Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

AC/DC electrical characteristics of epoxy-multi wall carbon nanotube nanocomposites

Expoxy nanocomposites with multiwell carbon nanotubes (mwcnts) filler up to 0.3%wt were prepared by sheer mixing and good dispersion of the MWCNTS in the epoxy was successfully achieved. The electrical behaviour was characterized by measurements of the alternating current (ac) and direct current (dc) conductives at room temperature. Typical percolation behaviour was observed at a low percolation threshold of 0.055%. Frequency independent ac conductivity was observed at low frequencies but not at high frequencies. An equivalent circuit models was used to predict the impedence response in these nanocomposites.

Fuzzy methods for analysis of microarrays and networks

Bioinformatics involves analyses of biological data such as DNA sequences, microarrays and protein-protein interaction (PPI) networks. Its two main objectives are the identification of genes or proteins and the prediction of their functions. Biological data often contain uncertain and imprecise information. Fuzzy theory provides useful tools to deal with this type of information, hence has played an important role in analyses of biological data. In this thesis, we aim to develop some new fuzzy techniques and apply them on DNA microarrays and PPI networks. We will focus on three problems: (1) clustering of microarrays; (2) identification of disease-associated genes in microarrays; and (3) identification of protein complexes in PPI networks. The first part of the thesis aims to detect, by the fuzzy C-means (FCM) method, clustering structures in DNA microarrays corrupted by noise. Because of the presence of noise, some clustering structures found in random data may not have any biological significance. In this part, we propose to combine the FCM with the empirical mode decomposition (EMD) for clustering microarray data. The purpose of EMD is to reduce, preferably to remove, the effect of noise, resulting in what is known as denoised data. We call this method the fuzzy C-means method with empirical mode decomposition (FCM-EMD). We applied this method on yeast and serum microarrays, and the silhouette values are used for assessment of the quality of clustering. The results indicate that the clustering structures of denoised data are more reasonable, implying that genes have tighter association with their clusters. Furthermore we found that the estimation of the fuzzy parameter m, which is a difficult step, can be avoided to some extent by analysing denoised microarray data. The second part aims to identify disease-associated genes from DNA microarray data which are generated under different conditions, e.g., patients and normal people. We developed a type-2 fuzzy membership (FM) function for identification of diseaseassociated genes. This approach is applied to diabetes and lung cancer data, and a comparison with the original FM test was carried out. Among the ten best-ranked genes of diabetes identified by the type-2 FM test, seven genes have been confirmed as diabetes-associated genes according to gene description information in Gene Bank and the published literature. An additional gene is further identified. Among the ten best-ranked genes identified in lung cancer data, seven are confirmed that they are associated with lung cancer or its treatment. The type-2 FM-d values are significantly different, which makes the identifications more convincing than the original FM test. The third part of the thesis aims to identify protein complexes in large interaction networks. Identification of protein complexes is crucial to understand the principles of cellular organisation and to predict protein functions. In this part, we proposed a novel method which combines the fuzzy clustering method and interaction probability to identify the overlapping and non-overlapping community structures in PPI networks, then to detect protein complexes in these sub-networks. Our method is based on both the fuzzy relation model and the graph model. We applied the method on several PPI networks and compared with a popular protein complex identification method, the clique percolation method. For the same data, we detected more protein complexes. We also applied our method on two social networks. The results showed our method works well for detecting sub-networks and give a reasonable understanding of these communities.

Low temperature synthesis of carbon nanotubes on indium tin oxide electrodes for organic solar cells

The electrical performance of indium tin oxide (ITO) coated glass was improved by including a controlled layer of carbon nanotubes directly on top of the ITO film. Multi-wall carbon nanotubes (MWCNTs) were synthesized by chemical vapor deposition, using ultra-thin Fe layers as catalyst. The process parameters (temperature, gas flow and duration) were carefully refined to obtain the appropriate size and density of MWCNTs with a minimum decrease of the light harvesting in the cell. When used as anodes for organic solar cells based on poly(3-hexylthiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM), the MWCNT-enhanced electrodes are found to improve the charge carrier extraction from the photoactive blend, thanks to the additional percolation paths provided by the CNTs. The work function of as-modified ITO surfaces was measured by the Kelvin probe method to be 4.95 eV, resulting in an improved matching to the highest occupied molecular orbital level of the P3HT. This is in turn expected to increase the hole transport and collection at the anode, contributing to the significant increase of current density and open circuit voltage observed in test cells created with such MWCNT-enhanced electrodes.

