Flat Rigid–ring Baffle [1] (FRB) is a common slosh suppression device in Long Moving Vessel (LMV)... more Flat Rigid–ring Baffle [1] (FRB) is a common slosh suppression device in Long Moving Vessel (LMV) to mitigate against oscillation-induced instability due to sloshing of its content but, its relative low performance is unacceptable for desirable safety standard thus, necessitating continuous efforts to investigate other baffle configurations. Investigation of Concave Baffles of varying geometries was carried out and analysed with the ANSYS/CFX [2] and the Computational Fluid Dynamics (CFD). Results were post-processed with the help of Mat lab [3-5] in a gravity milieu. This work was therefore designed to study the sloshing characteristics of Water-Carrying Cylindrical (WCC) tank equipped with three baffles. Model governing equations based on conservation of mass and momentum were developed and solved using Finite Element Analysis (FEA) technique. The model was used to evaluate Damping Ratio (DR) from Mile's equation [1] at 72, 66 and 59 percent standard positions, in a 75 percen...
This study, for the first time, adopts 20 simple empirical models to estimate daily global solar ... more This study, for the first time, adopts 20 simple empirical models to estimate daily global solar radiation (GSR) in selected meteorological stations in Togo, West Africa with a view to evaluating the performance of the models in predicting GSR over different climatic zones in the region. It used 3-year (1990–1992) daily mean ground station data obtained from the Togo Meteorological Agency for the models’ calibration at Lomé station to validate daily models’ simulations at other stations (Atakpamé, Sokodé, Kara and Mango). Models’ evaluation and ranking were done using performance indices such as root-mean-square error (RMSE), mean error (ME), percentage mean error (PME), Nash–Sutcliffe coefficient (NSE), and correlation coefficient (r). Our results suggested relatively low and insignificant negative biases (|PME|< 10%) in the simulated daily GSR for most of the models across the stations. It was revealed that the performance of the models in simulating daily GSR varied across different climatological zones and seasons. The top 25% ranking empirical models in all the stations in terms of RMSE, ME and t score were those that relate daily GSR to air temperatures and or sunshine duration, day length and extra-terrestrial radiation. Furthermore, inclusion of relative humidity in the GSR models enhanced the estimates of daily GSR over the study locations. We recommend the inclusion of temperature and or humidity as important predictors for estimation of GSR in West Africa.
This contribution reports on the investigation of correlation properties in an English scientific... more This contribution reports on the investigation of correlation properties in an English scientific text (engineering write-up) by means of a random walk. Though the idea to use a random walk to characterise correlations is not new (it was used e.g. in the genome analysis and in the analysis of texts), a random walk approach to the analysis of an English scientific text is still far from being exploited in its full strength as demonstrated in this paper. A method of high-dimensional embedding is proposed. Case examples were drawn arbitrarily from four engineering write-ups (Ph.D. synopsis) of three engineering departments in the Faculty of Technology, University of Ibadan, Nigeria. Thirteen additional analyses of non-engineering English texts were made and the results compared to the engineering English texts. Thus, a total of seventeen write-ups of eight Faculties and sixteen Departments of the University of Ibadan were considered. The characterising exponents which relate the average distance of random walkers away from a known starting position to the elapsed time steps were estimated for the seventeen cases according to the power law and in three different dimensional spaces. The average characteristic exponent obtained for the seventeen cases and over three different dimensional spaces studied was 1.42 to 2-decimal with a minimum and a maximum coefficient of determination (R 2 ) of 0.9495 and 0.9994 respectively. This is found to be 284% of the average characterising exponent value (0.5), as supported by the literature for random walkers based on the pseudo-random number generator. The average characteristic exponent obtained for the four cases that were engineering-based and over the three different dimensional studied spaces was 1.41 to 2-decimal (closer by 99.3% to 1.42) with a minimum and a maximum coefficient of determination (R 2 ) of 0.9507 and 0.9974 respectively. This is found to be 282% of the average characterising exponent value (0.5), as supported by the literature for random walkers based on the pseudo-random number generator. In view of the range of the average characterising exponent across Faculties and the closeness of the average characterising exponent in the engineering-based cases in particular, it can be concluded that the engineering writing is strongly correlated. This study recommends that a very high characterising exponent value (e.g 1.42) is a mark of a very good engineering write-up.
