Revealing Fano Combs in Directional Mie Scattering

The constructive interference of light reflecting on the inner surface of a dielectric sphere results in a rich Mie scattering spectrum. Each resonance can be understood through a quantum-mechanical analogy, while the structure of the full spectrum is predicted to be a series of Fano resonances. However, the overlap of all the different modes results in such a complex spectrum that an intuitive understanding of the full, underlying structure is still missing. Here we present a directional Mie spectrum obtained by selecting a particular polarization and direction of the scattering of levitating water droplets. We find a significantly simplified spectrum organized in distinct, consecutive Mie Fano Combs composed of equidistant resonances that smoothly evolve from wide Lorentzians into sharp Fano profiles. We then fully explain all these characteristics by expanding on the quantum-mechanical analogy. This makes it possible to understand Mie spectra intuitively without the need for computational simulations.

V-Function Method: Some Solutions of Direct and Inverse Dynamics Problems in A New Statement

Based on the V-function method, the properties of wave nature of object motion are studied for object uniform motion with constant speed and for harmonic oscillator. It follows from the V-function method that object wave motion is inseparably linked with its trajectory motion. The V-function method consists of the principle of local variation and a new statement of the direct and inverse dynamics problems. The proposed approach made it possible to make the optico-mechanical analogy that obtained a new continuation. A comparison is made with the results obtained by Schrödinger for a harmonic oscillator.

Use of a Simple Mechanical Analogy to Analytically Tune the PD Controller of a Flexible Manipulator System

A study is presented in this paper that uses a simple mechanical analogy to analytically tune the PD (proportional-derivative) controller of a linear flexible manipulator system. More specifically, the aim is to give simple closed-form solutions of the optimal P and D gains to yield the maximum bandwidth under a given damping requirement or conversely the maximum damping under a given bandwidth requirement. The idea of this study is based on the observation that the performance of the complete manipulator system is largely determined by the operational dynamics of the fundamental vibration mode. A lumped element method is thus applied to model this dynamics in terms of simple lumped mechanical elements. It subsequently turns out that the original servo control problem is analogous to a conventional Zener mount design problem, that is, mathematically, to optimize a third-order dynamic system consisting of the Zener model of a viscoelastic mount and an inertial object upon it. A design methodology is finally established to analytically determine the optimal elements of the mount, corresponding to the optimal control gains. Simulations and experiments were also conducted with a single-link flexible beam to support the model and the design methodology developed.

57 Harmonical oscillator and electro-mechanical analogy: an interdiscinary experiment to high precision mass variation measurements

In general, the traditional Physics courses needs examples of the aplications of the Physics concepts in other areas such as Chemistry and Biology. This lacks tend to demotivate Chemistry and Biology students regarding to deal with Physical concepts developed in classroom. In this work, the analogy among mechanic and electric oscillators is investigated to be applied in Chemistry and Biology areas, showing to be valuable due to its aplication in techniques that aims to measure mass variation with high precision. This measure could be made in a direct or indirect way. These techniques are known as electrogravimetric techniques and they are important in biosensor aplications. Thus, this paper explores the electromechanic analogy in an interdisciplinary way involving areas like Physics, Chemistry and Biology. Based on this analogy, it is proposed an experiment that can be applied in different ways, i.e. by an basic approach or more deeper, depending on the students specific formation, in other words, Physics, Chemistry or Biology.