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     

Blow-up rate for a nonlinear diffusion equation

In this work we study the blow-up rate for a nonlinear diffusion equation with an inner source and a nonlinear boundary flux, which is equivalent to a porous medium equation with convection. Depending upon the sign of a parameter included, the source can be positive or negative (absorption). By the scaling method, we obtain that the blow-up rate is independent of a negative source, while for the situation with a positive source, the blow-up rate is determined by the interaction between the inner source and the boundary flux. Comparing with the previous results for the porous medium model without convection, we observe that the gradient term included here does not affect the blow-up rates of solutions.     

A possible role of amorphous regions at grain-boundary vertex points as linear defects on flux pinning in MgB2 films with columnar grain structure

We measured the transport properties of MgB₂ films having columnar grain structure with their axis normal to the substrate. When an external magnetic field was applied parallel to the grain axis, an enhanced critical current density has been observed, and this result has been ascribed to flux pinning induced by grain boundaries. The shape of the angular dependence of critical current density and its magnetic field dependence showed a quite similar resemblance to those of YBa₂Cu₃O_x films containing columnar defects, implying a possible existence of linear defects in MgB₂ films of columnar structure. We propose that the amorphous regions at the vertex points of three or more grain boundaries observed in microstructural studies correspond to the linear defects and these linear defects anchor the end points of the flux line dislocations of Frank-Read sources, by which the shear in the flux line lattice is actuated. This assumed mechanism is found to reasonably explain the magnetic field dependence of the flux pinning force density of MgB₂ films with columnar grain structure.     

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.     

Magnetic hysteresis of the magnetoresistance and the critical current density in polycrystalline YBa2Cu3O7−δ–Ag superconductors

A systematic study of the magnetic hysteresis in transport properties of polycrystalline YBa₂Cu₃O_7−δ–Ag compounds has been made based on two kinds of measurements at 77 K and under applied magnetic fields up to 30 mT: critical current density J_c(B_a) and magnetoresistance R(B_a). The R(B_a) curves show a minimum in their decreasing branch occurring at B=B_min which was found to be both the excitation current I_ex and the maximum applied magnetic field B_am dependent. In addition, for a certain value of B_am>5 mT, we have observed that B_min increases with increasing I_ex and reaches a saturation value. The J_c(B_a) curves show a maximum in decreasing applied magnetic fields occurring at B=B_max. We have also found that B_max increases with increasing B_am and reaches a saturation value. The minimum in the R(B_a) and the maximum in J_c(B_a) curves were found to be related to the trapped flux within the grains. All the experimental results are discussed within the context of the flux dynamics and transport mechanisms in these high-T_c materials.     

水射流冷却过程中表面热流密度的预测

建立了由内部一点测量温度值,选取多个时间步长计算未知的表面热流密度与换热系数的导热反问题算法。该算法采用有限容积法离散方程,附加源项法处理边界条件。将该计算模型应用于求解浸没水射流冷却过程中表面热流密度,将计算温度值与实验测温值进行比较验证了算法的正确性。在此基础上分析了水射流冲击过程中薄钢片表面热流密度随表面温度与时间的变化特性。     

An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part I Non-isothermal flow

Tensor representation theory is used to derive an explicit algebraic model that consists of an explicit algebraic stress model (EASM) and an explicit algebraic heat flux model (EAHFM) for two-dimensional (2-D) incompressible non-isothermal turbulent flows. The representation methodology used for the heat flux vector is adapted from that used for the polynomial representation of the Reynolds stress anisotropy tensor. Since the methodology is based on the formation of invariants from either vector or tensor basis sets, it is possible to derive explicit polynomial vector expansions for the heat flux vector. The resulting EAHFM is necessarily coupled with the turbulent velocity field through an EASM for the Reynolds stress anisotropy. An EASM has previously been derived by Jongen and Gatski [10]. Therefore, it is used in conjunction with the derived EAHFM to form the explicit algebraic model for incompressible 2-D flows. This explicit algebraic model is analyzed and compared with previous formulations including its ability to approximate the commonly accepted value for the turbulent Prandtl number. The effect of pressure-scrambling vector model calibration on predictive performance is also assessed. Finally, the explicit algebraic model is validated against a 2-D homogeneous shear flow with a variety of thermal gradients. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University     

远程超低飞行轨道分析

研究了一种新的远程导弹飞行轨道的可行性,它的最大飞行高度约100 km.这种超低弹道,借鉴卫星模式,利用离心力抵抗重力.与卫星轨道运行不同的是,超低弹道周围的稀薄空气影响至关重要,必须考虑.计算和分析结果表明,在相同载荷条件和射程条件下,超低弹道和经典的最小能量弹道对于火箭动力的需求大致相当,射程10000km以上基本相同,头部半径为5cm的轴对称外形,沿超低弹道飞行时,其驻点热流在高度26km左右达到最大值50MW/m2,约为最小能量弹道驻点热流最大值的50%.由于超低弹道对升力没有要求,飞行过程中的气动加热问题,沿用成熟方法如烧蚀防热即可解决.总体而言,超低弹道对于火箭动力与外形气动力/热要求,现有技术容易满足,因此利用它增强远程导弹的突防能力是现实可能的.     

等热流密度加热垂直下降液膜的研究

利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明,模型方程在小到中等Reynolds数下都适用,并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加,展向不稳定性增长率则随着Marangoni数增加而增加,随着Reynolds数增加而减小,流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明,在等热流密度加热条件下,液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构,液膜与气体的换热也因溪流状结构的出现而加强;在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强,液膜会提前破裂;在随机扰动的基础上引入占优势地位的流向最不稳定扰动时,液膜的换热会增强,但不会提前破裂;在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时,换热会加强且液膜会提前破裂。     

An experimental technique for measuringtransient natural/forced convective heatfluxes in a vertical channel

A series of systematic experiments for measuring transient natural andforced convected heat fluxes in a one-sided heated vertical channel have beenconducted. The total heat input in transient natural and forced experiments iscomposed of four kinds modes: radiative heat loss, conductiveheat lossm, thermal capacity of the plate, and convective heat transfer in thetest channel. In the transient periods, the generalized correlations for estimatingtransient convective heat flux are proposed in natural and forced convectionexperiments. By using the proposed q_c^″ distributions, satisfactory agreementsare achieved between the transient Nu_x predictions and experimentaldata.