Rapid Random Fluctuations Research Articles

Stochastic Growth Model of Pollack <i>Gadus chalcogrammus</i> (Pallas, 1814)

A mathematical model is proposed that describes the age-related dynamics of the vector of means and the covariance matrix of characters of individuals in the Sakhalin pollock population Gadus chalcogrammus (Pallas, 1814). The model is based on the Bertalanffy and Gompertz equations. The covariance matrix is composed of two parts: noise (caused by rapid random fluctuations in environmental conditions) and structural (due to intrapopulation variability of the parameters included in the growth equations). The model well reproduces the age dynamics of the distribution of fish according to the quantitative characters of individuals. The age-related increase, the passing through a maximum at a young age, the subsequent decrease in dispersions and their stabilization at low levels in the length and mass of the body of adult fish have been described. The age-related decrease in the correlation between length and body mass has been explained.

Extended Taylor frozen-flow hypothesis and statistics of optical phase in aero-optics.

We present an extended Taylor frozen-flow model for the statistics of the spatiotemporal disturbances of the index of refraction of air and the phase of an optical beam propagated through the turbulent boundary and shear layers in a high-Reynolds-number flow. By incorporating rapid random fluctuations of the flow velocity about a mean convection velocity and an anisotropic spatial power spectrum for the index of refraction, we calculate both the short-delay temporal structure function and the power spectral density of these disturbances. We discuss the predicted scaling behaviors for these quantities in the context of existing experimental observations, showing specifically the agreement of these predictions with some optical phase data obtained by the Airborne Aero-Optical Laboratory.

A stochastic mechanism for signal propagation in the brain: Force of rapid random fluctuations in membrane potentials of individual neurons

There are two functionally important factors in signal propagation in a brain structural network: the very first synaptic delay–a time delay about 1ms–from the moment when signals originate to the moment when observation on the signal propagation can begin; and rapid random fluctuations in membrane potentials of every individual neuron in the network at a timescale of microseconds. We provide a stochastic analysis of signal propagation in a general setting. The analysis shows that the two factors together result in a stochastic mechanism for the signal propagation as described below. A brain structural network is not a rigid circuit rather a very flexible framework that guides signals to propagate but does not guarantee success of the signal propagation. In such a framework, with the very first synaptic delay, rapid random fluctuations in every individual neuron in the network cause an “alter-and-concentrate effect” that almost surely forces signals to successfully propagate. By the stochastic mechanism we provide analytic evidence for the existence of a force behind signal propagation in a brain structural network caused by rapid random fluctuations in every individual neuron in the network at a timescale of microseconds with a time delay of 1ms.

Detrimental consequences of small rapid laser fluctuations on stimulated Raman adiabatic passage

We discuss the detrimental effect of small rapid random fluctuations of laser-field amplitude and phase upon the efficiency of stimulated Raman adiabatic passage (STIRAP). Such fluctuations typically accompany the laser stabilization procedures that produce nearly monochromatic light on top of a much broader bandwidth Lorentz-profile pedestal which may carry only a few percent or less of the total power. As we will show, their effects differ qualitatively from the fluctuations that have hitherto been considered (for example, phase diffusion). We present analytic expressions for the population transfer efficiency of STIRAP when limited by stochastic fluctuations of this type. These expressions show, in contrast to situations discussed in the past in which population transfer improves with increasing peak Rabi frequencies, that for the weak broadband noise that accompanies a strong narrow-spectral component, there is an optimum value for the peak Rabi frequency and that the effect of fluctuations, although small, cannot be entirely eliminated in practice. The mission of the current work is to point out that, under the given circumstances, efforts in experiments trying to overcome the detrimental consequences of fluctuations by increasing the intensity, which is the intuitively proper approach, will not be successful.

Investigation of ionospheric irregularities and scintillation using TEC at high latitude

