School of Natural Sciences

STOCHASTICMODELLINGOFPREDATOR-PREYDYNAMICSINA THREE-PATCHECOSYSTEMWITHOPTIMALHARVESTING

Sat, 01 Nov 2025 00:00:00 GMT

STOCHASTICMODELLINGOFPREDATOR-PREYDYNAMICSINA THREE-PATCHECOSYSTEMWITHOPTIMALHARVESTING Mayabi, Lucian Talu Predator-prey interactions play a pivotal role in shaping ecological dynamics, and understand ing these interactions is critical for sustainable resource management and effective conservation. Existing literature predominantly focused on deterministic models incorporating optimum har vesting policy involving two ecosystems or less. Moreover, while stochastic models had been employed to account for randomness and uncertainty in ecological interactions, these studies were often limited to single-patch ecosystems. The stochastic dynamics of predator prey models involving more than two ecosystems had been given little attention in literature yet they are crit ical in conservation and resource management. Therefore, this research developed a stochastic predator-prey model with optimum harvesting for three patches namely “cages” which are within a lake, containing a predator-prey system involving large Nile perch as predators and smaller fish as prey. The dynamics of the prey population could transfer from one cage to the other. The study aims to investigate how randomness and harvesting controls affect population stability and sus tainability. Stability analysis of the deterministic part was carried out in order to study the long term behaviour of solutions around equilibrium points. Stability analysis of the stochastic model was done using stochastic Lyapunov function method assessing its impact on the system dynam ics. Numerical analysis was done to explain the analytic approach. From the results, when ei < 1 (ei is the predator’s efficiency in converting prey into a new predator), the lyapunov function, V(t), stays bounded indicating stochastic stability, and when ei > 1, V(t) grows without bound indicating that the system is unstable. An optimal control problem was formulated to derive harvesting functions that maximize resource utility while maintaining a sustainable ecosystem employing the Pontryagin’s Maximum Principle. From Numerical simulation, prey populations remained viable when the harvesting rates were maintained below ν1 = 0.02, ν2 = 0.02, and ν3 =0.02, and noise intensities were controlled at σ = 0.10, and σ = 0.90. The findings high light the impact of human activities, particularly harvesting, on ecosystem balance. They also contribute to conservation biology, fisheries management, and mathematical ecology, providing insights for sustainable resource management and effective conservation strategies.

THE STRUCTURES OF MATRICES AND INDICES OF ZERO DIVISOR GRAPHS OF 3,4-RADICAL ZERO COMPLETELY PRIMARY FINITE RINGS

Mon, 01 Sep 2025 00:00:00 GMT

THE STRUCTURES OF MATRICES AND INDICES OF ZERO DIVISOR GRAPHS OF 3,4-RADICAL ZERO COMPLETELY PRIMARY FINITE RINGS Ndago, Frank Omondi A zero divisor graph of the ring R is a graph whose vertices are entirely from the set of zero divisors of the ring and two vertices of the graph are adjacent if and only if their product is zero. The study of zero divisor graphs is important for it provides a better way of relating graph geometry to matrix conformations and formulation of encryption algorithms in coding therefore fundamental in interpretation of patterns, maps and networks in computer programs and modelling. Reasonable research has been done concerning zero divisor graphs of commutative rings with identity 1 ̸ = 0, however the generalization of the structures of the matrices of zero divisor graphs is still not extensive in the existing literature. Much of the recent works on zero divisor graphs of finite commutative rings have been restricted to the algebraic properties of the graphs such as colouring, girth, spectral radii and classification in terms of their completeness up to isomorphism. This has left the characterization of finite commutative rings via the structures of the matrices and indices of their graphs fairly untouched. In particular, matrices and indices of the zero divisor graph Γ(R) of finite commutative rings of 3-radical zero and 4-radical zero have not been characterized. This research has determined and investigated the properties of the matrices and indices of Γ(R) of finite rings R with unique maximal ideal J(R) such that J(R)3 = (0) and J(R)2 ̸ = (0); J(R)4 = (0) and J(R)3 ̸ = (0). It has also established the singularity and the relationship that exist between the eigenvalue multiplicities in the spectrum to the nullity of the graphs. We have validated the construction of these classes of rings using idealization procedure and the zero divisor graphs drawn from the isolated zero divisors using the Tikz Software. The matrices have been formulated from the graphs using standard definitions and the Mathematica software applied in investigating some of their algebraic properties. The results of this study can find an application to networking such as Google PageRank algorithms, developing more improved codes for better graph interpretation in operation systems. It will also advance the ring classification problem by revealing the interplay between ring theory, graph theory and linear algebra therefore contributing fundamentally to the literature of advanced algebra

