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The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Virtual oscillator based control architecture for grid forming converter with inner current control loop for additional objective accomplishments is proposed in this paper. In general, virtual oscillator is based on Lienard type of oscillator equation with a cubic nonlinearity. Virtual oscillator alone cannot accommodate unbalanced or harmonic mitigation while operating converters in grid forming mode. Therefore, to accomplish better tracking performance, incorporating the provision for nonlinear and/or unbalanced loads, an inner current control loop is utilized which is based upon Lyapunov energy function type control architecture due to its advantages. To reduce the overall cost of implementation and ensure proper phase difference in the generated voltages, the implemented virtual oscillator operates with only one voltage feedback from the point of common coupling as presented in this paper. To verify the effectiveness of the proposed approach, the overall system has been modeled in MATTLAB/Simulink and PLECS domain and case studies showing the successful production of low harmonic load voltages under nonideal loading condition along with other important results are presented in this paper.
A 0.36-scale model of a canard general-aviation airplane with a single pusher propeller and winglets was tested in the Langley 30- by 60-Foot Wind Tunnel to determine the static and dynamic stability and control and free-flight behavior of the configuration. Model variables made testing of the model possible with the canard in high and low positions, with increased winglet area, with outboard wing leading-edge droop, with fuselage-mounted vertical fin and rudder, with enlarged rudders, with dual deflecting rudders, and with ailerons mounted closer to the wing tips. The basic model exhibited generally good longitudinal and lateral stability and control characteristics. The removal of an outboard leading-edge droop degraded roll damping and produced lightly damped roll (wing rock) oscillations. In general, the model exhibited very stable dihedral effect but weak directional stability. Rudder and aileron control power were sufficiently adequate for control of most flight conditions, but appeared to be relatively weak for maneuvering compared with those of more conventionally configured models.
The normal dispersion analysis for linear adiabatic wave propagation in stratified atmospheres adopts a real frequency and solves for the complex vertical wavenumber. We show that an exponentially stratified atmosphere does not have any spatially bounded normal modes for real frequencies. The usual treatment involves a representation where the imaginary part of the vertical wavenumber yields a rho(sup -1/2) dependence of the velocity amplitude which diverges as the absolute value of z approaches infinity. This solution includes a cutoff frequency below which acoustic modes cannot propagate. The standard dispersion analysis is a local representation of the wave behavior in both space and time but which is assumed to represent the motion throughout - infinity is less than t is less than infinity and 0 is less than infinity. However, any solution which has a purely sinusoidal time dependence extends through this full domain and is divergent due to the rho(sup -1/2) dependence. We show that a proper description is in terms of a near field of a boundary piston which is driven arbitrarily as a function of space and time. The atmosphere which responds to this piston is a semi-infinite layer which has an initially constant sound speed but which has the usual gravitational stratification. In a restricted domain of space and time above this boundary, the wavelike behavior of the medium may be described by frequencies and vertical wavenumbers which are both complex. When both parameters are allowed to have imaginary components, a new range of solutions is found for which there is virtually no cutoff frequency. We show that vertical energy propagation can take place through the solar atmosphere as a result of oscillations below the nominal cutoff frequency. Previously, the largest amplitude oscillations which generally have low frequencies were dropped from the calculation of energy flux becuase their frequencies are below the cutoff frequency. This new family of near-field waves permits these modes to carry energy vertically outward and raises the possibility that the largest amplitude 5 minute oscillations play a substantial role in the transport of acoustic energy to the chromosphere.
Measurements of the discharge current in a cylindrical Hall thruster are presented to quantify plasma oscillations and instabilities without introducing an intrusive probe into the plasma. The time-varying component of the discharge current is measured using a current monitor that possesses a wide frequency bandwidth and the signal is Fourier transformed to yield the frequency spectra present, allowing for the identification of plasma oscillations. The data show that the discharge current oscillations become generally greater in amplitude and complexity as the voltage is increased, and are reduced in severity with increasing flow rate. The breathing mode ionization instability is identified, with frequency as a function of discharge voltage not increasing with discharge voltage as has been observed in some traditional Hall thruster geometries, but instead following a scaling similar to a large-amplitude, nonlinear oscillation mode recently predicted in for annular Hall thrusters. A transition from lower amplitude oscillations to large relative fluctuations in the oscillating discharge current is observed at low flow rates and is suppressed as the mass flow rate is increased. A second set of peaks in the frequency spectra are observed at the highest propellant flow rate tested. Possible mechanisms that might give rise to these peaks include ionization instabilities and interactions between various oscillatory modes.
