Kinetic Behaviors of a Competitive Population and Fitness System in Exchange-Driven Growth

We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer birth of fitness catalyzed by the population, where the fitness aggregates perform self-death process and the population aggregates perform self-birth process. The kinetic behaviors of the aggregate size distributions of the fitness and population were analyzed by the rate equation approach with their exchange rate kernel K1（k,j） = K1kj and K2（k,j） = K2kj, the fitness aggregate＇s self-death rate kernel J1 （ k ） = J1 k, population aggregate＇s self-birth rate kernel J2（ k ） = J2k and population-catalyzed fitness birth rate kernel I（k,j） = Ikj＇. The kinetic behavior of the fitness was found depending crucially on the parameter v, which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst （population） aggregate. （i） In the v ≤ 0 case, the effect of catalyzed-birth of fitness is rather weak and the exchange-driven aggregation and self-death of the fitness dominate the process, and the fitness aggregate size distribution αk（t） does not have scale form. （ii） When v ≥0, the effect of the population-catalyzed birth of fitness gets strong enough, and the catalyzed-birth and self-death of the fitness aggregates, together with the self-birth of the population aggregates dominate the evolution process of the fitness aggregates. The aggregate size distribution αk （t） approaches a generalized scaling form.

Mixing Characteristics and Bubble Behavior in an Airlift Internal Loop Reactor with Low Aspect Ratio

The present study summarizes the results of macro-and micro-mixing characteristics in an airlift internal loop reactor with low aspect ratio(H/D≤5) using the electrolytic tracer response technique and the method of parallel competing reactions respectively. The micro-mixing has never been investigated in airlift loop reactors. The dual-tip electrical conductivity probe technique is used for measurement of local bubble behavior in the reactor. The effects of several operating parameters and geometric variables are investigated. It is found that the increase in superficial gas velocity corresponds to the increase in energy input, liquid circulation velocity and shear rate, decreasing the macro-mixing time and segregation index. Moreover, it is shown that top clearance and draft diameter affect flow resistance. However, the bubble redistribution with a screen mesh on the perforated plate distributor for macro-mixing is insignificant. The top region with a high energy dissipation rate is a suitable location for feeding reactants. The analysis of present experimental data provides a valuable insight into the interaction between gas and liquid phases for mixing and improves the understanding of intrinsic roles of hydrodynamics upon the reactor design and operating parameter selection.

Effect of solidification rate on competitive grain growth in directional solidification of a nickel-base superalloy

The mechanism of grain structure evolution during directional solidification is a fundamental subject in material science. Within the published research there exist conflicting views on the mechanism of grain overgrowth. To study the effect of solidification rate on grain structure evolution, bi-crystals samples were produced in a nickel-base superalloy at different solidification rates. It was found that at the convergent grain boundaries those grains better aligned with respect to the heat flux more readily overgrew neighbouring grains with misaligned orientations and the effect became more pronounced as solidification rate was increased. However, at diverging grain boundaries the rate of overgrowth was invariant to the solidification rate. These experimental results were compared with models in the literature. Thus, a better insight into competitive grain growth in directional solidification processes was obtained.

Traveling wave solutions for a diffusive three-species intraguild predation model

The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper-lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper lower solution, the scheme of strictly con- tracting rectangle is applied. Finally, the minimal speed c＊ of traveling wave solutions of the model is characterized. If the wave speed is greater than c＊, we show the exis- tence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than c＊, the non-existence of such solutions is also established. Furthermore, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.