SYNCHROTRON-BASEDIN-SITUANDEX-SITUINVESTIGATIONOF PEROVSKITEFORPHOTOVOLTAICAPPLICATIONS

Sun, 01 Jun 2025 00:00:00 GMT

SYNCHROTRON-BASEDIN-SITUANDEX-SITUINVESTIGATIONOF PEROVSKITEFORPHOTOVOLTAICAPPLICATIONS Shatsala, Elly Miller The advancement of perovskite-based optoelectronic devices hinges on overcoming their intrinsic instability challenges. Synchrotron-based techniques have been widely employed to characterize various materials, including the structural and interactive properties of perovskite crystals and their complexes, using ex situ, in situ, and operando approaches. Grazing Incidence Wide-Angle X-ray Scattering (GIWAXS) and Small Angle X-ray Scattering (GISAXS) studies have revealed inherent crystal peaks in perovskite films through both in situ and ex situ methods. This thesis investigates the crystallization dynamics, humidity resilience, and defect passivation strategies of triple cation (Cs₀.₀₅(FA₀.₈₃MA₀.₁₇)₀.₉₅Pb(I₀.₈₃Br₀.₁₇)₃) perovskite thin films, along with co passivation strategies applied to Cs₀.₁FA₀.₉PbI₃ using phenylethylammonium chloride (PEACl) and 2,8-Bis(diphenylphosphoryl)dibenzo[b,d]furan (PPF), aiming to enhance structural, optical, and electronic properties for efficient photovoltaic applications. A comprehensive experimental approach was adopted, combining solvent engineering, anti-solvent optimization, and co-passivation strategies. Film fabrication and degradation behaviors were characterized using synchrotron-based in situ and ex situ GIWAXS techniques, micro-X-ray diffraction (μ-XRD), photoluminescence (PL) spectroscopy, UV-Vis absorption spectroscopy, Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM), and Energy Dispersive X-ray Spectroscopy (EDS) for detailed analysis. Results reveal that 5% cesium incorporation into triple cation perovskites yields superior crystal structures, minimizing δ-perovskite phase and PbI₂ formation while enhancing humidity resistance. Solvent treatments, particularly with ethyl acetate (EA) and chlorobenzene (CB), influenced grain size, surface morphology, and film smoothness. Co-passivation of Cs₀.₁FA₀.₉PbI₃ with PEACl and PPF slowed crystallization kinetics, regulated grain orientation, suppressed non-radiative recombination centers, and stabilized the thermodynamically favorable α-perovskite phase. GIWAXS data confirmed the evolution of highly oriented 2D/3D mixed-phase architectures with enhanced c-axis unit cell alignment. Surface and elemental analysis demonstrated uniform passivant distribution, stronger Pb–O bonding, and reduced ion migration pathways. Photo-physical studies showed narrowed PL peaks, bandgap tuning, and reduced trap densities. This work establishes a strategic framework for achieving high-quality, stable perovskite films, laying the foundation for fabricating full solar modules at MMUST Materials Research Laboratory. The outcomes also pave the way for future collaborations, contributing toward the commercialization of perovskite photovoltaics with power conversion efficiencies exceeding 40%. Additionally, ongoing work involving robot automation and Machine Learning for high-throughput experiments at the Advanced Light Source, along with the development of a new multimodal spin-coater design to eliminate overheating and mechanical wobbles, is expected to further enhance beamline studies for perovskite, polymer, and battery research.

