Numerically Research Articles

Forecasting municipal solid plastic waste generation and management policy using system dynamics: a case study of Khulna City in Bangladesh.

A comprehensive analysis of municipal solid plastic waste (MSPW) management while emphasizing plastic pollution severity in coastal cities around the world is mandatory to alleviate the augmenting plastic waste footprint in nature. Thus, decision-makers' persuasion for numerous management solutions of MSPW flow-control can be met through meditative systematic strategies at the regional level. To forecast solutions focused on systematic policies, an agent-based system dynamics (ASD) model has been developed and simulated from 2023 to 2040 while considering significant knit parameters for MSPW management of Khulna City in Bangladesh. Baseline simulation results show that per-capita plastic waste generation will increase to 11.6kg by 2040 from 8.92kg in 2023. Eventually, the landfilled quantity of plastic waste has accumulated to 70,000 tons within 18years. Moreover, the riverine discharge has increased to 834 tons in 2040 from a baseline quantity of 512 tons in 2023. So the plastic waste footprint index (PWFI) value rises to 24 by 2040. Furthermore, the absence of technological initiatives is responsible for the logarithmic rise of non-recyclable plastic waste to 1.35*1000=1350 tons. Finally, two consecutive policy scenarios with baseline factors such as controlled riverine discharge, increased collection and separation of plastic waste, expansion of recycle business, and locally achievable plastic conversion technologies have been simulated. Therefore, policy 2, with 69% conversion, 80% source separation, and 50% riverine discharge reduction of MSPW, has been found adequate from a sustainability perspective with the lowest PWFI ranges of 3.97 to 1.07 alongside a per-capita MSPW generation of 7.63 to 10kg from 2023 till 2040.

Signature of f(R) gravity via Lemaître–Tolman–Bondi inhomogeneous perturbations

We analyze inhomogeneous cosmological models in the local Universe, described by the Lemaître–Tolman–Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, in which the cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} is included in the LTB formalism, with inhomogeneous cosmological models based on fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} gravity. While radial perturbations follow a power-law in the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, Yukawa-like contributions appear in the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect.

On the efficacy of surface-attached air bubbles as thermal insulators for pressure-driven internal flow

There exists much research examining the role of surface-attached air bubbles in drag reduction. Most of this literature considers isothermal flows and so ignores temperature differences, e.g. with the solid boundary. Here, we relax this assumption and ask whether surface-attached air bubbles may prove useful as thermal insulators, e.g. when the solid temperature differs from that of the cargo liquid (water). Theoretical and numerical solutions, e.g. for the variation of the Nusselt number with bubble thickness, are presented for cases characterized by a uniform surface heat flux (USF). We examine channel and pipe flow geometries, and consider instances where the net mass flow rate within the (continuous) air bubble is zero or non-zero. When the thermal boundary condition is changed to uniform surface temperature (UST), our analysis limits attention to numerical solutions. We identify and discuss a remarkable connection between the drag reduction problem and the USF thermal insulation problem: the proportional change of water temperature with bubble thickness is identical to the proportional change of drag. Also, and although our analysis is conducted in the ‘perfect plastron limit’, we can, e.g. by evaluating hydrodynamic and thermal slip lengths, contrast our work against related studies where heat transfer occurs through the ridges or pillars that affix the air layer in place. This comparison indicates that the oft-applied adiabatic interface assumption may prove restrictive in some regions of the parameter space. We conclude by examining the implications of our work in the context of UST micro-channels, which are relevant to various lab-on-a-chip technologies.

