Deep gravity waves in moist-saturated atmospheric air

The equations of motion of a moist-saturated, dissipative, stratified atmosphere are used in the case of small Schmidt number to describe the propagation of linearized gravity waves in deep cloudy atmosphere: as in dry air, the consequence of the dissipation is the diffusion and the damping of waves through the medium. However, there exist particular cases of stratification, for which the moisture gives rise at locally undamped waves. This property justifies the existence of oscillatory unstable régimes when we study shallow convection in the medium.     

Saturated absorption spectroscopy of buffer-gas-cooled Barium monofluoride molecules

We report an experimental investigation on the Doppler-free saturated absorption spectroscopy of buffer-gas-cooled Barium monofluoride (BaF) molecules in a 4 K cryogenic cell. The obtained spectra with a resolution of 19 MHz, much smaller than previously observed in absorption spectroscopy, clearly resolve the hyperfine transitions. Moreover, we use these high-resolution spectra to fit the hyperfine splittings of excited A(v = 0) state and find the hyperfine splitting of the laser-cooling-relevant A²Π_1/2(v = 0, J = 1/2,+) state is about 18 MHz, much higher than the previous theoretically predicted value. This provides important missing information for laser cooling of BaF molecules.     

Nonconstant steady states and pattern formations of generalized 1D cross-diffusion systems with prey-taxis

Cross-diffusion effects and tactic interactions are the processes that preys move away from the highest density of predators preferentially, or vice versa. It is renowned that these effects have played significant roles in ecology and biology, which are also essential to the maintenance of diversity of species. To simulate the stability of systems and illustrate their spatial distributions, we consider positive nonconstant steady states of a generalized cross-diffusion model with prey-taxis and general functional responses in one dimension. By applying linear stability theory, we analyze the stability of the interior equilibrium and show that even in the case of negative cross-diffusion rate, which appeared in many models, the corresponding cross-diffusion model has opportunity to achieve its stability. Meanwhile, in addition to the cross-diffusion effect, tactic interactions can also destabilize the homogeneity of predator–prey systems if the tactic interaction coefficient is negative. Otherwise, taxis effects can stabilize the homogeneity.     

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foun- dation of finite height bounded to the surface of a saturated half-space.The foundation is subjected to time-harmonic vertical loadings.First,the transform solutions for the governing equations of the saturated media are obtained.Then,based on the assumption that the contact between the foundation and the half-space is fully relaxed and the half- space is completely pervious or impervious,this dynamic mixed boundary-value problem can lead to dual integral equations,which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures.In the numerical exam- ples,the dynamic compliances,displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system.In most of the cases,the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.     

Horizontal boundary-layer natural convection in a porous medium saturated with a gas

Boundary-layer analysis is performed for free convection flow over a hot horizontal surface embedded in a porous medium saturated with a gas of variable properties. The variable gas properties are accounted for via the assumption that thermal conductivity and dynamic viscosity are proportional to temperature. A similarity solution is shown to exist for the case of constant surface temperature. Numerical results for the stream function, horizontal velocity, and temperature profiles within the boundary layer as well as for the mass of entrained gas, surface slip velocity, and heat transfer rate at different values of the wall-temperature parameter are presented. Asymptotic solutions for large heating are also available to support the numerical work.     

On the unconditional subsequence property

We show that a construction of Johnson, Maurey and Schechtman leads to the existence of a weakly null sequence (fi) in ?₂(∑Lpi), where pi↓1, so that for all ε>0 and 1<q?2, every subsequence of (fi) admits a block basis (1+ε)-equivalent to the Haar basis for Lq. We give an example of a reflexive Banach space having the unconditional subsequence property but not uniformly so.     

On s-semipermutable subgroups of finite groups

Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.     

Modeling the drainage and groundwater table above the collecting pipe through 2D groundwater models

In order to understand the effects of the landfill operation on groundwater flow behavior, 2D horizontal groundwater simulation model was carried out. The model saved the memory of computer and time consumption comparing with 3D groundwater flow model. However, the most difficulty is the assignment of collecting pipe boundary in the study site. Therefore, 2D vertical model was applied to calculate the change of groundwater table above the collecting pipe. This paper paid attention to examine the validation of the assignment of the collecting pipe boundary by applying the results of 2D vertical model. 2D horizontal model was coupled with the recharge model to solve the partial differential equation of groundwater flow. Finite difference method and iterative successive over relaxation were applied. The drainage volume of leachate collection was summed up in the whole landfill site and compared with the average volume of treated waste water. The study demonstrated that the results of 2D vertical model validated and can be applied to 2D horizontal groundwater flow simulation.