scholarly journals Multifractal analysis of electron images of fossil coal surface

2018 ◽  
Vol 56 ◽  
pp. 01020 ◽  
Author(s):  
Vasiliy Malinnikov ◽  
Valeriy Zakharov ◽  
Denis Uchaev ◽  
Dmitry Uchaev ◽  
Olga Malinnikova
Keyword(s):  
Surface Structure ◽  
Multifractal Analysis ◽  
Structural Organization ◽  
Quantitative Difference ◽  
Fractal Dimensions ◽  
Coal Surface ◽  
Coal Specimen ◽  
Fossil Coal ◽  
Multifractal Spectra ◽  
The Right

The multifractal spectra of electronic images of fossil coal surfaces obtained from outburst-hazardous zones, outburst-nonhazardous (quiet) zones and outburst zones are studied. It is shown that the structural organization of coal surface elements can be represented by a multifractal with a corresponding f (α) -spectrum of fractal dimensions, which is suitable to determine quantitative difference in microstructures of coal specimens from outburst-hazardous and outburst-nonhazardous beds. Coals from outburst-hazardous and outburst-nonhazardous beds differ in the direction of skewness of multifractal spectra characterizing their surface structure. If the f (α) -spectrum is skewed to the right, then the analyzed coal specimen belongs to an outburst-hazardous bed, and on the contrary, if f (α) is skewed to the left, then it can be concluded that the coal specimen most likely belongs to an outburst-nonhazardous bed.

scholarly journals Manufacturing of macro scale composites with strengthening structure made with use of SLM technology – machinability

Mechanik ◽  
2018 ◽  
Vol 91 (10) ◽  
pp. 895-897
Author(s):  
Emilia Bachtiak-Radka ◽  
Damian Sobków ◽  
Krzysztof Filipowicz
Keyword(s):  
Surface Structure ◽  
Selective Laser Melting ◽  
Confocal Microscope ◽  
Laser Melting ◽  
Surface Parameters ◽  
Macro Scale ◽  
The Right

Attempts of defining of machinability of manufactured details relative to research aimed to create macro composites with defined strengthening structure made using selective laser melting (SLM technology) were presented. The structures are made of significant different materials than the filling and that causes a problem with choosing the right tools and parameters for the whole element. That is why there were manufactured preliminary tests of achieving similar surface structure while machining manufactured samples. Measurements of surface parameters were made using confocal microscope. Borders between strengthening structure and filler were observed in order to check if the materials were separated during machining. There was also observed wear of machining tools made of different materials after machining with different parameters.

Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks

2013 ◽  
pp. 16-46
Author(s):  
Oleg I. Sheluhin ◽  
Artem V. Garmashev
Keyword(s):  
Communication Systems ◽  
Multifractal Analysis ◽  
Fractal Dimensions ◽  
Multifractal Spectrum ◽  
Telecommunication Networks ◽  
Information Communication ◽  
Novel Approach ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima ◽  
Development Methods

In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and scaling functions, and methods used in their determination by means of Wavelet Transform Modulus Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum are presented. A method based on multifractal data analysis at network layer level by means of WTMM is proposed for the detection of traffic anomalies in computer and telecommunication networks. The chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimensions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum parameters is proposed for estimating queuing performance for the generalized multifractal traffic on the input of a buffering device. It is shown that the multifractal character of traffic has significant impact on queuing performance characteristics.

scholarly journals Heterogeneity in catchment properties: a case study of Grey and Buller catchments, New Zealand

2002 ◽  
Vol 6 (2) ◽  
pp. 167-184 ◽  
Author(s):  
U. Shankar ◽  
C. P. Pearson ◽  
V. I. Nikora ◽  
R. P. Ibbitt
Keyword(s):  
New Zealand ◽  
Fractal Dimensions ◽  
Affine Scaling ◽  
Stream Networks ◽  
Ecological Processes ◽  
Spectral Parameters ◽  
Scaling Behaviour ◽  
Multifractal Spectra ◽  
Box Counting Method ◽  
Landscape Patches