The occurrence of ionospheric irregularities at high latitudes, with dimensions of several kms down to decameter scale size shows strong correlation with geomagnetic disturbance, season and solar activity. Transionospheric radio waves propagating through these irregularities experience rapid random fluctuations in phase and/or amplitude of the signal at the receiver, termed scintillation, which can degrade GNSS services. Thus, investigation and prediction of this scintillation effect is very important. To investigate such scintillation effects, a GISTM (GPS Ionospheric Scintillation and TEC Monitoring) NovAtel dual frequency (L1/L2) GPS receiver has been installed at Trondheim, Norway (63.41° N, 10.4° E), capable of collecting scintillation indices at a 1min rate as well as the raw data (phase and intensity) of the satellite signals at a 50Hz sampling rate and TEC (Total Electron Content) at a 1Hz rate. Many researchers have reported that both phase and amplitude scintillation is closely associated with TEC fluctuations or associated with a significant developing enhancement or depletion in the TEC. In this study, a novel analogous phase index is developed which provides samples at a 1min rate. Generally the scintillation indices can help in estimating the irregularity scintillation effect at a one minute rate, but such procedures are time consuming if DFTs of the phase and/or amplitude at a 50Hz data are required. In this study, instead, this analogous phase index is estimated from 1Hz rate TEC values obtained from the raw signals and is then compared for weak, moderate and strong scintillation at Trondheim for one year of data collected from the installed GPS receiver. The spectral index of the irregularities (that is the inverse power law of their spatial spectrum) is determined from the resultant phase scintillation psd. The correlations of the scintillation indices and spectral indices with the analogous phase index have been investigated under different geomagnetic conditions (represented by the Kp index) and an approximate linear correlation of phase scintillation with the analogous phase index was found. Then a principal advantage of this index is that it achieves this correlation without requiring a high sampling data rate and the need for DFTs. Thus, the index seems a good candidate for developing a simple means of ionospheric scintillation prediction which could also be utilized in the development of alerts using regional mappings.

Cross Correlation and Deconvolution of Noise Signals in Randomly Layered Media

It is known that cross correlation of waves generated by noise sources, propagating in an unknown medium and recorded by a sensor array, can provide information about the medium. In this paper the medium is a three-dimensional small-scale randomly layered medium with slow macroscopic variations. The main objective here is to set forth a framework for analysis of cross correlations of waves generated by noise sources and propagating in such a medium and, moreover, to use this framework to design estimators for macroscale medium features. The noise sources are located at the bottom of a random medium slab and generate a random wave field that is scattered by the rapid random fluctuations of the medium and then recorded at the surface. Taking into account the pressure release boundary conditions at the surface, this situation corresponds to the so-called daylight configuration. The analysis is carried out in the asymptotic framework where the typical wavelength is small compared to the scale of the macroscopic variations of the background medium and large compared to the decoherence length of the microscopic random fluctuations of the medium. It is shown that the cross correlation of the waves recorded at the surface contains statistically stable information about the macroscopic background medium.

Background velocity estimation with cross correlations of incoherent waves in the parabolic scaling

In this paper the incoherent waves reflected by a random medium in the parabolic regime are considered. The case in which the medium has anisotropic three-dimensional rapid random fluctuations and one-dimensional slow variations is analyzed. First, it is shown how the second-order statistics of the reflected wave is determined by the slow spatial variations of the background velocity, the scattering coefficient and the absorption coefficient of the medium via a system of transport equations. Next, it is shown how observations of the time-dependent intensity, spatial radius and spectral radius of the reflected wave can be used to invert this system in order to reconstruct the parameters of the medium. Finally, it is shown that the analytic framework set forth can also be used to analyze the time dynamics of weak localization.

Dynamics of Discovery and Exploitation: The Case of the Scotian Shelf Groundfish Fisheries

The bases and shortcomings of the current models used in fisheries management are briefly examined. An alternative set of models in part based on the Volterra–Lotka equations are developed which incorporate recent advances in our understanding of the evolution of complex systems. Simulations based on a dynamic model of a Nova Scotia fishery reveal that human responses amplify rapid random fluctuations in recruitment and excite strong Volterra–Lotka type oscillations in a system that would normally repose in a stable stationary state. A dynamic, multispecies, muitifleet spatial model calibrated to the Nova Scotian groundfish fisheries is presented and used to explore the concepts of "discovery" and "exploitation." Two types of fishermen are identified, "stochasts" and "cartesians," characterized respectively as hunters, or high risk takers, and followers, or low risk takers. Significant results include the importance of calibration in providing models of relevance to the real world; the "out of phase" relationship between abundance and the ease with which fishermen locate a highly sought species and its converse; the importance of information exchange in defining the attractivity of a particular fishing zone to different fleets and the ability of the model to take into account coded information, misinformation, spying and lying; and the fact that models based on global principles, such as "optimal efficiency" or "maximum profit," are clearly of dubious relevance to the real world.

Reduction of Rapid Random Fluctuations of Beckman Flame Spectrophotometer

Reduction of Rapid Random Fluctuations of Beckman Flame Spectrophotometer