A semi-analytic boundary element method for parabolic problems

A new semi-analytic solution method is proposed for solving linear parabolic problems using the boundary element method. This method constructs a solution as an eigenfunction expansion using separation of variables. The eigenfunctions are determined using the dual reciprocity boundary element method. This separation of variables-dual reciprocity method (SOV-DRM) allows a solution to be determined without requiring either time-stepping or domain discretisation. The accuracy and computational efficiency of the SOV-DRM is found to improve as time increases. These properties make the SOV-DRM an attractive technique for solving parabolic problems.     

灌河潮流界位置确定与港口防淤探讨

盐城市位于江苏省中部,地处黄海之滨,承接里下河腹部区的排水,区内入海河流众多,在这些入海河流上大多建有挡潮闸坝。但由于盐城市近海为淤积型海岸,闸坝的建设改变了河口的自然状态,造成港口下游淤积严重,排水不畅。灌河作为江苏省沿海唯一下游没有建挡潮闸的重要入海河流,仍为自然状态,下游港口未淤积。本文通过对灌河水体涨、落潮中氯离子含量的监测,找出海水上溯的最大距离,确定其影响范围,为其它入海流河流的防淤提供借鉴。     

A scheme to randomly generate surface dust points for the 3D complex variable boundary element method (CVBEM)

A scheme to randomly generate dust points on the surface of a three-dimensional (3D) object is proposed. This scheme will potentially eliminate the bias of a density of points which are approximately equally spaced on the surface, as well as eliminate possible weighting requirements for areas of higher density. This method has the potential to reduce computational effort, as fewer points might be required to define the surface area. The global trial function vector can be assigned to these dust points and then entered into the complex variable boundary element method (CVBEM) commercial code. This scheme can be applied to each piece of a system that is comprised of a connected multiple geometry. A noticeable benefit of this approach is that the same problem can be studied several times, using a new random distribution of surface points each time. The smallest error can then be determined and that run selected. The Mathematica code used to generate the scheme is attached as an appendix.     

Shift in thinking to address the 21st century hunger gap

The present water policy debate is dominated by the 30 yr old mission to secure water supply and sanitation to all people. The water needed to produce a nutritionally acceptable diet for one person is however 70 times as large as the amount needed for domestic water supply. The food security dilemma is largest in arid climate regions, a situation constituting a formidable challenge. It is suggested that an additional 5 600 km³/yr of consumptive water use will be needed to produce an adequate amount of food by 2050 – i.e almost a doubling of today’s consumptive use of 6800 km³/yr. Past misinterpretations and conceptual deficiencies show the importance of a shift in thinking. Combining the scale of the challenge and the time scale of the efforts to feed humanity and eradicate hunger leads to an impression of great urgency. This urgency strengthens the call for international research both for supporting agricultural upgrading, and for much better handling of issues of environmental sustainability. What stands out is the need of a new generation of water professionals, able to handle complexity and able to incorporate water implications of land use and of ecosystem health in integrated water resources management. It will for those reasons be essential and urgent to upgrade the educational system to producing this new generation.     

三维精细积分法地震正演及边界条件

 将任意差分精细积分法用于三维波动方程地震正演，关键在于如何消除数值计算中有限波场区域边界引起的边界反射。文中采用Berenger给出的电磁波完全匹配层吸收边界条件，推导出三维波动方程任意差分精细积分法地震正演的完全匹配层吸收边界条件计算公式，并给出了完全匹配层吸收边界条件算例。计算结果表明，此方法压制边界反射效果明显。三维波动方程地震正演模拟实例表明，完全匹配层吸收边界条件的任意差分精细积分法为复杂区地震波传播规律研究提供了一种实用的正演模拟工具     

Effect of pH on the Crystallization of Homogeneously Precipitated Nanosized PZT Powder

