Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Does metabolic compensation explain the majority of less-than-expected weight loss in obese adults during a short-term severe diet and exercise intervention?

Objective: We investigated to what extent changes in metabolic rate and composition of weight loss explained the less-than-expected weight loss in obese men and women during a diet-plus-exercise intervention. Design: 16 obese men and women (41 ± 9 years; BMI 39 ± 6 kg/m2) were investigated in energy balance before, after and twice during a 12-week VLED (565–650 kcal/day) plus exercise (aerobic plus resistance training) intervention. The relative energy deficit (EDef) from baseline requirements was severe (74-87%). Body composition was measured by deuterium dilution and DXA and resting metabolic rate (RMR) by indirect calorimetry. Fat mass (FM) and fat-free mass (FFM) were converted into energy equivalents using constants: 9.45 kcal/gFM and 1.13 kcal/gFFM. Predicted weight loss was calculated from the energy deficit using the '7700 kcal/kg rule'. Results: Changes in weight (-18.6 ± 5.0 kg), FM (-15.5 ± 4.3 kg), and FFM (-3.1 ± 1.9 kg) did not differ between genders. Measured weight loss was on average 67% of the predicted value, but ranged from 39 to 94%. Relative EDef was correlated with the decrease in RMR (R=0.70, P<0.01) and the decrease in RMR correlated with the difference between actual and expected weight loss (R=0.51, P<0.01). Changes in metabolic rate explained on average 67% of the less-than-expected weight loss, and variability in the proportion of weight lost as FM accounted for a further 5%. On average, after adjustment for changes in metabolic rate and body composition of weight lost, actual weight loss reached 90% of predicted values. Conclusion: Although weight loss was 33% lower than predicted at baseline from standard energy equivalents, the majority of this differential was explained by physiological variables. While lower-than-expected weight loss is often attributed to incomplete adherence to prescribed interventions, the influence of baseline calculation errors and metabolic down-regulation should not be discounted.

Global flash multifocal electroretinogram : early detection of local functional changes and its correlations with optical coherence tomography and visual field loss in diabetic eyes

Purpose: To investigate the correlations of the global flash multifocal electroretinogram (MOFO mfERG) with common clinical visual assessments – Humphrey perimetry and Stratus circumpapillary retinal nerve fiber layer (RNFL) thickness measurement in type II diabetic patients. Methods: Forty-two diabetic patients participated in the study: ten were free from diabetic retinopathy (DR) while the remainder suffered from mild to moderate non-proliferative diabetic retinopathy (NPDR). Fourteen age-matched controls were recruited for comparison. MOFO mfERG measurements were made under high and low contrast conditions. Humphrey central 30-2 perimetry and Stratus OCT circumpapillary RNFL thickness measurements were also performed. Correlations between local values of implicit time and amplitude of the mfERG components (direct component (DC) and induced component (IC)), and perimetric sensitivity and RNFL thickness were evaluated by mapping the localized responses for the three subject groups. Results: MOFO mfERG was superior to perimetry and RNFL assessments in showing differences between the diabetic groups (with and without DR) and the controls. All the MOFO mfERG amplitudes (except IC amplitude at high contrast) correlated better with perimetry findings (Pearson’s r ranged from 0.23 to 0.36, p<0.01) than did the mfERG implicit time at both high and low contrasts across all subject groups. No consistent correlation was found between the mfERG and RNFL assessments for any group or contrast conditions. The responses of the local MOFO mfERG correlated with local perimetric sensitivity but not with RNFL thickness. Conclusion: Early functional changes in the diabetic retina seem to occur before morphological changes in the RNFL.

Abatement of energy loss by insulating system and designing automatic water heater

The most suitable temperature range for domestic purposes is about 200C to 260C .Besides, both cold and hot water appear to be essential frequently for industrial purposes. In summer bringing down the water temperature at a comfortable range causes significant energy consumption. This project aims at saving energy to control water temperature by making water tank insulated .Therefore applying better insulation system which would reduce the disparity between the desired temperature and the actual temperature and hence saving energy significantly. Following the investigation, this project used cotton jacket to insulate the tank and the tank was placed under a paddy straw shade with a view to attaining the maximum energy saving. Finally, it has been found that reduction in energy consumption is to be about 50-60% which is quite satisfactory. Since comfortable temperature range varies from person to person this project thus combines insulating effect with automatic water heater.

