The research sought to investigate the surface roughness parameter (Zo) and wind shear exponent (α) of Kisii region (elevation 1710m above sea level, 0.68°S, 34.79°E). A six-month experiment was set at three sites of Kisii region. Two PRO AcuRite 01036 Wireless Weather Stations with pro+ 5-in-1 Sensors were placed at different hub heights above the ground and data were sent and received by a display board set at a room through remote sensing at an interval of 12 minutes. Data was collected from the display board through the pc connect software, grouped into discrete data and then calculated to represent mean wind speed, diurnal variation, daily variation, and monthly variations. The calculated averages of wind speeds at hub heights of 10m and 13m were then used to determine the wind shear exponent and surface roughness parameter of the sites. The wind shear exponents were found to be 0.92, 0.41, and 0.54 for Nyamecheo, Kisii University, and Ikobe stations, respectively, with an average of 0.64. The roughness parameter was also calculated and found to be 3.75, 1.32, and 1.96 for Nyamecheo, Kisii University (KSU), and Ikobe, respectively, with an average of 2.35.

Migration of pollutant particles into subsurface water reservoirs through point sources is largely involved mixing processes within the system of water flow. Possible potential sources of pollution to these point sources include municipal wastes, septic loads, landfills, uncontrolled hazardous wastes, and sewage storage tanks. The mixing processes of pollutant significantly alter their predictive rate of flow in the water reservoirs, and therefore the time inherent in mixing processes need to be accounted for. In this study, pollution of subsurface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied through a conceptual perspective of mixing problem processes in water tanks. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of water reservoir pollution that involve single species contaminants such as nitrates, phosphorous, and detergents injecting from a point source. The concentration x t of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. The major assumption made in modeling of mixing problems using tanks is that mixing is instantaneous. Practical realities dictate that mixing cannot occur instantaneously throughout the tank. So as to accommodate these realities, the study refined the systems of ordinary differential equations (ODEs) generated from principles of mixing problems in cascading tanks, into a system of delayed differential equations (DDEs) so that the concentration of pollutant leaving the reservoir at time t would be equal to the average concentration at some earlier instant, t − τ for the delay τ > 0 . The formulated model is a mathematical discrete time delay model which can be used to describe the dynamics of subsurface water reservoir pollution through a point source. The model was simulated on municipal River Nyakomisaro in Kisii County, Kenya. Physical and kinematic parameters of the river (cross-sectional lengths, depths, flow velocities) at three river sectional reservoirs were measured and the obtained parameter values were then used to evaluate coefficients of the formulated model equation. The system of DDEs from this simulation was solved numerically on MATLAB using dde23 software. From the graphical views generated for concentration of pollutant x t versus time t , it was established that the developed DDEs cover longer time series solutions (characteristic curves) than that from the corresponding ODEs in the same reservoir indicating that time necessary for particle flow through water reservoirs is underestimated if ODEs are used to describe particle flow. Also, the graphical views indicated similar tendencies (characteristics) in particle flow with time elapse even though initial values of concentration x t were different for every potentially recognized single species pollutant considered in each river reservoir. Hence, longer values of time   t will imply more pollution in the water reservoir and vice versa. By introducing time delays due to constituent mixing processes in water quality simulation models that make use of advection-diffusion equation such as Qual2kw, the findings of this study can help for better understanding of the contaminant’s accumulation levels and their rate of transport in water resource. These will assist, for example, water-quality protection agencies such as Environmental Protection Agency (EPA), World Health Organization (WHO), and National Environmental Management Authority (NEMA) for the need to generate efficient and effective remedial strategies to control or mitigate hazardous or risks arising from water pollution.

Background. Global warming is a growing threat in the world today mainly due to the emission of CO2 caused by the burning of fossil fuel. Consequently, countries are being forced to seek potential alternative sources of energy such as wind, solar, and photovoltaic among many others. However, the realization of their benefits is faced with challenges. Though wind stands a chance to solve this problem, the lack of adequate site profiles, long-term behavioural information, and specific data information that enables informed choice on site selection, turbine selection, and expected power output has remained a challenge to its exploitation. In this research, Weibull and Rayleigh models are adopted. Wind speeds were analyzed and characterized in the short term and then simulated for a long-term measured hourly series data of daily wind speeds at a height of 10 m. The analysis included daily wind data which was grouped into discrete data and then calculated to represent the mean wind speed, diurnal variations, daily variations, and monthly variations. To verify the models, statistical tools of Chi square, RMSE, MBE, and correlational coefficient were applied. Also, the method of measure, correlate, and predict was adopted to check for the reliability of the data used. The wind speed frequency distribution at the height of 10 m was found to be 2.9 ms-1 with a standard deviation of 1.5. From the six months’ experiments, averages of wind speeds at hub heights of 10 m were calculated and found to be 1.7 m/s, 2.4 m/s, and 1.3 m/s, for Ikobe, Kisii University, and Nyamecheo stations, respectively. The wind power density of the region was found to be 29 W/m2. By a narrow margin, Rayleigh proves to be a better method over Weibull in predicting wind power density in the region. Wind speeds at the site are noted to be decreasing over the years. The region is shown as marginal on extrapolation to 30 m for wind energy generation hence adequate for nongrid connected electrical and mechanical applications. The strong correlation between the site wind profiles proves data reliability. The gradual decrease of wind power over the years calls for attention.

Increasing rate of seepage velocity from several formation characteristics, such as permeability and porosity, in water aquifer environment greatly prompt pollution of water reservoirs within a short period of time. Considerably, migration rate of dissolved heavy metals from Solid Waste Dumpsites (SWD), such as municipal dumpsites and landfills, through heterogeneous aquifer environment, and finally into nearby water reservoirs are mainly influenced by variation of seepage velocity within the soil and water environment. This presents a dynamic system for water pollution that was studied using a formulated mathematical model to describe the transport process of dissolved heavy metals, mainly characterized by seepage velocities, within the water aquiferous environment. Permeability, porosity, fluid pressure and concentration of heavy metals in aquiferous environment were used as principal parameters that influence seepage velocity of the metals, in dissolved state, through the structural formation of water aquifers. The derived mathematical equations that constitute the model of this study were generated through Darcy's law and the equation of continuity. The model was validated on structural river aquifer sediments, and it was solved using graphical method through matlab opensource software. The initial and boundary conditions were obtained by discretizing the geological setting of flow region so as to transform the gradient of the head, h x   into the time domain.

Cancer diseases lead to the second-highest death rate all over the world. The dynamics of invasion of cancer cells into the human body tissues and metastasis are the main causes of death in patients with cancer. This study deals with theoretical investigation of the dynamics of invasion of cancer cells for tumour growths in human body tissues using discretized Cahn-Hilliard, concentration and reaction-diffusion equations which were solved by Finite Difference Method with the aid of MATLAB computer software. A Crank-Nicolson numerical scheme was developed for the discretized model equations. The numerical result obtained was used to describe the dynamics of cancer invasion of tissues with respect to cancer cells density on tumour growth, turbulence and mobility and equilibrium between charge and discharge of cancer cells. The results of the study provide new insights into combating cancer disease by providing mitigating and intervention measures to this major health problem.