Numerical Approaches of Cluster Statistics for Stochastic Manganese Deposits

2014 ◽  
Vol 69 (10-11) ◽  
pp. 581-588 ◽  
Author(s):  
Mehmet Bayirli
Keyword(s):  
Critical Exponent ◽  
Power Law ◽  
Distribution Functions ◽  
Scaling Properties ◽  
Manganese Clusters ◽  
Sedimentary Deposits ◽  
Manganese Deposits ◽  
The Subject ◽  
Numerical Approaches ◽  
Number Of Particles

AbstractIn terms of origin, the most important manganese deposits are sedimentary deposits which grow on the surface and/or fractures of the natural magnesite ore. They reveal various morphological characteristic according to their location in origin. Some of them may be fractal in appearance. Although several studies have been completed with regards to their growth mechanism, it may be safe to say that their cluster statistics and scaling properties have rarely been subject an academic scrutiny. Hence, the subject of this study has been designed to calculate cluster statistics of manganese deposits by first; transferring the images of manganese deposits into a computer and then scaling them with the help of software. Secondly, the root-mean square (rms) thickness (also called as expected value in systems), the number of particles, clusters and cluster sizes are computed by means of scaling method. In doing so it has been found that the rms thickness and the number of particles are in correlation, a result which is called as power-law behaviour, T~N-ε (the critical exponent is computed as ε = 1.743). It has also been found that the correlation between the number of clusters and their sizes are determined with the power-law behaviour n(s)~s-τ (the critical exponent t may vary between 1.054 and 1.321). Finally, the distribution functions of natural manganese clusters on the magnesite subtract have been determined. All that may point to the fact that the manganese deposits may be formed according to a Poisson distribution. The results found and the conclusion reached in this study may be used to compare various natural deposits in geophysics.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

Beyond the heuristic approach to Kolmogorov-Smirnov theorems

1982 ◽  
Vol 19 (A) ◽  
pp. 359-365 ◽  
Author(s):  
David Pollard
Keyword(s):  
Weak Convergence ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Heuristic Approach ◽  
Convergence Theory ◽  
Simple Method ◽  
Starting Point ◽  
Kolmogorov Smirnov ◽  
The Subject

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.

scholarly journals Crackling noise and avalanches in minerals

2021 ◽  
Vol 48 (5) ◽  
Author(s):  
Ekhard K. H. Salje ◽  
Xiang Jiang
Keyword(s):  
Electric Fields ◽  
Power Law ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fractal Dimensions ◽  
Similar Time ◽  
Scaling Properties ◽  
Pattern Formations ◽  
Observation Method ◽  
Great Complexity

AbstractThe non-smooth, jerky movements of microstructures under external forcing in minerals are explained by avalanche theory in this review. External stress or internal deformations by impurities and electric fields modify microstructures by typical pattern formations. Very common are the collapse of holes, the movement of twin boundaries and the crushing of biominerals. These three cases are used to demonstrate that they follow very similar time dependences, as predicted by avalanche theories. The experimental observation method described in this review is the acoustic emission spectroscopy (AE) although other methods are referenced. The overarching properties in these studies is that the probability to observe an avalanche jerk J is a power law distributed P(J) ~ J−ε where ε is the energy exponent (in simple mean field theory: ε = 1.33 or ε = 1.66). This power law implies that the dynamic pattern formation covers a large range (several decades) of energies, lengths and times. Other scaling properties are briefly discussed. The generated patterns have high fractal dimensions and display great complexity.

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

scholarly journals Distribution of the components of the building mixture in the presence of secondary raw materials during rotary mixing

2020 ◽  
Vol 220 ◽  
pp. 01060
Author(s):  
Anna Kapranova ◽  
Daria Bahaeva ◽  
Dmitry Stenko ◽  
Alexander Vatagin ◽  
Anton Lebedev ◽  
...  
Keyword(s):  
Raw Materials ◽  
Physical And Mechanical Properties ◽  
Distribution Functions ◽  
Stochastic Description ◽  
Rarefied Flows ◽  
Secondary Raw Materials ◽  
Characteristic Angle ◽  
Two Stages ◽  
The Given ◽  
Number Of Particles

