Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Demonstration of microfiber knot laser

The authors demonstrate a 1.5 mu m wavelength microfiber laser formed by tightening a doped microfiber into a knot in air. The 2-mm-diameter knot, assembled using a 3.8-mu m-diameter microfiber that is directly drawn from Er:Yb-doped phosphate glass, serves as both active medium and resonating cavity for lasing. Single-longitudinal-mode laser with threshold of about 5 mW and output power higher than 8 mu W is obtained. Their initial results suggest a simple approach to highly compact lasers based on doped microscale optical fibers. (c) 2006 American Institute of Physics.

大功率微波与臭氧等复合因子对大棚蔬菜根结线虫及土壤的作

虫（nematodes）是世界农业生产的一大障碍，每年给世界农业生产造成约1000亿美元的巨额损失，是世界各国一直关注的重点病害之一。线虫可以危害各种大田作物和各种温室植物，几乎所有的栽培植物都有线虫危害发生。随着人们环保意识的增强以及健康意识的觉醒，传统防治根结线虫的药物如溴甲烷等因对环境的破坏作用，或者由于高毒、使用不便、抗药性等原因而迅速退出历史舞台，研究环保高效防治线虫成为世界各国竞相发展的技术之一。本研究尝试通过物理方式防治蔬菜根结线虫，并调查了对土壤质量的影响，主要内容包括： 1. 设计制造了功率20 Kw，频率为915 MHz的大功率土壤微波处理机，并通过了田间试验; 2. 设计制造了每小时120 g臭氧产量的便携式臭氧土壤处理机，并通过了田间试验; 3. 采用4因素3水平正交法L9(34)在山东寿光蔬菜大棚进行了蔬菜根结线虫的防治试验，综合考察微波、臭氧、微波吸收剂、EM菌等不同处理水平对根结线虫和对土壤质量的影响，结果表明： 1) 大棚土壤经微波60 s照射能够显著降低甜瓜根结线虫数和根结指数（p < 0.05），盆栽试验只需处理10 s即可显著防治甜瓜根结线虫（p < 0.01）;以120 g/h臭氧浓度处理5 s也能显著降低甜瓜根结线虫的数量（p < 0.05）;田间施入5 g/m2的EM菌，能够显著降低甜瓜根结线虫的数量（p < 0.05）;盆栽试验中微波吸收剂具有降低根结线虫数量的趋势，但是不同处理水平之间差异不显著，田间试验则具有增加根结线虫的趋势，不同处理水平之间也没有显著差异。 2) 微波不同处理水平之间对甜瓜单瓜重的影响没有显著差异;以120 g/h臭氧浓度处理甜瓜能够显著增加甜瓜单瓜重（p < 0.05）;200 g/m2微波吸收剂能够显著提高甜瓜单瓜重（p < 0.05）;以5 g/m2EM菌处理土壤则显著降低甜瓜单瓜重（p < 0.05）。 3) 微波、臭氧、微波吸收剂不同处理水平对甜瓜糖度的影响没有显著差异;以3 g/m2的EM菌处理甜瓜能够显著降低甜瓜的糖度。 4) 不同因素对甜瓜硬度的影响没有显著差异。 5) 微波处理60 s能够显著提高甜瓜的果型指数（p < 0.1），臭氧、微波吸收剂、EM菌等因素不同处理水平之间对果型指数影响差异不显著。 6) EM菌5 g/m2处理浓度能够显著降低甜瓜株高（p < 0.1），微波、臭氧、微波吸收剂不同处理水平之间对株高的影响没有显著差异。 7) EM菌5 g/m2处理浓度能够显著降低甜瓜根径（p < 0.1），微波、臭氧、微波吸收剂不同处理水平之间对根径的影响没有显著差异。 8) 微波处理60 s能够显著降低表层土壤（0-5 cm）的有机质含量（p < 0.01）;以120 g/h的臭氧浓度处理，则可以显著提高10-15 cm土壤的有机质含量（p < 0.05），其它处理因素的不同水平对有机质的影响差异不显著。 9) 微波不同处理水平对土壤全氮的影响没有显著差异（p < 0.05）;120 g/h臭氧处理浓度能够显著降低表层土壤（0-5 cm）的土壤全氮量（p < 0.1）;100 g/m2微波吸收剂处理水平能够显著提高10-15 cm土壤全氮量（p < 0.05）;EM菌3 g/m2的处理水平则显著降低5-10 cm土壤全氮量（p < 0.05）。 10) 微波、微波吸收剂、EM菌不同处理水平之间对土壤全磷没有显著影响;240 g/h臭氧浓度处理5 s能够显著降低10-15 cm土层的土壤全磷含量(p < 0.05)。 11) 微波、微波吸收剂对土壤全磷没有显著影响;臭氧处理具有降低土壤有效磷的趋势，EM菌处理则有提高土壤有效磷的趋势，但是 不同处理水平之间差异不显著（p > 0.05）。 12) 微波处理对土壤EC值没有显著影响;臭氧、微波吸收剂、EM菌处理具有降低土壤EC值的趋势，但是不同处理水平之间差异不显著（p > 0.05）。 13) 微波处理30 s能够显著降低表层土壤的pH值（p < 0.05），臭氧、微波吸收剂、EM菌处理具有提高土壤pH值的趋势，但是不同处理水平之间差异不显著。

Topological objects in the O(3) nonlinear sigma model

We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2 + 1)-dimensional spacetime with the CP1 field. Furthermore, we show that there are three kinds of topological defects-vortex lines, point defects and knot exist in the (3 + 1)-dimensional model, and their topological charges, locations and motions are determined by the phi-mapping topological current theory.

Topological objects in two-gap superconductor

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology pi(2)(S-2) and pi(1)(S-1), in addition to the well-known Abelian topology pi(1)(S-1). Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology pi(3)(S-2) is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB2, Sr2RuO4, He-3, and liquid metallic hydrogen.

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.

Studies on biodegradable poly(hexano-6-lactone) fibers 1. Structure and properties of drawn poly(hexano-6-lactone) fibers

Using high molecular weight (M-n=80,000) Poly(hexano-6-lactone) (PCL'), tough and high tenacity PCL monofilaments with various draw ratios (undrawn to 9 times drawn) were prepared by melt-spinning. The relationship between microstructure and properties of the PCL fibers is described in this current IUPAC Technical Report. Analysis of microstructure of the drawn PCL fibers by wide-angle X-ray diffraction revealed typical c-axis orientation with an increase in crystallinity. It was also supported by sonic velocity measurements. The thermal, mechanical, and dynamic mechanical properties of the PCL fibers were affected significantly by draw ratio. DSC thermograms showed that the melting temperature and the enthalpy of fusion increased with draw ratio. The temperature dependence curves of dynamic viscoelasticity showed that the temperature at tan delta peak of alpha dispersion corresponding to the glass transition temperature shifted toward higher temperature and the peak value of tan delta decreased with draw ratio. The dynamic storage modulus and the sonic modulus increased with draw ratio. These results are due to the increase in crystallinity and molecular orientation with drawing, and are responsible for an increase in tensile tenacity as well as knot tenacity of the PCL fibers.