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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
371

Transfert à très haute résolution d'une référence de fréquence ultra-stable par lien optique et application à la stabilisation d'un laser moyen infra-rouge / Ultra-stable frequency transfer with optical link and application to the phase-stabilization of a mid-infrared laser

Chanteau, Bruno 17 December 2013 (has links)
Ce manuscrit présente le transfert d’une référence de fréquence optique ultra-stable à un lien optique et son application à la stabilisation en fréquence d’un laser moyen-infrarouge. Un lien optique permet de transférer une fréquence ultra-stable par fibre optique sans dégrader sa stabilité grâce à une compensation du bruit apportée lors de la propagation. Nous avons étendu cette technique à des liens de grande longueur en transférant la référence de fréquence simultanément avec les données du réseau Internet. Ainsi des liens de 300 km puis 540 km ont été démontrés avec une stabilité de l’ordre de 10⁻ ¹⁹ à 10⁴ s. Ce dispositif à été utilisé au LPL pour asservir un laser CO² émettant à 10 µm sur une référence de fréquence développée au LNE-SYRTE, à l’Observatoire de Paris. Celle-ci est constituée d’un laser ultra-stable émettant à 1,54 µm, dont la fréquence est mesurée par rapport aux étalons primaires du LNE-SYRTE grâce à un laser femtoseconde. Cette référence est transférée par un lien optique jusqu’au LPL où elle permet de stabiliser la fréquence de répétition d’un second laser femtoseconde et de mesurer ou contrôler la fréquence d’un laser CO² . Lorsque celui-ci est asservi sur une référence moléculaire (OsO₄), la stabilité est de 4.10⁻¹⁴ à 1 s. Les performances sont encore meilleures lorsque le laser CO² est asservi directement sur la référence optique. Le laser stabilisé pourra ensuite être utilisé pour l’expérience d’observation de la violation de parité dans les molécules chirales développées au LPL. Ceci démontre la faisabilité d’expériences de spectroscopie moléculaire à ultra haute résolution dans les laboratoires ne disposant pas d’étalons de fréquence. / This manuscript details the transfer of an ultra-stable optical frequency reference by means of an optical link and its application to the phase-lock of a mid-infared laser. An optical fiber link allows the ultra-stable transfer of a frequency by using a scheme wich compensates the propagation noise. We extended this system to longer links, and transferred the optical frequency reference simultaneously witn internet data. A cascaded link of 300 km and a simple link of 540 km had been demonstrated with a stability of 10⁻ ¹⁹ at 10⁴ s. Such a link as been used to lock a CO² laser at LPL, emitting at 10 µm, to a frequency reference developed at LNE-SRTE, Observatoire de Paris. This reference is an ultra-stable laser, emitting at 1.54 µm, the frequency of wich is measured against the primary standards of LNE-SYRTE by using a femtosecond laser. This reference is tranferred by an optical link to LPL, in order to stabilize the repetition rate of a second femtosecondlaser and to measure or control the frenquency of a CO² laser. When the CO² laser is locked to a molecular reference (OsO₄), the stability is 4.10⁻¹⁴ at 1s. The performances are even better when the CO² laser is locked directly to the optical reference. Then the laser coulb be used for the experiment of observation of the parity violation in chiral molecules, in progress at LPL. This shows the feasability of high resolution molecular spectroscopy experiments in laboratoratories in wich there is no primary standards.
372

Optimisation d'une source vibratoire pour la détection des cavités souterraines par sismique réflexion haute résolution / Optimization of a vibratory source for cavity detection by high resolution seismic

