Fractal Dimension and Self-Similarity of the Devil's Staircase in a Josephson-Junction Simulator

1984 ◽  
Vol 52 (6) ◽  
pp. 480-480 ◽  
Author(s):  
W. J. Yeh ◽  
Da-Ren He ◽  
Y. H. Kao
Keyword(s):  
Fractal Dimension ◽  
Josephson Junction ◽  
Self Similarity ◽  
Devil's Staircase ◽  
Devil’S Staircase

ARNOL’D TONGUES, DEVIL’S STAIRCASE, AND SELF-SIMILARITY IN THE DRIVEN CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1743-1753 ◽  
Author(s):  
LADISLAV PIVKA ◽  
ALEXANDER L. ZHELEZNYAK ◽  
LEON O. CHUA
Keyword(s):  
Initial Conditions ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Self Similarity ◽  
Devil's Staircase ◽  
Algebraic Form ◽  
Chua's Circuit ◽  
Recurrent Relations ◽  
Devil’S Staircase ◽  
Self Similar

Empirical recurrent relations, governing the structure of the devil’s staircase in the driven Chua’s circuit are given, which reflect the self-similar structure in an algebraic form. In particular, it turns out that the same formulas hold for both winding and period numbers, but with different “initial conditions”. Some of the finer details such as period-doubling along with numerous coexistence phenomena within staircases of mode-locked states have been revealed by computing high-resolution bifurcation diagrams.

scholarly journals Structured chaos in a devil's staircase of the Josephson junction

2014 ◽  
Vol 24 (3) ◽  
pp. 033115 ◽  
Author(s):  
Yu. M. Shukrinov ◽  
A. E. Botha ◽  
S. Yu. Medvedeva ◽  
M. R. Kolahchi ◽  
A. Irie
Keyword(s):  
Josephson Junction ◽  
Devil's Staircase ◽  
Devil’S Staircase

NMR spectra and relaxation in incommensurate systems in the presence of a devil's staircase

1985 ◽  
Vol 46 (7) ◽  
pp. 1205-1209 ◽  
Author(s):  
R. Blinc ◽  
S. Žumer ◽  
D.C. Ailion ◽  
J. Nicponski
Keyword(s):  
Nmr Spectra ◽  
Devil's Staircase ◽  
Devil’S Staircase

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

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