Abstract. The scaling behaviour of landscape properties, including both morphological and landscape patchiness, is examined using monofractal and multifractal analysis. The study is confined to two neighbouring meso-scale catchments on the west coast of the South Island of New Zealand. The catchments offer a diverse but largely undisturbed landscape with population and development impacts being extremely low. Bulk landscape properties of the catchments (and their sub-basins) are examined and show that scaling of stream networks follow Hack’s empirical rule, with exponents ∼0.6. It is also found that the longitudinal and transverse scaling exponents of stream networks equate to νl ≈0.6 and νw≈ 0.4, indicative of self-affine scaling. Catchment shapes also show self-affine behaviour. Further, scaling of landscape patches show multifractal behaviour and the analysis of these variables yields the characteristic parabolic curves known as multifractal spectra. A novel analytical approach is adopted by using catchments as hydrological cells at various sizes, ranging from first to sixth order, as the unit of measure. This approach is presented as an alternative to the box-counting method as it may be much more representative of hydro-ecological processes at catchment scales. Multifractal spectra are generated for each landscape property and spectral parameters such as the range in α (Holder exponent) values and maximum dimension at α0, (also known as the capacity dimension Dcap), are obtained. Other fractal dimensions (information Dinf and correlation Dcor) are also calculated and compared. The dimensions are connected by the inequality Dcap≥Dinf≥Dcor. Such a relationship strongly suggests that the landscape patches are heterogeneous in nature and that their scaling behaviour can be described as multifractal. The quantitative parameters obtained from the spectra may provide the basis for improved parameterisation of ecological and hydrological models. Keywords: fractal, multifractal, scaling, landscape, patchiness

scholarly journals ON THE INVERSE MULTIFRACTAL FORMALISM

2009 ◽  
Vol 52 (1) ◽  
pp. 179-194 ◽  
Author(s):  
L. OLSEN
Keyword(s):  
Multifractal Analysis ◽  
Regularity Condition ◽  
Upper Bounds ◽  
Legendre Transform ◽  
Self Similarity ◽  
Multifractal Formalism ◽  
Multifractal Spectra ◽  
Physics Literature ◽  
Image Position ◽  
Legendre Transforms

AbstractTwo of the main objects of study in multifractal analysis of measures are the coarse multifractal spectra and the Rényi dimensions. In the 1980s it was conjectured in the physics literature that for ‘good’ measures the following result, relating the coarse multifractal spectra to the Legendre transform of the Rényi dimensions, holds, namely This result is known as the multifractal formalism and has now been verified for many classes of measures exhibiting some degree of self-similarity. However, it is also well known that there is an abundance of measures not satisfying the multifractal formalism and that, in general, the Legendre transforms of the Rényi dimensions provide only upper bounds for the coarse multifractal spectra. The purpose of this paper is to prove that even though the multifractal formalism fails in general, it is nevertheless true that all measures (satisfying a mild regularity condition) satisfy the inverse of the multifractal formalism, namely

LIII. Remarks on the bovey coal: In a letter to the right honourable George Earl of Macclesfield, president of the royal society

1759 ◽  
Vol 51 ◽  
pp. 534-553
Keyword(s):  
Royal Society ◽  
Fossil Wood ◽  
The Other ◽  
Fossil Coal ◽  
The Right

My Lord, The description, which the learned professor Hollman has given the society, of two remarkable strata of fossil wood in Germany, one in the neighbourhood of Munden, in the duchy of Grubenhagen, and the other near Allendorf in hesse, corresponds, in so many particulars, with some strata, discovered about fifteen years ago, in Devonshire, that it suggested to me a doubt, whether those German strata were really (what the learned professor supposes them) fossil wood, and formerly a vegetable substance, or (what he says the miners call them) fossil coal.

scholarly journals MULTIFRACTAL ANALYSIS OF MOUNT St. HELENS SEISMICITY AS A TOOL FOR IDENTIFYING ERUPTIVE ACTIVITY

Fractals ◽  
2006 ◽  
Vol 14 (03) ◽  
pp. 179-186 ◽  
Author(s):  
FILIPPO CARUSO ◽  
SERGIO VINCIGUERRA ◽  
VITO LATORA ◽  
ANDREA RAPISARDA ◽  
STEPHEN MALONE
Keyword(s):  
Time Distribution ◽  
Multifractal Analysis ◽  
Mechanical Response ◽  
Fractal Dimensions ◽  
Distribution Patterns ◽  
Fixed Number ◽  
Short Time Scale ◽  
Eruptive Activity ◽  
Seismic Swarms ◽  
Mount St Helens

We present a multifractal analysis of Mount St. Helens seismic activity during 1980–2002. The seismic time distribution is studied in relation to the eruptive activity, mainly marked by the 1980 major explosive eruptions and by the 1980–1986 dome building eruptions. The spectrum of the generalized fractal dimensions, i.e. Dq versus q, extracted from the data, allows us to identify two main earthquake time distribution patterns. The first one exhibits a multifractal clustering correlated to the intense seismic swarms of the dome building activity. The second one is characterized by an almost constant value of Dq ≈ 1, as for a random uniform distribution. The time evolution of Dq (for q = 0.2), calculated on a fixed number of events window and at different depths, shows that the brittle mechanical response of the shallow layers to rapid magma intrusions, during the eruptive periods, is revealed by sharp changes, acting at a short time scale (order of days), and by the lowest values of Dq (≈ 0.3). Conversely, for deeper earthquakes, characterized by intense seismic swarms, Dq do not show obvious changes during the whole analyzed period, suggesting that the earthquakes, related to the deep magma supply system, are characterized by a minor degree of clustering, which is independent of the eruptive activity.