The paradigm of the inflationary universe provides a possible explanation for several observed cosmological properties. In order for such solutions to be successful, the universe must convert the energy stored in the inflaton potential into standard model particles through a process known as reheating. In this paper, we reconsider the reheating process for the case where the inflaton potential respects an approximate (but spontaneously broken) conformal symmetry during the reheating epoch. After reviewing the Effective Field Theory of Reheating, we present solutions for the nonlinear oscillations of the inflaton field, derive the corresponding Hill’s equation for the coupled reheating field, and determine the stability diagram for parametric resonance. For this class of models —the simplest realization being a scalar field with a quartic term—the expansion of the universe drives the coupled field toward a more unstable part of parameter space, in contrast to the standard case. We also generalize this class of models to include quadratic breaking terms in the potential during the reheating epoch and address the process of stability in that universality class of models.
The application of general circulation models (GCM's) to stratospheric chemistry and transport both permits and requires a thorough investigation of stratospheric water vapor. The National Center for Atmospheric Research has redesigned its GCM, the Community Climate Model (CCM2), to enable studies of the chemistry and transport of tracers including water vapor; the importance of water vapor to the climate and chemistry of the stratosphere requires that it be better understood in the atmosphere and well represented in the model. In this study, methane is carried as a tracer and converted to water; this simple chemistry provides an adequate representation of the upper stratospheric water vapor source. The cold temperature bias in the winter polar stratosphere, which the CCM2 shares with other GCM's, produces excessive dehydration in the southern hemisphere, but this dry bias can be ameliorated by setting a minimum vapor pressure. The CCM2's water vapor distribution and seasonality compare favorably with observations in many respects, though seasonal variations including the upper stratospheric semiannual oscillation are generally too small. Southern polar dehydration affects midlatitude water vapor mixing ratios by a few tenths of a part per million, mostly after the demise of the vortex. The annual cycle of water vapor in the tropical and northern midlatitude lower stratosphere is dominated by drying at the tropical tropopause. Water vapor has a longer adjustment time than methane and had not reached equilibrium at the end of the 9 years simulated here.
Rational approximation of generalized Duffing equation, damped mass spring oscillator equation and generalized second order Riccati equation
Precision oscillators used in PTTI applications include quartz crystal, rubidium gas cell, cesium beam, and hydrogen maser oscillators. A general characterization and comparison of these devices is given including accuracy, stability, environmental sensitivity, size, weight, power consumption, availability and cost. Areas of special concern in practical applications are identified and a projection of future performance specifications is given. An attempt is made to predict physical and performance characteristics of new designs potentially available in the near future.
Deviations from resonance detected by sampling phases. Automatic tuner feedback control system derives error signal from E and H plane probe signals. Control objective to maintain phase difference between E and H at 90 degrees. Technique estimated to sensitive to fractional frequency deviation of about 5 X 10-16 and applicable not only to masers but also other microwave elements, including klystrons, general purpose oscillators, and frequency standards.
Since the development of the last CIRA in 1972, the number of radars providing winds in the upper middle atmosphere has increased significantly. These systems fill the data gap between 60 km and 110 km. The radars include medium frequency (MF) radars or partial reflection systems giving data from 60/70 to 100/110 km; meteor radars, 80 to 110 km, and M.S.T. radars operating as meteor radars. Data from 12 locations are shown, which represent a good Northern Hemispheric (NH) North American chain, an Oceanian chain which is mainly in the Southern Hemisphere (SH), and some Western Europe data. Generally tidal oscillations have been removed from days or groups of days, and the remaining mean winds and longer period oscillations plotted as height-time contours. Composite cross sections from the years 1978 to 1982 were formed where possible so that only the major temporal features remain.
The 12-year output of a 15-wavenumber GCM experiment is analyzed, with the objective of describing the spatial and temporal behavior of dominant intraseasonal variations. The parameters analyzed include five-day averages of wind, geopotential height, sea level pressure, and precipitation. It is demonstrated that the spatial structure, propagation characteristics, and seasonal dependence of the model features are consistent with observations reported in the literature. The model findings are interpreted in terms of the current theoretical understanding of tropical and extratropical motions.
A perturbative method, using Lie transforms, is given for calculating the Hannay angle for slow, cyclic evolutions of a classical system, taking into account the finite rate of change of the Hamiltonian. The method is applied to the generalized harmonic oscillator. The classical Aharonov-Anandan angle is also calculated. The interpretational ambiguity in the definitions of geometrical angles is discussed.
