The missing top of AdS resonance structure

We study a massless scalar field in AdS_{d+1} with a nonlinear coupling \phi^N and not limited to spherical symmetry. The free-field-eigenstate spectrum is strongly resonant, and it is commonly believed that the nonlinear coupling leads to energy transfer between eigenstates. We prove that when $Nd$ is even, the most efficient resonant channels to transfer energy are always absent. In particular, for N=3 this means no energy transfer at all. For N=4, this effectively kills half of the channels, leading to the same set of extra conservation laws recently derived for gravitational interactions within spherical symmetry.Comment: 12 pages, no figures, version 2 that mutes "showkeys" correctly and added one referenc

On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor–Green and Kida–Pelz velocity fields, which, at t = 0, satisfy ω·∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions

Fatigue crack growth in a particulate TiB2 reinforced powder metallurgy iron-based composite

Fatigue crack growth behavior has been examined in a particulate titanium diboride (TiB2)–reinforced iron-based composite that had been produced via a mechanical alloying process. Comparison with equivalent unreinforced material indicated that fatigue crack growth resistance in the composite was superior to monolithic matrix material in the near-threshold regime. The composite exhibited relatively low crack closure levels at threshold, indicative of a high intrinsic (effective) threshold growth resistance compared to the unreinforced iron. The lower closure levels of the composite were consistent with reduced fracture surface asperity sizes, attributable to the reinforcement particles limiting the effective slip distance for stage I–type facet formation. The observed shielding behavior was rationalized in terms of recent finite-element analysis of crack closure in relation to the size of crack wake asperities and the crack-tip plastic zone. The different intrinsic fatigue thresholds of the composite and unreinforced iron were closely consistent with the influences of stiffness and yield strength on cyclic crack-tip opening displacements. Cracks in the composite were generally seen to avoid direct crack-tip–particle interaction