scholarly journals Peculiarities and Applications of Stochastic Processes with Fractal Properties

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5960
Author(s):  
Oleg Semenovich Amosov ◽  
Svetlana Gennadievna Amosova
Keyword(s):  
Stochastic Processes ◽  
Microelectromechanical Systems ◽  
Inertial Sensors ◽  
Flaw Detection ◽  
Failure Detection ◽  
Self Similarity ◽  
Mobile Objects ◽  
Fractal Properties ◽  
Ultrasonic Echo ◽  
Non Destructive

In this paper, the fractal properties of stochastic processes and objects in different areas were specified and investigated. These included: measuring systems and sensors, navigation and motion controls, telecommunication systems and networks, and flaw detection technologies. Additional options that occur through the use of fractality were also indicated and exemplified for each application. Regarding the problems associated with navigation information processing, the following fractal nature processes were identified: errors of inertial sensors based on the microelectromechanical systems called MEMS, in particular gyroscopic drift and accelerometer bias, and; the trajectory movement of mobile objects. With regard to navigation problems specifically, the estimation problem statement and its solution are given by way of the Bayesian approach for processing fractal processes. The modified index of self-similarity for telecommunication series was proposed, and the self-similarity of network traffic based on the R/S method and wavelet analysis was identified. In failure detection, fractality manifested as porosity, wrinkles, surface fractures, and ultrasonic echo signals measured using non-destructive sensors used for rivet compound testing.

scholarly journals Graph fractal dimension and the structure of fractal networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Pavel Skums ◽  
Leonid Bunimovich
Keyword(s):  
Complex Networks ◽  
Evolutionary Biology ◽  
Real Life ◽  
Fractal Dimensions ◽  
Network Models ◽  
Self Similarity ◽  
Descriptive Complexity ◽  
Network Communities ◽  
Fractal Properties ◽  
Continuous Objects

Abstract Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

Spatial Distribution and Fractal Properties of Aggregating Magnetic and Non-Magnetic Particles

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 219-230 ◽  
Author(s):  
A. Provata ◽  
K. N. Trohidou
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Magnetic Particles ◽  
Composite System ◽  
System Size ◽  
Real Space ◽  
Magnetic Clusters ◽  
Self Similarity ◽  
Fractal Properties ◽  
Simple Connectivity

We study the spatial distribution in aggregating systems of mixtures of magnetic and non-magnetic particles using Monte-Carlo simulations together with scaling arguments. In particular, we show that (a) as the system size grows, the fractal dimension of the composite system is dominated by the smaller fractal dimension, (b) the system is realized as a back-bone consisting of magnetic particles (lower fractal dimension) with denser regions of non-magnetic particles attached to it at random positions. Using simple connectivity features observed in pure magnetic and non-magnetic clusters and self-similarity arguments we predict, via Real-Space-Renormalization, fractal exponents Dm = 1.25 ± 0.05 for the magnetic clusters and Dnm = 1.4 ± 0.1 for the non-magnetic clusters.

Tailoring of Stress Development in MEMS Packaging Systems

2002 ◽  
Vol 741 ◽  
Author(s):  
Satyajit S. Walwadkar ◽  
Junghyun Cho ◽  
P.W. Farrell ◽  
Lawrence E. Felton
Keyword(s):  
Microelectromechanical Systems ◽  
Inertial Sensors ◽  
Thermal Exposure ◽  
Origin And Evolution ◽  
Mems Packaging ◽  
Operation Conditions ◽  
Die Attach ◽  
Device Operation ◽  
Different Levels ◽  
Good Agreement

ABSTRACTA better understanding of the origin and evolution of the stresses is a crucial step in improving reliability of packaging systems for microelectromechanical systems (MEMS). Given its importance, we examine the stresses developed in hermetically packaged MEMS inertial sensors. For this purpose, an optical surface profilometer is employed to assess the stresses by measuring the curvature of dummy silicon dies (3.5×3.5 mm2) assembled in different types of packages and die attach adhesives. We also explore a temporal evolution of stresses during thermal exposure of the test packages in an effort to emulate actual packaging processes and device operation conditions. The result shows different levels of stresses generated from various adhesives and package types, and also a stress evolution during packaging processes. The mechanical stress data also show a good agreement with MEMS performance data obtained from actual accelerometers. Therefore, the stress data will not only be useful in better understanding performance of MEMS packages, but the testing protocol can also provide a diagnostic tool for very small packaging systems.

