Emergence of fractal behavior in condensation-driven aggregation.

@article{Hassan2009EmergenceOF,
  title={Emergence of fractal behavior in condensation-driven aggregation.},
  author={M. Kamrul Hassan and M. Zahedul Hassan},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2009},
  volume={79 2 Pt 1},
  pages={
          021406
        }
}
  • M. K. Hassan, M. Hassan
  • Published 2009
  • Mathematics, Medicine, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We investigate the condensation-driven aggregation model that we recently proposed whereby an initial ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo aggregation upon collision. We solved the model exactly by using scaling theory for the case when a particle, say of size x , grows by an amount alphax over the time it takes to collide with another particle of any size. It is shown that the particle size spectra exhibit… Expand
3 Citations
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
Is there always a conservation law behind the emergence of fractal and multifractal?
  • M. K. Hassan
  • Mathematics
  • The European Physical Journal Special Topics
  • 2019
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
Dyadic Cantor set and its kinetic and stochastic counterpart
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 - pExpand

References

SHOWING 1-10 OF 45 REFERENCES
Condensation-driven aggregation in one dimension.
  • M. K. Hassan, M. Hassan
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
A model for aggregation where particles are continuously growing by heterogeneous condensation in one dimension, and it is shown that the particle size spectra exhibit a transition to dynamic scaling c(x,t) approximately t-beta phi(x/tz) . 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
Long-time crossover phenomena in coagulation kinetics.
TLDR
The numerical results indicate the presence of an intermediate-time regime of behavior in coagulation kinetics, which is characterized by effective exponents whose values are consistent with scaling, and new fluctuation-controlled kinetic behavior below an upper critical dimension equal to 2 is reported. 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
Droplet nucleation and Smoluchowski's equation with growth and injection of particles
We show that models for homogeneous and heterogeneous nucleation of D-dimensional droplets in a d-dimensional medium are described in mean-field by a modified Smoluchowski equation for theExpand
Transitional aggregation kinetics in dry and damp environments.
  • Krapivsky, Redner
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
The kinetics of constant-kernel aggregation is investigated, which is augmented by evaporation of monomers from clusters, and continuous cluster growth or condensation, termed aggregation in a ‘‘damp’’ environment. Expand
Multiscaling in stochastic fractals
Abstract We introduce a simple kinetic model describing the formation of a stochastic Cantor set in arbitrary spatial dimension d. In one dimension, the model exhibits scaling asymptotic behavior.Expand
Polymerization with freezing
Irreversible aggregation processes involving reactive and frozen clusters are investigated using the rate equation approach. In aggregation events, two clusters join irreversibly to form a largerExpand
Smoluchowski's equation for cluster exogenous growth
We consider an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with = Asβ. A physical example, dropwise condensation, is provided,Expand
Time scaling regimes in aggregation of magnetic dipolar particles: scattering dichroism results.
TLDR
It is shown that the number of aggregated particles displays a long-time power-law dependence with exponents that correspond to two different aggregation regimes that coincide with 3D and 1D-like aggregation. Expand
...
1
2
3
4
5
...