Statistical Inhomogeneity Research Articles

Topological laws of the Rayleigh wave scattering on a statistical inhomogeneity of isotropic solid in the Rayleigh limit

Topological laws of the Rayleigh wave scattering on a statistical inhomogeneity of isotropic solid are obtained theoretically in the Rayleigh limit. They are completely defined by the inhomogeneity structure and include the Rayleigh law of scattering as a particular case. They violate the Rayleigh law in the case of a more general inhomogeneity topology, then the Rayleigh one. It enables first to construct theoretically arbitrary spectrum of scattering up to its oscillations and a strong angular anisotropy.

Relative Homogenization of Climatic Time Series

Homogenization of the time series of observed climatic data aims to remove non-climatic biases caused by technical changes during the history of the climate observations. The spatial redundancy of climate information helps to recognize station-specific inhomogeneities with statistical methods, but the correct detection and removal of inhomogeneity biases is generally not easy for the combined effects of individual inhomogeneities. In a homogenization procedure, several time series of a given climatic variable observed in one climatic region are usually homogenized together via a large number of spatial comparisons between them. Such procedures are called relative homogenization. A relative homogenization procedure may include one or more homogenization cycles where a cycle includes the steps of time series comparison, inhomogeneity detection and corrections for inhomogeneities, and they may include other steps like the filtering of outlier values or spatial interpolations for infilling data gaps. Relative homogenization methods differ according to the number and content of the individual homogenization cycles, the procedure for the time series comparisons, the statistical inhomogeneity detection method, the way of the inhomogeneity bias removal, among other specifics. Efficient homogenization needs the use of tested statistical methods to be included in partly or fully automated homogenization procedures. Due to the large number and high variety of homogenization experiments fulfilled in the Spanish MULTITEST project (2015–2017), its method comparison test results are still the most informative about the efficiencies of homogenization methods in use. This study presents a brief review of the advances in relative homogenization, recalls some key results of the MULTITEST project, and analyzes some theoretical aspects of successful homogenization.

Characterization of ejecta in shock experiments with multiple light scattering

Upon impact, the free surface of a solid metal may eject a cloud of fast and fine particles. Photon Doppler Velocimetry (PDV) is one of the optical diagnostics used to characterize these ejecta. Although the technique provides a direct way to estimate the particle velocities in the single scattering regime, it has been shown that multiple scattering cannot be neglected in real ejecta. Here, we derive a model for PDV measurements starting from the first principles of wave scattering. We establish rigorously the relationship between the specific intensity and the measured signal, as well as the Radiative Transport Equation (RTE) that describes the evolution of the specific intensity upon scattering and absorption in dynamic ejecta, including the effects of inelastic scattering and inhomogeneities in the optical properties. We also establish rigorously the connection between the Monte Carlo scheme used for numerical simulations and the solution to the RTE. Using numerical simulations, we demonstrate the crucial contribution of multiple scattering to PDV spectrograms as well as the effect of statistical inhomogeneities in particle size distribution. These results could substantially impact the analysis of ejecta by PDV.

Inertial range scaling of inhomogeneous turbulence

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$ . This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.

Improvement of the algorithm for adaptive separation of the vibroseis signal from its harmonics in case of strong additive noise

An algorithm for separating a vibroseis signal from its harmonics implies preliminary prediction of harmonics with their subsequent adaptive subtraction from the correlogram. To obtain the adaptation filter estimates, a statistical criterion is used that minimizes the energy of the subtraction result. The amplitudes of the signals in a seismic trace decay due to geometrical spreading, which leads to statistical inhomogeneity in the objective formed. Therefore, an increase in the statistical reliability of estimation should be associated with an increase in signal amplitudes at large recording times. On the other hand, the source records always contain additive noise, and the signal-to-noise ratio decreases at longer times. In order to provide a compromise between the growth of signal amplitudes and maintaining a satisfactory signal-to-noise ratio in the operator adjusting gate, self-tuning weighting functions are included into the objective. A method for modifying the objective is proposed, which enables increased performance of the algorithm.

Statistical properties of two-dimensional elastic turbulence.

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static pointlike numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly nonhomogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.

Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

Pandemic curves, such as COVID-19, often show multiple and unpredictable contamination peaks, often called second, third and fourth waves, which are separated by wide plateaus. Here, by considering the statistical inhomogeneity of age groups, we show a quantitative understanding of the different behaviour rules to flatten a pandemic COVID-19 curve and concomitant multi-peak recurrence. The simulations are based on the Verhulst model with analytical generalized logistic equations for the limited growth. From the log–lin plot, we observe an early exponential growth proportional to et/τgrow. The first peak is often τgrow ≅ 5 d. The exponential growth is followed by a recovery phase with an exponential decay proportional to e−t/τrecov. For the characteristic time holds: τgrow< τrecov. Even with isolation, outbreaks due to returning travellers can result in a recurrence of multi-peaks visible on log–lin scales. The exponential growth for the first wave is faster than for the succeeding waves, with characteristic times, τ of about 10 d. Our analysis ascertains that isolation is an efficient method in preventing contamination and enables an improved strategy for scientists, governments and the general public to timely balance between medical burdens, mental health, socio-economic and educational interests.

