Search Results (22)

Atmospheric image blur, “seeing”, is one of the key parameters that influences the selection of observatory sites and the performance of ground-based telescopes. In this review, the common definition of seeing based on the Kolmogorov turbulence model is recalled. The ability of this model to represent real, non-stationary fluctuations of the air refractive index is discussed. Even in principle, seeing (a model parameter) cannot be measured with arbitrary accuracy; consequently, describing atmospheric blur by a single number, seeing, is a crude approximation. The operating principles of current seeing monitors are outlined. They measure optical effects caused by turbulence, sampling certain regions of spatial and temporal spectrum of atmosphreic optical disturbances, and interpret their statistics in the framework of the standard model. Biases of seeing monitors (measurement noise, propagation, finite exposure time, optical defects, wind shake, etc.) should be quantified and corrected using simulations, while instrument comparison campaigns serve as a check. The elusive nature of seeing follows from its uniqueness (a given measurement cannot be repeated or checked later), its non-stationarity (dependence on time, location, and viewing direction), a substantial role of the highly variable surface layer, and a potential bias caused by the air flow in the immediate vicinity of the seeing monitors. The results of seeing measurements are outside the scope of this review. Full article

Satellite laser communication can achieve high-speed, high-precision, and high-security broadband communication without being constrained by the electromagnetic spectrum, which has attracted attention. So, this paper proposes the use of a high-altitude platform (HAP) under anisotropic non-Kolmogorov turbulence to improve the communication performance of the system. Cross quadrature amplitude modulation (XQAM) and hexagon quadrature amplitude modulation (HQAM) are applied to the ground–HAP–satellite (G-H-S) laser communication system. Considering the combined effects of uplink light intensity scintillation, beam wander, and the angle of arrival fluctuation, the G-H-S system’s bit error rate (BER) closure expression is derived under the EW distribution. Simultaneously, the relationship between the G-H-S system’s signal-to-noise ratio (SNR) and BER under different anisotropic factor u values is simulated and compared with the traditional ground–satellite (G-S) system. The results show that the communication performance of the G-H-S system with HQAM modulation is better. In addition, the effects of the zenith angle, receiving aperture, transmitter beam radius, and beam divergence angle on the BER performance of the system are also studied. Finally, the correctness of the analysis results is verified via Monte Carlo simulation. This research will benefit the design and optimization of satellite laser communication systems. Full article

In this paper, the Recurrent Singular Spectrum Decomposition (R-SSD) algorithm is proposed as an improvement over the Recurrent Singular Spectrum Analysis (R-SSA) algorithm for forecasting non-linear and non-stationary narrowband time series. R-SSD modifies the embedding step of the basic SSA method to reduce energy residuals. This paper conducts simulations and real-case studies to investigate the properties of the R-SSD method and compare its performance with R-SSA. The results show that R-SSD yields more accurate forecasts in terms of ratio root mean squared errors (RRMSEs) and ratio mean absolute errors (RMAEs) criteria. Additionally, the Kolmogorov–Smirnov Predictive Accuracy (KSPA) test indicates significant accuracy gains with R-SSD over R-SSA, as it measures the maximum distance between the empirical cumulative distribution functions of recurrent prediction errors and determines whether a lower error leads to stochastically less error. Finally, the non-parametric Wilcoxon test confirms that R-SSD outperforms R-SSA in filtering and forecasting new data points. Full article

This study aims to address the multi-beam transmission problem of optical wireless coherent communication systems under the influence of non-Kolmogorov turbulence. This paper establishes the mathematical model for mixing efficiency and BER of non-Kolmogorov turbulence wavefront distortion and multi-beam transmission coherent detection systems. The influence of factors such as spectral power-law index, zenith angle, and transmission distance on the communication performance of the system is analyzed, and an experimental system is built using adaptive optics equipment to test the proposed theory. Numerical analyses show that in a non-Kolmogorov turbulence environment, as the spectral power-law index, zenith angle, transmission distance, Fresnel zone, and pointing error attenuation increase, the mixing efficiency of the coherent detection system decreases and the BER increases; under the same conditions, the mixing efficiency and BER of the system are improved after increasing the number of transmission beams at the transmitting end. Experimental research shows that, for the coherent detection system after wavefront correction using adaptive optics, the wavefront PV and RMS variances are 1.68 μm² and 0.05 μm² when a single beam of light is transmitted at the transmitting end, and the wavefront PV and RMS variances are 0.23 μm² and 0.01 μm² when two beams are transmitted. It is verified that using multi-beam transmission wavefront superposition to suppress wavefront distortion and wavefront jitter can effectively improve the mixing efficiency and BER of the coherent detection system at the receiving end. Full article

