Random Frequency Fluctuations Research Articles

Human-environment feedback and the consistency of proenvironmental behavior.

Addressing global environmental crises such as anthropogenic climate change requires the consistent adoption of proenvironmental behavior by a large part of a population. Here, we develop a mathematical model of a simple behavior-environment feedback loop to ask how the individual assessment of the environmental state combines with social interactions to influence the consistent adoption of proenvironmental behavior, and how this feeds back to the perceived environmental state. In this stochastic individual-based model, individuals can switch between two behaviors, 'active' (or actively proenvironmental) and 'baseline', differing in their perceived cost (higher for the active behavior) and environmental impact (lower for the active behavior). We show that the deterministic dynamics and the stochastic fluctuations of the system can be approximated by ordinary differential equations and a Ornstein-Uhlenbeck type process. By definition, the proenvironmental behavior is adopted consistently when, at population stationary state, its frequency is high and random fluctuations in frequency are small. We find that the combination of social and environmental feedbacks can promote the spread of costly proenvironmental behavior when neither, operating in isolation, would. To be adopted consistently, strong social pressure for proenvironmental action is necessary but not sufficient-social interactions must occur on a faster timescale compared to individual assessment, and the difference in environmental impact must be small. This simple model suggests a scenario to achieve large reductions in environmental impact, which involves incrementally more active and potentially more costly behavior being consistently adopted under increasing social pressure for proenvironmentalism.

Deep cepstrum-wavelet autoencoder: A novel intelligent sonar classifier

Different marine vessels belonging to the same class may have different and time-varying radiated noise due to different and changing machinery configurations. Further, the time-varying radiated noise, which is propagated underwater, suffers from random fluctuations in frequency, amplitude, and phase. The ambient noise and time-varying multi-path effects further complicate the classification problem. In this study, for the first time, a deep wavelet autoencoder is proposed, evolving by a two-hybrid cepstral concept to reduce the multi-path distortion and time-varying shallow underwater channel effects. In this approach, the autoencoder is an automatic feature extractor, choosing the best feature composition without information loss and human intervention, and wavelet networks extract the periodic frequency signatures of vessels, which are fluctuating by various machinery regimes. Three underwater acoustic datasets, including synthetic, ShipsEar, and real experimental datasets, are exploited to evaluate the performance of the proposed model so that the performance of the designed model is compared with ten benchmark methods. The results show that the designed model with an average accuracy of 96.11% and average giga-multiplier–accumulators equal to 0.019 represents the best performance in terms of accuracy and complexity compared to benchmark methods. Besides, the cepstral liftering procedure and the average cepstral feature can significantly alleviate the shallow underwater channel’s multi-path distortion and time-varying channel effects. Furthermore, the proposed model is less sensitive to SNR level compare to other benchmark methods.

Статистические характеристики частоты электроэнергетической системы, связанной слабой связью с энергообъединением

The statistical characteristics of the frequency in a grid connected to a power pool via a weak link under the conditions of random load fluctuations at the network nodes are considered. It is supposed in the analysis that a small grid is connected to the power pool via a link that operates close to its limit mode, so that random load fluctuations, short circuit faults, and other disturbances give rise to short-term out-of-step modes. The average number of loss-of-synchronism and recovery occurrences, the parameters characterizing step-like changes of frequency and phase in the small grid, and other parameters depending on the mode severity and active power flow direction are considered. A switched model describing random frequency fluctuations in the small grid in normal and limit modes of its operation is presented. Step-like changes of frequency and phase in the smaller grid can serve as an indicator characterizing the proximity of the system to the limit (emergency) mode. An analogy in the behavior of phase and frequency in communication systems with frequency modulation (FM) and in electric power systems is pointed out.

Measuring Coupling of Rhythmical Time Series Using Cross Sample Entropy and Cross Recurrence Quantification Analysis.

The aim of this investigation was to compare and contrast the use of cross sample entropy (xSE) and cross recurrence quantification analysis (cRQA) measures for the assessment of coupling of rhythmical patterns. Measures were assessed using simulated signals with regular, chaotic, and random fluctuations in frequency, amplitude, and a combination of both. Biological data were studied as models of normal and abnormal locomotor-respiratory coupling. Nine signal types were generated for seven frequency ratios. Fifteen patients with COPD (abnormal coupling) and twenty-one healthy controls (normal coupling) walked on a treadmill at three speeds while breathing and walking were recorded. xSE and the cRQA measures of percent determinism, maximum line, mean line, and entropy were quantified for both the simulated and experimental data. In the simulated data, xSE, percent determinism, and entropy were influenced by the frequency manipulation. The 1 : 1 frequency ratio was different than other frequency ratios for almost all measures and/or manipulations. The patients with COPD used a 2 : 3 ratio more often and xSE, percent determinism, maximum line, mean line, and cRQA entropy were able to discriminate between the groups. Analysis of the effects of walking speed indicated that all measures were able to discriminate between speeds.

