Conditions aux limites approchées pour des milieux acoustiques à densités exponentielles. Application à l'heliosismologie.

We present equivalent boundary conditions and asymptotic models for the solution of a transmission problem set in a domain which represents the Sun and its atmosphere. This problem models the propagation of an acoustic wave in time-harmonic regime. The specific non-standard feature of this problem lies in the presence of a small parameter $\delta$ which represents the inverse rate of the exponential decay of the density in the atmosphere. The atmosphere can be approximated by local equivalent boundary conditions for small values of this parameter. We derive rigorously equivalent conditions up to the fourth order of approximation with respect to $\delta$ for the exact solution u. The construction of equivalent conditions is based on a multiscale expansion in power series of $\delta$ for u. Numerical results illustrate the good behavior of these equivalent boundary conditions for realistic values close to those observed for the Sun. Finally we measure the boundary layer phenomenon by introducing a "skin depth" function that turns out to depend on the mean curvature of the interface between the subdomains.Nous présentons des conditions aux limites équivalentes et des modèles asymptotiques en vue de la résolution de problèmes de transmission posés dans un domaine représentant le soleil et son atmosphère. Le problème modélise la propagation d'ondes acoustiques en régime harmonique. L'originalité de ce problème réside en la présence d'un petit paramètre $\delta$ qui représente l'inverse du taux de décroissance exponentielle de la masse volumique de l'atmosphère. Celle-ci peut être approchée par des conditions aux limites locales équivalentes pour des petites valeurs de ce paramètre. Nous dérivons rigoureusement des conditions équivalentes jusqu'à l'ordre 4 vis-à-vis de $\delta$ par rapport à la solution exacte u. La construction de conditions équivalentes se base sur un développement multi-échelle en puissances de $\delta$ pour u. Des résultats numériques illustrent le bon comportement de ces conditions aux limites équivalentes pour des valeurs réalistes proches de celles du Soleil. Enfin, nous quantifions un phénomène de couche limite en introduisant une fonction "épaisseur de peau" qui s'avère dépendre de la courbure moyenne de l'interface entre les deux domaines

Acoustic Waves

The concept of acoustic wave is a pervasive one, which emerges in any type of medium, from solids to plasmas, at length and time scales ranging from sub-micrometric layers in microdevices to seismic waves in the Sun's interior. This book presents several aspects of the active research ongoing in this field. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. Acoustic waves are a flexible probe to investigate the properties of very different systems, from thin inorganic layers to ripening cheese to biological systems. Acoustic waves are also a tool to manipulate matter, from the delicate evaporation of biomolecules to be analysed, to the phase transitions induced by intense shock waves. And a whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis

Interferometry of infragravity waves off New Zealand

Author Posting. © American Geophysical Union, 2014. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 119 (2014): 1103-1122, doi:10.1002/2013JC009395.Wave interferometry is a remote sensing technique, which is increasingly employed in helioseismology, seismology, and acoustics to retrieve parameters of the propagation medium from two-point cross-correlation functions of random wavefields. Here we apply interferometry to yearlong records of seafloor pressure at 28 locations off New Zealand's South Island to investigate propagation and directivity properties of infragravity waves away from shore. A compressed cross-correlation function technique is proposed to make the interferometry of dispersive waves more robust, decrease the necessary noise averaging time, and simplify retrieval of quantitative information from noise cross correlations. The emergence of deterministic wave arrivals from cross correlations of random wavefields is observed up to the maximum range of 692 km between the pressure sensors in the array. Free, linear waves with a strongly anisotropic distribution of power flux density are found to be dominant in the infragravity wavefield. Lowest-frequency components of the infragravity wavefield are largely isotropic. The anisotropy has its maximum in the middle of the spectral band and decreases at the high-frequency end of the spectrum. Highest anisotropy peaks correspond to waves coming from portions of the New Zealand's shoreline. Significant contributions are also observed from waves propagating along the coastline and probably coming from powerful sources in the northeast Pacific. Infragravity wave directivity is markedly different to the east and to the west of the South Island. The northwest coast of the South Island is found to be a net source of the infragravity wave energy.The collection of DPG data was supported by the National Science Foundation Continental Dynamics program under grants EAR-0409564, EAR-0409609, and EAR-0409835. This work was supported, in part, by the University of Colorado Seed Grant ‘‘Study of Ocean Infragravity Waves with a Large Array of Seafloor Seismometers,’’ the National Science Foundation award OCE 1129524, and the Office of Naval Research award N00014-13-1–0348.2014-08-1

Helioseismology and diagnostics of internal magnetic layers

Solar magnetic fields, as well as temperature changes, introduce pressure deviations that play a significant role in modulating the resonant frequencies of p-mode oscillations. Those pressure deviations occurring in the atmosphere or sub-surface of the Sun can explain the frequency shifts observed on the timescale of the solar activity cycle. A separate study of the contribution of internal magnetic layers can clarify the relative importance of surface effects. Results from helioseismology provide realistic constraints for choosing parameters suitable to represent the magnetic layers buried in the solar interior and available for modelling, i.e. at the base of the convection zone and in the sunspots’ anchoring zone. Diagnostics of the internal magnetic layers are obtained through a schematic model in which the Sun is plane-stratified. The influence of a buried magnetic field on p-modes is explored, and the nature of various waves and instabilities that can arise on such a buried magnetic field is assessed. By treating the effects of internal magnetic layers, this thesis contributes to the building of a bridge between theories and observations. On the one hand, the theoretical analysis is explored carefully in the course of its formulation, which generates new hypotheses that were not obvious so far. On the other hand, observations help to understand which explanations of the solar cycle frequency shifts may apply

