Papers by Oyebola Popoola
African Review of Physics, 2014
*Exact travelling wave solutions to nonlinear fracti onal partial differential equations in the s... more *Exact travelling wave solutions to nonlinear fracti onal partial differential equations in the sense of Jumarie’s modified Riemann-Liouville derivative via the generalized Bernoulli equation method are presented in this paper . A fractional complex transformation was applied to turn the fractional p artial differential equations into an equivalent in teger order ordinary differential equation. We applied this method to so lve the space and time fractional Sharma-Tasso-Olver and Jimbo-Miwa equations. This method is a simple, reliable and po werful tool for solving nonlinear partial different ial equations in physics, mathematics and other applications.
arXiv: Quantum Physics, 2017
In this work, we used a tool of conventional Nikiforov-Uvarov method to determine bound state sol... more In this work, we used a tool of conventional Nikiforov-Uvarov method to determine bound state solution of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigen values and the total wave function . We employed Hellmann-Feynmann Theorem (HFT) to compute expectation values for four different diatomic molecules: Hydrogen molecule (H2), Lithium hydride molecule (LiH), Hydrogen Chloride molecule (HCl) and Carbon(II)Oxide molecule. The resulting energy equation reduces to three well known potentials which are: Hulthen potential, Yukawa potential and inversely quadratic potential. We obtained the numerical bound state energies of the expectation values by implementing Matlab algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed a mathematica programming to obtain wave function and probability density plots for different orbital angular qua...
Physica D: Nonlinear Phenomena, 2021
Vibrational resonance (VR) is a phenomenon wherein the response of a nonlinear oscillator driven ... more Vibrational resonance (VR) is a phenomenon wherein the response of a nonlinear oscillator driven by biharmonic forces with two different frequencies, ω and Ω, such that Ω ≫ ω, is enhanced by optimizing the parameters of high-frequency driving force. In this paper, an counterintuitive scenario in which a biharmonically driven nonlinear oscillator does not vibrate under the well known VR conditions is reported. This behaviour was observed in a system with an integrable and asymmetric Toda potential driven by biharmonic forces in the usual VR configuration. It is shown that with constant dissipation and in the presence of biharmonic forces, VR does not take place, whereas with nonlinear displacement-dependent periodic dissipation multiple VR can be induced at certain values of high-frequency force parameters. Theoretical analysis are validated using numerical computation and Simulink implementation in MATLAB. Finally, the regime in parameter space of the dissipation for optimum occurrence of multiple VR in the Toda oscillator was estimated. This result would be relevant for experimental applications of dual-frequency driven laser models where the Toda potential is extensively employed.
Computational and Theoretical Chemistry, 2021
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Chaos, Solitons & Fractals, 2020
Insurgency is a large loophole to any nation's finances because of the monumental costs associate... more Insurgency is a large loophole to any nation's finances because of the monumental costs associated with fighting it. In this study, an epidemiological approach to modeling the dynamics of the spread of insurgents is introduced. Stability analysis of the steady states of the system were performed and the insurgency prevalence number R 0 , which is analogous to the reproduction number in epidemiological studies was obtained using the next generation matrix method. A fractional version of the model was introduced using the Atangana-Baleanu derivative and numerical simulations were performed for better understanding of the dynamics of the system. For effective counter-insurgency measures, the local and global sensitivity analysis of the insurgency prevalence number R 0 and the endemic states with respect to the parameters that define them were performed. Sensitivity analysis shows that counter-insurgency effort s must focus on increasing the recovery rate of insurgents and reducing the rate of radicalization of civilians. The developed model is a suitable tool with great potential for drawing inference in driving counter-insurgency policy making processes.
Communications in Theoretical Physics, 2020
In this work, we determine the Fisher and Shannon entropies, the expectation values and the squee... more In this work, we determine the Fisher and Shannon entropies, the expectation values and the squeeze state for a noncentral inversely quadratic plus exponential Mie-type potential analytically. The proposed potential is solved under the Schrodinger equation using a special Greene Aldrich approximation to the centrifugal term to obtain a normalised wave function within the framework of the Nikiforov–Uvarov method. Numerical results are obtained for different screening parameters: α = 0.1, 0.12 and 0.13 for varying real constant parameter (B). The numerical solutions are obtained only for ground state. The numerical results of Fisher entropy both for position and momentum spaces are in good agreement with existing literature. The normalisation constant, wave function, and probability density plots are carried out using a well designed Mathematica algorithm. The Fourier transform of position space entropy gives the momentum space entropy.
