Development of an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface

A comprehensive investigation on the static and dynamic responses of a sphere located at elastic and viscoelastic medium interfaces is performed in this study. First, the mathematical models commonly used for predicting the static displacement of a sphere located at an elastic medium interface are presented and their performances are compared. After that, based on the finite element analyses, an accurate mathematical model to predict the static displacement of a sphere located at an elastic medium interface valid for different Poisson’s ratios of the medium and small and large sphere displacements is proposed. Then, an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface is developed. In addition to the Young’s modulus of the medium and the radius of the sphere, the model takes into account the density, Poisson’s ratio and viscosity of the medium, the mass of the sphere and the radiation damping. The effects of the radiation damping, the Young’s modulus, density and viscosity of the medium and the density of the sphere on the dynamic response of the sphere located at a viscoelastic medium interface are explored. The developed model can be used to understand the dynamic responses of spherical objects located at viscoelastic medium interfaces in practical applications. Furthermore, the proposed model is a significant tool for graduate students and researchers in the fields of engineering, materials science and physics to gain insight into the dynamic responses of spheres located at viscoelastic medium interfaces.

Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction

Summary The dynamics of sliding friction is mainly governed by the frictional force. Previous studies have shown that the laboratory-scale friction is well described by an empirical law stated in terms of the slip velocity and the state variable. The state variable represents the detailed physicochemical state of the sliding interface. Despite some theoretical attempts to derive this friction law, there has been no unique equation for time evolution of the state variable. Major equations known to date have their own merits and drawbacks. To shed light on this problem from a new aspect, here we investigate the feasibility of periodic motion without the help of radiation damping. Assuming a patch on which the slip velocity is perturbed from the rest of the sliding interface, we prove analytically that three major evolution laws fail to reproduce stable periodic motion without radiation damping. Furthermore, we propose two new evolution equations that can produce stable periodic motion without radiation damping. These two equations are scrutinized from the viewpoint of experimental validity and the relevance to slow earthquakes.

Radiation damping strongly perturbs remote resonances in presence of homo-nuclear mixing sequences

In this work, it is experimentally shown that the weak oscillating magnetic field (known as the “radiation damping” field) caused by the inductive coupling between the transverse magnetization of nuclei and the radio frequency circuit perturbs remote resonances when homo-nuclear total correlation mixing sequences are applied. Numerical simulations are used to rationalize this effect.

Total wave power absorption by a multi-float wave energy converter and a semi-submersible wind platform with a fast far field model for arrays

Wave energy converters absorb wave power by mechanical damping for conversion into electricity and multi-float systems may have high capture widths. The kinetic energy of the floats causes waves to be radiated, generating radiation damping. The total wave power absorbed is thus due to mechanical and radiation damping. A floating offshore wind turbine platform also responds dynamically and damping plates are generally employed on semi-submersible configurations to reduce motion, generating substantial drag which absorbs additional wave power. Total wave power absorption is analysed here by linear wave diffraction–radiation–drag models for a multi-float wave energy converter and an idealised wind turbine platform, with response and mechanical power in the wave energy case compared with wave basin experiments, including some directional spread wave cases, and accelerations compared in the wind platform case. The total power absorption defined by capture width is input into a far field array model with directional wave spreading. Wave power transmission due a typical wind turbine array is only reduced slightly (less than 5% for a 10 × 10 platform array) but may be reduced significantly by rows of wave energy converters (by up to about 50%).

A Refutation Of Special Relativity: II. Charge Particle Motion in Magnetic and Electric Fields

Models for the radiation damping force of a charged particle in a magnetic or electric field by means of a flux-proportional Lentz force has been shown to be an elegant solution for the inward spiraling trajectories under magnetic fields, and the speed limited trajectories under electric fields. Our phenomenological formulation of the damping force in a magnetic field requires a new attenuation coefficient, α, that has only been evaluated using experimental data, but whose pure theoretical evaluation may lead to improved understanding of the mechanism of electron damping in electromagnetic fields. We believe that the synchrotron radiation and its observed coherence is already sufficient experimental evidence for our modeling of radiation damping. It is hoped that our model could be applied to improve the designs of free electron lasers as well as the design of particle accelerators.