Study of mass transport in rotating couple stress liquid under concentration modulation

A weakly non-linear stability analysis has been performed to examine the effect of time-periodic concentration modulation on the mass transport. We consider an infinite horizontal fluid layer is rotating with angular velocity Ω₁ about Z-axis subjected to an imposed time-periodic boundary concentration (ITBC). The concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated in this case. We have expanded the infinitesimal disturbances in terms of power series of amplitude of modulation, which is assumed to be small. Ginzburg–Landau equation is obtained to find the rate of mass transfer. It is found that, the effect of Taylor number is to stabilize the system. Effect of Schmidt number and Couple stress parameter on mass transfer are also discussed. Further, it is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation .     

低山丘陵坡耕地秸秆覆盖轮耕土壤WSOC的荧光特征

为了提高坡耕地的秸秆还田效率,增加土壤有机质,探索一种适于坡耕地的基于种养结合的保护性耕作方式。采用田间小区试验,研究了秸秆覆盖轮耕技术（包括当季秸秆覆盖+休闲、上季秸秆覆盖+旋耕）与常规耕作（秸秆移除后旋耕）对土壤水溶性有机碳（WSOC）荧光特征及团聚体有机碳的影响。结果表明：砂质暗棕壤坡耕地秸秆覆盖旋耕（SRT）、秸秆覆盖休闲（SFT）与秸秆不还田的常规耕作（CRT）处理土壤WSOC均解析出C1,C2,C3和C4等4组荧光组分,主要为紫外光区与可见光区类富里酸（Peak A 和Peak C）、类胡敏酸（F）和短波类色氨酸（类蛋白B、D峰）等成分。秸秆覆盖旋耕处理提高了类富里酸（Peak A和Peak C）和类蛋白组分C4含量,C1和C2组分较覆盖休闲和常规耕作分别提高112.73%,109.35%和107.77%,66.07%,C4组分较SFT与CRT处理提高28.26%和42.31%,差异显著,而常规耕作处理来自于自生源腐殖质组分的胡敏酸C3含量增加,较覆盖旋耕和覆盖休闲处理分别增加16.76%和49.74%;0～20 cm耕层土壤团聚体有机物主要分布在<0.053 mm的矿物质结合态（MOM）中,平均占比为63.90%,其次为0.25～0.053 mm细颗粒态有机物（oPOM）,占比为23.8%,粗颗粒态有机物（>0.25 mm）中含量最低,仅为11.2%;与秸秆不还田比较,坡耕地秸秆覆盖还田增加了植物来源的新鲜有机质的形成,表现为＞0.053 mm的闭蓄态有机碳（oPOC）含量的增加,以覆盖旋耕处理oPOC增加较大,而秸秆不还田的CRT处理增加了MOM占比;覆盖旋耕处理FI和HIX值增大,土壤腐殖质积累趋势增强,为低山丘陵区坡耕地实施秸秆覆盖还田的保护性耕作技术提供了科学依据。     

Recurrence Formula for Polynomials of Two Variables, Orthogonal with Respect to Rotation Invariant Measures

We give the recurrence formula satisfied by polynomials of two variables, orthogonal with respect to a rotation invariant measure. Moreover, we show that for polynomials satisfying such a recurrence formula, there exists an orthogonality measure which is rotation invariant. We also compute explicitly the recurrence coefficients for the disk polynomials. January 4, 1997. Date revised: October 15, 1997. Date accepted: October 21, 1997.     

Entropy generation of double-diffusive convection in the presence of rotation

In the present study, the entropy generation of double-diffusive convection in the presence of rotation is investigated for the first time. In order to reveal the effects of rotating of the enclosure (described by the ratio of buoyancy frequency to Coriolis frequency St) and the ratio of buoyancy forces R_p on entropy generation systematically, we divide the cases investigated in the present study into two groups: (1) R_p is fixed but St varies from 0.001 to 10; (2) St is fixed but R_p varies from 0.1 to 2. We find that only fast rotation has significant influence on entropy generation distribution. Moreover, the share of irreversibility due to concentration diffusion increases quickly with R_p and it becomes the main contributor to entropy generation since R_p>0.6.     

微分形式的亚椭圆性

本文研究了光滑流形上微分形式的亚椭圆性,利用遍历平均的方法,得到了二维环面上变系数1-形式是亚椭圆的充要条件.     

Note on open shell restricted SCF calculations for rotation barriers about C-C double bonds: Ethylene and allene

It is shown thatab initio open-shell SCF calculations yield acceptable results for rotation barriers about double bonds in contrast to more conventional closed-shell SCF calculations. Using basis sets of double zeta+polarization quality the SCF values for the rotation barriers of ethylene and allene are obtained to be 48 and 50 kcal/mole, respectively. An IEPA estimate of the influence of electron correlation leads to values of 64 and 52 kcal/mole, respectively, which are in reasonable agreement with the experimental values.     

Tolerance of start-up control of rotation in parametric pendulum by delayed feedback

In this Letter, we propose a control method for establishing periodic rotation inherent in parametric pendulum based on a delayed feedback control. The experiments elucidate the existing range of periodic rotation in the domain of delay. The range of existence possibly represents the tolerance of proposed control with mistuned delay. It is confirmed that forced synchronization governs the existence and the width. The result assures that the frequency synchronization characteristics overcome the mistuned difference of delay in the control through entrainment.     

Proof of a conjecture about rotation symmetric functions

Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. We prove the conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed in Cusick and St?nic? (2002) [2] and its generalization, thus the nonlinearity of such functions is determined.     

Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material

The present investigation is concerned with a study effect of non-homogeneous on the elastic stresses in rotating orthotropic infinite circular cylinder subjected to certain boundary conditions. Closed form stress solutions are obtained for rotating orthotropic cylinder with constant thickness for three cases: (1) a solid cylinder; (2) cylinder mounted on a circular rigid shaft; and (3) cylinder with a circular hole at the center. Analytical expressions for the components of the displacement and the stress in different cases are obtained. The effect of the rotation and non-homogeneity on the displacement and stress are studied. Numerical results are given and illustrated graphically for each case is considered. The effects rotating and non-homogeneity are discussed. Comparisons are made with the results predicted in the presence and absence of rotation.     

The Orthogonally Constrained Regression Revisited

The Penrose regression problem, including the orthonormal Procrustes problem and rotation problem to a partially specified target, is an important class of data matching problems arising frequently in multivariate analysis, yet its optimality conditions have never been clearly understood. This work offers a way to calculate the projected gradient and the projected Hessian explicitly. One consequence of this calculation is the complete characterization of the first order and the second order necessary and sufficient optimality conditions for this problem. Another application is the natural formulation of a continuous steepest descent ow that can serve as a globally convergent numerical method. Applications to the orthonormal Procrustes problem and Penrose regression problem with partially specified target are demonstrated in this article. Finally, some numerical results are reported and commented.