This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscill... more This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscillator using vibration absorber. The systems of t wo degrees of freedom governing equations were simu lated nu mer ically using classical fourth order Runge-Kutta algorith m for a constant time step. The solution time history, phase plots and Poincare maps were used to validate the simu lation. Essentially, the details of the Poincare map were used numerically to determine the periodicity of Duffing oscillator for spectrum of mass ratio at a constant step of 0.001. The time h istory, phase plots and the Poincare at mass ratio (µ), absorber parameters (α a ), and amp litude of excitation (F o ) are in agreement with what is obtained in open literature. The chaotic response of the Duffing-Absorber system at α a = 1.1, F o = 0.21; and, taken respectively, the Duffing and the absorber initial conditions to be (1.0, 0.0) and (0.0, 0.0), this chaotic response was rendered periodic for some selec...
This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear ... more This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear RLC electrical circuits. The relevant second order differential equations were solved for ranges of appropriate parameters using Runge-Kutta approach. The solutions obtained were employed to produce bifurcation diagrams using Microsoft excel 2007. The mean estimate of
This study investigated whether or not that the fractal disk dimension is a property associable t... more This study investigated whether or not that the fractal disk dimension is a property associable to Poincare section of harmonically excited pendulum. Five popular Runge-Kutta schemes (RK2, RK3, RK4, RK5, and RK6) were employed to simulate steady state Poincare sections for fixed drive frequency 2 3 D and excitation period ( D T ) based on time steps ( 10
The contribution of this paper to traffic engineering is the application of Laplace Transform to ... more The contribution of this paper to traffic engineering is the application of Laplace Transform to the quantification of speed control in the modelling of road bumps with hollow rectangular shape. The paper simulates the behaviour of a vehicle when passing over a series of bumps. In many countries the current practice used for lowering the vehicle speed is to raise road bumps above the road surface. If a hollow bump is used it may be economical and offers other advantages over road bumps raised above the road surfaces. The method models the vehicle as the classical one-degree-of-freedom system whose base follows the road profile, approximated by Laplace Transform. Then, a traditional vibration analysis is carried out and the isolation factor is calculated. A case study application is presented to substantiate the model developed. This case indicates how much difference the current model has compared to other existing models. Therefore, a relationship is established between the charact...
This contribution presents an analysis on two key approaches to studying the characterization of ... more This contribution presents an analysis on two key approaches to studying the characterization of English alphabets in doctoral thesis. The approaches (rescale range analysis (RSA) and fractal characterization (FC)) are discussed from the simulation point of view. For RSA, Hurst exponent value was used for the string of English alphabets in composing doctoral abstracts of engineering-based research work. FC involves the combined application of Cantor dust knowledge and fractal box dimension estimate by box counting and probability. For the two approaches, four engineering-based doctoral abstracts were studied with the total length of 512 alphabets in each case. The average computerized rescale range value was found to increase with the increase in data length for all cases. The Hurst exponent values for all cases distinctively range between 0.4146 and 0.4873 (i.e. negative correlation). The relative percentage error computed for the estimated fractal box dimension of Cantor Dust when...
Journal of Mechanical Engineering and Automation, 2013
This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscill... more This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscillator using vibration absorber. The systems of t wo degrees of freedom governing equations were simu lated nu mer ically using classical fourth order Runge-Kutta algorith m for a constant time step. The solution time history, phase plots and Poincare maps were used to validate the simu lation. Essentially, the details of the Poincare map were used numerically to determine the periodicity of Duffing oscillator for spectrum of mass ratio at a constant step of 0.001. The time h istory, phase plots and the Poincare at mass ratio (µ), absorber parameters (αa), and amp litude of excitation (Fo) are in agreement with what is obtained in open literature. The chaotic response of the Duffing-Absorber system at αa = 1.1, Fo = 0.21; and, taken respectively, the Duffing and the absorber initial conditions to be (1.0, 0.0) and (0.0, 0.0), this chaotic response was rendered periodic for some selected ma...
