An application to formable transform: Novel numerical approach to study the nonlinear oscillator

Basit, Muhammad Abdul; Tahir, Madeeha; Shah, Nehad Ali; Tag, Sayed M; Imran, Muhammad

doi:10.1177/14613484231216198

Cited by 7 publications

(1 citation statement)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gadelhak et al (2023) expressed that the FDM approach is more suitable for evaluating energy transfer through Williamson nano-liquid over a curved extendable medium. The numerical solution of a nonlinear oscillator is acquired by using the Laplace transform and investigating heat transport rate increment by adding motile microorganisms in the suspension [as mentioned in the following studies: Basit et al (2023a); Basit et al (2024a); Basit et al (2024b); Imran et al (2024)], and response surface methodology is implemented to check the optimality of the mathematical model. Salahuddin et al (2023) experimented with double stratification and activation energy impacts on the nanofluid stream over a stretchable medium.…”

Section: Introductionmentioning

confidence: 99%

Numerical scrutinization of heat transfer subject to physical quantities through bioconvective nanofluid flow via stretching permeable surfaces

Shang,

Yu,

Wang

et al. 2024

Front. Energy Res.

View full text Add to dashboard Cite

Background: The mechanics of heat and mass transfer via nanofluid flow across many media are currently being discussed. “Nanofluids” are fluids that include highly heat-conductive nanoparticles, and they are essential for resolving engineering problems. Under the effects of activation energy, thermal radiation, and motile microorganisms, the process of heat and mass transfer through steady nanofluid flow crosses over stretched surfaces in this scenario.Methodology: For mathematical evaluation, the system of partial differential equations (PDEs) is used to describe this physical framework. By introducing suitable similarity variables with a set of boundary conditions, this mathematical system of PDEs has become a system of ordinary differential equations (ODEs). To obtain numerical results, the MATLAB built-in program “bvp4c” is used to solve the system of first-order equations.Results: In the findings and discussion section, the resulting outcomes are thoroughly examined and visually shown. The flow rate in these systems increases due to the erratic movement of microorganisms. The graphical representation shows the impacts of involving physical factors on the microorganism, thermal, concentration, and momentum profiles. Variations/changes in these profiles can be observed by adjusting the parametric values, as depicted in the graphs. Consequently, thermal transport is boosted by 25%. Additionally, the skin friction, Nusselt, Sherwood, and microbe density numbers are determined numerically. The findings demonstrate that increasing the magnetic field parameter causes the velocity profile to decrease, increasing the radiation parameter leads to an increase in temperature description, and increasing the Lewis number causes the microorganism profile’s transport rate to decrease.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical scrutinization of heat transfer subject to physical quantities through bioconvective nanofluid flow via stretching permeable surfaces

Shang,

Yu,

Wang

et al. 2024

Front. Energy Res.

View full text Add to dashboard Cite

show abstract

Shear-driven diffusion with stochastic resetting

Abdoli,

Olsen,

Löwen

2024

Physics of Fluids

View full text Add to dashboard Cite

External flows, such as shear flow, add directional biases to particle motion, introducing anisotropic behavior into the system. Here, we explore the non-equilibrium dynamics that emerge from the interplay between linear shear flow and stochastic resetting. The particle diffuses with a constant diffusion coefficient while simultaneously experiencing linear shear and being stochastically returned to its initial position at a constant rate. We perturbatively derive the steady-state probability distribution that captures the effects of shear-induced anisotropy on the spatial structure of the distribution. We show that the dynamics, which initially spread diffusively, will at late times reach a steady state due to resetting. At intermediate timescales, the system approaches this steady state either by passing through a superdiffusive regime (in the shear-dominated case) or by exhibiting purely sub-diffusive behavior (in the resetting-dominated case). The steady state also gains cross correlations, a feature absent in simpler resetting systems. We also show that the skewness has a non-monotonic behavior when one passes from the shear-dominated to the resetting-dominated regime. We demonstrate that at small resetting rates, the energetic cost of maintaining the steady state becomes significantly higher due to the displacement caused by shear, a unique scaling not seen without shear. Surprisingly, if only the x-position is reset, the system can maintain a Brownian yet non-Gaussian diffusion pattern with non-trivial tails in the distribution.

show abstract

A universal application of the general integral transform: New technique for the analysis of nonlinear oscillator systems

Niu

2024

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

The wide applicability of a nonlinear oscillator is the main reason why it has gained so much attention from mathematicians and scientists, while it is difficult to be solved both numerically and theoretically. Variational iteration method is one of the numerical approaches which are used to investigate these nonlinear systems. In this paper, we present a nonlinear oscillator arising in a micro-electromechanical system as an example and derive its analytical solution by He’s frequency formula method and variational iteration method coupled with a new general integral transformation. The Lagrange multiplier is formulated and the new iterative format for the correction functional of the variational iteration method is given by the general integral transformation. The approximate nonlinear frequencies are achieved by this new technique and compared with the numerical ones obtained by the Runge–Kutta method. The new general integral transformation has the same essential qualities as those for Laplace and Fourier transform, and it becomes a promising tool to nonlinear problems when coupled with the variational iteration method.

show abstract

An application to formable transform: Novel numerical approach to study the nonlinear oscillator

Cited by 7 publications

References 62 publications

Numerical scrutinization of heat transfer subject to physical quantities through bioconvective nanofluid flow via stretching permeable surfaces

Numerical scrutinization of heat transfer subject to physical quantities through bioconvective nanofluid flow via stretching permeable surfaces

Shear-driven diffusion with stochastic resetting

A universal application of the general integral transform: New technique for the analysis of nonlinear oscillator systems

Contact Info

Product

Resources

About