GMRES and the minimal polynomial

We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size.Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight.Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.This research was partially supported by National Science Foundation grants DMS-9122745, DMS-9423705, CCR-9102853, CCR-9400921, DMS-9321938, DMS-9020915, and DMS-9403224.     

Simultaneous high speed PIV and CH PLIF using R-branch excitation in the C2Σ+-X2Π (0,0) band

Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) utilizing R-branch transitions in the C-X (0,0) band were performed at a 10-kHz repetition-rate in a turbulent premixed flame. The CH lines at 310.690?nm (from the R-branch of the C-X band) used here have greater efficiency than A-X and B-X transitions, which allows for high-framerate imaging with low laser pulse energy. Most importantly, the simultaneous imaging of both CH PLIF and PIV is enabled by the use of a custom edge filter, which blocks scattering at the laser wavelength (below ～311?nm) while efficiently transmitting fluorescence at longer wavelengths. The Hi-Pilot Bunsen burner operated with a turbulent Reynolds number of 7900 was used to demonstrate simultaneous PIV and CH PLIF utilizing this filtered detection scheme. Instances where pockets of products were observed well upstream of the mean flame brush are found to be the result of out-of-plane motion of the flame sheet. Such instances can lead to ambiguous results when interpreting the thickness of reaction layers. However, the temporally resolved nature of the present diagnostics facilitate the identification and proper treatment of such situations. The strategy demonstrated here can yield important information in the study of turbulent flames by providing temporally resolved flame dynamics in terms of flame sheet visualization and velocity fields.     

Four contact electrical measurements on the anisotropic high-Tc superconductors: voltage reversals

We describe three mechanisms for the anomalous voltage reversals which are occasionally observed during four contact current-voltage measurements on the high temperature superconductors. Voltage reversals have been frequently observed for whiskers of the bismuth strontium calcium copper oxide (BSSCO) compounds, and we describe measurements made on high quality whiskers of the 2:2:1:2 and 2:2:2:3 phases. A simple model based on extreme anisotropy plus offset contacts can explain the gross features of four contact measurements in the ohmic flux-flow regime, but not the wealth of reversal phenomena found for the IVVI configuration in the lower temperature irreversibility region.     

A dynamic study of earthworm feeding ecology -using stable isotopes

Changes in the specific diet of earthworms with time in relation to landuse changes and two different climates were studied by analysing (13)C and (15)N natural abundance in soils and animals. Soil samples from three depths (0-10, 10-20 and 20-30 cm) and earthworms were collected from two sites: Santiago (Northwest Spain) and North Wyke (Southwest England) both consisting of replicated long-term grasslands and recently converted to maize plots. Earthworms were hand-sorted in the field at the peak of the maize growth and after harvesting at both sites. In the Spanish plots, nine and eight earthworm species, all belonging to the three ecological categories (epigeic, anecic and endogeic), were found under maize and permanent pasture, whereas at the English site five and seven different species were, respectively, identified. At both sites (13)C isotopic values of the earthworm tissues reflected changes in diet from C(3) to C(4) with epigeic and epi/anecic worms in the maize plots showing one delta unit difference in relation to the ones found in the grassland plots. Anecic worms seemed to be less responsive to landuse changes. The higher (13)C values of the Spanish soils were also reflected in the earthworm tissues when compared with the English samples. (15)N values showed no clear relationship with the cropping treatments but were clearly related to the ecological grouping, with endogeic worms reaching the highest values whereas for the epigeic and epi/anecic species the lowest values were obtained. This finding was also previously recorded by other authors1 and suggests that, in the future, stable isotope techniques could also be a useful tool in taxonomic studies. Copyright 1999 John Wiley & Sons, Ltd.     

Secondary ion yields produced by keV atomic and polyatomic ion impacts on a self-assembled monolayer surface

A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd.