A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional (2-D) problems does not require any numerical integration at all. While the method has enjoyed many successful applications in linear elasticity, the above advantage has not been exploited for Stokes flow problems and incompressible media. In order to extend the BCM to these materials, this paper presents a development of the method based on the equations of Stokes flow and its 2-D kernel tensors. Potential functions are derived for quadratic boundary elements. Numerical solutions for some well-known examples are compared with the analytical ones to validate the development. IntroductionThe conventional boundary element method (BEM) for linear elasticity requires the numerical evaluation of line integrals for 2-D problems and surface integrals for threedimensional (3-D) ones (e.g., [1,2]). By observing that the integrand vector of the boundary integral equation (BIE) for the Laplace equation is divergence free, Lutz [3] has shown that a further reduction in dimensionality can be achieved. Nagarajan et al. [4,5] have extended the idea to linear elasticity and a numerical implementation of the approach is termed BCM. The divergence free property allows, for 3-D problems, the use of Stokes' theorem to transform surface integrals on the usual boundary elements into line integrals on the bounding contours of these elements (thus the name boundary contour method). For 2-D problems, a transformation based on this divergence free property converts line integrals to path-independent integrals which do not require any numerical integration: integrals are evaluated using potential functions in closedform. The above transformations are quite general and apply to boundary elements of arbitrary shapes. Thus, the BCM requires only numerical evaluation of line integrals for 3-D problems and simply the evaluation of potential functions at points on the boundary of a body for 2-D cases. The BCM also works for other linear problems such as potential theory [6], or Stokes flow as shown in this paper.Although the BCM is relatively new, a number of papers have been devoted to the development and application of the method. The primary development work reported in the literature has been for 2-D [4, 7-9] and for 3-D [5, 10, 11] linear elasticity problems. The method has also been successfully applied to design sensitivity analysis [12][13][14][15][16], shape optimization [14,17,18], analysis of thin films and layered coatings [19], fracture mechanics [20,21], and analysis of dual systems [22]. Note that due to the absence of numerical integration in 2-D, the BCM is particularly well-suited for modeling thin bodies or thin layers of fluid. Standard boundary element methods can exhibit numerical difficulties in dealing with the near singular integrals that arise from this type of geometry [23].This paper presents a development and numerical implementati...
Homoepitaxial film and semi-insulating bulk β-Ga2O3 with (001) orientation were studied using terahertz time-domain spectroscopy (THz-TDS) in the frequency region from 0.2 to 3.0 THz parallel to the [100] and [010] directions. The static permittivity of the bulk was determined to be 10.0 and 10.4 along the a-axis and b-axis, respectively, and the refractive index values at 0.2 THz are 3.17 and 3.23 for each axis. The electrical resistivity of the epilayer was extracted with good accuracy by employing the Drude–Lorentz model and without the use of electrical contacts. This noninvasive and contact-free material evaluation through THz-TDS proves to be a powerful tool for probing and obtaining various types of information about β-Ga2O3 materials such as bulk and thin films for the development of β-Ga2O3-based device applications.
The research recently conducted has demonstrated that the Boundary Contour Method (BCM) is very competitive with the Boundary Element Method (BEM) in linear elasticity Design Sensitivity Analysis (DSA). Design Sensitivity Coef®cients (DSCs), required by numerical optimization methods, can be ef®ciently and accurately obtained by two different approaches using the two-dimensional (2-D) BCM as presented in Refs.[1] and [2]. These approaches originate from the Boundary Integral Equation (BIE). As discussed in [2], the DSCs given by both BIE-based DSA approaches are identical, and thus the users can choose either of them in their applications. In order to show the advantages of this class of DSA in structural shape optimization, an ef®cient system is developed in which the BCM as well as a BIE-based DSA approach are coupled with a mathematical programming algorithm to solve optimal shape design problems. Numerical examples are presented.Key words Shape optimization, design sensitivity analysis, boundary contour method, boundary element method IntroductionShape optimization refers to the optimal design of the shape boundary of structural components, which is becoming increasingly important in mechanical engineering design. Current interest in structural shape optimization is largely motivated by demands for more cost competitive design throughout the industrial sector. Therefore, considerable effort has been devoted to developing ef®cient techniques for shape optimization.The BCM has recently emerged as an alternative numerical method to the Finite Element Method (FEM) and BEM in some applications such as stress analysis and shape optimization in linear elasticity. This young method has been surveyed in [3±6]. The remarkable achievement of the BCM is that, while conserving the advantage of boundary meshing as in the BEM (and as opposed to domain meshing required by the FEM), the method offers a further reduction in dimensionality of analysis problems with respect to the BEM. In other words, the BCM only requires numerical evaluation of 1-D line integrals for 3-D problems and simply the evaluation of functions (called potential functions) at endpoint nodes on the boundary of a body for 2-D cases.Most shape optimization problems employ mathematical programming methods where DSCs, which are de®ned as the rates of change of physical response quantities with respect to changes in the design variables, are required for determination of the optimum shape of a body. There are three methods for design sensitivity analysis, e.g. [7], namely, the Finite Difference
Golgi protein 73 (GP73) is a potential serum biomarker used in diagnosing human hepatocellular carcinoma (HCC). Compared to alpha-fetoprotein, detection of GP73 is expected to give better sensitivity and specificity and thus offers a better method for diagnosis of HCC at an early stage. In this paper, silicon nitride microcantilever was used to detect GP73. The cantilever was modified through many steps to contain antibody of GP73. The result shows that the cantilever can be used as a label-free sensor to detect this kind of biomarker.
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