Vibrational dynamics of a subjected system to external torque and excitation force

This work focuses on the dynamical response of a novel auto-parametric two-degrees-of-freedom (DOF) dynamical system when it is subjected to external torque and force. It consists of a forced oscillator with nonlinear stiffness that is connected to a linear spring. In accordance with the system’s DOF, an organizing system of equations of motion (EOM) is produced using Euler–Lagrange’s equations. To obtain the analytical approximate solutions (ASs) of the equations of this system, the multiple scales technique (MST) is employed. The provided solutions are being juxtaposed with the numerical solutions (NSs) for comparison to show how closely they agree, as well as the precision of the MST. In view of removing secular terms, the system’s solvability criteria are obtained. All arising resonance cases are classified, and two of them are then examined at once. The relevant system of modulation equations is solved numerically to illustrate the advantageous influence of diverse factors on the behavior of the modified phases and amplitudes. Based on the values of these parameters, the frequency response curves (FRCs) are drawn to explore different zones of stability and instability. A wide variety of values for the system’s parameters shows that its behavior is steady. The achieved outcomes are deemed novel, as the MST has been applied on a new dynamical model. The results have broad relevance and can be implemented in various engineering contexts, including the analysis of ship movements, in which nonlinear coupling between rolling and pitching motions can be found.

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

We present a flexible manipulation and control of solitons via Bose–Einstein condensates. In the presence of Rashba spin–orbit coupling and repulsive interactions within a harmonic potential, our investigation reveals the numerical local solutions within the system. By manipulating the strength of repulsive interactions and adjusting spin–orbit coupling while maintaining a zero-frequency rotation, diverse soliton structures emerge within the system. These include plane-wave solitons, two distinct types of stripe solitons, and odd petal solitons with both single and double layers. The stability of these solitons is intricately dependent on the varying strength of spin–orbit coupling. Specifically, stripe solitons can maintain a stable existence within regions characterized by enhanced spin–orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions. When rotational frequency is introduced to the system, solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation. The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin–orbit coupling. As a result, the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.

Quantum description of atomic diffraction by material nanostructures

We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications. Published by the American Physical Society 2024

Microscopic structure of electromagnetic whistler wave damping by kineticmechanisms in hot magnetized Vlasov plasmas

Abstract Electromagnetic transverse perturbations propagating parallel to the external magnetic field in a
warm electron plasma, specifically the warm electron whistler waves, are simulated in κ distributed
electrons. The Vlasov-Maxwell phase-space continuum simulations are applied to the stable and
unstable (i.e., isotropic and anisotropic) VDFs including those with energetic tail, i.e., κ distribution.
The variation of real frequency from both numerical solution of dispersion relation and simulations
show limited sensitivity to electron temperature in low wave-number regime as compared to high
wave number regime, however the opposite holds for the imaginary frequency or the decay rate. For
large amplitude, nonlinear cases, simulated with anisotropic κ distributions the very low anisotropy
cases find the growth rate increasing with increasing the κ while this trend reverses for higher
anisotropy. The phase-space portraits of the these cases show that after the linear damping phase
of the evolution, the particles are trapped in the wave magnetic field leading to the wave amplitudes
oscillating about a mean value which follow the theoretical analysis [1].

Aether Scalar Tensor (AeST) theory: Quasistatic spherical solutions and their phenomenology

Abstract There have been many efforts in the last three decades to embed the empirical MOND program into a robust theoretical framework. While many such theories can explain the profile of galactic rotation curves, they usually cannot explain the evolution of the primordial fluctuations and the formation of large-scale-structures in the Universe. The Aether Scalar Tensor (AeST) theory seems to have overcome this difficulty, thereby providing the first compelling example of an extension of general relativity able to successfully challenge the particle dark matter hypothesis. Here we study the phenomenology of this theory in the quasistatic weak-field regime and specifically for the idealised case of spherical isolated sources. We find the existence of three distinct gravitational regimes, that is, Newtonian, MOND and a third regime characterised by the presence of oscillations in the gravitational potential which do not exist in the traditional MOND paradigm. We identify the transition scales between these three regimes and discuss their dependence on the boundary conditions and other parameters in the theory. Aided by analytical and numerical solutions, we explore the dependence of these solutions on the theory parameters. Our results could help in searching for interesting observable phenomena at low redshift pertaining to galaxy dynamics as well as lensing observations, however, this may warrant proper N-body simulations that go beyond the idealised case of spherical isolated sources.

