Symplectic Reduction and Symmetry Algebra in Boundary Chern-Simons theory

We derive the Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary by using the symplectic reduction method and the Noether procedures.Comment: References are adde

Study of axial strain induced torsion of single wall carbon nanotubes by 2D continuum anharmonic anisotropic elastic model

Recent molecular dynamic simulations have found chiral single wall carbon nanotubes (SWNTs) twist during stretching, which is similar to the motion of a screw. Obviously this phenomenon, as a type of curvature-chirality effect, can not be explained by usual isotropic elastic theory of SWNT. More interestingly, with larger axial strains (before buckling), the axial strain induced torsion (a-SIT) shows asymmetric behaviors for axial tensile and compressing strains, which suggests anharmonic elasticity of SWNTs plays an important role in real a-SIT responses. In order to study the a-SIT of chiral SWNTs with actual sizes, and avoid possible deviations of computer simulation results due to the finite-size effect, we propose a 2D analytical continuum model which can be used to describe the the SWNTs of arbitrary chiralities, curvatures, and lengths, with the concerning of anisotropic and anharmonic elasticity of SWNTs. This elastic energy of present model comes from the continuum limit of lattice energy based on Second Generation Reactive Empirical Bond Order potential (REBO-II), a well-established empirical potential for solid carbons. Our model has no adjustable parameters, except for those presented in REBO-II, and all the coefficients in the model can be calculated analytically. Using our method, we obtain a-SIT responses of chiral SWNTs with arbitrary radius, chiralities and lengthes. Our results are in reasonable agreement with recent molecular dynamic simulations. [Liang {\it et. al}, Phys. Rev. Lett, ${\bf 96}$, 165501 (2006).] Our approach can also be used to calculate other curvature-chirality dependent anharmonic mechanic responses of SWNTs.Comment: 14 pages, 2 figure

Cation mono- and co-doped anatase TiO2_2 nanotubes: An {\em ab initio} investigation of electronic and optical properties

The structural, electronic, and optical properties of metal (Si, Ge, Sn, and Pb) mono- and co-doped anatase TiO$_{2}$ nanotubes are investigated, in order to elucidate their potential for photocatalytic applications. It is found that Si doped TiO$_{2}$ nanotubes are more stable than those doped with Ge, Sn, or Pb. All dopants lower the band gap, except the (Ge, Sn) co-doped structure, the decrease depending on the concentration and the type of dopant. Correspondingly, a redshift in the optical properties for all kinds of dopings is obtained. Even though a Pb mono- and co-doped TiO$_{2}$ nanotube has the lowest band gap, these systems are not suitable for water splitting, due to the location of the conduction band edges, in contrast to Si, Ge, and Sn mono-doped TiO$_{2}$ nanotubes. On the other hand, co-doping of TiO$_{2}$ does not improve its photocatalytic properties. Our findings are consistent with recent experiments which show an enhancement of light absorption for Si and Sn doped TiO$_{2}$ nanotubes.Comment: revised and updated, 23 pages (preprint style), 7 figures, 5 table

Superconducting transition of a two-dimensional Josephson junction array in weak magnetic fields

The superconducting transition of a two-dimensional (2D) Josephson junction array exposed to weak magnetic fields has been studied experimentally. Resistance measurements reveal a superconducting-resistive phase boundary in serious disagreement with the theoretical and numerical expectations. Critical scaling analyses of the $IV$ characteristics indicate contrary to the expectations that the superconducting-to-resistive transition in weak magnetic fields is associated with a melting transition of magnetic-field-induced vortices directly from a pinned-solid phase to a liquid phase. The expected depinning transition of vortices from a pinned-solid phase to an intermediate floating-solid phase was not observed. We discuss effects of the disorder-induced random pinning potential on phase transitions of vortices in a 2D Josephson junction array.Comment: 9 pages, 7 figures (EPS+JPG format), RevTeX

Spectral signatures of thermal spin disorder and excess Mn in half-metallic NiMnSb

Effects of thermal spin disorder and excess Mn on the electronic spectrum of half-metallic NiMnSb are studied using first-principles calculations. Temperature-dependent spin disorder, introduced within the vector disordered local moment model, causes the valence band at the $\Gamma$ point to broaden and shift upwards, crossing the Fermi level and thereby closing the half-metallic gap above room temperature. The spectroscopic signatures of excess Mn on the Ni, Sb, and empty sites (Mn$_\mathrm{Ni}$, Mn$_\mathrm{Sb}$, and Mn$_\mathrm{E}$) are analyzed. Mn$_\mathrm{Ni}$ is spectroscopically invisible. The relatively weak coupling of Mn$_\mathrm{Sb}$ and Mn$_\mathrm{E}$ spins to the host strongly deviates from the Heisenberg model, and the spin of Mn$_\mathrm{E}$ is canted in the ground state. While the half-metallic gap is preserved in the collinear ground state of Mn$_\mathrm{Sb}$, thermal spin disorder of the weakly coupled Mn$_\mathrm{Sb}$ spins destroys it at low temperatures. This property of Mn$_\mathrm{Sb}$ may be the source of the observed low-temperature transport anomalies.Comment: 5 pages, 7 figures, updated version with minor revisions and an additional figure, accepted in Phys. Rev. B (Rapid Communication

Segmentation, Reconstruction, and Analysis of Blood Thrombus Formation in 3D 2-Photon Microscopy Images

We study the problem of segmenting, reconstructing, and analyzing the structure growth of thrombi (clots) in blood vessels in vivo based on 2-photon microscopic image data. First, we develop an algorithm for segmenting clots in 3D microscopic images based on density-based clustering and methods for dealing with imaging artifacts. Next, we apply the union-of-balls (or alpha-shape) algorithm to reconstruct the boundary of clots in 3D. Finally, we perform experimental studies and analysis on the reconstructed clots and obtain quantitative data of thrombus growth and structures. We conduct experiments on laser-induced injuries in vessels of two types of mice (the wild type and the type with low levels of coagulation factor VII) and analyze and compare the developing clot structures based on their reconstructed clots from image data. The results we obtain are of biomedical significance. Our quantitative analysis of the clot composition leads to better understanding of the thrombus development, and is valuable to the modeling and verification of computational simulation of thrombogenesis