Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Tooth fracture risk analysis based on a new finite element dental structure models using micro-CT data

The finite element (FE) analysis is an effective method to study the strength and predict the fracture risk of endodontically-treated teeth. This paper presents a rapid method developed to generate a comprehensive tooth FE model using data retrieved from micro-computed tomography (μCT). With this method, the inhomogeneity of material properties of teeth was included into the model without dividing the tooth model into different regions. The material properties of the tooth were assumed to be related to the mineral density. The fracture risk at different tooth portions was assessed for root canal treatments. The micro-CT images of a tooth were processed by a Matlab software programme and the CT numbers were retrieved. The tooth contours were obtained with thresholding segmentation using Amira. The inner and outer surfaces of the tooth were imported into Solidworks and a three-dimensional (3D) tooth model was constructed. An assembly of the tooth model with the periodontal ligament (PDL) layer and surrounding bone was imported into ABAQUS. The material properties of the tooth were calculated from the retrieved CT numbers via ABAQUS user's subroutines. Three root canal geometries (original and two enlargements) were investigated. The proposed method in this study can generate detailed 3D finite element models of a tooth with different root canal enlargements and filling materials, and would be very useful for the assessment of the fracture risk at different tooth portions after root canal treatments.

Finite element analyses of lipped channel beams with Web openings in 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. Shear behaviour of LCBs with web openings is more complicated and their shear capacities are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs with web openings. 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. 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 with web openings. Improved design equations were therefore proposed for the shear strength of LCBs with web openings. This paper presents the details of this numerical study of LCBs with web openings, and the results.

Re-cementing in revision total hip replacement

Removal of well-fixed cement at revision surgery risks bone loss, cortical perforation and fracture, is time-consuming, technically demanding and carries increased risks for the patient. The cement-in-cement technique avoids these problems and when used appropriately has given favourable results at our centre when used on both the femoral and acetabular sides of the articulation. A modified technique has also been used in selected cases of infection and peri-prosthetic fracture. This chapter highlights the results to date and the operative techniques employed. It is essential to recognise that this technique relies fundamentally on the presence of a well-fixed cement mantle, and it is imperative that the criteria laid out are adhered to in order to achieve success. If there is loosening or lysis on the femoral side extending distal to the lesser trochanter or around more than just the periphery of the acetabular cement mantle, then alternative revision techniques should be employed.

Finite element modelling of load bearing steel stud walls under real building 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 given in ISO 834 (ISO, 1999). The standard time-temperature curve given in ISO 834 (ISO, 1999) originated from the application of wood burning furnaces in the early 1900s. 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 performance of LSF walls was undertaken using the developed real fire curves based on Eurocode parametric curves (ECS, 2002) and Barnett’s BFD curves (Barnett, 2002) using both full scale fire tests and numerical studies. It included LSF walls without any insulation, and the recently developed externally insulated composite panel system. This paper presents the details of the numerical studies and the results. It also includes brief details of the development of real building fire curves and experimental studies.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Performance evaluation of onsite sewage treatment : Evaluation of current research

