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A probabilistic approach is used to obtain an analytical solution to the Fokker-Planck equation used in the transient analysis of the phase-locked loop phase error process of the first-order phase-locked loop. The solution procedure, which is based on the Girsanov transformation, is described.
Unlike droplet nucleation near a liquid-gas critical point, the decay of metastable phases in crystalline materials is strongly affected by the presence of long-range forces. Field quench experiments performed on the ferroelectric barium titanate indicate that nucleation in this material is markedly different from that observed in liquids. In this paper, a theory for nucleation at a first-order phase transition in which the mediating forces are long range is presented. It is found that the long-range force induces cooperative nucleation and growth processes, and that this feedback mechanism produces a well-defined delay time with a sharp onset in the transformation to the stable phase. Closed-form expressions for the characteristic onset time and width of the transition are developed, in good agreement with numerical and experimental results.
Prognostics is centered on predicting the time of and time until adverse events in components, subsystems, and systems. It typically involves both a state estimation phase, in which the current health state of a system is identified, and a prediction phase, in which the state is projected forward in time. Since prognostics is mainly a prediction problem, prognostic approaches cannot avoid uncertainty, which arises due to several sources. Prognostics algorithms must both characterize this uncertainty and incorporate it into the predictions so that informed decisions can be made about the system. In this paper, we describe three methods to solve these problems, including Monte Carlo-, unscented transform-, and first-order reliability-based methods. Using a planetary rover as a case study, we demonstrate and compare the different methods in simulation for battery end-of-discharge prediction.
In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.
Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.
The kinetics of the reactions of chlorine nitrate with HCl and H2O are characterized using a static photolysis/Fourier transform infrared spectrophotometer apparatus. For the homogeneous gas-phase reaction with HCl, an upper limit for the rate constant of less than 8.4 x 10 to the -21st, and for the reaction with H2O, a limit of less than 3.4 x 10 to the -21st cu cm/molecule per s, were obtained at 296 + or - 2 K. The yield of HNO3 is almost unity in both cases, and no synergistic effect is noted between HCl and H2O. The kinetic behavior of the reaction with H2O is well described by simple first-order kinetics, while the behavior of the reaction with HCl is described in terms of the Langmuir adsorption isotherm.
There have been many developments of mine or metal detectors based on ground penetrating radar techniques, usually in hand-held or rover-mounted devices. In most mine or metal detector applications, conditions are in a stationary mode and detection speed is not an important factor. A novel, forward-looking, stepped-frequency ground penetrating radar (GPR) has been developed with a capability to detect improvised explosive devices (IEDs) at vehicular speeds of 15 to 20 mph (24 to 32 km/h), 10 to 20 m ahead of the vehicle, to ensure adequate time for response. The GPR system employs two horn antennas (1.7 to 2.6 GHz, 20 dBi) as transmit and receive. The detector system features a user-friendly instantaneous display on a laptop PC and is a low-power-consumption (3 W) compact system with minimal impact on vehicle operations. In practice, the whole GPR system and a laptop PC can be powered by plugging into a cigarette lighter of a vehicle. The stepped-frequency continuous-wave (CW) radar scans frequency from 1.7 to 2.6 GHz in 1,000 steps of 0.9 MHz, with the full frequency scan in 60 ms. The GPR uses a bi-static configuration with one horn antenna used as a transmitter and the other used as a receiver so that isolation between transmitter and receiver is improved. Since the horn antennas (20 dBi) are mounted on the roof of a vehicle at a shallow inclination angle (15 to 25 with respect to horizontal), there is a first-order reduction in ground reflection so that a significant amount of the total reflected power received by the GPR comes from the scattering of RF energy off of buried objects. The stepped-frequency technique works by transmitting a tone at a particular frequency, while the received signal is mixed with the transmitted tone. As a result, the output of the mixer produces a signal that indicates the strength of the received signal and the extent to which it is in phase or out of phase with the transmitted tone. By taking measurements of the phase relationship between the transmitted and received signals over a wide frequency range, an interference pattern is produced showing all target reflections. When a Fourier transform is performed on this pattern, the result is a time-domain representation of targets. Among the advantages of this technique over impulse radar is the ability to transmit and receive much more total energy, and to use non-damped, highly focused horn antennas. The novelty of the IED detector GPR has been achieved by miniaturization of GPR electronics (single electronics board, 10x5x2 cm), low power consumption (3 W), faster signal processing capability, and minimal impact on vehicle operations.
Those who design piloted aircraft simulations must contend with the finite size and speed of the available digital computer and the requirement for simulation reality. With a fixed computational plant, the more complex the model, the more computing cycle time is required. While increasing the cycle time may not degrade the fidelity of the simulated aircraft dynamics, the larger steps in the pilot cue feedback variables (such as the visual scene cues), may be disconcerting to the pilot. The first-order-hold interpolation (FOHI) digital-to-analog converter (DAC) is presented as a device which offers smooth output, regardless of cycle time. The Laplace transforms of these three conversion types are developed and their frequency response characteristics and output smoothness are compared. The FOHI DAC exhibits a pure one-cycle delay. Whenever the FOHI DAC input comes from a second-order (or higher) system, a simple computer software technique can be used to compensate for the DAC phase lag. When so compensated, the FOHI DAC has (1) an output signal that is very smooth, (2) a flat frequency response in frequency ranges of interest, and (3) no phase error. When the input comes from a first-order system, software compensation may cause the FOHI DAC to perform as an FOHE DAC, which, although its output is not as smooth as that of the FOHI DAC, has a smoother output than that of the ZOH DAC.
A modified nucleation theory is used to determine a critical nucleus size and a critical activation-energy barrier for second-order Ehrenfest thermodynamic transitions as functions of the degree of undercooling, the interfacial energy, the heat-capacity difference, the specific volume of the transformed phase, and the equilibrium transition temperature. The customary approximations of nucleation theory are avoided by expanding the Gibbs free energy in a Maclaurin series and applying analytical thermodynamic expressions to evaluate the expansion coefficients. Nonlinear correction terms for first-order-transition calculations are derived, and numerical results are presented graphically for water and polystyrene as examples of first-order and quasi-second-order transitions, respectively.
Based on the measured anisotropy of three-dimensional energetic ion distributions obtained from the Medium Energy Particle Instrument experiment of the ISEE 1 spacecraft, bulk flow, epsilon x B convection, and pressure gradients in magnetospheric plasmas are measured with two techniques. In the first technique, using a Compton-Getting transform into the appropriate rest frame in an iterative fashion and converging to the unique velocity that removes the first-order anisotropy from the flux angular distribution, the actual measured angular distribution, and spectrum at each angle, are employed. The second technique uses a first moment of the distribution function in which the shift in velocity space of the distribution function is obtained at two phase space density values. The convection contribution to the velocity shift is assumed to be perpendicular to the pressure gradient contribution if an MHD generator condition is assumed, rendering the two shifts separable, and a gradient scale and a lower limit to the convection electric field are derived in one calculation.