937 resultados para Odd third order intensity parameters
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We propose a new mechanism of high-order harmonic generation during an interaction of a high-intensity laser pulse with underdense plasma. A tightly focused laser pulse creates a cavity in plasma pushing electrons aside and exciting the wake wave and the bow wave. At the joint of the cavity wall and the bow wave boundary, an annular spike of electron density is formed. This spike surrounds the cavity and moves together with the laser pulse. Collective motion of electrons in the spike driven by the laser field generates high-order harmonics. A strong localization of the electron spike, its robustness to oscillations imposed by the laser field and, consequently, its ability to produce high-order harmonics is explained by catastrophe theory. The proposed mechanism explains the experimental observations of high-order harmonics with the 9 TW J-KAREN laser (JAEA, Japan) and the 120 TW Astra Gemini laser (CLF RAL, UK) [A. S. Pirozhkov, et al., arXiv:1004.4514 (2010); A. S. Pirozhkov et al, AIP Proceedings, this volume]. The theory is corroborated by high-resolution two- and three-dimensional particle-in-cell simulations.
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We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix ?1, ?2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.
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We employ the time-dependent R-matrix (TDRM) method to calculate anisotropy parameters for positive and negative sidebands of selected harmonics generated by two-color two-photon above-threshold ionization of argon. We consider odd harmonics of an 800-nm field ranging from the 13th to 19th harmonic, overlapped by a fundamental 800-nm IR field. The anisotropy parameters obtained using the TDRM method are compared with those obtained using a second-order perturbation theory with a model potential approach and a soft photon approximation approach. Where available, a comparison is also made to published experimental results. All three theoretical approaches provide similar values for anisotropy parameters. The TDRM approach obtains values that are closest to published experimental values. At high photon energies, the differences between each of the theoretical methods become less significant.
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The measurements reported here provide scaling laws for the ion acceleration process in the regime of ultrashort (50 fs), ultrahigh contrast (10) and ultrahigh intensity (> 10W/cm ), never investigated previously. The scaling of the accelerated ion energies was studied by varying a number of parameters such as target thickness (down to 10nm), target material (C and Al) and laser light polar- ization (circular and linear) at 35° and normal laser incidence. A twofold increase in proton energy and an order of magnitude enhancement in ion flux have been observed over the investigated thickness range at 35° angle of incidence. Further- more, at normal laser incidence, measured peak proton energies of about 20 MeV are observed almost independently of the target thickness over a wide range (50nm- 10 µm). 1. © 2012 by Società Italiana di Fisica.
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Using low-energy electron-diffraction (LEED) formalism, we demonstrate theoretically that LEED I-V spectra are characterized mainly by short-range order. We also show experimentally that diffuse LEED (DLEED) I-V spectra can be accurately measured from a disordered system using a video-LEED system even at very low coverage. These spectra demonstrate that experimental DLEED I-V spectra from disordered systems may be used to determine local structures. As an example, it is shown that experimental DLEED I-V spectra from K/Co {1010BAR} at potassium coverages of 0.07, 0.1, and 0.13 monolayer closely resemble calculated and experimental LEED I-V spectra for a well-ordered Co{1010BAR}-c(2X2)-K superstructure, leading to the conclusion that at low coverages, potassium atoms are located in the fourfold-hollow sites and that there is no large bond-length change with coverage.
