Diffusion, fragmentation and coagulation processes: Analytical and numerical results.

Poul Olesen, Jesper Ferkinghoff-Borg, Mogens Høgh Jensen, Joachim Mathiesen

Research output: Contribution to journalJournal articleResearchpeer-review


We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation, and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as exp(−x^3/2) for large x values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full nonlinear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay exp(−x) for large x and observe a crossover from the Bessel function for intermediate values of x. These findings are checked by numerical simulations, and we find perfect agreement between the theoretical predictions and numerical results.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Pages (from-to)031103
Publication statusPublished - 2005
Externally publishedYes


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