The development of statistical analysis methods for the study of correlations and statistical memory effects in the recorded data of physical experiments

This research aims to demonstrate the extent to which statistical analysis methods contribute to improving analytical review procedures in the Libyan environment. The descriptive analytical approach was used, and the research community was determined in the self-employed external audit offices affiliated with the Libyan Audit Bureau in the city of Tripoli. The research concluded that: the application of statistical analysis methods (time series, regression analysis) contributes to a high degree to improving analytical review procedures. The results also revealed the existence of obstacles that limit the use of statistical analysis methods in improving analytical review procedures in the Libyan environment. The researchers recommended: developing specialized training programs for auditors in the Libyan environment to enhance their knowledge and understanding of statistical analysis methods, providing software and technological tools to facilitate the application of statistical analysis methods at reasonable costs, developing clear professional standards governing the use of statistical analysis methods in analytical review, and conducting periodic qualification courses for auditors to raise their awareness about the importance and benefits of using statistical methods. Keywords: Statistical analysis methods, Analytical review, Libyan environment,

Fundamentals of flicker noise spectroscopy (FNS), a general phenomenological approach to analyzing dynamics and structure of complex nonlinear systems by extracting information contained in chaotic signals of diverse nature generated by such systems, are presented. The primary idea of FNS is to disclose information hidden in correlation links which are present in a sequence of various irregularities (spikes, jumps, discontinuities in derivatives of different orders) that occur in the measured dynamic variables at all levels of spatiotemporal hierarchy of systems under study. The information is derived from power spectra S(f) (f, frequency) and transient difference moments Φ(p)(τ)(τ, time delay parameter) of different orders p. The procedures of averaging over time interval T, which are introduced in FNS when computing S(f) and Φ(p)(τ), differ from the procedures of averaging in the Gibbs approach. In the latter case, due to the adoption of the ergodic hypothesis, the average values of dynamic quantities over time are replaced by the average values of the same quantities over a statistical ensemble. It came to pass that the Φ(p)(τ) functions are formed exclusively by jumps of a dynamic variable on different spatiotemporal levels of the system’s hierarchy, whereas the formation of S(f) is contributed to by spikes and jumps. The informative parameters extracted from S(f) and Φ(p)(τ) describe correlation times and characterize loss of “memory” (correlation links) in these correlation time intervals for the “spike” and “jump” irregularities. These parameters can be determined using the expressions derived for the case of steady-state evolution. Here the “steady state” implies an evolution state that is characterized by the same values of informative parameters on every level of the system’s hierarchy. In contrast to the scaling self-similarity in theory of fractals and renormgroup, FNS introduces a multiparametric self-similarity for the S(f) and Φ(p)(τ) functions, which is generally characterized by a set of parameters rather than one scaling factor. The S(f) and Φ(2)(τ) functions which are related to different types of information may be viewed, in the steady-state case, as fluctuation-dissipation relations that complement each other informatively. Examples of such generalized relations are presented for fluctuations of electric voltage under open-circuit conditions (the Nyquist theorem), the Levy diffusion, the hydrodynamic fluctuations at fully developed turbulence, and the flicker noise fluctuations of the electric current density in electron-conducting systems. To analyze the dynamics of non-steady processes, formulas are presented for calculating nonstationarity indicators (factors) and estimating time instants when most noticeable changes occur in systems under study, including those preceding catastrophic evolution changes. The studies carried out to date show that the FNS method can be used in solving problems of three types. The first is the determination of parameters or patterns that characterize the dynamics or specific features of structural organization of open complex systems. The second involves search for precursors of sharpest changes in the states of various open dissipative systems on the basis of available information conceming the dynamics of such systems. And the third problem concerns the dynamics of redistribution of perturbations in distributed systems. It is solved by analyzing dynamic correlations in chaotic signals that are measured simultaneously at different points in space. The review demonstrates some applications of the FNS methodology. In particular, it considers some physicochemical and natural processes the data for which were obtained from electrochemical and biological measurements.

