Partially Quenched QCD with Non-Degenerate Dynamical Quarks

We discuss the importance of using partially quenched theories with three degenerate quarks for extrapolating to QCD, and present some relevant results from chiral perturbation theory.Comment: LATTICE99 talk. 3 pages, 2 figures. Uses epsf and espcrc2.st

Homogeneous explosion and shock initiation for a three-step chain-branching reaction model

The role of chain-branching cross-over temperatures in shock-induced ignition of reactive materials is studied by numerical simulation, using a three-step chainbranching reaction model. In order to provide insight into shock initiation, the simpler problem of a spatially homogeneous explosion is first considered. It is shown that for ratios of the cross-over temperature to the initial temperature, T-B, sufficiently less than unity, the homogeneous explosion can be quantitatively described by a widely used two-step model, while for T-B sufficiently above unity the homogeneous explosion can be effectively described by the standard one-step model. From the matchings between these homogeneous-explosion solutions, the parameters of the reduced models are identified in terms of those of the three-step model. When T-B is close to unity, all the reactions of the three-step model have a leading role, and hence in this case the model cannot be reduced further. In the case of shock initiation, for T-B (which is now the ratio of the cross-over temperature to the initial shock temperature) sufficiently below unity, the three-step solutions are qualitatively described by those of the matched two-step model, but there are quantitative differences due to the assumption in the reduced model that a purely chain-branching explosion occurs instantaneously. For T-B sufficiently above unity, the matched one-step model is found to effectively describe the way in which the heat release and fluid dynamics couple. For T-B close to unity, the competition between chain branching and chain termination is important from the outset. In these cases the speed at which the forward moving explosion wave that emerges from the piston is sensitive to T-B, and changes from supersonic to subsonic for a value of T-B just below unity

Quenched Chiral Perturbation Theory for Baryons

We develop quenched chiral perturbation theory for baryons using the graded-symmetry formalism of Bernard and Golterman and calculate non-analytic contributions to the baryon masses coming from quenched chiral loops. The usual term proportional to $m_{q}^{3/2}$ is substantially altered due to the cancellation of diagrams with internal quark loops. In addition, the $\eta'$ ``hairpin'' vertex leads to a new correction, proportional to $m_{q}^{1/2}$. We compare our results to numerical lattice data and use them to estimate the size of the quenching error in the octet baryon masses.Comment: 7 pages (An abridged version of this note will appear in the proceedings of Lattice'93. Latex + 14 postscript files, bundled using uufiles. Needs psfig.) UW/PT-93-0

Measurements of mixed-mode crack surface displacements and comparison with theory

A theoretical and an experimental technique is used to determine crack surface displacements under mixed-mode conditions. Crack surface displacements proved to be quite useful in mode 1 fracture analysis in that they are directly related to strain energy release rate and stress intensity factor. It is felt that similar relationships can be developed for the mixed-mode case. A boundary-integral method was developed for application to two-dimensional fracture mechanics problems. This technique was applied to the mixed-mode problem. A laser interferometry technique, for measurement of crack surface displacements under mixed-mode conditions, is presented. The experimental measurements are reported and the results of the two approaches are compared and discussed

Kaon B parameter from quenched Lattice QCD

We present results of a large-scale simulation for the Kaon B parameter $B_K$ in quenched lattice QCD with the Kogut-Susskind quark action. Calculating $B_K$ at 1% statistical accuracy for seven values of lattice spacing in the range $a\approx 0.24-0.04$ fm on lattices up to $56^3\times 96$, we verify a quadratic $a$ dependence of $B_K$ theoretically predicted. Strong indications are found that, with our level of accuracy, $\alpha_{\bar{MS}}(1/a)^2$ terms arising from our one-loop matching procedure have to be included in the continuum extrapolation. We present $B_K$(NDR, 2 GeV)=0.628(42) as our final value, as obtained by a fit including the $\alpha_{\bar{MS}}(1/a)^2$ term.Comment: 8 pages, Latex(revtex, epsf), 2 epsf figure