Loss to assets : production of power from speed breaker

In this work, prospect and feasibility of power generation by using speed breakers has been investigated. In this project a mechanism to generate power by converting the potential energy generated by a vehicle going up on a speed breaker into kinetic energy. This arrangement is made one rotation as soon as the vehicle moves over the speed breaker and has been increased using gears. After the production electricity, a storing unit has been used to hoard the generated electricity during the day and will be used during the night. Two prototypes have made using rack and pinion gear, spur gear, springs and generator .From which a considerable amount of energy is obtained. Nonetheless the cost of the prototype was inexpensive which proves the feasibility of this project and the idea can be applied on heavy traffic roads. Further investigation is being carried on to introduce the technology for practical approach.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Terra Preta : bioenergy, soil restoration, urban agriculture, art algorithm

The 2010 LAGI competition was held on three underutilized sites in the United Arab Emirates. By choosing Staten Island, New York in 2012 the competition organises have again brought into question new roles for public open space in the contemporary city. In the case of the UEA sites, the competition produced many entries which aimed to create a sculpture and by doing so, they attracted people to the selected empty spaces in an arid climate. In a way these proposals were the incubators and the new characters of these empty spaces. The competition was thus successful at advancing understandings of the expanded role of public open spaces in EAU and elsewhere. LAGI 2012 differs significantly to the UAE program because Fresh Kills Park has already been planned as a public open space for New Yorkers - with or without these clean energy sculptures. Furthermore, Fresh Kills Park is already an (gas) energy generating site in its own right. We believe Fresh Kills Park, as a site, presents a problem which somewhat transcends the aims of the competition brief. Advancing a sustainable urban design proposition for the site therefore requires a fundamental reconsideration of the established paradigms public open space. Hence our strategy is to not only create an energy generating, site specific art work, but to create synergy between the public and the site engagement while at the same time complement the idiosyncrasies of the pre-existing engineered landscape. Current PhD research about energy generation in public open spaces informs this work.

Quantitative studies of lower motor neuron degeneration in amyotrophic lateral sclerosis : Evidence for exponential decay of motor unit numbers and greatest rate of loss at the site of onset

Objective: To use our Bayesian method of motor unit number estimation (MUNE) to evaluate lower motor neuron degeneration in ALS. Methods: In subjects with ALS we performed serial MUNE studies. We examined the repeatability of the test and then determined whether the loss of MUs was fitted by an exponential or Weibull distribution. Results: The decline in motor unit (MU) numbers was well-fitted by an exponential decay curve. We calculated the half life of MUs in the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and/or extensor digitorum brevis (EDB) muscles. The mean half life of the MUs of ADM muscle was greater than those of the APB or EDB muscles. The half-life of MUs was less in the ADM muscle of subjects with upper limb than in those with lower limb onset. Conclusions: The rate of loss of lower motor neurons in ALS is exponential, the motor units of the APB decay more quickly than those of the ADM muscle and the rate of loss of motor units is greater at the site of onset of disease. Significance: This shows that the Bayesian MUNE method is useful in following the course and exploring the clinical features of ALS. 2012 International Federation of Clinical Neurophysiology.

Visual sensitivity loss in the central thirty degrees of visual field is associated with diabetic peripheral neuropathy

Aims/hypothesis: Impaired central vision has been shown to predict diabetic peripheral neuropathy (DPN). Several studies have demonstrated diffuse retinal neurodegenerative changes in diabetic patients prior to retinopathy development, raising the prospect that non-central vision may also be compromised by primary neural damage. We hypothesise that type 2 diabetic patients with DPN exhibit visual sensitivity loss in a distinctive pattern across the visual field, compared with a control group of type 2 diabetic patients without DPN. Methods: Increment light sensitivity was measured by standard perimetry in the central 30 degree of visual field for two age-matched groups of type 2 diabetic patients, with and without neuropathy (n=40/30). Neuropathy status was assigned using the neuropathy disability score. Mean visual sensitivity values were calculated globally, for each quadrant and for three eccentricities (0-10 degree , 11-20 degree and 21-30 degree ). Data were analysed using a generalised additive mixed model (GAMM). Results: Global and quadrant between-group visual sensitivity mean differences were marginally but consistently lower (by about 1 dB) in the neuropathy cohort compared with controls. Between-group mean differences increased from 0.36 to 1.81 dB with increasing eccentricity. GAMM analysis, after adjustment for age, showed these differences to be significant beyond 15 degree eccentricity and monotonically increasing. Retinopathy levels and disease duration were not significant factors within the model (p=0.90). Conclusions/interpretation: Visual sensitivity reduces disproportionately with increasing eccentricity in type 2 diabetic patients with peripheral neuropathy. This sensitivity reduction within the central 30 degree of visual field may be indicative of more consequential loss in the far periphery.