This study utilised correlation and distribution analyses to investigate the acceptability of app... more This study utilised correlation and distribution analyses to investigate the acceptability of application of two fractal dimension estimators to characterise the waveforms originating from excited nonlinear pendulum. Parameters selection sensitive simulation of the excited nonlinear pendulum waveforms was performed with the constant time step fourth order Runge-Kutta algorithm with codes developed in FORTRAN90. However, the waveforms validated by Gregory and Jerry (1990) and treated as time series were characterized using developed codes of Carlos (1998) and Hurst fractal dimension estimation procedures. The validation results compare qualitatively well and the correlation coefficients between Carlos (1998)-based and Hurst’s exponent based dimension estimate for the angular displacement and velocity are respectively R2 = 0.68 and R2 = 0.66. A higher correlation coefficient ( R2 = 0.84 ) existed between the estimated Hurst’s exponent of the angular displacement and velocity. The Hurs...
This paper investigates the dynamical behaviour of a duffing oscillator using bifurcation diagram... more This paper investigates the dynamical behaviour of a duffing oscillator using bifurcation diagrams. There has been growing interest and challenges in engineering dynamics to characterize dynamical systems that are chaotic using bifurcation diagrams. The relevant second order differential equations using Runge-Kutta method were solved for ranges of appropriate parameters. The solutions obtained were used to produce the bifurcation diagrams using Microsoft excel 2007. Since an average estimate of 5 = 4.668 from the bifurcation diagrams produced is an approximate value of the Feigenbaum .constant as widely reported in the literatures, it can be deduced that the bifurcation diagrams conforms to the expected results. While the bifurcation diagrams revealed the dynamics of the duffing oscillator, it also shows that the dynamics depend strongly on the initial conditions.
This investigation derived its strong motivation in the adoption of versions of second-order Rung... more This investigation derived its strong motivation in the adoption of versions of second-order Runge-Kutta methods where there is presently dearth of relevant literature to re-establish the complicated nature of solution of Duffing oscillator dynamics. The choice of second-order Runge-Kutta methods hinged on its simplest algebraic formulation of relevant coefficients based on Taylor series expansion comparing with its higher order counterpart. Validation of FORTRAN-90 codes of algorithms was achieved by phase plots comparison reference to Dowell (1988) as standard. The nature of simulated solutions were visually determined with scatter plot of phase variables obtained from simultaneous implementation of large number of versions of second-order Runge-Kutta methods in conjunction with the corresponding literature results. Validation results are acceptable to within the accuracy limit of Runge-Kutta methods adopted. The scatter plots on phase plane for cases investigated are well structu...
This study aim is to investigate the properties of selected fourth order Runge-Kutta algorithms. ... more This study aim is to investigate the properties of selected fourth order Runge-Kutta algorithms. Fiftyfive versions of fourth order Runge-Kutta (RK_1, RK_2, RK_3 …, RK_55) methods; inclusive of the classical fourth order RK version, were selected. Thereafter, these versions were used to simulate, with a constant and adaptive step-size algorithm, the dynamics of the harmonically excited Duffing Oscillator over a range of parameters and initial conditions. The simulation was carried out with a FORTRAN program developed and validated by comparing the program generated Poincaré section with literature standard. The number of successive steps taken between start and end of simulation periods was recorded for each simulation run. A total of 91809 simulations were run. The number of successive steps taken between start and end of simulation periods show that significant variations exists among different versions of the same Runge-Kutta order used for seeking solution of Duffing oscillator dynamics. Ranking results by the number of successive steps showed that RK_55 is not the fastest version available, despite its popularity, as other versions including RK_17, RK_2, RK_14, RK_20, and RK_8 outperformed it. Furthermore, the version performance was observed to be highly dependent on the excitation frequency, but not on initial conditions.
This work was carried out in collaboration between all the five authors. Author OOA conceived the... more This work was carried out in collaboration between all the five authors. Author OOA conceived the research idea and carried out extensive literature study on the subject matter in order to establish a gap and formulate a problem statement. Author OOA discussed the idea with author AOO, It was jointly agreed by these two authors that a study should be carried out in order to provide explanations that can further enrich the literature on effect of zinc content on the mechanical and corrosion responses of aluminium based composites. Experimental procedures were jointly formulated by authors OOA and AOO, while laboratory experimental works were carried out by author AOO under the guidance of author OOA. Results obtained were used to prepare first draft of the manuscript for rigorous pre-review of authors TAOS, OSI and OMO, who were senior colleagues and more experienced research authors. Useful critics and suggestions offered in the pre-review process were jointly adopted by all authors to revise and produce the manuscript submitted to the journal for peer review processing. Response to CJAST reviewers' comments were jointly handled and approved by all the five authors.
