Competing role of catalysis-coagulation and catalysis-fragmentation in kinetic aggregation behaviours

We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.

New observations-with older ones reviewed-on mass migrations in millipedes based on a recent outbreak on Hachijojima(Izu Islands) of the polydesmid diplopod(Chamberlinius hualienensis,Wang 1956):Nothing appears to make much sense

Mass aggregations and migrations of millipedes despite numerous attempts to find causes for their occurrences are still an enigma. They have been reported from both southern and northern hemisphere countries, from highlands and lowlands of both tropical and temperate regions and they can involve species belonging to the orders Julida and Spirobolida, Polydesmida and Glomerida. According to the main suggestions put forward in the past, mass occurrences in Diplopoda occur：（1） because of a lack of food and a population increase beyond sustainable levels;（2） for the purpose of reproduction and in order to locate suitable oviposition sites;（3） to find overwintering or aestivation sites;（4） because of habitat disruption and changes in the local environment;（5） as a consequence of weather conditions the year（or winter and spring） before. A recent outbreak（November 2014） of a mass migration of the polydesmid Chamberlinius hualienensis Wang 1956 on the Japanese Izu Island of Hachijojima 300 km to the south of Tokyo gave this author an opportunity to review the existing literature on millipede mass migrations and to carry out additional observations on the phenomenon in the field as well as the laboratory. Hitherto unreported heavy infestations with phoretic deutonymphs of the mite Histiostoma sp. as well as dense populations of internal rhabditid nematodes（Oscheius cf. necromena and an unidentified species of the genus Fictor）, suggest that infestations of this kind could be necromenic and either have been a contributing factor for the mass migration or been a consequence of so manyindividuals occurring together at close proximity. It is concluded that mass migrations and aggregations in millipedes do not have one common cause, but represent phenomena that often are seasonally recurring events and appear identical in their outcome, but which have evolved as responses to different causes in different millipede taxa and therefore need to be examined on a case-to-case basis.