Some classical views on the parameters of the Grothendieck-Teichmüeller group

We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P1 {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL 2 (Z||Z2 ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.</p

Chemical Reaction between Single Hydrogen Atom and Graphene

We study chemical reaction between a single hydrogen atom and a graphene, which is the elemental reaction between hydrogen and graphitic carbon materials. In the present work, classical molecular dynamics simulation is used with modified Brenner's empirical bond order potential. The three reactions, that is, absorption reaction, reflection reaction and penetration reaction, are observed in our simulation. Reaction rates depend on the incident energy of the hydrogen atom and the graphene temperature. The dependence can be explained by the following mechanisms: (1) The hydrogen atom receives repulsive force by pi-electrons in addition to nuclear repulsion. (2) Absorbing the hydrogen atom, the graphene transforms its structure to the ``overhang'' configuration such as sp-3 state. (3) The hexagonal hole of the graphene is expanded during the penetration of the hydrogen atom.Comment: 10 pages, 9 figures. This paper was submitted to PR

Transport Coefficients of InSb in a Strong Magnetic Field

Improvement of a superconducting magnet system makes induction of a strong magnetic field easier. This fact gives us a possibility of energy conversion by the Nernst effect. As the first step to study the Nernst element, we measured the conductivity, the Hall coefficient, the thermoelectric power and the Nernst coefficient of the InSb, which is one of candidates of the Nernst elements. From this experiment, it is concluded that the Nernst coefficient is smaller than the theoretical values. On the other hand, the conductivity, the Hall coefficient ant the thermoelectric power has the values expected by the theory.Comment: 6 pages, Latex, This article was presented in the XVI International Conference on Thermoelectrics, Dresden, Germany (1997