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.

Applicability Range of Stoneys Formula and Modified Formulas for a Film/Substrate Bilayer

In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

Extended Stoney'S Formula For A Film-Substrate Bilayer With The Effect Of Interfacial Slip

The curvature-stress relation is studied for a film-substrate bilayer with the effect of interfacial slip and compared with that of an ideal interface without interfacial slip. The interfacial slip together with the dimensions, elastic and interfacial properties of the film and substrate layers can cause a significant deviation of curvature-stress relation from that with an ideal interface. The interfacial slip also results in the so-called free edge effect that the stress, constraint force, and curvature vary dramatically around the free edges. The constant curvature as predicted by Stoney's formula and the Timoshenko model of an ideal interface is no longer valid for a bilayer with a nonideal interface. The models with the assumption of an ideal interface can also lead to an erroneous evaluation on the true stress state inside a bilayer with a nonideal interface. The extended Stoney's formula incorporating the effects of both the layer dimensions and interfacial slip is presented.

Search For Critical Slip Surface In Slope Stability Analysis By Spline-Based Ga Method

The stability of a soil slope is usually analyzed by limit equilibrium methods, in which the identification of the critical slip surface is of principal importance. In this study the spline curve in conjunction with a genetic algorithm is used to search the critical slip surface, and Spencer's method is employed to calculate the factor of safety. Three examples are presented to illustrate the reliability and efficiency of the method. Slip surfaces defined by a series of straight lines are compared with those defined by spline curves, and the results indicate that use of spline curves renders better results for a given number of slip surface nodal points comparing with the approximation using straight line segments.

Modified formula of Malus' law for Glan-Taylor polarizing prisms

A simple three-axis model has been developed, which has been successfully applied to the analysis of the light transmittance in spatial incident angle and the simulation of modified formula of Malus' law for Glan-Taylor prisms. Our results indicate that the fluctuations on the cosine squared curve are due to specific misalignments between the axis of the optical system, the optical axis of the prism and the mechanical axis (rotation axis) of prism, which results in the fact that different initial relative location of the to-be-measured-prism in the testing system corresponds to different shape of Malus' law curve. Methods to get absolutely smooth curve are proposed. This analysis is available for other kinds of Glan-type prisms. (C) 2004 Elsevier B.V. All rights reserved.

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.

Can the occurrence of rare insertion/deletion polymorphisms in human mtDNA be verified from phylogeny?

Due to its specific characteristics, such as maternal inheritance and absence of recombination, each mtDNA belongs to certain monophyletic clade in the rooted mtDNA tree (haplogroup) according to the mutations it harbors. Rare mutation (excluding parallel mutation) occurring at multiple times in different haplogroups could thus be a potential reading error according to the mtDNA phylogeny. This experience has been widely used in double-checking the credibility of the rare mutations in human mtDNA sequences. However, no test has been performed so far for the feasibility of applying this strategy to the rare insertion/deletion (indel) events in mtDNA sequences. In this study, we attempted to relate the rare indels in mtDNAs to their haplogroup status in a total of 2352 individuals from 50 populations in China. Our results show that the insertion of A at position 16259 is restricted to a subclade of haplogroup C and can be verified. The other indel polymorphisms, which occur in the repeat of the deleted or inserted nucleotide(s), may not be distinguished from phantom mutations from a phylogenetic point of view. Independently and multiply sequencing the fragment with the indel is the best and the most reliable way for confirmation.

Lack of genetic association between the angiotensin-converting enzyme gene insertion/deletion polymorphism and longevity in a Han Chinese population

Introduction. The insertion/deletion polymorphism of the angiotensin-converting enzyme (ACE) gene has been reported to associate with human longevity. However, little information is available in a Han Chinese longevity Population. Therefore, we investigat

A miniature insertion element transposable in Microcystis sp FACHB 854

A 186-bp sequence with imperfect terminal inverted repeats and target direct repeats but without any transposase-encoding capacity was found to be transposable in an isolate derived from Microcystis sp. FACHB 854. This miniature insertion element, designated as ISM854-1, and with its homologues present at least 10 copies in the genome of Microcystis FACHB 854, is inserted into the 8-bp long and AT-rich target sequences, but none or few in other Microcystis strains. A variant of ISM854-1, denoted ISM854-1A, has perfect inverted repeat sequences and may transpose in pairs in a structure like a composite transposon. This is the first report of non-autonomous transposition of a mini-IS in a cyanobacterium.

Investigation of Electronic Energy Levels in InAs Quantum Dot with Shape of Lens by Using B-Spline Technique

The dependence of the electronic energy levels on the size of quantum dots (QDs) with the shape of spherical lens is studied by using the B-spline technique for the first time. Within the framework of the effective-mass theory, the values of electronic energy levels are obtained as a function of the height, radius and volume of QDs, respectively. When the height or radius of QDs increases, all the electronic energy levels lower, and the separations between the energy levels decrease. For lens-shape QDs, height is the key factor in dominating the energy levels comparing with the effect of radius, especially in dominating the ground-state level. These computational results are compared with that of other theoretical calculation ways. The B-spline technique is proved to be an effective way in calculating the electronic structure in QDs with the shape of spherical lens.

Rearrangeable nonblocking SOI waveguide thermooptic 4x4 switch matrix with low insertion loss and fast response

A rearrangeable nonblocking 4 x 4 thermooptic silicon-on-insulator waveguide switch matrix at 1.55-mu m integrated spot size converters is designed and fabricated for the first time. The insertion losses and polarization-dependent losses of the four channels are less than 10 and 0.8 dB, respectively. The extinction ratios are larger than 20 dB. The response times are 4.6 mu s for rising edge and 1.9 mu s for failing edge.

A silicon-on-insulator-based thermo-optic waveguide switch with low insertion loss and fast response

A silicon-on-insulator-based thermo-optic waveguide switch integrated with spot size converters is designed and fabricated by inductively coupled plasma reactive ion etching. The device shows good characteristics, including low, insertion loss of 8 +/- 1 dB for wavelength 1530-1580 nm and fast response times of 4.6 As for rising edge and 1.9 mu s for failing edge. The extinction ratios of the two channels are 19.1 and 18 dB, respectively.