New analytical solution of the fractal anharmonic oscillator using an ancient Chinese algorithm: Investigating how plasma frequency changes with fractal parameter values

Elı́as-Zúñiga, Alex; Martínez-Romero, Óscar; Olvera-Trejo, Daniel

doi:10.1177/14613484211070883

Cited by 6 publications

(1 citation statement)

References 76 publications

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“…The mathematical treatment of Equation (23) can be done considering the solutions procedures discussed in [ 57 , 58 , 59 , 60 ]. Recently, other fractal theory definitions [ 61 , 62 ], and solution methods have been proposed [ 63 , 64 , 65 , 66 ]. However, the discussion of our findings using fractal material constitutive equations shall be addressed in a forthcoming paper to be published somewhere else.…”

Section: Discussionmentioning

confidence: 99%

Soft Tissue Hybrid Model for Real-Time Simulations

et al. 2022

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In this article, a recent formulation for real-time simulation is developed combining the strain energy density of the Spring Mass Model (SMM) with the equivalent representation of the Strain Energy Density Function (SEDF). The resulting Equivalent Energy Spring Model (EESM) is expected to provide information in real-time about the mechanical response of soft tissue when subjected to uniaxial deformations. The proposed model represents a variation of the SMM and can be used to predict the mechanical behavior of biological tissues not only during loading but also during unloading deformation states. To assess the accuracy achieved by the EESM, experimental data was collected from liver porcine samples via uniaxial loading and unloading tensile tests. Validation of the model through numerical predictions achieved a refresh rate of 31 fps (31.49 ms of computation time for each frame), achieving a coefficient of determination R2 from 93.23% to 99.94% when compared to experimental data. The proposed hybrid formulation to characterize soft tissue mechanical behavior is fast enough for real-time simulation and captures the soft material nonlinear virgin and stress-softened effects with high accuracy.

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Section: Discussionmentioning

confidence: 99%

Soft Tissue Hybrid Model for Real-Time Simulations

et al. 2022

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Dynamic Response of a Fractal Cushioning Packaging System

Elı́as-Zúñiga¹,

Palacios-Pineda²,

Trejo³

et al. 2022

Fractals

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This paper focuses on predicting the shape, duration, and peak magnitude of the displacement, velocity, and acceleration curves while dropping weight over a viscoelastic fractal cushioning packaging system. Furthermore, to capture high-frequency harmonic components observed during the impact time span, the approximate frequency–amplitude expression of the governing equation of motion will be obtained via an ancient Chinese algorithm and He’s formulation by assuming initial trial solutions based on Jacobi elliptic functions. Numerical simulations confirmed the ability of the Jacobi elliptic functions to capture high-frequency harmonics observed during the cushioning packaging system dynamic response with a root mean square error (RMSE) value that does not exceed 0.0218, which is an indication of the great accuracy attained from our derived solution when compared to the exact numerical one. Furthermore, our derived approximate solution predicts that when a weight is dropped over the cushioning packaging, the cushion material with smaller porosity will absorb the produced kinetic energy faster.

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A Fractal Model for the Tunneling-Induced Ground Surface Settlement

MEI,

TIAN,

et al. 2023

Fractals

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The Gaussian function was initially adopted to model the tunneling-induced ground surface settlement, but it could not describe the porosity’s effect on the settlement. To solve the problem, Yu’s fractal theory is implemented to model the porous grand’s geometric property, and the surface settlement profile is modeled by a fractal solitary wave, furthermore, the effects of the maximal surface settlement, the porosity and Yu’s fractal dimension on the settlement’s profile are discussed. The new model offers a new view to predict the morphology of the surface settlement.

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New analytical solution of the fractal anharmonic oscillator using an ancient Chinese algorithm: Investigating how plasma frequency changes with fractal parameter values

Cited by 6 publications

References 76 publications

Soft Tissue Hybrid Model for Real-Time Simulations

Soft Tissue Hybrid Model for Real-Time Simulations

Dynamic Response of a Fractal Cushioning Packaging System

A Fractal Model for the Tunneling-Induced Ground Surface Settlement

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