Laser percussion drilling has the potential to become a fast growing method for rapid hole drilling in aerospace, automobile and pharmaceutical industries. However, recently, the authors have shown that, in laser percussion drilling, identical operating parameters may not produce holes of same sizes or shapes. The hole-size variations can be up to 14 % in terms of percentage standard deviation and this would not be acceptable for precision component manufacture in industries. Following authors’ previous work on characterising laser percussion drilling processes in terms of hole-geometry repeatability, this paper presents the use of statistical analysis method to optimise the laser drilling process in order to maximise process repeatability. Since same geometry holes can be drilled using different combinations of laser parameters, it becomes necessary to select a suitable set of parameters for the drilling process. In this work, six processing parameters have been considered for Nd:YAG laser drilling of mild steel. The work demonstrates that considerable improvement of process repeatability can be achieved through process optimisation.Laser percussion drilling has the potential to become a fast growing method for rapid hole drilling in aerospace, automobile and pharmaceutical industries. However, recently, the authors have shown that, in laser percussion drilling, identical operating parameters may not produce holes of same sizes or shapes. The hole-size variations can be up to 14 % in terms of percentage standard deviation and this would not be acceptable for precision component manufacture in industries. Following authors’ previous work on characterising laser percussion drilling processes in terms of hole-geometry repeatability, this paper presents the use of statistical analysis method to optimise the laser drilling process in order to maximise process repeatability. Since same geometry holes can be drilled using different combinations of laser parameters, it becomes necessary to select a suitable set of parameters for the drilling process. In this work, six processing parameters have been considered for Nd:YAG laser drilling of mi...

In this paper, within the framework of Memory Function Formalism, one of the analysis methods in statistical physics, we study bioelectric activity features of the brain for two groups of people. The first group consisted of 10 artists with a Master of Arts degree, the second was represented by 10 people without any art education. The subjects performed the tasks of visual perception and mental image. As a result of autocorrelation analysis, we identify regions of the cerebral cortex in the activity of which the most significant differences were manifested. We observe features of electroencephalogram spectral parameters for two groups of subjects. As a result, we show that the use of statistical analysis methods allows detecting the difference in the cognitive abilities of people when performing various cognitive tasks.

The investigation of complex physical systems utilizing sophisticated computer models has become commonplace with the advent of modern computational facilities. In many applications, experimental data on the physical systems of interest is extremely expensive to obtain and hence is available in limited quantities. The mathematical systems implemented by the computer models often include parameters having uncertain values. This article provides an overview of statistical methodology for calibrating uncertain parameters to experimental data. This approach assumes that prior knowledge about such parameters is represented as a probability distribution, and the experimental data is used to refine our knowledge about these parameters, expressed as a posterior distribution. Uncertainty quantification for computer model predictions of the physical system are based fundamentally on this posterior distribution. Computer models are generally not perfect representations of reality for a variety of reasons, such as inadequacies in the physical modeling of some processes in the dynamic system. The statistical model includes components that identify and adjust for such discrepancies. A standard approach to statistical modeling of computer model output for unsampled inputs is introduced for the common situation where limited computer model runs are available. Extensions of the statistical methods to functional outputs are available and discussed briefly.

The investigation of complex physical systems utilizing sophisticated computer models has become commonplace with the advent of modern computational facilities. In many applications, experimental data on the physical systems of interest is extremely expensive to obtain and hence is available in limited quantities. The mathematical systems implemented by the computer models often include parameters having uncertain values. This article provides an overview of statistical methodology for calibrating uncertain parameters to experimental data. This approach assumes that prior knowledge about such parameters is represented as a probability distribution, and the experimental data is used to refine our knowledge about these parameters, expressed as a posterior distribution. Uncertainty quantification for computer model predictions of the physical system are based fundamentally on this posterior distribution. Computer models are generally not perfect representations of reality for a variety of reasons, such as inadequacies in the physical modeling of some processes in the dynamic system. The statistical model includes components that identify and adjust for such discrepancies. A standard approach to statistical modeling of computer model output for unsampled inputs is introduced for the common situation where limited computer model runs are available. Extensions of the statistical methods to functional outputs are available and discussed briefly.

The mechanism of the formation of porous silicon (PS) is studied using flicker noise spectroscopy (FNS), a new phenomenological method that allows us to analyze the evolution of nonlinear dissipative systems in time, space and energy. FNS is based on the ideas of deterministic chaos in complex macro- and microsystems. It allows us to obtain a set of empiric parameters (“passport data”) which characterize the state of the system and change of its properties due to the evolution in time, energy, and space. The FNS method permits us to get new information about the kinetics of growth of PS and its properties. Thus, the PS formation mechanisms at n-Si and p-Si, as revealed using the FNS, seem to be essentially different. p-Si shows larger “memory” in the sequence of individual events involved in PS growth than n-Si (if anodized without light illumination). The influence of the anodization variables (such as current density, HF concentration, duration of the process, light illumination) onto the “passport data” of PS is envisaged. The increase of the current density increases memory of the PS formation process, when each forthcoming individual event is more correlated with the preceding one. Increasing current density triggers electrochemical reactions that are negligible at lower currents. Light illumination also produces a positive effect onto the “memory” of the system. The FNS makes it possible to distinguish different stages of the continuous anodization process which are apparently associated with increasing pore length. Thus, FNS is a very sensitive tool in analysis of the PS formation and other complex electrochemical systems as well.

