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Condensates in driven aggregation processes.

E Ben-Naim1, P L Krapivsky

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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Mass injection drives aggregation, leading to growing clusters. Analytic results reveal distinct phases and power-law distributions for cluster sizes based on aggregation rates, impacting system dynamics.

Area of Science:

  • Physics
  • Chemistry
  • Materials Science

Background:

  • Stochastic processes are fundamental in understanding complex systems.
  • Aggregation phenomena are observed across various scientific disciplines.

Purpose of the Study:

  • To investigate aggregation dynamics driven by continuous mass injection.
  • To analyze the impact of different aggregation rates on cluster size distributions.

Main Methods:

  • Analytical investigation of a stochastic aggregation model.
  • Examination of three classic aggregation rate kernels: constant, proportional to sum of sizes, and proportional to product of sizes.
  • Characterization of system phases (condensate and cluster) and cluster size distributions.

Main Results:

Related Experiment Videos

  • For constant aggregation rates, cluster size distribution decays exponentially.
  • For aggregation rates proportional to i+j or i*j, two distinct phases emerge: a condensate phase and a cluster phase.
  • In the condensate phase (r<2) and cluster phase (r>2), cluster size distributions exhibit power-law tails (c{k} ~ k^{-gamma}) when K{i,j} is proportional to i+j.

Conclusions:

  • The injection rate significantly influences the exponent of the power-law tail in cluster size distributions.
  • The study provides insights into the phase transitions and scaling behaviors of aggregating systems under continuous mass addition.