Theoretical investigation of the convective heat transfer mechanism along a cantilever shape

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n, Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient.

Study of Self-Excited Thermomechanical Oscillator with Shape Memory Alloys

In this paper, a new type of self-excited thermomechanical oscillator containing an oscillating shape memory alloy (SMA) filament with two symmetrically arranged spheres is investigated. The self-excitation of the oscillations is due to a heater of constant temperature, which causes periodic contractions of the filament when it approaches it. The contracted filament moves away from the heater a distance sufficient to cool it. Under the action of the weight of the spheres, the cooled filament re-approaches the heater, causing the above processes to repeat periodically. On the basis of experimental studies, approximating functions of the heater’s heat field distribution are derived. A dynamic model of the oscillator has been created, in which the minor and major hysteresis in the SMA alloy and the distribution of the heat field around the heater have been taken into account. Through numerical solutions of the differential equations, the laws of motion of the spheres are obtained. The displacements of the spheres in two perpendicular directions were measured using an experimental system. The obtained experimental results validate the proposed dynamic model and its assumptions with a high degree of confidence. Conclusions are drawn about the stochastic nature of the oscillations due to the hysteresis properties of the SMA and the temperature variation of the natural frequency of the oscillating system.

Application of Perturbation Method to Approximate the Solutions of Differential Equation

We investigate the core features of the perturbation method with the help of some simple but sophisticated problems and demonstrate how much accurately it predicts the solutions of the problems. To fulfill the target, we use the method for getting the solution of differential equations with initial and boundary conditions. Then the results obtained are compared with the series solution and the exact/numerical solution by using Mathematica and Fortran Programming. The comparisons are shown graphically. Also, the perturbation series approximation and the exact or numerical solution are in good agreement. Our investigation shows that a certain number of terms of the perturbation series gives an excellent approximation than the same number of terms of the numerical solution.

Analytical and numerical solutions to the Klein–Gordon model with cubic nonlinearity

In this paper, the nonlinear Klein–Gordon equation’s exact solutions are obtained through the application of an appropriate transformation based on He’s semi-inverse approach. This equation considered a generalization of other famous models in applied science, such as Phi-4 equation, Duffing equation, Fisher–Kolmogorov model through population dynamics and Hodgkin–Huxley equation that characterizes the propagation of electrical signals via nervous system. The suggested approach is simple, robust, and efficient, and its application in other partial differential equations in applied science seems promising. Numerical solution of the nonlinear Klein–Gordon equation is presented using finite difference method. The method’s accuracy is demonstrated by contrasting it with the exact solution that we obtained. The Von Neumann stability technique is applied to obtain the stability condition and a convergent test is presented Some 2D and 3D graphs matching to chosen solutions are simulated by taking into account appropriate values for the parameters.

Exploring the physical characteristics and nonlinear wave dynamics of a (3+1)-dimensional integrable evolution system

This study comprehensively explores the [Formula: see text]-dimensional Mikhailov–Novikov–Wang [Formula: see text] integrable equation, with the primary objective of elucidating its physical manifestations and establishing connections with analogous nonlinear evolution equations. The investigated model holds significant physical meaning across various disciplines within mathematical physics. Primarily, it serves as a fundamental model for understanding nonlinear wave propagation phenomena, offering insights into wave behaviors in complex media. Moreover, its relevance extends to nonlinear optics, where it governs the dynamics of optical pulses and solitons crucial for optical communication and signal processing technologies. Employing analytical methodologies, namely the unified [Formula: see text], Khater II ([Formula: see text]hat.II) method, and He’s variational iteration [Formula: see text] method, both numerical and analytical solutions are meticulously examined. Through this investigation, the intricate behaviors of the equation are systematically unveiled, shedding illuminating insights on various physical phenomena, notably including wave propagation in complex media and nonlinear optics. The outcomes not only underscore the efficacy of the analytical techniques deployed but also accentuate the equation’s pivotal role in modeling a broad spectrum of nonlinear wave dynamics. Consequently, this research significantly advances our comprehension of complex physical systems governed by nonlinear dynamics, thereby contributing notably to interdisciplinary pursuits in mathematical physics.

