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At least 19 records

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

Guo, Tong-Yi↗

Order reduction of z-transfer functions via multipoint Jordan continued-fraction expansion

The order reduction problem of z-transfer functions is solved by using the multipoint Jordan continued-fraction expansion (MJCFE) technique. An efficient algorithm that does not require the use of complex algebra is presented for obtaining an MJCFE from a stable z-transfer function with expansion points selected from the unit circle and/or the positive real axis of the z-plane. The reduced-order models are exactly the multipoint Pade approximants of the original system and, therefore, they match the (weighted) time-moments of the impulse response and preserve the frequency responses of the system at some characteristic frequencies, such as gain crossover frequency, phase crossover frequency, bandwidth, etc.

Lee, Ying-Chin↗

Rapid computation of the Voigt profile

Computational procedures for evaluating the Voigt profile function with maximum relative error about one part in ten thousand are discussed. The computational region is split up into four subregions, each of which is worked on with a different computational technique (Chebyshev expansion, continued fraction expansion, 2-point Gauss-Hermite quadrature, and 4-point Gauss-Hermite quadrature). The overall procedure is designed for line-by-line transmittance calculations and similar applications, and an efficient FORTRAN IV subprogram is outlined in an appendix.

Drayson, S. R.↗

A canonical state-space representation for SISO systems using multipoint Jordan CFE

A canonical state-space realization based on the multipoint Jordan continued-fraction expansion (CFE) is presented for single-input-single-output (SISO) systems. The similarity transformation matrix which relates the new canonical form to the phase-variable canonical form is also derived. The presented canonical state-space representation is particularly attractive for the application of SISO system theory in which a reduced-dimensional time-domain model is necessary.

Hwang, Chyi↗

Rational positive real approximations for LQG optimal compensators arising in active stabilization of flexible structures

In this paper the approximation problem for a class of optimal compensators for flexible structures is considered. The particular case of a simply supported truss with an offset antenna is dealt with. The nonrational positive real optimal compensator transfer function is determined, and it is proposed that an approximation scheme based on a continued fraction expansion method be used. Comparison with the more popular modal expansion technique is performed in terms of stability margin and parameters sensitivity of the relative approximated closed loop transfer functions.

Desantis, A.↗

Convergent perturbation analysis of intense coherent multiphoton interactions

Use has been made of flow graphs to deduce Feenberg perturbation expansions for radiative interactions. It is demonstrated that these expansions can in certain cases be summed to provide closed form expressions for the molecular response. In particular, it is shown that the coherent state response can be obtained by the summation of a continued fraction perturbation expansion for the harmonic oscillator. Anharmonicity in the lower levels is treated and its shown to introduce Rabi flopping identifiable with multiphoton transitions among isolated tightly coupled subsystems of levels. Relevance to laser induced multiphoton excitation and energy level shift calculations in the presence of a strong field are also discussed.

Gower, M. C.↗

Series solution for the planar asymmetric blunt-body problem

Accurate semianalytic solutions to the inverse blunt-body problem have been obtained using a method of series expansion. Rational fractions are employed for series summation and analytic continuation. Angles of incidence up to 30 deg and Mach numbers as low as 2 have been considered. The maximum-entropy streamline will not wet the body surface in asymmetric flow. It may pass either above or below the stagnation streamline. Limit lines appear in the supersonic portion of the flow field, both in the shock layer and in its upstream analytic continuation.

Schwartz, L. W.↗

Magnetic energy dissipation in force-free jets

It is shown that a magnetic pressure-dominated, supersonic jet which expands or contracts in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to occur, the effective reconnection time must be a fraction of the expansion time. The dissipation rate for the axisymmetric minimum-energy field configuration is analytically derived. The results indicate that the field relaxation process could be a viable mechanism for powering the synchrotron emission in extragalactic jets if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.

Choudhuri, Arnab Rai↗

Properties of Low-Expansion Laminates

Laminate elastic constants and coefficients of thermal expansion calculated for near-zero-expansion graphite/aluminum and graphite/ magnesium composites. Report presents results in graphic form for these properties as function of laminate angle and fiber volume fraction for four high-modulus continuous-pitch fiber.

Kural, M.↗

Fractionation of the Early Terrestrial Atmospheres: Dynamical Escape

Hydrodynamic escape may have played a significant role in the early fractionation of the atmospheres of the terrestrial planets. This possibility has been demonstrated in the last two decades by numerous models that show radial, transonic flow of hydrogen can occur in the presence of sufficient solar EUV Hydrodynamic escape may have played a significant role in the early fractionation of the atmospheres of the terrestrial planets. This possibility has been demonstrated in the last two decades by numerous models that show radial, transonic flow of hydrogen can occur in the presence of sufficient solar EUV flux, thought to exist in the first 500 My. The models show that the larger the solar flux the greater the mass of the fractionating species, which are accelerated to escape speeds by the hydrogen wind through drag processes. As the atmospheres evolve and the solar EUV flux wanes, the maximum mass of flowing gas constituents decreases until all gases become static. We show that fractionation can continue beyond this point when non-radial flow and dynamically enhanced Jeans escape are considered. For example, the early terrestrial atmospheres are thought to have had large hydrogen contents, resulting in exobase altitudes of a planetary radius or more. In this case, rotational speeds at the exobases of Earth and Mars would be large enough so that light constituents would "spin" off and fractionate, especially at equatorial latitudes. Also, in the presence of transonic flow of hydrogen only, non-radial expansion throws heavier gases to high altitudes in the exosphere, accompanied by strong bulk speeds at the exobase, which results in enhanced thermal escape fluxes and fractionation. flux, thought to exist in the first 500 My. The models show that the larger the solar flux the greater the mass of the fractionating species, which are accelerated to escape speeds by the hydrogen wind through drag processes. As the atmospheres evolve and the solar EUV flux wanes, the maximum mass of flowing gas constituents decreases until all gases become static. We show that fractionation can continue beyond this point when non-radial flow and dynamically enhanced Jeans escape are considered. For example, the early terrestrial atmospheres are thought to have had large hydrogen contents, resulting in exobase altitudes of a planetary radius or more. In this case, rotational speeds at the exobases of Earth and Mars would be large enough so that light constituents would "spin" off and fractionate, especially at equatorial latitudes. Also, in the presence of transonic flow of hydrogen only, non-radial expansion throws heavier gases to high altitudes in the exosphere, accompanied by strong bulk speeds at the exobase, which results in enhanced thermal escape fluxes and fractionation.

