Unique decompositions, faces, and automorphisms of separable states

Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a representation as a convex combination of k pure product states, or fewer. If m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that V_k is dense and open in S_k, and such that each state in V_k has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decompositions for a set of separable states that properly contains V_k. In both cases we describe the associated faces of the space of separable states, which in the first case are simplexes, and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras. As an application of these results, we characterize all affine automorphisms of the convex set of separable states, and all automorphisms of the state space of B(C^m otimes C^n). that preserve entanglement and separability.Comment: Since original version:Cor. 6 revised and renamed Thm 6, some definitions added before Cor. 11, introduction revised and references added, typos correcte

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods

Writing in the STEM classroom: Faculty conceptions of writing and its role in the undergraduate classroom

Writing is widely recognized as fundamental to the construction and communication of scientific knowledge. Building on this relationship between writing and knowledge construction, writing‐to‐learn (WTL) activities have shown to be effective in many science classrooms, but have not been widely implemented at the postsecondary level. To address the lack of implementation, we investigated potential adopters of this pedagogy. Potential adopters, postsecondary faculty, are unique given the key role writing plays in their professional practice as researchers. Because of this unique feature and the fact that an instructor’s theoretical orientation toward a construct impacts their instruction of that construct, an investigation of postsecondary faculty’s conceptions of writing instruction is necessary to understand the way writing is being used in the postsecondary classroom. To this end, 33 STEM faculty across multiple disciplines and positions were interviewed about writing and its role in their classes. A phenomenographic analysis resulted in four faculty “types” consisting of unique combinations of concept and practice, organized according to compatibility with WTL. Profiles were built that describe unique conceptions, desired outcomes, and challenges for each type. These profiles provide an understanding of the relationship between faculty’s conceptions and instructional practices regarding writing and lay the groundwork for understanding how writing is used in the postsecondary classroom.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146379/1/sce21454_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146379/2/sce21454.pd

Searching for Weak or Complex Magnetic Fields in Polarized Spectra of Rigel

Seventy-eight high-resolution Stokes V, Q and U spectra of the B8Iae supergiant Rigel were obtained with the ESPaDOnS spectropolarimeter at CFHT and its clone NARVAL at TBL in the context of the Magnetism in Massive Stars (MiMeS) Large Program, in order to scrutinize this core-collapse supernova progenitor for evidence of weak and/or complex magnetic fields. In this paper we describe the reduction and analysis of the data, the constraints obtained on any photospheric magnetic field, and the variability of photospheric and wind lines.Comment: IAUS272 - Active OB Stars: Structure, Evolution, Mass Loss and Critical Limit

Lack of Peripherally Induced Tolerance to Established Skin Allografts in Immunologically Reconstituted Scid Mice

The mechanism by which the antigen-specific immune system distinguishes between foreign antigens (toward which it mounts an immune response) and self-antigens (of which it is tolerant) is not completely understood. Studies using “superantigens” and transgenic mice have allowed investigations into some of the mechanisms of clonal deletion, anergy, and peripheral tolerance. In the present report, we have attempted to develop a new model system to investigate the possible mechanism(s) of peripheral tolerance to allografts. In this system, skin grafts from C57BL/6J (B6; H-2b mice are grafted onto T- and B-lymphocyte-deficient C.B-17-scid/scid (H-2d; hereafter referred to as scid) mice. Because of their lack of functional lymphocytes, the scid mice readily accept the allogeneic skin grafts. After the allografts healed, the scid mice were reconstituted with T-cell-deficient fetal liver from coisogeneic C.B-17-∤/∤ mice or bone marrow from weanling congenitally athymic BALB/c-nu/nu (H-2d; hereafter referred to as nude) mice. Upon immunological reconstitution, the scid mice reiected the established B6 skin allografts, suggesting that an immune system developing in the presence of an intact peripheral skin allograft fails to develop tolerance to the peripheral allograft. This model system may be useful for the study of the mechanisms required for the induction of peripheral tolerance

Tetracarbon­ylbis(η5-cyclo­penta­dien­yl)bis(diphenyl­phosphine)dimolybdenum(Mo—Mo) hexane solvate

The title compound, [Mo2(C5H5)2(C12H11P)2(CO)4]·C6H14, is a centrosymmetric Mo complex in which two Mo atoms are connected by an Mo—Mo bond [3.2072 (12) Å]. Each Mo atom is coordinated by an η5-cyclo­penta­dienyl ligand, two carbonyl ligands and a diphenyl­phosphine ligand in a piano-stool fashion

Investigating the Magnetospheres of Rapidly Rotating B-type Stars

Recent spectropolarimetric surveys of bright, hot stars have found that ~10% of OB-type stars contain strong (mostly dipolar) surface magnetic fields (~kG). The prominent paradigm describing the interaction between the stellar winds and the surface magnetic field is the magnetically confined wind shock (MCWS) model. In this model, the stellar wind plasma is forced to move along the closed field loops of the magnetic field, colliding at the magnetic equator, and creating a shock. As the shocked material cools radiatively it will emit X-rays. Therefore, X-ray spectroscopy is a key tool in detecting and characterizing the hot wind material confined by the magnetic fields of these stars. Some B-type stars are found to have very short rotational periods. The effects of the rapid rotation on the X-ray production within the magnetosphere have yet to be explored in detail. The added centrifugal force due to rapid rotation is predicted to cause faster wind outflows along the field lines, leading to higher shock temperatures and harder X-rays. However, this is not observed in all rapidly rotating magnetic B-type stars. In order to address this from a theoretical point of view, we use the X-ray Analytical Dynamical Magnetosphere (XADM) model, originally developed for slow rotators, with an implementation of new rapid rotational physics. Using X-ray spectroscopy from ESA's XMM-Newton space telescope, we observed 5 rapidly rotating B-type stars to add to the previous list of observations. Comparing the observed X-ray luminosity and hardness ratio to that predicted by the XADM allows us to determine the role the added centrifugal force plays in the magnetospheric X-ray emission of these stars.Comment: IAUS Conference Proceeding

A Portrait of MWrite as a Research Program: A Review of Research on Writing-to-Learn in STEM through the MWrite Program

The writing-to-learn (WTL) literature is varied in how assignments are structured and implemented in the classroom, making it difficult for instructors to identify how to incorporate writing effectively. Drawing on the WTL literature, the MWrite program was established to work with STEM faculty to design, implement, and assess evidence- based WTL assignments. Herein we present a review of the WTL research generated through the MWrite program, situating our findings in a four-dimensional framework of engagement to identify how the MWrite WTL assignment design and implementation has supported students’ learning. Our analysis indicates that the multi-faceted design of MWrite WTL assignments supports students’ development of conceptual knowledge and disciplinary thinking. The assignments’ rhetorical features (i.e., context, audience, and genre) guide how students write about content, and peer review and revision stages encourage a collaborative, knowledge building process between students and their peers