The thesis is concerned with the use of 3D mathematical modelling for flow simulation and separation efficiency in a single side weir CSO chambers. Analysis of the effect of turbulence model and computational grid on simulation results has been carried out in order to maximize the efficiency of numerical simulations. The goal of the thesis is to examine the effect of scum board position on separation efficiency of a single side weir CSO chamber.

In a digital world where algorithms and mathematical models impact students’ lives and society as a whole, it is important to learn critical thinking to understand and reflect upon what is happening. How will students perceive an inclusion of mathematical models that affect society in their mathematics lessons? Prior research shows that mathematical modelling is a valuable skill. However, critical thinking regarding models is currently not included in the curriculum. The theory in the study is based on critical mathematics and will include four different types of knowledge regarding mathematical modelling: pure mathematical knowledge, technical knowledge, reflective knowledge and extra-mathematical knowledge. In this study a field study was conducted in two Swedish upper secondary schools, together with a survey and focus group interviews. The study found that students’ experiences during the lessons show resemblance with critical mathematics while working with mathematical models and that the students are capable of evaluating the impact that the models have on society. The student’s experiences working with mathematical models that affect society alludes to a possibility to work towards including democracy in the mathematical classroom. This study focuses on the students’ perspective, further research regarding the teachers’ perspective could provide additional insight.

Accurate day-ahead grid loss forecasts are, among other things, essential to determine the electricity price for the upcoming day. The more accurate forecast, the closer the trading on the 'day-ahead' electricity market can become the actual operation the next day, which dedcrease the need for correcting production on the balancing market. Followingly, the need for extra imbalance costs, which make the electricity price higher, is reduced with accurate forecasts. This project's purpose was to explore a wide range of mathematical models to increase the energy comapny Fortum's day-ahead grid loss forecasting accuracy, and thereby contribute to lower the risk for high imbalance costs.  Two electrical grids located in Sweden, with different characteristics, were studied. One electrical grid was located in Dalarna and the other one was located in Värmland. Four different model types were tested for each grid. The linear models ARIMAX and SARIMAX were explored and the two artificial neural networks FNN (Feedforward Neural Network) and LSTM-RNN (Long-SHort Term Memory Recurrent Neural Network) were explored. By constructing different model structures of each model type, as well as statistically testing which predictors to include as input to the models, the most accurate model for grid loss forecasting was found. The models' forecasting accuracy were validated based on the MAPE (Mean Absolute Percentage Error). Variables important as predictors were found to be power production, electricity prices and grid losses at previous time steps. For the grid in Dalarna ARIMAX(2,0,2) was the model generating most accurate day-ahead grid loss forecasts and for the grid in Värmland, SARIMAX(1,0,0)(0,0,1)[24] was the most accurate model. That is, different models were found as the most accurate one for grid loss foracsting, as the two studied electricity grids had different characteristics. Hence, this result implies that there is no universal model that is the most adequate at modelling all types of grid losses. To find useful models when forecasting grid losses day-ahead, an analysis of the particular grid losses being studied is therefore not irrelevant.

The basal ganglia form an important structure centrally placed in the brain. They receive input from motor, associative and limbic areas, and produce output mainly to the thalamus and the brain stem. The basal ganglia have been implied in cognitive and motor functions. One way to understand the basal ganglia is to take a look at the diseases that affect them. Both Parkinson's disease and Huntington's disease with their motor problems are results of malfunctioning basal ganglia. There are also indications that these diseases affect cognitive functions. Drug addiction is another example that involves this structure, which is also important for motivation and selection of behaviour. In this licentiate thesis I am laying the groundwork for a detailed model of the striatum, which is the input stage of the basal ganglia. The striatum receives glutamatergic input from the cortex and thalamus, as well as dopaminergic input from substantia nigra. The majority of the neurons in the striatum are medium spiny (MS) projection neurons that project mainly to globus pallidus but also to other neurons in the striatum and to both dopamine producing and GABAergic neurons in substantia nigra. In addition to the MS neurons there are fast spiking (FS) interneurons that are in a position to regulate the firing of the MS neurons. These FS neurons are few, but connected into large networks through electrical synapses that could synchronise their effect. By forming strong inhibitory synapses on the MS neurons the FS neurons have a powerful influence on the striatal output. The inhibitory output of the basal ganglia on the thalamus is believed to keep prepared motor commands on hold, but once one of them is disinhibited, then the selected motor command is executed. This disinhibition is initiated in the striatum by the MS neurons. Both MS and FS neurons are active during so called up-states, which are periods of elevated cortical input to striatum. Here I have studied the FS neurons and their ability to detect such up-states. This is important because FS neurons can delay spikes in MS neurons and the time between up-state onset and the first spike in the MS neurons is correlated with the amount of calcium entering the MS neuron, which in turn might have implications for plasticity and learning of new behaviours. The effect of different combinations of electrical couplings between two FS neurons has been tested, where the location, number and strength of these gap junctions have been varied. I studied both the ability of the FS neurons to fire action potentials during the up-state, and the synchronisation between neighbouring FS neurons due to electrical coupling. I found that both proximal and distal gap junctions synchronised the firing, but the distal gap junctions did not have the same temporal precision. The ability of the FS neurons to detect an up-state was affected by whether the neighbouring FS neuron also received up-state input or not. This effect was more pronounced for distal gap junctions than proximal ones, due to a stronger shunting effect of distal gap junctions when the dendrites were synaptically activated. We have also performed initial stochastic simulations of the Ca2+-calmodulin-dependent protein kinase II (CaMKII). The purpose here is to build the knowledge as well as the tools necessary for biochemical simulations of intracellular processes that are important for plasticity in the MS neurons. The simulated biochemical pathways will then be integrated into an existing model of a full MS neuron. Another venue to explore is to build striatal network models consisting of MS and FS neurons and using experimental data of the striatal microcircuitry. With these different approaches we will improve our understanding of striatal information processing. / QC 20101116