Kosecki, Arkadiusz 07 December 2009 (has links)
L’objectif principal de cette thèse est de développer et d’optimiser les outils d’acquisition de la technique de Sismique réflexion haute résolution (SHR) afin d’améliorer ses performances pour la détection des cavités souterraines. Il est communément admis que l’imagerie SHR est d’autant plus complexe que la profondeur de la cible est petite. Les travaux menés dans le cadre de cette thèse devraient remédier à certains problèmes les plus critiques identifiés lors des applications de la SHR.L’utilisation des sources vibratoires présente des avantages indéniables (non destructivité, contrôle du signal émis...) par rapport aux sources « classiques » (i.e. impulsionnelles, destructives) mais leur application optimale nécessite un choix correct du signal émis.Ainsi, les travaux de recherche réalisés ont permis de (1) développer un système complet de pilotage par ordinateur d’une mini-source vibratoire destinée à l’imagerie SHR, (2) développer une méthode de génération de signaux émis. En établissant un lien entre le signal d’entrée et l’image sismique obtenue, cette procédure offre la possibilité à l’utilisateur de choisir le signal émis en fonction des conditions de terrain, et des objectifs des mesures, (3) tester le fonctionnement du système développé avec plusieurs mini-vibrateurs.Le système développé ainsi est testé et validé dans les tests à petite échelle. Ensuite, il a été utilisé dans les conditions réelles avec l’objectif « détection des cavités » dans le contexte salin (anciennes mines de sel en Lorraine, profondeur : 160 m - 180 m) et les marnières de Haute Normandie (anciennes carrières de craie, profondeur : 15 m - 45 m) / The main objective of this thesis is to develop and optimize the acquisition tools for High Resolution Reflection Seismic (HRS) technique in order to improve its performances in the detection of underground cavities. It is commonly admitted that HRS imaging becomes more complicated with when the depth of interest is decreased. The work carried out in the frame of this thesis aims to bring solutions to some of the most critical problems identified in application of the HRS.The vibratory sources show undeniable advantages (non destructivity, controllable output signal) over “classic” (impulsive, destructive) sources. However, the optimal use of these sources depends on the proper choice of emitted signal.Thus, the research work carried out resulted in (1) development of a complete, computer-based vibrator control system allowing piloting small vibratory source intended to use for HRS surveys, (2) development of a method for generating the source signal. The proposed procedure links the entry signal with seismic image and thus allows the choice of the signal in terrain conditions and with regard to the measurement goals, (3) extensive testing of the developed system with several portable vibratory sources.The developed system was tested and validated in small-scale tests. Afterwards it was used in real conditions with the goal of “cavity detection” in salt-mining context (old salt mines in Lorraine region at depths between 160 m and 180 m) as well as in chalk-mining area (ancient marl-pit quarries in the Normandy region at depths 15 m - 45 m)
373

The Study of Tissue-Specific DNA Methylation as a Method for the Epigenetic Discrimination of Forensic Samples

Antunes, Joana AP 21 November 2017 (has links)
In forensic sciences, the serological methods used to determine which body fluid was collected from the crime scene are merely presumptive or labor intensive since they rely on protein detection or on microscopic identification of cells. Given that certain forensic cases may need the precise identification of a body fluid to determine criminal contact, such is the example of a suspected sexual assault of a minor; certainty in the body fluid of origin may depict a precise picture of the events. The identification of loci that show differences in methylation according to the tissue of origin can aid forensic analysts in determining the origin of a DNA sample. The process of DNA methylation occurs naturally in the genome of living organisms and consists in the presence of a methyl group on the carbon 5 of a cytosine, which is typically followed by a guanine (CpG). Analyzing patterns of DNA methylation in body fluids collected from a crime scene is preferential to the analysis of proteins or mRNA since the same extracted DNA used for STR typing can be used for DNA methylation analysis. We have validated and identified loci able to discriminate blood, saliva, semen and vaginal epithelia. In the current study, we have also established the minimum amount of DNA able to provide reliable results using methodologies such as pyrosequencing and high-resolution melt (HRM) analysis for the different markers identified. Lastly, we performed an alternative bioinformatic analysis of data collected using an array that studied methylation in over 450,000 individual cytosines on the human genome. We were able to sort the locations that showed potentially higher methylation differences between body fluids and investigated over 100 of them using HRM analysis. The results of that study, allowed the identification of three new loci able to distinguish blood and two new loci able to distinguish saliva and vaginal epithelia, respectively. The use of DNA methylation patterns to aid forensic investigations started with a publication in 2010, therefore each small contribution such as this work may, similarly to what occured in the biochemistry field, result in the discovery of a method able to put the technology in the hands of forensic analysts.
374