Hartle, Richard E.↗

Martian tidal pressure and wind fields obtained from the Mariner 9 infrared spectroscopy experiment

Using temperature fields derived from the Mariner 9 infrared spectroscopy experiment, the Martian atmospheric tidal pressure and wind fields are calculated. Temperature as a function of local time, latitude, and atmospheric pressure level is obtained by secular and longitudinal averaging of the data. The resulting temperature field is approximated by a spherical harmonic expansion, retaining one symmetric and one asymmetric term for wavenumber zero and wavenumber one. Vertical averaging of the linearized momentum and continuity equations results in an inhomogeneous tidal equation for surface pressure fluctuations with the driving function related to the temperature field through the geopotential function and the hydrostatic equation. Solutions of the tidal equation show a diurnal fractional pressure amplitude approximately equal to one half of the vertically averaged diurnal fractional temperature amplitude.

Pirraglia, J. A.↗

Martian tidal pressure and wind fields obtained from the Mariner 9 infrared spectroscopy experiment

Using temperature fields derived from the Mariner 9 infrared spectroscopy experiment, the Martian atmospheric tidal pressure and wind fields are calculated. Temperature as a function of local time, latitude, and atmospheric pressure level is obtained by secular and longitudinal averaging of the data. The resulting temperature field is approximated by a spherical harmonic expansion, retaining one symmetric and one asymmetric term each for wavenumber zero and wavenumber one. Vertical averaging of the linearized momentum and continuity equations results in an inhomogeneous tidal equation for surface pressure fluctuations with the driving function related to the temperature field through the geopotential function and the hydrostatic equation. Solutions of the tidal equation show a diurnal fractional pressure amplitude approximately equal to one-half the vertically averaged diurnal fractional temperature amplitude.

Pirraglia, J. A.↗

Test Medium Effects on Ignition, Combustion and Flameholding Processes in Scramjet Combustors

The total temperatures (enthalpies) required to ground-test air-breathing (aero-propulsion) engines at high Mach number flight conditions can be achieved in a number of ways. Among these are: 1. Heat exchangers, including pre-heated ceramic beds. 2. direct electrical heating, e.g., arc discharge and resistance heaters. 3. Compression heating. 4. Shock heating, and 5. In-stream combustion, with oxygen replenishment to match air content. Each method has distinct advantages, disadvantages and limitations. All have a common characteristic of being designed for intermittent flow, due to the extreme energy required for continuous operation at simulated Mach numbers above about 3. All also distort the composition of atmospheric air to some degree, due to the high temperatures that occur in the plenum section prior to expansion of the flow to simulated flight conditions. In the case of in-stream combustion, the resulting test medium is commonly referred to as "vitiated air", being composed of oxygen, nitrogen and some fraction of combustion products.

Chinitz, W.↗

Free-stream disturbance, continuous Eigenfunctions, boundary-layer instability and transition

A rational foundation is presented for the application of the linear shear flows to transition prediction, and an explicit method is given for carrying out the necessary calculations. The expansions used are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbances in the inner boundary layer, near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer in that the amplitudes of the discrete Tollmien-Schlicting waves are an extremely small fraction of the amplitude of the disturbance.

Grosch, C. E.↗

Free-stream disturbances, continuous eigenfunctions, boundary-layer instability and transition

A rational foundation is provided for the application of the linear stability theory of parallel shear flows to transition prediction. An explicit method is given for carrying out the necessary calculations. The expansions are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbance in the inner boundary layer near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer, in that the amplitudes of the discrete Tollmein-Schlichting waves are an extremely small fraction of the amplitude of the disturbance.

Salwen, H.↗

Energetic ion anisotropies in the geomagnetic tail. I - A statistical survey. II - Magnetic field and substorm characteristics

A comprehensive data set from the ISEE 2 spacecraft is used here to perform a statistical study of events in the earth's central magnetotail that are characterized by high anisotropies of energetic ions. In about 75 percent of the cases the anisotropy vector deviates no more than 45 deg from the tidal axis. High-anisotropy samples within 45 deg of the tidal axis are dominated by the earthward fraction. High ion anisotropies are observed continuously for longer than 1 min only in a few cases. The probability of observing high ion anisotropies is significantly enhanced beyond about 16 R(E) downtail distance within a few earth radii of the neutral sheet and on the duskside of the magnetotail. The analysis is extended with respect to the local magnetic field and to the relationship between energetic ion anisotropies and substorm phases. It is found that the events can be well organized in terms of substorm expansion phase and substorm recovery. These relations and the magnetic field characteristics during the events support the notion that the near-earth source of tailward streaming ions is identical with a substorm neutral line.

Kettmann, Georg↗