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RESUMO: Os mais recentes métodos de neuro imagem tal como a Ressonância Magnética (RM) permitiram obter imagens detalhadas do cérebro humano in vivo. Essas imagens revelam, muitas vezes, achados imprevistos face ao padrão normal, com elevada propensão para os indivíduos idosos e franca coexistência com fatores de risco vascular, como característica dum processo de envelhecimento normal. Embora na última década tenham surgido várias publicações sobre este assunto, ele continua ainda pouco explicado. Um pouco por todo o mundo têm emergido os programas de prevenção da doença e promoção da saúde desenvolvidos pela Saúde Pública suportadas sobretudo pelo avanço das tecnologias médicas que resultaram, entre outros impactos, num crescimento da população idosa. Estima-se, em 2030, uma composição demográfica com 20% de indivíduos acima dos 65 anos. Neste contexto, a doença microvascular cerebral é a causa mais frequente de comprometimento cognitivo vascular no idoso sendo as características senescentes na imagem por RM do tipo lesões isquémicas da Substância Branca (Leukoaraiosis) e enfartes lacunares (Status lacunar), atrofia cerebral, gliose e acumulação excessiva de ferro nos núcleos da base. Esta tese, considerando a linha de investigação de que deriva – Ciências da Vida - especialização em Medicina Clinica - Biotecnologia, reúne e reflete sobre três vertentes ligadas à RM e interdependentes em relação a uma problemática comum. A primeira trata da caracterização da Tecnologia por Ressonância Magnética existente em Portugal, a qual inclui uma avaliação exploratória da aplicação da técnica de Difusão Anisotrópica nos estudos cerebrais. As dimensões analíticas estudadas foram a Tecnológica, Sociodemográfica e Económica. Na recolha de dados recorreu-se a várias fontes de informação e a uma metodologia exploratória faseada, validada pela triangulação dos resultados. A sua análise obedeceu a critérios de estratificação e agrupamento segundo as mesmas dimensões analíticas. Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular A segunda descreve o estudo anátomo – radiológico que recaiu sobre parâmetros de quantificação assente na temática do cérebro do idoso em cadáver segundo uma metodologia experimental aplicada às métricas da difusão por RM. Na terceira, e última, é apresentado o estudo técnico - radiológico para avaliação e otimização da imagem ponderada em difusão em estudos clínicos associados ao cérebro do idoso “The Usual Brain Aging” ou Envelhecimento Cerebral Normal, com base metodológica assente nos critérios e indicadores estabelecidos pelo Estudo de Imagem de Roterdão (Rotterdam Scan Study - RSS). Como principais resultados obteve-se que não existem em Portugal estruturas para avaliação dos equipamentos pesados ou Agência de Avaliação das Tecnologias da Saúde para desenvolver o importante papel da produção de estudos comparativos entre os equipamentos disponíveis no mercado, a relação preço-qualidade e a sua afetação às necessidades clínico-epidemiológicas. Constatou-se que a implementação de equipamentos de RM está fortemente assente em critérios económicos carecendo de recomendações e diretivas para o uso racionalizado destas tecnologias. Quanto a dados quantitativos concluímos que a maioria dos equipamentos está instalada em instituições privadas (80,2%); a intensidade de campo magnético mais frequente é [1,5T] com 119 equipamentos; os equipamentos estão instalados maioritariamente nos distritos de Lisboa (55 unidades) e do Porto (39 unidades); o rácio médio de equipamentos por habitante em Portugal é de 1 para 65 195 habitantes; a amplitude de gradientes com maior expressão na amostra é 30-39mT/m; a maioria dos equipamentos foi instalada no intervalo temporal [2009-2012] com 59 equipamentos; apenas 6 instituições desenvolvem investigação clinica e a maioria das bobinas para estudos de crânio são do tipo Array. O estudo de otimização da técnica da difusão revelou, quanto à avaliação dos valoresb, que os mais baixos (b=500 s/mm2 e b=1000 s/mm2), apresentam maior IS e SNR sendo esta uma boa medida referente à qualidade de imagem, no entanto, os valores-b mais elevados (b=2000 s/mm2) apresentam maior CNR e CR, face aos anteriores, o Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular que apesar de proporcionar inferior detalhe anatómico e consequentemente inferior qualidade de imagem, num encéfalo normal, pode auxiliar na interpretação e apresentar vantagens na identificação de lesões microvasculares sempre que persistirem dúvidas em relação ao diagnóstico diferencial de doença microvascular do tipo