STUDY OF THE EFFECT OF SUNFLOWER OIL AND WATER ON THERMAL STORAGE PROPERTIES OF A FLAT PLATE SOLAR WATER HEATING COLLECTOR

Tue, 01 Jul 2025 00:00:00 GMT

STUDY OF THE EFFECT OF SUNFLOWER OIL AND WATER ON THERMAL STORAGE PROPERTIES OF A FLAT PLATE SOLAR WATER HEATING COLLECTOR Ng’anga, David Osiyo Solar collectors can convert the solar radiation energy to thermal energy when it hits a surface. A flat plate solar collector is a medium-temperature glazed plate heater manufactured to warm water or air to 80 Cmaximum. The simplest and effective way of tapping solar energy is by domestic water heating. Weather changes also have a big effect on the solar heater output water temperature. Behaviour, complexity and size of a solar water heating system are largely affected by the changes of ambient temperature and solar radiation in different weather conditions. Therefore, there is the necessity to use thermal storage fluids such as sunflower oil that has been documented to be an excellent heat transfer fluid (HTF) in addition to the heat storage fluid also necessitating the use of heat storage fluids such as sunflower oil since it is easily accessible, non-corrosive and non-poisonous. The main objective of the study was to compare the thermal storage capacity parameters of a flat plate solar water heater using sunflower oil versus water as thermal storage fluids. Specific objectives were to: determine instantaneous receiver heat gain by solar collector and compare the thermal storage effect of water and sunflower oil on output temperatures from a flat plate solar collector, evaluate the effect of both fluids on heat loss and heat exchange parameters of a flat plate solar collector, compare the overall system efficiency when using water versus sunflower oil as thermal storage media compare and analyse the KOLEKTOR 2.2 simulation results with the experimental data. Flat plate solar water heating collectors containing sunflower oil, and water as thermal storage fluids were designed and constructed for this study. The absorber plate was made of mild steel welded on galvanized iron riser pipes. The stated objectives were achieved by applying appropriate equations and measuring parameters affecting the thermal storage of a solar water heater such as area of the receiver, incident solar radiation, mass flow rate, wind speed, humidity, ambient temperature, fluid inlet and outlet temperatures. The efficiency of solar water heating systems was deduced by considering the incident solar energy on the collectors and the useful energy output from the systems. This takes into account conductive, convective and radiative thermal losses. The experimental measurements were done using k-type thermocouples connected to a data logger and a computer. Simulation and theoretical modeling were done using KOLEKTOR 2.2 software while experimental data computation and analysis were done using MATLAB. Research findings showed that sunflower oil and air attained a peak temperature of 75℃, while that of water was 65℃ from 12 noon to 3.30 pm. Overall heat loss coefficients for air, water and sunflower oil as -38.40 W/m2K, -20.94 W/m2K and -15.80 W/m2K respectively Sunflower oil has the longest stagnation (steady) temperature duration.FR of 0.8934, 0.846 and 0.785 for sunflower oil water and air respectively. However, from the KOLEKTOR 2.2 model, the heat removal factor for sunflower oil is 0.937, while water and air have heat removal factors of 0.918, and 0.910 respectively. Both experimental and theoretical results showed that sunflower oil has a higher removal factor FR and efficiency factor F1 than water. From the KOLEKTOR model, efficiency factor F1 values of sunflower oil, water and air 0.922, 0.916 and 0.818 respectively. Sunflower oil is also a better thermal storage fluid than water since has a lower heat loss coefficient than water. Other studies have also shown that sensible heat storage media improve efficiency by reducing thermal losses. The information from this study would be useful for effective utilization of intermittent solar energy for heating applications. Thus reducing water heating expenses, and conserving our environment.