A multiple scales approach to crack front waves

Perturbation of a propagating crack with a straight edge is solved using the method of matched asymptotic expansions (MAE). This provides a simplified analysis in which the inner and outer solutions are governed by distinct mechanics. The inner solution contains the explicit perturbation and is governed by a quasi-static equation. The outer solution determines the radiation of energy away from the tip, and requires solving dynamic equations in the unperturbed configuration. The outer and inner expansions are matched via the small parameter L/l defined by the disparate length scales: the crack perturbation length L and the outer length scale l associated with the loading. The method is first illustrated for a scalar crack model and then applied to the elastodynamic mode I problem. The dispersion relation for crack front waves is found by requiring that the energy release rate is unaltered under perturbation. The wave speed is calculated as a function of the nondimensional parameter kl where k is the crack front wavenumber, and dispersive properties of the crack front wave speed are described for the first time. The example problems considered here demonstrate that the potential of using MAE for moving boundary value problems with multiple scales.Comment: 25 pages, 5 figure

Calibrating AIS images using the surface as a reference

A method of evaluating the initial assumptions and uncertainties of the physical connection between Airborne Imaging Spectrometer (AIS) image data and laboratory/field spectrometer data was tested. The Tuscon AIS-2 image connects to lab reference spectra by an alignment to the image spectral endmembers through a system gain and offset for each band. Images were calibrated to reflectance so as to transform the image into a measure that is independent of the solar radiant flux. This transformation also makes the image spectra directly comparable to data from lab and field spectrometers. A method was tested for calibrating AIS images using the surface as a reference. The surface heterogeneity is defined by lab/field spectral measurements. It was found that the Tuscon AIS-2 image is consistent with each of the initial hypotheses: (1) that the AIS-2 instrument calibration is nearly linear; (2) the spectral variance is caused by sub-pixel mixtures of spectrally distinct materials and shade, and (3) that sub-pixel mixtures can be treated as linear mixtures of pure endmembers. It was also found that the image can be characterized by relatively few endmembers using the AIS-2 spectra

Angular dependent vortex pinning mechanisms in YBCO coated conductors and thin films

We present a comparative study of the angular dependent critical current density in YBa2Cu3O7 films deposited on IBAD MgO and on single crystal MgO and SrTiO3 substrates. We identify three angular regimes where pinning is dominated by different types of correlated and uncorrelated defects. We show that those regimes are present in all cases, indicating that the pinning mechanisms are the same, but their extension and characteristics are sample dependent, reflecting the quantitative differences in texture and defect density. In particular, the more defective nature of the films on IBAD turns into an advantage as it results in stronger vortex pinning, demonstrating that the critical current density of the films on single crystals is not an upper limit for the performance of the IBAD coated conductors.Comment: 14 pages, 3 figures. Submitted to AP

Far-UV FUSE spectroscopy of the OVI resonance doublet in Sand2 (WO)

We present Far-Ultraviolet Spectroscopic Explorer (FUSE) spectroscopy of Sand 2, a LMC WO-type Wolf-Rayet star, revealing the OVI resonance P Cygni doublet at 1032-38A. These data are combined with HST/FOS ultraviolet and Mt Stromlo 2.3m optical spectroscopy, and analysed using a spherical, non-LTE, line-blanketed code. Our study reveals exceptional stellar parameters: T*=150,000K, v_inf=4100 km/s, log (L/Lo)=5.3, and Mdot=10^-5 Mo/yr if we adopt a volume filling factor of 10%. Elemental abundances of C/He=0.7+-0.2 and O/He=0.15(-0.05+0.10) by number qualitatively support previous recombination line studies. We confirm that Sand 2 is more chemically enriched in carbon than LMC WC stars, and is expected to undergo a supernova explosion within the next 50,000 yr.Comment: 17 pages, 4 figures, AASTeX preprint format. This paper will appear in a special issue of ApJ Letters devoted to the first scientific results from the FUSE missio

Fluoride adsorption onto an acid treated lateritic mineral from Kenya: Equilibrium studies

Adsorption of fluoride (F) ions from water using acid treated lateritic mineral (LM-1) from Kenya was studied by batch experiments. The effect of acid-treatment of adsorbent and change in temperature, mass of LM-1, pH and selected competing ions was evaluated. The adsorption process was strongly influenced by temperature, pH and adsorbent dosage. The percentage F removal increased the presence of the nitrate and the chlorate ions but decreased the presence of sulphates, chloride and phosphate ions. Adsorption isotherms were classified according to Giles’ classification and the adsorption data validated using Langmuir and Freundlich isotherms. The data correlated to both the Langmuir and Freundlich isotherms although the data fit to the Freundlich model was somehow better. This showed that F adsorption onto LM-1 followed a mixed adsorption mechanism in which physisorption reactions involving intra-particle diffusion of F into mesoporous sites in LM-1 became increasingly important at higher concentrations and temperatures whereas ion-exchange mechanism involving surface OH- appear to dominate at low surface coverage in more alkaline conditions. With maximum adsorption capacity of 10.5 mg/g, LM-1 could be used to remove F water.Key words: Equilibrium analysis, fluoride adsorption, Langmuir and Freundlich isotherms, Lateritic mineral adsorbent, low-cost adsorbents

Charge Exchange Processes between Excited Helium and Fully Stripped Ions

We made a classical trajectory Monte Carlo (CTMC) calculation of state selective cross sections for processes between some light ions and excited helium. The results, useful for analysis of spectroscopic data of fusion devices, are in good agreement with theoretical predictions of scaling laws.Comment: LaTex, 8 pages, 4 figures (available on request to the authors), DFPD/94/TH/57, to be published in Phys. Rev.

Near-Threshold Production of omega Mesons in the pp -> pp omega Reaction

The total cross section for omega production in the pp -> pp omega reaction has been measured at five c.m. excess energies from 3.8 to 30 MeV. The energy dependence is easily understood in terms of a strong proton-proton final state interaction combined with a smearing over the width of the state. The ratio of near-threshold phi and omega production is consistent with the predictions of a one-pion-exchange model and the degree of violation of the OZI rule is similar to that found in the pi-p -> n omega/phi reactions.Comment: Report in LaTeX2e. 12 pages with 2 eps figure

Onset of Propagation of Planar Cracks in Heterogeneous Media

The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along the crack front which is non-monotonic in time due to the elastic waves in the medium. In the quasistatic limit with instantaneous stress transfer, the crack front exhibits dynamic critical phenomenon, with a second order like transition from a pinned to a moving phase as the applied load is increased through a critical value. At criticality, the crack-front is self-affine, with a roughness exponent $\zeta =0.34\pm 0.02$. The dynamic exponent $z$ is found to be equal to $0.74\pm 0.03$ and the correlation length exponent $\nu =1.52\pm 0.02$. These results are in good agreement with those obtained from an epsilon expansion. Sound-travel time delays in the stress transfer do not change the static exponents but the dynamic exponent $z$ becomes exactly one. Real elastic waves, however, lead to overshoots in the stresses above their eventual static value when one part of the crack front moves forward. Simplified models of these stress overshoots are used to show that overshoots are relevant at the depinning transition leading to a decrease in the critical load and an apparent jump in the velocity of the crack front directly to a non-zero value. In finite systems, the velocity also shows hysteretic behaviour as a function of the loading. These results suggest a first order like transition. Possible implications for real tensile cracks are discussed.Comment: 51 pages + 20 figur