The purpose of this study is a stochastic description of the distribution of solid dispersed components, including those from secondary raw materials, according to the characteristic angle of scattering ϴij when receiving a construction mixture at the first stage of operation of the rotary apparatus. Two stages of the formation of rarefied flows are assumed: when scattering particles of components by elastic blades of a rotating drum and when interacting with the baffle surface. Modeling method this is energy method of Klimontovich Yu.L. The analysis of the efficiency of the first stage (rotary mixing) is carried out based on the obtained distribution functions of the number of particles of bulk components over the scattering angle, taking into account their physical and mechanical properties and a variety of design and operating parameters of the apparatus. The bulk of the particles of the mixed components are scattered at the initial angles of rotation of the mixing drum, when the deformation of the elastic blades is most significant. This is accompanied by the characteristic first bursts of the obtained distribution curves (ϴij< 0.1 rad) for the number of particles of the tested bulk materials at the given ranges of parameters.

scholarly journals New insight on tide-dominated estuary and delta in the Eocene-Miocene Mrayt Group, North-Western Rif, Morocco

2021 ◽  
Author(s):  
Hamoumi Naima ◽  
choukri chacrone ◽  
Silvia Spezzaferri
Keyword(s):  
Sedimentary Facies ◽  
Carbonate Sediments ◽  
Sedimentary Deposits ◽  
Depositional Processes ◽  
Sea Level Fluctuation ◽  
The Subject ◽  
Depositional Systems ◽  
New Interpretation ◽  
Petrographic Study ◽  
North Western

The sedimentary deposits of Eocene-Miocene Mrayt Group, North-Western Rif, Morocco has been the subject of controversy by previous authors regarding their depositional environment. Detailed sedimentological study based on petrographic and sedimentary facies analysis, ichnofacies interpretation and paleocurrent measurements, leads to several results and new insights. Petrographic study provided the first evidence of mixed siliciclastic and carbonate sediments and their nomenclature: silty micrites, micritic siltstones, micritic sandstones, sandy micrite, and allochemic sandstones, as well as the nature of the sources and its geological context. Twenty two sedimentary facies that have never been described before are identified, and based on their succession and association a new interpretation of depositional processes and depositional systems are proposed. The paleoenvironments of the Mrayt Group are interpreted as littoral and shallow marine settings: tides- dominated estuary, tides-dominated delta systems and open coast tidal flat, under complex hydrodynamics strongly influenced by river discharge, tidal currents, waves and storms action.Sedimentation occurred in “the Maghrebian basin” under the interplay of: i) tectonics related to the Cenozoic collision of the African and Eurasian continental plates, ii) Cenozoic alternation of warm climate and cooling due to the increasing influence of Antarctica glaciation, iii) sediments supplies induced by rejuvenation of sedimentary sources and iv) sea level fluctuation related to the advance and retreat of ice-sheet on Antarctica.

On Higher-Order Crack-Tip Fields in Creeping Solids

1999 ◽  
Vol 67 (2) ◽  
pp. 372-382 ◽  
Author(s):  
B. N. Nguyen ◽  
P. R. Onck ◽  
E. van der Giessen
Keyword(s):  
Power Law ◽  
Crack Tip ◽  
Small Strain ◽  
Higher Order ◽  
Single Edge ◽  
Constraint Effect ◽  
Scaling Properties ◽  
Crack Tip Fields ◽  
Asymptotic Development ◽  
Loading Parameter

In view of the near-tip constraint effect imposed by the geometry and loading configuration, a creep fracture analysis based on C* only is generally not sufficient. This paper presents a formulation of higher-order crack-tip fields in steady power-law creeping solids which can be derived from an asymptotic development of near-tip fields analogous to that of Sharma and Aravas and Yang et al. for elastoplastic bodies. The higher-order fields are controlled by a parameter named A2*, similar as in elastoplasticity, and a second loading parameter, σ∞. By means of the scaling properties for power-law materials, it is shown that A2* for a flat test specimen is independent of the loading level. Finally, we carry out small-strain finite element analyses of creep in single-edge notched tension, centered crack panel under tension, and single-edge notched bending specimens in order to determine the corresponding values of A2* for mode I cracks under plane-strain conditions. [S0021-8936(00)01202-2]

