Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Oxygen delivery through high-flow nasal cannulae increase end-expiratory lung volume and reduce respiratory rate in post-cardiac surgical patients

Background: High-flow nasal cannulae (HFNC) create positive oropharyngeal airway pressure but it is unclear how their use affects lung volume. Electrical impedance tomography (EIT) allows assessment of changes in lung volume by measuring changes in lung impedance. Primary objectives were to investigate the effects of HFNC on airway pressure (Paw) and end-expiratory lung volume (EELV), and to identify any correlation between the two. Secondary objectives were to investigate the effects of HFNC on respiratory rate (RR), dyspnoea, tidal volume and oxygenation; and the interaction between body mass index (BMI) and EELV. Methods: Twenty patients prescribed HFNC post-cardiac surgery were investigated. Impedance measures, Paw, PaO2/FiO2 ratio, RR and modified Borg scores were recorded first on low flow oxygen (nasal cannula or Hudson face mask) and then on HFNC. Results: A strong and significant correlation existed between Paw and end-expiratory lung impedance (EELI) (r=0.7, p<0.001). Compared with low flow oxygen, HFNC significantly increased EELI by 25.6% (95% CI 24.3, 26.9) and Paw by 3.0 cmH2O (95% CI 2.4, 3.7). RR reduced by 3.4 breaths per minute (95% CI 1.7, 5.2) with HFNC use, tidal impedance variation increased by 10.5% (95% CI 6.1, 18.3) and PaO2/FiO2 ratio improved by 30.6 mmHg (95% CI 17.9, 43.3). HFNC improved subjective dyspnoea scoring (p=0.023). Increases in EELI were significantly influenced by BMI, with larger increases associated with higher BMIs (p<0.001). Conclusions: This study suggests that HFNC improve dyspnoea and oxygenation by increasing both EELV and tidal volume, and are most beneficial in patients with higher BMIs.

Investigation of phenol degradation : True reaction kinetics on fixed film titanium dioxide photocatalyst

This study of photocatalytic oxidation of phenol over titanium dioxide films presents a method for the evaluation of true reaction kinetics. A flat plate reactor was designed for the specific purpose of investigating the influence of various reaction parameters, specifically photocatalytic film thickness, solution flow rate (1–8 l min−1), phenol concentration (20, 40 and 80 ppm), and irradiation intensity (70.6, 57.9, 37.1and 20.4 W m−2), in order to further understand their impact on the reaction kinetics. Special attention was given to the mass transfer phenomena and the influence of film thickness. The kinetics of phenol degradation were investigated with different irradiation levels and initial pollutant concentration. Photocatalytic degradation experiments were performed to evaluate the influence of mass transfer on the reaction and, in addition, the benzoic acid method was applied for the evaluation of mass transfer coefficient. For this study the reactor was modelled as a batch-recycle reactor. A system of equations that accounts for irradiation, mass transfer and reaction rate was developed to describe the photocatalytic process, to fit the experimental data and to obtain kinetic parameters. The rate of phenol photocatalytic oxidation was described by a Langmuir–Hinshelwood type law that included competitive adsorption and degradation of phenol and its by-products. The by-products were modelled through their additive effect on the solution total organic carbon.

