School of Natural Science

SECOND ORDER EXTENDED ENSEMBLE FILTER (SoEEF) FOR NON-LINEAR FILTERING

2026-07-16T11:29:09Z

SECOND ORDER EXTENDED ENSEMBLE FILTER (SoEEF) FOR NON-LINEAR FILTERING Midenyo, Kevin Whenever the state of a system is estimated from information that is character ized with errors, a state estimator is employed to fuse the data with the model to produce an accurate estimate of the state. When the system dynamics and obser vation models are linear, the Kalman Filter, which is optimal, is used. However, in most applications of interest the system dynamics and observations equations are not-linear and suitable extensions of the Kalman Filter have been developed; for example, the Extended Kalman Filter(EKF). The Extended Kalman Filter is based on linearization by the Taylor series expansion about the mean of the state. This filtering process is however computationally expensive especially in high dimensional data. The cause for this is the high cost of integrating the equation of evolution of covariances. Due to this complexity in integration, new methods were sought known as the particle filters. They replace linearisation of non-linearities with Monte Carlo methods. They also formed a basis for Ensemble Kalman Filter (EnKF) an exten sion of Kalman filter to non-linear models. The EnKF reduced the computational cost but its innovation process did not capture information sufficiently hence there is need to improve its performance. This study has developed a new filter, Second order Extended Ensemble Filter (SoEEF). We derived it from stochastic state models by expansion of expected values to the second order by use of Taylor series together with Monte Carlo method. We used Lorenz 63 system of ordinary differential equations to test the performance of the new filter using the MATLAB. Then we compared its performance with four other filters like Bootstrap Particle Filter (BPF), First order Kalman Bucy Filter (FoEKBF), Second order Kalman Bucy Filter (SoKBF) and First order Extended Ensemble Filter (FoEEF). The performance of SoEEKF improves with the increase in ensemble size.

RELATIVISTIC DYNAMICS AND STRUCTURE FORMATION IN A MATTER—DOMINATED FRIEDMANN UNIVERSE

2026-07-16T11:23:20Z

RELATIVISTIC DYNAMICS AND STRUCTURE FORMATION IN A MATTER—DOMINATED FRIEDMANN UNIVERSE NYAGISERA, ROBERT NYAKUNDI Cosmology as the study of the Universe as a whole, addresses questions on its origin and development and among the fundamental problems in cosmology today is the formation and evolution of structures in the Universe. One of the proposed successful cosmological models tested experimentally in addressing this problem is the Friedmann model based on the cosmological principle. This thesis explores the fundamental cosmological principle, with a specific focus on the homogeneity and isotropy assumptions inherent in the Friedmann model underpinning the standard model. The cosmological principle says that the Universe is isotropic and homogeneous on large scales. However, current three dimensional redshift surveys that map the Universe depict inhomogeneities at all scales contrary to the cosmological principle view that cosmic matter distribution is statistically isotropic and homogeneous at large length scales. Additionally, there has been an ongoing cosmological debate on whether or not the analyses showing fractal clustering is carried using proper treatment of data, most notably a reliable and accurate amount of available statistical data. These galaxy surveys provide limited statistical data depended on our ability to measure distance accurately. The uncertainties associated with cosmic distance measures are huge and unresolved to date while the availability of huge observational data will wait for the next generation of bigger and advanced telescopes. To address this challenge, the research proposed a modified Friedmann model describing relativistic dynamics, structure formation and evolution based on the distribution of luminous matter in the Universe. In the modified model in which the redshift scale factor relation has been modified, it was assumed that there is huge and accurate astronomical data for measured redshift, number density of galaxies counts per solid angle in a given direction and light intensity counts . Interconnections between these three astronomical quantities was found using Einstein Field Equations. Computer simulations of the derived analytical results produced and obtained results related to structure formation in a matter―dominated modified Friedmann Universe without dark energy. Galaxy formation, evolution and distribution explained with a modified redshift formalism and compared to the standard model predictions. Analysis of the results suggests that the model can account for cosmic acceleration expansion without the need for dark energy. Simulations based on these models have illuminated structure formation and evolution processes of the early Universe running into the future. The simulations and analytical solutions reveal a unique pattern in the formation and evolution of cosmic structures, particularly in galaxy formation. This pattern shows a significant burst of activity between redshifts 0 < z < 0.4, which then progresses rapidly until approximately z ≈ 0.9, indicating that majority of cosmic structures formed during this period. Subsequently, the process slows down considerably, reaching a nearly constant rate until around z ≈ 1.6, after which a gradual decline begins. There is a distinctive redshift transition around z ≈ 0.9 is observed before the onset of dark―matter―induced accelerated expansion. This transition is proportional to mass matter density and geometry of the Universe. The model’s ability to explain cosmic acceleration without requiring fine-tuning of the cosmological constant highlights its novelty, providing a fresh perspective on the dynamic evolution of the universe.

