Normal mode

Summary

A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. The most general motion of a linear system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. General definitions Mode In the wave theory of physics and engineering, a mode in a dynamical system is a standi

Official source

https://en.wikipedia.org/wiki/Normal_mode

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A Multi-Site Campaign To Measure Solar-Like Oscillations In Procyon. Ii. Mode Frequencies

We have analyzed data from a multi-site campaign to observe oscillations in the F5 star Procyon. The data consist of high-precision velocities that we obtained over more than three weeks with 11 telescopes. A new method for adjusting the data weights allows us to suppress the sidelobes in the power spectrum. Stacking the power spectrum in a so-called echelle diagram reveals two clear ridges, which we identify with even and odd values of the angular degree (l = 0 and 2, and l = 1 and 3, respectively). We interpret a strong, narrow peak at 446 mu Hz that lies close to the l = 1 ridge as a mode with mixed character. We show that the frequencies of the ridge centroids and their separations are useful diagnostics for asteroseismology. In particular, variations in the large separation appear to indicate a glitch in the sound-speed profile at an acoustic depth of similar to 1000 s. We list frequencies for 55 modes extracted from the data spanning 20 radial orders, a range comparable to the best solar data, which will provide valuable constraints for theoretical models. A preliminary comparison with published models shows that the offset between observed and calculated frequencies for the radial modes is very different for Procyon than for the Sun and other cool stars. We find the mean lifetime of the modes in Procyon to be 1.29(-0.49)(+0.55) days, which is significantly shorter than the 2-4 days seen in the Sun.

2010

Further miniaturisation of magnetic storage devices requires an advent of new types of magnets, since classical ferromagnetic materials show lack of remanence at nano- and subnanoscale. A single atom can represent the smallest possible bit of information. Even though the isolated single atoms are paramagnetic, the interaction of surface adsorbed atoms with a substrate can result in high magnetic anisotropy energy and long magnetisation lifetime. In this thesis the magnetic properties of surface supported rare-earth single atoms are investigated with X-ray absorption spectroscopy, X-ray magnetic circular dichroism and multiplet simulations. The first goal of the project was to find new adatom/substrate combinations that exhibit a long adatom magnetic lifetime, possibly extending the current limits of the atomic magnetic moment stability to higher temperatures and longer spin relaxation times. The second objective was to implement the external electric field control of the adatom magnetic properties.Firstly, we present the experimental and theoretical research on Dy and Ho single atoms deposited on BaO. A comparison of our results with similar studies sheds light on the impact of the substrate crystal field, in particular Dy-O bond covalency, on the magnetic stability of the rare-earth adatoms. Next, the detailed experimental investigation of Dy single atoms on ZnO is presented. This adatom/substrate pair is used as first attempt to implement the electric field control of the adatom magnetic properties. Lastly, we study the Dy adatoms on graphene layers grown on various metals. The vibrational modes of the metallic substrates are shown to strongly affect the Dy spin lifetime, while addition of a second graphene layer does not allow to significantly improve the adatom magnetic stability.

EPFL2022

Recent years have seen spectacular developments in the domain of nano-optics. Alongside the well-known techniques of super-resolution microscopy progress in nanofabrication has enabled important improvements in the fields of optical imaging and spectroscopy. Nowadays enhancements of specific near-field interactions by nano-antennae/cavities allows the optical readout of single molecule properties in a number of different systems. The observation of normal modes of vibration for example carries essential information on the orientation, link to the interface and environment in which the molecule is embedded. This thesis develops firstly a novel theoretical frame for these vibration-cavity interactions by following the optomechanical formalism, which has proven to be an accurate treatment of a wide variety of mechanical systems interacting with a laser field. By leveraging this framework, we investigate on the one hand several quantum limits. On the other hand, for the parameter space experimentally available and for well-designed cavities, novel regimes of interaction between the collective mode of vibration of an ensemble of molecules and an optical tone seem within reach. In parallel, this thesis experimentally explores one specific realization of such a system. In collaboration with the group of Christophe Galland we constructed the optical setups necessary to interrogate our nanostructures. The class of structures constructed, known as self-assembled nanojunctions or nanoparticles on mirror, reaches confinement of electric fields via plasmonic modes close to its fundamental limit and enables the study of many different mechanical systems whose thickness consist in a single molecule. Along this research we have developed techniques to characterize mechanical, electronic and thermal observables of nanojunctions interacting with an optical field. Our experimental study has enabled the discovery of a novel effect related to the electronic confinement of these quasi-0-dimensional structures. The characteristic photoluminescence of metallic nanostructures is found to consistently blink in nanojunctions akin to other quantum emitters. The mechanisms explaining in detail this blinking remain debatable but the numerous experimental data collected highlight the key role of the interface in the specificities of the blinking observed. This finding opens novel ways to characterize the important and to date ill-described question of the interfaces in nanojunctions. The observed modifications of the nanojunctions optical properties might constitute an interesting step towards the development of a novel class of functional materials ('gap-materials') with enhanced and tailored electro-optical properties. The last part of this thesis considers one technological application for this class of material by conceptually developing a new kind of detector based on the upconversion of an infrared photon to the visible; exploiting thus in a unique way the optical properties of the molecular system. The study of the quantum noises of these detectors highlights two exciting and technologically relevant directions for such devices : at room temperature these systems operate with levels of noise below state of the art devices, at lower temperatures these systems open an unexplored path towards single photon detection in a spectral range where this technology remains unavailable to date.

EPFL2020