Exact Combinatorial Approach to Finite Coagulating Systems Through Recursive Equations

@article{Lepek2019ExactCA,
  title={Exact Combinatorial Approach to Finite Coagulating Systems Through Recursive Equations},
  author={Michal Lepek and Pawel Kukli'nski and Agata Fronczak and Piotr Fronczak},
  journal={Reports on Mathematical Physics},
  year={2019}
}
5 Citations

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References

SHOWING 1-10 OF 39 REFERENCES
Exact combinatorial approach to finite coagulating systems.
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of
Coagulation kinetics beyond mean field theory using an optimised Poisson representation.
TLDR
Using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population.
Exact kinetics of a coagulating system with the kernel K = 1
The time evolution of a system of coagulating particles is studied within the Marcus–Lushnikov scheme. Each state of the system is characterized by the probability of finding a given set of
Gelation in coagulating systems
Exact kinetics of the sol-gel transition.
  • A. A. Lushnikov
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
The evolution equation for the generating functional defining all properties of coagulating systems is solved exactly for this particular kernel and the final output is the exact expression for the single-particle mass spectrum as a function of time.
Exact kinetics of the sol-gel transition.
The formation of a gel in a disperse system wherein binary coagulation alone governs the temporal changes of particle mass spectra is studied under the assumption that the coagulation kernel is
Random fragmentation and coagulation processes
Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by
Exact solutions for random coagulation processes
Smoluchowski's coagulation equation can only derive physical validity as the limit of a random coagulation process. For coagulation rateKij=a+b(i+j) and no fragmentation, random coagulation is
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