The South Pacific Journal of Natural and Applied Sciences
The prediction of emission characteristics of sawdust particles immediately after the cutting ope... more The prediction of emission characteristics of sawdust particles immediately after the cutting operation from the interaction of band saw?s blade and plank is a growing research area. Still, a wide gap exists with respect to understanding the behaviour of sawdust particles as they collide with one another. Previous efforts have focused on non-collision states of sawdust particles. However, in real life, collision of particles must occur, with several particles colliding after the cutting operation. This paper establishes a new perspective of the fractal properties of sawdust particles in motion as a motivation to understanding how to control its toxicity of effects on sawmill workers and maintain sustainable sawmilling activities. In particular, the possibility of predicting the fractal dimension of the randomly moving sawdust particles in sawmills that is generated as fractal curves using the combination of probabilities and theoretical fractal dimensions is investigated for the fir...
Heart acoustics can be used as an early diagnostic tool, to quickly and accurately identify medic... more Heart acoustics can be used as an early diagnostic tool, to quickly and accurately identify medical patients who may be at risk of unfavourable cardiovascular outcomes. However, at present, there remains no universally accepted standard or technique for detecting abnormalities using Phonocardiograms. To address this, a large database containing normal and abnormal heart sound recordings of patients were studied with the rescaled range technique and the Hurst exponent, a measure of persistence for non-linear dynamic data. Using the Hurst exponent (H) as a benchmark, we compared the values of the Hurst exponent for normal heart sound recordings with that of the abnormal heart sound recordings. For this study, the recording length was limited to the first 10 seconds for all 578 distinct recordings, which were selected randomly from the database. Furthermore, two Hurst exponent values were obtained for each recording, by subjecting them to time intervals of 1 and 2 milliseconds respecti...
Flat Rigid–ring Baffle [1] (FRB) is a common slosh suppression device in Long Moving Vessel (LMV)... more Flat Rigid–ring Baffle [1] (FRB) is a common slosh suppression device in Long Moving Vessel (LMV) to mitigate against oscillation-induced instability due to sloshing of its content but, its relative low performance is unacceptable for desirable safety standard thus, necessitating continuous efforts to investigate other baffle configurations. Investigation of Concave Baffles of varying geometries was carried out and analysed with the ANSYS/CFX [2] and the Computational Fluid Dynamics (CFD). Results were post-processed with the help of Mat lab [3-5] in a gravity milieu. This work was therefore designed to study the sloshing characteristics of Water-Carrying Cylindrical (WCC) tank equipped with three baffles. Model governing equations based on conservation of mass and momentum were developed and solved using Finite Element Analysis (FEA) technique. The model was used to evaluate Damping Ratio (DR) from Mile's equation [1] at 72, 66 and 59 percent standard positions, in a 75 percen...
This study, for the first time, adopts 20 simple empirical models to estimate daily global solar ... more This study, for the first time, adopts 20 simple empirical models to estimate daily global solar radiation (GSR) in selected meteorological stations in Togo, West Africa with a view to evaluating the performance of the models in predicting GSR over different climatic zones in the region. It used 3-year (1990–1992) daily mean ground station data obtained from the Togo Meteorological Agency for the models’ calibration at Lomé station to validate daily models’ simulations at other stations (Atakpamé, Sokodé, Kara and Mango). Models’ evaluation and ranking were done using performance indices such as root-mean-square error (RMSE), mean error (ME), percentage mean error (PME), Nash–Sutcliffe coefficient (NSE), and correlation coefficient (r). Our results suggested relatively low and insignificant negative biases (|PME|< 10%) in the simulated daily GSR for most of the models across the stations. It was revealed that the performance of the models in simulating daily GSR varied across different climatological zones and seasons. The top 25% ranking empirical models in all the stations in terms of RMSE, ME and t score were those that relate daily GSR to air temperatures and or sunshine duration, day length and extra-terrestrial radiation. Furthermore, inclusion of relative humidity in the GSR models enhanced the estimates of daily GSR over the study locations. We recommend the inclusion of temperature and or humidity as important predictors for estimation of GSR in West Africa.