Efficient management of domestic wastewater is a primary requirement for human well being. Failure to adequately address issues of wastewater collection, treatment and disposal can lead to adverse public health and environmental impacts. The increasing spread of urbanisation has led to the conversion of previously rural land into urban developments and the more intensive development of semi urban areas. However the provision of reticulated sewerage facilities has not kept pace with this expansion in urbanisation. This has resulted in a growing dependency on onsite sewage treatment. Though considered only as a temporary measure in the past, these systems are now considered as the most cost effective option and have become a permanent feature in some urban areas. This report is the first of a series of reports to be produced and is the outcome of a research project initiated by the Brisbane City Council. The primary objective of the research undertaken was to relate the treatment performance of onsite sewage treatment systems with soil conditions at site, with the emphasis being on septic tanks. This report consists of a ‘state of the art’ review of research undertaken in the arena of onsite sewage treatment. The evaluation of research brings together significant work undertaken locally and overseas. It focuses mainly on septic tanks in keeping with the primary objectives of the project. This report has acted as the springboard for the later field investigations and analysis undertaken as part of the project. Septic tanks still continue to be used widely due to their simplicity and low cost. Generally the treatment performance of septic tanks can be highly variable due to numerous factors, but a properly designed, operated and maintained septic tank can produce effluent of satisfactory quality. The reduction of hydraulic surges from washing machines and dishwashers, regular removal of accumulated septage and the elimination of harmful chemicals are some of the practices that can improve system performance considerably. The relative advantages of multi chamber over single chamber septic tanks is an issue that needs to be resolved in view of the conflicting research outcomes. In recent years, aerobic wastewater treatment systems (AWTS) have been gaining in popularity. This can be mainly attributed to the desire to avoid subsurface effluent disposal, which is the main cause of septic tank failure. The use of aerobic processes for treatment of wastewater and the disinfection of effluent prior to disposal is capable of producing effluent of a quality suitable for surface disposal. However the field performance of these has been disappointing. A significant number of these systems do not perform to stipulated standards and quality can be highly variable. This is primarily due to houseowner neglect or ignorance of correct operational and maintenance procedures. The other problems include greater susceptibility to shock loadings and sludge bulking. As identified in literature a number of design features can also contribute to this wide variation in quality. The other treatment processes in common use are the various types of filter systems. These include intermittent and recirculating sand filters. These systems too have their inherent advantages and disadvantages. Furthermore as in the case of aerobic systems, their performance is very much dependent on individual houseowner operation and maintenance practices. In recent years the use of biofilters has attracted research interest and particularly the use of peat. High removal rates of various wastewater pollutants have been reported in research literature. Despite these satisfactory results, leachate from peat has been reported in various studies. This is an issue that needs further investigations and as such biofilters can still be considered to be in the experimental stage. The use of other filter media such as absorbent plastic and bark has also been reported in literature. The safe and hygienic disposal of treated effluent is a matter of concern in the case of onsite sewage treatment. Subsurface disposal is the most common and the only option in the case of septic tank treatment. Soil is an excellent treatment medium if suitable conditions are present. The processes of sorption, filtration and oxidation can remove the various wastewater pollutants. The subsurface characteristics of the disposal area are among the most important parameters governing process performance. Therefore it is important that the soil and topographic conditions are taken into consideration in the design of the soil absorption system. Seepage trenches and beds are the common systems in use. Seepage pits or chambers can be used where subsurface conditions warrant, whilst above grade mounds have been recommended for a variety of difficult site conditions. All these systems have their inherent advantages and disadvantages and the preferable soil absorption system should be selected based on site characteristics. The use of gravel as in-fill for beds and trenches is open to question. It does not contribute to effluent treatment and has been shown to reduce the effective infiltrative surface area. This is due to physical obstruction and the migration of fines entrained in the gravel, into the soil matrix. The surface application of effluent is coming into increasing use with the advent of aerobic treatment systems. This has the advantage that treatment is undertaken on the upper soil horizons, which is chemically and biologically the most effective in effluent renovation. Numerous research studies have demonstrated the feasibility of this practice. However the overriding criteria is the quality of the effluent. It has to be of exceptionally good quality in order to ensure that there are no resulting public health impacts due to aerosol drift. This essentially is the main issue of concern, due to the unreliability of the effluent quality from aerobic systems. Secondly, it has also been found that most householders do not take adequate care in the operation of spray irrigation systems or in the maintenance of the irrigation area. Under these circumstances surface disposal of effluent should be approached with caution and would require appropriate householder education and stringent compliance requirements. However despite all this, the efficiency with which the process is undertaken will ultimately rest with the individual householder and this is where most concern rests. Greywater too should require similar considerations. Surface irrigation of greywater is currently being permitted in a number of local authority jurisdictions in Queensland. Considering the fact that greywater constitutes the largest fraction of the total wastewater generated in a household, it could be considered to be a potential resource. Unfortunately in most circumstances the only pretreatment that is required to be undertaken prior to reuse is the removal of oil and grease. This is an issue of concern as greywater can considered to be a weak to medium sewage as it contains primary pollutants such as BOD material and nutrients and may also include microbial contamination. Therefore its use for surface irrigation can pose a potential health risk. This is further compounded by the fact that most householders are unaware of the potential adverse impacts of indiscriminate greywater reuse. As in the case of blackwater effluent reuse, there have been suggestions that greywater should also be subjected to stringent guidelines. Under