Yes / CO2 capture from natural gas was experimentally and theoretically studied using a dead-end polymeric permeation cell. A numerical model was proposed for the separation of CO2/CH4 using Polytetrafluoroethylene (PTFE) in a flat sheet membrane module and developed based upon the continuity, momentum and mass transfer equations. The slip velocity condition was considered to show the reflection of gas flow in contact with the membrane surface. The solution method was based on the well-known SIMPLE algorithm and implemented using MATLAB to determine the velocity and concentration profiles. Due to change in velocity direction in the membrane module, the hybrid differencing scheme was used to solve the diffusion-convection equation. The results of the model were compared with the experimental data obtained as part of this work and good agreement was observed. The distribution of CO2 concentration inside the feed and permeate chambers was shown and the velocity profile at the membrane surface was also determined using reflection factor for polymericmembrane. The modelling result revealed that increasing the amount of CO2 in gas feed resulted in an increase in the CO2 in the permeate stream while the gas feed pressure increased. By changing the permeability, the model developed by use of the solution-diffusion concept could be used for all polymeric membranes with flat sheet modules.

Yes / Reverse osmosis (RO) has long been recognised as an efficient separation method for treating and removing harmful pollutants, such as dimethylphenol in wastewater treatment. This research aims to study the effects of RO network configuration of three modules of a wastewater treatment system using a spiral-wound RO membrane for the removal of dimethylphenol from its aqueous solution at different feed concentrations. The methodologies used for this research are based on simulation and optimisation studies carried out using a new simplified model. This takes into account the solution-diffusion model and film theory to express the transport phenomena of both solvent and solute through the membrane and estimate the concentration polarization impact respectively. This model is validated by direct comparison with experimental data derived from the literature and which includes dimethylphenol rejection method performed on a small-scale commercial single spiral-wound RO membrane system at different operating conditions. The new model is finally implemented to identify the optimal module configuration and operating conditions that achieve higher rejection after testing the impact of RO configuration. The optimisation model has been formulated to maximize the rejection parameters under optimal operating conditions of inlet feed flow rate, pressure and temperature for a given set of inlet feed concentration. Also, the optimisation model has been subjected to a number of upper and lower limits of decision variables, which include the inlet pressure, flow rate and temperature. In addition, the model takes into account the pressure loss constraint along the membrane length commensurate with the manufacturer’s specifications. The research clearly shows that the parallel configuration yields optimal dimethylphenol rejection with lower pressure loss.

After undergoing a study about current engine modelling and mapping approaches as well as the engine modelling requirements for different applications, a major problem found to be present is the extensive and time consuming mapping procedure that every engine has to go through so that all control parameters can be derived from experimental data. To improve this, a cycle-by-cycle modelling approach has been chosen to mathematically represent reciprocating engines starting by a complete dynamics crankshaft mechanism model which forms the base of the complete engine model. This system is modelled taking into account the possibility of a piston pin offset on the mechanism. The derived Valvetrain model is capable of representing a variable valve lift and phasing Valvetrain which can be used while modelling most modern engines. A butterfly type throttle area model is derived as well as its rate of change which is believed to be a key variable for transient engine control. In addition, an approximation throttle model is formulated aiming at real-time applications. Furthermore, the engine inertia is presented as a mathematical model able to be used for any engine. A spark ignition engine simulation (SIES) framework was developed in MATLAB SIMULINK to form the base of a complete high fidelity cycle-by-cycle simulation model with its major target to provide an environment for virtual engine mapping procedures. Some experimental measurements from an actual engine are still required to parameterise the model, which is the reason an engine mapping (EngMap) framework has been developed in LabVIEW, It is shown that all the moving engine components can be represented by a single cyclic variable which can be used for flow model development.

The uninterrupted spread of malaria, besides its seasonal uncertainty, is due to the lack of suitable planning and intervention mechanisms and tools. Several studies have been carried out to understand the factors that affect the development and transmission of malaria, but these efforts have been largely limited to piecemeal specific methods, hence they do not offer comprehensive solutions to predict disease outbreaks. This thesis introduces a ’holistic’ approach to understand the relationship between climate parameters and the occurrence of malaria using both mathematical and computational methods. In this respect, we develop new climate-based models using mathematical, agent-based and data-driven modelling techniques. A malaria model is developed using mathematical modelling to investigate the impact of temperature-dependent delays. Although this method is widely applicable, but it is limited to the study of homogeneous populations. An agent-based technique is employed to address this limitation, where the spatial and temporal variability of agents involved in the transmission of malaria are taken into account. Moreover, whilst the mathematical and agent-based approaches allow for temperature and precipitation in the modelling process, they do not capture other dynamics that might potentially affect malaria. Hence, to accommodate the climatic predictors of malaria, an intelligent predictive model is developed using machine-learning algorithms, which supports predictions of endemics in certain geographical areas by monitoring the risk factors, e.g., temperature and humidity. The thesis not only synthesises mathematical and computational methods to better understand the disease dynamics and its transmission, but also provides healthcare providers and policy makers with better planning and intervention tools.

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