The higher direct images of locally constant group schemes from the Kummer log flat topology to the classical flat topology

Let $S$ be an fs log scheme, and let $F$ be a group scheme over the underlying scheme which is \'etale locally representable by (1) a finite dimensional $\mathbb{Q}$-vector space, or (2) a finite rank free abelian group, or (3) a finite abelian group. We give a full description of all the higher direct images of $F$ from the Kummer log flat site to the classical flat site. In particular, we show that: in case (1) the higher direct images of $F$ vanish; and in case (2) the first higher direct image of $F$ vanishes and the $n$-th ($n>1$) higher direct image of $F$ is isomorphic to the $(n-1)$-th higher direct image of $F\otimes_{\mathbb{Z}}\mathbb{Q}/\mathbb{Z}$. In the end, we make some computations when the base is a standard log trait or a Dedekind scheme endowed with the log structure associated to a finite set of closed points.Comment: 28 page

Log prismatic Dieudonn\'e theory for log pp-divisible groups over OK\mathcal{O}_{K}

Let $\mathcal{O}_{K}$ be a complete discrete valuation ring of mixed characteristic with perfect residue field, endowed with its canonical log-structure. We prove that log $p$-divisible groups over $\mathcal{O}_{K}$ correspond to Dieudonn\'e crystals on the absolute log-prismatic site of $\mathcal{O}_{K}$ endowed with the Kummer log-flat topology. The proof uses log-descent to reduce the problem to the classical prismatic correspondence, recently established by Ansch\"utz-Le Bras.Comment: 19 page

Log p-divisible groups associated to log 1-motives

We first provide a detailed proof of Kato's classification theorem of log $p$-divisible groups over a henselian local ring. Exploring Kato's idea further, we then define the notion of a standard extension of a classical finite \'etale group scheme (resp. classical \'etale $p$-divisible group) by a classical finite flat group scheme (resp. classical $p$-divisible group) in the category of finite Kummer flat group log schemes (resp. log $p$-divisible groups), with respect to a given chart on the base. We show that the finite Kummer flat group log scheme $T_n(M):=H^{-1}(M\otimes_{\mathbb{Z}}^L\mathbb{Z}/n\mathbb{Z})$ (resp. the log $p$-divisible group $M[p^{\infty}]$) of a log 1-motive $M$ over an fs log scheme is \'etale locally a standard extension. We further show that $M[p^{\infty}]$ and its infinitesimal deformations are formally log smooth. At last, as an application of these formal log smoothness results, we give a proof of the Serre-Tate theorem for log abelian varieties with constant degeneration.Comment: 36 page

Field emission properties of nano-composite carbon nitride films

A modified cathodic arc technique has been used to deposit carbon nitride thin films directly on n+ Si substrates. Transmission Electron Microscopy showed that clusters of fullerene-like nanoparticles are embedded in the deposited material. Field emission in vacuum from as-grown films starts at an electric field strength of 3.8 V/micron. When the films were etched in an HF:NH4F solution for ten minutes, the threshold field decreased to 2.6 V/micron. The role of the carbon nanoparticles in the field emission process and the influence of the chemical etching treatment are discussed.Comment: 22 pages, 8 figures, submitted to J. Vac. Sc. Techn.

Mass spectrometric and first principles study of Aln_nC−^- clusters

We study the carbon-dope aluminum clusters by using time-of-flight mass spectrum experiments and {\em ab initio} calculations. Mass abundance distributions are obtained for anionic aluminum and aluminum-carbon mixed clusters. Besides the well-known magic aluminum clusters such as Al$_{13}^-$ and Al$_{23}^-$, Al$_7$C$^-$ cluster is found to be particularly stable among those Al$_n$C$^-$ clusters. Density functional calculations are performed to determine the ground state structures of Al$_n$C$^-$ clusters. Our results show that the Al$_7$C$^-$ is a magic cluster with extremely high stability, which might serve as building block of the cluster-assembled materials.Comment: 4 pages, 6 figure

Density functional study of Aun_n (n=2-20) clusters: lowest-energy structures and electronic properties

We have investigated the lowest-energy structures and electronic properties of the Au$_n$(n=2-20) clusters based on density functional theory (DFT) with local density approximation. The small Au$_n$ clusters adopt planar structures up to n=6. Tabular cage structures are preferred in the range of n=10-14 and a structural transition from tabular cage-like structure to compact near-spherical structure is found around n=15. The most stable configurations obtained for Au$_{13}$ and Au$_{19}$ clusters are amorphous instead of icosahedral or fcc-like, while the electronic density of states sensitively depend on the cluster geometry. Dramatic odd-even alternative behaviors are obtained in the relative stability, HOMO-LUMO gaps and ionization potentials of gold clusters. The size evolution of electronic properties is discussed and the theoretical ionization potentials of Au$_n$ clusters compare well with experiments.Comment: 6 pages, 7 figure