On the Use of Approximation Methods for Microcrack Shielding Problems

There is experimental evidence that stress-induced microcracking near a macrocrack tip enhances the fracture toughness of brittle materials. In considering the interaction of the macrocrack with multiple microcracks using a discrete model, it is essential to use approximation methods in order to keep the amount of the computation to a tractable level. However, when crack distances are small, the results of the approximation methods can be significantly different from the numerical solution based upon the exact formulation. The results obtained by these approximation methods will be compared with the numerical solution to show the applicability ranges in which the errors are acceptably small. The use of results obtained by the approximation methods outside applicability ranges in literature is shown to lead to incorrect conclusions concerning microcrack shielding

Malmquist Bias and the Distance to the Virgo Cluster

This paper investigates the impact of Malmquist bias on the distance to the Virgo cluster determined by the H_0 Key Project using M100, and consequently on the derived value of H_0. Malmquist bias is a volume-induced statistical effect which causes the most probable distance to be different from the raw distance measured. Consideration of the bias in the distance to the Virgo cluster raises this distance and lowers the calculated value of H_0. Monte Carlo simulations of the cluster have been run for several possible distributions of spirals within the cluster and of clusters in the local universe. Simulations consistent with known information regarding the cluster and the errors of measurement result in a bias of about 6.5%-8.5%. This corresponds to an unbiased distance of 17.2-17.4 Mpc and a value of H_0 in the range 80-82 km/s/Mpc. The problem of determining the bias to Virgo illustrates several key points regarding Malmquist bias. Essentially all conventional astronomical distance measurements are subject to this bias. In addition, the bias accumulates when an attempt is made to construct "distance ladders" from measurements which are individually biased. As will be shown in the case of Virgo, the magnitude and direction of the bias are sensitive to the spatial distribution of the parent poputation from which the observed object is drawn - a distribution which is often poorly known. This leads to uncertainty in the magnitude of the bias, and adds to the importance of minimizing the number of steps in "distance ladders".Comment: 19 pages, 3 figures, Latex, To appear in Ap

Characterizing normal crossing hypersurfaces

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito's theory of free divisors, also a characterization in terms of logarithmic differential forms and vector fields is found and and finally another one in terms of the logarithmic residue using recent results of M. Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2 figure

Manipulating the torsion of molecules by strong laser pulses

A proof-of-principle experiment is reported, where torsional motion of a molecule, consisting of a pair of phenyl rings, is induced by strong laser pulses. A nanosecond laser pulse spatially aligns the carbon-carbon bond axis, connecting the two phenyl rings, allowing a perpendicularly polarized, intense femtosecond pulse to initiate torsional motion accompanied by an overall rotation about the fixed axis. The induced motion is monitored by femtosecond time-resolved Coulomb explosion imaging. Our theoretical analysis accounts for and generalizes the experimental findings.Comment: 4 pages, 4 figures, submitted to PRL; Major revision of the presentation of the material; Correction of ion labels in Fig. 2(a

Massless Thirring model in canonical quantization scheme

It is shown that the exact solvability of the massless Thirring model in the canonical quantization scheme originates from the intrinsic linearizability of its Heisenberg equations in the method of dynamical mappings. The corresponding role of inequivalent representations of free massless Dirac field is elucidated.Comment: 10 page

Apollo experience report: Simulation of manned space flight for crew training

Through space-flight experience and the development of simulators to meet the associated training requirements, several factors have been established as fundamental for providing adequate flight simulators for crew training. The development of flight simulators from Project Mercury through the Apollo 15 mission is described. The functional uses, characteristics, and development problems of the various simulators are discussed for the benefit of future programs

Vortex critical behavior at the de-confinement phase transition

The de-confinement phase transition in SU(2) Yang-Mills theory is revisited in the vortex picture. Defining the world sheets of the confining vortices by maximal center projection, the percolation properties of the vortex lines in the hypercube consisting of the time axis and two spatial axis are studied. Using the percolation cumulant, the temperature for the percolation transition is seen to be in good agreement with the critical temperature of the thermal transition. The finite size scaling function for the cumulant is obtained. The critical index of the finite size scaling function is consistent with the index of the 3D Ising model.Comment: 4 pages, 4 PS figures, using revtex4, paragraph and refs added, typo correcte

On the relevance of center vortices to QCD

In a numerical experiment, we remove center vortices from an ensemble of lattice SU(2) gauge configurations. This removal adds short-range disorder. Nevertheless, we observe long-range order in the modified ensemble: confinement is lost and chiral symmetry is restored (together with trivial topology), proving that center vortices are responsible for both phenomena. As for the Abelian monopoles, they survive but their percolation properties are lost.Comment: 4 pages, 5 figures; discussion expanded, text compressed... to appear in Phys. Rev. Let

Post-merger Signatures of Red-sequence Galaxies in Rich Abell Clusters at z≲0.1z\lesssim 0.1

We have investigated the post-merger signatures of red-sequence galaxies in rich Abell clusters at $z \lesssim$ 0.1: A119, A2670, A3330 and A389. Deep images in u', g', r' and medium-resolution galaxy spectra were taken using MOSAIC 2 CCD and Hydra MOS mounted on a Blanco 4-m telescope at CTIO. Post-merger features are identified by visual inspection based on asymmetric disturbed features, faint structures, discontinuous halo structures, rings and dust lanes. We found that ~ 25% of bright (M_r < -20) cluster red-sequence galaxies show post-merger signatures in four clusters consistently. Most (~ 71%) of the featured galaxies were found to be bulge-dominated, and for the subsample of bulge-dominated red-sequence galaxies, the post-merger fraction rises to ~ 38%. We also found that roughly 4% of bulge-dominated red-sequence galaxies interact (on-going merger). A total of 42% (38% post-merger, 4% on-going merger) of galaxies show merger-related features. Compared to a field galaxy study with a similar limiting magnitude (van Dokkum 2005), our cluster study presents a similar post-merger fraction but a markedly lower on-going merger fraction. The merger fraction derived is surprisingly high for the high density of our clusters, where the fast internal motions of galaxies are thought to play a negative role in galaxy mergers. The fraction of post-merger and on-going merger galaxies can be explained as follows. Most of the post-merger galaxies may have carried over their merger features from their previous halo environment, whereas interacting galaxies interact in the current cluster in situ. According to our semi-analytic calculation, massive cluster haloes may very well have experienced tens of halo mergers over the last 4-5 Gyr; post-merger features last that long, allowing these features to be detected in our clusters today. (Abridged)Comment: 16 pages, 15 figures, 7 tables, accepted for publication in ApJ