The use of the Traffic Accident statistical analysis method by the Padang Pariaman Police Traffic Unit as an Effort to Reduce Traffic Accident Rates is by means of quantitative analysis, namely by including definite and qualitative figures, namely by not including exact figures, but only mentioning "Increase", "Decrease". ” levels of “worrying”, and so on. In order to determine the relationship and interrelationships between accident variables, the statistical analysis method used is correlation. There are two criteria highlighted for correlation analysis, namely whether the existing sample data provide sufficient evidence that there is a relationship between variables. And second, if there is a relationship, how strong is the relationship between these variables. The variables tested were the type of accident, the cause of the accident, the behavior of the driver that caused the accident, the type of vehicle, the time of the accident, and the profession of the perpetrator of the accident. Effectiveness The use of statistical analysis methods by the Padang Pariaman Police Traffic Unit as an Effort to Reduce Traffic Accident Rates is already effective. It can be seen that there is a decrease in the number of accidents, although in 2019 there was an increase but in 2020 there was a decrease in the number of accidents, namely 284 cases from 363 cases in 2019. This statistical analysis data is very useful for the community as an early warning to be more careful when passing through roads where accidents often occur.

The paper presents results of numerical modeling of flow of the vortex flowmeter for the three grids with different number of cells. The essence of the problem to be solved is to determine the influence of the number of grid cells for the geometry of the flow on the accuracy of the simulation results, and more specifically on the amplitude-frequency characteristics of a vortex flowmeter. To resolve we use the comparison of numerical calculations for the three types of grids one running and one of the current regime. Numerical simulation of the flow of the vortex flowmeter with flow around the body in the form of a wing, carried out with the help of a supercomputer “SKIF-URAL” on the software ANSYS CFX and Cosmos Flow Simulation. To check the reproducibility calculations carried out on three types of grids containing 2 million. Cells, 6 million. And 18 million cells. The frequency of the oscillations of the vortices obtained by applying the method of frequency analysis based on Fourier expansion for the resulting pressure drop on the wing. Results are presented for the incompressible medium (water) as a dependency of the amplitude-frequency characteristics of the time. The dependence of the accuracy of the numerical simulation results, depending on the amount of grid cells. Analysis of the results indicates a satisfactory agreement between the results of numerical simulation and a data of experiment. Relative error data of numerical modeling does not exceed 9%, and the longest match is obtained on computational grid containing 6 million. Cell and using SST-turbulence model (difference of not more than 2.4%). Comparison of the data of numerical and physical experiments showed satisfactory quantitative agreement. As a working mesh is recommended to take a grid containing 6 million cells and using SST-turbulence model.

This paper describes past and present techniques and technologies for the transport of digital data in recent physics experiments. After an overview of the typical requirements for modern data acquisition systems in the field of large scale experimental physics, we detail the successes and failures observed over the last 20 years of evolution of high-speed point-to-point link technology, networking standards and products. Modern data transport technology is presented along with several applications to experiments under construction. Advanced techniques, emerging technologies and trends in the field of highspeed digital data transport are outlined in the perspective of future experiments

This paper describes past and present techniques and technologies for the transport of digital data in recent physics experiments. After an overview of the typical requirements for modern data acquisition systems in the field of large scale experimental physics, we detail the successes and failures observed over the last 20 years of evolution of high-speed point-to-point link technology, networking standards and products. Modtextern data transport technology is presented along with several applications to experiments under construction. Advanced techniques, emerging technologies and trends in the field of high-speed digital data transport are outlined in the perspective of future experiments.

This article traces the influence of physical models of the electromagnetic medium on electrodynamics. The connection between the ability of the electrodynamic equations to describe the processes under study and the adequacy of the model of the electromagnetic medium used in their derivation to the known data is shown. It is revealed that the assumption of the absence of the existence of the electromagnetic medium leads to certain methodological difficulties in deriving the electrodynamic equations. The paper highlights the main milestones in the evolution of the physical model of electromagnetic medium. As a rule, the existence of electromagnetic medium in physics has been denied up to the present time due to the lack of its consistent model. A new physical model of the electromagnetic medium is developed and based on it a system of electrodynamic equations is derived that agree with the known data of physical experiments and astronomical observations. On the basis of the proposed physical model, a mathematical description of the method of detecting the electromagnetic medium is obtained. The developed physical model made it possible not only to explain the data of known electromagnetic phenomena and experiments, but also to propose the Galilean relativity principle within the framework of classical mechanics. Possible consequences of detection of the electromagnetic medium are discussed.

