Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of small points if it is a non-special subvariety. The key of the proof is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of equidistribution theory due to Gubler. This article includes an appendix by Walter Gubler. He shows that the minimal dimension of the components of a canonical measure is equal to the dimension of the abelian part of the subvariety. We can apply this result to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page

Sol-Gel Synthesis of 5 V LiCuxMn2−xO4 as a Cathode Material for Lithium Rechargeable Batteries

Spinel LiCuxMn2−xO4 0.025 x 0.1 has been synthesized using oxalic acid as the chelating agent using a sol-gel method to obtain submicrometer-sized particles, good surface morphology, homogeneity, agglomeration, and high crystallinity involving short heating time. X-ray diffraction XRD, scanning electron microscopy SEM, Fourier transform infrared spectroscopy, and thermogravimetric and differential thermal analysis were carried out for the physical characterization of the synthesized powder. The XRD patterns of LiCuxMn2−xO4 show the single-phase spinel product, which is in good agreement with the JCPDS card 35-782. SEM images show that the particles, on the average, are of 50 nm in size and are present as agglomerated clusters at all dopant levels. Electrochemical cycling studies of the compound were carried out between 3 and 5 V to understand the redox behavior of Cu2+ ions. The charge–discharge cycling studies of spinel material with Cu stoichiometry of x = 0.1 calcined at 850°C exhibit an initial discharge capacity of 130 mAh g−1 and stabilized at 120 mAh g−1

Fuel-cell performance of multiply-crosslinked polymer electrolyte membranes prepared by two-step radiation technique

A multiply-crosslinked polymer electrolyte membrane was prepared by the radiation-induced co-grafting of styrene and a bis(vinyl phenyl)ethane (BVPE) crosslinker into a radiation-crosslinked polytetrafluoroethylene (cPTFE) film. We then investigated its H2/O2 fuel-cell performance at 60 and 80ºC in terms of the effect of radiation and chemical crosslinking. At 60ºC, all the membranes initially exhibited similar performance, but only the cPTFE-based membranes were durable at 80ºC, indicating the necessity of radiation crosslinking in the PTFE main chains. Importantly, cell performance of the multiply-crosslinked membrane was found high enough to reach that of a Nafion112 membrane. This is probably because the BVPE crosslinks in the graft component improved the membrane-electrode interface in addition to membrane durability. After severe OCV hold tests at 80 and 95ºC, the performance deteriorated, while no significant change was observed in ohmic resistivity. Accordingly, our membranes seemed so chemically stable that an influence on overall performance loss could be negligible

Phonon-phonon interactions and phonon damping in carbon nanotubes

We formulate and study the effective low-energy quantum theory of interacting long-wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory. A general and analytical derivation of all three- and four-phonon processes is provided, and the relevant coupling constants are determined in terms of few elastic coefficients. Due to the low dimensionality and the parabolic dispersion, the finite-temperature density of noninteracting flexural phonons diverges, and a nonperturbative approach to their interactions is necessary. Within a mean-field description, we find that a dynamical gap opens. In practice, this gap is thermally smeared, but still has important consequences. Using our theory, we compute the decay rates of acoustic phonons due to phonon-phonon and electron-phonon interactions, implying upper bounds for their quality factor.Comment: 15 pages, 2 figures, published versio

Peierls Mechanism of the Metal-Insulator Transition in Ferromagnetic Hollandite K2Cr8O16

Synchrotron X-ray diffraction experiment shows that the metal-insulator transition occurring in a ferromagnetic state of a hollandite K$_2$Cr$_8$O$_{16}$ is accompanied by a structural distortion from the tetragonal $I4/m$ to monoclinic $P112_{1}/a$ phase with a $\sqrt{2}\times\sqrt{2}\times 1$ supercell. Detailed electronic structure calculations demonstrate that the metal-insulator transition is caused by a Peierls instability in the quasi-one-dimensional column structure made of four coupled Cr-O chains running in the $c$-direction, leading to the formation of tetramers of Cr ions below the transition temperature. This furnishes a rare example of the Peierls transition of fully spin-polarized electron systems.Comment: Phys. Rev. Lett., in press, 5 pages, 3 figure

Properties of Ridges in Elastic Membranes

When a thin elastic sheet is confined to a region much smaller than its size the morphology of the resulting crumpled membrane is a network of straight ridges or folds that meet at sharp vertices. A virial theorem predicts the ratio of the total bending and stretching energies of a ridge. Small strains and curvatures persist far away from the ridge. We discuss several kinds of perturbations that distinguish a ridge in a crumpled sheet from an isolated ridge studied earlier (A. E. Lobkovsky, Phys. Rev. E. 53 3750 (1996)). Linear response as well as buckling properties are investigated. We find that quite generally, the energy of a ridge can change by no more than a finite fraction before it buckles.Comment: 13 pages, RevTeX, acknowledgement adde

Valence band excitations in V_2O_5

We present a joint theoretical and experimental investigation of the electronic and optical properties of vanadium pentoxide. Electron energy-loss spectroscopy in transmission was employed to measure the momentum-dependent loss function. This in turn was used to derive the optical conductivity, which is compared to the results of band structure calculations. A good qualitative and quantitative agreement between the theoretical and the experimental optical conductivity was observed. The experimentally observed anisotropy of the optical properties of V_2O_5 could be understood in the light of an analysis of the theoretical data involving the decomposition of the calculated optical conductivity into contributions from transitions into selected energy regions of the conduction band. In addition, based upon a tight binding fit to the band structure, values are given for the effective V3d_xy-O2p hopping terms and are compared to the corresponding values for alpha'-NaV_2O_5.Comment: 6 pages (revtex),6 figures (jpg

Biaxial magnetic alignment in twinned REBa[2]Cu[3]O[y]superconductors

Biaxial magnetic alignment of REBa[2]Cu[3]O[y] (RE123, RE = Y, Nd, Sm, Dy, and Er) superconductor powders containing twin microstructures was demonstrated. Appropriate choice of RE effectively improved the degrees of in-plane and c-axis orientation in RE123 powder samples aligned under modulated rotating magnetic fields at room temperature. From the relationship between the magnetic field strength and the degrees of orientation, it is concluded that heavy RE ions induced the improvement of the in-plane magnetic anisotropies in RE123 grains with twin microstructures