Flaw Detection in Welded Metal Using Magnetic Induction Tomography

2014 ◽  
Vol 896 ◽  
pp. 722-725 ◽  
Author(s):  
Dona Sutisna ◽  
Syahrul Ullum ◽  
Warsito Purwo Taruno ◽  
Al Amin Saichul Iman ◽  
Marlin Ramadhan Baidillah ◽  
...  
Keyword(s):  
Magnetic Induction ◽  
Superposition Principle ◽  
Flaw Detection ◽  
Potential Method ◽  
Welded Steel ◽  
Radiographic Testing ◽  
Field Sensitivity ◽  
Experiment Method ◽  
Magnetic Induction Tomography ◽  
Non Destructive

Various defects on welded metal can lead to failure of material, so that it needs some routine examination to maintain the material quality. The development of Magnetic Induction Tomography (MIT) in recent years made MIT a potential method for Non Destructive Test (NDT) to be applied in industries. We perform an MIT inspection technique to detect flaw using 2-coils MIT planar sensor that consist of transmitter and receiver coils which is able to detect flaw based on different electrical conductivity and measured as phase shift. This study involves experiment method with measurement of welded steel in two areas, there are normal and defective welded area which amounts to 72 measurement points that conducted with superposition principle. Then simulation of 2-coils planar sensor using Finite Element Method (FEM) software to obtain magnetic field sensitivity using parameter as in the experiment. Result from this measurement showed that phase value in normal welded area is higher than defective welded area, then those data is processed further on reconstruction step by using specific algorithm to obtain reconstructed image. This image able to show the presence of flaw in welded area which is indicated by red spot, and it has a relatively good correlation when compared with radiographic testing film.

SELF-SIMILARITY OF FREE STOCHASTIC PROCESSES

2006 ◽  
Vol 09 (03) ◽  
pp. 451-469 ◽  
Author(s):  
ZHAOZHI FAN
Keyword(s):  
Stochastic Processes ◽  
Self Similarity ◽  
Strict Stability ◽  
Classical Analogue ◽  
Self Similar

In this paper we study self-similarity of free stochastic processes. We establish the noncommutative counterpart of Lamperti's self-similar processes. We develop the characterization of noncommutative self-similar processes through a modification of Voiculescu transform, the free cumulant transform. We study the connection between free self-similarity, strict ⊞-stability and ⊞-self-decomposability. In particular, we derive the properties of free self-similar processes and their connection to strict ⊞-stability and ⊞-self-decomposability, that turn out to be consistent with their classical analogue.

Flaw Detection in Aluminum Plate by Shear Horizontal Guided Wave Based on Magnetostriction EMAT

2014 ◽  
Vol 614 ◽  
pp. 287-290
Author(s):  
Le Chen ◽  
Yue Min Wang ◽  
Hai Quan Geng
Keyword(s):  
Guided Waves ◽  
Flaw Detection ◽  
Test Sample ◽  
Guided Wave ◽  
Sh Waves ◽  
Electromagnetic Acoustic Transducers ◽  
Acoustic Transducers ◽  
Non Destructive ◽  
Viable Method ◽  
Shear Horizontal

Shear horizontal (SH) guided waves have been proved to be a viable method in the Non-Destructive Evaluation (NDE). Electromagnetic acoustic transducers (EMAT) can excite SH waves easily. By bonding the Fe-Co alloy to the test sample, the SH guided waves based on magnetostriction effect can be used to detect the flaw in nonferromagnetic material. The principle of exciting and receiving SH waves is introduced, and an experiment is carried out to validate the result.

scholarly journals Experience in the application of the non-destructive method of acoustic emission in the production of titanium billets and products of transport engineering

2021 ◽  
Vol 2094 (4) ◽  
pp. 042018
Author(s):  
E Yu Remshev ◽  
A I Olehver ◽  
S A Voinash ◽  
V A Sokolova ◽  
A A Ivanov ◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Mechanical Treatment ◽  
Flaw Detection ◽  
Vt22 Titanium Alloy ◽  
Ultrasonic Flaw Detection ◽  
Ultrasonic Flaw ◽  
Titanium Surfaces ◽  
And Control ◽  
Non Destructive

Abstract The article discusses the issue of using the non-destructive method of acoustic emission at the stage of blank production. So, due to the violation of the heat treatment modes, various defects are formed in the starting material, which affects the operational properties of the finished products. To eliminate this problem, the stages of production of titanium blanks and products of transport engineering were studied, such as: heat and mechanical treatment, ultrasonic quality control, determination of the level of mechanical properties and control of the structure. In the course of the research, a method of acoustic emission control was developed and tested. The experiment on setting the locations of defects was carried out on ingots of VT22 titanium alloy during cooling. The reliability of the developed method is confirmed by the existing method of ultrasonic flaw detection. It has been established that this method can be effectively used to control workpieces and machined workpieces for the manufacture of particularly critical mirrors for searching for inhomogeneous inclusions and increasing the efficiency of the technological process by eliminating machining of VT1-0 titanium surfaces with inhomogeneous inclusions. In addition, this method can be used to search for defects commensurate with the grain size of the ingot, as well as significantly smaller sizes.

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