Comparing charge transport predictions for a ternary electrolyte using the Maxwell–Stefan and Nernst–Planck equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.

Modelling bus lost time : an additional parameter influencing bus dwell time and station platform capacity at a BRT station platform

The common approach to estimate bus dwell time at a BRT station is to apply the traditional dwell time methodology derived for suburban bus stops. In spite of being sensitive to boarding and alighting passenger numbers and to some extent towards fare collection media, these traditional dwell time models do not account for the platform crowding. Moreover, they fall short in accounting for the effects of passenger/s walking along a relatively longer BRT platform. Using the experience from Brisbane busway (BRT) stations, a new variable, Bus Lost Time (LT), is introduced in traditional dwell time model. The bus lost time variable captures the impact of passenger walking and platform crowding on bus dwell time. These are two characteristics which differentiate a BRT station from a bus stop. This paper reports the development of a methodology to estimate bus lost time experienced by buses at a BRT platform. Results were compared with the Transit Capacity and Quality of Servce Manual (TCQSM) approach of dwell time and station capacity estimation. When the bus lost time was used in dwell time calculations it was found that the BRT station platform capacity reduced by 10.1%.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Quantification of particle emission characteristics and development of an emission model for use in transport microenvironments affected by traffic emissions

Vehicle emitted particles are of significant concern based on their potential to influence local air quality and human health. Transport microenvironments usually contain higher vehicle emission concentrations compared to other environments, and people spend a substantial amount of time in these microenvironments when commuting. Currently there is limited scientific knowledge on particle concentration, passenger exposure and the distribution of vehicle emissions in transport microenvironments, partially due to the fact that the instrumentation required to conduct such measurements is not available in many research centres. Information on passenger waiting time and location in such microenvironments has also not been investigated, which makes it difficult to evaluate a passenger’s spatial-temporal exposure to vehicle emissions. Furthermore, current emission models are incapable of rapidly predicting emission distribution, given the complexity of variations in emission rates that result from changes in driving conditions, as well as the time spent in driving condition within the transport microenvironment. In order to address these scientific gaps in knowledge, this work conducted, for the first time, a comprehensive statistical analysis of experimental data, along with multi-parameter assessment, exposure evaluation and comparison, and emission model development and application, in relation to traffic interrupted transport microenvironments. The work aimed to quantify and characterise particle emissions and human exposure in the transport microenvironments, with bus stations and a pedestrian crossing identified as suitable research locations representing a typical transport microenvironment. Firstly, two bus stations in Brisbane, Australia, with different designs, were selected to conduct measurements of particle number size distributions, particle number and PM2.5 concentrations during two different seasons. Simultaneous traffic and meteorological parameters were also monitored, aiming to quantify particle characteristics and investigate the impact of bus flow rate, station design and meteorological conditions on particle characteristics at stations. The results showed higher concentrations of PN20-30 at the station situated in an open area (open station), which is likely to be attributed to the lower average daily temperature compared to the station with a canyon structure (canyon station). During precipitation events, it was found that particle number concentration in the size range 25-250 nm decreased greatly, and that the average daily reduction in PM2.5 concentration on rainy days compared to fine days was 44.2 % and 22.6 % at the open and canyon station, respectively. The effect of ambient wind speeds on particle number concentrations was also examined, and no relationship was found between particle number concentration and wind speed for the entire measurement period. In addition, 33 pairs of average half-hourly PN7-3000 concentrations were calculated and identified at the two stations, during the same time of a day, and with the same ambient wind speeds and precipitation conditions. The results of a paired t-test showed that the average half-hourly PN7-3000 concentrations at the two stations were not significantly different at the 5% confidence level (t = 0.06, p = 0.96), which indicates that the different station designs were not a crucial factor for influencing PN7-3000 concentrations. A further assessment of passenger exposure to bus emissions on a platform was evaluated at another bus station in Brisbane, Australia. The sampling was conducted over seven weekdays to investigate spatial-temporal variations in size-fractionated particle number and PM2.5 concentrations, as well as human exposure on the platform. For the whole day, the average PN13-800 concentration was 1.3 x 104 and 