On the geometry of spaces of oriented geodesics

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space, and consider the space L(M) of oriented geodesics of M. The space L(M) is a smooth homogeneous manifold and in this paper we describe all invariant symplectic structures, (para)complex structures, pseudo-Riemannian metrics and (para)Kähler structure on L(M).     

A combined effective fragment potential-fragment molecular orbital method. II. Analytic gradient and application to the geometry optimization of solvated tetraglycine and chignolin

The gradient for the fragment molecular orbital (FMO) method interfaced with effective fragment potentials (EFP), denoted by FMO∕EFP, was developed and applied to polypeptides solvated in water. The structures of neutral and zwitterionic tetraglycine immersed in water layers of 2.0, 2.5, 3.0, 3.5, 4.0, and 4.5 A? are investigated by performing FMO∕EFP geometry optimizations at the RHF∕cc-pVDZ level of theory for the solutes. The geometries optimized with FMO-RHF∕EFP are compared to those from the conventional RHF∕EFP and are found to be in very close agreement. Using the optimized geometries, the stability of the hydrated zwitterionic and neutral structures is discussed structurally and in terms of energetics at the second-order M?ller-Plesset theory (MP2)∕cc-pVDZ level. To demonstrate the potential of the method for proteins, the geometry of hydrated chignolin (protein data bank ID: 1UAO) was optimized, and the importance of the inclusion of water was examined by comparing the solvated and gas phase structures of chignolin with the experimental NMR structure.     

Transformation of ionic liquid into carbon nanotubes in confined nanospace

We have developed a two-step filling process for the nano-reaction of ionic liquid in a tip-closed SWNT, where fullerenes are inserted at the end of the host SWNT as a plug to prevent the leakage of the confined ionic liquid during heat treatment.     

Engineering of a redox protein for DNA-directed assembly

Engineered enzyme conjugate of the small laccase enzyme from Streptomyces coelicolor and zinc finger DNA binding domain from Zif268 is demonstrated to bind double stranded DNA in a site specific manner while retaining enzymatic activity.     

Three-dimensional imaging of sulfides in silicate rocks at submicron resolution with multiphoton microscopy

We report the first application of multiphoton microscopy (MPM) to generate three-dimensional (3D) images of natural minerals (micron-sized sulfides) in thick (～120 μm) rock sections. First, reflection mode (RM) using confocal laser scanning microscopy (CLSM), combined with differential interference contrast (DIC), was tested on polished sections. Second, two-photon fluorescence (TPF) and second harmonic signal (SHG) images were generated using a femtosecond-laser on the same rock section without impregnation by a fluorescent dye. CSLM results show that the silicate matrix is revealed with DIC and RM, while sulfides can be imaged in 3D at low resolution by RM. Sulfides yield strong autofluorescence from 392 to 715 nm with TPF, while SHG is only produced by the embedding medium. Simultaneous recording of TPF and SHG images enables efficient discrimination between different components of silicate rocks. Image stacks obtained with MPM enable complete reconstruction of the 3D structure of a rock slice and of sulfide morphology at submicron resolution, which has not been previously reported for 3D imaging of minerals. Our work suggests that MPM is a highly efficient tool for 3D studies of microstructures and morphologies of minerals in silicate rocks, which may find other applications in geosciences.     

Temperature dependence of crystal growth of hexagonal ice (I(h))

The transformations between water and ice have many implications across numerous fields of study. A better understanding of this process would benefit many areas of science and technology such as medicine, biology, and atmospheric and material sciences. In the present work the temperature dependence of the rate of growth (melting) of the basal face of hexagonal ice I(h) and the effect of system size are investigated in molecular dynamics simulations. Using an effective pair potential model of water, systems are studied over temperatures ranging from T(M) - 40 to T(M) + 16 K, where T(M) is the melting temperature of the model. It is found that the growth rates reach a maximum value of 0.7 ? ns(-1) (7 cm s(-1)) at about 12 K below the melting temperature. A noticeable effect of the system size on the melting temperature and ice growth rates is observed; it is shown that the size effect arises in smaller systems due to the artificial ordering under periodic conditions. The decrease in melting entropy in the smallest system by 0.4 J (mol K)(-1) relative to the largest system results in an up-shift in the melting temperature by about 2 K. An almost 60% increase in the maximum growth rate is observed for the smallest system.     

Crystal growth simulations of methane hydrates in the presence of silica surfaces

We present a molecular dynamics simulation study of the crystal growth of methane hydrates in the presence of model silica (SiO(2)) surfaces. The crystal growth under apparent steady-state conditions shows a clear preference for bulk solution. We observe rather disordered water arrangements very close to the silica surface within about 5 ? in both liquid and crystalline regions of the system. These disordered structures have dynamic and structural properties intermediate between those exhibited by molecules in bulk liquid and crystalline phases. The presence of methane molecules appears to help stabilize these structures. We observe that under appropriate conditions, the hydroxylated silica surfaces can serve as a source of methane molecules which can help promote hydrate growth near the surfaces.     

Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves

We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-Ginzburg models. In particular, we show that the derived category of coherent sheaves on a Del Pezzo surface X _k obtained by blowing up ℂℙ² at k points is equivalent to the derived category of vanishing cycles of a certain elliptic fibration W _k :M _k →ℂ with k+3 singular fibers, equipped with a suitable symplectic form. Moreover, we also show that this mirror correspondence between derived categories can be extended to noncommutative deformations of X _k , and give an explicit correspondence between the deformation parameters for X _k and the cohomology class [B+iω]∈H ²(M _k ,ℂ).