scholarly journals Fractal analysis of the ULF geomagnetic data obtained at Izu Peninsula, Japan in relation to the nearby earthquake swarm of June–August 2000

2003 ◽  
Vol 3 (3/4) ◽  
pp. 229-236 ◽  
Author(s):  
K. Gotoh ◽  
M. Hayakawa ◽  
N. Smirnova
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Active Region ◽  
Fractal Analysis ◽  
Flicker Noise ◽  
Earthquake Swarm ◽  
Fractal Dimensions ◽  
Izu Peninsula ◽  
Geomagnetic Data ◽  
Fractal Characteristics

Abstract. In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions) before the earthquake: appearance of the flicker-noise signatures and increase of the time series fractal dimension. Here we analyze ULF geomagnetic data obtained in a seismic active region of Izu Peninsula, Japan during a swarm of the strong nearby earthquakes of June–August 2000 and compare the results obtained in both regions. We apply the same methodology of data processing using the FFT procedure, Higuchi method and Burlaga-Klein approach to calculate the spectral exponents and fractal dimensions of the ULF time series. We found the common features and specific peculiarities in the behavior of fractal characteristics of the ULF time series before Izu and Guam earthquakes. As a common feature, we obtained the same increase of the ULF time series fractal dimension before the earthquakes, and as specific peculiarity – this increase appears to be sharp for Izu earthquake in comparison with gradual increase of the ULF time series fractal dimension for Guam earthquake. The results obtained in both regions are discussed on the basis of the SOC (self-organized criticality) concept taking into account the differences in the depths of the earthquake focuses. On the basis of the peculiarities revealed, we advance methodology for extraction of the earthquake precursory signatures. As an adjacent step, we suggest the combined analysis of the ULF time series in the parametric space polarization ratio – fractal dimension. We reason also upon the advantage of the multifractal approach with respect to the mono-fractal analysis for study of the earthquake preparation dynamics.

scholarly journals FRACTAL ANALYSIS OF THE NANOSTRUCTURE OF A HETEROGENEOUS HIGH COERCITY ALLOY

2021 ◽  
pp. 368-375
Author(s):  
Елена Михайловна Семенова ◽  
Марина Борисовна Ляхова ◽  
Дмитрий Викторович Иванов ◽  
Артем Игоревич Синкевич ◽  
Александр Сергеевич Антонов ◽  
...  
Keyword(s):  
Atomic Force Microscopy ◽  
Fractal Dimension ◽  
Elemental Composition ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Phase Component ◽  
Force Microscopy ◽  
Atomic Force ◽  
Fractal Characteristics ◽  
Microscopy Data

Методом атомно-силовой микроскопии получены изображения наноструктры составляющих гетерогенного интерметаллида SmCoCuFeZr в высококоэрцитивном состоянии. На микроуровне в сплавах выделили два типа областей (фазовых составляющих) отличающихся по интегральному элементному составу и интервалам коэрцитивности. На основе данных атомно-силового микроскопа проводится анализ фрактальных характеристик поверхности этих областей. Показано, что фрактальная размерность наноструктуры коррелирует с локальной коэрцитивностью фазовых составляющих. Фазовая составляющая с относительно низкой коэрцитивностью демонстрирует возможность существования структур с фрактальной размерностью в диапазоне 2,396 - 2,475, что соответствует умеренно развитому фрактальному рельефу. При этом высококоэрцитивная составляющая с регулярной наноструктурой характеризуется более высокой фрактальной размерностью 2,452 - 2,508, а на отдельных участках образца встречались области с фрактальной размерностью до 2,577 . The atomic force microscopy was used to obtain images of the nanostructure of components of a heterogeneous intermetallic SmCoCuFeZr compound in a highly coercive state. At the microlevel, two types of regions were distinguished in the alloys, differing in integral elemental composition and coercivity intervals. Based on the atomic force microscopy data, an analysis of the fractal characteristics of the surface is carried out on both of the above types of areas. It is shown that the fractal dimension of the nanostructure correlates with the local coercivity of the phase components. The phase component with a relatively low coercivity demonstrates the possibility of the existence of structures with fractal dimensions in the 2,396 - 2,475 range corresponding to a moderately developed fractal relief. In this case, the high-coercive component with a regular nanostructure is characterized by a higher fractal dimension of 2,452 - 2,508, and in some areas of the sample there were regions with a fractal dimension up to the value of 2,577.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

Application of Fractal Theory in Aggregate Gradation Research

2012 ◽  
Vol 204-208 ◽  
pp. 1923-1928
Author(s):  
Bo Tan ◽  
Rui Hua Yang ◽  
Yan Ting Lai
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Aggregate Gradation ◽  
Structure Characteristics ◽  
Aggregate Distribution ◽  
Dimension Formula ◽  
Mass Fractal ◽  
Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

scholarly journals The Impacts of Matrix Compositions on Nanopore Structure and Fractal Characteristics of Lacustrine Shales from the Changling Fault Depression, Songliao Basin, China

