二维流面上的流动问题的速度图方法

对于一些特殊的流动,尤其是平面上的位势流动,速度图方法有其显著的优点．对于理想流体来说,流面总是存在的,在流面上,流动的速度向量总是在其切空间里．通过引入流函数和势函数,采用张量分析作为工具,给出了二维曲流面上位势流动的速度图方法,得到了流函数满足的速度图方程,为一些特殊的流动问题提供了一类分析方法．并且,对于得到的二维速度图方程,得到了相应的特征方程和特征根,从而可以对方程的类型进行分类．最后,给出了一些特殊流动的实例．     

Geochemical Sources and Availability of Amidophosphates on the Early Earth

Phosphorylation of (pre)biotically relevant molecules in aqueous medium has recently been demonstrated using water‐soluble diamidophosphate (DAP). Questions arise relating to the prebiotic availability of DAP and other amidophosphosphorus species on the early earth. Herein, we demonstrate that DAP and other amino‐derivatives of phosphates/phosphite are generated when Fe₃P (proxy for mineral schreibersite), condensed phosphates, and reduced oxidation state phosphorus compounds, which could have been available on early earth, are exposed to aqueous ammonia solutions. DAP is shown to remain in aqueous solution under conditions where phosphate is precipitated out by divalent metals. These results show that nitrogenated analogues of phosphate and reduced phosphite species can be produced and remain in solution, overcoming the thermodynamic barrier for phosphorylation in water, increasing the possibility that abiotic phosphorylation reactions occurred in aqueous environments on early earth.     

Point Interactions: $$\mathcal{P}\mathcal{T}$$ -Hermiticity and Reality of the Spectrum

General point interactions for the second derivative operator in one dimension are studied. In particular, he09/11005_2004_Article_405937_TeX2GIFIE2.gif" alt=" $$\mathcal{P}\mathcal{T}$$ " align="middle" border="0"> -self-adjoint point interactions with the support at the origin and at points ±l are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.     

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G _D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G _D(r,r′, N) = G ₀(r,r′, N) - G ₀(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.