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.

Performance evaluation of onsite wastewater treatment : field sampling and preliminary evaluation of results

Background The onsite treatment of sewage and effluent disposal within the premises is widely prevalent in rural and urban fringe areas due to the general unavailability of reticulated wastewater collection systems. Despite the seemingly low technology of the systems, failure is common and in many cases leading to adverse public health and environmental consequences. Therefore it is important that careful consideration is given to the design and location of onsite sewage treatment systems. It requires an understanding of the factors that influence treatment performance. The use of subsurface effluent absorption systems is the most common form of effluent disposal for onsite sewage treatment and particularly for septic tanks. Additionally in the case of septic tanks, a subsurface disposal system is generally an integral component of the sewage treatment process. Therefore location specific factors will play a key role in this context. The project The primary aims of the research project are: • to relate treatment performance of onsite sewage treatment systems to soil conditions at site; • to identify important areas where there is currently a lack of relevant research knowledge and is in need of further investigation. 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 the research project has been on septic tanks. Therefore 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. In the evaluation to be undertaken, the treatment performance of soil absorption systems will be related to the physico-chemical characteristics of the soil. Five broad categories of soil types have been considered for this purpose. The number of systems investigated was based on the proportionate area of urban development within the Brisbane region located on each soil types. In the initial phase of the investigation, though the majority of the systems evaluated were septic tanks, a small number of aerobic wastewater treatment systems (AWTS) were also included. This was primarily to compare the effluent quality of systems employing different generic treatment processes. It is important to note that the number of different types of systems investigated was relatively small. As such this does not permit a statistical analysis to be undertaken of the results obtained. This is an important issue considering the large number of parameters that can influence treatment performance and their wide variability. The report This report is the second 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 work undertaken included site investigation and testing of sewage effluent and soil samples taken at distances of 1 and 3 m from the effluent disposal area. The project component discussed in the current report formed the basis for the more detailed investigation undertaken subsequently. The outcomes from the initial studies have been discussed, which enabled the identification of factors to be investigated further. Primarily, this report contains the results of the field monitoring program, the initial analysis undertaken and preliminary conclusions. Field study and outcomes Initially commencing with a list of 252 locations in 17 different suburbs, a total of 22 sites in 21 different locations were monitored. These sites were selected based on predetermined criteria. To obtain house owner agreement to participate in the monitoring study was not an easy task. Six of these sites had to be abandoned subsequently due to various reasons. The remaining sites included eight septic systems with subsurface effluent disposal and treating blackwater or combined black and greywater, two sites treating greywater only and six sites with AWTS. In addition to collecting effluent and soil samples from each site, a detailed field investigation including a series of house owner interviews were also undertaken. Significant observations were made during the field investigations. In addition to site specific observations, the general observations include the following: • Most house owners are unaware of the need for regular maintenance. Sludge removal has not been undertaken in any of the septic tanks monitored. Even in the case of aerated wastewater treatment systems, the regular inspections by the supplier is confined only to the treatment system and does not include the effluent disposal system. This is not a satisfactory situation as the investigations revealed. • In the case of separate greywater systems, only one site had a suitably functioning disposal arrangement. The general practice is to employ a garden hose to siphon the greywater for use in surface irrigation of the garden. • In most sites, the soil profile showed significant lateral percolation of effluent. As such, the flow of effluent to surface water bodies is a distinct possibility. • The need to investigate the subsurface condition to a depth greater than what is required for the standard percolation test was clearly evident. On occasion, seemingly permeable soil was found to have an underlying impermeable soil layer or vice versa. The important outcomes from the testing program include the following: • Though effluent treatment is influenced by the physico-chemical characteristics of the soil, it was not possible to distinguish between the treatment performance of different soil types. This leads to the hypothesis that effluent renovation is significantly influenced by the combination of various physico-chemical parameters rather than single parameters. This would make the processes involved strongly site specific. • Generally the improvement in effluent quality appears to take place only within the initial 1 m of travel and without any appreciable improvement thereafter. This relates only to the degree of improvement obtained and does not imply that this quality is satisfactory. This calls into question the value of adopting setback distances from sensitive water bodies. • Use of AWTS for sewage treatment may provide effluent of higher quality suitable for surface disposal. However on the whole, after a 1-3 m of travel through the subsurface, it was not possible to distinguish any significant differences in quality between those originating from septic tanks and AWTS. • In comparison with effluent quality from a conventional wastewater treatment plant, most systems were found to perform satisfactorily with regards to Total Nitrogen. The success rate was much lower in the case of faecal coliforms. However it is important to note that five of the systems exhibited problems with regards to effluent disposal, resulting in surface flow. This could lead to possible contamination of surface water courses. • The ratio of TDS to EC is about 0.42 whilst the optimum recommended value for use of treated effluent for irrigation should be about 0.64. This would mean a higher salt content in the effluent than what is advisable for use in irrigation. A consequence of this would be the accumulation of salts to a concentration harmful to crops or the landscape unless adequate leaching is present. These relatively high EC values are present even in the case of AWTS where surface irrigation of effluent is being undertaken. However it is important to note that this is not an artefact of the treatment process but rather an indication of the quality of the wastewater generated in the household. This clearly indicates the need for further research to evaluate the suitability of various soil types for the surface irrigation of effluent where the TDS/EC ratio is less than 0.64. • Effluent percolating through the subsurface absorption field may travel in the form of dilute pulses. As such the effluent will move through the soil profile forming fronts of elevated parameter levels. • The downward flow of effluent and leaching of the soil profile is evident in the case of podsolic, lithosol and kransozem soils. Lateral flow of effluent is evident in the case of prairie soils. Gleyed podsolic soils indicate poor drainage and ponding of effluent. In the current phase of the research project, a number of chemical indicators such as EC, pH and chloride concentration were employed as indicators to investigate the extent of effluent flow and to understand how soil renovates effluent. The soil profile, especially texture, structure and moisture regime was examined more in an engineering sense to determine the effect of movement of water into and through the soil. However it is not only the physical characteristics, but the chemical characteristics of the soil also play a key role in the effluent renovation process. Therefore in order to understand the complex processes taking place in a subsurface effluent disposal area, it is important that the identified influential parameters are evaluated using soil chemical concepts. Consequently the primary focus of the next phase of the research project will be to identify linkages between various important parameters. The research thus envisaged will help to develop robust criteria for evaluating the performance of subsurface disposal systems.

