一维问题的一种积分形式的流量重构算法

1引言我们考虑如下一维二阶椭圆边界值问题(-(β(x)p′)(x))′=f(x),x∈(a,b) p(a)=p(b)=0(1))其中β=β(x)是一恒正函数,且β∈H~1(a,b),f∈L~2(a,b)．事实上,在此条件下,我们可保证p∈H~2(a,b)(见[1],[2])．(1)之弱形式为：求p∈H_0~1(a,b)使得a(p,q)=(f,q),(?)q∈H_0~1(a,b),(2)其中a(p,q)=(?)_a~bβp′q′dx,(f,g)=(?)_a~bfqdx．给定(a,b)的一个分割α=x_0＜x_1＜…＜x_(n-1)＜x_n=b,令h=(?)(x_i-x_(i-1)),(?)_i表示通常相应于节点x_i的形状函数,即(?)_i是连续的分段线性函数且满足(?)_i(x_k)=δ_(ik),这里δ_(ik)=(?)i,k=0,1,…,n．又记V_h~0=span{(?)_1,(?)_2,…,(?)_(n-1)),取V_h~0作为p的逼近空间,则求解(1)的标准有限元格式为：求ph∈V_h~0使得     

Floer–Novikov cohomology and the flux conjecture

We study Floer–Novikov cohomology with local coefficients and prove the flux conjecture for general closed symplectic manifolds. Received: February 2005, Revised: May 2006, Accepted: May 2006 Partially supported by the Grant-in-Aid for Scientific Research No. 14003419, Japan Society for the Promotion of Sciences.     

Modeling of mixed liquor inorganic suspended solids and membrane flux at different ratio of SRT to HRT in a submerged membrane bioreactor

In order to investigate the influence of mixed liquor inorganic suspended solids (MLISS) on membrane flux at different ratio of sludge retention time (SRT) to hydraulic retention time (HRT) in a submerged membrane bioreactor (SMBR), a pilot scale test was conducted for 452 days using traditional Chinese medicine (TCM) wastewater as influent. SRT/HRT was controlled at 150, 480 and 750, respectively. The experimental results showed that the average values of MLISS were 1271.9, 1664.5 and 6898.8 mg/L at different SRT/HRT, respectively; MLISS were accumulated from 265.5 g/h to 4912.93 g/h, which indicated that SMBR could not steadily operate for a long period without sludge withdrawal. Sludge oxygen utilized rate (SOUR) decreased from 5.115 to 1.292 mgO₂/(gVSS h) and volume oxygen utilized rate (VOUR) increased from 10.84 to 18.13 mgO₂/(L h). Model of membrane flux and MLISS were developed under different temperature and operational pressure by regressions, which were then satisfactorily employed to predict the trend of membrane flux during the experiment.     

Reargument over E ～ j relation of high temperature superconductors

The E ∼ j relation of an HTSC slab is solved strictly within the Bean’s model in two different situations where the system does and does not reach equilibrium state under the magnetic relaxation respectively, with both forward and backward hopping taken into consideration (the backward hopping means the hopping from the barriers with low energy to high ones). Our results suggest and rigorously prove that the In E ∼ In j curves show only positive curvature on the side of slab where the directions of current-created field and the applied field are the same, while they show both positive and negative curvatures at a certain field range on the other side where the directions are opposite. The relationship of the positive and negative curvatures with the critical current, applied field and temperature is also discussed.     

A nonlinear diffusion system coupled via nonlinear boundary flux

In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Wang et al. [Nonlinear Anal. 71 (2009) 2134-2140] and Li et al. [J. Math. Anal. Appl. 340 (2008) 876-883] to more general equations.     

Semidiscrete central-upwind scheme for conservation laws with a discontinuous flux function in space

In this paper, a modified semidiscrete central-upwind scheme is derived for the scalar conservation laws with a discontinuous flux function in space. The new scheme is based on dealing with the phase transition at the stationary discontinuity, where the unknown variable function is not continuous, but the flux function is continuous. The main advantages of the new scheme are the same as them of the original semidiscrete central-upwind scheme. Numerical results are displayed to illustrate the efficiency of the methods.     

The heat transfer problem in the wall region of a turbulent boundary layer

The problem of heat transfer in the wall region of a turbulent boundary layer has been investigated. The resonant triad in the theory of hydrodynamic stability was used to obtain the velocity field induced by the coherent structures in the wall region of the turbulent boundary layer, while the small scale turbulence was represented by a simple model. By such a new approach of modeling, the 3-D temperature field is calculated, the mean temperature profile in the wall region and the Nusselt number characterizing the heat flux, which was found to be in good agreement with the experimental observations are obtained. The instantaneous temperature field had streaky structures, thus offering a mechanism for their generation found in numerical simulations. Project supported by the National Natural Science Foundation of China (Grant No. 19132011).     

Pulsatile flow between permeable beds

Pulsatile flow of a viscous fluid between two permeable beds is analyzed. The flow between and through the permeable beds are governed by the Navier-Stokes equations and Darcy's law, respectively. The velocity field and the volume flux are obtained for several cases and discussed. Further, when the permeability parameter k→0, the results agree with those of Wang (J. Appl. Mech. 38 (1971) 553).     

Argument for E

In high temperature superconductors (HTSC), when magnetic relaxation approaches the equilibrium state and the superconductor is applied with current, theE × j relation is calculated by considering both forward and backward hopping of thermally activated flux (where backward hopping means hopping from the barriers with low energy to the ones with high energy). It is pointed out that the InE× Inj curve shows positive curvature. And the results are compared with other models. The discussion on the topic that whether p approaches zero asj → 0 is carried out.