ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

ASYMPTOTIC FORMULA OF ECCENTRIC DISTANCE SUM FOR VICSEK NETWORK

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850027 ◽  
Author(s):  
QIANQIAN YE ◽  
LONG HE ◽  
QIN WANG ◽  
LIFENG XI
Keyword(s):  
Asymptotic Formula ◽  
The Self ◽  
Self Similarity ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

In this work, we study the eccentric distance sum of Vicsek networks. To obtain the eccentric distance sum of networks, we investigate the corresponding integral on self-similar measure for Vicsek fractals. We use the self-similarity of distance and measure to solve the integral.

AVERAGE GEODESIC DISTANCE OF NODE-WEIGHTED SIERPINSKI NETWORKS

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950110
Author(s):  
LIFENG XI ◽  
QIANQIAN YE ◽  
JIANGWEN GU
Keyword(s):  
Asymptotic Formula ◽  
Geodesic Distance ◽  
Sierpinski Gasket ◽  
Weight Vector ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar

This paper discusses the asymptotic formula of average distances on node-weighted Sierpinski skeleton networks by using the integral of geodesic distance in terms of self-similar measure on the Sierpinski gasket with respect to the weight vector.

AVERAGE GEODESIC DISTANCE OF SIERPINSKI GASKET AND SIERPINSKI NETWORKS

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750044 ◽  
Author(s):  
SONGJING WANG ◽  
ZHOUYU YU ◽  
LIFENG XI
Keyword(s):  
Complex Networks ◽  
Finite Type ◽  
Geodesic Distance ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Geodesic Distances

The average geodesic distance is concerned with complex networks. To obtain the limit of average geodesic distances on growing Sierpinski networks, we obtain the accurate value of integral in terms of average geodesic distance and self-similar measure on the Sierpinski gasket. To provide the value of integral, we find the phenomenon of finite pattern on integral inspired by the concept of finite type on self-similar sets with overlaps.

From 1 → 3 dendritic designs to fractal supramacromolecular constructs: understanding the pathway to the Sierpiński gasket

2015 ◽  
Vol 44 (12) ◽  
pp. 3954-3967 ◽  
Author(s):  
George R. Newkome ◽  
Charles N. Moorefield
Keyword(s):  
Self Assembly ◽  
Sierpinski Gasket ◽  
Building Blocks ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket

The potential to incorporate dendritic characteristics, such as self-similarity into new fractal-based materials is exemplified in the self-assembly of novel, polyterpyridine-based, building blocks.

scholarly journals SPECTRA OF SELF-SIMILAR LAPLACIANS ON THE SIERPINSKI GASKET WITH TWISTS

Fractals ◽  
2008 ◽  
Vol 16 (01) ◽  
pp. 43-68 ◽  
Author(s):  
ANNA BLASIAK ◽  
ROBERT S. STRICHARTZ ◽  
BARIS EVREN UGURCAN
Keyword(s):  
Sierpinski Gasket ◽  
Outer Approximation ◽  
Invariant Set ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Constant Multiple ◽  
Self Similar ◽  
Definition Of ◽  
Two Parameter ◽  
Present Experimental Evidence

We study the spectra of a two-parameter family of self-similar Laplacians on the Sierpinski gasket (SG) with twists. By this we mean that instead of the usual IFS that yields SG as its invariant set, we compose each mapping with a reflection to obtain a new IFS that still has SG as its invariant set, but changes the definition of self-similarity. Using recent results of Cucuringu and Strichartz, we are able to approximate the spectra of these Laplacians by two different methods. To each Laplacian we associate a self-similar embedding of SG into the plane, and we present experimental evidence that the method of outer approximation, recently introduced by Berry, Goff and Strichartz, when applied to this embedding, yields the spectrum of the Laplacian (up to a constant multiple).

Fractal sequences derived from the self-similar extensions of the Sierpinski gasket

1988 ◽  
Vol 21 (8) ◽  
pp. 1925-1928 ◽  
Author(s):  
A Lakhtakia ◽  
R Messier ◽  
V K Varadan ◽  
V V Varadan
Keyword(s):  
Sierpinski Gasket ◽  
The Self ◽  
Sierpiński Gasket ◽  
Self Similar

NODE-WEIGHTED AVERAGE FERMAT DISTANCES OF FRACTAL TREE NETWORKS

Fractals ◽  
2021 ◽  
Author(s):  
CHEN CHEN ◽  
YING MA ◽  
LIFENG XI
Keyword(s):  
Asymptotic Formula ◽  
Weighted Average ◽  
The Self ◽  
Similar Measure ◽  
Tree Networks ◽  
Self Similar

In this paper, we investigate a class of self-similar networks modeled on a self-similar fractal tree, and use the self-similar measure and the method of finite pattern to obtain the asymptotic formula of node-weighted average Fermat distances on fractal tree networks.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

WEIGHTED AVERAGE GEODESIC DISTANCE OF PENTADENDRITE NETWORKS

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050075
Author(s):  
YUANYUAN LI ◽  
XIAOMIN REN ◽  
KAN JIANG
Keyword(s):  
Complex Networks ◽  
Geodesic Distance ◽  
Average Distance ◽  
Weighted Average ◽  
Similar Measure ◽  
Important Index ◽  
Self Similar

The average geodesic distance is an important index in the study of complex networks. In this paper, we investigate the weighted average distance of Pentadendrite fractal and Pentadendrite networks. To provide the formula, we use the integral of geodesic distance in terms of self-similar measure with respect to the weighted vector.

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