Hamiltonian Reduction and Topological Conformal Algebra in c≤1c\leq 1 Non-critical Strings

We study the hamiltonian reduction of affine Lie superalgebra $sl(2|1)^{(1)}$. Based on a scalar Lax operator formalism, we derive the free field realization of the classical topological topological algebra which appears in the $c\leq1$ non-critical strings. In the quantum case, we analyze the BRST cohomology to get the quantum free field expression of the algebra.Comment: 13 pages Latex, UTHEP-26

Lie Superalgebra and Extended Topological Conformal Symmetry in Non-critical W3W_{3} Strings

We obtain a new free field realization of $N=2$ super $W_{3}$ algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra $sl(3|2)^{(1)}$ associated with a non-standard $sl(2)$ embedding. After twisting and a similarity transformation, this $W$ algebra can be identified as the extended topological conformal algebra of non-critical $W_{3}$ string theory.Comment: 14pages, UTHEP-27

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

Incident angle dependence of reactions between graphene and hydrogen atom by molecular dynamics simulation

Incident angle dependence of reactions between graphene and hydrogen atoms are obtained qualitatively by classical molecular dynamics simulation under the NVE condition with modified Brenner reactive empirical bond order (REBO) potential. Chemical reaction depends on two parameters, i.e., polar angle $\theta$ and azimuthal angle $\phi$ of the incident hydrogen. From the simulation results, it is found that the reaction rates strongly depend on polar angle $\theta$. Reflection rate becomes larger with increasing $\theta$, and the $\theta$ dependence of adsorption rate is also found. The $\theta$ dependence is caused by three dimensional structure of the small potential barrier which covers adsorption sites. $\phi$ dependence of penetration rate is also found for large $\theta$.Comment: 4 pages, 7 figure