Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

Regional and local contributions to ambient non-methane volatile organic compounds at a polluted rural/coastal site in Pearl River Delta, China

Identification of major sources of airborne pollutants and their contribution to pollutant loadings are critical in developing effective pollution control and mitigation strategies. In this study, a comprehensive dataset of non-methane volatile organic compounds (NMVOCs) collected from August 2001 to December 2002 at a polluted rural/coastal site in the Pearl River Delta (PRD) is analyzed to assess the relative contributions of major pollution sources to ambient NMVOC mixing ratios. A unique approach based on emission ratios of individual chemical species was used to classify the bulk air samples in order to apportion regional and local source contributions to the measured mixing ratios. The collected air samples fell into four major groups, including air masses from the inner PRD region and Hong Kong (HK) urban area. To estimate the source apportionment of NMVOCs, a principal component analysis/absolute principal component scores receptor model was applied to the classified data points. The results indicate that the regional and local source contributions to ambient NMVOC levels at the site were significantly different due to the differences in local versus regional energy use and industrial activities. For air masses originating from HK, vehicular emissions accounted for approximately 39% of the total NMVOC levels, followed by industrial emissions (35%), gasoline evaporation (14%) and commercial/domestic liquefied petroleum gas/natural gas use (12%). By contrast, for air masses originating from the PRD the industrial emissions accounted for 43% of the total NMVOC burden, followed by vehicular emissions (32%) and biomass burning (25%). In particular, the higher regional contribution of biomass burning found in this study as compared to existing emission inventories suggests that further efforts are necessary to refine the emission inventories of NMVOCs in the PRD region. © 2006 Elsevier Ltd. All rights reserved

Measurements of trace gases in the inflow of South China Sea background air and outflow of regional pollution at Tai O, Southern China

We present a 16-month record of ozone (O3), carbon monoxide (CO), total reactive nitrogen (NOy), sulphur dioxide (SO2), methane (CH4), C2 - C8 non-methane hydrocarbons (NMHCs), C1 - C2 halocarbons, and dimethyl sulfide (DMS) measured at a southern China coastal site. The study aimed to establish/update seasonal profiles of chemically active trace gases and pollution tracers in subtropical Asia and to characterize the composition of the 'background' atmosphere over the South China Sea (SCS) and of pollution outflow from the industrialized Pearl River Delta (PRD) region and southern China. Most of the measured trace gases of anthropogenic origin exhibited a winter maximum and a summer minimum, while O3 showed a maximum in autumn which is in contrast to the seasonal behavior of O3 in rural eastern China and in many mid-latitude remote locations in the western Pacific. The data were segregated into two groups representing the SCS background air and the outflow of regional continental pollution (PRD plus southern China), based on CO mixing ratios and meteorological conditions. NMHCs and halocarbon data were further analyzed to examine the relationships between their variability and atmospheric lifetime and to elucidate the extent of atmospheric processing in the sampled air parcels. The trace gas variability (S) versus lifetime (τ) relationship, defined by the power law, Slnx = Aτ-b, (where X is the trace gas mixing ratio) gives a fit parameter A of 1.39 and exponent b of 0.42 for SCS air, and A of 2.86 and b of 0.31 for the regional continental air masses. An examination of ln[n-butane]/ln[ethane] versus ln[propane]/ln[ethane] indicates that their relative abundance was dominated by mixing as opposed to photochemistry in both SCS and regional outflow air masses. The very low ratios of ethyne/CO, propane/ethane and toluene/benzene suggest that the SCS air mass has undergone intense atmospheric processing since these gases were released into the atmosphere. Compared to the results from other polluted rural sites and from urban areas, the large values of these species in the outflow of PRD/southern China suggest source(s) emitting higher levels of ethyne, benzene, and toluene, relative to light alkanes. These chemical characteristics could be unique indicators of anthropogenic emissions from southern China. © Springer Science + Business Media, Inc. 2005

The Circumstellar Extinction of Planetary Nebulae

We analyze the dependence of circumstellar extinction on core mass for the brightest planetary nebulae (PNe) in the Magellanic Clouds and M31. We show that in all three galaxies, a statistically significant correlation exists between the two quantities, such that high core mass objects have greater extinction. We model this behavior, and show that the relation is a simple consequence of the greater mass loss and faster evolution times of high mass stars. The relation is important because it provides a natural explanation for the invariance of the [O III] 5007 planetary nebula luminosity function (PNLF) with population age: bright Population I PNe are extinguished below the cutoff of the PNLF. It also explains the counter-intuitive observation that intrinsically luminous Population I PNe often appear fainter than PNe from older, low-mass progenitors.Comment: 12 pages, 2 figures, accepted for ApJ, April 10, 199

Source contributions to ambient VOCs and CO at a rural site in eastern China

Ambient data on volatile organic compounds (VOCs) and carbon monoxide (CO) obtained at a rural site in eastern China are analyzed to investigate the nature of emission sources and their relative contributions to ambient concentrations. A principal component analysis (PCA) showed that vehicle emissions and biofuel burning, biomass burning and industrial emissions were the major sources of VOCs and CO at the rural site. The source apportionments were then evaluated using an absolute principal component scores (APCS) technique combined with multiple linear regressions. The results indicated that 71%±5% (average±standard error) of the total VOC emissions were attributed to a combination of vehicle emissions and biofuel burning, and 7%±3% to gasoline evaporation and solvent emissions. Both biomass burning and industrial emissions contributed to 11%±1% and 11%±0.03% of the total VOC emissions, respectively. In addition, vehicle emissions and biomass and biofuel burning accounted for 96%±6% of the total CO emissions at the rural site, of which the biomass burning was responsible for 18%±3%. The results based on PCA/APCS are generally consistent with those from the emission inventory, although a larger relative contribution to CO from biomass burning is indicated from our analysis. © 2004 Elsevier Ltd. All rights reserved

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is employed to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. We also calculate the thermal emissions based on the reciprocity and energy conservation principles. The effects of the random roughness at the air-ice, and ice-water interfaces are accounted for by adding the surface scattering to the volume scattering return incoherently. The above theoretical model, which has been successfully applied to analyze the radar backscatter data of the first-year sea ice near Point Barrow, AK, is used to interpret the measurements performed in the CRRELEX program

Collapse of the vortex-lattice inductance and shear modulus at the melting transition in untwinned YBa2Cu3O7\rm YBa_2Cu_3O_7

The complex resistivity $\hat{\rho}(\omega)$ of the vortex lattice in an untwinned crystal of 93-K $\rm YBa_2Cu_3O_7$ has been measured at frequencies $\omega/2\pi$ from 100 kHz to 20 MHz in a 2-Tesla field $\bf H\parallel c$, using a 4-probe RF transmission technique that enables continuous measurements versus $\omega$ and temperature $T$. As $T$ is increased, the inductance ${\cal L}_s(\omega) ={\rm Im} \hat{\rho}(\omega)/ \omega$ increases steeply to a cusp at the melting temperature $T_m$, and then undergoes a steep collapse consistent with vanishing of the shear modulus $c_{66}$. We discuss in detail the separation of the vortex-lattice inductance from the `volume' inductance, and other skin-depth effects. To analyze the spectra, we consider a weakly disordered lattice with a low pin density. Close fits are obtained to $\rho_1(\omega)$ over 2 decades in $\omega$. Values of the pinning parameter $\kappa$ and shear modulus $c_{66}$ obtained show that $c_{66}$ collapses by over 4 decades at $T_m$, whereas $\kappa$ remains finite.Comment: 11 pages, 8 figures, Phys. Rev. B, in pres

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