Dyadic Cantor set and its kinetic and stochastic counterpart

@article{Hassan2014DyadicCS,
  title={Dyadic Cantor set and its kinetic and stochastic counterpart},
  author={M. K. Hassan and N. I. Pavel and R. K. Pandit and J. Kurths},
  journal={Chaos Solitons \& Fractals},
  year={2014},
  volume={60},
  pages={31-39}
}
Abstract Firstly, we propose and investigate a dyadic Cantor set (DCS) and its kinetic counterpart where a generator divides an interval into two equal parts and removes one with probability ( 1 - p ) . The generator is then applied at each step to all the existing intervals in the case of DCS and to only one interval, picked with probability according to interval size, in the case of kinetic DCS. Secondly, we propose a stochastic DCS in which, unlike the kinetic DCS, the generator divides an… Expand

Figures from this paper

Multi-multifractality, dynamic scaling and neighbourhood statistics in weighted planar stochastic lattice
Abstract The dynamics of random sequential partitioning of a square into ever smaller mutually exclusive rectangular blocks, which we call weighted planar stochastic lattice (WPSL), is governed byExpand
Is there always a conservation law behind the emergence of fractal and multifractal?
Abstract One of the most basic ingredients of fractal or multifractal is its scale-invariance or self-similar property albeit they appear seemingly disordered or apparently bewildering. In thisExpand
Evolution through the stochastic dyadic Cantor Set: the uniqueness of mankind in the Universe
  • D. Mahecha
  • Physics
  • International Journal of Astrobiology
  • 2015
Abstract The search for intelligent life or any type of life involves processes with nonlinear chaotic behaviours throughout the Universe. Through the sensitive dependence condition, chaotic dynamicsExpand
On the Broader Sense of Life and Evolution: Its Mechanisms, Origin and Probability across the Universe
We consider connection between the mechanisms of evolution of life and the existence of conditions suitable for life in the universe. In particular we review the problem of calculating the number ofExpand

References

SHOWING 1-10 OF 31 REFERENCES
Multiscaling in Stochastic Fractals
The notion of a fractal has been widely used to describe self-similar structures [1]. The simplest way to construct a fractal is to repeat a given operation over and over again. The classical exampleExpand
Emergence of fractal behavior in condensation-driven aggregation.
  • M. K. Hassan, M. Hassan
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
It is shown that the particle size spectra exhibit transition to scaling c(x,t) approximately t;{-beta}varphi(xt{z}) accompanied by the emergence of a fractal of dimension d {f}=1/(1+2alpha) accompaniedBy using scaling theory for the case when a particle grows by an amount alphax over the time it takes to collide with another particle of any size. Expand
Multifractality and the shattering transition in fragmentation processes.
  • Hassan
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
A hierarchy of independent exponents suggest the existence of multiple phase boundary for the shattering transition when two orthogonal cracks are placed randomly on a fragments (Model A) and a unique exponent suggesting a single phase boundary when four equal sized fragments are produced at each fragmentation event is found. Expand
Random walk with shrinking steps
We outline the properties of a symmetric random walk in one dimension in which the length of the nth step equalsl, with l,1. As the number of steps N→`, the probability that the end point is at xExpand
Emergence of fractals in aggregation with stochastic self-replication.
TLDR
A simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication with dynamic scaling is proposed and investigated and it is shown analytically that the particle size distribution function exhibits dynamic scaling. Expand
FRACTAL DIMENSION AND DEGREE OF ORDER IN SEQUENTIAL DEPOSITION OF MIXTURE
We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . WeExpand
Fractals: Form, Chance and Dimension
This is the most extraordinarily beautiful book in thought and in form that I have read for many years, and that is all the more peculiar for its being a somewhat technically mathematical treatise.Expand
Wave propagation through Cantor-set media: chaos, scaling, and fractal structures.
TLDR
It is shown that transmission coefficients exhibit a local scaling behavior near complete transmission if the complete transmission is achieved at a wave number kappa=kappa* with a rational kappa*/pi. Expand
Kinetics of random sequential parking on a line
We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the knownExpand
Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term.
TLDR
The method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation with a source term for arbitrary homogeneous coagulation kernel to derive a "locality criterion," expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissible solution. Expand
...
1
2
3
4
...