The pioneering applications of the methods of theoretical physics to the turbulence statistical closure problem are summarised. These are: the direct-interaction approximation (DIA) of Kraichnan, the self-consistent-field theory of Edwards, and the self-consistent-field theory of Herring. Particular attention is given to the latter, in terms of its elegance and its pedagogical value. We then concentrate on the assessment of these theories and take the historical route of Kraichnan’s diagnosis of the failure of DIA, followed by Edwards’s analysis of the failure of his self-consistent theory, when compared to the Kolmogorov spectrum. As all three theories are closely related, these analyses also shed light on Herring’s theory. The second-generation theories that grew out of this assessment are then discussed. First, there were the Lagrangian theories, initially stemming from the work of Kraichnan and Herring, and later the purely Eulerian local energy-transfer (LET) theory. The latter is significant because its development exposes the underlying problems with the pioneering theories in terms of the basic physics of the inertial energy transfer. In particular, later work allows us to assign a unified explanation of the incompatibility of all three pioneering theories with the Kolmororov spectrum, in that they are all Markovian approximations (in wavenumber) to the non-Markovian phenomenon of fluid turbulence. In the interests of completeness, we briefly review the formalisms of Wyld and Martin, Siggia, and Rose. More recent developments are also discussed, in order to bring the subject up to the present day. Full article

Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov vectors (OLVs), singular vectors (SVs), Floquet vectors and finite-time normal modes (FTNMs) are examined for periodic and aperiodic systems. In the phase-space of FTNM coefficients, SVs are shown to equate with unit norm FTNMs at critical times. In the long-time limit, when SVs approach OLVs, the Oseledec theorem and the relationships between OLVs and CLVs are used to connect CLVs to FTNMs in this phase-space. The covariant properties of both the CLVs, and the FTNMs, together with their phase-space independence, and the norm independence of global Lyapunov exponents and FTNM growth rates, are used to establish their asymptotic convergence. Conditions on the dynamical systems for the validity of these results, particularly ergodicity, boundedness and non-singular FTNM characteristic matrix and propagator, are documented. The findings are deduced for systems with nondegenerate OLVs, and, as well, with degenerate Lyapunov spectrum as is the rule in the presence of waves such as Rossby waves. Efficient numerical methods for the calculation of leading CLVs are proposed. Norm independent finite-time versions of the Kolmogorov-Sinai entropy production and Kaplan-Yorke dimension are presented. Full article

We study the propagation characteristics (spectral intensity and degree of coherence) of a new type of Lorentz non-uniformly correlated (LNUC) beam based on the extended Huygens–Fresnel principle and the spatial power spectrum of oceanic turbulence. The effects of the oceanic turbulence parameters and initial beam parameters on the evolution propagation characteristics of LNUC beams are studied in detail by numerical simulation. The results indicate that such beams exhibit self-focusing propagation features in both free space and oceanic turbulence. Decreasing the dissipation rate of kinetic energy per unit mass of fluid and the Kolmogorov inner scale, or increasing the relative strength of temperature to salinity undulations and the dissipation rate of mean-square temperature of the turbulent ocean tends to increase the negative effects on the beams. Furthermore, we propose a strategy of increasing the beam width and decreasing the coherence length, to reduce the negative effects of the turbulence. Full article

