An analysis of the fragmentation of remolded soils, with regard to self-mulching behavior

Soil Research ◽  
1995 ◽  
Vol 33 (4) ◽  
pp. 569 ◽  
Author(s):  
CD Grant ◽  
CW Watts ◽  
AR Dexter ◽  
BS Frahn
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Aggregate Size ◽  
Physical Significance ◽  
Size Distributions ◽  
Wetting And Drying ◽  
Remoulded Soil ◽  
Power Law Function ◽  
D Values ◽  
Range Of Values

A power-law relation was used to analyse the (mass-derived) number-size distributions of fragments generated by wetting and drying remoulded soils. Various soils from Europe and Australia produced a range of values for the two fragmentation coefficients, d and k, generated by the power-law function. Both coefficients had physical significance with respect to self-mulching behaviour. Likened to a fractal dimension, the d coefficient varied directly with the tendency of the remoulded soil to fragment during wetting and drying. Assessment of the number of generated fragments >1 cm was made with the k coefficient. Consideration of both coefficients together in a plot of k v. d enabled similar soils to be grouped and falsely large values of d to be identified; k values were small for limited fragmentations even if the size distribution of the fragments that were produced gave large values of d. Most strongly self-mulching soils produced d values >1 . 5 after three wet/dry cycles, and k values that increased sharply after one cycle and declined with subsequent wetting and drying. Other soils with lesser abilities to self-mulch generally produced smaller d values and more variable k values. Reasonable correlations were found between these two coefficients and other measurements of self-mulching behaviour, particularly after three cycles of wetting/drying. Examination of the aggregate size distributions produced from remoulded soils in this way offers the potential to understand more clearly the dynamics of structure regeneration in soils exhibiting various degrees of self-mulching behaviour.

Unbiased estimation of the fractal dimension of soil aggregate size distributions

1994 ◽  
Vol 31 (2-3) ◽  
pp. 187-198 ◽  
Author(s):  
E. Perfect ◽  
B.D. Kay ◽  
V. Rasiah
Keyword(s):  
Fractal Dimension ◽  
Aggregate Size ◽  
Soil Aggregate ◽  
Unbiased Estimation ◽  
Size Distributions

Evaluation of Flaw Size Distributions Responsible for Size Effects in Strength of Small-Scale MEMS Specimens

2007 ◽  
Vol 121-123 ◽  
pp. 1425-1428
Author(s):  
Kai Duan ◽  
Xiao Zhi Hu
Keyword(s):  
Power Law ◽  
Structural Integrity ◽  
Single Crystal Silicon ◽  
Flaw Size ◽  
Small Scale ◽  
Size Distributions ◽  
Mems Devices ◽  
Crystal Silicon ◽  
Power Law Function ◽  
Increased Strength

This paper describes a statistical method for evaluating the surface flaw distributions responsible for the improved strength and reliability of small-scale MEMS specimens. The method uses a power-law function, which, though empirical in form, is consistent with the conventional two-parameter Weibull distribution, to approximate the flaw size distributions on specimen tensile surfaces. The parameters in the power-law function are determined from Weibull strength plots. Literature data for single-crystal silicon beam specimens covering a range of widths from mm to nm are analyzed using this method. The analysis indicates a reduction in scatter in addition to increase in strength with diminishing specimen size, and quantifies a systematic tightening in flaw distribution associated with refinement in fabrication method and the limitations of physical sizes on flaw dimensions, which is consistent with the experimental observations. Furthermore, the implications of the increased strength and reduced strength scatter to the processing techniques and structural integrity of MEMS devices are discussed.

