Traffic and nucleation events as main sources of ultrafine particles in high-insolation developed world cities

Road traffic emissions are often considered the main source of ultrafine particles (UFP, diameter smaller than 100 nm) in urban environments. However, recent studies worldwide have shown that - in high-insolation urban regions at least - new particle formation events can also contribute to UFP. In order to quantify such events we systematically studied three cities located in predominantly sunny environments: Barcelona (Spain), Madrid (Spain) and Brisbane (Australia). Three long term datasets (1-2 years) of fine and ultrafine particle number size distributions (measured by SMPS, Scanning Mobility Particle Sizer) were analysed. Compared to total particle number concentrations, aerosol size distributions offer far more information on the type, origin and atmospheric evolution of the particles. By applying k-Means clustering analysis, we categorized the collected aerosol size distributions in three main categories: “Traffic” (prevailing 44-63% of the time), “Nucleation” (14-19%) and “Background pollution and Specific cases” (7-22%). Measurements from Rome (Italy) and Los Angeles (California) were also included to complement the study. The daily variation of the average UFP concentrations for a typical nucleation day at each site revealed a similar pattern for all cities, with three distinct particle bursts. A morning and an evening spike reflected traffic rush hours, whereas a third one at midday showed nucleation events. The photochemically nucleated particles burst lasted 1-4 hours, reaching sizes of 30-40 nm. On average, the occurrence of particle size spectra dominated by nucleation events was 16% of the time, showing the importance of this process as a source of UFP in urban environments exposed to high solar radiation. On average, nucleation events lasting for 2 hours or more occurred on 55% of the days, this extending to >4hrs in 28% of the days, demonstrating that atmospheric conditions in urban environments are not favourable to the growth of photochemically nucleated particles. In summary, although traffic remains the main source of UFP in urban areas, in developed countries with high insolation urban nucleation events are also a main source of UFP. If traffic-related particle concentrations are reduced in the future, nucleation events will likely increase in urban areas, due to the reduced urban condensation sinks.

Variability in exposure to ambient ultrafine particles in urban schools: Comparative assessment between Australia and Spain

Ambient ultrafine particle number concentrations (PNC) have inhomogeneous spatio-temporal distributions and depend on a number of different urban factors, including background conditions and distant sources. This paper quantitatively compares exposure to ambient ultrafine particles at urban schools in two cities in developed countries, with high insolation climatic conditions, namely Brisbane (Australia) and Barcelona (Spain). The analysis used comprehensive indoor and outdoor air quality measurements at 25 schools in Brisbane and 39 schools in Barcelona. PNC modes were analysed with respect to ambient temperature, land use and urban characteristics, combined with the measured elemental carbon concentrations, NOx (Brisbane) and NO2 (Barcelona). The trends and modes of the quantified weekday average daily cycles of ambient PNC exhibited significant differences between the two cities. PNC increases were observed during traffic rush hours in both cases. However, the mid-day peak was dominant in Brisbane schools and had the highest contribution to total PNC for both indoors and outdoors. In Barcelona, the contribution from traffic was highest for ambient PNC, while the mid-day peak had a slightly higher contribution for indoor concentrations. Analysis of the relationships between PNC and land use characteristics in Barcelona schools showed a moderate correlation with the percentage of road network area and an anti-correlation with the percentage of green area. No statistically significant correlations were found for Brisbane. Overall, despite many similarities between the two cities, school-based exposure patterns were different. The main source of ambient PNC at schools was shown to be traffic in Barcelona and mid-day new particle formation in Brisbane. The mid-day PNC peak in Brisbane could have been driven by the combined effect of background and meteorological conditions, as well as other local/distant sources. The results have implications for urban development, especially in terms of air quality mitigation and management at schools.

Land use regression model (LUR) for ultrafine particles in Brisbane

Traffic-related air pollution has been associated with a wide range of adverse health effects. One component of traffic emissions that has been receiving increasing attention is ultrafine particles(UFP, < 100 nm), which are of concern to human health due to their small diameters. Vehicles are the dominant source of UFP in urban environments. Small-scale variation in ultrafine particle number concentration (PNC) can be attributed to local changes in land use and road abundance. UFPs are also formed as a result of particle formation events. Modelling the spatial patterns in PNC is integral to understanding human UFP exposure and also provides insight into particle formation mechanisms that contribute to air pollution in urban environments. Land-use regression (LUR) is a technique that can use to improve the prediction of air pollution.

