An experimental study of flow-induced fiber orientation and concentration distributions in a concentrated suspension flow through a slit channel containing a cylinder

Flow-induced fiber orientation and concentration distributions were measured in a concentrated fiber suspension (CFS) and a dilute one (DFS). The channel has a thin slit geometry containing a circular cylinder. In the previous work, many researchers have qualitatively studied fiber orientation and concentration distributions in injection-molded products of fiber-reinforced plastics. In the present work, however, they are quantitatively estimated by direct observation of fibers in the concentrated suspension flow. For the CFS, some fibers rotate in an expansion part between the channel wall and the circular cylinder, and the fiber orientation becomes almost random state. On the other hand, fibers are perfectly aligned along the flow direction owing to the elongational flow near the centerline downstream of the cylinder. The fiber concentration has a flat distribution except near the channel wall and the centerline. For the DFS a minimum in the fiber concentration distribution was clearly observed on the centerline, and two peaks beside the centerline and near the channel wall. This characteristic distribution is caused by the fiber-wall and fiber-cylinder interactions. It is found that the obstacle such as the circular cylinder in the channel significantly affects the fiber orientation downstream of the obstacle for the CFD, while it affects the fiber concentration distribution for the DFS.     

A classification of sharp tridiagonal pairs

Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A:V→V and A^∗:V→V that satisfy the following conditions: (i) each of A,A^∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A^∗V_i⊆V_i-1+V_i+V_i+1 for 0?i?d, where V_-1=0 and V_d+1=0; (iii) there exists an ordering of the eigenspaces of A^∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W, A^∗W⊆W, W≠0, W≠V. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide. The pair A,A^∗ is called sharp whenever . It is known that if F is algebraically closed then A,A^∗ is sharp. In this paper we classify up to isomorphism the sharp tridiagonal pairs. As a corollary, we classify up to isomorphism the tridiagonal pairs over an algebraically closed field. We obtain these classifications by proving the μ-conjecture.     

A revised taxonomy of the ammonoid genus Desmoceras from Japan and southern Sakhalin

Based on the stratigraphically well sorted material from Japan and southern Sakhalin, the ammonoid species belonging to the genus Desmoceras are classified as follows in ascending order: D. latidorsatum (Michelin) (Middle to mid-Upper Albian), D. dawsoni shikokuense (Yabe and Shimizu) (Upper Albian), D. kossmati Matsumoto (uppermost Albian–Lower Cenomanian), D. japonicum Yabe (uppermost Albian–Cenomanian), and D. ezoanum Matsumoto (mid-Upper Cenomanian–mid-Lower Turonian). D. japonicum can be subdivided into the earlier and later subspecies. D. poronaicum Yabe is a junior synonym of D. japonicum. Despite the scarcely ornamented shell, each taxon can be defined by its own characters.     

General description of mechanical anisotropy of semicrystalline polymers in relation to orientation of structural units composed of crystalline and noncrystalline materials

A mathematical representation of the transformation of an orientation function between two sets of Cartesian coordinates is discussed in terms of a series expansion of the distribution function in generalized spherical harmonics. A general procedure for calculating the mechanical anisotropy of a single-phase system (a polycrystalline material) from the orientation of its structural units and the intrinsic mechanical anisotropy of the structural unit is discussed in relation to the transformation of the orientation distribution function, i.e., mutual conversion of the coefficients in the expansion of the distribution function between the two sets of Cartesian coordinates. The procedure is extended to a two-phase systems (semicrystalline polymers) containing structural units composed of crystalline and noncrystalline materials in three different geometrical arrangements.     

1,3,4,6-Tetrakis(isopropylthio)thieno[3,4-c]thiophenium bis(tetrafluoroborate): X-ray crystal structure of a stable thieno[3,4-c]thiophene dication

The structure of the 1,3,4,6-tetrakis(isopropylthio)thieno[3,4-c]thiophene dication ( 2 ) prepared from 1,3,4,6-tetrakis(isopropylthio)thieno[3,4-c]thiophene ( 1 ) by two-electron oxidation was investigated by X-ray crystallographic analysis. The results revealed that the positive charges are largely delocalized on the two i-PrS-C-C-C-SPr-i moieties.     

Composite lattice pattern formation in a wide-aperture thin-slice solid-state laser with imperfect reflective ends

We observed self-formations of multiple lasing channels and two-dimensional lasing patterns consisting of composite local modes having different lasing frequencies in a laser-diode-pumped wide-aperture thin-slice solid-state laser with imperfect reflective end surfaces. Global patterns resembling higher-order Hermite-Gaussian modes or possessing N-fold rotational symmetries were experimentally shown to appear due to the standard polished surface roughness of closely spaced reflective ends and nonlinear modal interactions.