X-radiation of the moon and Roentgen cosmic background according to data of AMS ''Luna-12''

Satellite measurements of lunar soft X radiation, and Roentgen cosmic backgroun

The theoretical DFT study of electronic structure of thin Si/SiO2 quantum nanodots and nanowires

The atomic and electronic structure of a set of proposed thin (1.6 nm in diameter) silicon/silica quantum nanodots and nanowires with narrow interface, as well as parent metastable silicon structures (1.2 nm in diameter), was studied in cluster and PBC approaches using B3LYP/6-31G* and PW PP LDA approximations. The total density of states (TDOS) of the smallest quasispherical silicon quantum dot (Si85) corresponds well to the TDOS of the bulk silicon. The elongated silicon nanodots and 1D nanowires demonstrate the metallic nature of the electronic structure. The surface oxidized layer opens the bandgap in the TDOS of the Si/SiO2 species. The top of the valence band and the bottom of conductivity band of the particles are formed by the silicon core derived states. The energy width of the bandgap is determined by the length of the Si/SiO2 clusters and demonstrates inverse dependence upon the size of the nanostructures. The theoretical data describes the size confinement effect in photoluminescence spectra of the silica embedded nanocrystalline silicon with high accuracy.Comment: 22 pages, 5 figures, 1 tabl

Multiterminal Nanowire Junctions of Silicon: A Theoretical Prediction of Atomic Structure and Electronic Properties

Using empirical scheme, atomic structure of a new exotic class of silicon nanoclusters was elaborated upon the central icosahedral core (Si-IC) and pentagonal petals (Si-PP) growing from Si-IC vertexes. It was shown that Si-IC/Si-PP interface formation is energetically preferable. Some experimental observations of silicon nanostructures can be explained by presence of the proposed objects. The Extended Huckel Theory electronic structure calculations demonstrate an ability of the proposed objects to act as nanoscale tunnel junctions.Comment: 13 pages, 3 figures, 1 tabl

Singularities of nn-fold integrals of the Ising class and the theory of elliptic curves

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for $n=1, 2, 3, 4$ and only modulo some primes for $n=5$ and $6$, thus providing a large set of (possible) new singularities of the $\chi^{(n)}$. We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to $n= 6$) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a {\em finite number of one dimensional integrals}. Among the singularities found, we underline the fact that the quadratic polynomial condition $1+3 w +4 w^2 = 0$, that occurs in the linear differential equation of $\chi^{(3)}$, actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure