FREE VIBRATION ANALYSIS OF ARBITRARY SHAPED PLATES BY BOUNDARY KNOT METHOD

The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.     

Characterization of structural knot distributions in UHMWPE fibers

Microbeam wide-angle X-ray diffraction (WAXD) experiments were carried out at different structural knot positions of SIOC and M4 fibers of ultra-high molecular weight polyethylene (UHMWPE). The optical microscope images revealed that SIOC fiber had bamboo-like structural knots, and M4 fiber had chaotic distribution of structural knots. WAXD patterns showed the monoclinic unit cell in the whole M4 fiber, but different lamellar orientations in the bamboo joint of SIOC fiber. In addition, small-angle X-ray scattering (SAXS) patterns confirmed that the SIOC fiber contained uniform distribution of shish structures, and differential scanning calorimetry (DSC) measurements showed that its less branched and short chains benefited the orthorhombic-hexagonal phase transformation.     

三维高频声波的矩阵压缩边界节点法模拟

本文采用边界节点法(Boundary Knot Method, BKM)求解三维高频声场．由于高频赫姆霍兹方程的解是振荡的，极大影响了数值求解的精确度，需要在计算区域增加离散点，这会增加计算量．同时对于大规模声学问题，依靠边界节点法形成的插值矩阵为满秩，导致计算量过高和存储量过大．所以本文采用矩阵压缩技术(Matrix Compression, MC)，在有效继承边界节点法高精确度的基础上减少计算内存需求和时间，从而提高计算效率．数值实验表明，MC-BKM 求解精度高、收敛速度快、计算时间少，在高频大规模声波问题中应用前景广泛．     

Topological structures of vortex and helicity analysis

In this paper, we discuss the topological structures of the vortex filaments and vortex tubes with an exact solution of a straight spiral vortex tube. We find that there are some confusions about the calculation of the helicities of a knotted vortex filament and some linked vortex filaments by using different methods. We explain how to unify these methods and give the right results. This work is supported by the National Basic Research Important Project “Nonlinear Science”     

微液滴在仿蛛丝结构TiO_2纤维表面的定向运动与粘附

制备了具有响应性的仿蛛丝周期纺锤节TiO2纤维。通过改变纤维表面微观结构、紫外光照和超声波等手段,仿蛛丝结构TiO2纤维表面浸润性会发生响应性变化。纤维表面的这种浸润性变化,不仅实现了水滴从纺锤节两端到中心处的定向运动,而且可以使得水滴被纤维纺锤节粘附。当仿蛛丝结构TiO2纤维表面为亲水状态时,无论纺锤节光滑还是粗糙,水都是从纺锤节两端向中心方向运动;当仿蛛丝结构TiO2纤维表面疏水时,水滴会被具有粗糙表面的纺锤节两端粘附。     

Controlling the mechanical properties of poly(L‐lactide– ε‐caprolactone) monofilament sutures by an acetone/water treatment

For monofilament biodegradable sutures fabricated from the L ‐lactide–ε‐caprolactone (75/25) copolymer [P(LLA/CL)], there have been some concerns regarding their mechanical properties, such as the knot‐pull strength and stiffness. This article demonstrates the further potentiality of these sutures through improvements in those properties. With the aim of diminishing the molecular orientation, particularly in the suture surface region, we adopted an expedient method to treat P(LLA/CL) sutures with an acetone/water mixture, using different times and time patterns. The changes in the molecular orientation distributions across the suture cross sections were characterized by the specific index of birefringence measured with an interference microscope. The crystal orientations, knot‐pull strengths, tensile strengths, and bending rigidity were measured. The conformational changes in suture breaking during knot‐pull tests were analyzed with high‐speed‐video observations. Morphological analyses of the fractural surfaces were performed with scanning electron microscopy. The knot‐pull strength tended to rise, in comparison with that of untreated samples, up to a certain treatment time and was accompanied by a minimal decrement of the tensile strength. The knot‐pull strength did not show an increasing trend with further treatment, whereas the tensile strength declined remarkably. The birefringence, crystal orientation, bending rigidity, fractured surface analysis, and high‐speed‐video observations revealed molecular disorientation mainly in the filament outer layers for that particular treatment causing the sutures to be considerably softer. The suture softness played a role in changing the deformation behavior of the knot when a load was applied and caused the knot‐pull strength to rise. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2449–2462, 2002     

Real Places and Torus Bundles

If M is a hyperbolic once-punctured torus bundle over S ¹, then the trace field of M has no real places.     

Peripheral polynomials of hyperbolic knots

If K is a hyperbolic knot in S³, an algebraic component of its character variety containing one holonomy of the complete hyperbolic structure of finite volume of S³K is an algebraic curve . The traces of the peripheral elements of K define polynomial functions in , which are related in pairs by polynomials (peripheral polynomials). These are determined by just two adjacent peripheral polynomials. The curves defined by the peripheral polynomials are all birationally equivalent to , with only one possible exception. The canonical peripheral polynomial relating the trace of the meridian with the trace of the canonical longitude of K, is a factor of the A-polynomial.