Cosmological Distance Scale. Part 12. Confluent Analysis, Rank Inversion, and Lack-of-Fit Tests

The measuring problem of calibrating the cosmological distance scale is considered from the perspective of applicability conditions for regression analysis. The rank inversion and statistical inhomogeneity of information on SN Ia supernovae, used in the works of 1998–1999 and 2004–2007 to detect the “accelerating expansion of the Universe” and as an “extraordinary evidence” of its existence, respectively, are demonstrated to be the reason for the discrepancy and inconsistency of the obtained parametric estimates of the Friedman–Robertson–Walker model. Although the use of lack-of-fit tests for cosmological distance scale models reduces the above negative effects, the fact remains that the cosmological distance scale based on the redshift has neither metric nor ordinal status.

Space-scale-time dynamics of liquid–gas shear flow

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The illusion of a Kolmogorov cascade

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Structure function tensor equations in inhomogeneous turbulence

Exact budget equations for the second-order structure function tensor ⟨𝛿u$_{i}$𝛿u$_{j}$⟩, where 𝛿u is the difference of the i th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of ⟨𝛿u$_{i}$𝛿u$_{j}$⟩. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of Re$_{𝜏}$ = 200 is considered. The off-diagonal component ⟨-𝛿u𝛿υ⟩, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at Re$_{𝜏}$ = 500 and 1000. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.

Cancer Survival Data Representation for Improved Parametric and Dynamic Lifetime Analysis.

Survival functions are often characterized by a median survival time or a 5-year survival. Whether or not such representation is sufficient depends on tumour development. Different tumour stages have different mean survival times after therapy. The validity of an exponential decay and the origins of deviations are substantiated. The paper shows, that representation of survival data as logarithmic functions visualizes differences better, which allows for differentiating short- and long-term dynamic lifetime. It is more instructive to represent the changing lifetime expectancy for an individual who has survived a certain time, which can be significantly different from the initial expectation just after treatment. Survival data from 15 publications on cancer are compared and re-analysed based on the well-established: (i) exponential decay (ii) piecewise constant hazard (iii) Weibull model and our proposed parametric survival models, (iv) the two-τ and (v) the sliding-τ model. The new models describe either accelerated aging or filtering out of defects with numerical parameters with a physical meaning and add information to the usually provided log-rank P-value or median survival. The statistical inhomogeneity in a group by mixing up different tumour stages, metastases and treatments is the main origin for deviations from the exponential decay.

Study on propagation characteristics of laser in turbulent Rayleigh–Bénard thermal convection

The turbulent Rayleigh–Bénard (R–B) convection system contains the plume and the large-scale circulation structure, which causes the statistical inhomogeneity of the flow field. The high coherence of the laser leads to the completely different transmission characteristics in the R–B flow field than in the free space. In this study, the transient scattering field of the laser in the R–B flow field is calculated by using the Maxwell numerical integration method under the Rytov approximation. The experimental device was designed, the comparison experiment was carried out, and several satisfactory contrast results were given.

Context Dependent Fuzzy Associated Statistical Model for Intensity Inhomogeneity Correction From Magnetic Resonance Images.

In this paper, a novel context-dependent fuzzy set associated statistical model-based intensity inhomogeneity correction technique for magnetic resonance image (MRI) is proposed. The observed MRI is considered to be affected by intensity inhomogeneity and it is assumed to be a multiplicative quantity. In the proposed scheme the intensity inhomogeneity correction and MRI segmentation is considered as a combined task. The maximum a posteriori probability (MAP) estimation principle is explored to solve this problem. A fuzzy set associated Gibbs’ Markov random field (MRF) is considered to model the spatio-contextual information of an MRI. It is observed that the MAP estimate of the MRF model does not yield good results with any local searching strategy, as it gets trapped to local optimum. Hence, we have exploited the advantage of variable neighborhood searching (VNS)-based iterative global convergence criterion for MRF-MAP estimation. The effectiveness of the proposed scheme is established by testing it on different MRIs. Three performance evaluation measures are considered to evaluate the performance of the proposed scheme against existing state-of-the-art techniques. The simulation results establish the effectiveness of the proposed technique.

Correlation matrix methods to assess the stirring performance of electromagnetic reverberation chambers

The use of correlation matrices to evaluate the number of uncorrelated stirrer positions of electromagnetic reverberation chambers has widespread applications in electromagnetic compatibility. We present a review of recent methods based on multivariate correlation functions that relates statistical inhomogeneities in space (frequency) to the reduction of uncorrelated cavity configurations. Full wave finite-difference time domain simulations of an actual reverberation chamber are performed through an in-house parallel code. The efficiency of this code allows for capturing extensive inhomogeneous/anisotropic reverberation fields at frequencies close to the lowest usable frequency (LUF) of the chamber. The concept of effective independent position is revised in light of random sampling and a model-driven relation with the probability distribution of correlation matrix entries is used to take into account spatial (frequency) inhomogeneities. Driven by extensive simulation data, an empirical probability density function is found for the correlation matrix elements to be non-central t-student distributed with asymmetry increasing towards low frequencies.