these circumstances the surface application of any wastewater requires careful consideration. The other option available for the disposal effluent is the use of evaporation systems. The use of evapotranspiration systems has been covered in this report. Research has shown that these systems are susceptible to a number of factors and in particular to climatic conditions. As such their applicability is location specific. Also the design of systems based solely on evapotranspiration is questionable. In order to ensure more reliability, the systems should be designed to include soil absorption. The successful use of these systems for intermittent usage has been noted in literature. Taking into consideration the issues discussed above, subsurface disposal of effluent is the safest under most conditions. This is provided the facility has been designed to accommodate site conditions. The main problem associated with subsurface disposal is the formation of a clogging mat on the infiltrative surfaces. Due to the formation of the clogging mat, the capacity of the soil to handle effluent is no longer governed by the soil’s hydraulic conductivity as measured by the percolation test, but rather by the infiltration rate through the clogged zone. The characteristics of the clogging mat have been shown to be influenced by various soil and effluent characteristics. Secondly, the mechanisms of clogging mat formation have been found to be influenced by various physical, chemical and biological processes. Biological clogging is the most common process taking place and occurs due to bacterial growth or its by-products reducing the soil pore diameters. Biological clogging is generally associated with anaerobic conditions. The formation of the clogging mat provides significant benefits. It acts as an efficient filter for the removal of microorganisms. Also as the clogging mat increases the hydraulic impedance to flow, unsaturated flow conditions will occur below the mat. This permits greater contact between effluent and soil particles thereby enhancing the purification process. This is particularly important in the case of highly permeable soils. However the adverse impacts of the clogging mat formation cannot be ignored as they can lead to significant reduction in the infiltration rate. This in fact is the most common cause of soil absorption systems failure. As the formation of the clogging mat is inevitable, it is important to ensure that it does not impede effluent infiltration beyond tolerable limits. Various strategies have been investigated to either control clogging mat formation or to remediate its severity. Intermittent dosing of effluent is one such strategy that has attracted considerable attention. Research conclusions with regard to short duration time intervals are contradictory. It has been claimed that the intermittent rest periods would result in the aerobic decomposition of the clogging mat leading to a subsequent increase in the infiltration rate. Contrary to this, it has also been claimed that short duration rest periods are insufficient to completely decompose the clogging mat, and the intermediate by-products that form as a result of aerobic processes would in fact lead to even more severe clogging. It has been further recommended that the rest periods should be much longer and should be in the range of about six months. This entails the provision of a second and alternating seepage bed. The other concepts that have been investigated are the design of the bed to meet the equilibrium infiltration rate that would eventuate after clogging mat formation; improved geometry such as the use of seepage trenches instead of beds; serial instead of parallel effluent distribution and low pressure dosing of effluent. The use of physical measures such as oxidation with hydrogen peroxide and replacement of the infiltration surface have been shown to be only of short-term benefit. Another issue of importance is the degree of pretreatment that should be provided to the effluent prior to subsurface application and the influence exerted by pollutant loadings on the clogging mat formation. Laboratory studies have shown that the total mass loadings of BOD and suspended solids are important factors in the formation of the clogging mat. It has also been found that the nature of the suspended solids is also an important factor. The finer particles from extended aeration systems when compared to those from septic tanks will penetrate deeper into the soil and hence will ultimately cause a more dense clogging mat. However the importance of improved pretreatment in clogging mat formation may need to be qualified in view of other research studies. It has also shown that effluent quality may be a factor in the case of highly permeable soils but this may not be the case with fine structured soils. The ultimate test of onsite sewage treatment system efficiency rests with the final disposal of effluent. The implication of system failure as evidenced from the surface ponding of effluent or the seepage of contaminants into the groundwater can be very serious as it can lead to environmental and public health impacts. Significant microbial contamination of surface and groundwater has been attributed to septic tank effluent. There are a number of documented instances of septic tank related waterborne disease outbreaks affecting large numbers of people. In a recent incident, the local authority was found liable for an outbreak of viral hepatitis A and not the individual septic tank owners as no action had been taken to remedy septic tank failure. This illustrates the responsibility placed on local authorities in terms of ensuring the proper operation of onsite sewage treatment systems. Even a properly functioning soil absorption system is only capable of removing phosphorus and microorganisms. The nitrogen remaining after plant uptake will not be retained in the soil column, but will instead gradually seep into the groundwater as nitrate. Conditions for nitrogen removal by denitrification are not generally present in a soil absorption bed. Dilution by groundwater is the only treatment available for reducing the nitrogen concentration to specified levels. Therefore based on subsurface conditions, this essentially entails a maximum allowable concentration of septic tanks in a given area. Unfortunately nitrogen is not the only wastewater pollutant of concern. Relatively long survival times and travel distances have been noted for microorganisms originating from soil absorption systems. This is likely to happen if saturated conditions persist under the soil absorption bed or due to surface runoff of effluent as a result of system failure. Soils have a finite capacity for the removal of phosphorus. Once this capacity is exceeded, phosphorus too will seep into the groundwater. The relatively high mobility of phosphorus in sandy soils have been noted in the literature. These issues have serious implications in the design and siting of soil absorption systems. It is not only important to ensure that the system design is based on subsurface conditions but also the density of these systems in given areas is a critical issue. This essentially involves the adoption of a land capability approach to determine the limitations of an individual site for onsite sewage disposal. The most limiting factor at a particular site would determine the overall capability classification for that site which would also dictate the type of effluent disposal method to be adopted.