Fuzzy-fractional modeling and simulation of electric circuits using extended He-Laplace-Carson algorithm

In literature, most of the electric circuits are found to be at integer order, which are unable to capture the involved uncertainties and memory effects. To understand these effects, the current study is focused on modeling and analysis of fuzzy-fractional L˜C˜ circuit, R˜C˜ circuit, R˜L˜ circuit, and R˜L˜C˜ circuit. Triangular fuzzy numbers (TFNs) are utilized to introduce uncertainties in circuits. The memory effect is considered through fractional derivative in Caputo sense. A hybrid homotopy perturbation method (HPM) is established for solution purpose, in which standard HPM is combined with Laplace-Carson transformation in fuzzy-Caputo sense. This leads to an excellent and well-organized approach to calculate numerical solutions in the aspect of fuzzy logic and fractional calculus. The results obtained through proposed approach are validated by comparing them with already existing results in literature. Residual errors are also calculated across the domain of r at fractional order to determine the convergence and stability of electric circuit models. To study the dynamics of inductor, resistor, and capacitor on current along with fractional and fuzzy parameters involved in the electric circuits, contour and three-dimensional plots are constructed. Several plots specifying the fuzzy membership function of models across various parameter values are also demonstrated. The results achieved through this study indicate that He-Laplace-Carson method can assist engineers and researchers when dealing with electric circuits characterized by fuzzy and fractional dynamics.

Slender phoretic loops and knots

We present an asymptotic theory for solving the dynamics of slender autophoretic loops and knots. Our formulation is valid for nonintersecting three-dimensional center lines, with arbitrary chemical patterning and varying (circular) cross-sectional radius, allowing a broad class of slender active loops and knots to be studied. The theory is amenable to closed-form solutions in simpler cases, allowing us to analytically derive the swimming speed of chemically patterned tori, and the pumping strength (stresslet) of a uniformly active slender torus. Using simple numerical solutions of our asymptotic equations, we then elucidate the behavior of many exotic active particle geometries, such as a bumpy uniformly active torus that spins and a Janus trefoil knot, which rotates as it swims forwards. Published by the American Physical Society 2024

Efficient semianalytical investigation of a fractional model describing human cornea shape

Purpose: This study presents a novel application of the semianalytical residual power series method to investigate a one-dimensional fractional anisotropic curvature equation describing the human cornea, the outermost layer of the eye. The fractional boundary value problem, involving the fractional derivative of curvature, poses challenges that conventional methods struggle to address. Methods: The analytical results are obtained by utilizing the simple and efficient residual power series method. The proposed method is accessible to researchers in all medical fields and is extendable to various models in disease spread and control. Results: The derived solution is a crucial outcome of this study. Through the application of the proposed method to the corneal shape model, an explicit formula for the curvature profile is obtained. To validate the solution, direct comparisons are made with numerical solutions for the integer case and other analytical solutions available in the literature for the fractional case. Conclusion: Our findings highlight the potential of the proposed method to significantly contribute to the diagnosis and treatment of various ophthalmological conditions.