This contribution reports on the investigation of correlation properties in an English scientific... more This contribution reports on the investigation of correlation properties in an English scientific text (engineering write-up) by means of a random walk. Though the idea to use a random walk to characterise correlations is not new (it was used e.g. in the genome analysis and in the analysis of texts), a random walk approach to the analysis of an English scientific text is still far from being exploited in its full strength as demonstrated in this paper. A method of high-dimensional embedding is proposed. Case examples were drawn arbitrarily from four engineering write-ups (Ph.D. synopsis) of three engineering departments in the Faculty of Technology, University of Ibadan, Nigeria. Thirteen additional analyses of non-engineering English texts were made and the results compared to the engineering English texts. Thus, a total of seventeen write-ups of eight Faculties and sixteen Departments of the University of Ibadan were considered. The characterising exponents which relate the average distance of random walkers away from a known starting position to the elapsed time steps were estimated for the seventeen cases according to the power law and in three different dimensional spaces. The average characteristic exponent obtained for the seventeen cases and over three different dimensional spaces studied was 1.42 to 2-decimal with a minimum and a maximum coefficient of determination (R 2 ) of 0.9495 and 0.9994 respectively. This is found to be 284% of the average characterising exponent value (0.5), as supported by the literature for random walkers based on the pseudo-random number generator. The average characteristic exponent obtained for the four cases that were engineering-based and over the three different dimensional studied spaces was 1.41 to 2-decimal (closer by 99.3% to 1.42) with a minimum and a maximum coefficient of determination (R 2 ) of 0.9507 and 0.9974 respectively. This is found to be 282% of the average characterising exponent value (0.5), as supported by the literature for random walkers based on the pseudo-random number generator. In view of the range of the average characterising exponent across Faculties and the closeness of the average characterising exponent in the engineering-based cases in particular, it can be concluded that the engineering writing is strongly correlated. This study recommends that a very high characterising exponent value (e.g 1.42) is a mark of a very good engineering write-up.
This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscill... more This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscillator using vibration absorber. The systems of t wo degrees of freedom governing equations were simu lated nu mer ically using classical fourth order Runge-Kutta algorith m for a constant time step. The solution time history, phase plots and Poincare maps were used to validate the simu lation. Essentially, the details of the Poincare map were used numerically to determine the periodicity of Duffing oscillator for spectrum of mass ratio at a constant step of 0.001. The time h istory, phase plots and the Poincare at mass ratio (µ), absorber parameters (α a ), and amp litude of excitation (F o ) are in agreement with what is obtained in open literature. The chaotic response of the Duffing-Absorber system at α a = 1.1, F o = 0.21; and, taken respectively, the Duffing and the absorber initial conditions to be (1.0, 0.0) and (0.0, 0.0), this chaotic response was rendered periodic for some selec...
This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear ... more This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear RLC electrical circuits. The relevant second order differential equations were solved for ranges of appropriate parameters using Runge-Kutta approach. The solutions obtained were employed to produce bifurcation diagrams using Microsoft excel 2007. The mean estimate of
This study investigated whether or not that the fractal disk dimension is a property associable t... more This study investigated whether or not that the fractal disk dimension is a property associable to Poincare section of harmonically excited pendulum. Five popular Runge-Kutta schemes (RK2, RK3, RK4, RK5, and RK6) were employed to simulate steady state Poincare sections for fixed drive frequency 2 3 D and excitation period ( D T ) based on time steps ( 10
The contribution of this paper to traffic engineering is the application of Laplace Transform to ... more The contribution of this paper to traffic engineering is the application of Laplace Transform to the quantification of speed control in the modelling of road bumps with hollow rectangular shape. The paper simulates the behaviour of a vehicle when passing over a series of bumps. In many countries the current practice used for lowering the vehicle speed is to raise road bumps above the road surface. If a hollow bump is used it may be economical and offers other advantages over road bumps raised above the road surfaces. The method models the vehicle as the classical one-degree-of-freedom system whose base follows the road profile, approximated by Laplace Transform. Then, a traditional vibration analysis is carried out and the isolation factor is calculated. A case study application is presented to substantiate the model developed. This case indicates how much difference the current model has compared to other existing models. Therefore, a relationship is established between the charact...
