The type IIA/IIB effective actions compactified on T d are known to be invariant under the T -duality group SO(d, d; Z), although the invariance of the R-R sector cannot be seen so directly. Inspired by a work of Brace, Morariu and Zumino, we introduce new potentials, which are mixtures of R-R potentials and the NS-NS 2-form, in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO (d, d; Z), the effective actions are indeed invariant under the T -duality group. The argument is made in such a way that it can apply to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new fields simplify all the expressions, including the Chern-Simons term. * )
A zone heating method, which imposes the moving temperature-gradient (▿T) field on ordering
process of various melts in general, enabled to control a macroscopic orientation of microdomain structures in
block copolymer bulk. We applied the method to a polystyrene-block-polyisoprene diblock copolymer forming
hexagonally packed cylindrical domains (hex−cyl) in the absence of external fields. We discovered that the
method creates the following special texture of hex−cyl: (1) The texture seemingly consists of volume-filled
columnar grains with the grain axis parallel to the ▿T axis (defined as the Oz axis). (2) The cylinder axis always
orients perpendicular to the Oz axis with a rotational angle φ of the cylinder axis around the Oz axis being fixed
within a grain but statistically varying randomly among different grains. (3) One set of the (100) plane of hex−cyl preferentially oriented perpendicular to Oz axis with a small rotational degree of freedom around the cylinder
axis. We interpret that the special texture is a consequence of the surface-induced order−disorder transition of
the block copolymer under the moving ▿T field.
SANS‐J (a pinhole small‐angle neutron scattering spectrometer at research reactor JRR3, Tokai, Japan) was reconstructed as a focusing and polarized neutron small‐angle scattering spectrometer (SANS‐J‐II). By employing focusing lenses of a biconcave MgF2 crystal or of a sextupole permanent magnet and a high‐resolution photomultiplier, the minimum accessible magnitude of the scattering vector qmin was improved from 3 × 10−3Å−1 to an ultra‐small‐angle scattering (USAS) of 3 × 10−4 Å−1. Compared with a Bonse–Hart double‐crystal method, the advantages of focusing USAS are the efficient detection of anisotropic USAS with an area detector, an improvement in q resolution Δq/q at conventional magnitudes of the scattering vector q ~ 10−3 Å−1 and a gain in neutron flux in the conventional q region of q ~ 10−3 Å−1.
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