Absorption cross-section fluctuations driven by continuous and discrete laser frequency variations

Abstract Though the operational definition of a photon’s absorption cross-section is straightforward, the definition has a fundamental and well-known subtlety. In order to make contact with theory, the incident photons must be monoenergetic and should impinge on the target atom or molecule at a constant rate. To some extent, however, these two constraints are always violated: no field is perfectly monochromatic and laser photons bunch (for both technical and fundamental reasons). Thus, the textbook definition of cross-section must be understood in terms of a mean, in which case the quantum nature of a field and the practicability of its realization must be recognized as sources of cross-section variance. Here, we consider the role that continuous and discrete random frequency fluctuations play in determining the variance of an absorption cross-section. In particular, we investigate the differing roles of phase diffusion and mode-partition noise, finding that discontinuous mode variations have a significant and not easily discerned effect on an absorption cross-section’s variance. As a by-product of our studies, agreement between theory and experiment highlights the utility of a hybrid absorption cross-section for use in the quasi-static approximation, and also suggests an exponential relationship between the rate of mode hops and injection current in cleaved-facet diode lasers.

Effect of spontaneous frequency fluctuations on the emission line of a semiconductor laser with pseudorandom modulation of the pump current

The effect of random frequency fluctuations due to spontaneous emission and generation-recombination noise on the shape of the emission line of a semiconductor laser with pseudorandom modulation of the pump current is studied numerically. The roles of spontaneous emission and chirp modulation in forming the lasing spectrum are separated out. The dependence of the output spectral characteristics of the laser on the parameters and type of modulation is analyzed.

Measurement of the attributes of complex tonal components commonly found in product sound

All rotating components in machinery produce sounds that contain tonal components, and the presence of these tones can significantly affect the quality of the product sound. Tone corrections for metrics based on weighted, average sound pressure level have been used since the late 1960s to assess annoyance due to aircraft noise and to rate climate control machinery. Much research has also been focused on measuring the strength of well separated tones in noise. Metrics such as the Prominence Ratio, the Tone-to-Noise Ratio, and variants, as well as more complex models such as the Joint Nordic Method, Aures Tonalness, and Virtual Pitch, produce values that often correlate well with subjects judgments on the level of the tonal features that they perceive when listening to the sound. However, when sounds are more complex, these metrics do not always work well. Models for the tonalness of two types of tonal sounds are considered here: narrow-band random noise and tones with random frequency fluctuations. The influence of bandwidth and roll-off rate on perceived tonalness are explored for the narrow-band sounds, and the effect of the range and the rate of change of the frequency variation on perceived tonalness is explored for frequency modulated sounds. It was found that roll-off rate affected the perception of tonalness, and that when frequency variations could be tracked or were very small, metrics derived from averaged spectra produced inaccurate predictions of tonalness. Based on the results of these two investigations modifications to tonal metrics are proposed. © 2003 Institute of Noise Control Engineering.

Examination of a crystal oscillator's frequency fluctuations during the enhanced space-radiation environment of a solar flare

Though the ubiquitous quartz crystal oscillator finds application onboard diverse spacecraft, the space-radiation environment can be severe, particularly during periods of enhanced solar activity. The question we address concerns the influence of enhanced space-radiation on a crystal oscillator's random frequency fluctuations, which, in addition to radiation-induced deterministic effects, can have a pronounced effect on the oscillator's timekeeping ability. Examining the response of the Milstar FLT-1 spacecraft's crystal oscillator to the large solar flares of July 14 and November 9, 2000, we find clear evidence of a flare-induced deterministic change in oscillator frequency. However, examining the random fluctuations of the oscillator's frequency about this deterministic variation, we find no evidence of a concomitant change in the nature of the oscillator's stochastic behavior. Though limited to a somewhat unique satellite experiment, this result nonetheless suggests that spacecraft timekeeping need not be unduly perturbed during periods of enhanced solar activity, so long as the spacecraft can compensate for the deterministic change in crystal oscillator frequency.

Spectral Diffusion in Proteins: A Simple Phenomenological Model

Previous experimental studies on a modified cytochrome c have shown that optical hole widths have a power-law dependence on waiting time. We show that a phenomenological model, which assumes Gaussian random frequency fluctuations whose two-point time-correlation function is a stretched exponential, is consistent with the experimental data.

Low temperature limitation on the quality factor of quartz resonators

The quality factor (Q) for different resonators driven at several overtones has been determined between 1.5 and 300 K. These measurements give an improved interpretation of the Q-factor limitation. A significant consequence is a better understanding of the relationship between Q and random frequency fluctuations. The curves of 1/Q=F(T) show the usual features between 20 and 300 K. These include the sodium ion peak at 55 K as well as a peak at 20 K. However, the region of principal interest lies between 1.5 and 20 K. At very low temperatures, a plateau is always observed. If for a given resonator, the 1/Q value of this plateau is subtracted from the experimental values, the residual 1/Q is almost a linear function of T/sup 4/. This variation obeys the Landau-Rumer theory of acoustic wave absorption caused by phonon-phonon interaction in the crystal. Thus the authors conclude that between 6 and 20 K the main limitation in Q is due to the crystal itself, but the plateau is not caused by intrinsic crystal properties. Data for different overtones enable the elimination, at least for the seventh overtone, of damping effects of the crystal supports. Measurements have also been carried out on crystals with crystal surfaces with different roughness characteristics. These roughness characteristics have been measured using optical interferometry. With a well polished, good crystal the authors measured, for the seventh overtone at 3 K a loaded Q of 25 million corresponding to an unloaded Q of 33 million. Better control of surface roughness and crystal quality could lead to a Q of about 100 million in the liquid helium region. This value would be for an 11 MHz, seventh overtone crystal having an diameter of 15 mm. >

Laser-noise-induced intensity fluctuations in an optical interferometer.

