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

Pattern stabilization through parameter alternation in a nonlinear optical system

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation, and the measured spatial frequencies of the patterns.Comment: 12 pages, 5 figures. To appear in PR

Heavy-Meson Observables at One-Loop in Partially Quenched Chiral Perturbation Theory

I present one-loop level calculations of the Isgur-Wise functions for B -> D^{(*)} + e + nu, of the matrix elements of isovector twist-2 operators in B and D mesons, and the matrix elements for the radiative decays D^* -> D + gamma in partially quenched heavy quark chiral perturbation theory. Such expressions are required in order to extrapolate from the light quark masses used in lattice simulations of the foreseeable future to those of nature.Comment: 13 pages, 3 fig

Deconstructing Noncommutativity with a Giant Fuzzy Moose

We argue that the worldvolume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit `deconstruction' of a wide class of noncommutative theories. This also provides insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite `fuzzy moose' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.Comment: 22 pages, 3 figures, typos caught and refs added; expanded interpretation of discrete torsio

Quenched Chiral Perturbation Theory for Vector Mesons

We develop quenched chiral perturbation theory for vector mesons made of light quarks, in the limit where the vector meson masses are much larger than the pion mass. We use this theory to extract the leading nonanalytic dependence of the vector meson masses on the masses of the light quarks. By comparing with analogous quantities computed in ordinary chiral perturbation theory, we estimate the size of quenching effects, observing that in general they can be quite large. This estimate is relevant to lattice simulations, where the $\rho$ mass is often used to set the lattice spacing.Comment: 18 pages, 8 figures, uses REVTeX and epsf.st

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

Applications of Partially Quenched Chiral Perturbation Theory

Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B_K and the K+ decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta are also considered. We find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in Phys. Rev.

Short fatigue crack behavior in notched 2024-T3 aluminum specimens

Single-edge, semi-circular notched specimens of Al 2024-T3, 2.3 mm thick, were cyclicly loaded at R-ratios of 0.5, 0.0, -1.0, and -2.0. The notch roots were periodically inspected using a replica technique which duplicates the bore surface. The replicas were examined under an optical microscope to determine the initiation of very short cracks and to monitor the growth of short cracks ranging in length from a few tens of microns to the specimen thickness. In addition to short crack growth measurements, the crack opening displacement (COD) was measured for surface cracks as short as 0.035 mm and for through-thickness cracks using the Interferometric Strain/Displacement Gage (ISDG), a laser-based optical technique. The growth rates of short cracks were faster than the long crack growth rates for R-ratios of -1.0 and -2.0. No significant difference between short and long crack growth rates was observed for R = 0.0. Short cracks had slower growth rates than long cracks for R = 0.5. The crack opening stresses measured for short cracks were smaller than those predicted for large cracks, with little difference appearing for positive R-ratios and large differences noted for negative R-ratios

Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how it is possible that, for physical quark masses of O(a^2), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.Comment: 26 pages, 2 figures (using psfig). Version to appear in PRD (clarifications added to introduction and section 6; typos corrected; references updated

Chiral Lagrangian Parameters for Scalar and Pseudoscalar Mesons

The results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched lattice QCD are presented. For two values of lattice spacing, $\beta=5.7$ ($a \approx .18$ fm) and 5.9 ($a \approx .12$ fm), we probe the light quark mass region using clover improved Wilson fermions with the MQA pole-shifting ansatz to treat the exceptional configuration problem. The quenched chiral loop parameters $m_0$ and $\alpha_{\Phi}$ are determined from a study of the pseudoscalar hairpin correlator. From a global fit to the meson correlators, estimates are obtained for the relevant chiral Lagrangian parameters, including the Leutwyler parameters $L_5$ and $L_8$. Using the parameters obtained from the singlet and nonsinglet pseudoscalar correlators, the quenched chiral loop effect in the nonsinglet scalar meson correlator is studied. By removing this QCL effect from the lattice correlator, we obtain the mass and decay constant of the ground state scalar, isovector meson $a_0$.Comment: 36 pages, 12 figures, LaTe