NUMERICS OF AEROSOL SYSTEMS
Some basics about aerosols
Aerosol system: System of suspended particles (soot, pollutants, ...)
Aerosol dynamics (coagulation): upon collision, two particles with masses m and n may merge to a particle with mass m+n (details)
Smoluchowski equation: infinite-dimensional system of ordinary differential equations (in the space homogeneous case) modeling aerosol dynamics (details)
Gelation: Formation of "macroparticles" of infinite size in finite time (details)
Numerical simulation: Coagulation and approach to the gelation phase
Marcus-Lushnikov process: Simulation of a physical aerosol system by statistical means
This is very intuitive but numerically not efficient since sample size decreases due to coagulation which leads to bad statistics
Mass flow process: Stochastic integration of Smoluchowski equation using virtual unit mass particles
This process (first proposed in [1]) produces samples with constant statistical properties (details)
Hybrid code combining deterministic numerical scheme (for small particles) with mass flow process (for large particles); first proposed in [4]
(more information, literature: 11/2006, 12/2005, 23/2004)
Numerical experiments ...
... for space-dependent diffusion-coagulation systems
Metastability: Destabilization of seemingly stable states due to random effects (see [3]) (description; Video)
Spreading of gelation areas: Evolution of gelation areas depends strongly on diffusion model (description; Video)
Acknowledgment
This project has been carried out jointly with W. Wagner, WIAS Berlin, and supported by Deutsche Forschungsgemeinschaft since 1997, partly in the DFG Priority Program "Interaction stochastic systems of high complexity"
Literature
[1] H.B.: "On a Monte Carlo scheme for Smoluchowski's coagulation equation", Monte Carlo Methods and Applications, 5:1--18, 1999
[2] H.B.: "Gelation of stochastic diffusion-coagulation systems", Physica D, 222: 54-62, 2006
[3] H.B.: "The Impact of Random Fluctuations on the Gelation Process", Bull. Inst. of Math., Academia Sinica, 2:329-347, 2007
[4] H.B.: "Approximations to the gelation phase of an aerosol", Preprint 11/06, Inst. f. Math., TU Ilmenau, 2006