status lacunar ou Hiperintensidades da Substância Branca. As alterações deste parâmetro são particularmente refletidas nas diferenças da avaliação da qualidade de imagem na região fronto-calos Concluímos da avaliação quantitativa da concentração média de ferro (26Fe) em todas as faixas etárias que os núcleos da base que apresentam maior concentração são, por ordem decrescente: Substância Nigra, Globus Pallidus, Putamen, Tálamo, Núcleo Rubro e Núcleo Caudado; que existe uma predominância na concentração de ferro (26Fe) no hemisfério esquerdo e que os indivíduos do género masculino apresentam mais ferro (26Fe) que os do género feminino nas faixas etárias [30-40[, [40-50[ e [50-60[. Como principal conclusão do estudo da concentração média de ferro em relação à idade destacamos que a concentração média de ferro (26Fe) é superior nos grupos etários superiores, logo aumenta com a idade, sobretudo na Substância Nigra e no Núcleo Lenticular. No estudo técnico-radiológico encontrámos evidências do aumento da difusibilidade da água na substância branca subcortical dos sujeitos idosos comparativamente aos mais jovens. Uma relação idêntica foi avaliada nos tálamos. O aumento relacionado com a idade parece ser predominantemente observado em doentes com mais de 65 anos de idade o que pode refletir alterações estruturais ligeiras associados ao envelhecimento normal. Os resultados indicam que a análise quantitativa das imagens ponderadas em difusão fornece informações, sobre a estrutura do cérebro, as quai s não estão disponíveis apenas por inspeção visual, tanto nas imagens ponderadas em difusão como em outras sequências de aplicação clínica de rotina. Para fazer face às desvantagens dos sistemas de quantificação das HSB os quais são dispendiosos, complexos, requererem tecnologia e formação específicas, recomendamos que a aplicação automatizada GUIAL, desenvolvida ao longo do nosso trabalho é de utilização elementar e prática para que seja introduzida nos sistemas de aquisição de imagem por RM com o fim de integrar o processamento de imagem nos indivíduos portadores de fatores de risco vascular. A avaliação do ADC, nesta amostra, permitiu concluir que a variação desta variável é explicada estatisticamente pela existência da condição clínica de status lacunar em ambos os hemisférios ou por outras palavras, o status lacunar influencia o valor de ADC. Embora uma pequena percentagem da variação do ADC seja explicada pelo género, o ADC nos homens foi superior ao das mulheres o que não nos surpreende, pois são também os homens onde a frequência de doença microvascular se revelou mais expressiva. Os valores do ADC, globalmente, entre os hemisférios cerebrais não mostraram alterações exceto na SB entre os idosos e não idosos. A SB da região frontal mostrou valores diminuídos na anisotropia e isotropia face às restantes áreas anatómicas. Os estudos indicam que na idade avançada existe uma maior predisposição para suscetibilidades de estrutura com status de desconexão. A classificação das HSB foi superior em indivíduos mais velhos e com status lacunar, e em menor quantidade (inferior rating de classificação) nos indivíduos idosos sem status lacunar. As alterações volumétricas foram mais frequentes no homem do que na mulher, presumivelmente devido à associação com a elevada classificação de status lacunar. Um aumento do índice de Evan correspondeu, neste estudo, ao aumento das HSB, à diminuição do volume cerebral total, à expansão ventrículo-sulcal frontal e ao aumento da medida do ângulo caloso. Estes resultados foram agravados pela classificação elevada de status lacunar nos indivíduos que apresentaram indícios de doença de pequenos vasos, com manifesto aumento dos espaços de Virchow-Robin,enfartes lacunares ou HSB. Esses resultados foram mais expressivos no género masculino do que no feminino revelando uma maior vulnerabilidade sobretudo na atrofia frontal nos homens. Por sua vez as dimensões do Corpo Caloso tornaram-se reduzidas devido à compressão dos ventrículos laterais e terceiro ventrículo. Estes indicadores tiveram expressão particularmente nos indivíduos com mais de 65 anos. ---------------------------------------------------------------------------------------------ABSTRACT: The latest neuroimaging methods, such as Magnetic Resonance Imaging (MRI), have enabled detailed images of in vivo human brain. These images reveal often unexpected findings related to the normal pattern, with high predisposition for the elderly people with forthright coexistence with vascular risk factors such as characteristics of a normal aging process. Although it has been, in the last decade, several