Revision total hip replacement using the cement-in-cement technique for the acetabular component : technique and results for 60 hips

The technique of femoral cement-in-cement revision is well established, but there are no previous series reporting its use on the acetabular side at the time of revision total hip arthroplasty. We describe the surgical technique and report the outcome of 60 consecutive cement-in-cement revisions of the acetabular component at a mean follow-up of 8.5 years (range 5-12 years). All had a radiologically and clinically well fixed acetabular cement mantle at the time of revision. 29 patients died. No case was lost to follow-up. The 2 most common indications for acetabular revision were recurrent dislocation (77%) and to compliment a femoral revision (20%). There were 2 cases of aseptic cup loosening (3.3%) requiring re-revision. No other hip was clinically or radiologically loose (96.7%) at latest follow-up. One case was re-revised for infection, 4 for recurrent dislocation and 1 for disarticulation of a constrained component. At 5 years, the Kaplan-Meier survival rate was 100% for aseptic loosening and 92.2% (95% CI; 84.8-99.6%) with revision for all causes as the endpoint. These results support the use of the cement-in-cement revision technique in appropriate cases on the acetabular side. Theoretical advantages include preservation of bone stock, reduced operating time, reduced risk of complications and durable fixation.

Evaluation of the cost-effectiveness of strategies claiming to reduce the risk of surgical site infections following primary total hip arthroplasty

