scholarly journals An Approximative Calculation of the Fractal Structure in Self-Similar Tilings

2011 ◽  
Vol E94-A (2) ◽  
pp. 846-849 ◽  
Author(s):  
Yukio HAYASHI
Keyword(s):  
Fractal Structure ◽  
Self Similar

scholarly journals Turbulence and magnetic fields in molecular clouds

1991 ◽  
Vol 147 ◽  
pp. 83-92
Author(s):  
R. N. Henriksen
Keyword(s):  
Magnetic Fields ◽  
Wavelet Analysis ◽  
Molecular Clouds ◽  
Fractal Structure ◽  
Compressible Turbulence ◽  
Dynamo Theory ◽  
First Results ◽  
Self Similar

in this paper I first review some of the simple structural concepts associated with compressible turbulence. In particular the hierarchical or self-similar fractal structure to be expected is formulated in a manner readily compared to the observations, and to previous work. In the next section I present the first results of a wavelet analysis on molecular clouds, which seem to comfirm the hierarchical scaling. I conclude with an extention of the theory to include magnetic fields. This latter theory represents an alternative to the more conventional dynamo theory.

A fractal continuum model of the pulmonary arterial tree

1992 ◽  
Vol 72 (6) ◽  
pp. 2225-2237 ◽  
Author(s):  
G. S. Krenz ◽  
J. H. Linehan ◽  
C. A. Dawson
Keyword(s):  
Fractal Structure ◽  
Cumulative Distribution ◽  
Total Resistance ◽  
Arterial Tree ◽  
Vascular Volume ◽  
Capillary Bed ◽  
Pulmonary Arterial ◽  
Self Similar ◽  
The Mean ◽  
Level Order

The extant morphometric data from the intrapulmonary arteries of dog, human, and cat lungs produce graphs of the log of the vessel number, (N) or length (l) in each level vs. the log of the mean diameter (D) in each level that are sufficiently linear to suggest that a scale-independent self-similar or fractal structure may underlie the observed relationships. These data can be correlated by the following formulas: Nj = a1Dj-beta 1, and lj = a2Dj beta 2, where j denotes the level (order or generation) number measured from the largest vessel at the entrance to the arterial tree to the smallest vessel at the entrance to the capillary bed. With the hemodynamic resistance (R) represented by Rj = 128 microliterj/(Nj pi Dj4) and the vascular volume (Q) by Qj = Nj pi Dj2lj/4, the continuous cumulative distribution of vascular resistance (Rcum) vs. cumulative vascular volume (Qcum) (where Rcum and Qcum represent the total resistance or volume, respectively, upstream from the jth level) can be calculated from [formula: see text] where r = Dj/Dj+1 is a constant independent of j. Analogous equations are developed for the inertance and compliance distributions, providing simple formulas to represent the hemodynamic consequences of the pulmonary arterial tree structure.

ON THE FRACTAL STRUCTURE OF ELECTRON AVALANCHES

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 939-946 ◽  
Author(s):  
Z. DONKÓ ◽  
I. PÓCSIK
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Inelastic Collision ◽  
Fractal Structure ◽  
Secondary Electrons ◽  
Electron Multiplication ◽  
Helium Gas ◽  
Self Similar ◽  
Collision Processes ◽  
Electron Avalanches

The motion of electrons in helium gas in the presence of a homogeneous external electric field was studied. Moving between the two electrodes, the electrons participate in elastic and inelastic collision processes with gas atoms. In ionizing collisions, secondary electrons are also created and in this way self-similar electron avalanches build up. The statistical distribution of the fractal dimension and electron multiplication of electron avalanches was obtained based on the simulation of a large number of electron avalanches. The fractal dimension shows a power-law dependence on electron multiplication with an exponent of ≈0.33.

scholarly journals Study on tumor cell RNA cross-anticancer mechanism in non-tumor mice experimental model

2018 ◽  
Author(s):  
Qiwang Xu
Keyword(s):  
Tumor Cell ◽  
Fractal Structure ◽  
Basic Research ◽  
Tissue Response ◽  
Biological Behavior ◽  
Cross Resistance ◽  
Specific Procedure ◽  
Anticancer Mechanism ◽  
Self Similar ◽  
Play Action

