Laser pulse design for coherent laser control of potassium atoms

In this paper, the dynamics of coherent laser control of potassium atoms is studied by using the time-dependent multilevel approach （TDMA）. The calculation results of population transfer are presented with different laser fields. The results show that the population can be transferred to target state completely by a specially designed laser field.

Evaluating the Ryman-Laikre effect for marine stock enhancement and aquaculture

The Ryman-Laikre （R-L） effect is an increase in inbreeding and a reduction in total effective population size （NET） in a combined captive-wild system, which arises when a few captive parents produce large numbers of offspring. To facilitate evaluation of the R-L effect for scenarios that are relevant to marine stock enhancement and aquaculture, we extended the original R-L formula to explicitly account for several key factors that determine NeT, including the numbers of captive and wild adults, the ratio of captive to wild Ne/N （β）, productivity of captive and wild breeders, and removal of individuals from the wild for captive breeding. We show how to provide quantitative answers to questions such as： What scenarios lead to no loss of effective size？ What is the maximum effective size that can be achieved？ and What scenarios insure that NeTWill be no smaller than a specified value？ Important results include the following： （1） For large marine populations, the value of β becomes increasingly important as the captive contribution increases. Captive propagation will sharply reduce NeT unless the captive contribution is very small or β is very large （～10^3 or higher）. （2） Very large values of β are only possible if wild Ne/N is tiny. Therefore, large wild populations undergoing captive enhancement at even modest levels will suffer major reductions in effective size unless wild Ne is a tiny fraction of the census size （about 10 4 or lower）.

Consensus of Flocks under M-Nearest-Neighbor Rules

This paper investigates a class of flocks with an M-nearest-neighbor rule,where each agent's neighbors are determined according to M nearest agents with M being a given integer,rather than all the agents within a fixed metric distance as in the well-known Vicsek's model.Such a neighbor rule has been validated by biologists through experiments and the authors will prove that,similar to the Vicsek's model,such a new neighbor rule can also achieve consensus under some conditions imposed only on the system's speed and the number M,n,without resorting to any priori connectivity assumptions on the trajectory of the system.In particular,the authors will prove that if the number M is proportional to the population size n,then for any speed v,the system will achieve consensus with large probability if the population size is large enough.

Small value probabilities for continuous state branching processes with immigration

We consider the small value probability of supercritical continuous state branching processes with immigration. From Pinsky （1972） it is known that under regularity condition on the branching mechanism and immigration mechanism, the normalized population size converges to a non-degenerate finite and positive limit PV as t tends to infinity. We provide sharp estimate on asymptotic behavior of P（W≤ε〈） as ε→ 0＋ by studying the Laplace transform of W. Without immigration, we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition.

The effect of diffusion loss on the time-varying giant Panda population

It has been certificated that corridors can help giant pandas to keep their habitat from fragmenting. However there are still losses during the process of moving along corridors. In this study, a mathematical model with Allee effect is carried out to describe the diffusion of giant pandas between n patches. Some criteria are obtained to keep the system persisting. It is proved that the system has a unique positive w-periodic solution which is globally asymptotically stable. The ecological meanings of these findings are discussed following the results. And some numerical simulations in the Qinling Mountain giant panda nature reservation area are also presented in the end.