Performance evaluation of onsite sewage treatment : results of soil investigations

Background The onsite treatment of sewage and effluent disposal is widely prevalent in rural and urban fringe areas due to the general unavailability of reticulated wastewater collection systems. Despite the low technology of the systems, failure is common and in many cases leading to adverse public health and environmental consequences. It is important therefore that careful consideration is given to the design and location of onsite sewage treatment systems. This requires an understanding of the factors that influence treatment performance. The use of subsurface absorption systems is the most common form of effluent disposal for onsite sewage treatment, particularly for septic tanks. Also, in the case of septic tanks, a subsurface disposal system is generally an integral component of the sewage treatment process. Site specific factors play a key role in the onsite treatment of sewage. The project The primary aims of the research project were: • to relate treatment performance of onsite sewage treatment systems to soil conditions at site; • to evaluate current research relating to onsite sewage treatment; and, • to identify key issues where currently there is a lack of relevant research. These tasks were undertaken with the objective of facilitating the development of performance based planning and management strategies for onsite sewage treatment. The primary focus of this research project has been on septic tanks. By implication, the investigation has been confined to subsurface soil absorption systems. The design and treatment processes taking place within the septic tank chamber itself did not form a part of the investigation. Five broad categories of soil types prevalent in the Brisbane region have been considered in this project. The number of systems investigated was based on the proportionate area of urban development within the Brisbane region located on each of the different soil types. In the initial phase of the investigation, the majority of the systems evaluated were septic tanks. However, a small number of aerobic wastewater treatment systems (AWTS) were also included. The primary aim was to compare the effluent quality of systems employing different generic treatment processes. It is important to note that the number of each different type of system investigated was relatively small. Consequently, this does not permit a statistical analysis to be undertaken of the results obtained for comparing different systems. This is an important issue considering the large number of soil physico-chemical parameters and landscape factors that can influence treatment performance and their wide variability. The report This report is the last in a series of three reports focussing on the performance evaluation of onsite treatment of sewage. The research project was initiated at the request of the Brisbane City Council. The project component discussed in the current report outlines the detailed soil investigations undertaken at a selected number of sites. In the initial field sampling, a number of soil chemical properties were assessed as indicators to investigate the extent of effluent flow and to help understand what soil factors renovate the applied effluent. The soil profile attributes, especially texture, structure and moisture regime were examined more in an engineering sense to determine the effect of movement of water into and through the soil. It is important to note that it is not only the physical characteristics, but also the chemical characteristics of the soil as well as landscape factors play a key role in the effluent renovation process. In order to understand the complex processes taking place in a subsurface effluent disposal area, influential parameters were identified using soil chemical concepts. Accordingly, the primary focus of this final phase of the research project was to identify linkages between various soil chemical parameters and landscape patterns and their contribution to the effluent renovation process. The research outcomes will contribute to the development of robust criteria for evaluating the performance of subsurface effluent disposal systems. The outcomes The key findings from the soil investigations undertaken are: • Effluent renovation is primarily undertaken by a combination of various soil physico-chemical parameters and landscape factors, thereby making the effluent renovation processes strongly site dependent. • Decisions regarding site suitability for effluent disposal should not be based purely in terms of the soil type. A number of other factors such as the site location in the catena, the drainage characteristics and other physical and chemical characteristics, also exert a strong influence on site suitability. • Sites, which are difficult to characterise in terms of suitability for effluent disposal, will require a detailed soil physical and chemical analysis to be undertaken to a minimum depth of at least 1.2 m. • The Ca:Mg ratio and Exchangeable Sodium Percentage are important parameters in soil suitability assessment. A Ca:Mg ratio of less than 0.5 would generally indicate a high ESP. This in turn would mean that Na and possibly Mg are the dominant exchangeable cations, leading to probable clay dispersion. • A Ca:Mg ratio greater than 0.5 would generally indicate a low ESP in the profile, which in turn indicates increased soil stability. • In higher clay percentage soils, low ESP can have a significant effect. • The presence of high exchangeable Na can be counteracted by the presence of swelling clays, and an exchange complex co-dominated by exchangeable Ca and exchangeable Mg. This aids absorption of cations at depth, thereby reducing the likelihood of dispersion. • Salt is continually added to the soil by the effluent and problems may arise if the added salts accumulate to a concentration that is harmful to the soil structure. Under such conditions, good drainage is essential in order to allow continuous movement of water and salt through the profile. Therefore, for a site to be sustainable, it would have a maximum application rate of effluent. This would be dependent on subsurface characteristics and the surface area available for effluent disposal. • The dosing regime for effluent disposal can play a significant role in the prevention of salt accumulation in the case of poorly draining sites. Though intermittent dosing was not considered satisfactory for the removal of the clogging mat layer, it has positive attributes in the context of removal of accumulated salts in the soil.