Undersampling power-law size distributions: effect on the assessment of extreme natural hazards

2014 ◽  
Vol 72 (2) ◽  
pp. 565-595 ◽  
Author(s):  
Eric L. Geist ◽  
Tom Parsons
Keyword(s):  
Natural Hazards ◽  
Power Law ◽  
Size Distributions

scholarly journals The fractal dimension of the tree of life

2014 ◽  
Author(s):  
Xiaofei Lv ◽  
Yuping Wu ◽  
Bin Ma
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Dimensions ◽  
Predictive Modelling ◽  
Tree Of Life ◽  
Fundamental Question ◽  
Theoretical Studies ◽  
Structure Pattern ◽  
Intermediate Size ◽  
Taxonomic Groups

The structure pattern of the tree of life clues on the key ecological issues; hence knowing the fractal dimension is the fundamental question in understanding the tree of life. Yet the fractal dimension of the tree of life remains unclear since the scale of the tree of life has hypergrown in recent years. Here we show that the tree of life display a consistent power-law rules for inter- and intra-taxonomic levels, but the fractal dimensions were different among different kingdoms. The fractal dimension of hierarchical structure (Dr) is 0.873 for the entire tree of life, which smaller than the values of Dr for Animalia and Plantae but greater than the values of Dr for Fungi, Chromista, and Protozoa. The hierarchical fractal dimensions values for prokaryotic kingdoms are lower than for other kingdoms. The Dr value for Viruses was lower than most eukaryotic kingdoms, but greater than prokaryotes. The distribution of taxa size is governed by fractal diversity but skewed by overdominating taxa with large subtaxa size. The proportion of subtaxa in taxa with small and large sizes was greater than in taxa with intermediate size. Our results suggest that the distribution of subtaxa in taxa can be predicted with fractal dimension for the accumulating taxa abundance rather than the taxa abundance. Our study determined the fractal dimensions for inter- and intra-taxonomic levels of the present tree of life. These results emphases the need for further theoretical studies, as well as predictive modelling, to interpret the different fractal dimension for different taxonomic groups and skewness of taxa with large subtaxa size.

scholarly journals Power Law Size Distributions in Geoscience Revisited

2019 ◽  
Author(s):  
Álvaro Corral ◽  
Álvaro González
Keyword(s):  
Power Law ◽  
Size Distributions

scholarly journals Almost additive entropy

2014 ◽  
Vol 11 (05) ◽  
pp. 1450040 ◽  
Author(s):  
Nikos Kalogeropoulos
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Power Law ◽  
Physical Significance ◽  
Small Deviations ◽  
Phase Space Volume ◽  
Composition Property ◽  
Flat Manifolds ◽  
Special Case ◽  
Space Volume

We explore consequences of a hyperbolic metric induced by the composition property of the Harvda–Charvat/Daróczy/Cressie–Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter q ≈ 1 from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.

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 Unveiling the Evolution of Type I AGNs in the IR (15μm) — As Seen by ISO in the ELAIS-S1 Region

2002 ◽  
Vol 184 ◽  
pp. 167-172
Author(s):  
Israel Matute ◽  
Fabio La Franca ◽  
Carlotta Gruppioni ◽  
Francesca Pozzi ◽  
Carlo Lari
Keyword(s):  
Power Law ◽  
Luminosity Function ◽  
Evolution Model ◽  
Cosmological Evolution ◽  
Type I ◽  
Infrared Background ◽  
Power Law Function ◽  
Cosmic Infrared Background ◽  
Luminosity Evolution

AbstractWe present the first estimate of the evolution of type 1 AGNs in the IR (15 μm) obtained from the ELAIS survey in the S1 region. We find that the luminosity function (LF) of Type 1 AGNs at 15μm is fairly well represented by a double power-law function with a bright slope of 2.9 and a faint slope of 1.1. There is evidence for significant cosmological evolution according to a pure luminosity evolution model L15(z)α(l+z)k, with in a (Ωm,ΩΛ)=(1.0,0.0) cosmology. This evolution is similar to what is observed at other wavebands. From the luminosity function and its evolution, we estimate a contribution of ~ 2% from Type 1 AGN to the total Cosmic Infrared Background (CIRB) at 15 μm.

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