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It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
A general criterion is derived for the stability of a negative-resistance oscillator with respect to small perturbations in the operating point. The derivation applies when the oscillator output consists of an arbitrary number of related frequency components, including possible nonharmonic components. Examples are given of the application of the stability criterion to coaxial IMPATT oscillator circuits, with experimental verification of the frequency and output power at theoretically determined stable operating points.
We examine intraseasonal oscillations in a three-year, perpetual-January simulation using a version.
This paper presents the Small Explorer WIRE Failure Investigation Report in viewgraph form. Some of the diagrams include: 1) Overview of the Pyro Box and key interfaces; 2) Schematic Diagram of the A1020 FPGA (Field Programmable Gate Array) inputs; 3) Three critical FPGA reset signals shown in detail; 4) State machines for firing the cover pyrotechnic devices; 5) Oscillator Overview; and 6) General Crystal Oscillator Startup Characteristics.
The investigation of the lateral stability of an automatically controlled glide bomb led also to the attempt of clarifying the influence of a phugoid oscillation or of any general longitudinal oscillation on the lateral stability of a glide bomb. Under the assumption that its period of oscillation considerably exceeds the rolling and yawing oscillation and that c(sub a) is, at least in sections, practically constant, the result of this test is quite simple. It becomes clear that the influence of the phugoid oscillation may be replaced by suitable variation of the rolling-yawing moment on a rectilinear flight path instead of the phugoid oscillation. If the flying weight of the glide bomb of unchanged dimensions is increased, an increase of the flight velocity will be more favorable than an increase of the lift coefficient. The arrangement of the control permits lateral stability to be achieved in every case; a minimum rolling moment due to sideslip proves of great help.
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Operations of a three-channel 100-kW class nested Hall thruster at total power levels from 5 to 102 kW and discharge currents from 16 to 247 A were successful. The thruster was operated in all seven available channel combinations at discharge voltages of 300, 400, and 500 V and at current densities that were 0.60 and 0.95 of the nominal value. Additional test points were also collected at 1.20 the nominal current density. The thruster was throttled through a total of forty-six unique operating conditions. At each condition, thruster performance was measured using a high-power thrust stand designed to measure up to 8 N of thrust. From these thrust measurements, specific impulse and efficiency were calculated. All seven channel combinations showed similar performance at a given discharge voltage and current density. The largest thrust recorded was 5.42 N at 99 kW, 400 V discharge voltage. Total efficiency values 0.54 to 0.67, and total specific impulse ranged from 1800 seconds to 2650 seconds. Discharge current oscillations were also measured. Generally these oscillations increased on the inner and middle channels during multi-channel mode but stayed roughly a constant fraction of the channel discharge current for the outer channel in both single- and multi-channel operation. We also found that the thrust of the three channels firing together was not significantly higher than the sum of each channel _ring individually, a result that differs from what was found previously for nested Hall thrusters.
Variations in atmospheric angular momentum (AAM) are examined in a three-year simulation of the large-scale atmosphere with perpetual January forcing. The simulation is performed with a version of the University of California at Los Angeles (UCLA) general circulation model that contains no tropical Madden-Julian Oscillation (MJO). In addition, the results of three shorter experiments with no topography are analyzed. The three-year standard topography run contains no significant intraseasonal AAM periodicity in the tropics, consistent with the lack of the MJO, but produces a robust, 42-day AAM oscillation in the Northern Hemisphere (NH) extratropics. The model tropics undergoes a barotropic, zonally symmetric oscillation, driven by an exchange of mass with the NH extratropics. No intraseasonal periodicity is found in the average tropical latent heating field, indicating that the model oscillation is dynamically rather than thermodynamically driven. The no-mountain runs fail to produce an intraseasonal AAM oscillation, consistent with a topographic origin for the NH extratropical oscillation in the standard model. The spatial patterns of the oscillation in the 500-mb height field, and the relationship of the extratropical oscillation to intraseasonal variations in the tropics, will be discussed in Part 2 of this study.