Analyse/Synthèse tridimensionnelle de textures fibreuses / Tridimensional analysis and synthesis of fibrous texture

Chapoullie, Cedric 10 September 2014 (has links)
Cette thèse s‘inscrit dans le contexte de l‘étude de matériaux fibreux tissés et traite de l‘analyse morphologique de leur texture et de la simulation des arrangements des fibres dans un fil. Le volet « analyse » consiste à extraire des données caractérisant la géométrie des fibres et des fils composant le renfort tissé et s‘appuie sur des images tridimensionnelles issues de tomographies rayon X à haute résolution. Une chaine de traitement d‘images visant à séparer et identifier les fils et les fibres est proposée. Elle s‘appuie sur un algorithme de labellisation du fil et des fibres. Les caractéristiques telles que les diamètres et les orientations de fibres et la densité locale de fibres dans le fil sont ensuite calculées. Le volet « simulation » vise à générer un renfort fibreux « virtuel ». Un algorithme fondé sur la résolution de modèles dynamiques permet de placer au sein d‘un fil, des objets représentant les fibres tout en respectant des contraintes issues des paramètres issus du volet « analyse » ou choisis arbitrairement par l‘utilisateur. L‘ensemble des fibres composant le fil sont alors synthétisés en respect de ces contraintes. Ces deux volets sont appliqués avec succès à la caractérisation et à la synthèse de renforts fibreux de composites thermostructuraux. Les caractéristiques géométriques, estimées sur des tomographies à haute résolution, font ressortir des phénomènes tels que le cisaillement intra fils. La synthèse permet de simuler le placement de fibres à partir de paramètres géométriques obtenus à haute résolution, au sein d‘un fil dont l‘enveloppe est obtenue à basse résolution et donc sur une longueur plus représentative du tissage. / The aim of this work is to study fibrous woven materials and to develop morphological analysis of their texture enabling simulation of fibrous layout in yarns. The ―analysis‖ stage consists in data extraction to characterize the geometry of fibers and yarns constituting the woven material, based on tridimensional images generated by high resolution X-ray tomography. An image processing workflow to separate and identify fibers and yarn is proposed. Then, diameters, fiber orientations and local fiber density in yarns are computed. The ―simulation‖ stage targets to generate virtual fibrous materials. An algorithm based on the resolution of a dynamic model allows placing objects representing fibers into a yarn. It uses as input the characteristic parameters previously extracted in the analysis stage or arbitrarily chosen ones. Consequently, all fibers are synthesized according to these constraints. These two stages are successfully applied to characterize and synthesize woven ceramic matrix composites. Geometrical characteristics, extracted from the high-resolution tomographic images, highlight yarn phenomena like shearing planes. The synthesis simulates fibers placement, merging geometrical parameters extracted on high and low resolution. Indeed, using fiber parameters extracted from high resolution images and yarn envelopes from low resolution ones enable generating a result with a more representative woven length.
375

Developing land management units using Geospatial technologies: An agricultural application

Warren, Georgina January 2007 (has links)
This research develops a methodology for determining farm scale land managementunits (LMUs) using soil sampling data, high resolution digital multi-spectral imagery (DMSI) and a digital elevation model (DEM). The LMUs are zones within a paddock suitable for precision agriculture which are managed according to their productive capabilities. Soil sampling and analysis are crucial in depicting landscape characteristics, but costly. Data based on DMSI and DEM is available cheaply and at high resolution.The design and implementation of a two-stage methodology using a spatiallyweighted multivariate classification, for delineating LMUs is described. Utilising data on physical and chemical soil properties collected at 250 sampling locations within a 1780ha farm in Western Australia, the methodology initially classifies sampling points into LMUs based on a spatially weighted similarity matrix. The second stage delineates higher resolution LMU boundaries using DMSI and topographic variables derived from a DEM on a 10m grid across the study area. The method groups sample points and pixels with respect to their characteristics and their spatial relationships, thus forming contiguous, homogenous LMUs that can be adopted in precision agricultural applications. The methodology combines readily available and relatively cheap high resolution data sets with soil properties sampled at low resolution. This minimises cost while still forming LMUs at high resolution.The allocation of pixels to LMUs based on their DMSI and topographic variables has been verified. Yield differences between the LMUs have also been analysed. The results indicate the potential of the approach for precision agriculture and the importance of continued research in this area.
376