OPTIMIZATION AND ANALYSIS OF FLUIDIZED BED DRYER FOR IMPROVED THERMAL EFFICIENCY IN TEA FACTORIES

2026-07-16T08:24:19Z

OPTIMIZATION AND ANALYSIS OF FLUIDIZED BED DRYER FOR IMPROVED THERMAL EFFICIENCY IN TEA FACTORIES OTEDO, BONFACE OCHIENG Drying is a vital process in most agricultural industries to increase finished product shelf life and storage. This thesis focused on optimization of thermal energy consumption in black tea drying process using a fluidized bed dryer (FBD) in tea factories. The research also covered laboratory practical experiment and drying simulation using computational fluid dynamics (CFD). A quantitatively evaluation and examination of laboratory drying was done by means of computational fluid dynamics in ANYS Fluent. Tea drying input variables considered in the study were hot air temperature, velocity and time. Energy utilization (EU), energy utilization ratio (EUR), exergetic efficiency were investigated under the same dryer input parameters to determine the dryer’s performance. The response variables in the experiment were the black tea moisture content and thermal energy utilization. The velocity of hot air was varied between 0.21 m/s and 0.55 m/s while the dryer hot air temperature was varied between 70 °C and 130 °C. The drying time varied between 0 minute to 20 minutes. Box Behnken methodology under response surface design was used to design experimental models. The Resulting fifteen (15) experimental models guided in conducting black tea drying experiments in the macerated tea laboratory at Sotik Tea Company Limited using the miniature fluidized bed dryer Sherwood Tornado model 501. From the experiment results, it took 20 minutes to lower the dhool moisture content from 72 % to 3.5 %. The data obtained from the drying experiment was used to develop black tea drying curve and black tea drying rate. The Box Behnken design under response surface design methodology in Minitab software was used to analyse and optimize the black tea drying variables. The optimum variables were found to be hot air temperature of 100 °C, hot air velocity of 0.38 m/s and drying time of 12.9 minutes. The optimal drying variables above, resulted in a more acceptable moisture content in the final black tea of 3.5 % db which falls between the acceptable black tea moisture content of 3 % to 4 % . From the energy and exergy results, EU and EUR increased with increase of drying air temperature also EU and EUR decreased with increase of drying time. Similarly, exergy utilization decreased with increase in drying time likewise exergy loss increased by increasing drying air temperature.

MECHANICAL PROPERTIES OF Aluminium-Magnesium-Silicon ALLOYS FOR AUTOMOTIVE AND AEROSPACE APPLICATIONS: A DENSITY FUNCTIONAL THEORY-BASED STUDY

2026-07-16T07:23:31Z

MECHANICAL PROPERTIES OF Aluminium-Magnesium-Silicon ALLOYS FOR AUTOMOTIVE AND AEROSPACE APPLICATIONS: A DENSITY FUNCTIONAL THEORY-BASED STUDY Kipkorir, Kirui Pius Aluminum and its alloys are utilized in various purposes, including aircraft skin, cookware, building cladding, train carriages, and electrical lines. This is attributable to their advantages, which encompass low density (physical density of 2.7g/cm3, which is approximately a third that of steel), non-corrosivity, formability, good thermal and electrical conductivity, and availability. Moreover, its non-corrosivity diminishes with alloying. Several studies, mostly experimental, have been done on aluminum magnesium-silicon (Al-Mg-Si) alloys (6xxx series). Mechanical properties, especially strength and ductility, have been explored in those earlier studies. However, other mechanical properties such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, Pugh’s ratio, creep, and resilience have not been explored extensively. While this study touched on ductility and hardness, it also explored the bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, Pugh’s ratio, and yield strength of Al-Mg-Si alloys. The main objective of this study was to determine the alloy composition that could yield stronger, harder, and more ductile materials that are appropriate for both aerospace and automotive industries by making use of density functional theory (DFT) calculations. The modeling of the structures was done using an aluminum cell as the starting structure, whose crystallographic information file was downloaded from the Crystallography.net website. It was then transferred to Burai software, where the unit cell was visualized and then transformed into 3 × 3 × 3 supercells containing 108 atoms, after which the supercells were alloyed with the appropriate number of Mg and Si atoms. Nine structures of Al-Mg-Si alloys with different percentages of Al, Mg, and Si were investigated. Structural optimization of the alloyed supercells was done as a preliminary to the study. The variable-cell relaxation was done using the Brodyden-Fletcher Goldfarb-Shanno (BFGS) algorithm. The stress-strain method was employed in the calculation of elastic stiffness constants, from which mechanical properties were obtained. The elastic constants were calculated using Density Functional Theory (DFT) with the Perdew-Burke-Ernzerhof for Solids (PBESOL) functional, as implemented in the Quantum Espresso software. This work has conclusively demonstrated that the Si/Mg ratio is a pivotal determinant of the mechanical properties of Al-Mg-Si alloys. The optimal parameters identified in this study include a density of 2762 kg/m³, a bulk modulus of 83.3 GPa, a shear modulus of 34.4 GPa, a Vickers hardness of 2.79 GPa, a Poisson’s ratio of 0.413, a Pugh’s ratio of 5.42, and a yield strength of 8.38 GPa. The ideal Si/Mg ratio for the majority of characteristics is 4.5. The alloys exhibiting these optimal features are suitable for industrial applications that necessitate such characteristics, including aircraft skins and mining equipment, particularly those with maximum hardness and yield strength. Their superior ductility enables their application in the fabrication of motor vehicle components and rail carriages. The alloys' low density renders them appropriate for manufacturing airplane components, as they enhance load capacity by minimizing part weight.