Fluctuations in stmospheric angular momentum (AAM) are examined in a three-year simulation of the perpetual-January climate, performed with of a version of the UCLA general circulation model which contains no tropical, Madden-Julian oscillation (MJO).
A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.
A general overview of piezoelectric resonators is given with emphasis on evolution of the resonator design. Superconducting cavities and crystals at low temperature and the use of resonant frequencies are also discussed.
A generalization of previous treatments of quantum phase is presented. Restrictions on the class of realizable phase statistics are thereby removed; thus, permitting 'phase wavefunction collapse' (and other advantages). This is accomplished by exciting the auxiliary mode of the measurement apparatus in a time-reversed fashion. The mathematical properties of this auxiliary mode are studied in the hope that they will lead to an identification of a physical apparatus which can realize the quantum phase measurement.
Observational evidence has been presented for the existence of quasi-periodic fluctuations of the tropical circulation with periods around two weeks and around 40 days. It is expected that an understanding of the mechanisms of these quasi-periodic oscillations in the tropical atmosphere will improve the predictability of the short range climate fluctuations in the tropics. The present study evolved as an outgrowth of an investigation conducted by Goswami et al. (1984). In this investigation remarkable oscillations of the Hadlay circulation for an ocean covered earth were observed. In the current study evidence is presented regarding the episodic behavior of the tropical circulation in general, and the propagation characteristics of these oscillations in the lower atmosphere. Attention is given to the results of six different experiments.
The purpose is the verification of the virial mass estimations for small galaxy groups. The dynamical evolution of triple and quintuple galaxies was studied by the numerical simulations. The dependence of the virial coefficient k(t) versus time was derived. Initial k(O) = O. The function k(t) has some strong oscillations from 0.02 to 0.99. Generally, these oscillations are quasiperiodical ones. Such a behavior of k(t) is caused by formation in a system of close isolated temporary double subsystems. A strong correlation between the virial coefficient and the least mutual distance in the system is observed. Such wide oscillations may add into the estimation of virial mass of the galaxy groups an uncertainty of more than one order. An additional uncertainty is introduced by the projection effect. This uncertainty for the individual estimations of the masses approach three orders. Thus any individual estimation of the virial mass is impossible for small galaxy groups. Some possibility of statistical estimation (median or average) of the total mass, including a hidden mass, is shown for the homogeneous samples. The authors propose a method for these estimations based on a comparison of the medians of dynamical parameters (a mean size in projection and a dispersion of relative radial velocities) for the simulated and observed ensembles of the galaxy groups. This method has been applied to a sample of 46 probably physical triplets of galaxies. The probable median of the hidden mass in a volume of the triplet is about 4 M, where M is the total mass of visible matter.
The Eastern Interconnection Situational Awareness Monitoring System (ESAMS) project demonstrated the feasibility of aggregating synchrophasor measurements from across an interconnection, analyzing them, and providing real-time wide-area situational awareness to system operators who may have excellent visibility within their footprint but lack an interconnection-wide view. An application within ESAMS that has garnered industry interest involves detecting forced oscillations visible across multiple areas, identifying the region where the oscillation originated from, quantifying the uncertainty in source localization results, and notifying users in real-time if the detected oscillation amplitudes cross a specified threshold. It is expected that system operators will utilize their internal SCADA/EMS/synchrophasor systems in conjunction with information provided by ESAMS to take effective mitigation actions if forced oscillation notifications are received. This report provides some general guidance on how the ESAMS information can be used for source localization and coordination among multiple reliability coordinators; and also identifies potential enhancements to ESAMS notifications for improved interpretability.
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
Coherent states for a family of isospectral oscillator Hamiltonians are derived from a suitable choice of annihilation and creation operators. The Fock-Bargmann representation is also obtained.
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