High-Resolution Studies of Silicide-films for Nano IC-Components

Jarmar, Tobias January 2005 (has links)
<p>The function of titanium- and nickel-silicides is to lower the series resistance and contact resistivity in gate, source and drain contacts of an integrated circuit transistor. </p><p>With decreasing dimensions, the low resistivity C54 TiSi<sub>2</sub> is not formed and stays in its high resistivity phase C49. It was found that a layer of niobium interposed between titanium and silicon, which is supposed to promote the C54 phase, led to the formation of the high resistivity C40 (Ti,Nb)Si<sub>2</sub> in both small and large contacts. </p><p>Increased interest in Si<sub>1-x</sub>Ge<sub>x</sub> layers led to the inclusion of the Ni-Si-Ge system in this project. The interaction between nickel and poly-Si<sub>0.42</sub>Ge<sub>0.58</sub> was found to be different from nickel and poly-silicon in the meaning of the phases formed during high temperature annealing. High-resistivity NiSi<sub>2</sub> was formed at 750°C, but nickel and Si<sub>0.42</sub>Ge<sub>0.58</sub> formed no disilicide. A massive out-diffusion of germanium from the NiSi<sub>1-u</sub>Ge<sub>u</sub> resulted in agglomeration at lower temperatures than for NiSi. This was ascribed to the larger enthalpy of formation for nickel reacting with silicon than with germanium. Ternary phase diagrams, with and without the disilicide phase, were calculated. According to the tie lines, NiSi<sub>1-u</sub>Ge<sub>u</sub> will be in thermodynamic equilibrium with Si<sub>1-x</sub>Ge<sub>x</sub> when u is smaller than x. This was confirmed experimentally, where a balanced germanium concentration in NiSi<sub>1-u</sub>Ge<sub>u</sub> and Si<sub>1-x</sub>Ge<sub>x</sub>, stabilized the germanosilicide. When nickel interacted with strained and relaxed silicon-germanium it was established that a strained substrate led to a morphologically unstable NiSi<sub>1-u</sub>Ge<sub>u</sub>. The germanosilicide was highly textured on both (001) and (111) substrates. The texturing was explained by the absence of Ni(SiGe)<sub>2</sub> which forced NiSiGe to reorient so as not to resemble a digermanosilicide at the film/substrate interface. NiSi<sub>0.82</sub>Ge<sub>0.18</sub> formed on p<sup>+</sup>-Si<sub>0.82</sub>Ge<sub>0.18</sub> in CBKs grew laterally under the SiO<sub>2</sub>, defining the contact hole. The contact resistivity extracted by 3D modelling was 5×10<sup>-8</sup> Ωcm<sup>2</sup>.</p>
377

Convectively-Generated Potential Vorticity in Rainbands and Secondary Eyewall Formation in Hurricanes

