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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 5 (1990), S. 323-357 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Often it is important to consider the expansion of a quantum state ⋎ ψ) in terms of physically meaningful basis states. For example, molecular orbitals can be expressed as linear combinations of atomic orbitals, or vibrational states can be expressed as super positions of local or normal mode eigenstates. In such expansions, it then becomes desirable to determine how much “character” a quantum state has in one of these basis states. One way of accimplishing this task is to calculate the projected probability of |ψ) on basis state |j). In this paper, we consider this general quantum mechanical problem. If the basis states are orthonormal, then the projected probability of|ψ) on |j) is of course |〈ψ|j〉|2. However, if the basis states are not orthogonal, then this result is no longer valid and one must develop a more general theory to calculate these projected probabilities. An earlier paper used one-dimensional projection operators to initiate this theory and gave closed form results for the case of two non-orthogonal basis states [1]. One- and many-dimensional projection operators, together with linear algebraic techniques, are used to extend this theory to the n non-orthogonal basis state case. Explicit closed form results are given for the two- and three-state cases, and a general algorithm is developed for the case of four or more basis states. Application of the theory is made to atomic populations in three- to six-atom molecules, and comparisons are made to the related work of Mulliken.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 1992-07-15
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 3
    Publication Date: 1992-02-24
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
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  • 4
    Publication Date: 1994-02-01
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
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  • 5
    Publication Date: 1993-01-01
    Print ISSN: 0148-0227
    Electronic ISSN: 2156-2202
    Topics: Geosciences
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  • 6
    Publication Date: 2011-08-24
    Description: The frequency and intensity of rain attenuation affecting the communication between a satellite and an earth terminal is an important consideration in planning satellite links. The NASA Lewis Research Center Satellite Link Attenuation Model Program (LeRC-SLAM) provides a static and dynamic statistical assessment of the impact of rain attenuation on a communications link established between an earth terminal and a geosynchronous satellite. The program is designed for use in the specification, design and assessment of satellite links for any terminal location in the continental United States. The basis for LeRC-SLAM is the ACTS Rain Attenuation Prediction Model, which uses a log-normal cumulative probability distribution to describe the random process of rain attenuation on satellite links. The derivation of the statistics for the rainrate process at the specified terminal location relies on long term rainfall records compiled by the U.S. Weather Service during time periods of up to 55 years in length. The theory of extreme value statistics is also utilized. The user provides 1) the longitudinal position of the satellite in geosynchronous orbit, 2) the geographical position of the earth terminal in terms of latitude and longitude, 3) the height above sea level of the terminal site, 4) the yearly average rainfall at the terminal site, and 5) the operating frequency of the communications link (within 1 to 1000 GHz, inclusive). Based on the yearly average rainfall at the terminal location, LeRC-SLAM calculates the relevant rain statistics for the site using an internal data base. The program then generates rain attenuation data for the satellite link. This data includes a description of the static (i.e., yearly) attenuation process, an evaluation of the cumulative probability distribution for attenuation effects, and an evaluation of the probability of fades below selected fade depths. In addition, LeRC-SLAM calculates the elevation and azimuth angles of the terminal antenna required to establish a link with the satellite, the statistical parameters that characterize the rainrate process at the terminal site, the length of the propagation path within the potential rain region, and its projected length onto the local horizontal. The IBM PC version of LeRC-SLAM (LEW-14979) is written in Microsoft QuickBASIC for an IBM PC compatible computer with a monitor and printer capable of supporting an 80-column format. The IBM PC version is available on a 5.25 inch MS-DOS format diskette. The program requires about 30K RAM. The source code and executable are included. The Macintosh version of LeRC-SLAM (LEW-14977) is written in Microsoft Basic, Binary (b) v2.00 for Macintosh II series computers running MacOS. This version requires 400K RAM and is available on a 3.5 inch 800K Macintosh format diskette, which includes source code only. The Macintosh version was developed in 1987 and the IBM PC version was developed in 1989. IBM PC is a trademark of International Business Machines. MS-DOS is a registered trademark of Microsoft Corporation. Macintosh is a registered trademark of Apple Computer, Inc.