1.0 x 104 particle/cm3 at the centre and end of the platform, respectively, of which PN50-100 accounted for the largest proportion to the total count. Furthermore, the contribution of exposure at the bus station to the overall daily exposure was assessed using two assumed scenarios of a school student and an office worker. It was found that, although the daily time fraction (the percentage of time spend at a location in a whole day) at the station was only 0.8 %, the daily exposure fractions (the percentage of exposures at a location accounting for the daily exposure) at the station were 2.7% and 2.8 % for exposure to PN13-800 and 2.7% and 3.5% for exposure to PM2.5 for the school student and the office worker, respectively. A new parameter, “exposure intensity” (the ratio of daily exposure fraction and the daily time fraction) was also defined and calculated at the station, with values of 3.3 and 3.4 for exposure to PN13-880, and 3.3 and 4.2 for exposure to PM2.5, for the school student and the office worker, respectively. In order to quantify the enhanced emissions at critical locations and define the emission distribution in further dispersion models for traffic interrupted transport microenvironments, a composite line source emission (CLSE) model was developed to specifically quantify exposure levels and describe the spatial variability of vehicle emissions in traffic interrupted microenvironments. This model took into account the complexity of vehicle movements in the queue, as well as different emission rates relevant to various driving conditions (cruise, decelerate, idle and accelerate), and it utilised multi-representative segments to capture the accurate emission distribution for real vehicle flow. This model does not only helped to quantify the enhanced emissions at critical locations, but it also helped to define the emission source distribution of the disrupted steady flow for further dispersion modelling. The model then was applied to estimate particle number emissions at a bidirectional bus station used by diesel and compressed natural gas fuelled buses. It was found that the acceleration distance was of critical importance when estimating particle number emission, since the highest emissions occurred in sections where most of the buses were accelerating and no significant increases were observed at locations where they idled. It was also shown that emissions at the front end of the platform were 43 times greater than at the rear of the platform. The CLSE model was also applied at a signalled pedestrian crossing, in order to assess increased particle number emissions from motor vehicles when forced to stop and accelerate from rest. The CLSE model was used to calculate the total emissions produced by a specific number and mix of light petrol cars and diesel passenger buses including 1 car travelling in 1 direction (/1 direction), 14 cars / 1 direction, 1 bus / 1 direction, 28 cars / 2 directions, 24 cars and 2 buses / 2 directions, and 20 cars and 4 buses / 2 directions. It was found that the total emissions produced during stopping on a red signal were significantly higher than when the traffic moved at a steady speed. Overall, total emissions due to the interruption of the traffic increased by a factor of 13, 11, 45, 11, 41, and 43 for the above 6 cases, respectively. In summary, this PhD thesis presents the results of a comprehensive study on particle number and mass concentration, together with particle size distribution, in a bus station transport microenvironment, influenced by bus flow rates, meteorological conditions and station design. Passenger spatial-temporal exposure to bus emitted particles was also assessed according to waiting time and location along the platform, as well as the contribution of exposure at the bus station to overall daily exposure. Due to the complexity of the interrupted traffic flow within the transport microenvironments, a unique CLSE model was also developed, which is capable of quantifying emission levels at critical locations within the transport microenvironment, for the purpose of evaluating passenger exposure and conducting simulations of vehicle emission dispersion. The application of the CLSE model at a pedestrian crossing also proved its applicability and simplicity for use in a real-world transport microenvironment.

Modelling port water collision risk using traffic conflicts

Navigational collisions are one of the major safety concerns for many seaports. Despite the extent of work recently done on collision risk analysis in port waters, little is known about the influencing factors of the risk. This paper develops a technique for modeling collision risks in port waterways in order to examine the associations between the risks and the geometric, traffic, and regulatory control characteristics of waterways. A binomial logistic model, which accounts for the correlations in the risks of a particular fairway at different time periods, is derived from traffic conflicts and calibrated for the Singapore port fairways. Estimation results show that the fairways attached to shoreline, traffic intersection and international fairway attribute higher risks, whereas those attached to confined water and local fairway possess lower risks. Higher risks are also found in the fairways featuring higher degree of bend, lower depth of water, higher numbers of cardinal and isolated danger marks, higher density of moving ships and lower operating speed. The risks are also found to be higher for night-time conditions.