Judt, Falko 01 January 2009 (has links)
Concentric eyewall formation and eyewall replacement cycles are intrinsic processes that determine the intensity of a tropical cyclone, as opposed to purely environmental factors such as wind shear or the ocean heat content. Although extensive research has been done in this area, there is not a single widely accepted theory on the formation of secondary eyewall structures. Many previous studies focused on dynamic processes in the inner core of a tropical cyclone that would precede and ultimately lead to the formation of a secondary eyewall. Hurricanes Katrina and Rita in 2005 were frequently sampled by research aircraft which gathered a copious amount of data. During this time, Rita developed a secondary eyewall which eventually replaced the original eyewall. This thesis will investigate the formation of a secondary eyewall with particular emphasis on the rainband region, as observations show that an outer principal rainband transformed into the secondary ring. A high resolution, full physics model (MM5) initialized with global model forecast fields correctly predicted the secondary eyewall formation in Rita. The model output will be used to investigate both Katrina and Rita in terms of their PV generation characteristics since PV and vorticity maxima correlate well with wind maxima that accompany the eyewall and rainbands. Furthermore, dynamical processes such as vortex Rossby wave (VRW) activity in the inner core region will be analyzed. Comparison of the differences in the two storms might shed some light on dynamics that can lead to structure changes. Comparison of the model data with aircraft observation is used to validate the results. Doppler radar derived wind fields will be used to calculate the vertical vorticity. The vorticity field is closely related to PV and thus a manifestation of the PV generation process in the rainband. The investigation has shown that Rita?s principal rainband features higher PV generation rates at radii beyond 80 km. Both the azimuthal component and the projection of asymmetric PV generated by convection onto the azimuthal mean connected with the principal band are hypothesized to be of importance for the formation of the secondary eyewall. VRW were found not to be important for the initial formation of the ring but might enhance convective activity once the outer eyewall contracts.
378

Quantitative infrared Fourier transform spectroscopy: absolute intensities for 13CO2 and HOBr/Spectroscopie quantitative par transformée de Fourier dans le domaine infrarouge: intensités absolues pour 13CO2 et HOBr.