publications on this subject, it is still little explained. All over the world have emerged disease prevention programs and health promotion developed by the Public Health sector, supported mainly by the advancement of medical technologies that have resulted, among other impacts, in a growing of the elderly population. It is estimated, in 2030, a demographic composition with 20% o people over 65 years. In this context, microvascular disease is the most common cause of cognitive vascular impairment in the elderly and senescent characteristics in the MRI trough ischemic lesions of the white matter (Leukoaraiosis) and lacunar infarcts (lacunar status), cerebral atrophy, gliosis and iron accumulation in the basal ganglia in excess.This thesis, considering the research line that stems - Life Sciences - specialization in Clinical Medicine, Biotechnology, gathers and reflects on three aspects linked to MR, interdependent and related to a common problem. The first deals with the Magnetic Resonance Technology characterization in Portugal, which includes an exploratory evaluation of the implementation of Anisotropic Diffusion technique in brain studies. The analytical dimensions studied were the Technologic, Socio-demographic and Economics. Collecting data was supported by different sources of information and was applied an exploratory methodology whose results were validated by triangulation. The research method was grouped and stratified criteria under the same analytical dimensions. The second describes the anatomical study - which was focused on radiological measurement parameters, based on the brain’s specimen under an experimental methodology applied to MRI diffusion metrics. Radiological evaluation and optimization of the weighted image diffusion in clinical studies were associated with the brain of the elderly "The Usual Brain Aging" with methodological basis based on established criteria and indicators by Rotterdam Scan Study (RSS). The main results obtained reveal the inexistence frameworks in Portugal for evaluation of equipments or Agency of Health Technology to produce studies comparing the equipment available on the market, the value for money and its allocation to clinical and epidemiological needs. It was found that the implementation of MRI equipment is strongly based on economic criteria lacking recommendations and guidelines for the rationalized use of these technologies. As the quantitative data we conclude that most of the scanners are located in private clinical institutions (80,2%); the most frequent magnetic field intensity is [1.5T] with 119 scanners; the scanners are mainly installed in Lisbon (55 units) and Porto (39 units) districts; the average ratio of equipment per capita in Portugal is 1 to 65 195 people; the gradient power with higher expression in the sample is 30-39mT / m;most of the scanners were installed in the years range [2009-2012 years] with 59 equipment; only 6 clinical placements develop clinical research and the most coils for brain studies are of Array type. The optimization study of diffusion technique revealed, as the assessment of the bvalues, the lower (b = 500 s / mm2 and b = 1000 s / mm 2), promotes an increase in the SI and SNR being this measure related to a higher image quality, however the highest b values (b = 2000 s / mm 2) have a higher CNR (Contrast to Noise-Ratio) and CR (Contrast Ratio), compared to the previous ones. This may provide less anatomical details and, thus, ower image quality, of a normal brain, however can help the interpretation and have advantages in identifying microvascular injuries when doubts persist regarding the differential diagnosis of microvascular disease of lacunar or WMH (White Matter Hyperintensities) status type. Changes on this parameter are Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular particularly reflected in the differences of image quality evaluation in the frontocallosum anatomical area. We conclude from the quantitative assessment of the average concentration of iron (26Fe), in all age groups to the basal ganglia, that the higher concentrations are, in descending order: Nigral Substantia, Globus pallidus, Putamen, Thalamus, Rubio nucleus and Caudate nucleus; that there is a predominance in the concentration of iron (26Fe) in the left hemisphere and that male gender show higher iron (26Fe) level tha females, in the age groups [30-40 [[40-50 [and [50- 60 [. Regarding a main conclusion of the mean concentration study of iron, in terms of age we point out that the average concentration of iron (26Fe) is higher among older groups and increases with age, especially