Classifying Novel Phases of Spinor Atoms

We consider many-body states of bosonic spinor atoms which, at the mean-field level, can be characterized by a single-particle wave function. Such states include BEC phases and insulating Mott states with one atom per site. We describe and apply a classification scheme that makes explicit spin symmetries of such states and enables one to naturally analyze their collective modes and topological excitations. Quite generally, the method allows classification of a spin F system as a polyhedron with 2F vertices. After discussing the general formalism we apply it to the many-body states of bosons with hyperfine spins two and three. For spin-two atoms we find the ferromagnetic state, a continuum of nematic states, and a state having the symmetry of the point group of the regular tetrahedron. For spin-three atoms we obtain similar ferromagnetic and nematic phases as well as states having symmetries of various types of polyhedra with six vertices: the hexagon, the pyramid with pentagonal base, the prism, and the octahedron.Comment: Added references, corrected typos, minor changes in tex

Tapered LIGA mold insert

The applications of microstructures produced by the LIGA process are useful in a broad range of fields including: microfluidics, heat transfer, and mechanics. The Microsystems Engineering Team at Louisiana State University has used the LIGA process as a foundation for the team’s productivity in these areas. Many advances in the processes involved in producing these microstructures have been made in the past increasing the efficiency of the entire process. A modified exposure technique in the lithography stage of the LIGA process is being developed to produce microstructures with a draft angle as opposed to the standard straight walled structures. Electroformed mold inserts produced previously have encountered high ejection forces causing deformation or tearing of the molded products. The tapered sidewalls produced in the modified exposure mirror those already used in macro-scale injection molds, and will dramatically reduce the forces resulting in superior parts with improved cycle times. The two objectives that define this research project are: i) to successfully manufacture a LIGA high aspect ratio microstructure mold insert with tapered features, and ii) to use the manufactured mold insert and successfully mold and eject parts using a injection molding machine. A LIGA based mold insert approximately one millimeter in depth was produced with a three degree draft angle. This insert was then used with a injection molding machine to produce and efficiently eject cyclic olefin copolymer (COC) plastic parts

A Song Of Confusion And Annoyance: Kant On The Beauty Of Absolute Music

Kant\u27s evaluation of music in the Critique of Judgement stands as a blemish on an otherwise appealing system of judgments of beauty and of assigning aesthetic worth. In order to resolve this tension, I will present an argument in three parts. First, I will delve further into Kantian judgments of beauty to provide solid contextual grounds for why he draws his conclusions about music and will further elaborate on his various positions concerning music. Second, I will look at a few potential answers for the problem of music given by others in the philosophy of music and briefly evaluate their effectiveness. Third, I will turn to my answers for the central hurdles preventing Kant from classifying music as a beautiful/fine art form: the problems of representation, content, and beauty being symbolic of morality