Turbulence in space plasmas usually exhibits an energy cascade in which large-scale magnetic fluctuations are dominated by non-linear MHD wave–wave interactions following a Kolmogorov-like power-law spectrum. In addition, at scales at which kinetic effects take place, the magnetic spectrum follows a steeper power-law $k^{-\alpha }$ shape given by a spectral index $\alpha >5/3$. In a recent publication, a quasilinear model was used to study the evolution of ion temperatures in a collisionless plasma in which electromagnetic waves propagate along the background magnetic field, and it was found that the interaction between the plasma and a turbulent spectrum of ion-cyclotron waves may lead the plasma to states out of thermal equilibrium characterized by enhanced temperature anisotropies $T_{\perp }>T_{\Vert }$ and with a reduction in the parallel proton beta, which is consistent with space observations. Here, we complement such studies by analyzing the quasilinear interaction between plasma and a solar-wind-like turbulent spectrum of fast magnetosonic waves, and study the role of firehose instability (FHI) in the regulation of temperature anisotropy. Our results show that the presence of turbulence significantly modifies the FHI marginal stability threshold, as predicted from linear theory. Moreover, depending on the value of the plasma $\beta$, a turbulent magnetosonic spectrum may lead an initially thermally isotropic plasma to develop anisotropic states in which $T_{\perp }<T_{\Vert }$. Full article

The Mie-scattering lidar can detect atmospheric turbulence intensity by using the return signals of Gaussian beams at different heights. The power spectrum method and Zernike polynomial method are used to simulate the non-Kolmogorov turbulent phase plate, respectively, and the power spectrum method with faster running speed is selected for the subsequent simulation. In order to verify the possibility of detecting atmospheric turbulence by the Mie-scattering lidar, some numerical simulations are carried out. The power spectrum method is used to simulate the propagation of the Gaussian beam from the Mie-scattering lidar in a vertical path. The propagation characteristics of the Gaussian beam using a non-Kolmogorov turbulence model are obtained by analyzing the intensity distribution and spot drift effect. The simulation results show that the scintillation index of simulation is consistent with the theoretical value trend, and the accuracy is very high, indicating that the method of atmospheric turbulence detection using Mie-scattering lidar is effective. The simulation plays a guiding role for the subsequent experimental platform construction and equipment design. Full article

In most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process. This theory correctly explains the universal power-law energy spectrum observed in all turbulent flows. Finer observations however prove that this picture is too simplistic, owing to intermittency of energy dissipation and high velocity derivatives. In this review, we discuss how such intermittency can be explained and fitted into a new picture of turbulence. We first discuss how the concept of multi-fractality (invented by Parisi and Frisch in 1982) enables to generalize the concept of self-similarity in a non-homogeneous environment and recover a universality in turbulence. We further review the local extension of this theory, and show how it enables to probe the most irregular locations of the velocity field, in the sense foreseen by Lars Onsager in 1949. Finally, we discuss how the multi-fractal theory connects to possible singularities, in the real or in the complex plane, as first investigated by Frisch and Morf in 1981. Full article

It is accepted that there exists two kinds of atmospheric turbulence in the Earth’s aerosphere—Kolmogorov and non-Kolmogorov turbulence; therefore, it is important to research their combined impacts on laser-satellite communications. In this paper, the exponential power spectra of refractive-index fluctuations for non-Kolmogorov turbulence in the free troposphere and stratosphere are proposed, respectively. Based on these two spectra, using the Markov approximation, beam wander displacement variances of a Gaussian-beam wave are derived, respectively, which are valid under weak turbulent fluctuations condition. On this basis, using a three-layer altitude-dependent turbulent spectrum model for vertical/slant path, the combined influence of a three-layer atmospheric turbulence on wander of a Gaussian-beam wave as the carrier wave in laser-satellite communication is studied. This three-layer spectrum is more accurate than a two-layer model. Moreover, the variations of beam wander displacement with beam radius, zenith angles, and nominal value of the refractive-index structure parameter on the ground are estimated. The theory of optical wave propagation through non-Kolmogorov atmospheric turbulence is further enriched and a theoretical model of a three-layer atmospheric turbulence beam wander for a satellite-ground laser communication uplink is established. Full article