FRACTAL BEHAVIOR OF NUCLEAR FRAGMENTS IN HIGH ENERGY INTERACTIONS

Fractals ◽  
2003 ◽  
Vol 11 (04) ◽  
pp. 331-343 ◽  
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
MITALI MONDAL ◽  
SWARNAPRATIM BHATTACHARYYA ◽  
JAYITA GHOSH
Keyword(s):  
Specific Heat ◽  
Multifractal Analysis ◽  
Fractal Dimensions ◽  
High Energy ◽  
Factorial Moments

The multifractal analysis of data on nuclear fragments obtained from 28 Si-AgBr interactions at 14.5 A GeV is performed using three different methods (the factorial moments, G-moments and Takagi moments). The generalized fractal dimensions Dq is determined from all these methods. Data reflects multifractal geometry for the nuclear fragments. From the knowledge of Dq, the multifractal specific heat is calculated for this data and also for 16 O-AgBr interactions at 60 A GeV and 32 S-AgBr interactions at 200 A GeV.

scholarly journals Coal surface structure and thermodynamics. Final report

10.2172/49114 ◽  
1994 ◽  
Author(s):  
J.W. Larsen ◽  
P.C. Wernett ◽  
A.S. Glass ◽  
D. Quay ◽  
J. Roberts
Keyword(s):  
Surface Structure ◽  
Final Report ◽  
Coal Surface

scholarly journals Multifractal spectra of branching measure on a Galton-Watson tree

2002 ◽  
Vol 39 (01) ◽  
pp. 100-111 ◽  
Author(s):  
Narn-Rueih Shieh ◽  
S. James Taylor
Keyword(s):  
Hausdorff Dimension ◽  
Local Dimension ◽  
Exceptional Points ◽  
Exceptional Sets ◽  
Multifractal Spectra ◽  
The Right ◽  
Finite Moments ◽  
Dimension Index

IfZis the branching mechanism for a supercritical Galton-Watson tree with a single progenitor and E[ZlogZ] < ∞, then there is a branching measure μ defined on ∂Γ, the set of all paths ξ which have a unique node ξ|nat each generationn. We use the natural metric ρ(ξ,η) = e−n, wheren= max{k: ξ|k= η|k}, and observe that the local dimension index isd(μ,ξ) = limn→∞log(μB(ξ|n))/(-n) = α = logm, for μ-almost every ξ. Our objective is to consider the exceptional points where the above display may fail. There is a nontrivial ‘thin’ spectrum for ̄d(μ,ξ) whenp1= P{Z= 1} > 0 andZhas finite moments of all positive orders. Because ̱d(μ,ξ) =afor all ξ, we obtain a ‘thick’ spectrum by introducing the ‘right’ power of a logarithm. In both cases, we find the Hausdorff dimension of the exceptional sets.

scholarly journals Small-Angle Scattering and Multifractal Analysis of DNA Sequences

2020 ◽  
Vol 21 (13) ◽  
pp. 4651
Author(s):  
Eugen Mircea Anitas
Keyword(s):  
Dna Sequences ◽  
Small Angle ◽  
Multifractal Analysis ◽  
Small Angle Scattering ◽  
Spatial Inhomogeneity ◽  
Chaos Game Representation ◽  
Model Based ◽  
Angle Scattering ◽  
Box Counting Dimension ◽  
Multifractal Spectra

The arrangement of A, C, G and T nucleotides in large DNA sequences of many prokaryotic and eukaryotic cells exhibit long-range correlations with fractal properties. Chaos game representation (CGR) of such DNA sequences, followed by a multifractal analysis, is a useful way to analyze the corresponding scaling properties. This approach provides a powerful visualization method to characterize their spatial inhomogeneity, and allows discrimination between mono- and multifractal distributions. However, in some cases, two different arbitrary point distributions, may generate indistinguishable multifractal spectra. By using a new model based on multiplicative deterministic cascades, here it is shown that small-angle scattering (SAS) formalism can be used to address such issue, and to extract additional structural information. It is shown that the box-counting dimension given by multifractal spectra can be recovered from the scattering exponent of SAS intensity in the fractal region. This approach is illustrated for point distributions of CGR data corresponding to Escherichia coli, Phospholamban and Mouse mitochondrial DNA, and it is shown that for the latter two cases, SAS allows extraction of the fractal iteration number and the scaling factor corresponding to “ACGT” square, or to recover the number of bases. The results are compared with a model based on multiplicative deterministic cascades, and respectively with one which takes into account the existence of forbidden sequences in DNA. This allows a classification of the DNA sequences in terms of random and deterministic fractals structures emerging in CGR.

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