Thermal Treatments of Fe—Mn Alkoxide of Glycerol: Infrared absorption and emission

Synthetic Fe—Mn alkoxide of glycerol samples are submitted to controlled heating conditions and examined by IR absorption spectroscopy. On the other hand, the same sample is studied by infrared emission spectroscopy (IRES), upon heating in situ from 100 to 600°C. The spectral techniques employed in this contribution, especially IRES, show that as a result of the thermal treatments ferromagnetic oxides (manganese ferrite) are formed between 350 and 400°C. Some further spectral changes are seen at higher temperatures.

Airborne particulate matter at a bus station : concentration levels and governing parameters

Traffic emissions are an important contributor to ambient air pollution, especially in large cities featuring extensive and high density traffic networks. Bus fleets represent a significant part of inner city traffic causing an increase in exposure to general public, passengers and drivers along bus routes and at bus stations. Limited information is available on quantification of the levels, and governing parameters affecting the air pollution exposure at bus stations. The presented study investigated the bus emissions-dominated ambient air in a large, inner city bus station, with a specific focus on submicrometer particles. The study’s objectives were (i) quantification of the concentration levels; (ii) characterisation of the spatio-temporal variation; (iii) identification of the parameters governing the emissions levels at the bus station and (iv) assessment of the relationship between particle concentrations measured at the street level (background) and within the bus station. The results show that up to 90% of the emissions at the station are ultrafine particles (smaller than 100 nm), with the concentration levels up to 10 times the value of urban ambient air background (annual) and up to 4 times the local ambient air background. The governing parameters affecting particle concentration at the station were bus flow rate and meteorological conditions (wind velocity). Particle concentration followed a diurnal trend, with an increase in the morning and evening, associated with traffic rush hours. Passengers’ exposure could be significant compared to the average outdoor and indoor exposure levels.

Particle number and mass emission factors from combustion of wood samples collected from Queensland forest

Knowledge of particle emission characteristics associated with forest fires and in general, biomass burning, is becoming increasingly important due to the impact of these emissions on human health. Of particular importance is developing a better understanding of the size distribution of particles generated from forest combustion under different environmental conditions, as well as provision of emission factors for different particle size ranges. This study was aimed at quantifying particle emission factors from four types of wood found in South East Queensland forests: Spotted Gum (Corymbia citriodora), Red Gum (Eucalypt tereticornis), Blood Gum (Eucalypt intermedia), and Iron bark (Eucalypt decorticans); under controlled laboratory conditions. The experimental set up included a modified commercial stove connected to a dilution system designed for the conditions of the study. Measurements of particle number size distribution and concentration resulting from the burning of woods with a relatively homogenous moisture content (in the range of 15 to 26 %) and for different rates of burning were performed using a TSI Scanning Mobility Particle Sizer (SMPS) in the size range from 10 to 600 nm and a TSI Dust Trak for PM2.5. The results of the study in terms of the relationship between particle number size distribution and different condition of burning for different species show that particle number emission factors and PM2.5 mass emission factors depend on the type of wood and the burning rate; fast burning or slow burning. The average particle number emission factors for fast burning conditions are in the range of 3.3 x 1015 to 5.7 x 1015 particles/kg, and for PM2.5 are in the range of 139 to 217 mg/kg.

Long-term trends in fine particle number concentrations in the urban atmosphere of Brisbane : the relevance of traffic emissions and new particle formation