Physical Science International Journal, 2018
We proposed a novel potential called Hulthen plus Inversely Quadratic Exponential Mie-Type potent... more We proposed a novel potential called Hulthen plus Inversely Quadratic Exponential Mie-Type potential (HIQEMP). We use parametric Nikiforov-Uvarov method to study approximate solutions of Schrödinger and Klein-Gordon equations with the novel potential. We obtain bound state energies and the normalized wave function expressed in terms of Jacobi polynomial. The proposed potential is applicable in the field of vibrational and rotational spectroscopy. To ascertain the accuracy of our results, we apply the nonrelativistic limit to the Klein-Gordon equation to obtain the energy equation which is exactly the same as nonrelativistic Schrodinger energy equation. This is a proof that relativistic equation can be converted to nonrelativistic equation using a nonrelativistic limit with the help of Greene-Aldrich approximation to the centrifugal term. The wave functions were normalized Original Research Article
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation, 2019
In this study, we perform the Jacobi stability analysis of the Lotka Volterra type predator-prey ... more In this study, we perform the Jacobi stability analysis of the Lotka Volterra type predator-prey models with Holling-type II and III functional responses. The Jacobi stability analysis is based on the geometry of Finsler spaces and is generally known as the Kosambi, Cartan and Chern (KCC) theory. In the KCC theory, one associates a non-linear connection, and a Berwald type connection to the dynamical systems, and five geometrical invariants were obtained. The second invariant known as the curvature deviation tensor gives the Jacobi stability of the system which is a measure of the robustness of the system to small perturbations of the whole trajectory. Particularly in this study, we review the linear stability of the models and perform a full Jacobi stability analysis of the models via the KCC theory. The Jacobi stability of equilibrium points of the models was studied and a comparative study of the linear stability and Jacobi stability was done to determine the special regions where they both overlap. Conclusively, the time evolution of the components of the deviation near each equilibrium point of the predator-prey models was also considered. We observed that the Jacobi stability of equilibrium points for the Holling-type II and III model guarantees linear stability. Also, parameter regions were the Jacobi and Linear stability overlaps were presented in the form of phase diagrams. The torsion tensor components which geometrically characterizes the chaotic behaviour of dynamical systems are all equal to zero for the models. This eliminates the possibility of the onset of chaos in the studied models.
Pramana, 2019
We examine the vibrational resonance (VR) of particles moving in a strongly nonlinear damped medi... more We examine the vibrational resonance (VR) of particles moving in a strongly nonlinear damped medium with a harmonically perturbed potential consisting of a background smooth triple-well potential superimposed by a fast oscillating periodic function and subjected to weak and high-frequency (HF) driving forces. The combined effects of the nonlinear damping inhomogeneity and roughness induced by the harmonic perturbation on the phenomenon of VR were theoretically and numerically analysed. It was found that damping inhomogeneity contributed significantly to the enhancement of resonant states, while potential roughness can be optimised by the HF signal to assist resonance enhancement. Furthermore, the traditional smooth VR shapes occurring in the absence of roughness experienced significant distortion occasioned by potential roughness manifesting as spikes that could ultimately be optimised by large amplitudes of the fast signal to energetically facilitate the potential barrier crossing process, thereby enabling VR enhancement.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016
The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven... more The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking (sb) bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations.
International Journal of Recent advances in Physics, 2015
We apply an approximation to centrifugal term to find bound state solutions to Schrodinger equati... more We apply an approximation to centrifugal term to find bound state solutions to Schrodinger equation with Hulthen Plus generalized exponential Coulomb potential Using Nikiforov-Uvarov Method. Using this method, we obtained the energy-eigen value and the total wave function. We implement C++ algorithm, to obtained the numerical values of the energy for different quantum state starting from the first excited state for different values of the screening parameter.
International Journal of Recent advances in Physics, 2014
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon ... more In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy eigen value and its associated total wave function. This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter. The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1) shows the different energy levels for a particular quantum number.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2021
The vibrational resonance (VR) phenomenon has received a great deal of research attention over th... more The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems.This article is part of the theme issue ‘Vibrational and...
International Journal of Recent Advances in Physics, 2015
We apply an approximation to centrifugal term to find bound state solutions to Schrodinger equati... more We apply an approximation to centrifugal term to find bound state solutions to Schrodinger equation with
Hulthen Plus generalized exponential Coulomb potential Using Nikiforov-Uvarov Method. Using this
method, we obtained the energy-eigen value and the total wave function. We implement C++ algorithm, to
obtained the numerical values of the energy for different quantum state starting from the first excited state
for different values of the screening parameter.
Journal of the Nigerian Association of Mathematical Physics, 2007
ABSTRACT
One of the vital ingredients for development of any nation is knowledge of basic science, of whic... more One of the vital ingredients for development of any nation is knowledge of basic science, of which physics is the root source. There is poor enrollment of women in physics at both secondary and tertiary levels of education in Nigeria. Recently, the number of women enrolling in physics in Nigeria has increased slightly, but women are yet to distinguish themselves
Physics and Chemistry of Liquids, 2005
A theoretical formalism that links thermodynamic properties to transport properties has been used... more A theoretical formalism that links thermodynamic properties to transport properties has been used to study the viscosity of Sn–Zn and In–Zn liquid alloys at various temperatures. The formalism was successful at describing the thermodynamic properties of these alloys and showed a better estimation of the viscosity of the Sn–Zn alloy than that of the In–Zn alloy.
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Papers by Oyebola Popoola
Hulthen Plus generalized exponential Coulomb potential Using Nikiforov-Uvarov Method. Using this
method, we obtained the energy-eigen value and the total wave function. We implement C++ algorithm, to
obtained the numerical values of the energy for different quantum state starting from the first excited state
for different values of the screening parameter.
Hulthen Plus generalized exponential Coulomb potential Using Nikiforov-Uvarov Method. Using this
method, we obtained the energy-eigen value and the total wave function. We implement C++ algorithm, to
obtained the numerical values of the energy for different quantum state starting from the first excited state
for different values of the screening parameter.