Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Studies of Solar Activity with Emphasis on Quasi-Periodic Oscillations

In this thesis mainly long quasi-periodic solar oscillations in various solar atmospheric structures are discussed, based on data obtained at several wavelengths, focussing, however, mainly on radio frequencies. Sunspot (Articles II and III) and quiet Sun area (QSA) (Article I) oscillations are investigated along with quasi-periodic pulsations (QPP) in a flaring event with wide-range radio spectra (Article IV). Various oscillation periods are detected; 3–15, 35–70 and 90 minutes (QSA), 10-60 and 80-130 minutes (in sunspots at various radio frequencies), 3-5, 10-23, 220-240, 340 and 470 minutes (in sunspots at photosphere) and 8-12 and 15-17 seconds (in a solar flare at radio frequencies). Some of the oscillation periods are detected for the first time, while some of them have been confirmed earlier by other research groups. Solar oscillations can provide more information on the nature of various solar structures. This thesis presents the physical mechanisms of some solar structure oscillations. Two different theoretical approaches are chosen; magnetohydrodynamics (MHD) and the shallow sunspot model. These two theories can explain a wide range of solar oscillations from a few seconds up to some hours. Various wave modes in loop structures cause solar oscillations (<45 minutes) both in sunspots and quiet Sun areas. Periods lasting more than 45 minutes in the sunspots (and a fraction of the shorter periods) are related to sunspot oscillations as a whole. Sometimes similar oscillation periods are detected both in sunspot area variations and respectively in magnetic field strength changes. This result supports a concept that these oscillations are related to sunspot oscillations as a whole. In addition, a theory behind QPPs at radio frequencies in solar flares is presented. The thesis also covers solar instrumentation and data sources. Additionally, the data processing methods are presented. As the majority of the investigations in this thesis focus on radio frequencies, also the most typical radio emission mechanisms are presented. The main structures of the Sun, which are related to solar oscillations, are also presented. Two separate projects are included in this thesis. Solar cyclicity is studied using the extensively large solar radio map archieve from Metsähovi Radio Observatory (MRO) at 37 GHz, between 1978 and 2011 (Article V) covering two full solar cycles. Also, some new solar instrumentation (Article VI) was developed during this thesis.

Fracture modes and acoustic emission characteristics of hydrogen-assisted cracking in high-strength low-alloy steel weldment

The aim of the present paper is to study the relationship between the fracture modes in hydrogen-assisted cracking (HAC) in microalloied steel and the emission of acoustic signals during the fracturing process. For this reason, a flux-cored arc weld (FCAW) was used in a high-strength low-alloy steel. The consumable used were the commercially available AWS E120T5-K4 and had a diameter of 1.6 mm. Two different shielding gases were used (CO2 and CO2+5% H2) to obtain complete phenomenon characterization. The implant test was applied with three levels of restriction stresses. An acoustic emission measurement system (AEMS) was coupled to the implant test apparatus. The output signal from the acoustic emission sensor was passed through an electronic amplifier and processed by a root mean square (RMS) voltage converter. Fracture surfaces were examined by scanning electron microscopy (SEM) and image analysis. Fracture modes were related with the intensity, the energy and the number of the peaks of the acoustic emission signal. The shielding gas CO2+5% H2 proved to be very useful in the experiments. Basically, three different fracture modes were identified in terms of fracture appearance: microvoid coalescence (MVC), intergranular (IG) and quasi-cleavage (QC). The results show that each mode of fracture presents a characteristic acoustic signal.

