Rotation and twist regular modes for trapped ghosts

A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: $2J/r^3$. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat's poles with respect to the other.Comment: 11 pages, 3 figures; General Relativity and Gravitation - 201

Size Dependence of Metal-Insulator Transition in Stoichiometric Fe3O4 Nanocrystals

Magnetite (Fe3O4) is one of the most actively studied materials with a famous metal-insulator transition (MIT), so-called the Verwey transition at around 123 K. Despite the recent progress in synthesis and characterization of Fe3O4 nanocrystals (NCs), it is still an open question how the Verwey transition changes on a nanometer scale. We herein report the systematic studies on size dependence of the Verwey transition of stoichiometric Fe3O4 NCs. We have successfully synthesized stoichiometric and uniform-sized Fe3O4 NCs with sizes ranging from 5 to 100 nm. These stoichiometric Fe3O4 NCs show the Verwey transition when they are characterized by conductance, magnetization, cryo-XRD, and heat capacity measurements. The Verwey transition is weakly size-dependent and becomes suppressed in NCs smaller than 20 nm before disappearing completely for less than 6 nm, which is a clear, yet highly interesting indication of a size effect of this well-known phenomena. Our current work will shed new light on this ages-old problem of Verwey transition.Comment: 18 pages, 4 figures, Nano Letters (accepted

Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary

Unfolding grain size effects in barium titanate ferroelectric ceramics

Grain size effects on the physical properties of polycrystalline ferroelectrics have been extensively studied for decades; however there are still major controversies regarding the dependence of the piezoelectric and ferroelectric properties on the grain size. Dense BaTiO3 ceramics with different grain sizes were fabricated by either conventional sintering or spark plasma sintering using micro- and nano-sized powders. The results show that the grain size effect on the dielectric permittivity is nearly independent of the sintering method and starting powder used. A peak in the permittivity is observed in all the ceramics with a grain size near 1μm and can be attributed to a maximum domain wall density and mobility. The piezoelectric coefficient d33 and remnant polarization Pr show diverse grain size effects depending on the particle size of the starting powder and sintering temperature. This suggests that besides domain wall density, other factors such as back fields and point defects, which influence the domain wall mobility, could be responsible for the different grain size dependence observed in the dielectric and piezoelectric/ferroelectric properties. In cases where point defects are not the dominant contributor, the piezoelectric constant d33 and the remnant polarization Pr increase with increasing grain size