How to construct a coordinate representation of a Hamiltonian operator on a torus

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.Comment: 17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript fil

Structure and mobility of a series of poly(alkyl L-glutamate)s studied by VT C-13 CPMAS NMR spectroscopy

VT CPMAS NMR measurements were carried out for a series of poly(alkyl L-glutamate)s (PALG) which have n-alkyl side chains with carbon numbers ranging from 2 to 12 in order to investigate the structure and mobility of the main and the side chains. From the temperature dependencies of the peak intensities for the PALGs, the relative mobilities of the main and side chains are discussed. For PG-2 and PG-4, the molecular motions of both the main and side chains are not very fast. From the amount ratio between the main and side chains, the main chain dominates the entire mobility of the polymer. As the side chain length increases, the side chain motion is drastically activated by a temperature change. In addition, the main chain motion is induced by the side chain motion. For PALGs with long alkyl side chains, the mobilities of the polymers are governed by the structure and mobility of the side chain

Molecular motion of the main chain for a series of poly(alkyl L-glutamate)s as studied by H-2 NMR

H-2 NMR measurements were carried out for a series of poly(alkyl L-glutamate)s (PALG) in which the H-1 of the amide group in the main chain is replaced by H-2 in order to investigate the mobility and motional mode of the main chain. At low temperature, the H-2 spectra were typical powder patterns, which have three principal values. The temperature dependencies for the H-2 NMR spectra varied with the side chain length. For PALG with a short side chain length, Deltanu(1), Deltanu(2), and Deltanu(3) are almost constant in all temperature ranges. As the side chain length increases, the difference between the peaks and shoulders decreased with temperature. For PG-12-N-D, the peaks and shoulders are fused at high temperature in a liquid crystalline state. The mobility and molecular motion of the main chain is discussed based on the obtained H-2 NMR spectra

Morphology of drawn syndiotactic polypropylene films

Morphological studies were conducted to investigate the drawability of melt-quenched (MQ) and slowly cooled (MSC) films of syndiotactic polypropylene (sPP) with a high syndiotactic pentad fraction. Transmission electron microscopy (TEM) using the ruthenium tetraoxide staining and ultrathin sectioning method revealed that amorphous chains as the matrix of MQ film played a role in drawability of the film by their alignment to machine direction (MD) and partial crystallizations into nanofibrils. On the other hand, the initial strain induced, rotations of clusters of long lamellar crystals as the major entity of MSC film accompanying breaks of long lamellae and formation of crazes and microvoids at the cluster boundary. Compared with a homogeneous thinning of MQ film by drawing, ca. 100 nm-thick layer slips along MD and parallel to the film surface took place in MSC film. This gave rise to the formation of V-shaped bent lamellar morphology and their further break into a smaller cluster of stacked lamellae which were aligned oblique by ca. 35 from MD. With elongation, some nanofibrils formed from chains generated by the partial breaks of lamellae are aligned perpendicular to the remained oblique lamellae and others parallel to MD in region where lamellar morphology almost disappeared. No chain slips in the nanofibrils can be related to a low elongation at break, i.e. a low ductility of sPP films. The lower elongation at break for MSC film than for MQ one can be interpreted by microvoids initially formed in the neck region and later moved to the fully drawn part, the microvoids initiating the break of the drawn film

Synthesis and properties of radiopaque polymer hydrogels: polyion complexes of copolymers of acrylamide derivatives having triiodophenyl and carboxyl groups and p-styrene sulfonate and polyallylamine

In order to pursue a possibility of application of radiopaque polymer hydrogels to vascular embolization, studies were done on synthesis of iodine-containing copolyanions and properties of their hydrogels with polycation via formation of polyion complexes. Acrylamide derivatives having triiodophenyl and carboxyl groups were synthesized and copolymerized with sodium styrene sulfonate at various molar ratios of initiator to monomer and temperatures. Hydrogels were prepared by mixing aqueous solutions of the obtained radiopaque copolyanions and polyallylamine. Embolization was examined by injection of these hydrogels into vein of a removed porcine kidney as a preliminary test for transcatheter arterial embolization (TAE) for hepatocellular carcinoma. It was found that the hydrogels prepared from the copolycation obtained under particular conditions give high X-ray contrasts of the vein and remained there, though copolycations with low molecular weights had a tendency to drain through the capillaries to the peripheral tissues. It is therefore concluded that the hydrogels examined in the present study are promising for vascular embolization

Site-Dilution in quasi one-dimensional antiferromagnet Sr2(Cu1-xPdx)O3: reduction of Neel Temperature and spatial distribution of ordered moment sizes

We investigate the Neel temperature of Sr2CuO3 as a function of the site dilution at the Cu (S=1/2) sites with Pd (S=0), utilizing the muon spin relaxation (muSR) technique. The Neel temperature, which is Tn=5.4K for the undoped system, becomes significantly reduced for less than one percent of doping Pd, giving a support for the previous proposal for the good one-dimensionality. The Pd concentration dependence of the Neel temperature is compared with a recent theoretical study (S. Eggert, I. Affleck and M.D.P. Horton, Phys. Rev. Lett. 89, 47202 (2002)) of weakly coupled one-dimensional antiferromagnetic chains of S=1/2 spins, and a quantitative agreement is found. The inhomogeneity of the ordered moment sizes is characterized by the muSR time spectra. We propose a model that the ordered moment size recovers away from the dopant S=0 sites with a recovery length of \xi = 150-200 sites. The origin of the finite recovery length \xi for the gapless S=1/2 antiferromagnetic chain is compared to the estimate based on the effective staggered magnetic field from the neighboring chains.Comment: 10 pages, 9 figures, submitted to PR

Multifactorial Origins of Heart and Gut Defects in nipbl-Deficient Zebrafish, a Model of Cornelia de Lange Syndrome

nipbl-deficient zebrafish provide evidence that heart and gut defects in Cornelia de Lange Syndrome are caused by combined effects of multiple gene expression changes that occur during early embryonic development