Influence of organic matter in road deposited particulates in heavy metal accumulation and transport

The research study discussed in the paper investigated the influence of organic matter on heavy metal adsorption for different particle size ranges of build-up solids. Samples collected from road surfaces were assessed for organic matter content, mineral composition, particle size distribution and effective cation exchange capacity. It was found that the organic matter plays a key role in >75µm particles in the adsorption of Zinc, Lead, Nickel and Copper, which are generated by traffic activities. Clay forming minerals and metal oxides of Iron, Aluminium and Manganese was found to be important for heavy metal adsorption to <75µm particles. It was also found that heavy metals adsorbed to organic matter are strongly bound to particles and these metal ions will not be bio-available if the chemical quality of the media remains stable.

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.

Semi-parametric modelling of ultrafine particle number concentration

Quantifying spatial and/or temporal trends in environmental modelling data requires that measurements be taken at multiple sites. The number of sites and duration of measurement at each site must be balanced against costs of equipment and availability of trained staff. The split panel design comprises short measurement campaigns at multiple locations and continuous monitoring at reference sites [2]. Here we present a modelling approach for a spatio-temporal model of ultrafine particle number concentration (PNC) recorded according to a split panel design. The model describes the temporal trends and background levels at each site. The data were measured as part of the “Ultrafine Particles from Transport Emissions and Child Health” (UPTECH) project which aims to link air quality measurements, child health outcomes and a questionnaire on the child’s history and demographics. The UPTECH project involves measuring aerosol and particle counts and local meteorology at each of 25 primary schools for two weeks and at three long term monitoring stations, and health outcomes for a cohort of students at each school [3].

On the commonly accepted assumptions regarding observed motor vehicle crash counts at transport system locations

Readily accepted knowledge regarding crash causation is consistently omitted from efforts to model and subsequently understand motor vehicle crash occurrence and their contributing factors. For instance, distracted and impaired driving accounts for a significant proportion of crash occurrence, yet is rarely modeled explicitly. In addition, spatially allocated influences such as local law enforcement efforts, proximity to bars and schools, and roadside chronic distractions (advertising, pedestrians, etc.) play a role in contributing to crash occurrence and yet are routinely absent from crash models. By and large, these well-established omitted effects are simply assumed to contribute to model error, with predominant focus on modeling the engineering and operational effects of transportation facilities (e.g. AADT, number of lanes, speed limits, width of lanes, etc.) The typical analytical approach—with a variety of statistical enhancements—has been to model crashes that occur at system locations as negative binomial (NB) distributed events that arise from a singular, underlying crash generating process. These models and their statistical kin dominate the literature; however, it is argued in this paper that these models fail to capture the underlying complexity of motor vehicle crash causes, and thus thwart deeper insights regarding crash causation and prevention. This paper first describes hypothetical scenarios that collectively illustrate why current models mislead highway safety researchers and engineers. It is argued that current model shortcomings are significant, and will lead to poor decision-making. Exploiting our current state of knowledge of crash causation, crash counts are postulated to arise from three processes: observed network features, unobserved spatial effects, and ‘apparent’ random influences that reflect largely behavioral influences of drivers. It is argued; furthermore, that these three processes in theory can be modeled separately to gain deeper insight into crash causes, and that the model represents a more realistic depiction of reality than the state of practice NB regression. An admittedly imperfect empirical model that mixes three independent crash occurrence processes is shown to outperform the classical NB model. The questioning of current modeling assumptions and implications of the latent mixture model to current practice are the most important contributions of this paper, with an initial but rather vulnerable attempt to model the latent mixtures as a secondary contribution.

A catchment modelling approach integrating surface and groundwater processes, land use and distribution of nutrients : Elimbah Creek, southeast Queensland

