A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at √sNN=2.76 TeV

The anisotropy of the azimuthal distributions of charged particles produced in √sNN=2.76 TeV PbPb collisions is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter, v2, defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee-Yang zeros. The anisotropy is presented as a function of transverse momentum (pT), pseudorapidity (η) over a broad kinematic range, 0.3

Multiresolution spherical wavelet analysis in global seismic tomography

Every seismic event produces seismic waves which travel throughout the Earth. Seismology is the science of interpreting measurements to derive information about the structure of the Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's interiors. Tomographic models obtained at the global and regional scales are an underlying tool for determination of geodynamical state of the Earth, showing evident correlation with other geophysical and geological characteristics. The global tomographic images of the Earth can be written as a linear combinations of basis functions from a specifically chosen set, defining the model parameterization. A number of different parameterizations are commonly seen in literature: seismic velocities in the Earth have been expressed, for example, as combinations of spherical harmonics or by means of the simpler characteristic functions of discrete cells. With this work we are interested to focus our attention on this aspect, evaluating a new type of parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution. The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency components, and then study each component with resolution matched to its scale, so they are especially useful in the analysis of non stationary process that contains multi-scale features, discontinuities and sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel for analysis to extract information about the process. These two types of applications of wavelets in geophysical field, are object of study of this work. At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet analysis in the representation of two different type of synthetic models; then we apply it to real data, obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an other type of parametrization (i.e., block parametrization). For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability and then apply the same analysis to real data to obtain Local Correlation Maps between different model at same depth or between different profiles of the same model.

Quaternary oxygen isotope record of planktonic foraminifera from ODP Site 805 on the Ontong Java Plateau

The oxygen isotope records of G. sacculifer and Pulleniatina in the uppermost three cores at Ocean Drilling Program Hole 805C span the last 1.6 m.y., an estimate based on Fourier stratigraphy. The last 700,000 yr are dominated by both eccentricity and obliquity-related orbital fluctuations. The range of variation of delta18O values is about 1.5?, of which ca. 75% may be assigned to global ice-volume effect. The remainder of the range is shared by the effects of surface temperature variation, thermocline depth change (in the case of Pulleniatina, especially), and differential dissolution. Before 1 Ma, obliquity-related fluctuations dominate. The transition between obliquity- and eccentricity-dominated time occurs between ca. 1 and 0.7 Ma. It is marked by irregularities in phase relationships, the source of which is not clear. The age of the Brunhes/Matuyama boundary is determined as 794,000 yr by obliquity counting. However, an age of 830,000 yr also is compatible with the counts of both eccentricity and obliquity cycles. In the first case, Stage 19 (which contains the boundary) is coincident with the crest of the 19th obliquity cycle, setting the first crest downcore equal to zero, and counting backward (o19). In the second, Stage 19 coincides with o20. No evidence was found for fluctuations related to precession (23 and 19 k.y.) rising above the noise level, using plain Fourier expansion on the age model of the entire series. Detailed stratigraphic comparison with the Quaternary record of Hole 806B allows the recognition of major dissolution events (which increase the difference in delta18O values of G. sacculifer at the two sites). These occur at Stages 11-13, 16-17, and near 1.5 Ma (below o33).

Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.

Orbit and altimetric corrections for the ERS satellites through analysis of single and dual satellite crossovers