Minerals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 127 ◽  
Author(s):  
Zhuo Li ◽  
Zhikai Liang ◽  
Zhenxue Jiang ◽  
Fenglin Gao ◽  
Yinghan Zhang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Dimensions ◽  
Organic Medium ◽  
Songliao Basin ◽  
Sem Images ◽  
Fractal Characteristics ◽  
Inorganic Mineral ◽  
Nanopore Structure ◽  
High Fractal Dimension

The Lower Cretaceous Shahezi shales are the targets for lacustrine shale gas exploration in Changling Fault Depression (CFD), Southern Songliao Basin. In this study, the Shahezi shales were investigated to further understand the impacts of rock compositions, including organic matters and minerals on pore structure and fractal characteristics. An integrated experiment procedure, including total organic carbon (TOC) content, X-ray diffraction (XRD), field emission-scanning electron microscope (FE-SEM), low pressure nitrogen physisorption (LPNP), and mercury intrusion capillary pressure (MICP), was conducted. Seven lithofacies can be identified according to on a mineralogy-based classification scheme for shales. Inorganic mineral hosted pores are the most abundant pore type, while relatively few organic matter (OM) pores are observed in FE-SEM images of the Shahezi shales. Multimodal pore size distribution characteristics were shown in pore width ranges of 0.5–0.9 nm, 3–6 nm, and 10–40 nm. The primary controlling factors for pore structure in Shahezi shales are clay minerals rather than OM. Organic-medium mixed shale (OMMS) has the highest total pore volumes (0.0353 mL/g), followed by organic-rich mixed shale (ORMS) (0.02369 mL/g), while the organic-poor shale (OPS) has the lowest pore volumes of 0.0122 mL/g. Fractal dimensions D1 and D2 (at relative pressures of 0–0.5 and 0.5–1 of LPNP isotherms) were obtained using the Frenkel–Halsey–Hill (FHH) method, with D1 ranging from 2.0336 to 2.5957, and D2 between 2.5779 and 2.8821. Fractal dimensions are associated with specific lithofacies, because each lithofacies has a distinctive composition. Organic-medium argillaceous shale (OMAS), rich in clay, have comparatively high fractal dimension D1. In addition, organic-medium argillaceous shale (ORAS), rich in TOC, have comparatively high fractal dimension D2. OPS shale contains more siliceous and less TOC, with the lowest D1 and D2. Factor analysis indicates that clay contents is the most significant factor controlling the fractal dimensions of the lacustrine Shahezi shale.

scholarly journals Scaling characteristics of ULF geomagnetic fields at the Guam seismoactive area and their dynamics in relation to the earthquake

2001 ◽  
Vol 1 (3) ◽  
pp. 119-126 ◽  
Author(s):  
N. Smirnova ◽  
M. Hayakawa ◽  
K. Gotoh ◽  
D. Volobuev
Keyword(s):  
Time Series ◽  
Flicker Noise ◽  
Fractal Dimensions ◽  
Large Earthquake ◽  
Local Times ◽  
Noise Structure ◽  
Gradual Evolution ◽  
Self Organized Criticality ◽  
Geomagnetic Fields ◽  
Spectrum Slope

Abstract. The long-term evolution of scaling (fractal) characteristics of the ULF geomagnetic fields in the seismoactive region of the Guam Island is studied in relation to the strong (Ms = 8.0) nearby earthquake of 8 August 1993. The selected period covers 10 months before and 10 months after the earthquake. The FFT procedure, Burlaga-Klein approach and Higuchi method, have been applied to calculate the scaling exponents and fractal dimensions of the ULF time series. It is found that the spectrum of ULF emissions exhibits, on average, a power law behaviour S(f ) α f -b , which is a fingerprint of the typical fractal (self-affine) time series. The spectrum slope b fluctuates quasi-periodically during the course of time in a range of b = 2.5–0.7, which corresponds to the fractional Brownian motion with both persistent and antipersistent behaviour. An tendency is also found for the spectrum slope to decrease gradually when approaching the earthquake date. Such a tendency manifests itself at all local times, showing a gradual evolution of the structure of the ULF noise to a typical flicker noise structure in proximity to the large earthquake event. We suggest considering such a peculiarity as an earthquake precursory signature. One more effect related to the earthquake is revealed: the longest quasi-period, which is 27 days, disappeared from the variations of the ULF emission spectrum slope during the earthquake, and it reappeared three months after the event. Physical interpretation of the peculiarities revealed has been done on the basis of the SOC (self-organized criticality) concept.