Uniqueness and numerical inversion in bioluminescence tomography with time-dependent boundary measurement

Abstract In the paper, an inverse source problem in bioluminescence tomography (BLT) is investigated. BLT is a method of light imaging and offers many advantages such as sensitivity, cost-effectiveness, high signal-to-noise ratio and non-destructivity. It thus has promising prospects for many applications such as cancer diagnosis, drug discovery and development as well as gene therapies. In the literature, BLT is extensively studied based on the (stationary) diffusion approximation (DA) equation, where the distribution of peak sources is reconstructed and no solution uniqueness is guaranteed without proper a priori information. In this work, motivated by solution uniqueness, a novel dynamic coupled DA model is proposed. Theoretical analysis including the well-posedness of the forward problem and the solution uniqueness of the inverse problem are given. Based on the new model, iterative inversion algorithms under the framework of regularizing schemes are introduced and applied to reconstruct the smooth and non-smooth sources. We discretize the regularization functional with the finite element method and give the convergence rate of numerical solutions. Several numerical examples are implemented to validate the effectiveness of the new model and the proposed algorithms.

Numerical solution of generalized fractional Lane Emden-Fowler equation using Haar wavelet method

Numerical solution of generalized fractional Lane Emden-Fowler equation using Haar wavelet method

Unsteady MHD flow analysis of hybrid nanofluid over a shrinking surface with porous media and heat generation: Computational study on entropy generation and Bejan number

The use of hybrid nanofluids in real-world situations is essential for enhancing the efficiency of heat transmission, especially in cooling semiconductor technology and industrial processes. The entropy generation on unsteady Al2O3-Cu/H2O hybrid nanofluid flow over a three-dimensional shrinking sheet is addressed numerically in this study, taking into account the effects of magnetohydrodynamic (MHD), nonlinear thermal radiation, porous media, heat generation, viscous dissipation, joule heating, and convective conditions. Using well-known non-similarity transformations, the model is carefully converted from partial differential equations (PDEs) to ordinary differential equations (ODEs). Afterwards, the behaviors of critical physical characteristics are uncovered across different parameter configurations by a numerical solution using the finite difference technique in bvp4c MATLAB. The velocity profiles of hybrid nanofluid grow proportionately with increases in the values of ϕ2,M,A,K and λ parameters. As Rd,θw,Ec,Bi,H and ϕ2 increase, the temperature of the hybrid nanofluid rises, but as M and A increase, the temperature falls. The local skin friction in both the x and y- directions is increased by enhancing the unsteadiness A, nanoparticle volume fraction ϕ2, magnetic M, porous media K, and the ratio of strain rate λ parameter on the shrinking surface. The local Nusselt number is improved by cumulative the unsteadiness A, nanoparticle volume fraction ϕ2, magnetic M, and Biot number Bi parameter in the direction of a shrinking surface, while the Nusselt number decreases when Eckert number Ec, thermal radiation Rd, heat production H, and temperature ratio θw are improved. An upsurge in the magnetic parameter leads to the development of entropy generation. Increasing levels of the magnetic parameters led to a reduction in the Bejan number. At a nanoparticle volume fraction of 1 % and a nonlinearity radiation scenario, where the unsteadiness values are 0.5, the Nusselt number for hybrid nanofluid shows an estimated improvement of 10.55 % compared to regular nanofluid.

Exact solitary wave propagations for the stochastic Burgers’ equation under the influence of white noise and its comparison with computational scheme

In this manuscript, the well-known stochastic Burgers’ equation in under investigation numerically and analytically. The stochastic Burgers’ equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results. The existence of results is shown by the help of Schauder fixed point theorem. For the approximate results the proposed stochastic finite difference scheme is constructed. The analysis of the proposed scheme is analyzed by presented the consistency and stability of scheme. The consistency is checked under the mean square sense while the stability condition is gained by the help of Von-Neumann criteria. Meanwhile, the stochastic exact solutions are constructed by using the generalized exponential rational function method. These exact stochastic solutions are obtained in the form of hyperbolic, trigonometric and exponential functions. Mainly, the comparison of both numerical and exact solutions are analyzed via simulations. The unique physical problems are constructed from the newly constructed soliton solutions to compare the numerical results with exact solutions under the presence of randomness. The 3D and line plots are dispatched that are shown the similar behavior by choosing the different values of parameters. These results are the main innovation of this study under the noise effects.