TWO-POINT RESISTANCES IN SAILBOAT FRACTAL NETWORKS

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050027
Author(s):  
JIALI ZHU ◽  
LI TIAN ◽  
JIAQI FAN ◽  
LIFENG XI
Keyword(s):  
Sum Rules ◽  
Recursive Algorithm ◽  
Effective Resistance ◽  
Substitution Principle ◽  
Self Similar ◽  
Fractal Network

The two-point resistance of fractal network has been studied extensively by mathematicians and physicists. In this paper, for a class of self-similar networks named sailboat networks, we obtain a recursive algorithm for computing resistance between any two nodes, using elimination principle, substitution principle and local sum rules on effective resistance.

scholarly journals Using fractal geometry for solving divide-and-conquer recurrences

1995 ◽  
Vol 37 (2) ◽  
pp. 145-171 ◽  
Author(s):  
Simant Dube
Keyword(s):  
Fractal Geometry ◽  
Recursive Function ◽  
Time Complexity ◽  
Recursive Algorithm ◽  
Dynamic Structure ◽  
Divide And Conquer ◽  
Function System ◽  
Fractal Image ◽  
Dimensional Measure ◽  
Self Similar

AbstractA relationship between the fractal geometry and the analysis of recursive (divide-and-conquer) algorithms is investigated. It is shown that the dynamic structure of a recursive algorithm which might call other algorithms in a mutually recursive fashion can be geometrically captured as a fractal (self-similar) image. This fractal image is defined as the attractor of a mutually recursive function system. It then turns out that the Hausdorff-Besicovich dimension D of such an image is precisely the exponent in the time complexity of the algorithm being modelled. That is, if the Hausdorff D-dimensional measure of the image is finite then it serves as the constant of proportionality and the time complexity is of the form Θ(nD), else it implies that the time complexity is of the form Θ(nD logpn), where p is an easily determined constant.

Infinitesimal resistance metrics on Sierpinski gasket type fractals

Analysis ◽  
2008 ◽  
Vol 28 (3) ◽  
Author(s):  
Mihai Cucuringu ◽  
Robert S. Strichartz
Keyword(s):  
Sierpinski Gasket ◽  
Periodic Points ◽  
Effective Resistance ◽  
Sierpiński Gasket ◽  
Boundary Points ◽  
Junction Points ◽  
Self Similar ◽  
Zoom In

We prove the existence of an infinitesimal resistance metric on the Sierpinski gasket (SG) at boundary points, junction points and periodic points. This is a renormalized limit of the effective resistance metric as we zoom in on the point, and satisfies a self-similar identity. We obtain similar results on PCF fractals with three boundary points.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar
Sign in / Sign up

Export Citation Format

Share Document