The Earth’s atmosphere is the living environment in which we live and cannot escape. Atmospheric turbulence is a typical random inhomogeneous medium, which causes random fluctuations of both the amplitude and phase of optical wave propagating through it. Currently, it is widely accepted that there exists two kinds of turbulence in the aerosphere: one is Kolmogorov turbulence, and the other is non-Kolmogorov turbulence, which have been confirmed by both increasing experimental evidence and theoretical investigations. The results of atmospheric measurements have shown that the structure of atmospheric turbulence in the Earth’s atmosphere is composed of Kolmogorov turbulence at lower levels and non-Kolmogorov turbulence at higher levels. Since the time of Newton, people began to study optical wave propagation in atmospheric turbulence. In the early stage, optical wave propagation in Kolmogorov atmospheric turbulence was mainly studied and then optical wave propagation in non-Kolmogorov atmospheric turbulence was also studied. After more than half a century of efforts, the study of optical wave propagation in atmospheric turbulence has made great progress, and the theoretical results are also used to guide practical applications. On this basis, we summarize the development status and latest progress of propagation theory in atmospheric turbulence, mainly including propagation theory in conventional Kolmogorov turbulence and one in non-Kolmogorov atmospheric turbulence. In addition, the combined influence of Kolmogorov and non-Kolmogorov turbulence in Earth’s atmosphere on optical wave propagation is also summarized. This timely summary is very necessary and is of great significance for various applications and development in the aerospace field, where the Earth’s atmosphere is one part of many links. Full article

Throughout the years, measuring the complexity of networks and graphs has been of great interest to scientists. The Kolmogorov complexity is known as one of the most important tools to measure the complexity of an object. We formalized a method to calculate an upper bound for the Kolmogorov complexity of graphs and networks. Firstly, the most simple graphs possible, those with $O\left(1\right)$ Kolmogorov complexity, were identified. These graphs were then used to develop a method to estimate the complexity of a given graph. The proposed method utilizes the simple structures within a graph to capture its non-randomness. This method is able to capture features that make a network closer to the more non-random end of the spectrum. The resulting algorithm takes a graph as an input and outputs an upper bound to its Kolmogorov complexity. This could be applicable in, for example evaluating the performances of graph compression methods. Full article

With the in-depth study of atmospheric turbulence, scholars have identified that the anisotropy of turbulence cells should not be forgotten. The anisotropic non-Kolmogorov turbulence model can better characterize the actual situation of atmospheric turbulence. However, the results of recent experiments by Wang et al. and Beason et al. demonstrate that the turbulence cell has an anisotropic tilt angle, i.e., the long axis of turbulence cell may not be horizontal to the ground but has a certain angle with the ground. In this paper, we derive the anisotropic non-Kolmogorov turbulence spectra for the horizontal and satellite links with anisotropic tilt angle. Then by use of these spectra, the analytical expressions of scintillation index in the horizontal and satellite links are derived for the weak fluctuation condition. The calculation results display that the scintillation index for the horizontal and satellite links vary with the changes of anisotropic tilt angle and azimuth angle. Therefore, the anisotropic tilt angle is indispensable in the horizontal and satellite links. Full article

A partial receiving scheme based on limited angular aperture multi-beam receiving and demultiplexing can solve the difficulty caused by the divergence of the vortex beam in the conventional whole beam receiving scheme and realize the long-distance transmission of the vortex wave. The propagation of the radio vortex beam in atmospheric turbulence is of significant importance in theoretical study and practical applications. In this paper, the influence of atmospheric turbulence on the performance of a radio vortex (RV) communication system based on a partial angular aperture receiving (PAAR) scheme under the horizontal non-Kolmogorov channel model is studied. The spiral spectrum of the PAAR scheme and the channel capacity of the RV communication system using the PAAR scheme are derived. Simulation results demonstrate that the selected transmission frequency range has a great influence on the RV communication system based on the PAAR scheme, and the choice of the orbital angular momentum (OAM) mode number L has an influence on the propagation distance. The capacity of RV communication systems based on the PAAR scheme increases with the increase of the transmission frequency in the selected transmission frequency range of 10 GHz–60 GHz. When the number of orbital angular momentum (OAM) modes L is small, we can improve the signal-to-noise ratio (SNR) to obtain a larger capacity of the RV communication system based on the PAAR scheme over a longer propagation distance. Full article