Family violence or woman abuse? Putting gender back into the Canadian research equation

Research on violence against women has been among the most scrutinized areas in social science. From the beginning, efforts to empirically document the prevalence, incidence, and characteristics of violence against women have been hotly debated (DeKeseredy, 2011; Dragiewicz & DeKeseredy, forthcoming; Minaker & Snider, 2006). Objections that violence against women was rare have given way to acknowledgement that it is more common than once thought. Research on the outcomes of woman abuse has documented the serious ramifications of this type of violence for individual victims and the broader community. However, violence against women was not simply “discovered” by scholars in the 1960s, leading to a progressive growth of the literature. Knowledge production around violence against women has been fiercely contested, and feminist insights in particular have always been met with backlash(Gotell, 2007; Minkaer & Snider, 2006; Randall, 1989; Sinclair, 2003)...

Fertility and infertility : studies in reproductive epidemiology in Australia

Worldwide, there are few large-scale epidemiological studies on infertility. In Australia, population-based research on infertility is limited to a few small-scale studies. Therefore, the prevalence of infertility and unmet need for specialist medical advice and treatment cannot be estimated reliably. Women who have used assisted reproductive technologies (ART) are recorded in treatment registries. However, there are many infertile women who are excluded from these clinical populations because they neither seek advice nor use treatment. The thesis was based on a biopsychosocial model of health and used the methods of reproductive epidemiology to address the lack of national data on the prevalence of infertility in Australia. Firstly, numbers of births and pregnancy losses were investigated in two generations of women participating in the Australian Longitudinal Study on Women’s Health (ALSWH). The ALSWH is a broad-ranging, longitudinal examination of biological, psychological and social factors that impact on women’s health and wellbeing. Women from three age cohorts were randomly sampled from the population using the universal public health insurance (i.e., Medicare) database and ALSWH participants were representative of the female population. However, the studies in the thesis only involved data from two cohorts. The younger cohort were born in 1973-78 and completed up to four mailed surveys between 1996 (when they were aged 18-23 years, n=14247) and 2006 (28-33 years, n=9145). The mid-aged cohort were born in 1946-51 and completed four mailed surveys between 1996 (when they were aged 45-50 years n=13715) and 2004 (53-58 years, n=10905). Compared to other studies that focus on outcomes of single pregnancies, these studies included all pregnancy outcomes by developing comprehensive reproductive histories for each woman. Pregnancy outcomes included birth, miscarriage, stillbirth, termination and ectopic pregnancy. Women in the youngest cohort (born in 1973-78) were only just reaching their peak childbearing years and many (44%) had yet to report their first pregnancy outcome. Women from the mid-aged cohort (born 1946-51) had completed their reproductive lives and 92% were able to report on their lifetime pregnancy outcomes. Pregnancy losses, especially miscarriage, were common for both generations of women. Secondly, the prevalence of infertility, seeking medical advice and using treatment was identified for these two generations of women. For the older generation, the lifetime prevalence of infertility and demand for treatment was investigated in the context of the specialist medical services which became available circa 1980. By this time, however, most of these older women had already been pregnant and completed their families. For women who experienced infertility (11%), their options for advice and treatment were limited and less than half (42%) had used any treatment. More recently for the younger generation of women, who were aged 28-33 years in 2006, specialist advice and treatment were extensively available. Among women who had tried to conceive or had been pregnant (n=5936), 17% had experienced infertility and the majority (72%) were able to access medical advice. However, after seeking advice only half of these infertile women had used treatment with fertility hormones or in vitro fertilisation (IVF). Overall for infertile women aged up to 33 years, only one-third had used these treatments. Thirdly, the barriers to accessing medical advice and using treatment for infertility were identified for women aged less than 34 years. Among a community sample of infertile women aged 28-33 years (ALSWH participants), self-reported depression was found to be a barrier to accessing medical advice. The characteristics of these infertile women in the community who had (n=121) or had not (n=110) used treatment were compared to infertile women aged 27-33 years (n=59) attending four fertility clinics. Compared to infertile women in the community, living in major cities and having private health insurance were associated with early use of treatment for infertility at specialist clinics by women aged <34 years. In contrast to most clinical studies of IVF, the final study reported in the thesis took into account repeated IVF cycles and the impact of women’s individual histories on IVF outcomes. Among 121 infertile women (aged 27-46 years) who had 286 IVF cycles, older age and prolonged use of the oral contraceptive pill were associated with fewer eggs collected. Further, women in particular occupations had lower proportions of eggs fertilised normally than women in other occupational groups. These studies form the first large-scale epidemiological examination of infertility in Australia. The finding that two-thirds of women with infertility had not used treatment indicates that there is an unmet need for specialist treatment in women aged less than 34 years. However, barriers to accessing treatment prevent women using ART at a younger age when there is a higher chance of pregnancy.