The measurement of submicrometre (< 1.0 m) and ultrafine particles (diameter < 0.1 m) number concentration have attracted attention since the last decade because the potential health impacts associated with exposure to these particles can be more significant than those due to exposure to larger particles. At present, ultrafine particles are not regularly monitored and they are yet to be incorporated into air quality monitoring programs. As a result, very few studies have analysed their long-term and spatial variations in ultrafine particle concentration, and none have been in Australia. To address this gap in scientific knowledge, the aim of this research was to investigate the long-term trends and seasonal variations in particle number concentrations in Brisbane, Australia. Data collected over a five-year period were analysed using weighted regression models. Monthly mean concentrations in the morning (6:00-10:00) and the afternoon (16:00-19:00) were plotted against time in months, using the monthly variance as the weights. During the five-year period, submicrometre and ultrafine particle concentrations increased in the morning by 105.7% and 81.5% respectively whereas in the afternoon there was no significant trend. The morning concentrations were associated with fresh traffic emissions and the afternoon concentrations with the background. The statistical tests applied to the seasonal models, on the other hand, indicated that there was no seasonal component. The spatial variation in size distribution in a large urban area was investigated using particle number size distribution data collected at nine different locations during different campaigns. The size distributions were represented by the modal structures and cumulative size distributions. Particle number peaked at around 30 nm, except at an isolated site dominated by diesel trucks, where the particle number peaked at around 60 nm. It was found that ultrafine particles contributed to 82%-90% of the total particle number. At the sites dominated by petrol vehicles, nanoparticles (< 50 nm) contributed 60%-70% of the total particle number, and at the site dominated by diesel trucks they contributed 50%. Although the sampling campaigns took place during different seasons and were of varying duration these variations did not have an effect on the particle size distributions. The results suggested that the distributions were rather affected by differences in traffic composition and distance to the road. To investigate the occurrence of nucleation events, that is, secondary particle formation from gaseous precursors, particle size distribution data collected over a 13 month period during 5 different campaigns were analysed. The study area was a complex urban environment influenced by anthropogenic and natural sources. The study introduced a new application of time series differencing for the identification of nucleation events. To evaluate the conditions favourable to nucleation, the meteorological conditions and gaseous concentrations prior to and during nucleation events were recorded. Gaseous concentrations did not exhibit a clear pattern of change in concentration. It was also found that nucleation was associated with sea breeze and long-range transport. The implications of this finding are that whilst vehicles are the most important source of ultrafine particles, sea breeze and aged gaseous emissions play a more important role in secondary particle formation in the study area.

Development of a particle number and particle mass vehicle emissions inventory for an urban fleet

Motor vehicles are major emitters of gaseous and particulate pollution in urban areas, and exposure to particulate pollution can have serious health effects, ranging from respiratory and cardiovascular disease to mortality. Motor vehicle tailpipe particle emissions span a broad size range from 0.003-10µm, and are measured as different subsets of particle mass concentrations or particle number count. However, no comprehensive inventories currently exist in the international published literature covering this wide size range. This paper presents the first published comprehensive inventory of motor vehicle tailpipe particle emissions covering the full size range of particles emitted. The inventory was developed for urban South-East Queensland by combining two techniques from distinctly different disciplines, from aerosol science and transport modelling. A comprehensive set of particle emission factors were combined with traffic modelling, and tailpipe particle emissions were quantified for particle number (ultrafine particles), PM1, PM2.5 and PM10 for light and heavy duty vehicles and buses. A second aim of the paper involved using the data derived in this inventory for scenario analyses, to model the particle emission implications of different proportions of passengers travelling in light duty vehicles and buses in the study region, and to derive an estimate of fleet particle emissions in 2026. It was found that heavy duty vehicles (HDVs) in the study region were major emitters of particulate matter pollution, and although they contributed only around 6% of total regional vehicle kilometres travelled, they contributed more than 50% of the region’s particle number (ultrafine particles) and PM1 emissions. With the freight task in the region predicted to double over the next 20 years, this suggests that HDVs need to be a major focus of mitigation efforts. HDVs dominated particle number (ultrafine particles) and PM1 emissions; and LDV PM2.5 and PM10 emissions. Buses contributed approximately 1-2% of regional particle emissions.

Investigation into submicrometer particle and gaseous emissions from airport ground running procedures

