Methyl group dynamics in a confined glass

We present a neutron scattering investigation on methyl group dynamics in glassy toluene confined in mesoporous silicates of different pore sizes. The experimental results have been analysed in terms of a barrier distribution model, such a distribution following from the structural disorder in the glassy state. Confinement results in a strong decreasing of the average rotational barrier in comparison to the bulk state. We have roughly separated the distribution for the confined state in a bulk-like and a surface-like contribution, corresponding to rotors at a distance from the pore wall respectively larger and smaller than the spatial range of the interactions which contribute to the rotational potential for the methyl groups. We have estimated a distance of 7 Amstrong as a lower limit of the interaction range, beyond the typical nearest-neighbour distance between centers-of-mass (4.7 Amstrong).Comment: 5 pages, 3 figures. To be published in European Physical Journal E Direct. Proceedings of the 2nd International Workshop on Dynamics in Confinemen

Phase Space Reduction for Star-Products: An Explicit Construction for CP^n

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we can give an easy algebraic description of this star-product. Moreover, going over to a modified star-product on $C^{n+1} \setminus \{ 0 \}$, obtained by an equivalence transformation, this description can be even further simplified, allowing the explicit computation of a closed formula for the star-product on \CP^n which can easily transferred to the domain $SU(n+1)/S(U(1)\times U(n))$.Comment: LaTeX, 17 page

On Gammelgaard's formula for a star product with separation of variables

We show that Gammelgaard's formula expressing a star product with separation of variables on a pseudo-Kaehler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal Fock space. We prove this inversion formula directly and thus offer an alternative approach to Gammelgaard's formula which gives more insight into the question why the directed graphs in his formula have no cycles.Comment: 29 pages, changes made in the last two section

The Stability of Bredigite and Other Ca-Mg Silicates

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65844/1/j.1151-2916.1980.tb10213.x.pd

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.Comment: 21 pages, 15 figure