A DIMENSION FORMULA FOR SELF-SIMILAR AND SELF-AFFINE FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 525-531 ◽  
Author(s):  
GREG HUBER ◽  
MOGENS H. JENSEN ◽  
KIM SNEPPEN
Keyword(s):  
Time Series ◽  
Size Distribution ◽  
Fragment Size ◽  
General Relation ◽  
Fractal Dimensions ◽  
Directed Percolation ◽  
Fragment Size Distribution ◽  
Scaling Properties ◽  
Dimension Formula ◽  
Self Similar

A geometric and very general relation between the size distribution and the fractal dimensions of a set of objects is presented. The applications are numerous, ranging from fragmentation experiments to time series. For example, it may be used to understand the fragment-size distribution of fragmenting gypsum. The formalism also generalizes to self-affine fractals, and here it is applied to the scaling properties of self-interactions in (1+1)-d directed percolation.

scholarly journals Fractal Characteristic of Rock Cutting Load Time Series

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hongxiang Jiang ◽  
Changlong Du ◽  
Songyong Liu ◽  
Kuidong Gao
Keyword(s):  
Time Series ◽  
Size Distribution ◽  
Fragment Size ◽  
Fractal Theory ◽  
Rock Cutting ◽  
Water Jet ◽  
Fragment Size Distribution ◽  
Fractal Characteristic ◽  
Box Counting ◽  
Box Counting Dimension

A test-bed was developed to perform the rock cutting experiments under different cutting conditions. The fractal theory was adopted to investigate the fractal characteristic of cutting load time series and fragment size distribution in rock cutting. The box-counting dimension for the cutting load time series was consistent with the fractal dimension of the corresponding fragment size distribution, which indicated that there were inherent relations between the rock fragmentation and the cutting load. Furthermore, the box-counting dimension was used to describe the fractal characteristic of cutting load time series under different conditions. The results show that the rock compressive strength, cutting depth, cutting angle, and assisted water-jet types all have no significant effect on the fractal characteristic of cutting load. The box-counting dimension can be an evaluation index to assess the extent of rock crushing or cutting. Rock fracture mechanism would not be changed due to water-jet in front of or behind the cutter, but it would be changed when the water-jet was in cutter.

scholarly journals Fragmentation as an aggregation process

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150678 ◽  
Author(s):  
A. Vledouts ◽  
N. Vandenberghe ◽  
E. Villermaux
Keyword(s):  
Size Distribution ◽  
First Principles ◽  
Self Assembly ◽  
Fragment Size ◽  
Similar Distribution ◽  
Fragment Size Distribution ◽  
One Dimensional ◽  
Complicated Process ◽  
Self Similar ◽  
Individual Particles

When severely impacted, a cohesive object deforms and eventually breaks into fragments. Cohesion forces keeping the material together and momentum driving the fragmentation couple through a complicated process involving crack propagation on a deforming substrate, so that a comprehensive scenario for the build-up of the full fragment size distribution of broken objects is still lacking. We use necklaces of cohesive particles (magnetized spheres) as an experimental model of a one-dimensional material, which we expand radially in an impulsive way. Exploring in real time the intermediate state where the particles are no longer in contact, but still in interaction as they separate, we demonstrate that the final fragments result from the self-assembly of individual particles and that their size distribution converges to a stable self-similar distribution whose parameters, interpreted from first principles, depend on the expansion and cohesion strengths.

NEW UNIVERSALITY CLASS OF IMPACT FRAGMENTATION

Fractals ◽  
2003 ◽  
Vol 11 (04) ◽  
pp. 369-376 ◽  
Author(s):  
HAJIME INAOKA ◽  
MAREKAZU OHNO
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Fragment Size ◽  
Universality Class ◽  
Fragment Size Distribution ◽  
Space Filling ◽  
Impact Fragmentation

We conducted a set of experiments of impact fragmentation of samples with voids, such as pumice stones and bricks. We discovered that the fragment size distribution follows a power law, but that the exponent of the distribution is different from that of the distribution by the fragmentation of a space-filling sample like a gypsum ball. The value of the exponent is about 0.9. And the value seems universal for samples with voids.

scholarly journals Fragment Size Distribution in Blasting

2003 ◽  
Vol 44 (5) ◽  
pp. 951-956 ◽  
Author(s):  
Sang Ho Cho ◽  
Masaaki Nishi ◽  
Masaaki Yamamoto ◽  
Katsuhiko Kaneko
Keyword(s):  
Size Distribution ◽  
Fragment Size ◽  
Fragment Size Distribution

scholarly journals Fragment size distribution statistics in dynamic fragmentation of laser shock-loaded tin

AIP Advances ◽  
2017 ◽  
Vol 7 (6) ◽  
pp. 065306 ◽  
Author(s):  
Weihua He ◽  
Jianting Xin ◽  
Yongqiang Zhao ◽  
Genbai Chu ◽  
Tao Xi ◽  
...  
Keyword(s):  
Size Distribution ◽  
Fragment Size ◽  
Laser Shock ◽  
Fragment Size Distribution ◽  
Dynamic Fragmentation

Drop breakup and fragment size distribution in shear flow

2003 ◽  
Vol 47 (5) ◽  
pp. 1283-1298 ◽  
Author(s):  
V. Cristini ◽  
S. Guido ◽  
A. Alfani ◽  
J. Bławzdziewicz ◽  
M. Loewenberg
Keyword(s):  
Shear Flow ◽  
Size Distribution ◽  
Fragment Size ◽  
Fragment Size Distribution ◽  
Drop Breakup
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