We calculate the intensity fluctuations of the light transmitted by a Fabry-Perot interferometer when a broadband laser is incident upon it. The laser field is assumed to have a Lorentzian spectrum and to be broadened by random amplitude fluctuations (real or complex) or random frequency fluctuations. In each case we obtain closed-form expressions for the intensity autocorrelation function, from which we can obtain the magnitude of the intensity fluctuations, as well as the power spectrum. These results indicate a strong dependence of the transmitted intensity fluctuations on the higher-order statistical properties of the incident field. Agreement with similar results concerning atomic fluorescence fluctuations is very good.

Ultimate Stability of Methane-Stabilized Lasers

Random frequency fluctuations of the 3.39 µm He-Ne lasers stabilized on an absorption line of methane are theoretically investigated. The minimum detectable frequency deviations are calculated for the method of linear absorption in an external cell and for the method of saturated absorption in an internal cell, and compared with each other. The method of saturated absorption in an internal cell of 1 Pa (7.5 milli-torr) pressure requires a few milli-watts of power flow in a beam of 1 mm radius. The minimum detectable frequency fluctuation for saturated absorption is found to be almost equal to that for linear absorption with a power of 1 mW through the cell. With an ideal detector of 100 percent quantum efficiency the calculated stability is ±7×10-15t-1/2 in either method, where t is the averaging time in seconds. By employing a larger power through an external cell, still higher stabilities will be achieved, if the gas and the detector are kept at low temperatures.

Preliminary measurements of laser short-term frequency fluctuations

Preliminary but relatively detailed measurements have been made of the short-term frequency or phase fluctuations of two short stable single-frequency 6328 Å He-Re lasers (Spectra-Physics Model 119). Both lasers were essentially free-running in a quiet stable environment, with no frequency-stabilization or temperature-control loops except for a slow AFC loop (one-half-second response time) which kept one laser frequency at a nominal 30-MHz spacing from the other by piezoelectric tuning. The random frequency fluctuations of the 30-MHz beat note between the lasers were measured in three ways: a) The power spectral density of the 30-MHz beat note (measured by slowly scanning an RF spectrum analyzer) was found to be accurately Gaussian, with a standard deviation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sigma_{f} \approx 8.1</tex> kHz. b) The mean-square accumulated phase jitter during an interval of length τ seconds (measured by a sampling technique) was found to vary as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\Phi^{2}(\tau) \approx 0.96 \times 10^{10} \tau^{2} rad^{2}</tex> over the range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">100 \leq \tau \leq 1200</tex> us. Less accurate measurements extending up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tau = 30\mu</tex> s indicated a slightly slower increase ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim \tau^{4/3}</tex> ) for longer times. c) The spectral density of the instantaneous beat frequency variations (measured by scanning the video output from a 30-MHz frequency discriminator with an audio wave analyzer) was found to vary as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G_{\phi}(f) \approx 6.6 \times 10^{8}/f^{2} rad^{2}</tex> .s down to at least 50 Hz and probably lower. These results, which are all qualitatively compatible, and quantitatively in agreement to within better than a factor of two, indicate random Gaussian perturbation of the laser's instantaneous frequency by internal or environmental disturbances (plasma noise, acoustic noise, etc.) that have not yet been clearly identified. By improving these characteristics somewhat, and operating one laser at a very much lower power level in order to enhance its quantum phase fluctuations, it appears feasible to measure the ultimate quantum frequency fluctuations caused by random walk of the oscillator phase under the influence of spontaneous emission.

Further Aspects of the Theory of the Maser

The theory of the molecular transitions which are induced by the microwave field in a maser and the effects of various design parameters are examined in detail. It is shown that the theoretical minimum detectable beam intensity when the maser is used as a spectrometer for the 3-3 line of ammonia is about ${10}^{9}$ molecules/sec under typical experimental conditions. Various systematic frequency shifts and random frequency fluctuations of the maser oscillator are discussed and evaluated. The most prominent of the former are the frequency-pulling effect, which arises from detuning of the cavity, and the Doppler shift due to the asymmetrical coupling of the beam with the two traveling wave components of the standing waves which are set up in the cavity. These two effects may produce fractional shifts as large as one part in ${10}^{9}$. If adequate precautions are taken, however, they can be reduced to one part in ${10}^{10}$ or possibly less. The random fluctuations are shown to be of the order of one part in ${10}^{13}$ under typical operating conditions. For molecular beams in which the electric-dipole transition is used, the $T{M}_{010}$ mode is usually the most suitable for the maser; while in atomic beams in which magnetic transitions are utilized, the $T{E}_{011}$ mode is to be preferred.