scholarly journals IDEAL-MODIFIED BOSONIC GAS TRAPPED IN AN ARBITRARY THREE-DIMENSIONAL POWER-LAW POTENTIAL

2012 ◽  
Vol 27 (31) ◽  
pp. 1250181 ◽  
Author(s):  
E. CASTELLANOS ◽  
C. LÄMMERZAHL
Keyword(s):  
Dispersion Relation ◽  
Power Law ◽  
Three Dimensional ◽  
Particle Dispersion ◽  
Einstein Condensate ◽  
Gravity Models ◽  
Condensation Temperature ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose–Einstein condensate trapped in a generic three-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. In addition, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.

GROWTH OF COLLOIDAL CRYSTALS UNDER MICROGRAVITY

2002 ◽  
Vol 16 (01n02) ◽  
pp. 338-345 ◽  
Author(s):  
M. ISHIKAWA ◽  
H. MORIMOTO ◽  
T. OKUBO ◽  
T. MAEKAWA
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Brownian Dynamics ◽  
Normal Gravity ◽  
Colloidal Crystals ◽  
Growth Dynamics ◽  
Sounding Rocket ◽  
Microgravity Experiment ◽  
Colloidal Crystallization ◽  
Number Of Particles

The growth dynamics of colloidal crystallization was evaluated under sedimentation free conditions using sounding rocket and Brownian Dynamics (BD) simulation. The Bragg's reflections of colloidal crystals were measured during microgravity flight and average sizes of crystallites were obtained by the Sherrer's method. Results showed a power-law relationship between size and time, L ∝ tα where L is the size of crystallites and t is time. The obtained α s were 0.33 ± 0.03 in microgravity and 0.25 ± 0.02 in normal gravity, respectively. Browninan Dynamics (BD) simulation showed the time evolution of ordered domains that consisted of connected structures of crystalline clusters. The power law relationship n ∝ t0.5 in post-nucleation period was confirmed between the number of particles (n) in clusters and time. The calculated power was related to α using the fractal dimension of crystalline clusters and α = 0.31 was obtained. The value was matched well with that of the microgravity experiment.

scholarly journals Discrete Source Synthesis of the X-Ray Background

1980 ◽  
Vol 92 ◽  
pp. 233-233 ◽  
Author(s):  
A. Cavaliere ◽  
L. Danese ◽  
G. De Zotti ◽  
A. Franceschini
Keyword(s):  
Power Law ◽  
Energy Content ◽  
High Energy ◽  
Discrete Source ◽  
Distribution Functions ◽  
Mean Values ◽  
X Ray ◽  
X Ray Background ◽  
Luminosity Evolution

The recent deep X-ray surveys suggest that discrete sources comprise most, if not all, of the energy content of the background (cf. Giacconi, this volume). We have shown that, if sources have flat power law spectra and relatively sharp high-energy cutoffs, their combined emission can also mimic very accurately its extended (2 - 400 keV) spectral shape. A broad distribution of cutoff energies Ec is required, in this case, to model the high-energy (E ≳ 20 - 40 keV) part: a power law envelope of distribution functions of various types of sources can be envisaged; alternatively, the well-known fact that most of the 2 − 10 keV background should be produced by low flux, low Ec sources can suggest that Ec ∝ (1 + z)−η. The quality of the fit turns out to be not very sensitive to the amount of number/luminosity evolution assumed, though the minimum χ2 test slightly favours strongly evolving sources. In the case of differential luminosity ∝ E−γ and evolution ∝ (1 + z)α with 0 ≤ α ≤ 6, the best fits to pre HEAO-1 data are obtained for mean values of the spectral index γ ≈ 0.5 − 0.9 and for dispersions Δγ ≃ 0.5 - 0.7. Rather wide ranges of values of γ and Δγ are, however, still allowed; e.g., for α = 6, the allowed intervals are 0.2 ≤ γ ≤ 1.3, 0 ≤ Δγ ≤ 0.7.

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