Background Total hip arthroplasty (THA) is a commonly performed procedure and numbers are increasing with ageing populations. One of the most serious complications in THA are surgical site infections (SSIs), caused by pathogens entering the wound during the procedure. SSIs are associated with a substantial burden for health services, increased mortality and reduced functional outcomes in patients. Numerous approaches to preventing these infections exist but there is no gold standard in practice and the cost-effectiveness of alternate strategies is largely unknown. Objectives The aim of this project was to evaluate the cost-effectiveness of strategies claiming to reduce deep surgical site infections following total hip arthroplasty in Australia. The objectives were: 1. Identification of competing strategies or combinations of strategies that are clinically relevant to the control of SSI related to hip arthroplasty 2. Evidence synthesis and pooling of results to assess the volume and quality of evidence claiming to reduce the risk of SSI following total hip arthroplasty 3. Construction of an economic decision model incorporating cost and health outcomes for each of the identified strategies 4. Quantification of the effect of uncertainty in the model 5. Assessment of the value of perfect information among model parameters to inform future data collection Methods The literature relating to SSI in THA was reviewed, in particular to establish definitions of these concepts, understand mechanisms of aetiology and microbiology, risk factors, diagnosis and consequences as well as to give an overview of existing infection prevention measures. Published economic evaluations on this topic were also reviewed and limitations for Australian decision-makers identified. A Markov state-transition model was developed for the Australian context and subsequently validated by clinicians. The model was designed to capture key events related to deep SSI occurring within the first 12 months following primary THA. Relevant infection prevention measures were selected by reviewing clinical guideline recommendations combined with expert elicitation. Strategies selected for evaluation were the routine use of pre-operative antibiotic prophylaxis (AP) versus no use of antibiotic prophylaxis (No AP) or in combination with antibiotic-impregnated cement (AP & ABC) or laminar air operating rooms (AP & LOR). The best available evidence for clinical effect size and utility parameters was harvested from the medical literature using reproducible methods. Queensland hospital data were extracted to inform patients’ transitions between model health states and related costs captured in assigned treatment codes. Costs related to infection prevention were derived from reliable hospital records and expert opinion. Uncertainty of model input parameters was explored in probabilistic sensitivity analyses and scenario analyses and the value of perfect information was estimated. Results The cost-effectiveness analysis was performed from a health services perspective using a hypothetical cohort of 30,000 THA patients aged 65 years. The baseline rate of deep SSI was 0.96% within one year of a primary THA. The routine use of antibiotic prophylaxis (AP) was highly cost-effective and resulted in cost savings of over $1.6m whilst generating an extra 163 QALYs (without consideration of uncertainty). Deterministic and probabilistic analysis (considering uncertainty) identified antibiotic prophylaxis combined with antibiotic-impregnated cement (AP & ABC) to be the most cost-effective strategy. Using AP & ABC generated the highest net monetary benefit (NMB) and an incremental $3.1m NMB compared to only using antibiotic prophylaxis. There was a very low error probability that this strategy might not have the largest NMB (<5%). Not using antibiotic prophylaxis (No AP) or using both antibiotic prophylaxis combined with laminar air operating rooms (AP & LOR) resulted in worse health outcomes and higher costs. Sensitivity analyses showed that the model was sensitive to the initial cohort starting age and the additional costs of ABC but the best strategy did not change, even for extreme values. The cost-effectiveness improved for a higher proportion of cemented primary THAs and higher baseline rates of deep SSI. The value of perfect information indicated that no additional research is required to support the model conclusions. Conclusions Preventing deep SSI with antibiotic prophylaxis and antibiotic-impregnated cement has shown to improve health outcomes among hospitalised patients, save lives and enhance resource allocation. By implementing a more beneficial infection control strategy, scarce health care resources can be used more efficiently to the benefit of all members of society. The results of this project provide Australian policy makers with key information about how to efficiently manage risks of infection in THA.

Total Solar Eclipse in North Queensland 14 Nov 2012

This article is a brief introduction to the total solar eclipse Wed 14 November 2012 in north Queensland that will be seen in a narrow strip of land just 140 km wide in the vicinity of Cairns.

Ergodic capacity of the slotted amplify and forward relay channel with finite relays

Abstract—In this paper we investigate the capacity of a general class of the slotted amplify and forward (SAF) relaying protocol where multiple, though a finite number of relays may transmit in a given cooperative slot and the relay terminals being half-duplex have a finite slot memory capacity. We derive an expression for the capacity per channel use of this generalized SAF channel assuming all source to relay, relay to destination and source to destination channel gains are independent and modeled as complex Gaussian. We show through the analysis of eigenvalue distributions that the increase in limiting capacity per channel use is marginal with the increase of relay terminals.

Complications related to therapeutic anticoagulation in total hip arthroplasty

Bleeding related wound complications cause significant morbidity in lower limb arthroplasty surgery. Patients who require therapeutic anticoagulation in the peri operative period are potentially at higher risk of these complications. This is a retrospective case control study reviewing all primary total hip replacements performed in a single center over a five year period and comparing outcomes of the patients on warfarin with a double-matched control group of patients not on warfarin. The warfarin group had significantly higher risk of deep joint infection (9% vs 2.2%), haematoma/ wound ooze (28% vs 4%) and superficial infection (13.5% vs 2.2%). Managing the total hip arthroplasty patient with therapeutic anticoagulation is a balance between the risk of thromboembolic disease and bleeding related complications. Improved understanding of this risk will better allow the patient to make an informed decision regarding their elective arthroplasty surgery.