As the world’s population is growing, so is the demand for agricultural products. However, natural nitrogen (N) fixation and phosphorus (P) availability cannot sustain the rising agricultural production, thus, the application of N and P fertilisers as additional nutrient sources is common. It is those anthropogenic activities that can contribute high amounts of organic and inorganic nutrients to both surface and groundwaters resulting in degradation of water quality and a possible reduction of aquatic life. In addition, runoff and sewage from urban and residential areas can contain high amounts of inorganic and organic nutrients which may also affect water quality. For example, blooms of the cyanobacterium Lyngbya majuscula along the coastline of southeast Queensland are an indicator of at least short term decreases of water quality. Although Australian catchments, including those with intensive forms of land use, show in general a low export of nutrients compared to North American and European catchments, certain land use practices may still have a detrimental effect on the coastal environment. Numerous studies are reported on nutrient cycling and associated processes on a catchment scale in the Northern Hemisphere. Comparable studies in Australia, in particular in subtropical regions are, however, limited and there is a paucity in the data, in particular for inorganic and organic forms of nitrogen and phosphorus; these nutrients are important limiting factors in surface waters to promote algal blooms. Therefore, the monitoring of N and P and understanding the sources and pathways of these nutrients within a catchment is important in coastal zone management. Although Australia is the driest continent, in subtropical regions such as southeast Queensland, rainfall patterns have a significant effect on runoff and thus the nutrient cycle at a catchment scale. Increasingly, these rainfall patterns are becoming variable. The monitoring of these climatic conditions and the hydrological response of agricultural catchments is therefore also important to reduce the anthropogenic effects on surface and groundwater quality. This study consists of an integrated hydrological–hydrochemical approach that assesses N and P in an environment with multiple land uses. The main aim is to determine the nutrient cycle within a representative coastal catchment in southeast Queensland, the Elimbah Creek catchment. In particular, the investigation confirms the influence associated with forestry and agriculture on N and P forms, sources, distribution and fate in the surface and groundwaters of this subtropical setting. In addition, the study determines whether N and P are subject to transport into the adjacent estuary and thus into the marine environment; also considered is the effect of local topography, soils and geology on N and P sources and distribution. The thesis is structured on four components individually reported. The first paper determines the controls of catchment settings and processes on stream water, riverbank sediment, and shallow groundwater N and P concentrations, in particular during the extended dry conditions that were encountered during the study. Temporal and spatial factors such as seasonal changes, soil character, land use and catchment morphology are considered as well as their effect on controls over distributions of N and P in surface waters and associated groundwater. A total number of 30 surface and 13 shallow groundwater sampling sites were established throughout the catchment to represent dominant soil types and the land use upstream of each sampling location. Sampling comprises five rounds and was conducted over one year between October 2008 and November 2009. Surface water and groundwater samples were analysed for all major dissolved inorganic forms of N and for total N. Phosphorus was determined in the form of dissolved reactive P (predominantly orthophosphate) and total P. In addition, extracts of stream bank sediments and soil grab samples were analysed for these N and P species. Findings show that major storm events, in particular after long periods of drought conditions, are the driving force of N cycling. This is expressed by higher inorganic N concentrations in the agricultural subcatchment compared to the forested subcatchment. Nitrate N is the dominant inorganic form of N in both the surface and groundwaters and values are significantly higher in the groundwaters. Concentrations in the surface water range from 0.03 to 0.34 mg N L..1; organic N concentrations are considerably higher (average range: 0.33 to 0.85 mg N L..1), in particular in the forested subcatchment. Average NO3-N in the groundwater has a range of 0.39 to 2.08 mg N L..1, and organic N averages between 0.07 and 0.3 mg N L..1. The stream bank sediments are dominated by organic N (range: 0.53 to 0.65 mg N L..1), and the dominant inorganic form of N is NH4-N with values ranging between 0.38 and 0.41 mg N L..1. Topography and soils, however, were not to have a significant effect on N and P concentrations in waters. Detectable phosphorus in the surface and groundwaters of the catchment is limited to several locations typically in the proximity of areas with intensive animal use; in soil and sediments, P is negligible. In the second paper, the stable isotopes of N (14N/15N) and H2O (16O/18O and 2H/H) in surface and groundwaters are used to identify sources of dissolved inorganic and organic N in these waters, and to determine their pathways within the catchment; specific emphasis is placed on the relation of forestry