Nanosized lead zirconate titanate (PZT) powder with Zr:Ti ratio in the morphotropic phase boundary region was synthesized by homogeneous precipitation of metal ions. The powder precipitated at 90°C and at pH 6.7 resulted single-phase perovskite lead zirconate titanate powder when calcined at 550°C and above for 4 hours in air. The solution pH and the precipitation temperature strongly affect the composition of the calcined powder. The results obtained by structural characterization of homogeneously precipitated powder were compared with that obtained from the conventional precipitation method using ammonia in terms of crystallization, homogeneity, and microstructure. The homogeneously precipitated powder showed smaller particle size, minimum agglomeration and uniform shape on calcination and annealing. Powdered samples that precipitated by homogeneous precipitation crystallized directly to perovskite PZT, without any intermediate pyrochlore phase formation. In contrast, the NH₃ precipitated powder converted to perovskite PZT via metastable pyrochlore and it showed phase segregation upon annealing at higher temperatures. The reaction kinetics has been studied by X-ray diffraction, differential thermal analysis, and differential scanning calorimetry.     

Flow Control Through the Use of Topography

In this work, optimal shaft shapes for flow in the annular space between a rotating shaft with axially-periodic radius and a fixed coaxial outer circular cylinder, are investigated. Axisymmetric steady flows in this geometry are determined by solving the full Navier-Stokes equations in the actual domain. A measure of the flow field, a weighted convex combination of the volume averaged square of the L₂-norm of the velocity and vorticity vectors, is employed. It has been demonstrated that boundary shape can be used to influence the characteristics of the flow field, such as its velocity component distribution, kinetic energy, or even vorticity. This ability to influence flow fields through boundary shape may be employed to improve microfluidic mixing or, possibly, to minimize shear in biological applications.     

Symmetric BEM formulations for 2-D steady-state and transit potential problems

This paper presents a new concept for symmetric boundary element method (SBEM) applicable to 2-D steady-state and transit potential problems. Two kinds of SBEM formulations are derived. Symmetry is obtained simply through matrix manipulation, and no hypersingularity appears. Therefore, SBEM is much easier than the traditional symmetric Galerkin BEM. Compared with the traditional asymmetric BEM, the present SBEM can reduce the computational cost for time domain problems only. However, when applied to BEM/FEM coupling procedure, SBEM can reduce the computational cost for both steady-state and time domain problems. Three numerical examples are included to illustrate the effectiveness and accuracy of the present formulations.     

Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

This work is an experimental study of mechanisms for transition to turbulence in the boundary layer on a rotating disk. In one case, the focus was on a triad resonance between pairs of traveling cross-flow modes and a stationary cross-flow mode. The other was on the temporal growth of traveling modes through a linear absolute instability mechanism first discovered by Lingwood (1995, J Fluid Mech 314:373–405). Both research directions made use of methods for introducing controlled initial disturbances. One used a distributed array of ink dots placed on the disk surface to enhance a narrow band of azimuthal and radial wave numbers of both stationary and traveling modes. The size of the dots was small so that the disturbances they produce were linear. Another approach introduced temporal disturbances by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. Hot-wire sensors primarily sensitive to the azimuthal velocity component, were positioned at different spatial (r,θ) locations on the disk to document the growth of disturbances. Spatial correlation measurements were used with two simultaneous sensors to obtain wavenumber vectors. Cross-bicoherence was used to identify three-frequency phase locking. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. The space–time evolution of the leading and trailing edges of the wave packets were followed past the critical radius for the absolute instability, r _{c A} . With documented linear amplitudes, the spreading of the disturbance wave packets did not continue to grow in time as r _{c A} was approached. Rather, the spreading of the trailing edge of the wave packet decelerated and asymptotically approached a constant. This result supports the linear DNS simulations of Davies and Carpenter (2003, J Fluid Mech 486:287–329) who concluded that the absolute instability mechanism does not result in a global mode, and that linear-disturbance wave packets are dominated by the convective instability. In contrast, wave-number matching between traveling cross-flow modes confirmed a triad resonance that lead to the growth of a low azimuthal number (n = 4) stationary mode. At transition, this mode had the largest amplitude. Signs of this mechanism can be found in past flow visualization of transition to turbulence in rotating disk flows.