The flammability of metallic materials in normal and reduced gravity

Metallic materials exposed to oxygen-enriched atmospheres – as commonly used in the medical, aerospace, aviation and numerous chemical processing industries – represent a significant fire hazard which must be addressed during design, maintenance and operation. Hence, accurate knowledge of metallic materials flammability is required. Reduced gravity (i.e. space-based) operations present additional unique concerns, where the absence of gravity must also be taken into account. The flammability of metallic materials has historically been quantified using three standardised test methods developed by NASA, ASTM and ISO. These tests typically involve the forceful (promoted) ignition of a test sample (typically a 3.2 mm diameter cylindrical rod) in pressurised oxygen. A test sample is defined as flammable when it undergoes burning that is independent of the ignition process utilised. In the standardised tests, this is indicated by the propagation of burning further than a defined amount, or „burn criterion.. The burn criterion in use at the onset of this project was arbitrarily selected, and did not accurately reflect the length a sample must burn in order to be burning independent of the ignition event and, in some cases, required complete consumption of the test sample for a metallic material to be considered flammable. It has been demonstrated that a) a metallic material.s propensity to support burning is altered by any increase in test sample temperature greater than ~250-300 oC and b) promoted ignition causes an increase in temperature of the test sample in the region closest to the igniter, a region referred to as the Heat Affected Zone (HAZ). If a test sample continues to burn past the HAZ (where the HAZ is defined as the region of the test sample above the igniter that undergoes an increase in temperature of greater than or equal to 250 oC by the end of the ignition event), it is burning independent of the igniter, and should be considered flammable. The extent of the HAZ, therefore, can be used to justify the selection of the burn criterion. A two dimensional mathematical model was developed in order to predict the extent of the HAZ created in a standard test sample by a typical igniter. The model was validated against previous theoretical and experimental work performed in collaboration with NASA, and then used to predict the extent of the HAZ for different metallic materials in several configurations. The extent of HAZ predicted varied significantly, ranging from ~2-27 mm depending on the test sample thermal properties and test conditions (i.e. pressure). The magnitude of the HAZ was found to increase with increasing thermal diffusivity, and decreasing pressure (due to slower ignition times). Based upon the findings of this work, a new burn criterion requiring 30 mm of the test sample to be consumed (from the top of the ignition promoter) was recommended and validated. This new burn criterion was subsequently included in the latest revision of the ASTM G124 and NASA 6001B international test standards that are used to evaluate metallic material flammability in oxygen. These revisions also have the added benefit of enabling the conduct of reduced gravity metallic material flammability testing in strict accordance with the ASTM G124 standard, allowing measurement and comparison of the relative flammability (i.e. Lowest Burn Pressure (LBP), Highest No-Burn Pressure (HNBP) and average Regression Rate of the Melting Interface(RRMI)) of metallic materials in normal and reduced gravity, as well as determination of the applicability of normal gravity test results to reduced gravity use environments. This is important, as currently most space-based applications will typically use normal gravity information in order to qualify systems and/or components for reduced gravity use. This is shown here to be non-conservative for metallic materials which are more flammable in reduced gravity. The flammability of two metallic materials, Inconel® 718 and 316 stainless steel (both commonly used to manufacture components for oxygen service in both terrestrial and space-based systems) was evaluated in normal and reduced gravity using the new ASTM G124-10 test standard. This allowed direct comparison of the flammability of the two metallic materials in normal gravity and reduced gravity respectively. The results of this work clearly show, for the first time, that metallic materials are more flammable in reduced gravity than in normal gravity when testing is conducted as described in the ASTM G124-10 test standard. This was shown to be the case in terms of both higher regression rates (i.e. faster consumption of the test sample – fuel), and burning at lower pressures in reduced gravity. Specifically, it was found that the LBP for 3.2 mm diameter Inconel® 718 and 316 stainless steel test samples decreased by 50% from 3.45 MPa (500 psia) in normal gravity to 1.72 MPa (250 psia) in reduced gravity for the Inconel® 718, and 25% from 3.45 MPa (500 psia) in normal gravity to 2.76 MPa (400 psia) in reduced gravity for the 316 stainless steel. The average RRMI increased by factors of 2.2 (27.2 mm/s in 2.24 MPa (325 psia) oxygen in reduced gravity compared to 12.8 mm/s in 4.48 MPa (650 psia) oxygen in normal gravity) for the Inconel® 718 and 1.6 (15.0 mm/s in 2.76 MPa (400 psia) oxygen in reduced gravity compared to 9.5 mm/s in 5.17 MPa (750 psia) oxygen in normal gravity) for the 316 stainless steel. Reasons for the increased flammability of metallic materials in reduced gravity compared to normal gravity are discussed, based upon the observations made during reduced gravity testing and previous work. Finally, the implications (for fire safety and engineering applications) of these results are presented and discussed, in particular, examining methods for mitigating the risk of a fire in reduced gravity.

Natural convection flow in a porous enclosure with localized heating from below

Natural convection flow in a two-dimensional fluid saturated porous enclosure with localized heating from below, symmetrical cooling from the sides and the top and rest of the bottom walls are insulated, has been investigated numerically. Darcy’s law for porous media along with the energy equation based on the 1st law of thermodynamics has been considered. Implicit finite volume method with TDMA solver is used to solve the governing equations. Localized heating is simulated by a centrally located isothermal heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered. The effect of heat source length and the Rayleigh number on streamlines and isotherms are presented, as well as the variation of the local rate of heat transfer in terms of the local Nusselt number from the heated wall. Finally, the average Nusselt number at the heated part of the bottom wall has been shown against Rayleigh number for the non-dimensional heat source length.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury

Free convection in a triangular enclosure with fluid-saturated porous medium and internal heat generation

Unsteady natural convection inside a triangular cavity has been studied in this study. The cavity is filled with a saturated porous medium with non-isothermal left inclined wall while the bottom surface is isothermally heated and the right inclined surface is isothermally cold. An internal heat generation is also considered which is dependent of the fluid temperature. The governing equations are solved numerically by finite element method. The Prandtl number of the fluid is considered as 0.7 (air) while the aspect ratio and the Rayleigh number are considered as 0.5 and 105 respectively. The effect of the porosity of the medium and heat generation on the fluid flow and heat transfer have been presented as a form of streamlines and isotherms. The rate of heat transfer through three surfaces of the enclosure is also presented.