Deleporte, Thomas 19 December 2008 (has links)
This thesis falls within the field of high resolution Fourier transform spectroscopy of gas phase molecules in the far to near infrared ranges. It is focused on quantitative aspects of gas phase spectroscopy: absolute line intensity measurements. Both stable and unstable molecules, of atmospheric interest, are investigated. With this work, we aim to provide the reference spectroscopic information needed to analyze spectra of planetary atmospheres and improve our understanding of the physical chemistry of these environments. We studied two molecules of atmospheric interest: the 13C16O2 isotopologue of carbon dioxide, which is a stable molecule, and the H16O79Br and H16O81Br isotopologues of hypobromous acid which are short-lived unstable molecules. The work carried out in the 2 and 1.6 µm regions of 13C16O2 falls in the framework of highly precise remote sensing of carbon dioxide in the Earth’s atmosphere, needing more and more accurate reference spectroscopic information. We measured 872 absolute line intensities corresponding to 317 different lines in seven vibration-rotation bands of 13C16O2. These measurements, together with measurements performed in the Laboratoire de Spectrométrie Physique (Université Joseph Fourier, Grenoble, France) led to the improvement of the theoretical description of the spectrum of carbon dioxide, performed in the Laboratory of Theoretical Spectroscopy, (Institute of Atmospheric Optics, Tomsk, Russia). This study is preceeded by a preliminary work on the main isotopologue of carbon dioxide, 12C16O2 in the same spectral regions, aimed to determine the best suited line profile to model the observed line shapes of 13C16O2. HOBr exists only in equilibrium with its decomposition products, like Br2O and H2O. Quantitative spectroscopy on such an unstable molecule therefore implied the use of a specific method to determine the concentration of HOBr in the studied gas sample. Simultaneously, Tunable Diode Laser (TDL) infrared spectra of some lines of the nu2 band and a far infrared Fourier transform spectrum of pure rotation lines of HOBr were recorded. The measured intensities of pure rotation lines together with the permanent electric dipole moment of the molecule were used to determine the partial pressure of HOBr, thus allowing absolute intensities of the lines probed by the TDL to be determined. These infrared absolute line intensities were then used to “calibrate” the relative line intensities in the nu2 band, measured in a Fourier transform spectrum recorded separately. Cette thèse s’inscrit dans le cadre de la spectroscopie è haute résolution de molécules en phase gazeuse dans l’infrarouge proche à lointain. Ce travail se concentre sur les aspects quantitatifs de la spectroscopie en phase gazeuse: la mesure d’intensités absolues. Des molécules d’interêt atmosphérique stables et instables ont été étudiées. Le but de ce travail est de fournir des informations spectroscopiques de référence utiles à l’analyse de spectres d’atmosphères planétaires et, ainsi, améliorer notre compréhension de la physico-chimie de ces environnements. Nous avons étudié deux molécules d’interêt atmosphérique: l’isotopologue 13C16O2 du dioxyde de carbone, qui est une molécule stable, et les isotopologues H16O79Br et H16O81Br de l’acide hypobromeux qui sont des molécules instables. Le travail effectué sur les régions spectrales à 2 et 1.6 µm de 13C16O2 s’inscrit dans le cadre des mesures à distance à très haute précision du dioxyde de carbone présent dans l’atmosphère terrestre. Nous avons mesuré 872 intensités absolues correspondant à 317 raies d’absorption dans sept bandes de vibration-rotation de 13C16O2. Ces mesures, ainsi que celles réalisées au Laboratoire de Spectrométrie Physique (Université Joseph Fourier, Grenoble, France) ont abouti à l’amélioration de la description théorique du spectre du dioxyde de carbone, réalisée au Laboratory of Theoretical Spectroscopy (Institute of Atmospheric Optics, Tomsk, Russie). Cette étude est précédée par un travail préliminaire sur l’isotopologue principal du dioxyde de carbone, 12C16O2 dans les mêmes régions spectrales, visant à déterminer le profil de raie le plus adapté pour modéliser les profils observés de 13C16O2. HOBr existe uniquement en équilibre avec ses produits de décomposition tels que Br2O and H2O. Effectuer des mesures quantitatives pour ce type de molécule instable implique dès lors l’utilisation d’une technique spécifique afin de déterminer la pression partielle de HOBr. Un spectre infrarouge en Diode Laser Accordable (DLA) de quelques raies de la bande nu2 de HOBr et un spectre infrarouge lointain en transformée de Fourier d’un même échantillon gazeux ont été enregistrés simultanément. Les intensités mesurées de raies de rotation pure combinées au moment dipolaire électrique permanent de la molécule ont été utilisées pour déterminer la pression partielle de HOBr, nous permettant ainsi de déterminer les intensités absolues des raies mesurées à l’aide de la DLA. Ces intensit´es absolues ont ensuite été utilisées pour “calibrer” les intensités relatives des raies de la bande nu2, mesurées dans un spectre à transformée de Fourier enregistré séparément.
379

High-Resolution Studies of Silicide-films for Nano IC-Components

Jarmar, Tobias January 2005 (has links)
The function of titanium- and nickel-silicides is to lower the series resistance and contact resistivity in gate, source and drain contacts of an integrated circuit transistor. With decreasing dimensions, the low resistivity C54 TiSi2 is not formed and stays in its high resistivity phase C49. It was found that a layer of niobium interposed between titanium and silicon, which is supposed to promote the C54 phase, led to the formation of the high resistivity C40 (Ti,Nb)Si2 in both small and large contacts. Increased interest in Si1-xGex layers led to the inclusion of the Ni-Si-Ge system in this project. The interaction between nickel and poly-Si0.42Ge0.58 was found to be different from nickel and poly-silicon in the meaning of the phases formed during high temperature annealing. High-resistivity NiSi2 was formed at 750°C, but nickel and Si0.42Ge0.58 formed no disilicide. A massive out-diffusion of germanium from the NiSi1-uGeu resulted in agglomeration at lower temperatures than for NiSi. This was ascribed to the larger enthalpy of formation for nickel reacting with silicon than with germanium. Ternary phase diagrams, with and without the disilicide phase, were calculated. According to the tie lines, NiSi1-uGeu will be in thermodynamic equilibrium with Si1-xGex when u is smaller than x. This was confirmed experimentally, where a balanced germanium concentration in NiSi1-uGeu and Si1-xGex, stabilized the germanosilicide. When nickel interacted with strained and relaxed silicon-germanium it was established that a strained substrate led to a morphologically unstable NiSi1-uGeu. The germanosilicide was highly textured on both (001) and (111) substrates. The texturing was explained by the absence of Ni(SiGe)2 which forced NiSiGe to reorient so as not to resemble a digermanosilicide at the film/substrate interface. NiSi0.82Ge0.18 formed on p+-Si0.82Ge0.18 in CBKs grew laterally under the SiO2, defining the contact hole. The contact resistivity extracted by 3D modelling was 5×10-8 Ωcm2.
380

