scholarly journals Hausdorff, large deviation and Legendre multifractal spectra of Lévy multistable processes

2020 ◽  
Vol 130 (4) ◽  
pp. 2032-2057
Author(s):  
R. Le Guével ◽  
J. Lévy Véhel
Keyword(s):  
Large Deviation ◽  
Multifractal Spectra

Study of the structural degradation of steel 15Kh5M upon continuous duty

2020 ◽  
Vol 86 (1) ◽  
pp. 38-43
Author(s):  
Vladimir A. Kim ◽  
Valeriya V. Lysenko ◽  
Anna A. Afanaseva ◽  
Khasan I. Turkmenov
Keyword(s):  
Grain Boundaries ◽  
Structural Changes ◽  
Structural Transformations ◽  
Structural Degradation ◽  
Structural Arrangement ◽  
Dispersed Particles ◽  
Complex Process ◽  
Multifractal Spectra ◽  
Steel 15Kh5m ◽  
Complex Indicators

Structural degradation of the material upon long-term thermal and force impacts is a complex process which includes migration of the grain boundaries, diffusion of the active elements of the external and technological environment, hydrogen embrittlement, aging, grain boundary corrosion and other mechanisms. Application of the fractal and multifractal formalism to the description of microstructures opens up wide opportunities for quantitative assessment of the structural arrangement of the material, clarifies and reveals new aspects of the known mechanisms of structural transformations. Multifractal parameterization allows us to study the processes of structural degradation from the images of microstructures and identify structural changes that are hardly distinguishable visually. Any quantitative structural indicator can be used to calculate the multifractal spectra of the microstructure, but the most preferable is that provides the maximum range of variation in the numerical values of the multifractal components. The results of studying structural degradation of steel 15Kh5M upon continuous duty are presented. It is shown that structural degradation of steel during operation under high temperatures and stresses is accompanied by enlargement of the microstructural objects, broadening of the grain boundaries and allocation of the dispersed particles which are represented as point objects in the images. The processes of structural degradation lead to an increase in the range of changes in the components of the multifractal spectra. High values of complex indicators of structural arrangement indicate to an increase in heterogeneity and randomness at the micro-scale level, but at the same time, to manifestation of the ordered combinations of individual submicrostructures. Those structural transformations adapt the material to external impacts and provide the highest reliability and fracture resistance of the material.

Self-organization

2018 ◽  
Author(s):  
Stuart P. Wilson
Keyword(s):  
Large Deviation ◽  
Natural World ◽  
Self Organization ◽  
Global Order ◽  
Deterministic Systems ◽  
Working Definition ◽  
Complex Forms ◽  
Robust To Noise ◽  
Organizing Principles ◽  
Self Organizing

Self-organization describes a dynamic in a system whereby local interactions between individuals collectively yield global order, i.e. spatial patterns unobservable in their entirety to the individuals. By this working definition, self-organization is intimately related to chaos, i.e. global order in the dynamics of deterministic systems that are locally unpredictable. A useful distinction is that a small perturbation to a chaotic system causes a large deviation in its trajectory, i.e. the butterfly effect, whereas self-organizing patterns are robust to noise and perturbation. For many, self-organization is as important to the understanding of biological processes as natural selection. For some, self-organization explains where the complex forms that compete for survival in the natural world originate from. This chapter outlines some fundamental ideas from the study of simulated self-organizing systems, before suggesting how self-organizing principles could be applied through biohybrid societies to establish new theories of living systems.

scholarly journals Vicarious Radiometric Calibration of Ocean Color Bands for FY-3D/MERSI-II at Lake Qinghai, China

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 139
Author(s):  
Shengli Chen ◽  
Xiaobing Zheng ◽  
Xin Li ◽  
Wei Wei ◽  
Shenda Du ◽  
...  
Keyword(s):  
Infrared Imaging ◽  
Large Deviation ◽  
Ocean Color ◽  
Calibration Method ◽  
Surface Measurement ◽  
Radiometric Calibration ◽  
Lake Qinghai ◽  
Vicarious Calibration ◽  
Calibration Methods ◽  
Spectral Imager

To calibrate the low signal response of the ocean color (OC) bands and test the stability of the Fengyun-3D (FY-3D)/Medium Resolution Spectral Imager II (MERSI-II), an absolute radiometric calibration field test of FY-3D/MERSI-II at the Lake Qinghai Radiometric Calibration Site (RCS) was carried out in August 2018. The lake surface and atmospheric parameters were mainly measured by advanced observation instruments, and the MODerate spectral resolution atmospheric TRANsmittance algorithm and computer model (MODTRAN4.0) was used to simulate the multiple scattering radiance value at the altitude of the sensor. The results showed that the relative deviations between bands 9 and 12 are within 5.0%, while the relative deviations of bands 8, and 13 are 17.1%, and 12.0%, respectively. The precision of the calibration method was verified by calibrating the Aqua/Moderate-resolution Imaging Spectroradiometer (MODIS) and National Polar-orbiting Partnership (NPP)/Visible Infrared Imaging Radiometer (VIIRS), and the deviation of the calibration results was evaluated with the results of the Dunhuang RCS calibration and lunar calibration. The results showed that the relative deviations of NPP/VIIRS were within 7.0%, and the relative deviations of Aqua/MODIS were within 4.1% from 400 nm to 600 nm. The comparisons of three on-orbit calibration methods indicated that band 8 exhibited a large attenuation after launch and the calibration results had good consistency at the other bands except for band 13. The uncertainty value of the whole calibration system was approximately 6.3%, and the uncertainty brought by the field surface measurement reached 5.4%, which might be the main reason for the relatively large deviation of band 13. This study verifies the feasibility of the vicarious calibration method at the Lake Qinghai RCS and provides the basis and reference for the subsequent on-orbit calibration of FY-3D/MERSI-II.

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

1990 ◽  
Vol 27 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Claudine Robert
Keyword(s):  
Artificial Intelligence ◽  
Maximum Entropy ◽  
Large Deviation ◽  
Maximum Entropy Principle ◽  
Statistical Modelling ◽  
Linear Constraints ◽  
Descriptive Statistics ◽  
Entropy Principle ◽  
Maximum Entropy Distribution ◽  
Mathematical Justification

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

Sign in / Sign up

Export Citation Format

Share Document