# Emergence of fractal behavior in condensation-driven aggregation.

@article{Hassan2009EmergenceOF, title={Emergence of fractal behavior in condensation-driven aggregation.}, author={M. K. Hassan and M. Hassan}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={79 2 Pt 1}, pages={ 021406 } }

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.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2013

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?

- Mathematics
- 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 this… Expand

Dyadic Cantor set and its kinetic and stochastic counterpart

- Mathematics, Physics
- 2014

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… Expand

#### References

SHOWING 1-10 OF 45 REFERENCES

Condensation-driven aggregation in one dimension.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2008

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

- Physics
- 1997

We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We… Expand

Long-time crossover phenomena in coagulation kinetics.

- Physics, Medicine
- Physical review. A, General physics
- 1986

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.

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

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

- Mathematics, Physics
- 1998

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 the… Expand

Transitional aggregation kinetics in dry and damp environments.

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

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

- Physics
- 1994

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

- Chemistry, Physics
- 2005

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 larger… Expand

Smoluchowski's equation for cluster exogenous growth

- Physics
- 1997

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.

- Physics, Medicine
- Physical review letters
- 2001

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