and agriculture. Forestry is predominantly concentrated in the northern subcatchment (Beerburrum Creek) while agriculture is mainly found in the southern subcatchment (Six Mile Creek). Results show that agriculture (horticulture, crops, grazing) is the main source of inorganic N in the surface waters of the agricultural subcatchment, and their isotopic signature shows a close link to evaporation processes that may occur during water storage in farm dams that are used for irrigation. Groundwaters are subject to denitrification processes that may result in reduced dissolved inorganic N concentrations. Soil organic matter delivers most of the inorganic N to the surface water in the forested subcatchment. Here, precipitation and subsequently runoff is the main source of the surface waters. Groundwater in this area is affected by agricultural processes. The findings also show that the catchment can attenuate the effects of anthropogenic land use on surface water quality. Riparian strips of natural remnant vegetation, commonly 50 to 100 m in width, act as buffer zones along the drainage lines in the catchment and remove inorganic N from the soil water before it enters the creek. These riparian buffer zones are common in most agricultural catchments of southeast Queensland and are indicated to reduce the impact of agriculture on stream water quality and subsequently on the estuary and marine environments. This reduction is expressed by a significant decrease in DIN concentrations from 1.6 mg N L..1 to 0.09 mg N L..1, and a decrease in the �15N signatures from upstream surface water locations downstream to the outlet of the agricultural subcatchment. Further testing is, however, necessary to confirm these processes. Most importantly, the amount of N that is transported to the adjacent estuary is shown to be negligible. The third and fourth components of the thesis use a hydrological catchment model approach to determine the water balance of the Elimbah Creek catchment. The model is then used to simulate the effects of land use on the water balance and nutrient loads of the study area. The tool that is used is the internationally widely applied Soil and Water Assessment Tool (SWAT). Knowledge about the water cycle of a catchment is imperative in nutrient studies as processes such as rainfall, surface runoff, soil infiltration and routing of water through the drainage system are the driving forces of the catchment nutrient cycle. Long-term information about discharge volumes of the creeks and rivers do, however, not exist for a number of agricultural catchments in southeast Queensland, and such information is necessary to calibrate and validate numerical models. Therefore, a two-step modelling approach was used to calibrate and validate parameters values from a near-by gauged reference catchment as starting values for the ungauged Elimbah Creek catchment. Transposing monthly calibrated and validated parameter values from the reference catchment to the ungauged catchment significantly improved model performance showing that the hydrological model of the catchment of interest is a strong predictor of the water water balance. The model efficiency coefficient EF shows that 94% of the simulated discharge matches the observed flow whereas only 54% of the observed streamflow was simulated by the SWAT model prior to using the validated values from the reference catchment. In addition, the hydrological model confirmed that total surface runoff contributes the majority of flow to the surface water in the catchment (65%). Only a small proportion of the water in the creek is contributed by total base-flow (35%). This finding supports the results of the stable isotopes 16O/18O and 2H/H, which show the main source of water in the creeks is either from local precipitation or irrigation waters delivered by surface runoff; a contribution from the groundwater (baseflow) to the creeks could not be identified using 16O/18O and 2H/H. In addition, the SWAT model calculated that around 68% of the rainfall occurring in the catchment is lost through evapotranspiration reflecting the prevailing long-term drought conditions that were observed prior and during the study. Stream discharge from the forested subcatchment was an order of magnitude lower than discharge from the agricultural Six Mile Creek subcatchment. A change in land use from forestry to agriculture did not significantly change the catchment water balance, however, nutrient loads increased considerably. Conversely, a simulated change from agriculture to forestry resulted in a significant decrease of nitrogen loads. The findings of the thesis and the approach used are shown to be of value to catchment water quality monitoring on a wider scale, in particular the implications of mixed land use on nutrient forms, distributions and concentrations. The study confirms that in the tropics and subtropics the water balance is affected by extended dry periods and seasonal rainfall with intensive storm events. In particular, the comprehensive data set of inorganic and organic N and P forms in the surface and groundwaters of this subtropical setting acquired during the one year sampling program may be used in similar catchment hydrological studies where these detailed information is missing. Also, the study concludes that riparian buffer zones along the catchment drainage system attenuate the transport of nitrogen from agricultural sources in the surface water. Concentrations of N decreased from upstream to downstream locations and were negligible at the outlet of the catchment.

