The bicomplex quantum Coulomb potential problem

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi is a bicomplex number. Following Pauli's algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrodinger's time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J. Phy

Warped quasi-asymptotically conical Calabi-Yau metrics

We construct many new examples of complete Calabi-Yau metrics of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones with smooth cross-sections. A detailed description of the geometry at infinity of these metrics is given in terms of a compactification by a manifold with corners obtained through the notion of weighted blow-up for manifolds with corners. A key analytical step in the construction of these Calabi-Yau metrics is to derive good mapping properties of the Laplacian on some suitable weighted H\"older spaces. Our methods also produce singular Calabi-Yau metrics with an isolated conical singularity modelled on a Calabi-Yau cone distinct from the tangent cone at infinity, in particular yielding a transition behavior between different Calabi-Yau cones as conjectured by Yang Li. This is used to exhibit many examples where the tangent cone at infinity does not uniquely specify a complete Calabi-Yau metric with exact K\"ahler form.Comment: 64 pages, added the construction of singular Calabi-Yau metrics with an isolated conical singularity modelled on a Calabi-Yau cone distinct from the tangent cone at infinity, thus interpolating between two different Calabi-Yau cone

Compilation of a Database of Research Information on Legume Based Grazing Systems; a Part of the Leggraze Research Project

The establishment of a publicly accessible web-resident database of published and current European research on agronomy, animal production and environmental impact of legume based grazing systems is reported. This database facilitates the sharing of information among the partners of the Low input animal production based on forage legumes for grazing systems (Leggraze), a research project funded by the UE (QL K5 CT-2001-02328). It also forms an important tool for transferring the results of the project to the wider research community and to end users in the agricultural sector and to policy makers at national and community level

Doppler temperatures from O(¹D) airglow in the daytime thermosphere as observed by the Wind Imaging Interferometer (WINDII) on the UARS satellite

International audienceFrom 1992 to 1997, the WINDII interferometer on board the UARS satellite acquired a large set of thermospheric data from the O(1D) and O(1S) airglows. We report here for the first time on daytime O(1D) Doppler temperatures obtained with version 5.11 of the WINDII data processing software. Using a statistical analysis of the temperatures independently measured by the two WINDII fields of view, we estimate that the temperature variations larger than 40 K can be considered as geophysical. Comparisons of WINDII temperatures measured during magnetically quiet days with temperatures obtained by the MSIS-90 and DTM-94 thermospheric models show a 100 K bias. We demonstrate, however, that the modeled temperature variations represent very well the mean temperature variation observed by WINDII over 4 years. We also show that the observed latitudinal/local time variation is in very good agreement with the two empirical models. Finally, the temperature variations during a magnetically disturbed day are found to be qualitatively well represented in form by the models, but largely underestimated. The presence of non-thermal atoms and instrument related issues are discussed as possible explanations for the 100 K bias between the WINDII Doppler temperatures and the empirical models

Flat H Frangible Joint Evolution

Space vehicle staging and separation events require pyrotechnic devices. They are single-use mechanisms that cannot be tested, nor can failure-tolerant performance be demonstrated in actual flight articles prior to flight use. This necessitates the implementation of a robust design and test approach coupled with a fully redundant, failure-tolerant explosive mechanism to ensure that the system functions even in the event of a single failure. Historically, NASA has followed the single failure-tolerant (SFT) design philosophy for all human-rated spacecraft, including the Space Shuttle Program. Following the end of this program, aerospace companies proposed building the next generation human-rated vehicles with off-the-shelf, non-redundant, zero-failure-tolerant (ZFT) separation systems. Currently, spacecraft and launch vehicle providers for both the Orion and Commercial Crew Programs (CCPs) plan to deviate from the heritage safety approach and NASA's SFT human rating requirements. Both programs' partners have base-lined ZFT frangible joints for vehicle staging and fairing separation. These joints are commercially available from pyrotechnic vendors. Non-human-rated missions have flown them numerous times. The joints are relatively easy to integrate structurally within the spacecraft. In addition, the separation event is debris free, and the resultant pyro shock is lower than that of other design solutions. It is, however, a serious deficiency to lack failure tolerance. When used for critical applications on human-rated vehicles, a single failure could potentially lead to loss of crew (LOC) or loss of mission (LOM)). The Engineering and Safety & Mission Assurance directorates within the NASA Johnson Space Center took action to address this safety issue by initiating a project to develop a fully redundant, SFT frangible joint design, known as the Flat H. Critical to the ability to retrofit on launch vehicles being developed, the SFT mechanisms must fit within the same three-dimensional envelope as current designs as well as meet structural loads requirements. There is increased mass associated with the redundant design, and the goal is to minimize the weight impact as much as possible. These requirements presented significant challenges, both technically and financially; these challenges will be explored in this paper. Perhaps greater than the technical issues confronted during this design process, were the financial considerations. These were a significant part of the story of this design and development plan. Insufficient financial and labor resources were formidable barriers to completing this project. Nevertheless, JSC personnel successfully conducted several test series at JSC with very useful results. The many lessons learned drove design improvements, performance efficiency, and increased functional reliability. This paper examines the significant technical and financial challenges that these requirements posed to the project team. It discusses the evolution of the SFT frangible joint design, including optimization, testing, and successful partnering of the Johnson Space Center (JSC) engineering and JSC safety organizations, to enhance the flight safety margin for America's next generation of human-rated space vehicles