A Variable Resolution Global Spectral Method With Finer Resolution Over The Tropics

Janakiraman, S 08 1900 (has links)
Variable resolution method helps to study the local scale phenomenon of interest within the context of global scale atmosphere/ocean dynamics. Global spectral methods based on spherical harmonics as basis functions are known to resolve a given function defined on the sphere, in an uniform manner. Though known for its mathematical elegance and higher order accuracy, global spectral methods are considered to be restrictive for developing mesh-refinement strategies. The only mesh refinement strategy available until now is due to the pioneering work of F. Schmidt. Schmidt transformation can study only one region with higher resolution. The study of tropical dynamics is an interesting theme due to the presence of teleconnections between various phenomena, especially Indian Monsoon and the El-Nino. The Inter-Tropical Convergence Zone (ITCZ)is a continental scale phenamenon. It is in the ITCZ, many monsoon systems and tropical cyclones do occur. To study such phenomena under variable resolution method, high resolution is required in the entire tropical belt. Hitherto such a kind of mesh refinement strategies were not available in global spectral models. In this work, a new variable resolution method is developed that can help to study the tropical sub-scale phenomena with high resolution, in global spectral models. A new conformal coordinate transformation named ’High resolution Tropical Belt Transformation(HTBT)’ is developed to generate high resolution in the entire tropical belt. Mathematical demonstrations are given to show the existence of additional conformal transformations available on the sphere, indicating additional degrees of freedom available to create variable resolution global spectral method. Variable resolution global spectral method with high resolution over tropics is created through HTBT. The restriction imposed by Schmidt’s framework that the map-ping factor of the transformation need to have a finite-decomposition in the spectral space of the transformed domain is relaxed, by introduction of a new framework. The new framework uses transformed spherical harmonics Bnm as basis for spectral computations. With the use of FFT algorithm and Gaussian quadrature, the efficiency of the traditional spectral method is retained with the variable resolution global spectral method. The newly defined basis functions Bnm are the eigenvalues of the transformed Laplacian operator . This property of Bnm provide an elegant direct solver for the transformed Helmholtz operator on the sphere. The transformed Helmholtz equations are solved accurately with the variable resolution method. Advection experiments conducted with variable resolution spectral transport scheme on the HTBT variable grid produces near-dispersion free advection on the tropical belt. Transport across homogeneous resolution regions produce very less dispersion errors. Transport of a feature over the poles result in severe grid representation errors. It is shown that an increase in resolution around the poles greatly reduces this error. Transport of a feature from a point close to poles but not over it, does not produce such representation errors. Fourth-order Runge-Kutta scheme improves the accuracy of the transport scheme. The second order Magazenkov time-scheme proves to be better accurate than the leap-frog scheme with Asselin filter. The non-divergent barotropic vorticity equation is tested with two exact solutions namely Rochas solution and Rossby-Haurwitz wave solutions. Each of the solution tests certain unique and contrasting characteristic of the system. The numerical behaviour of the solutions show non-linear interactions in them. The singularity at the poles, arising due to the unbounded nature of the latitudinal derivative of the map factor of HTBT, triggers Gibbs phenomena for certain functions. However the recent advances in spectral methods, especially spectral viscosity method and Boyd-Vandeven filtering strategy provide ways to control the Gibbs oscillation and recover higher accuracy; make the variable resolution global spectral method viable for accurate meteorological computations.

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