Due to the failure of PRARE the orbital accuracy of ERS-1 is typically 10-15 cm radially as compared to 3-4cm for TOPEX/Poseidon. To gain the most from these simultaneous datasets it is necessary to improve the orbital accuracy of ERS-1 so that it is commensurate with that of TOPEX/Poseidon. For the integration of these two datasets it is also necessary to determine the altimeter and sea state biases for each of the satellites. Several models for the sea state bias of ERS-1 are considered by analysis of the ERS-1 single satellite crossovers. The model adopted consists of the sea state bias as a percentage of the significant wave height, namely 5.95%. The removal of ERS-1 orbit error and recovery of an ERS-1 - TOPEX/Poseidon relative bias are both achieved by analysis of dual crossover residuals. The gravitational field based radial orbit error is modelled by a finite Fourier expansion series with the dominant frequencies determined by analysis of the JGM-2 co-variance matrix. Periodic and secular terms to model the errors due to atmospheric density, solar radiation pressure and initial state vector mis-modelling are also solved for. Validation of the dataset unification consists of comparing the mean sea surface topographies and annual variabilities derived from both the corrected and uncorrected ERS-1 orbits with those derived from TOPEX/Poseidon. The global and regional geographically fixed/variable orbit errors are also analysed pre and post correction, and a significant reduction is noted. Finally the use of dual/single satellite crossovers and repeat pass data, for the calibration of ERS-2 with respect to ERS-1 and TOPEX/Poseidon is shown by calculating the ERS-1/2 sea state and relative biases.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Congruences in modular, Jacobi, Siegel, and mock modular forms with applications

We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the Fourier expansion. We have several applications. We describe the Ramanujan congruences in the counting functions for overparitions, overpartition pairs, crank differences, and Andrews' two-coloured generalized Frobenius partitions. We also study Ramanujan congruences in the Fourier coefficients of certain ratios of Eisenstein series. We also determine the exact number of holomorphic modular forms with Ramanujan congruences when the weight is large enough. In a chapter based on joint work with Olav Richter, we study Ramanujan congruences in the coefficients of Jacobi forms and Siegel modular forms of degree two. Finally, the last chapter contains a completely unrelated result about harmonic weak Maass forms.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

RITZ ANALYSIS OF THE FOURIER SPECTRUM OF CH3OH BETWEEN 350 AND 950 CM(-1)

A new ''Ritz'' program has been used for revising and expanding the assignment of the Fourier transform infrared and far-infrared spectrum of CH3OH. This program evaluates the energy levels involved in the assigned transitions by the Rydberg-Ritz combination principle and can tackle such perturbations as Fermi-type resonances or Coriolis interactions. Up to now this program has evaluated the energies of 2768 levels belonging to A-type symmetry and 4133 levels belonging to E-type symmetry of CH3OH. Here we present the assignment of almost 9600 lines between 350 and 950 cm(-1). The Taylor expansion coefficients for evaluating the energies of the levels involved in the transitions are also given. All of the lines presented in this paper correspond to transitions involving torsionally excited levels within the ground vibrational state. (C) 1995 Academic Press, Inc.

Ultra-structural mapping of sugarcane bagasse after oxalic acid fiber expansion (OAFEX) and ethanol production by Candida shehatae and Saccharomyces cerevisiae

Background: Diminishing supplies of fossil fuels and oil spills are rousing to explore the alternative sources of energy that can be produced from non-food/feed-based substrates. Due to its abundance, sugarcane bagasse (SB) could be a model substrate for the second-generation biofuel cellulosic ethanol. However, the efficient bioconversion of SB remains a challenge for the commercial production of cellulosic ethanol. We hypothesized that oxalic-acid-mediated thermochemical pretreatment (OAFEX) would overcome the native recalcitrance of SB by enhancing the cellulase amenability toward the embedded cellulosic microfibrils. Results: OAFEX treatment revealed the solubilization of hemicellulose releasing sugars (12.56 g/l xylose and 1.85 g/l glucose), leaving cellulignin in an accessible form for enzymatic hydrolysis. The highest hydrolytic efficiency (66.51%) of cellulignin was achieved by enzymatic hydrolysis (Celluclast 1.5 L and Novozym 188). The ultrastructure characterization of SB using scanning electron microscopy (SEM), atomic force microscopy (AFM), Raman spectroscopy, Fourier transform-near infrared spectroscopy (FT-NIR), Fourier transform infrared spectroscopy (FTIR), and X-ray diffraction (XRD) revealed structural differences before and after OAFEX treatment with enzymatic hydrolysis. Furthermore, fermentation mediated by C. shehatae UFMG HM52.2 and S. cerevisiae 174 showed fuel ethanol production from detoxified acid (3.2 g/l, yield 0.353 g/g; 0.52 g/l, yield, 0.246 g/g) and enzymatic hydrolysates (4.83 g/l, yield, 0.28 g/g; 6.6 g/l, yield 0.46 g/g). Conclusions: OAFEX treatment revealed marked hemicellulose degradation, improving the cellulases ability to access the cellulignin and release fermentable sugars from the pretreated substrate. The ultrastructure of SB after OAFEX and enzymatic hydrolysis of cellulignin established thorough insights at the molecular level. © 2013 Chandel et al; licensee BioMed Central Ltd.

