Numerical simulation and laboratory measurements on the influence of fractal dimension on the acoustic beam modulation of a Polyadic Cantor Fractal lenses

Tarrazó-Serrano, Daniel; Castiñeira-Ibáñez, Sergio; Candelas, Pilar; Fuster, J.M.; Rubio, Constanza

doi:10.1016/j.apacoust.2018.12.012

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…However, there exist in nature attractors with self‐similarities; this class cannot be captured neither with classical differentiation nor with classical fractional and new trends in fractional differentiation and integration. Many technics have been suggested to solve and model such problems; for instance, the concept of fractal including Julia set, the Mandelbrot set, and many other sets has been used to capture self‐similarities, but those self‐similarities do not come from chaotic attractors, neither they come from mathematical models 7–14 . Additionally, these self‐similarities obtained from these complex sets cannot be used to predict the evolution in time, as they are not time dependent; however, they are very useful for other purpose.…”

Section: Introductionmentioning

confidence: 99%

“…Many technics have been suggested to solve and model such problems; for instance, the concept of fractal including Julia set, the Mandelbrot set, and many other sets has been used to capture self-similarities, but those self-similarities do not come from chaotic attractors, neither they come from mathematical models. [7][8][9][10][11][12][13][14] Additionally, these self-similarities obtained from these complex sets cannot be used to predict the evolution in time, as they are not time dependent; however, they are very useful for other purpose. Up to 2016, the question was still unsolved as these types of differential and integral operators were not available in literature.…”

Section: Introductionmentioning

confidence: 99%

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New chaotic attractors: Application of fractal‐fractional differentiation and integration

Gómez‐Aguilar

Atangana

2020

Math Methods in App Sciences

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Very recently, the concept of fractal differentiation and fractional differentiation has been combined to produce new differentiation operators. The new operators were constructed using three different kernels, namely, power law, exponential decay, and the generalized Mittag‐Leffler function. The new operators have two parameters: the first is considered as fractional order and the second as fractal dimension. In this work, we applied these new operators to model some chaotic attractors, and the models were solved numerically using a new and very efficient numerical scheme. We presented numerical simulations for some specific fractional order and fractal dimension. The classical fractional differential models could be recovered when the fractal dimension is equal to 1; in these cases, the obtained attractors with power law presented no similarities. Nevertheless, those obtained via Caputo‐Fabrizio and the Atangana‐Baleanu derivative show some crossover effects, which is due to non‐index law property. However, those obtained from fractal‐fractional, in particular, those with the Mittag‐Leffler kernel, show very strange and new attractors with self‐similarities; these results are obtained for the first time. We conclude that this new concept is the future to modelling complexities with self‐similarities.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Gómez‐Aguilar

Atangana

2020

Math Methods in App Sciences

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Fractal lenses based on Cantor binary sequences for ultrasound focusing applications

et al. 2019

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Review and perspective on acoustic metamaterials: From fundamentals to applications

Zhang

Wang

2023

Applied Physics Letters

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In the past two decades, the research on acoustic metamaterials has flourished, which is also benefited from the development of additive manufacturing technology. The exotic physical phenomena and principles exhibited by acoustic metamaterials have attracted widespread attention from academia and engineering communities, which can be applied to noise reduction and acoustic nondestructive testing in industrial; invisible cloaking and camouflage in the military; medical ultrasound imaging in national health; acoustic stealth in defense security, detection in the ocean, communication, and other fields, i.e., acoustic metamaterials have important scientific research value and broad application prospects. This review summarizes the history and research status of acoustic metamaterials, focusing on the main research progress of metamaterials in nonlinear acoustic and acoustic coatings fields, including the research on acoustic coatings with cavities of our group. Finally, the future development direction of acoustic metamaterials is prospected, and the difficulties and challenges faced by the actual engineering of acoustic metamaterials are discussed, such as difficulties in mass production, hydrostatic pressure resistant property, omnidirectional wave control, high production costs, and so on.

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Numerical simulation and laboratory measurements on the influence of fractal dimension on the acoustic beam modulation of a Polyadic Cantor Fractal lenses

Cited by 3 publications

References 19 publications

New chaotic attractors: Application of fractal‐fractional differentiation and integration

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Fractal lenses based on Cantor binary sequences for ultrasound focusing applications

Review and perspective on acoustic metamaterials: From fundamentals to applications

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