in Nigral Substantia and Lenticular Nucleus. On the technical and radiological study we found evidence of an increased in water /diffusivity in the ubcortical white matter of the elderly compared with younger subjects. A similar relationship was assessed in the Thalamus. The increase agerelated seems to be predominantly observed in patients over 65 years which may reflect minor structural changes associated with normal aging. The results indicate that quantitative analysis of diffusion weighted imaging can provide information about the structure of the brain which is not reached only by visual inspection or standard sequences applied in clinical routine. To address the disadvantages the systems of quantification of WMH which the authors state that are costly, complex, require specific technology and training, we recommend that the automated application GUIAL, developed over our work is basic and practical to use and to be introduced in MR image systems acquisition in order to integrate image processing in patients with vascular risk factors. The evaluation of the ADC showed that its variation is statistically explained by the existence of the medical condition of lacunar status, in both hemispheres, or in other words, the lacunar status influences the ADC value. Although a small percentage of the ADC variation is explained by gender, the ADC in men was higher than women which Otimização da anisotropia fronto-calosa e [RM 1,5T] no idoso normal e com risco cérebro-vascular do not surprise us, since they are also men where the frequency of microvasculardisease has proved more significant. The values of ADC, overall, between the cerebral hemispheres showed no changes but were different in WM among the elderly and non-elderly subjects.The WM's forehead showed decreased values in anisotropy and isotropy face the other anatomical areas. The studies indicate that in old age there is a greater tendency to higher susceptibility to disconnection- status framework. The classification of WMH was higher in elderly people and lacunar status, and fewer (lower classification rating) in the elderly without lacunar status. volumetric changes were more frequent in men than in women, most probably because of its association with high lacunar status rating. An increase of Evan index corresponded, in this study, to an increase in WMH, to a decreased of total brain volume, to a ventricle sulcal frontal and callous angle expansion. These results were wound up by high ranking of lacunar status in subjects who had small vessel disease, clear increase in spaces of Virchow-Robin, lacunar infarctions or WMH. These results were more significant in males than in females revealing vulnerability particularly in the frontal atrophy in men. In turn the size of Corpus Callosum because reduced due to the compression of the lateral and third ventricles. These indicators had expression particularly in individuals over 65 years.
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Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined
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A certificate from the Grand Lodge of Ontario Independent Order of Odd Fellows to brother William H. Cowan. He has been admitted as a member of Livingstone Lodge No. 130 at Merritton 19 October 1909. The certificate is signed and dated by W. Brooks (Secretary) and S.A. Poplestoise (Grand Master) December 7, 1911. Cowan received the Degree of Truth.
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Objectif: Cette thèse avait pour objectif principal la mise en oeuvre et la validation de la faisabilité, chez l'humain, du paradigme de modulation du réflexe acoustique de sursaut par un court silence (GPIAS) afin de l'utiliser comme mesure objective de l'acouphène. Pour ce faire, trois expériences ont été réalisées. L'expérience 1 avait pour objectif de valider l'inhibition du réflexe de sursaut par un court silence chez des participants humains normo-entendants (sans acouphène) lors de la présentation d'un bruit de fond centré en hautes et en basses fréquences afin de déterminer les paramètres optimaux du paradigme. L'expérience 2 avait pour objectif de valider la précision et la fidélité d'une méthode de caractérisation psychoacoustique de l'acouphène (appariement en intensité et en fréquence). Finalement, l'expérience 3 avait pour objectif d'appliquer le paradigme d'objectivation de l'acouphène par le réflexe de sursaut à des participants atteints d'acouphènes chroniques en utilisant les techniques développées lors des expériences 1 et 2. Méthodologie : L'expérience 1 incluait 157 participants testés dans