This contribution presents an analysis on two key approaches to studying the characterization of ... more This contribution presents an analysis on two key approaches to studying the characterization of English alphabets in doctoral thesis. The approaches (rescale range analysis (RSA) and fractal characterization (FC)) are discussed from the simulation point of view. For RSA, Hurst exponent value was used for the string of English alphabets in composing doctoral abstracts of engineering-based research work. FC involves the combined application of Cantor dust knowledge and fractal box dimension estimate by box counting and probability. For the two approaches, four engineering-based doctoral abstracts were studied with the total length of 512 alphabets in each case. The average computerized rescale range value was found to increase with the increase in data length for all cases. The Hurst exponent values for all cases distinctively range between 0.4146 and 0.4873 (i.e. negative correlation). The relative percentage error computed for the estimated fractal box dimension of Cantor Dust when...
Journal of Mechanical Engineering and Automation, 2013
This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscill... more This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscillator using vibration absorber. The systems of t wo degrees of freedom governing equations were simu lated nu mer ically using classical fourth order Runge-Kutta algorith m for a constant time step. The solution time history, phase plots and Poincare maps were used to validate the simu lation. Essentially, the details of the Poincare map were used numerically to determine the periodicity of Duffing oscillator for spectrum of mass ratio at a constant step of 0.001. The time h istory, phase plots and the Poincare at mass ratio (µ), absorber parameters (αa), and amp litude of excitation (Fo) are in agreement with what is obtained in open literature. The chaotic response of the Duffing-Absorber system at αa = 1.1, Fo = 0.21; and, taken respectively, the Duffing and the absorber initial conditions to be (1.0, 0.0) and (0.0, 0.0), this chaotic response was rendered periodic for some selected ma...
This study utilised correlation and distribution analyses to investigate the acceptability of app... more This study utilised correlation and distribution analyses to investigate the acceptability of application of two fractal dimension estimators to characterise the waveforms originating from excited nonlinear pendulum. Parameters selection sensitive simulation of the excited nonlinear pendulum waveforms was performed with the constant time step fourth order Runge-Kutta algorithm with codes developed in FORTRAN90. However, the waveforms validated by Gregory and Jerry (1990) and treated as time series were characterized using developed codes of Carlos (1998) and Hurst fractal dimension estimation procedures. The validation results compare qualitatively well and the correlation coefficients between Carlos (1998)-based and Hurst’s exponent based dimension estimate for the angular displacement and velocity are respectively R2 = 0.68 and R2 = 0.66. A higher correlation coefficient ( R2 = 0.84 ) existed between the estimated Hurst’s exponent of the angular displacement and velocity. The Hurs...
This paper investigates the dynamical behaviour of a duffing oscillator using bifurcation diagram... more This paper investigates the dynamical behaviour of a duffing oscillator using bifurcation diagrams. There has been growing interest and challenges in engineering dynamics to characterize dynamical systems that are chaotic using bifurcation diagrams. The relevant second order differential equations using Runge-Kutta method were solved for ranges of appropriate parameters. The solutions obtained were used to produce the bifurcation diagrams using Microsoft excel 2007. Since an average estimate of 5 = 4.668 from the bifurcation diagrams produced is an approximate value of the Feigenbaum .constant as widely reported in the literatures, it can be deduced that the bifurcation diagrams conforms to the expected results. While the bifurcation diagrams revealed the dynamics of the duffing oscillator, it also shows that the dynamics depend strongly on the initial conditions.
This investigation derived its strong motivation in the adoption of versions of second-order Rung... more This investigation derived its strong motivation in the adoption of versions of second-order Runge-Kutta methods where there is presently dearth of relevant literature to re-establish the complicated nature of solution of Duffing oscillator dynamics. The choice of second-order Runge-Kutta methods hinged on its simplest algebraic formulation of relevant coefficients based on Taylor series expansion comparing with its higher order counterpart. Validation of FORTRAN-90 codes of algorithms was achieved by phase plots comparison reference to Dowell (1988) as standard. The nature of simulated solutions were visually determined with scatter plot of phase variables obtained from simultaneous implementation of large number of versions of second-order Runge-Kutta methods in conjunction with the corresponding literature results. Validation results are acceptable to within the accuracy limit of Runge-Kutta methods adopted. The scatter plots on phase plane for cases investigated are well structu...