A reefed 12.2-meter nominal-diameter (40-ft) disk-gap-band parachute was flight tested as part of the NASA Supersonic High Altitude Parachute Experiment (SHAPE) program. A three-stage rocket was used to drive the instrumented payload to an altitude of 43.6 km (143,000 ft), a Mach number of 2.58, and a dynamic pressure of 972 N/m(exp 2) (20.3 lb/ft(exp 2)) where the parachute was deployed by means of a mortar. The parachute deployed satisfactorily and reached a partially inflated condition characterized by irregular variations in parachute projected area. A full, stable reefed inflation was achieved when the system had decelerated to a Mach number of about 1.5. The steady, reefed projected area was 49 percent of the steady, unreefed area and the average drag coefficient was 0.30. Disreefing occurred at a Mach number of 0.99 and a dynamic pressure of 81 N/m(exp 2) (1.7 lb/ft(exp 2)). The parachute maintained a steady inflated shape for the remainder of the deceleration portion of the flight and throughout descent. During descent, the average effective drag coefficient was 0.57. There was little, if any, coning motion, and the amplitude of planar oscillations was generally less than 10 degrees. The film also shows a wind tunnel test of a 1.7-meter-diameter parachute inflating at Mach number 2.0.
The gravity wave (GW)-resolving capabilities of 118-GHz saturated thermal radiances acquired throughout the stratosphere by the Microwave Limb Sounder (MLS) on the Aura satellite are investigated and initial results presented. Because the saturated (optically thick) radiances resolve GW perturbations from a given altitude at different horizontal locations, variances are evaluated at 12 pressure altitudes between 21 and 51 km using the 40 saturated radiances found at the bottom of each limb scan. Forward modeling simulations show that these variances are controlled mostly by GWs with vertical wavelengths z 5 km and horizontal along-track wavelengths of y 100-200 km. The tilted cigar-shaped three-dimensional weighting functions yield highly selective responses to GWs of high intrinsic frequency that propagate toward the instrument. The latter property is used to infer the net meridional component of GW propagation by differencing the variances acquired from ascending (A) and descending (D) orbits. Because of improved vertical resolution and sensitivity, Aura MLS GW variances are 5?8 times larger than those from the Upper Atmosphere Research Satellite (UARS) MLS. Like UARS MLS variances, monthly-mean Aura MLS variances in January and July 2005 are enhanced when local background wind speeds are large, due largely to GW visibility effects. Zonal asymmetries in variance maps reveal enhanced GW activity at high latitudes due to forcing by flow over major mountain ranges and at tropical and subtropical latitudes due to enhanced deep convective generation as inferred from contemporaneous MLS cloud-ice data. At 21-28-km altitude (heights not measured by the UARS MLS), GW variance in the tropics is systematically enhanced and shows clear variations with the phase of the quasi-biennial oscillation, in general agreement with GW temperature variances derived from radiosonde, rocketsonde, and limb-scan vertical profiles.
Classic tonal screech noise created by under-expanded supersonic jets; Long Penetration Mode (LPM) supersonic phenomenon -Under-expanded counter-flowing jet in supersonic free stream -Demonstrated in several wind tunnel tests -Modeled in several computational fluid dynamics (CFD) simulations; Discussion of LPM acoustics feedback and fluid interactions -Analogous to the aero-acoustics interactions seen in screech jets; Lessons Learned: Applying certain methodologies to LPM -Developed and successfully demonstrated in the study of screech jets -Discussion of mechanically induced excitation in fluid oscillators in general; Conclusions -Large body of work done on jet screech, other aero-acoustic phenomenacan have direct application to the study and applications of LPM cold flow jets
This is our first study of the magnetic Rayleigh-Taylor instability at the inner edge of an astrophysical disc around a central back hole. We derive the equations governing small-amplitude oscillations in general relativistic ideal magnetodydrodynamics and obtain a criterion for the onset of the instability. We suggest that static disc configurations where magnetic field is held by the disc material are unstable around a Schwarzschild black hole. On the other hand, we find that such configurations are stabilized by the space-time rotation around a Kerr black hole. We obtain a crude estimate of the maximum amount of poloidal magnetic flux that can be accumulated around the centre, and suggest that it is proportional to the black hole spin. Finally, we discuss the astrophysical implications of our result for the theoretical and observational estimations of the black hole jet power.
Determine how film thickness changes with different deposition methods. Analyze relationship between film thickness and optical constants. The deposition rate of intrinsic polysilicon is higher during initial deposition then begins to slow down as deposition time increases. Longer depositions of polysilicon are more crystalline in structure than shorter depositions. N-type doping of polysilicon is more crystalline in structure than p-type doping, despite similar film thicknesses.