РЕЖИМ ПРИЗЕМНОЙ АТМОСФЕРНОЙ ЦИРКУЛЯЦИИ В РАЙОНЕ АНТАРКТИЧЕСКОГО ПОЛУОСТРОВА

The main objective of the research is to analyze the near-surface wind regime in accordance with the data from Ukrainian Antarctic Akademik Vernadsky station and compare it with the state of the atmosphere circulation in order to supplement knowledge of the regional climate. Traditional methods of climatological processing, correlation analysis were used. According to the data of Vernadsky station, there is an increase in surface wind speed in conditions of air temperature rise. The statistical inhomogeneity in the wind speed series is detected. The main conclusion is that the air temperature growth and the increase in surface wind speed is a single manifestation of climate change in the region of the study that reflects changes in atmospheric circulation, intensification of westerly and deepening of cyclogenesis in Antarctica.

Discrete-element modeling of nacre-like materials: Effects of random microstructures on strain localization and mechanical performance

Natural materials such as nacre, collagen, and spider silk are composed of staggered stiff and strong inclusions in a softer matrix. This type of hybrid microstructure results in remarkable combinations of stiffness, strength, and toughness and it now inspires novel classes of high-performance composites. However, the analytical and numerical approaches used to predict and optimize the mechanics of staggered composites often neglect statistical variations and inhomogeneities, which may have significant impacts on modulus, strength, and toughness. Here we present an analysis of localization using small representative volume elements (RVEs) and large scale statistical volume elements (SVEs) based on the discrete element method (DEM). DEM is an efficient numerical method which enabled the evaluation of more than 10,000 microstructures in this study, each including about 5,000 inclusions. The models explore the combined effects of statistics, inclusion arrangement, and interface properties. We find that statistical variations have a negative effect on all properties, in particular on the ductility and energy absorption because randomness precipitates the localization of deformations. However, the results also show that the negative effects of random microstructures can be offset by interfaces with large strain at failure accompanied by strain hardening. More specifically, this quantitative study reveals an optimal range of interface properties where the interfaces are the most effective at delaying localization. These findings show how carefully designed interfaces in bioinspired staggered composites can offset the negative effects of microstructural randomness, which is inherent to most current fabrication methods.

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-Graining Approach

AbstractA coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates, and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer, rely on the assumption of statistical homogeneity or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique because of a gauge freedom. Here, it is argued that a Galilean-invariant subfilter-scale (SFS) flux is a suitable quantity to properly measure energy scale transfer in the ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale transfer of energy. The paper presents geographic maps of the energy scale transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions near the Gulf Stream and in the Equatorial Countercurrent have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extratropical energy scale transfer over regions of O(103) km in size.

Statistical inhomogeneity of dates of sudden stratospheric warmings in the wintertime northern hemisphere

Using the data of meteorological information reanalysis, a statistical analysis of dates of the main sudden stratospheric warmings observed in 1958–2014 has been performed and their inhomogeneous distribution in winter months with maximums in the beginning of January, from the end of January to the beginning of February, and in the end of February has been shown. To explain these regularities, a climatological analysis of variations in the amplitudes and vertical components of Eliassen–Palm fluxes created by large-scale planetary waves (PWs), as well as of zonal-mean winds and deviations of temperature from their winter-average values in high northern latitudes at heights of up to 50 km from the surface has been carried out using the 20-year (1995–2014) collection of daily meteorological information from the UK Met Office database. During the aforementioned intervals of observing more frequent sudden stratospheric warmings, climatological maximums of temperature perturbations, local minimums of eastward winds, and local maximums of the amplitude and Eliassen–Palm fluxes of PWs with a zonal wavenumber of 1 in the high-latitude northern stratosphere were found. Distinctions between atmospheric characteristics averaged over two last decades have been revealed.

Exterior statistics based boundary conditions for establishing statistically equivalent representative volume elements of statistically nonhomogeneous elastic microstructures

The exterior statistics-based boundary conditions or ESBCs have been developed as optimally effective boundary conditions that can be applied to statistically equivalent representative volume elements or SERVEs of heterogeneous microstructures for predicting homogenized response functions in Ghosh and Kubair (2016). However the initial development was for nonuniform, but statistically homogeneous microstructures with no localized features like clustering. In this case, the radial distribution function S2(r) is adequate for the statistically informed Green’s functions needed for the development of ESBCs. However, when the microstructure includes statistical inhomogeneities in the form of fiber clusters or matrix-rich regions, the distance-based radial distribution function becomes ineffective. This paper overcomes this shortcoming by introducing the joint, distance (radial) and orientation-based two-point correlation functions S2(r, θ) in the statistically informed Green’s functions needed for the ESBCs. The efficacy of the ESBCs is illustrated through validation simulations that compare its results with those generated by affine transformation based displacement and periodicity boundary conditions. Additionally, comparisons are made with the statistical volume elements or SVE methods. It is concluded that the simulations with ESBCs prescribed on the SERVEs have a definite advantage over other methods in defining optimal sized SERVEs without any iteration.