    Keywords: SPACE COMMUNICATIONS, SPACECRAFT COMMUNICATIONS, COMMAND AND TRACKING
    Type: LEW-14979
    Format: text
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  • 7
    Publication Date: 2011-08-24
    Description: The frequency and intensity of rain attenuation affecting the communication between a satellite and an earth terminal is an important consideration in planning satellite links. The NASA Lewis Research Center Satellite Link Attenuation Model Program (LeRC-SLAM) provides a static and dynamic statistical assessment of the impact of rain attenuation on a communications link established between an earth terminal and a geosynchronous satellite. The program is designed for use in the specification, design and assessment of satellite links for any terminal location in the continental United States. The basis for LeRC-SLAM is the ACTS Rain Attenuation Prediction Model, which uses a log-normal cumulative probability distribution to describe the random process of rain attenuation on satellite links. The derivation of the statistics for the rainrate process at the specified terminal location relies on long term rainfall records compiled by the U.S. Weather Service during time periods of up to 55 years in length. The theory of extreme value statistics is also utilized. The user provides 1) the longitudinal position of the satellite in geosynchronous orbit, 2) the geographical position of the earth terminal in terms of latitude and longitude, 3) the height above sea level of the terminal site, 4) the yearly average rainfall at the terminal site, and 5) the operating frequency of the communications link (within 1 to 1000 GHz, inclusive). Based on the yearly average rainfall at the terminal location, LeRC-SLAM calculates the relevant rain statistics for the site using an internal data base. The program then generates rain attenuation data for the satellite link. This data includes a description of the static (i.e., yearly) attenuation process, an evaluation of the cumulative probability distribution for attenuation effects, and an evaluation of the probability of fades below selected fade depths. In addition, LeRC-SLAM calculates the elevation and azimuth angles of the terminal antenna required to establish a link with the satellite, the statistical parameters that characterize the rainrate process at the terminal site, the length of the propagation path within the potential rain region, and its projected length onto the local horizontal. The IBM PC version of LeRC-SLAM (LEW-14979) is written in Microsoft QuickBASIC for an IBM PC compatible computer with a monitor and printer capable of supporting an 80-column format. The IBM PC version is available on a 5.25 inch MS-DOS format diskette. The program requires about 30K RAM. The source code and executable are included. The Macintosh version of LeRC-SLAM (LEW-14977) is written in Microsoft Basic, Binary (b) v2.00 for Macintosh II series computers running MacOS. This version requires 400K RAM and is available on a 3.5 inch 800K Macintosh format diskette, which includes source code only. The Macintosh version was developed in 1987 and the IBM PC version was developed in 1989. IBM PC is a trademark of International Business Machines. MS-DOS is a registered trademark of Microsoft Corporation. Macintosh is a registered trademark of Apple Computer, Inc.
    Keywords: SPACE COMMUNICATIONS, SPACECRAFT COMMUNICATIONS, COMMAND AND TRACKING
    Type: LEW-14977
    Format: text
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  • 8
    Publication Date: 2011-08-24
    Description: New observations of Jovian narrow-band kilometric (nKOM) radio emissions were made by the Unified Radio and Plasma Wave (URAP) experiment on the Ulysses spacecraft during the Ulysses-Jupiter encounter in early February 1992. These observations have demonstrated the unique capability of the URAP instrument for determining both the direction and polarization of nKOM radio sources. An important result is the discovery that nKOM radio emission originates from a number of distinct sources located at different Jovian longitudes and at the inner and outermost regions of the Io plasma torus. These sources have been tracked for several Jovian rotations, yielding their corotational lags, their spatial and temporal evolution, and their radiation characteristics at both low latitudes far from Jupiter and at high latitudes near the planet. Both right-hand and left-hand circularly polarized nKOM sources were observed. The polarizations observed for sources in the outermost regions of the torus seem to favor extraordinary mode emission.
