The Coagulation Equation Under Time Reversal

In this article we examine the possibility of integrating backward in time the coagulation equation in order to find the aerosol particle size distribution at earlier times. In theory, time reversal solution of the coagulation equation allows backward prediction of past distributions in any circumstances. There are, however, a few restrictions on the practical use of this approach. First, the impossibility of working with infinitely small numbers in any computer prevents retrieval of past distributions when some particle concentrations have decayed to extremely small values. Second, the recovery of very narrow, quasi-monodisperse distributions is also problematic. In most practical situations in which not too narrowly distributed and not extremely concentrated aerosols coagulate for not too long periods of time, it is possible to predict back the original size distribution with high accuracy.We greatly appreciate very helpful discussions with Dr. Loscertales about some parts of this paper.Peer reviewe

The Coagulation Equation Under Time Reversal

In this article we examine the possibility of integrating backward in time the coagulation equation in order to find the aerosol particle size distribution at earlier times. In theory, time reversal solution of the coagulation equation allows backward prediction of past distributions in any circumstances. There are, however, a few restrictions on the practical use of this approach. First, the impossibility of working with infinitely small numbers in any computer prevents retrieval of past distributions when some particle concentrations have decayed to extremely small values. Second, the recovery of very narrow, quasi-monodisperse distributions is also problematic. In most practical situations in which not too narrowly distributed and not extremely concentrated aerosols coagulate for not too long periods of time, it is possible to predict back the original size distribution with high accuracy.We greatly appreciate very helpful discussions with Dr. Loscertales about some parts of this paper.Peer reviewe