We investigate the generic behaviour of marginally trapped tubes (roughly time-evolved apparent horizons) using simple, spherically symmetric examples of dust and scalar field collapse/accretion onto pre-existing black holes. We find that given appropriate physical conditions the evolution of the marginally trapped tube may be either null, timelike, or spacelike and further that the marginally trapped two-sphere cross-sections may either expand or contract in area. Spacelike expansions occur when the matter falling into a black hole satisfies ρ − P ≤ 1/A, where A is the area of the horizon while ρ and P are respectively the density and pressure of the matter. Timelike evolutions occur when (ρ − P ) is greater than this cut-off and so would be expected to be more common for large black holes. Physically they correspond to horizon "jumps" as extreme conditions force the formation of new horizons outside of the old.

Why does the second peak of pair correlation functions split in quasi-two-dimensional disordered films? Appl. Phys. Lett. 102, 071907 (2013) Low-bias electron transport properties of germanium telluride ultrathin films J. Appl. Phys. 113, 063711 (2013) P(VDF-TrFE-CFE) terpolymer thin-film for high performance nonvolatile memory Appl. Phys. Lett. 102, 063103 (2013) Investigation of the near-surface structures of polar InN films by chemical-state-discriminated hard X-ray photoelectron diffraction Appl. Phys. Lett. 102, 031914 (2013) Effects of grain microstructure on magnetic properties in FePtAg-C media for heat assisted magnetic recording J. Appl. Phys. 113, 043910 (2013) Additional information on J. Appl. Phys. Cu-implanted SiO 2 films on Si͑100͒ have been studied and compared to unimplanted SiO 2 on Si͑100͒ using x-ray methods, transmission electron microscopy, Rutherford backscattering, and Brillouin spectroscopy. The x-ray results indicate the preferred orientation of Cu ͕111͖ planes parallel to the Si substrate surface without any directional orientation for Cu-implanted SiO 2 /Si͑100͒ and for Cu-implanted and annealed SiO 2 /Si͑100͒. In the latter case, transmission electron microscopy reveals the presence of spherical nanocrystallites with an average size of ϳ2.5 nm. Rutherford backscattering shows that these crystallites ͑and the Cu in the as-implanted film͒ are largely confined to depths of 0.4− 1.2 m below the film surface. Brillouin spectra contain peaks due to surface, film-guided and bulk acoustic modes. Surface ͑longitudinal͒ acoustic wave velocities for the implanted films were ϳ7% lower ͑ϳ2% higher͒ than for unimplanted SiO 2 /Si͑100͒. Elastic constants were estimated from the acoustic wave velocities and film densities. C 11 ͑C 44 ͒ for the implanted films was ϳ10% higher ͑lower͒ than that for the unimplanted film. The differences in acoustic velocities and elastic moduli are ascribed to implantation-induced compaction and/or the presence of Cu in the SiO 2 film.