Emissions from airport operations are of significant concern because of their potential impact on local air quality and human health. The currently limited scientific knowledge of aircraft emissions is an important issue worldwide, when considering air pollution associated with airport operation, and this is especially so for ultrafine particles. This limited knowledge is due to scientific complexities associated with measuring aircraft emissions during normal operations on the ground. In particular this type of research has required the development of novel sampling techniques which must take into account aircraft plume dispersion and dilution as well as the various particle dynamics that can affect the measurements of the aircraft engine plume from an operational aircraft. In order to address this scientific problem, a novel mobile emission measurement method called the Plume Capture and Analysis System (PCAS), was developed and tested. The PCAS permits the capture and analysis of aircraft exhaust during ground level operations including landing, taxiing, takeoff and idle. The PCAS uses a sampling bag to temporarily store a sample, providing sufficient time to utilize sensitive but slow instrumental techniques to be employed to measure gas and particle emissions simultaneously and to record detailed particle size distributions. The challenges in relation to the development of the technique include complexities associated with the assessment of the various particle loss and deposition mechanisms which are active during storage in the PCAS. Laboratory based assessment of the method showed that the bag sampling technique can be used to accurately measure particle emissions (e.g. particle number, mass and size distribution) from a moving aircraft or vehicle. Further assessment of the sensitivity of PCAS results to distance from the source and plume concentration was conducted in the airfield with taxiing aircraft. The results showed that the PCAS is a robust method capable of capturing the plume in only 10 seconds. The PCAS is able to account for aircraft plume dispersion and dilution at distances of 60 to 180 meters downwind of moving a aircraft along with particle deposition loss mechanisms during the measurements. Characterization of the plume in terms of particle number, mass (PM2.5), gaseous emissions and particle size distribution takes only 5 minutes allowing large numbers of tests to be completed in a short time. The results were broadly consistent and compared well with the available data. Comprehensive measurements and analyses of the aircraft plumes during various modes of the landing and takeoff (LTO) cycle (e.g. idle, taxi, landing and takeoff) were conducted at Brisbane Airport (BNE). Gaseous (NOx, CO2) emission factors, particle number and mass (PM2.5) emission factors and size distributions were determined for a range of Boeing and Airbus aircraft, as a function of aircraft type and engine thrust level. The scientific complexities including the analysis of the often multimodal particle size distributions to describe the contributions of different particle source processes during the various stages of aircraft operation were addressed through comprehensive data analysis and interpretation. The measurement results were used to develop an inventory of aircraft emissions at BNE, including all modes of the aircraft LTO cycle and ground running procedures (GRP). Measurements of the actual duration of aircraft activity in each mode of operation (time-in-mode) and compiling a comprehensive matrix of gas and particle emission rates as a function of aircraft type and engine thrust level for real world situations was crucial for developing the inventory. The significance of the resulting matrix of emission rates in this study lies in the estimate it provides of the annual particle emissions due to aircraft operations, especially in terms of particle number. In summary, this PhD thesis presents for the first time a comprehensive study of the particle and NOx emission factors and rates along with the particle size distributions from aircraft operations and provides a basis for estimating such emissions at other airports. This is a significant addition to the scientific knowledge in terms of particle emissions from aircraft operations, since the standard particle number emissions rates are not currently available for aircraft activities.

Particle emission factors during cooking activities

Exposure to particles emitted by cooking activities may be responsible for a variety of respiratory health effects. However, the relationship between these exposures and their subsequent effects on health cannot be evaluated without understanding the properties of the emitted aerosol or the main parameters that influence particle emissions during cooking. Whilst traffic-related emissions, stack emissions and ultrafine particle concentrations (UFP, diameter < 100 nm) in urban ambient air have been widely investigated for many years, indoor exposure to UFPs is a relatively new field and in order to evaluate indoor UFP emissions accurately, it is vital to improve scientific understanding of the main parameters that influence particle number, surface area and mass emissions. The main purpose of this study was to characterise the particle emissions produced during grilling and frying as a function of the food, source, cooking temperature and type of oil. Emission factors, along with particle number concentrations and size distributions were determined in the size range 0.006-20 m using a Scanning Mobility Particle Sizer (SMPS) and an Aerodynamic Particle Sizer (APS). An infrared camera was used to measure the temperature field. Overall, increased emission factors were observed to be a function of increased cooking temperatures. Cooking fatty foods also produced higher particle emission factors than vegetables, mainly in terms of mass concentration, and particle emission factors also varied significantly according to the type of oil used.

Uncertainty budget in the measurement of typical airborne number, surface area and mass particle distributions

