroform: Methanol and the extract washed with aqueous ammonium acetate, before analysis by electrospray ionization tandem mass spectrometry (ESI-MS/MS). RESULTS. Twenty-three molecular lipids from the sphingomyelin (SM) and phosphatidylcholine (PC) classes were detected in tears, with total concentrations of each class determined to be 5 ± 1 pmol/μL (~3.8 μg/mL) and 6 ± 1 pmol/μL (~ 4.6μg/mL), respectively. The profile of individual phospholipids in both of these classes was shown to be similar in contact lens deposits. Deposition of representative polar and nonpolar lipids were shown to be significantly higher on senofilcon A contact lenses, with ~59 ng/lens SM, 195 ng/lens PC, and 9.9 μg/lens cholesterol detected, whereas balafilcon A lens extracts contained ~19 ng/lens SM, 19 ng/lens PC, and 3.9 μg/lens cholesterol. Extracts from lenses disinfected and cleaned with two lens care solutions showed no significant differences in total PC and SM concentrations; however, a greater proportion of PC than SM was observed, compared with that in tears. CONCLUSIONS. Phospholipid deposits extracted from worn contact lenses show a molecular profile similar to that in tears. The concentration of representative polar and nonpolar lipids deposited onto contact lenses is significantly affected by lens composition. There is a differential efficacy in the removal of PC and SM with lens care solutions.

Numerical modelling of porous injection in a radical farming scramjet

A numerical investigation of the behaviour of fuel injection through a porous surface in an inlet-fuelled, radial-farming scramjet is presented. The performance of porous fuel injection is compared to discrete port hole injection at an equivalence ratio of φ ≈ 0.4 for both cases. The comparison is performed at a Mach 6.5 flow condition with a total specific enthalpy of 4.3 MJ/kg. The numerical results are compared to experiments performed in the T4 shock tunnel where available. The presented results demonstrate for the first time, that porous fuel injection has the potential to outperform port hole injectors in scramjet engines in terms of fuel-air mixing, ignition delays and achievable combustion efficiencies despite reduced fuel penetration heights.

Numerical investigation of the influence of topography on simulated downburst wind fields

A, dry, non-hydrostatic sub-cloud model is used to simulate an isolated stationary downburst wind event to study the influence topographic features have on the near-ground wind structure of these storms. It was generally found that storm maximum wind speeds could be increased by up to 30% because of the presence of a topographic feature at the location of maximum wind speeds. Comparing predicted velocity profile amplification with that of a steady flow impinging jet, similar results were found despite the simplifications made in the impinging jet model. Comparison of these amplification profiles with those found in the simulated boundary layer winds reveal reductions of up to 30% in the downburst cases. Downburst and boundary layer amplification profiles were shown to become more similar as the topographic feature height was reduced with respect to the outflow depth.

Numerical simulation of downburst winds

The wind field of an intense idealised downburst wind storm has been studied using an axisymmetric, dry, non-hydrostatic numerical sub-cloud model. The downburst driving processes of evaporation and melting have been paramaterized by an imposed cooling source that triggers and sustains a downdraft. The simulated downburst exhibits many characteristics of observed full-scale downburst events, in particular the presence of a primary and counter rotating secondary ring vortex at the leading edge of the diverging front. The counter-rotating vortex is shown to significantly influence the development and structure of the outflow. Numerical forcing and environmental characteristics have been systematically varied to determine the influence on the outflow wind field. Normalised wind structure at the time of peak outflow intensity was generally shown to remain constant for all simulations. Enveloped velocity profiles considering the velocity structure throughout the entire storm event show much more scatter. Assessing the available kinetic energy within each simulated storm event, it is shown that the simulated downburst wind events had significantly less energy available for loading isolated structures when compared with atmospheric boundary layer winds. The discrepancy is shown to be particularly prevalent when wind speeds were integrated over heights representative of tall buildings. A similar analysis for available full scale measurements led to similar findings.

Numerical simulation of idealised three-dimensional downburst wind fields

Convective downburst wind storms generate the peak annual gust wind speed for many parts of the non-cyclonic world at return periods of importance for ultimate limit state design. Despite this there is little clear understanding of how to appropriately design for these wind events given their significant dissimilarities to boundary layer winds upon which most design is based. To enhance the understanding of wind fields associated with these storms a three-dimensional numerical model was developed to simulate a multitude of idealised downburst scenarios and to investigate their near-ground wind characteristics. Stationary and translating downdraft wind events in still and sheared environments were simulated with baseline results showing good agreement with previous numerical work and full-scale observational data. Significant differences are shown in the normalised peak wind speed velocity profiles depending on the environmental wind conditions in the vicinity of the simulated event. When integrated over the height of mid- to high rise structures, all simulated profiles are shown to produce wind loads smaller than an equivalent 10 m height matched open terrain boundary layer profile. This suggests that for these structures the current design approach is conservative from an ultimate loading standpoint. Investigating the influence of topography on the structure of the simulated near-ground downburst wind fields, it is shown that these features amplify wind speeds in a manner similar to that expected for boundary layer winds, but the extent of amplification is reduced. The level of reduction is shown to be dependent on the depth of the simulated downburst outflow.

An integrated approach for earthwork allocation, sequencing and routing

Planning techniques for large scale earthworks have been considered in this article. To improve these activities a “block theoretic” approach was developed that provides an integrated solution consisting of an allocation of cuts to fills and a sequence of cuts and fills over time. It considers the constantly changing terrain by computing haulage routes dynamically. Consequently more realistic haulage costs are used in the decision making process. A digraph is utilised to describe the terrain surface which has been partitioned into uniform grids. It reflects the true state of the terrain, and is altered after each cut and fill. A shortest path algorithm is successively applied to calculate the cost of each haul, and these costs are summed over the entire sequence, to provide a total cost of haulage. To solve this integrated optimisation problem a variety of solution techniques were applied, including constructive algorithms, meta-heuristics and parallel programming. The extensive numerical investigations have successfully shown the applicability of our approach to real sized earthwork problems.

Numerical modelling and design of lipped channel beams subject to shear

Cold-formed steel members are increasingly used as primary structural elements in buildings due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. Many research studies have been carried out to evaluate the behaviour and design of LCBs subject to pure bending actions. However, limited research has been undertaken on the shear behaviour and strength of LCBs. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs. Finite element models of simply supported LCBs with aspect ratios of 1.0 and 1.5 were considered under a mid-span load. They were then validated by comparing their results with test results and used in a detailed parametric study based on the validated finite element models. Numerical studies were conducted to investigate the shear buckling and post-buckling behaviour of LCBs. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs. Improved design equations were therefore proposed for the shear strength of LCBs. This paper presents the details of this numerical study of LCBs and the results.