Ray-theoretical modeling of secondary microseism P-waves

Secondary microseism sources are pressure fluctuations close to the ocean surface. They generate acoustic P-waves that propagate in water down to the ocean bottom where they are partly reflected, and partly transmitted into the crust to continue their propagation through the Earth. We present the theory for computing the displacement power spectral density of secondary microseism P-waves recorded by receivers in the far field. In the frequency domain, the P-wave displacement can be modeled as the product of (1) the pressure source, (2) the source site effect that accounts for the constructive interference of multiply reflected P-waves in the ocean, (3) the propagation from the ocean bottom to the stations, (4) the receiver site effect. Secondary microseism P-waves have weak amplitudes, but they can be investigated by beamforming analysis. We validate our approach by analyzing the seismic signals generated by Typhoon Ioke (2006) and recorded by the Southern California Seismic Network. Back projecting the beam onto the ocean surface enables to follow the source motion. The observed beam centroid is in the vicinity of the pressure source derived from the ocean wave model WAVEWATCH IIIR. The pressure source is then used for modeling the beam and a good agreement is obtained between measured and modeled beam amplitude variation over time. This modeling approach can be used to invert P-wave noise data and retrieve the source intensity and lateral extent.

Analyse de profils de chaussées: Effet du gel saisonnier et de la dégradation du pergélisol

Des techniques adaptées aux contextes routiers sont nécessaires pour maintenir et réhabiliter des chaussées construites sur pergélisol ou en contexte de gel saisonnier. Plusieurs problématiques peuvent engendrer une augmentation des coûts de réparation et entretien, une diminution de la durée de vie des chaussées et des problèmes reliés à la sécurité des usagers de la route. L’objectif du projet consiste donc à élaborer un outil d’aide à la décision, qui contribuerait à localiser les zones sensibles au gel saisonnier et à la dégradation du pergélisol, à discerner les causes de dégradation des chaussées dues au gel saisonnier et à sélectionner les meilleures stratégies d’atténuation et de réfection à moindre coût. Le projet de recherche est divisé en deux volets distincts. Le premier volet traite des problématiques de gel de chaussées en contexte de gel saisonnier. Actuellement, il existe des méthodes de diagnostic qui permettent de détecter les endroits où un problème de gélivité est susceptible d’être présent. Par contre, ces méthodes ne permettent pas de discerner si le problème de gel est en profondeur ou en surface de la chaussée; en d’autres mots si le problème est lié à un soulèvement différentiel du sol ou à un soulèvement de fissures. De plus, les méthodes utilisées ne sont pas adaptées aux chaussées en contexte municipal. Selon les problématiques connues de certains sites, il a été possible de développer un abaque permettant de différencier si la problématique de gel se situe en surface ou en profondeur dans une chaussée. Puis, une analyse d’imagerie 3D a été réalisée pour complémenter l’abaque créé. À l’aide de cette technologie, une nouvelle méthode sera mise au point pour détecter des problématiques de gel grâce aux profils transversaux. Le deuxième volet porte sur les chaussées construites sur pergélisol. Les méthodes actuelles de détection de la dégradation du pergélisol sous les chaussées manquent de précision et ont besoin d’être raffinées, surtout dans le contexte actuel de réchauffement climatique. Pour ce faire, trois sites d’essais ont été étudiés sur l’Alaska Highway au Yukon. En fonction de différentes analyses telles que des analyses de profils longitudinaux, de la densité spectrale et de longueurs d’onde, des tendances ont été décelées pour caractériser l’instabilité du pergélisol.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Wavelet analysis and hierarchical clustering of ofm phenotypic population's variations originated from southern america and europe and attempts of a first relation to molecular divergence.

In this work we compare Grapholita molesta Busck (Lepidoptera: Tortricidae) populations originated from Brazil, Chile, Spain, Italy and Greece using power spectral density and phylogenetic analysis to detect any similarities between the population macro- and the molecular micro-level. Log-transformed population data were normalized and AR(p) models were developed to generate for each case population time series of equal lengths. The time-frequency/scale properties of the population data were further analyzed using wavelet analysis to detect any population dynamics frequency changes and cluster the populations. Based on the power spectral of each population time series and the hierarchical clustering schemes, populations originated from Southern America (Brazil and Chile) exhibit similar rhythmic properties and are both closer related with populations originated from Greece. Populations from Spain and especially Italy, have higher distance by terms of periodic changes on their population dynamics. Moreover, the members within the same cluster share similar spectral information, therefore they are supposed to participate in the same temporally regulated population process. On the contrary, the phylogenetic approach revealed a less structured pattern that bears indications of panmixia, as the two clusters contain individuals from both Europe and South America. This preliminary outcome will be further assessed by incorporating more individuals and likely employed a second molecular marker.

Cross-sectional study of a microsatellite marker in the low density lipoprotein receptor gene in obese normotensives

1. The low density lipoprotein receptor is an important regulator of serum cholesterol which may have implications for the development of both hypertension and obesity. In this study, genotypes for a low density lipoprotein receptor gene (LDLR) dinucleotide polymorphism were determined in both lean and obese normotensive populations. 2. In previous cross-sectional association studies an ApaLI and a HincII polymorphism for LDLR were shown to be associated with obesity in essential hypertensives. However, these polymorphisms did not show an association with obesity in normotensives. 3. In contrast, this study reports that preliminary results for an LDLR microsatellite marker, located more towards the 3' end of the gene, show a significant association with obesity in the normotensive population studied. These results indicate that LDLR could play an important role in the development of obesity, which might be independent of hypertension.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.

Spectral narrowing of negatively chirped femtosecond pulse by cross-phase modulation in a single-mode optical fiber

We demonstrate theoretically that the negatively chirped femtosecond laser pulse can be spectrally narrowed by cross-phase modulation. The new view is well Supported by numerical simulation. The negative chirp method in fibers might be useful in all optical wavelength switching applications. (c) 2005 Elsevier B.V. All rights reserved.

Resonant two-photon cross-section calculations for transitions to 4f5d state in Pr3+: YAG using density matrix theory

The density matrix resonant two-photon absorption (TPA) theory is applied to a rare-earth ion-doped laser crystal. TPA cross sections for transitions from the ground state to the first 4f5d state in Pr3+:YAG are calculated. The results indicate the density matrix TPA theory is attractive in studying TPA in laser crystals. (C) 2000 Elsevier Science B.V. All rights reserved.

Effect of cross-linking of high-density polyethylene. I. On spherulitic structures

Crystallization behavior and spherulitic structure of linear high-density polyethylene (HDPE), after being irradiated in its molten state by gamma -rays, was investigated by small-angle laser scattering (SALS) and differential scanning calorimetry (DSC). Significant changes in the crystallization of HDPE during cooling in air before and after being irradiated in the melt were observed. A critical minimum average molar mass between cross-links (200 carbon-carbon bonds) for spherulite formation in such an irradiated HDPE network was obtained.