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Modelling bluetooth and fusing with loops

The invited presentation was delivered at Queensland Department of Main Roads, Brisbane Australia, 17th June 2013

Multicomponent charge transport in electrolyte solutions

The work presented in this thesis investigates the mathematical modelling of charge transport in electrolyte solutions, within the nanoporous structures of electrochemical devices. We compare two approaches found in the literature, by developing onedimensional transport models based on the Nernst-Planck and Maxwell-Stefan equations. The development of the Nernst-Planck equations relies on the assumption that the solution is infinitely dilute. However, this is typically not the case for the electrolyte solutions found within electrochemical devices. Furthermore, ionic concentrations much higher than those of the bulk concentrations can be obtained near the electrode/electrolyte interfaces due to the development of an electric double layer. Hence, multicomponent interactions which are neglected by the Nernst-Planck equations may become important. The Maxwell-Stefan equations account for these multicomponent interactions, and thus they should provide a more accurate representation of transport in electrolyte solutions. To allow for the effects of the electric double layer in both the Nernst-Planck and Maxwell-Stefan equations, we do not assume local electroneutrality in the solution. Instead, we model the electrostatic potential as a continuously varying function, by way of Poisson’s equation. Importantly, we show that for a ternary electrolyte solution at high interfacial concentrations, the Maxwell-Stefan equations predict behaviour that is not recovered from the Nernst-Planck equations. The main difficulty in the application of the Maxwell-Stefan equations to charge transport in electrolyte solutions is knowledge of the transport parameters. In this work, we apply molecular dynamics simulations to obtain the required diffusivities, and thus we are able to incorporate microscopic behaviour into a continuum scale model. This is important due to the small size scales we are concerned with, as we are still able to retain the computational efficiency of continuum modelling. This approach provides an avenue by which the microscopic behaviour may ultimately be incorporated into a full device-scale model. The one-dimensional Maxwell-Stefan model is extended to two dimensions, representing an important first step for developing a fully-coupled interfacial charge transport model for electrochemical devices. It allows us to begin investigation into ambipolar diffusion effects, where the motion of the ions in the electrolyte is affected by the transport of electrons in the electrode. As we do not consider modelling in the solid phase in this work, this is simulated by applying a time-varying potential to one interface of our two-dimensional computational domain, thus allowing a flow field to develop in the electrolyte. Our model facilitates the observation of the transport of ions near the electrode/electrolyte interface. For the simulations considered in this work, we show that while there is some motion in the direction parallel to the interface, the interfacial coupling is not sufficient for the ions in solution to be "dragged" along the interface for long distances.

Modelling client puzzles and denial-of-service resistant protocols

Denial-of-service (DoS) attacks are a growing concern to networked services like the Internet. In recent years, major Internet e-commerce and government sites have been disabled due to various DoS attacks. A common form of DoS attack is a resource depletion attack, in which an attacker tries to overload the server's resources, such as memory or computational power, rendering the server unable to service honest clients. A promising way to deal with this problem is for a defending server to identify and segregate malicious traffic as earlier as possible. Client puzzles, also known as proofs of work, have been shown to be a promising tool to thwart DoS attacks in network protocols, particularly in authentication protocols. In this thesis, we design efficient client puzzles and propose a stronger security model to analyse client puzzles. We revisit a few key establishment protocols to analyse their DoS resilient properties and strengthen them using existing and novel techniques. Our contributions in the thesis are manifold. We propose an efficient client puzzle that enjoys its security in the standard model under new computational assumptions. Assuming the presence of powerful DoS attackers, we find a weakness in the most recent security model proposed to analyse client puzzles and this study leads us to introduce a better security model for analysing client puzzles. We demonstrate the utility of our new security definitions by including two hash based stronger client puzzles. We also show that using stronger client puzzles any protocol can be converted into a provably secure DoS resilient key exchange protocol. In other contributions, we analyse DoS resilient properties of network protocols such as Just Fast Keying (JFK) and Transport Layer Security (TLS). In the JFK protocol, we identify a new DoS attack by applying Meadows' cost based framework to analyse DoS resilient properties. We also prove that the original security claim of JFK does not hold. Then we combine an existing technique to reduce the server cost and prove that the new variant of JFK achieves perfect forward secrecy (the property not achieved by original JFK protocol) and secure under the original security assumptions of JFK. Finally, we introduce a novel cost shifting technique which reduces the computation cost of the server significantly and employ the technique in the most important network protocol, TLS, to analyse the security of the resultant protocol. We also observe that the cost shifting technique can be incorporated in any Diffine{Hellman based key exchange protocol to reduce the Diffie{Hellman exponential cost of a party by one multiplication and one addition.