This study aim is to investigate the properties of selected fourth order Runge-Kutta algorithms. ... more This study aim is to investigate the properties of selected fourth order Runge-Kutta algorithms. Fiftyfive versions of fourth order Runge-Kutta (RK_1, RK_2, RK_3 …, RK_55) methods; inclusive of the classical fourth order RK version, were selected. Thereafter, these versions were used to simulate, with a constant and adaptive step-size algorithm, the dynamics of the harmonically excited Duffing Oscillator over a range of parameters and initial conditions. The simulation was carried out with a FORTRAN program developed and validated by comparing the program generated Poincaré section with literature standard. The number of successive steps taken between start and end of simulation periods was recorded for each simulation run. A total of 91809 simulations were run. The number of successive steps taken between start and end of simulation periods show that significant variations exists among different versions of the same Runge-Kutta order used for seeking solution of Duffing oscillator dynamics. Ranking results by the number of successive steps showed that RK_55 is not the fastest version available, despite its popularity, as other versions including RK_17, RK_2, RK_14, RK_20, and RK_8 outperformed it. Furthermore, the version performance was observed to be highly dependent on the excitation frequency, but not on initial conditions.
This work was carried out in collaboration between all the five authors. Author OOA conceived the... more This work was carried out in collaboration between all the five authors. Author OOA conceived the research idea and carried out extensive literature study on the subject matter in order to establish a gap and formulate a problem statement. Author OOA discussed the idea with author AOO, It was jointly agreed by these two authors that a study should be carried out in order to provide explanations that can further enrich the literature on effect of zinc content on the mechanical and corrosion responses of aluminium based composites. Experimental procedures were jointly formulated by authors OOA and AOO, while laboratory experimental works were carried out by author AOO under the guidance of author OOA. Results obtained were used to prepare first draft of the manuscript for rigorous pre-review of authors TAOS, OSI and OMO, who were senior colleagues and more experienced research authors. Useful critics and suggestions offered in the pre-review process were jointly adopted by all authors to revise and produce the manuscript submitted to the journal for peer review processing. Response to CJAST reviewers' comments were jointly handled and approved by all the five authors.
The South Pacific Journal of Natural and Applied Sciences
The prediction of emission characteristics of sawdust particles immediately after the cutting ope... more The prediction of emission characteristics of sawdust particles immediately after the cutting operation from the interaction of band saw?s blade and plank is a growing research area. Still, a wide gap exists with respect to understanding the behaviour of sawdust particles as they collide with one another. Previous efforts have focused on non-collision states of sawdust particles. However, in real life, collision of particles must occur, with several particles colliding after the cutting operation. This paper establishes a new perspective of the fractal properties of sawdust particles in motion as a motivation to understanding how to control its toxicity of effects on sawmill workers and maintain sustainable sawmilling activities. In particular, the possibility of predicting the fractal dimension of the randomly moving sawdust particles in sawmills that is generated as fractal curves using the combination of probabilities and theoretical fractal dimensions is investigated for the fir...
Heart acoustics can be used as an early diagnostic tool, to quickly and accurately identify medic... more Heart acoustics can be used as an early diagnostic tool, to quickly and accurately identify medical patients who may be at risk of unfavourable cardiovascular outcomes. However, at present, there remains no universally accepted standard or technique for detecting abnormalities using Phonocardiograms. To address this, a large database containing normal and abnormal heart sound recordings of patients were studied with the rescaled range technique and the Hurst exponent, a measure of persistence for non-linear dynamic data. Using the Hurst exponent (H) as a benchmark, we compared the values of the Hurst exponent for normal heart sound recordings with that of the abnormal heart sound recordings. For this study, the recording length was limited to the first 10 seconds for all 578 distinct recordings, which were selected randomly from the database. Furthermore, two Hurst exponent values were obtained for each recording, by subjecting them to time intervals of 1 and 2 milliseconds respecti...
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