ABSTRACTTo report the experiments of fractal structure and self-similar function in biological coupled oscillation brings life system waving growth in life organism. At the same time by self-organization the system openness come into being to maintain stability features of growth survival. From this, the orderly oscillation of tumor cell RNA was recognized that this process could lead to system sequentiality openness. According to waving growth of basic research the procedure could be sure to turn into a model as out of control of growing in tumor. Then in complete contrast that derived from the same component which have cross resistance effect. It shows that its biological behavior is converted as only a single physical power to play action by inactivated processing. Subsequent further confirms the essential roles whether essential roles link up with recovery of physiological function. The result in that it could exhibit feature of anticancer owing to be endowed tissue embryonization response. So that it also exerts preventing on senile chronic diseases. In theory, the concept of this tissue response in life organism closely link up with the single physical power of RNA component so as to bring up specific procedure of growing and subsisting that deal with keeping life vigor generalized explanatory.

Fractal structure and hydration-driven shape memory of duck down in the dry–wet state

2021 ◽  
pp. 004051752110600
Author(s):  
Wei-dong Yu ◽  
Zhaoqun Du ◽  
Hongling Liu ◽  
Weidong Yu
Keyword(s):  
Shape Memory ◽  
Fractal Structure ◽  
Fiber Diameter ◽  
Synthetic Polymers ◽  
Natural State ◽  
Filling Material ◽  
Bifurcation Structure ◽  
Heat Setting ◽  
Memory Mechanism ◽  
Self Similar

Duck down, as a natural keratin material, has been widely used as a filling material. The multilevel bifurcation structure of down has been observed and characterized through scanning electron microscopy. The structure is a complex fractal structure composed of four-level self-similar structures including five units, that is, the calamus, main barb, barb, barbule, and node or prong. The differential friction effect of the dynamic friction coefficients of the barb was reduced from 0.4 (dry state) to 0.23 (wet state), namely a decrease of 42.5%. The friction locking effect decreases due to the swelling of the fiber diameter. The down is zero gravity in water, and under the action of vibration and internal stress, down that has been subjected to friction or heat setting treatment can quickly return to its original shape in water. This shape memory mechanism was further confirmed, in which down after heat setting can restore its shape to the natural state by shaking it quickly and vigorously. This research provides inspiration to investigate more complicated functions of natural materials and encourages the creation of very intelligent synthetic polymers.

scholarly journals Nucleotide spacing distribution analysis for human genome

2021 ◽  
Author(s):  
Andrzej Z. Górski ◽  
Monika Piwowar
Keyword(s):  
Human Genome ◽  
Long Range ◽  
Short Range ◽  
Fractal Structure ◽  
Random Sequence ◽  
Distribution Analysis ◽  
Long Range Correlations ◽  
Spacing Distribution ◽  
Self Similar ◽  
Characteristic Features

AbstractThe distribution of nucleotides spacing in human genome was investigated. An analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution has no self-similar (fractal) structure. The results nevertheless revealed several characteristic features: (i) the distribution for short-range spacing is quite similar to the purely stochastic sequences; (ii) the distribution for long-range spacing essentially deviates from the random sequence distribution, showing strong long-range correlations; (iii) the differences between (A, T) and (C, G) nucleotides are quite significant; (iv) the spacing distribution displays tiny oscillations.

scholarly journals Combinatorial configurations, fractals, fractal dimension of combinatorial sets

2021 ◽  
pp. 170-174
Author(s):  
Nadija Tymofijeva
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
Self Similar ◽  
Combinatorial Configurations

Combinatorial configurations and their sets are considered. The definitions of these objects are given, recurrent combinatorial operators are introduced, with the help of which they are formed, and rules are formulated according to which their sets are ordered. The property of periodicity, which takes place in the generation of combinatorial configurations, is described. It follows from the recurrent way of their formation and ordering. The fractal structure of combinatorial sets is formed due to the described rules, in which the property of periodicity is used. Analysis of these structures shows that they are self-similar, both finite and infinite, which is characteristic of fractals. Their fractal dimension is introduced, which follows from the rules of generating combinatorial configurations and corresponds to the number of these objects in their set.

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