Mathematical modelling and symbolic dynamics analysis of three new Galton board models

Daud, Auni Aslah Mat

doi:10.1016/j.cnsns.2014.03.011

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…After innumerable nail collisions, it was piled up at the bottom. The final slot that a single ball is falling into is unintentional, but the majority of balls eventually fall into the center slots, with a tiny number of balls falling into slots on both sides [22][23][24][25]. Similar to balls moving in nails, bubbles in the spaces of soil particles eventually overflow the water in large quantities from the central area.…”

Section: Resultsmentioning

confidence: 99%

A 3D DEM Model for Air Sparging Technology in the Saturated Granular Soils

Liu

et al. 2022

Front. Phys.

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This work provides a three-dimensional discrete element simulation (DEM) model to study the air sparging technology. The simulations have taken into account the multi-phases of bubble (gas) - fluid (water) - soil (solid) particles. Bubbles are treated as discrete individual particles, with buoyancy and drag forces applied to bubbles and soil particles. The trajectory of each discrete bubble particle can be tracked using the discrete element model. It is found that the diffusion of the whole bubble is inverted conical though the motion behavior of a single bubble particle is random. Furthermore, the distribution of the radius of influence (ROI) is not uniform. The bubbles become more concentrated as in the center of the inverted cone. The number of bubbles dissipated from the water surface is normally distributed. The DEM simulation is a novel approach to studying air sparging technology that can provide us a deeper insight into bubble migration at the microscopic level.

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Section: Resultsmentioning

confidence: 99%

A 3D DEM Model for Air Sparging Technology in the Saturated Granular Soils

Liu

et al. 2022

Front. Phys.

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Numerical study of calton board experiment via discrete element method simulation

Hlosta¹,

Čermák

Žurovec³

et al. 2020

International Conference of Numerical Analysis and Applied Mathematics Icnaam 2019

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The acoustic Galton board

Zhang,

Zheng,

Guo

et al. 2024

Eur. J. Phys.

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Phononic crystals are a class of materials with periodic structures that influence the propagation characteristics of acoustic waves through periodically arranged structural units. Here, we have developed the Acoustic Galton Board (AGB), a groundbreaking apparatus that serves as a cost-effective and user-friendly tool for demonstrating phononic crystal properties such as bandgaps, Bragg scattering, and local resonance. The device comprises an elastic wave signal generator, an enhanced Galton board featuring a sophisticated pillar-nail array, and a signal receiver. The experimental results we have obtained demonstrate the significant impact of the AGB on elastic wave dispersion, effectively creating bandgaps that impede wave transmission within specific frequency ranges while allowing unhindered propagation in others. Furthermore, the AGB can simulate phononic crystals using both the Bragg scattering mechanism, achieved through the design of periodic rigid pillar-nail arrays, and the locally resonant mechanism, facilitated by the design of pillar-nail arrays with composite material structures. Additionally, the AGB can extend its applications to serve as a simulation tool for elastic metamaterials.

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Mathematical modelling and symbolic dynamics analysis of three new Galton board models

Cited by 4 publications

References 27 publications

A 3D DEM Model for Air Sparging Technology in the Saturated Granular Soils

A 3D DEM Model for Air Sparging Technology in the Saturated Granular Soils

Numerical study of calton board experiment via discrete element method simulation

The acoustic Galton board

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