New percentage body fat prediction equations for Japanese females

Anthropometry is a simple and cost-efficient method for the assessment of body composition. However prediction equations to estimate body composition using anthropometry should be ‘population-specific’. Most popular body composition prediction equations for Japanese females were proposed more than 40 years ago and there is some concern regarding their usefulness in Japanese females living today. The aim of this study was to compare percentage body fat (%BF) estimated from anthropometry and dual energy x-ray absorptiometry (DXA) to examine the applicability of commonly used prediction equations in young Japanese females. Body composition of 139 Japanese females aged between 18 and 27 years of age (BMI range: 15.1–29.1 kg/m2) was measured using whole-body DXA (Lunar DPX-LIQ) scans. From anthropometric measurements %BF was estimated using four equations developed from Japanese females. The results showed that the traditionally employed prediction equations for anthropometry significantly (p<0.01) underestimate %BF of young Japanese females and therefore are not valid for the precise estimation of body composition. New %BF prediction equations were proposed from the DXA and anthropometry results. Application of the proposed equations may assist in more accurate assessment of body fatness in Japanese females living today.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Field study of air change and flow rate in six automobiles

For many people, a relatively large proportion of daily exposure to a multitude of pollutants may occur inside an automobile. A key determinant of exposure is the amount of outdoor air entering the cabin (i.e. air change or flow rate). We have quantified this parameter in six passenger vehicles ranging in age from 18 years to <1 year, at three vehicle speeds and under four different ventilation settings. Average infiltration into the cabin with all operable air entry pathways closed was between 1 and 33.1 air changes per hour (ACH) at a vehicle speed of 60 km/h, and between 2.6 and 47.3 ACH at 110 km/h, with these results representing the most (2005 Volkswagen Golf) and least air-tight (1989 Mazda 121) vehicles, respectively. Average infiltration into stationary vehicles parked outdoors varied between ~0 and 1.4 ACH and was moderately related to wind speed. Measurements were also performed under an air recirculation setting with low fan speed, while airflow rate measurements were conducted under two non-recirculate ventilation settings with low and high fan speeds. The windows were closed in all cases, and over 200 measurements were performed. The results can be applied to estimate pollutant exposure inside vehicles.

Economic growth and suicide rate changes : a case in China from 1982 to 2005

It is to estimate the trend of suicide rate changes during the past three decades in China and try to identify its social and economic correlates. Official data of suicide rates and economic indexes during 1982–2005 from Shandong Province of China were analyzed. The suicide data were categorized for the rural / urban location and gender, and the economic indexes include GDP, GDP per capita, rural income, and urban income, all adjusted for inflation. We found a significant increase of economic development and decrease of suicide rates over the past decades under study. The suicide rate decrease is correlated with the tremendous growth of economy. The unusual decrease of Chinese suicide rates in the past decades is accounted for within the Chinese cultural contexts and maybe by the Strain Theory of Suicide.

Wound healing angiogenesis : the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

Adaptive bilateral filtering using saliency map for deblocking low bit rate videos

This paper proposes a novel approach to video deblocking which performs perceptually adaptive bilateral filtering by considering color, intensity, and motion features in a holistic manner. The method is based on bilateral filter which is an effective smoothing filter that preserves edges. The bilateral filter parameters are adaptive and avoid over-blurring of texture regions and at the same time eliminate blocking artefacts in the smooth region and areas of slow motion content. This is achieved by using a saliency map to control the strength of the filter for each individual point in the image based on its perceptual importance. The experimental results demonstrate that the proposed algorithm is effective in deblocking highly compressed video sequences and to avoid over-blurring of edges and textures in salient regions of image.

Statistical modelling of wind effects on signal propagation for wireless sensor networks

A wireless sensor network system must have the ability to tolerate harsh environmental conditions and reduce communication failures. In a typical outdoor situation, the presence of wind can introduce movement in the foliage. This motion of vegetation structures causes large and rapid signal fading in the communication link and must be accounted for when deploying a wireless sensor network system in such conditions. This thesis examines the fading characteristics experienced by wireless sensor nodes due to the effect of varying wind speed in a foliage obstructed transmission path. It presents extensive measurement campaigns at two locations with the approach of a typical wireless sensor networks configuration. The significance of this research lies in the varied approaches of its different experiments, involving a variety of vegetation types, scenarios and the use of different polarisations (vertical and horizontal). Non–line of sight (NLoS) scenario conditions investigate the wind effect based on different vegetation densities including that of the Acacia tree, Dogbane tree and tall grass. Whereas the line of sight (LoS) scenario investigates the effect of wind when the grass is swaying and affecting the ground-reflected component of the signal. Vegetation type and scenarios are envisaged to simulate real life working conditions of wireless sensor network systems in outdoor foliated environments. The results from the measurements are presented in statistical models involving first and second order statistics. We found that in most of the cases, the fading amplitude could be approximated by both Lognormal and Nakagami distribution, whose m parameter was found to depend on received power fluctuations. Lognormal distribution is known as the result of slow fading characteristics due to shadowing. This study concludes that fading caused by variations in received power due to wind in wireless sensor networks systems are found to be insignificant. There is no notable difference in Nakagami m values for low, calm, and windy wind speed categories. It is also shown in the second order analysis, the duration of the deep fades are very short, 0.1 second for 10 dB attenuation below RMS level for vertical polarization and 0.01 second for 10 dB attenuation below RMS level for horizontal polarization. Another key finding is that the received signal strength for horizontal polarisation demonstrates more than 3 dB better performances than the vertical polarisation for LoS and near LoS (thin vegetation) conditions and up to 10 dB better for denser vegetation conditions.