modeling of continuous frequency spectrum of the imaginary part of a complex electronic polarizability. An important part of the method used is the indirect visualization of electron atomic structure of the unit cell of the diamond. This visualization of the structural features of the crystal parsed performed by the spatial geometric modeling nodal points of its nuclear atomic skeleton, surrounded by electron shells of a certain configuration. For indirect identification of necessary geometrical parameters include relatively simple computational methods that rely on the use of a small number of easily generated experimental data. In turn, the definition of geometric parameters of the electronic configuration of particulate matter can be realized by optimizing the frequency characteristics of an elastic electronic polarization. It is proposed to use the original “cybernetic” model of these processes, created on the basis of the classical theory of the polarization of the preconditions given explicit allocation of causality, objectively existing in the traditional description of the Lorentz local field strength. Findings: The article presents the results of simulation of continuous frequency spectrum of the imaginary part of a complex electronic polarizability of the diamond based on the consideration of physical models, which were calculated in the framework of the described techniques. Comparing the data of physical experiment, the traditional interpretation of covalent diamond connection with the results of a computational experiment, it should be noted that the use of the existing model does not allow to achieve high-quality real-compliance and the model spectra. The differences lie in the presence of the physical characteristics of a complex dual-output, and on the simulated curve - single output. In addition, the use of core-electron interpretation electronic diamond configuration does not allow to achieve high-quality real-compliance and the model spectra, obtained on the basis of a simulation of the spectrum. In this case, the differences lie in the displacement of the simulated electron emission caused by the polarization of core-electron pairs in the region of deep electronic resonances. However, the authors proposed a modified model of the carbon of the diamond connection allows you to get it close enough to the dielectric characteristics of the data of physical experiment. Thus, a modified model of the structure of the internal structure of the material allows for the most precise study of its optical properties. Improvements: Practical use the mathematical techniques of mediated visualization of the electronic structure of the diamond should be useful for the further evolution of the theoretical foundations of modern nanotechnology.

Subject of Research.The paper considers turbulent flow and heat exchange in a closed axisymmetric cavity with a rotating disk, which is a model of two-way axial thrust bearing, as well as the other important elements of turbomachines, for example, blade ring labyrinth seals of axial compressor stage. Method. The flow and heat transfer characteristics are studied depending on the relative gap between the fixed housing and the rotating disc and the Reynolds number. Comparison of the local and integral flow characteristics obtained on the basis of various models of turbulence with the data of physical experiment is given. Main Results. The flow structure and heat transfer characteristics are studied depending on the relative gap between the fixed body and the rotating disc and the Reynolds number. Comparison of the local and integral characteristics of the flow with the data of the physical experiment shows that the best matching is given by the application of the k-ε model with Kato-Launder corrections for the turbulence production term and the corrections to the curvature of the streamlines, as well as the two-layer k-ε / k-1 turbulence model. The application of the Spalart-Allmares turbulence model and the Reynolds stress transfer model leads to significant errors in calculating the heat flux distribution over the stator surface. Practical Relevance. The considered problem is a model problem and it gives the possibility to make a conclusion about the applicability of various flow models and models of turbulence in such units of compressors and gas turbines as seals of the blade ring, axial and radial gas and liquid bearings, rotating heat exchangers.

Defining the basis for the development of a country’s start-up ecosystems as the basis for activating entrepreneurship is an urgent task of restoring the country’s economy. The purpose of this study is to identify ways to improve the country’s start-up ecosystem based on the construction of economic and mathematical models for activating business activities. The research methodology is based on statistical research methods, namely dynamics analysis; to assess the strength of the influence of each component of the start-up ecosystem on the change in position in the rating, regression correlation analysis was chosen, which allows identifying the strength of the influence of factors on the final indicator. The components of the start-up ecosystem were investigated, which means an interactive and interdependent set of institutions whose activities create an environment for the qualitative and quantitative growth of start-ups as subjects of innovative entrepreneurship development. The use of statistical analysis methods for the data of the countries, which were grouped into 5 clusters, allowed determining the absolute changes in the values of the Global Start-up Ecosystem Index rating indicators from Start-up Blink: rating change, quantitative component, qualitative component, business environment, general summary. Based on regression-correlation analysis, economicmathematical models were built, which describe the influence of the components of the country’s ecosystem on the change in the rating positions in the section of four clusters, demonstrating: a strong connection between the factors and the result (Clusters 2, 4). Weak connection for the countries of Clusters 3, 5, which indicates the dependence of the development of start-up ecosystems on other factors that are not considered in their description and which affect the development of start-ups and entrepreneurship in the countries of Clusters 3, 5. The practical value of this paper is that the results of the study can serve as the basis for the local and state authorities to form strategies to develop start-up ecosystems at the national and regional level