Feasibility of agent-based modelling of articular cartilage including a conceptual representation of its structure

Articular cartilage is a complex structure with an architecture in which fluid-swollen proteoglycans constrained within a 3D network of collagen fibrils. Because of the complexity of the cartilage structure, the relationship between its mechanical behaviours at the macroscale level and its components at the micro-scale level are not completely understood. The research objective in this thesis is to create a new model of articular cartilage that can be used to simulate and obtain insight into the micro-macro-interaction and mechanisms underlying its mechanical responses during physiological function. The new model of articular cartilage has two characteristics, namely: i) not use fibre-reinforced composite material idealization ii) Provide a framework for that it does probing the micro mechanism of the fluid-solid interaction underlying the deformation of articular cartilage using simple rules of repartition instead of constitutive / physical laws and intuitive curve-fitting. Even though there are various microstructural and mechanical behaviours that can be studied, the scope of this thesis is limited to osmotic pressure formation and distribution and their influence on cartilage fluid diffusion and percolation, which in turn governs the deformation of the compression-loaded tissue. The study can be divided into two stages. In the first stage, the distributions and concentrations of proteoglycans, collagen and water were investigated using histological protocols. Based on this, the structure of cartilage was conceptualised as microscopic osmotic units that consist of these constituents that were distributed according to histological results. These units were repeated three-dimensionally to form the structural model of articular cartilage. In the second stage, cellular automata were incorporated into the resulting matrix (lattice) to simulate the osmotic pressure of the fluid and the movement of water within and out of the matrix; following the osmotic pressure gradient in accordance with the chosen rule of repartition of the pressure. The outcome of this study is the new model of articular cartilage that can be used to simulate and study the micromechanical behaviours of cartilage under different conditions of health and loading. These behaviours are illuminated at the microscale level using the socalled neighbourhood rules developed in the thesis in accordance with the typical requirements of cellular automata modelling. Using these rules and relevant Boundary Conditions to simulate pressure distribution and related fluid motion produced significant results that provided the following insight into the relationships between osmotic pressure gradient and associated fluid micromovement, and the deformation of the matrix. For example, it could be concluded that: 1. It is possible to model articular cartilage with the agent-based model of cellular automata and the Margolus neighbourhood rule. 2. The concept of 3D inter connected osmotic units is a viable structural model for the extracellular matrix of articular cartilage. 3. Different rules of osmotic pressure advection lead to different patterns of deformation in the cartilage matrix, enabling an insight into how this micromechanism influences macromechanical deformation. 4. When features such as transition coefficient were changed, permeability (representing change) is altered due to the change in concentrations of collagen, proteoglycans (i.e. degenerative conditions), the deformation process is impacted. 5. The boundary conditions also influence the relationship between osmotic pressure gradient and fluid movement at the micro-scale level. The outcomes are important to cartilage research since we can use these to study the microscale damage in the cartilage matrix. From this, we are able to monitor related diseases and their progression leading to potential insight into drug-cartilage interaction for treatment. This innovative model is an incremental progress on attempts at creating further computational modelling approaches to cartilage research and other fluid-saturated tissues and material systems.