Holography

This book depicts some differences from the typical scientific and technological literature on the theoretical study of holography and its applications. It offers topics that are not very commercial nor known, which will allow a different view of the field of optics. This is evident in chapters such as "Electron Holography of Magnetic Materials", "Polarization Holographic Gratings in Polymer Dispersed Formed Liquid Crystals", and "Digital Holography: Computer-generated Holograms and Diffractive Optics in Scalar Diffraction Domain". The readers will gain a different view of the application areas of holography and the wide range of possible directions that can guide research in the fields of optics

proceedings of a workshop held at Göttingen September 27 - 29, 2006

An international workshop entitled: Modern Solar Facilities - Advanced Solar Science was held in Göttingen from September 27 until September 29, 2006. The workshop, which was attended by 88 participants from 24 different countries, gave a broad overview of the current state of solar research, with emphasis on modern telescopes and techniques, advanced observational methods and results, and on modern theoretical methods of modelling, computation, and data reduction in solar physics. This book collects written versions of contributions that were presented at the workshop as invited or contributed talks, and as poster contributions.Vom 27. bis 29. September 2006 fand in Göttingen ein internationaler Workshop zum Thema: Modern Solar Facilities - Advanced Solar Science statt, der von 88 Teilnehmern aus 24 verschiedenen Ländern besucht wurde und der einen breiten Überblick über den gegenwärtigen Stand der sonnenphysikalischen Forschung gab, unter Betonung moderner Teleskope und Techniken, fortschrittlicher Beobachtungsmethoden und Ergebnisse, sowie zu modernen theoretischen Verfahren der Modellierung, Berechnung und Datenreduktion in der Sonnenphysik. Dieser Band fasst die schriftlichen Versionen von Beiträgen zusammen, die auf der Konferenz als eingeladene oder angemeldete Vorträge, sowie als Posterbeiträge präsentiert worden sind.conferenc

The FIP and Inverse FIP Effects in Solar and Stellar Coronae

We review our state of knowledge of coronal element abundance anomalies in the Sun and stars. We concentrate on the first ionization potential (FIP) effect observed in the solar corona and slow-speed wind, and in the coronae of solar-like dwarf stars, and the "inverse FIP" effect seen in the corona of stars of later spectral type; specifically M dwarfs. These effects relate to the enhancement or depletion, respectively, in coronal abundance with respect to photospheric values of elements with FIP below about 10~eV. They are interpreted in terms of the ponderomotive force due to the propagation and/or reflection of magnetohydrodynamic waves in the chromosphere. This acts on chromospheric ions, but not neutrals, and so can lead to ion-neutral fractionation. A detailed description of the model applied to closed magnetic loops, and to open field regions is given, accounting for the observed difference in solar FIP fractionation between the slow and fast wind. It is shown that such a model can also account for the observed depletion of helium in the solar wind. The helium depletion is sensitive to the chromospheric altitude where ion-neutral separation occurs, and the behavior of the helium abundance in the closed magnetic loop strongly suggests that the waves have a coronal origin. This, and other similar inferences may be expected to have a strong bearing on theories of solar coronal heating. Chromospheric waves originating from below as acoustic waves mode convert, mainly to fast mode waves, can also give rise to ion-neutral separation. Depending on the geometry of the magnetic field, this can result in FIP or Inverse FIP effects. We argue that such configurations are more likely to occur in later-type stars (known to have stronger field in any case), and that this explains the occurrence of the Inverse FIP effect in M dwarfs.Comment: Review paper submitted to Living Reviews in Solar Physics. 74 pages. Some material revised and updated from astro-ph/0405230, arXiv:0901.3350, arXiv:1110.435

Magnetohydrodynamic surface waves in the solar atmosphere

In this thesis the nature of magnetoacoustic surface waves at a single magnetic interface is examined for the case of parallel propagation. Above the interface is an isothermal medium permeated by a horizontal magnetic field. The lower region is a field-free medium of different density to the magnetic atmosphere. We consider both the incompressible and compressible situations and the effect of including gravity. In each case a transcendental dispersion relation is solved numerically for a range of parameters and the resulting dispersion curves plotted. In the first chapter we provide a general introduction to the work, reviewing previous work in this area and considering applications of surface waves. In the second chapter we consider the existence of surface waves for the case when the media are incompressible either side of the interface. We consider the cases of both uniform and non-uniform distributions of densities and the effect of including gravity. We show that the f-mode exists in a restricted band of horizontal wavenumber. In the subsequent chapters we consider the effect of compressibility on surface waves. The media either side of the interface are taken to be isothermal. In the absence of gravity the interface may support one or two surface modes determined by the relative temperatures and magnetism of the two media. This case is studied in Chapter 3 where phase-speeds and penetration depths of the waves and the associated pressure perturbations are investigated for a variety of field strengths and sound speeds. In Chapters 4 and 5 we consider the effect of gravity on the compressible modes described in Chapter 3. In Chapter 4 an exact dispersion relation is obtained for the case of a constant Alfven speed, whilst in Chapter 5 the case of a uniform magnetic field is considered. In the absence of the magnetic field the transcendental dispersion relation may be reduced to a polynomial. This polynomial possesses two acceptable solutions, only one of which may exist at any given circumstance depending on the densities either side of the interface. If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate; otherwise, a magnetic surface gravity mode propagates. As in the incompressible case, the f-mode exists in a restricted band of horizontal wavenumber. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfven speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths