Estimating solar radiation in Ikeja and Port Harcourt via correlation with relative humidity and temperature

This paper is part of the Proceedings of the 6th International Conference on Energy and Sustainability (ESUS 2015). http://www.witconferences.comRelative humidity and temperature data are more readily available to obtain from observatories than sunshine hour data. In this work, 10 years (1986–1987, 1990–1997) monthly average measurement of relative solar radiation, daily temperature range, relative humidity and the ratio of minimum to maximum temperature were used to establish the coefficient of eight models for estimating solar radiation in Ikeja and Port Harcourt. Coefficient of correlation (R), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t-statistic and the rank score were used as performance indicators. In Port Harcourt, the equation producing the best result with MBE, RMSE, MPE and t-statistic value of −0.1078, 0.9850, −0.4373% and 0.3653, respectively, is given by: Rs/Ro = 3.266 − 0.306(RH)0,5. In Ikeja, the equation producing the best estimation with MBE, RMSE, MPE and t-statistic value of 0.1590, 1.0110, 2.0559% and 0.5281, respectively, is given by: Rs/Ro = 2.042 − 2.136(θ)

Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana-Baleanu fractional derivative

We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model’s steady states was carried out, and the reproduction number R0, a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R0 declined from 2.452 – 9.179 during the first phase of the infection to 1.374 – 2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R0 remains below unity irrespective of the disease infection rate. Keeping R0 values below unity leads to a decrease in COVID-19 prevalence

Effect of a modulated acoustic field on the dynamics of a vibrating charged bubble

We investigate the effect of amplitude-modulated acoustic irradiation on the dynamics of a charged bubble vibrating in a liquid. We show that the potential V (x) of the bubble, and the number and stability of its equilibria, depend on the magnitude of the charge it carries. Under high-frequency amplitude-modulation, a modulation threshold, Gth, was found for the onset of increased bubble amplitude oscillations. For some pressure field values, charge can facilitate the control of chaotic dynamics via reversed period-doubling bifurcation sequences. There is evidence for peak-shouldering and shock waves. The Mach number increases rapidly with the drive amplitude G. In the supersonic regime, for G > 1.90 Pa, the high-frequency modulation raises both Blake’s and the transient cavitation thresholds. We found a decrease in the bubble’s maximum charge threshold, and threshold modulation amplitude for the occurrence Vibrational resonance (VR). VR occurs due to the modulated oscillatory pressure field, and the influence on VR of the electrostatic charge, and other parameters of the system are investigated. In contrast to the cases of VR reported earlier, where the amplitude G of the high-frequency driving is typically much higher than the amplitude of the low-frequency driving (Ps), the VR resonance peaks occur here at relatively low G values (0 < G < 10Pa) compared to the acoustic driving pressure Ps ∼ 105 Pa. The optimal parameter values for enhanced response could be useful in acoustic cavitation applications

Novel bursting oscillations in a nonlinear gyroscope oscillator

We report the occurrence of bursting oscillations in a gyroscope oscillator driven by low-frequency external period forcing. The bursting patterns arise when either the frequency or amplitude of the excitation force is varied. They take the form of pulse-shaped explosions (PSEs) wherein periodic attractors of lower periodicity disappear due to the loss of asymptotic stability of the equilibrium point between resting and active states. The process involves the appearance of zero eigenvalues and the creation of new attractors of higher periodicity. Both point-cycle and cycle-cycle bursting is seen. It is accompanied by the birth of periodic attractors, ranging from period one to period four, depending on an integer n in the frequency of the parametric driving force. The dynamics of the oscillator is shown to exhibit a fold bifurcation related to critical escape transitions