Graph coloring applied to secure computation in non-Abelian groups

We study the natural problem of secure n-party computation (in the computationally unbounded attack model) of circuits over an arbitrary finite non-Abelian group (G,⋅), which we call G-circuits. Besides its intrinsic interest, this problem is also motivating by a completeness result of Barrington, stating that such protocols can be applied for general secure computation of arbitrary functions. For flexibility, we are interested in protocols which only require black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our investigations focus on the passive adversarial model, where up to t of the n participating parties are corrupted.

Multiscale coupling and multiphysics approaches in earth sciences : theory

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

Effect of Coulomb blockade, gold resistance, and thermal expansion on the electrical resistance of ultrathin gold films

Controlling the electrical resistance of granular thin films is of great importance for many applications, yet a full understanding of electron transport in such films remains a major challenge. We have studied experimentally and by model calculations the temperature dependence of the electrical resistance of ultrathin gold films at temperatures between 2 K and 300 K. Using sputter deposition, the film morphology was varied from a discontinuous film of weakly coupled meandering islands to a continuous film of strongly coupled coalesced islands. In the weak-coupling regime, we compare the regular island array model, the cotunneling model, and the conduction percolation model with our experimental data. We show that the tunnel barriers and the Coulomb blockade energies are important at low temperatures and that the thermal expansion of the substrate and the island resistance affect the resistance at high temperatures. At low temperatures our experimental data show evidence for a transition from electron cotunneling to sequential tunneling but the data can also be interpreted in terms of conduction percolation. The resistivity and temperature coefficient of resistance of the meandering gold islands are found to resemble those of gold nanowires. We derive a simple expression for the temperature at which the resistance changes from non-metal-like behavior into metal-like behavior. In the case of strong island coupling, the total resistance is solely determined by the Ohmic island resistance.

Micro paddy lysimeter for monitoring solute transport in paddy environment

The micro paddy lysimeter (MPL) was developed and evaluated for its performance to simulate solute transport in paddy environment under laboratory conditions. MPLs were constructed using soil collected from Field Museum Honmachi of Tokyo University of Agriculture and Technology, Japan. For the physical characteristics of the hardpan layer, parameters such as thickness, and soil aggregate size, affecting the percolation rate were studied. For the plow layer, two types of plow soils, sieved and un-sieved soils were compared. The sieved soil plow layer was produced by mixing air-dried soils of different aggregate sizes of D > 9.50, 9.50 ≥ D > 4.75, 4.75 ≥ D > 2.0 mm and D ≤ 2.0 mm at 47.1, 19.5, 20.6, and 12.8%, respectively. The un-sieved plow layer soil was directly used after collecting from the field. Inert tracer was applied to ponding water with controlled boundary conditions to evaluate the reproducibility of the soil hydraulic characteristics. HYDRUS-1D was used to evaluate the movement of bromide tracer in the MPL. The proposed conditions of the MPL were that the hardpan layer can be made from soil aggregates smaller than 0.425 mm with 2 cm thickness and that the plow layer can be prepared with sieved or un-sieved soils. With these conditions, the obtained results proved that MPLs can be a useful tool to simulate solute transport in paddy environment.