The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halide molecules /

TITLE: The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halides. AUTHOR: J. L. Brema SUPERVISOR: Dr. D. C. Moule NUMBER OF PAGES: 89 ABSTRACT: The vibrational assignment of the five-in-plane fundamental modes of CSClBr has been made on the basis of infrared gas phase and liquid Raman spectral analyses to supplement our earlier vibrational studies. Even though the one out-of-plane fundamental was not observed spectroscopically an attempt has been made to predict its frequency. The vibrational spectra contained impurity bands and the CSClBr assignment was made only after a thorough analysis of the impurities themselves. A normal co-ordinate analysis calculation was performed assuming a Urey-Bradley force field. This calculation yielded the fundamental frequencies in good agreement with those observed after refinement of the originally transferred force constants. The theoretical frequencies are the eigenvalues of the secular equation and the calculation also gave the corresponding eigenvectors in the form of the very important LLj matrix. The [l] matrix is the transfoirmation between internal co-ordinates and normal co-ordinates and it is essential for Franck-Condon calculations on electronically excited molecules and for infrared Integrated band intensity studies. Using a self-consistent molecular orbital calculation termed "complete neglect of differential overlap" (CNDO/2) , theoretical values of equilibrium bond lengths and angleswere calcuted for a series of carbonyl and thlocarbonyl molecules. From these calculations valence force field force constants were also determined but with limited success. With the CNIX)/2 method theoretical dipole moment derivatives with respect to symmetrized internal co-ordinates were calculated and the results should be useful in a correlation with experimentally determined values.

Le droit au respect des modes de vie minoritaires et autochtones dans les contentieux internationaux des droits de l'homme

Thèse de doctorat réalisée en cotutelle avec la Faculté de droit de l'Université Aix-Marseille 3.

Les modes de conceptualisation métaphorique en neuroanatomie : étude de la description anatomique du cervelet et de la moelle spinale

La présente étude s’inscrit dans une lignée de travaux de recherche en traductologie réalisés dans un cadre de sémantique cognitive et visant à dégager les modes de conceptualisation métaphorique dans les domaines de spécialité, et plus précisément dans les sciences biomédicales. Notre étude se concentre sur les modes de conceptualisation métaphorique utilisés en neuroanatomie en français, en anglais et en allemand, dans une perspective d’application à la traduction. Nous nous penchons plus spécifiquement sur la description anatomique de deux structures du système nerveux central : la moelle spinale et le cervelet. Notre objectif est de repérer et de caractériser les indices de conceptualisation métaphorique (ICM). Notre méthode s'appuie sur un corpus trilingue de textes de référence traitant de ces structures et fait appel à une annotation sémantique en langage XML, ce qui autorise une interrogation des corpus annotés au moyen du langage XQuery. Nous mettons en évidence que les ICM jouent un rôle prédominant dans la phraséologie et les dénominations propres à la description anatomique du système nerveux, comme c'est le cas en biologie cellulaire et en anatomie des muscles, des nerfs périphériques et des vaisseaux sanguins. Sous l’angle lexical, il faut distinguer les ICM prédicatifs, les ICM non prédicatifs ainsi que les ICM quasi prédicatifs. La plupart des modes de conceptualisation métaphorique préalablement repérés en biologie cellulaire et en anatomie sont également présents dans le domaine plus spécifique de la neuroanatomie. Certains ICM et modes de conceptualisation sont toutefois spécifiques à des éléments des régions étudiées. Par ailleurs, les modes de conceptualisation métaphorique en français, en anglais et en allemand sont semblables, mais sont exprimés par des réseaux lexicaux d'ICM dont la richesse varie. De plus, la composition nominale étant une des caractéristiques de l'allemand, la forme linguistique des ICM présente des caractéristiques spécifiques. Nos résultats mettent en évidence la richesse métaphorique de la neuroanatomie. Cohérents avec les résultats des études antérieures, ils enrichissent cependant la typologie des ICM et soulignent la complexité, sur les plans lexical et cognitif, de la métaphore conceptuelle.

On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. $F\,{>}\,F_\mathrm{critical}\,{\equiv}\, \upi^2/2$), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia–gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baro-clinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin–Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. $\hbox{\it Ri}\,{<}\,\hbox{\it Ri}_\mathrm{critical}\,{\equiv}\, 1$), and are therefore consistent with generation by a Kelvin–Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia–gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia–gravity waves generated by spontaneous adjustment of the large-scale flow.