Ultra-structural mapping of sugarcane bagasse after oxalic acid fiber expansion (OAFEX) and ethanol production by Candida shehatae and Saccharomyces cerevisiae

Background Diminishing supplies of fossil fuels and oil spills are rousing to explore the alternative sources of energy that can be produced from non-food/feed-based substrates. Due to its abundance, sugarcane bagasse (SB) could be a model substrate for the second-generation biofuel cellulosic ethanol. However, the efficient bioconversion of SB remains a challenge for the commercial production of cellulosic ethanol. We hypothesized that oxalic-acid-mediated thermochemical pretreatment (OAFEX) would overcome the native recalcitrance of SB by enhancing the cellulase amenability toward the embedded cellulosic microfibrils. Results OAFEX treatment revealed the solubilization of hemicellulose releasing sugars (12.56 g/l xylose and 1.85 g/l glucose), leaving cellulignin in an accessible form for enzymatic hydrolysis. The highest hydrolytic efficiency (66.51%) of cellulignin was achieved by enzymatic hydrolysis (Celluclast 1.5 L and Novozym 188). The ultrastructure characterization of SB using scanning electron microscopy (SEM), atomic force microscopy (AFM), Raman spectroscopy, Fourier transform–near infrared spectroscopy (FT-NIR), Fourier transform infrared spectroscopy (FTIR), and X-ray diffraction (XRD) revealed structural differences before and after OAFEX treatment with enzymatic hydrolysis. Furthermore, fermentation mediated by C. shehatae UFMG HM52.2 and S. cerevisiae 174 showed fuel ethanol production from detoxified acid (3.2 g/l, yield 0.353 g/g; 0.52 g/l, yield, 0.246 g/g) and enzymatic hydrolysates (4.83 g/l, yield, 0.28 g/g; 6.6 g/l, yield 0.46 g/g). Conclusions OAFEX treatment revealed marked hemicellulose degradation, improving the cellulases’ ability to access the cellulignin and release fermentable sugars from the pretreated substrate. The ultrastructure of SB after OAFEX and enzymatic hydrolysis of cellulignin established thorough insights at the molecular level.

Broadband Fourier transform rotational spectroscopy for structure determination: The water heptamer

Over the recent years chirped-pulse, Fourier-transform microwave (CP-FTMW) spectrometers have chan- ged the scope of rotational spectroscopy. The broad frequency and large dynamic range make possible structural determinations in molecular systems of increasingly larger size from measurements of heavy atom (13C, 15N, 18O) isotopes recorded in natural abundance in the same spectrum as that of the parent isotopic species. The design of a broadband spectrometer operating in the 2–8 GHz frequency range with further improvements in sensitivity is presented. The current CP-FTMW spectrometer performance is benchmarked in the analyses of the rotational spectrum of the water heptamer, (H2O)7, in both 2– 8 GHz and 6–18 GHz frequency ranges. Two isomers of the water heptamer have been observed in a pulsed supersonic molecular expansion. High level ab initio structural searches were performed to pro- vide plausible low-energy candidates which were directly compared with accurate structures provided from broadband rotational spectra. The full substitution structure of the most stable species has been obtained through the analysis of all possible singly-substituted isotopologues (H218O and HDO), and a least-squares rm(1) geometry of the oxygen framework determined from 16 different isotopic species compares with the calculated O–O equilibrium distances at the 0.01 Å level.