    Keywords: LUNAR AND PLANETARY EXPLORATION
    Type: Journal of Geophysical Research (ISSN 0148-0227); 98; E7; p. 13,163-13,176.
    Format: text
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  • 9
    Publication Date: 2013-08-31
    Description: Many spacecraft missions in the next decade will require both a high degree of agility and precision pointing. Agility includes both rotational maneuvering for retargeting and translational motion for orbit adjustment and threat avoidance. The major challenge associated with such missions is the need for control over a wide range of amplitudes and frequencies, ranging from tens of degrees at less than 1 Hz to a few micron radians at hundreds of Hz. TRW's internally funded Precision Control of Agile Spacecraft (PCAS) project is concerned with developing and validating in hardware the tools necessary to successfully complete the combined agile maneuvering/precision pointing missions. Development has been undertaken on a number of fronts for quietly slewing flexible structures. Various methods for designing slew torque profiles have been investigated. Prime candidates for slew/settle scenarios include Inverse Dynamics and Parameterized Function Space. Joint work with Processor Bayo at the University of California, Santa Barbara and Professor Flashner at the University of Southern California has led to promising torque profile design methods. Active and passive vibration suppression techniques also play a key role for rapid slew/settle mission scenarios. Active members with local control loops and passive members with high loss factor viscoelastic material have been selected for hardware verification. Progress in each of these areas produces large gains in the quiet slewing of flexible spacecraft. The main thrust of the effort to date has been the development of a modular testbed for hardware validation of the precision control concepts. The testbed is a slewing eighteen foot long flexible truss. Active and passive members can be interchanged with the baseline aluminum members to augment the inherent damping in the system. For precision control the active members utilize control laws running on a high speed digital structural control processor. Tip and midspan motions of the truss are determined using optical sensors while accelerometers can be used to monitor the motions of other points of interest. Preliminary results indicate that a mix of technologies produces the greatest benefit. For example, shaping the torque profile produces large improvements in slew/settle performance, but without added damping settling times may still be excessive. With the introduction of moderate amounts of damping, slew/settle performance is vastly improved. On the other hand, introducing damping without shaping the torque profile may not yield the desired level of performance.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: NASA. Langley Research Center, The Fifth NASA(DOD Controls-Structures Interaction Technology Conference, Part 2; p 617-637
    Format: application/pdf
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  • 10
    Publication Date: 2013-08-31
    Description: Conventional end-to-end ground tests for verification of control system performance become increasingly complicated with the development of large, multiple flexible body spacecraft structures. The expense of accurately reproducing the on-orbit dynamic environment and the attendant difficulties in reducing and accounting for ground test effects limits the value of these tests. TRW has developed a building block approach whereby a combination of analysis, simulation, and test has replaced end-to-end performance verification by ground test. Tests are performed at the component, subsystem, and system level on engineering testbeds. These tests are aimed at authenticating models to be used in end-to-end performance verification simulations: component and subassembly engineering tests and analyses establish models and critical parameters, unit level engineering and acceptance tests refine models, and subsystem level tests confirm the models' overall behavior. The Precision Control of Agile Spacecraft (PCAS) project has developed a control structural interaction testbed with a multibody flexible structure to investigate new methods of precision control. This testbed is a model for TRW's approach to verifying control system performance. This approach has several advantages: (1) no allocation for test measurement errors is required, increasing flight hardware design allocations; (2) the approach permits greater latitude in investigating off-nominal conditions and parametric sensitivities; and (3) the simulation approach is cost effective, because the investment is in understanding the root behavior of the flight hardware and not in the ground test equipment and environment.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: JPL, Proceedings of the Fifth NASA(NSF)DOD Workshop on Aerospace Computational Control; p 507-524
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