scholarly journals Fractal Characteristics of Chip Morphology and Tool Wear in High-Speed Turning of Iron-Based Super Alloy

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 1020
Author(s):  
Xu Zhang ◽  
Guangming Zheng ◽  
Xiang Cheng ◽  
Rufeng Xu ◽  
Guoyong Zhao ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Tool Wear ◽  
High Speed ◽  
Cutting Speed ◽  
Fractal Dimensions ◽  
Chip Morphology ◽  
Color Changes ◽  
Fractal Characteristics ◽  
Iron Based ◽  
Super Alloy

Considering that iron-based super alloy is a kind of difficult-to-cut material, it is easy to produce work hardening and serious tool wear during machining. Therefore, this work aims to explore the chip change characteristics and tool wear mechanism during the processing of iron-based super alloy, calculate the fractal dimensions of chip morphology and tool wear morphology, and use fractals to analyze their change trend. Meanwhile, a new cutting tool with a super ZX coating is used for a high-speed dry turning experiment. The results indicate that the morphology of the chip is saw-tooth, and its color changes gradually, due to the oxidation reaction. The main wear mechanisms of the tool involve abrasive wear, adhesive wear, oxidation wear, coating spalling, microcracking and chipping. The fractal dimension of the tool wear surface and chip is increased with the improvement of cutting speed. This work investigates the fractal characteristics of chip morphology and tool wear morphology. The fractal dimension changes regularly with the change of tool wear, which plays an important role in predicting this tool wear. It is also provides some guidance for the efficient processing of an iron-based super alloy.

scholarly journals Use of fractal analysis to evaluate the surface quality of agricultural machinery parts

2020 ◽  
Vol 17 ◽  
pp. 00189
Author(s):  
Oleg Bavykin ◽  
Tatyana Levina ◽  
Vladlena Matrosova ◽  
Anatoly Klochkov ◽  
Vitaliy Enin
Keyword(s):  
Time Series ◽  
Computer Program ◽  
Surface Quality ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
High Accuracy ◽  
Agricultural Machinery ◽  
Fractal Characteristics

The research of the determination of the fractal characteristics of the surface of a material proposes the use of a stationary profilograph and a computer program for calculating the Hurst exponent. The low accuracy of fractal analysis using the well-known computer program Fractan is revealed. A computer program developed in VBA for the fractal analysis of the time series is described. The high accuracy of the algorithms for calculating the Hurst exponent incorporated in this program is shown.

scholarly journals Review about the Application of Fractal Theory in the Research of Packaging Materials

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 860
Author(s):  
Qingshan Duan ◽  
Jiejie An ◽  
Hanling Mao ◽  
Dongwu Liang ◽  
Hao Li ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Theory ◽  
Inorganic Materials ◽  
Packaging Materials ◽  
Analysis Method ◽  
Characteristic Parameters ◽  
Fractal Characteristic ◽  
Fractal Characteristics ◽  
The Relationship

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

scholarly journals Evaluation of ULF electromagnetic phenomena associated with the 2000 Izu Islands earthquake swarm by wavelet transform analysis

2011 ◽  
Vol 11 (3) ◽  
pp. 965-970 ◽  
Author(s):  
P. Han ◽  
K. Hattori ◽  
Q. Huang ◽  
T. Hirano ◽  
Y. Ishiguro ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Data Analysis ◽  
Earthquake Swarm ◽  
Magnetic Anomalies ◽  
Reference Station ◽  
Similar Data ◽  
Izu Peninsula ◽  
Geomagnetic Data ◽  
Wavelet Transform Analysis ◽  
Izu Islands

Abstract. There have been many reports on ULF electromagnetic phenomena associated with the 2000 Izu Islands earthquake swarm. In this study, seismo-magnetic anomalies are presented by examining energy variations of signatures at the periods around 100 s. Geomagnetic data observed at three stations in Izu Peninsula from 1 January 2000 to 30 April 2001 have been analyzed and wavelet transform has been performed. In order to indentify anomalous changes from ionosphere disturbances, Kakioka station has been chosen as a reference station, and the similar data analysis has been performed. The results suggest that the unusual energy enhancement of the Z component, which only appears in Izu Peninsula from late June until early November 2000, might possibly be one of electromagnetic phenomena associated with the 2000 Izu Islands earthquake swarm.

THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 217-229 ◽  
Author(s):  
FRANK B. TATOM
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractional Calculus ◽  
Fractal Dimensions ◽  
Linear Functions ◽  
Fractal Curve ◽  
Random Fractal ◽  
Fractal Functions ◽  
Decay Exponent ◽  
The Relationship

The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).

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