l'une des conditions de durée du court silence (5, 25, 50, 100, 200 ms) et dans l'un des deux paradigmes (court silence à l'intérieur du bruit de fond ou suivant celui-ci) à l'aide de bruits de fond en hautes et en basses fréquences. L'expérience 2 incluait deux groupes de participants avec acouphène, l'un musicien (n=16) et l'autre sans expérience musicale (n=16) ainsi qu'un groupe de simulateur sans acouphène (n=18). Ils tous ont été évalués sur leur capacité d'appariement en fréquence et en intensité de leur acouphène. Les mesures ont été reprises chez un sous-groupe de participants plusieurs semaines plus tard. L'expérience 3 incluait 15 participants avec acouphène et 17 contrôles évalués à l'aide du paradigme d'inhibition du réflexe de sursaut à l'aide d'un court silence (GPIAS). Les paramètres psychoacoustiques de l'acouphène ont également été mesurés. Toutes les mesures ont été reprises plusieurs mois plus tard chez un sous-groupe de participants. Résultats : Expérience 1 : le paradigme d'inhibition du réflexe acoustique de sursaut par un court silence est applicable chez l'humain normo-entendant. Expérience 2 : les mesures psychoacoustiques informatisées de l'acouphène incluant l'appariement en fréquence et en intensité sont des mesures précises et fidèles du percept de l'acouphène. Expérience 3 : un déficit d'inhibition au paradigme du GPIAS a été retrouvé chez le groupe de participants avec acouphène pour les bruits de fond en hautes et en basses fréquences au test et au retest. Les mesures d'appariement en fréquence ont révélé un acouphène dont la fréquence prédominante était d'environ 16 000 Hz chez la plupart des participants. Discussion : Il est possible d'appliquer le paradigme d'inhibition du réflexe acoustique de sursaut par un court silence à des participants humains atteints d'acouphène, tel qu'il est utilisé en recherche animale pour « objectiver » la présence d'acouphène. Toutefois, le déficit d'inhibition mesuré n'est pas spécifique à la fréquence de l'acouphène lorsque validé à partir des données d'appariement psychoacoustique. Nos résultats soulèvent des questions quant à l'interprétation originale du paradigme pour détecter la présence d'un acouphène chez les animaux.
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Atmospheric surface boundary layer parameters vary anomalously in response to the occurrence of annular solar eclipse on 15th January 2010 over Cochin. It was the longest annular solar eclipse occurred over South India with high intensity. As it occurred during the noon hours, it is considered to be much more significant because of its effects in all the regions of atmosphere including ionosphere. Since the insolation is the main driving factor responsible for the anomalous changes occurred in the surface layer due to annular solar eclipse, occurred on 15th January 2010, that played very important role in understanding dynamics of the atmosphere during the eclipse period because of its coincidence with the noon time. The Sonic anemometer is able to give data of zonal, meridional and vertical wind as well as the air temperature at a temporal resolution of 1 s. Different surface boundary layer parameters and turbulent fluxes were computed by the application of eddy correlation technique using the high resolution station data. The surface boundary layer parameters that are computed using the sonic anemometer data during the period are momentum flux, sensible heat flux, turbulent kinetic energy, frictional velocity (u*), variance of temperature, variances of u, v and w wind. In order to compare the results, a control run has been done using the data of previous day as well as next day. It is noted that over the specified time period of annular solar eclipse, all the above stated surface boundary layer parameters vary anomalously when compared with the control run. From the observations we could note that momentum flux was 0.1 Nm 2 instead of the mean value 0.2 Nm-2 when there was eclipse. Sensible heat flux anomalously decreases to 50 Nm 2 instead of the mean value 200 Nm 2 at the time of solar eclipse. The turbulent kinetic energy decreases to 0.2 m2s 2 from the mean value 1 m2s 2. The frictional velocity value decreases to 0.05 ms 1 instead of the mean value 0.2 ms 1. The present study aimed at understanding the dynamics of surface layer in response to the annular solar eclipse over a tropical coastal station, occurred during the noon hours. Key words: annular solar eclipse, surface boundary layer, sonic anemometer
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In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.