The effects of particulate matter on environment and public health have been widely studied in recent years. A number of studies in the medical field have tried to identify the specific effect on human health of particulate exposure, but agreement amongst these studies on the relative importance of the particles’ size and its origin with respect to health effects is still lacking. Nevertheless, air quality standards are moving, as the epidemiological attention, towards greater focus on the smaller particles. Current air quality standards only regulate the mass of particulate matter less than 10 μm in aerodynamic diameter (PM10) and less than 2.5 μm (PM2.5). The most reliable method used in measuring Total Suspended Particles (TSP), PM10, PM2.5 and PM1 is the gravimetric method since it directly measures PM concentration, guaranteeing an effective traceability to international standards. This technique however, neglects the possibility to correlate short term intra-day variations of atmospheric parameters that can influence ambient particle concentration and size distribution (emission strengths of particle sources, temperature, relative humidity, wind direction and speed and mixing height) as well as human activity patterns that may also vary over time periods considerably shorter than 24 hours. A continuous method to measure the number size distribution and total number concentration in the range 0.014 – 20 μm is the tandem system constituted by a Scanning Mobility Particle Sizer (SMPS) and an Aerodynamic Particle Sizer (APS). In this paper, an uncertainty budget model of the measurement of airborne particle number, surface area and mass size distributions is proposed and applied for several typical aerosol size distributions. The estimation of such an uncertainty budget presents several difficulties due to i) the complexity of the measurement chain, ii) the fact that SMPS and APS can properly guarantee the traceability to the International System of Measurements only in terms of number concentration. In fact, the surface area and mass concentration must be estimated on the basis of separately determined average density and particle morphology. Keywords: SMPS-APS tandem system, gravimetric reference method, uncertainty budget, ultrafine particles.

Development of a particle number and particle mass emissions inventory for an urban fleet : a study in South-East Queensland

Motor vehicles are a major source of gaseous and particulate matter pollution in urban areas, particularly of ultrafine sized particles (diameters < 0.1 µm). Exposure to particulate matter has been found to be associated with serious health effects, including respiratory and cardiovascular disease, and mortality. Particle emissions generated by motor vehicles span a very broad size range (from around 0.003-10 µm) and are measured as different subsets of particle mass concentrations or particle number count. However, there exist scientific challenges in analysing and interpreting the large data sets on motor vehicle emission factors, and no understanding is available of the application of different particle metrics as a basis for air quality regulation. To date a comprehensive inventory covering the broad size range of particles emitted by motor vehicles, and which includes particle number, does not exist anywhere in the world. This thesis covers research related to four important and interrelated aspects pertaining to particulate matter generated by motor vehicle fleets. These include the derivation of suitable particle emission factors for use in transport modelling and health impact assessments; quantification of motor vehicle particle emission inventories; investigation of the particle characteristic modality within particle size distributions as a potential for developing air quality regulation; and review and synthesis of current knowledge on ultrafine particles as it relates to motor vehicles; and the application of these aspects to the quantification, control and management of motor vehicle particle emissions. In order to quantify emissions in terms of a comprehensive inventory, which covers the full size range of particles emitted by motor vehicle fleets, it was necessary to derive a suitable set of particle emission factors for different vehicle and road type combinations for particle number, particle volume, PM1, PM2.5 and PM1 (mass concentration of particles with aerodynamic diameters < 1 µm, < 2.5 µm and < 10 µm respectively). The very large data set of emission factors analysed in this study were sourced from measurement studies conducted in developed countries, and hence the derived set of emission factors are suitable for preparing inventories in other urban regions of the developed world. These emission factors are particularly useful for regions with a lack of measurement data to derive emission factors, or where experimental data are available but are of insufficient scope. The comprehensive particle emissions inventory presented in this thesis is the first published inventory of tailpipe particle emissions prepared for a motor vehicle fleet, and included the quantification of particle emissions covering the full size range of particles emitted by vehicles, based on measurement data. The inventory quantified particle emissions measured in terms of particle number and different particle mass size fractions. It was developed for the urban South-East Queensland fleet in Australia, and included testing the particle emission implications of future scenarios for different passenger and freight travel demand. The thesis also presents evidence of the usefulness of examining modality within particle size distributions as a basis for developing air quality regulations; and finds evidence to support the relevance of introducing a new PM1 mass ambient air quality standard for the majority of environments worldwide. The study found that a combination of PM1 and PM10 standards are likely to be a more discerning and suitable set of ambient air quality standards for controlling particles emitted from combustion and mechanically-generated sources, such as motor vehicles, than the current mass standards of PM2.5 and PM10. The study also reviewed and synthesized existing knowledge on ultrafine particles, with a specific focus on those originating from motor vehicles. It found that motor vehicles are significant contributors to both air pollution and ultrafine particles in urban areas, and that a standardized measurement procedure is not currently available for ultrafine particles. The review found discrepancies exist between outcomes of instrumentation used to measure ultrafine particles; that few data is available on ultrafine particle chemistry and composition, long term monitoring; characterization of their spatial and temporal distribution in urban areas; and that no inventories for particle number are available for motor vehicle fleets. This knowledge is critical for epidemiological studies and exposure-response assessment. Conclusions from this review included the recommendation that ultrafine particles in populated urban areas be considered a likely target for future air quality regulation based on particle number, due to their potential impacts on the environment. The research in this PhD thesis successfully integrated the elements needed to quantify and manage motor vehicle fleet emissions, and its novelty relates to the combining of expertise from two distinctly separate disciplines - from aerosol science and transport modelling. The new knowledge and concepts developed in this PhD research provide never before available data and methods which can be used to develop comprehensive, size-resolved inventories of motor vehicle particle emissions, and air quality regulations to control particle emissions to protect the health and well-being of current and future generations.

