A Swing of Beauty: Pendulums, Fluids, Forces, and Computers

[Experimental and numerical investigation of fluid-particle-interactions in water]

For the development of improved sediment transport models, the basic understanding of the interaction between the solid particle and the moving fluid (water) is important. In this article, current developments in the field of fluid-particle interaction are presented based on two research articles by Gold et al. (2023) and Worf et al. (2022). One presented in this article uses state of the art measurement methods to investigate the flow around spheres of different densities that oscillate in initially resting body of water. For the spherical pendulum a similar vortex shedding characteristic was observed for all investigated fluid density ratios (m * = ρ S / ρ F = 1.14 , 14.95 , density ratio between solid and fluid). A new object tracking method (DOT) is also presented, which enables temporally and spatially resolved analysis of flow structures in the fluid field. The experimental results of Gold et al. (2023) show, that vortex shedding occurs during the first period. This vortex propagates downward and eventually dissipates. Furthermore, a damping optimum of the spherical pendulum in the range of m * = 2.50 was observed. Additionally, an experiment with a cylindrical pendulum with m ∗ = 4 . 98 was investigated numerically utilizing an immersed boundary method. The process of creation and separation up to the dissipation of a vortex ring was described. Furthermore, this investigation by Worf et al. (2022) described the creation of tip vortices. These were connected with the development of the three-dimensional flow and added mass coefficient.

Pendulum Search Algorithm: An Optimization Algorithm Based on Simple Harmonic Motion and Its Application for a Vaccine Distribution Problem

The harmonic motion of pendulum swinging centered at a pivot point is mimicked in this work. The harmonic motion’s amplitude at both side of the pivot are equal, damped, and decreased with time. This behavior is mimicked by the agents of the pendulum search algorithm (PSA) to move and look for an optimization solution within a search area. The high amplitude at the beginning encourages exploration and expands the search area while the small amplitude towards the end encourages fine-tuning and exploitation. PSA is applied for a vaccine distribution problem. The extended SEIR model of Hong Kong’s 2009 H1N1 influenza epidemic is adopted here. The results show that PSA is able to generate a good solution that is able to minimize the total infection better than several other methods. PSA is also tested using 13 multimodal functions from the CEC2014 benchmark function. To optimize multimodal functions, an algorithm must be able to avoid premature convergence and escape from local optima traps. Hence, the functions are chosen to validate the algorithm as a robust metaheuristic optimizer. PSA is found to be able to provide low error values. PSA is then benchmarked with the state-of-the-art particle swarm optimization (PSO) and sine cosine algorithm (SCA). PSA is better than PSO and SCA in a greater number of test functions; these positive results show the potential of PSA.

Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin's immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library,IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

Numerical analysis of grasshopper escapement

The dynamics of a driven, damped pendulum as used in mechanical clocks is numerically investigated. In addition to the analysis of well-known mechanisms such as chronometer escapement, the unusual properties of Harrison's grasshopper escapement are explored, giving some insights regarding the dynamics of this system. Both the steady-state operation and transient effects are discussed, indicating the optimal condition for stable long-term clock accuracy. The possibility of chaotic motion is investigated.