Demazure Characters and Affine Fusion Rules

The Demazure character formula is applied to the Verlinde formula for affine fusion rules. We follow Littelmann's derivation of a generalized Littlewood-Richardson rule from Demazure characters. A combinatorial rule for affine fusions does not result, however. Only a modified version of the Littlewood-Richardson rule is obtained that computes an (old) upper bound on the fusion coefficients of affine $A_r$ algebras. We argue that this is because the characters of simple Lie algebras appear in this treatment, instead of the corresponding affine characters. The Bruhat order on the affine Weyl group must be implicated in any combinatorial rule for affine fusions; the Bruhat order on subgroups of this group (such as the finite Weyl group) does not suffice.Comment: 23 pages, TeX, uses harvma

On Fusion Algebras and Modular Matrices

We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix $S$, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the $A_r$ fusion algebra at level $k$. We prove that for many choices of rank $r$ and level $k$, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most $r$ and $k$. We also find new, systematic sources of zeros in the modular matrix $S$. In addition, we obtain a formula relating the entries of $S$ at fixed points, to entries of $S$ at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of $S$, and by the fusion (Verlinde) eigenvalues.Comment: 28 pages, plain Te

High Speed Balancing Applied to the T700 Engine

The work performed under Contracts NAS3-23929 and NAS3-24633 is presented. MTI evaluated the feasibility of high-speed balancing for both the T700 power turbine rotor and the compressor rotor. Modifications were designed for the existing Corpus Christi Army Depot (CCAD) T53/T55 high-speed balancing system for balancing T700 power turbine rotors. Tests conducted under these contracts included a high-speed balancing evaluation for T700 power turbines in the Army/NASA drivetrain facility at MTI. The high-speed balancing tests demonstrated the reduction of vibration amplitudes at operating speed for both low-speed balanced and non-low-speed balanced T700 power turbines. In addition, vibration data from acceptance tests of T53, T55, and T700 engines were analyzed and a vibration diagnostic procedure developed

Creating movable interfaces by micro-powder injection moulding

This paper presents a novel in situ technique to produce articulated components with high-precision, micro-scale movable interfaces by micro-powder injection moulding (μPIM). The presented process route is based on the use of micro-scale sacrificial layer between the movable subcomponents which is eliminated during the debinding step, creating a dimensionally-controlled, micro-scale mobile interface. The fabrication technique combines the advantages of micro-powder overmoulding, catalytic debinding and sintering. The demonstrated example was a finger bone prosthesis joint consisting of two sub-components with an interface between components of 200 μm in size. The geometries of the sub-components were designed such that they are inseparable throughout the process whilst allowing them to move relative to each other after the debinding stage. The components produced showed the feasibility of the process route to produce readily-assembled meso-, and potentially micro-, scale articulated system

On Robin boundary conditions and the Morse potential in quantum mechanics

The physical origin is investigated of Robin boundary conditions for wave functions at an infinite reflecting wall. We consider both Schr\"odinger and phase-space quantum mechanics (a.k.a. deformation quantization), for this simple example of a contact interaction. A non-relativistic particle moving freely on the half-line is treated as moving on the full line in the presence of an infinite potential wall, realized as a limit of a Morse potential. We show that the wave functions for the Morse states can become those for a free particle on the half-line with Robin boundary conditions. However, Dirichlet boundary conditions (standard walls) are obtained unless a mass-dependent fine tuning (to a reflection resonance) is imposed. This phenomenon was already observed for piece-wise flat potentials, so it is not removed by smoothing. We argue that it explains why standard quantum walls are standard. Next we consider the Wigner functions (the symbols of both diagonal and off-diagonal density operator elements) of phase-space quantum mechanics. Taking the (fine-tuned) limit, we show that our Wigner functions do reduce to the expected ones on the half-line. This confirms that the Wigner transform should indeed be unmodified for this contact interaction.Comment: 19 page