User\u27s Guide to MBC3: Multi-Blade Coordinate Transformation Code for 3-Bladed Wind Turbine

The dynamics of wind turbine rotor blades are conventionally expressed in rotating frames attached to the individual blades. The tower-nacelle subsystem though, sees the combined effect of all rotor blades, not the individual blades. Also, the rotor responds as a whole to excitations such as aerodynamic gusts, control inputs, and tower-nacelle motion—all of which occur in a nonrotating frame. Multi-blade coordinate transformation (MBC) helps integrate the dynamics of individual blades and express them in a fixed (nonrotating) frame. MBC involves two steps: transforming the rotating degrees of freedom and transforming the equations of motion. Reference 1 details the MBC operation. This guide summarizes the MBC concept and underlying transformations

Limits over categories of extensions

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.Comment: 18 page

Lie Dimension Subrings

We compare, for L a Lie ring over the integers, its lower central series (\gamma_n(L))_{n>0} and its dimension series defined by \delta_n(L):=L\cap \varpi^n(L) in the universal enveloping algebra of L. We show that \gamma_n(L)=\delta_n(L) for all n<4, but give an example showing that they may differ if n=4. We introduce simplicial methods to describe these results, and to serve as a possible tool for further study of the dimension series.Comment: Small typos fixed wrt v

Comment on "Froehlich Mass in GaAs-Based Structures"

The results of recent measurements of the cyclotron resonance (CR) spectra for a GaAs quantum well are interpreted in terms of the resonant magnetopolaron effect. Owing to this effect, the CR peaks split near the TO-phonon frequency and also change their positions with respect to those obtained without electron-phonon interaction. The theoretical peak positions of the CR spectra calculated within the many-polaron approach compare well with experimental data, as distinct from the CR energies calculated without electron-phonon interaction, which show no particular features in the region of the optical-phonon frequencies. We conclude that the Froehlich polaron concept is valid and even necessary to interpret the CR spectra of quantum wells.Comment: 1 page, 1 figure, E-mail addresses: [email protected], [email protected]