1,744 research outputs found
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
- …