Department of Physical Sciences

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Browsing Department of Physical Sciences by Author "Vincent, Uchechukwu"

Now showing 1 - 11 of 11
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    Acoustic Vibrational Resonance in a Rayleigh-Plesset Bubble Oscillator
    (Elsevier, 2020-09-23) Vincent, Uchechukwu
    The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.
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    Chaos Synchronization Based on Linear and Adaptive Controls: Theory and Experiment
    (2021-10-30) Vincent, Uchechukwu
    In this paper, we report on the theoretical and experimental investigation of chaotic synchronization using of a single-variable linear feedback and adaptive controllers. Based on the Lyapunov stability theory, theoretical approaches to the design of controls are presented, and the results are validated numerically and by employing electronic circuit experiments. We used two typical oscillators, namely, the Lorenz and Sprott chaotic systems to demonstrate our results; while off-the-shelf components on breadboard were used to experimentally implement the proposed single variable controllers. We specifically show that synchronization of two chaotic systems can be experimentally realized when the strength of the feedback exceeds a theoretically determined threshold
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    Introduction to the Dynamics of Driven Nonlinear Systems
    (Taylor & Francis, 2021-01-28) Vincent, Uchechukwu
    The dynamics of nonlinear systems has emerged as an active interdisciplinary research field at the interface of biology, chemistry, mathematics, physics and engineering. This article introduces the discipline with emphasis on driven nonlinear systems. It examines the concepts from beginner's level while also highlighting some advanced topics and current research likely to lead to further advances in the field, such as the multistability and hidden attractors, basins of attractions, chaos control, synchronisation, nonlinear resonances, bursting oscillations and oscillation quenching. The concepts are illustrated by consideration of the dynamics of a driven particle in a ratchet potential as an archetypical-driven dynamical system whose behaviour captures the essential features of driven nonlinear systems more generally.
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    Nonlinear Growth and Mathematical Modelling of COVID-19 in some African Countries with the Atangana–Baleanu Fractional Derivative
    (Elsevier, 2021-10-19) Vincent, Uchechukwu
    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 , 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 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 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 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 remains below unity irrespective of the disease infection rate. Keeping values below unity leads to a decrease in COVID-19 prevalence.
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    Occurrence of Vibrational Resonance in an Oscillator with an Asymmetric Toda Potential
    (Elsevier, 2021-01-30) Vincent, Uchechukwu
    Vibrational resonance (VR) is a phenomenon wherein the response of a nonlinear oscillator driven by biharmonic forces with two different frequencies, and , such that , 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.
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    Quantum Vibrational Resonance of Biharmonically Driven Tietz-Hua Quantum Well
    (American Physical Society, 2020-05-28) Vincent, Uchechukwu
    We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, the transition probability amplitude shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in the transition probability amplitude. However, the transition probability amplitude maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.
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    Vibrational and Stochastic Resonances in Driven Nonlinear Systems
    (2021-12) Vincent, Uchechukwu
    Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora of interesting and important properties—one of the most prominent being that of resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this 2-part Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances—addressing their analysis, occurrence and applications from either the theoretical, numerical or experimental perspectives, or through combinations of these.
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    Vibrational and Stochastic Resonances in Driven Nonlinear Systems: part 2
    (Royal Society of London, 2021-02-16) Vincent, Uchechukwu
    Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena—one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems.
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    Vibrational resonance in an Oscillator Modelled by Dihedral Potential
    (Nigerian Association of Mathematical Physics, 2021-02) Vincent, Uchechukwu
    This paper examines and analyses the vibrations of a particle situated in a dihedral potential and subjected to dual frequency forcing. Based on the method of separation of time scales, the response amplitude of the particle at low-frequency (LF) is theoretically derived. It is found that a close agreement exists between the theoretical prediction and numerical simulation which validates the theoretical analysis. The presence of externally applied electric field give rise to multiple vibrational resonances. Furthermore, the VR shapes manifests as spikes that could be optimized by large amplitudes of the high frequency signal to enable the enhancement of VR thereby expediting the potential barrier crossing of the particle.
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    The Vibrational Resonance of Ammonia Molecule with Doubly-Singular Position-Dependent Mass
    (Springer, 2022-04-26) Vincent, Uchechukwu
    We examine vibrational resonance (VR) in a position-dependent mass (PDM) oscillator with doubly-singular mass distribution function describing the vibrational inversion mode of NH3 molecule. The impacts of the PDM parameters on VR was studied by computing the response amplitudes as functions of the amplitude of high-frequency component of the dual-frequency driving forces and the PDM parameters. We show for the first time that, beside the significant roles played by the parameters of the variable mass in inducing and controlling resonances similar to the forcing parameters, the variable mass parameters impacts on the resonance characteristics by leading the system from single resonance into double resonance.
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    Vibrational Resonances in Driven Oscillators with Position-dependent Mass
    (The Royal Society of London, 2021-01-18) Vincent, Uchechukwu
    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.