Local modes and x,K relations for ethene and propadiene

The results recently obtained by Mills and Robiette on local-mode effects in H2O, NH3 and CH4 type molecules are extended to ethene (C2H4) and propadiene (C3H4) type molecules. General relations among the anharmonic xrs constants and the Darling-Dennison Krrss constants for the stretching vibrations are derived, called “x,K relations”, which allow local-mode effects to be generated by adding the appropriate anharmonic and Darling-Dennison constants to the familiar normal-mode model of molecular vibrations. The general utility of x,K relations is discussed, and the results are reviewed for the molecular types for which they have so far been derived.

C–H local modes in cyclobutene. II. Laser photoacoustic studies 10 000–17 000 cm−1. Vibrational structure and C–H local mode dynamics

In part I of this study [Baggott, Clase, and Mills, Spectrochim. Acta Part A 42, 319 (1986)] we presented FTIR spectra of gas phase cyclobutene and modeled the v=1–3 stretching states of both olefinic and methylenic C–H bonds in terms of a local mode model. In this paper we present some improvements to our original model and make use of recently derived ‘‘x,K relations’’ to find the equivalent normal mode descriptions. The use of both the local mode and normal mode approaches to modeling the vibrational structure is described in some detail. We present evidence for Fermi resonance interactions between the methylenic C–H stretch overtones and ring C–C stretch vibrations, revealed in laser photoacoustic spectra in the v=4–6 region. An approximate model vibrational Hamiltonian is proposed to explain the observed structure and is used to calculate the dynamics of the C–H stretch local mode decay resulting from interaction with lower frequency ring modes. The implications of our experimental and theoretical studies for mode‐selective photochemistry are discussed briefly.

Local mode and normal mode interpretations of the CH and CD stretching vibrational manifolds of 1,1-dideuteroethene

The =CH2 AND =CD2 stretching vibrational overtones of H2C=CD2 have been studied up to V= 6 and V= 3, respectively. We report their interpretation in terms of a transition from normal to local modes, involving Fermi resonance with the C=C stretching and CH2 scissoring vibrations. We discuss the alternative representation of the vibrational Hamiltonian matrix in local mode and normal mode basis functions, and conclude that the normal mode basis offers greater flexibility in representing small anharmonic couplings with other modes.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere

During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.

Annular modes and apparent eddy feedbacks in the Southern Hemisphere

Lagged correlation analysis is often used to infer intraseasonal dynamical effects but is known to be affected by non-stationarity. We highlight a pronounced quasi-two-year peak in the anomalous zonal wind and eddy momentum flux convergence power spectra in the Southern Hemisphere, which is prima facie evidence for non-stationarity. We then investigate the consequences of this non-stationarity for the Southern Annular Mode and for eddy momentum flux convergence. We argue that positive lagged correlations previously attributed to the existence of an eddy feedback are more plausibly attributed to non-stationary interannual variability external to any potential feedback process in the mid-latitude troposphere. The findings have implications for the diagnosis of feedbacks in both models and re-analysis data as well as for understanding the mechanisms underlying variations in the zonal wind.

From decoherence-free channels to decoherence-free and quasi-free subspaces within bosonic dissipative networks

We present a technique to build, within a dissipative bosonic network, decoherence-free channels (DFCs): a group of normal-mode oscillators with null effective damping rates. We verify that the states protected within the DFC define the well-known decoherence-free subspaces (DFSs) when mapped back into the natural network oscillators. Therefore, our technique to build protected normal-mode channels turns out to be an alternative way to build DFSs, which offers advantages over the conventional method. It enables the computation of all the network-protected states at once, as well as leading naturally to the concept of the decoherence quasi-free subspace (DQFS), inside which a superposition state is quasi-completely protected against decoherence. The concept of the DQFS, weaker than that of the DFS, may provide a more manageable mechanism to control decoherence. Finally, as an application of the DQFSs, we show how to build them for quasi-perfect state transfer in networks of coupled quantum dissipative oscillators.