Theoretical investigation of mechanisms of formation and interaction of nanoparticles

In this thesis an investigation into theoretical models for formation and interaction of nanoparticles is presented. The work presented includes a literature review of current models followed by a series of five chapters of original research. This thesis has been submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by publication and therefore each of the five chapters consist of a peer-reviewed journal article. The thesis is then concluded with a discussion of what has been achieved during the PhD candidature, the potential applications for this research and ways in which the research could be extended in the future. In this thesis we explore stochastic models pertaining to the interaction and evolution mechanisms of nanoparticles. In particular, we explore in depth the stochastic evaporation of molecules due to thermal activation and its ultimate effect on nanoparticles sizes and concentrations. Secondly, we analyse the thermal vibrations of nanoparticles suspended in a fluid and subject to standing oscillating drag forces (as would occur in a standing sound wave) and finally on lattice surfaces in the presence of high heat gradients. We have described in this thesis a number of new models for the description of multicompartment networks joined by a multiple, stochastically evaporating, links. The primary motivation for this work is in the description of thermal fragmentation in which multiple molecules holding parts of a carbonaceous nanoparticle may evaporate. Ultimately, these models predict the rate at which the network or aggregate fragments into smaller networks/aggregates and with what aggregate size distribution. The models are highly analytic and describe the fragmentation of a link holding multiple bonds using Markov processes that best describe different physical situations and these processes have been analysed using a number of mathematical methods. The fragmentation of the network/aggregate is then predicted using combinatorial arguments. Whilst there is some scepticism in the scientific community pertaining to the proposed mechanism of thermal fragmentation,we have presented compelling evidence in this thesis supporting the currently proposed mechanism and shown that our models can accurately match experimental results. This was achieved using a realistic simulation of the fragmentation of the fractal carbonaceous aggregate structure using our models. Furthermore, in this thesis a method of manipulation using acoustic standing waves is investigated. In our investigation we analysed the effect of frequency and particle size on the ability for the particle to be manipulated by means of a standing acoustic wave. In our results, we report the existence of a critical frequency for a particular particle size. This frequency is inversely proportional to the Stokes time of the particle in the fluid. We also find that for large frequencies the subtle Brownian motion of even larger particles plays a significant role in the efficacy of the manipulation. This is due to the decreasing size of the boundary layer between acoustic nodes. Our model utilises a multiple time scale approach to calculating the long term effects of the standing acoustic field on the particles that are interacting with the sound. These effects are then combined with the effects of Brownian motion in order to obtain a complete mathematical description of the particle dynamics in such acoustic fields. Finally, in this thesis, we develop a numerical routine for the description of "thermal tweezers". Currently, the technique of thermal tweezers is predominantly theoretical however there has been a handful of successful experiments which demonstrate the effect it practise. Thermal tweezers is the name given to the way in which particles can be easily manipulated on a lattice surface by careful selection of a heat distribution over the surface. Typically, the theoretical simulations of the effect can be rather time consuming with supercomputer facilities processing data over days or even weeks. Our alternative numerical method for the simulation of particle distributions pertaining to the thermal tweezers effect use the Fokker-Planck equation to derive a quick numerical method for the calculation of the effective diffusion constant as a result of the lattice and the temperature. We then use this diffusion constant and solve the diffusion equation numerically using the finite volume method. This saves the algorithm from calculating many individual particle trajectories since it is describes the flow of the probability distribution of particles in a continuous manner. The alternative method that is outlined in this thesis can produce a larger quantity of accurate results on a household PC in a matter of hours which is much better than was previously achieveable.