On the efficient application of weighted essentially nonoscillatory scheme

In this paper, the efficient application of high‐order weighted essentially nonoscillatory (WENO) reconstruction to the subsonic and transonic engineering problems is studied. On the basis of the physical considerations, two techniques are proposed to enhance the accuracy and efficiency of the WENO reconstruction. First, it is observed that the WENO scheme using characteristic variable has better accuracy and convergence speed than the scheme using primitive variable. For engineering problems with shock of moderate amplitude, on the basis of the Rankine–Hugoniot conditions, a simplified characteristic‐variable‐based WENO is developed. The simplified version significantly reduces the cost overhead without sacrificing the shock‐capturing capability. Second, in this work, it is found for viscous case that it is better to include the viscous effect. On the basis of a simple analysis, the viscous correction to the parameter ε in the WENO reconstruction is proposed. Numerical results indicate, with the proposed simplified characteristic‐variable‐based reconstruction and the viscous correction, that the nonlinear WENO interpolation is sharply activated in the region of shock jump, whereas in the shockless area, the WENO interpolation weights are tuned towards the designed optimal value for better accuracy. Compared with the original characteristic‐variable‐based WENO, the current implementation has similar accuracy and reduced cost. At the same time, compared with the primitive variable‐based WENO, better accuracy and convergence speed are obtained at marginal cost overhead. Several practical cases are calculated to demonstrate the accuracy and efficiency of the current methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of a meshless solver for high Reynolds number flow

In this paper, the extension of an upwind least‐square based meshless solver to high Reynolds number flow is explored, and the properties of the meshless solver are analyzed both theoretically and numerically. Existing works have verified the meshless solver mostly with inviscid flows and low Reynolds number flows, and in this work, we are interested in the behavior of the meshless solver for high Reynolds number flow, especially in the near‐wall region. With both theoretical and numerical analysis, the effects of two parameters on the meshless solver are identified. The first one is the misalignment effect caused by the significantly skewed supporting points, and it is found that the meshless solver still yields accurate prediction. It is a very interesting property and is opposite to the median‐dual control volume based vertex‐centered finite volume method, which is known to give degraded result with stretched triangular/tetrahedral cells in the near‐wall region. The second parameter is the curvature, and according to theoretical analysis, it is found in the region with both large aspect ratio and curvature, and the streamwise residual is less affected; however, the wall‐normal counterpart suffers from accuracy degradation. In this paper, an improved method that uses a meshless solver for the streamwise residual and finite difference for wall‐normal residual is developed. This method is proved to be less sensitive to the curvature and provides improved accuracy. This work presents an understanding of the meshless solver for high Reynolds number flow computation, and the analysis in this paper is verified with a series of numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

The surjectivity of the canonical homomorphism from singular homology to Cech homology

Let be a locally -connected compact metric space. Then, the canonical homomorphism from the singular homology group to the Cech homology group is surjective. Consequently, if a compact metric space is locally connected, then the canonical homomorphism from to is surjective.

     

Crosscap numbers of pretzel knots

The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable surfaces bounded by the knot. In this paper, we determine the crosscap numbers of a large class of pretzel knots. The key ingredient to obtain the result is the algorithm of enumerating all essential surfaces for Montesinos knots developed by Hatcher and Oertel.     

Symmetry-Breaking Phenomena in an Optimization Problem for some Nonlinear Elliptic Equation

Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz boundary, $\lambda >0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p< +\infty$ if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs to the class $ {\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\} $ for the prescribed $\beta\in (0, |\Omega|).$ For any $D\in{\cal C}_{\beta}$, it is well known that there exists a unique global minimizer $u\in H^1_0(\Omega)$, which we denote by $u_D$, of the functional \[\quad J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\, dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx -\int_{\Omega}\chi_Dv\,dx \] on $H^1_0(\Omega)$. We consider the optimization problem $ E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D) $ and say that a subset $D^*\in {\cal C}_{\beta}$ which attains $E_{\beta,\Omega}$ is an optimal configuration to this problem. In this paper we show the existence, uniqueness and non-uniqueness, and symmetry-preserving and symmetry-breaking phenomena of the optimal configuration $D^*$ to this optimization problem in various settings.     

Endoscopic Observation of Tissue by Narrowband Illumination

We propose a new illumination method for a medical endoscope: narrow band imaging (NBI), in which the spectral bandwidth of the filtered light is narrowed. To confirm how the spectral specifications of the filtered light influence a reproduced image, an experiment was conducted observing the endoscopic images of the back mucosa of a human tongue. In addition, the effect of NBI on endoscopic images was investigated through preliminary clinical tests in colonoscopy and upper gastrointestinal endoscopy. It has been shown that NBI can enhance the capillary pattern and the crypt pattern on the mucosa. These patterns are useful features for diagnosing an early cancer.     

Intra-abdominal fat area is a predictor for new onset of individual components of metabolic syndrome: MEtabolic syndRome and abdominaL ObesiTy (MERLOT study)

Objective: To investigate the significance of intra-abdominal fat area (IAFA) on new onset of individual components of the metabolic syndrome: high blood pressure, dyslipidemia, or hyperglycemia. Methods: We conducted a longitudinal study using checkup data of a hospital from 1994 to 2010. Of 25,255 subjects, we examined 1,380 Japanese, who underwent computed tomography to measure IAFA and had no metabolic syndrome components at baseline. Results: During 3.6 years of the mean follow-up period, one of metabolic syndrome components occurred in 752 subjects. Of three components, high blood pressure was more prevalent. The multiple Cox regression analysis disclosed that IAFA is significantly associated with onset of metabolic syndrome components (HR: 1.05 per 10 cm², 95%CI: 1.03–1.07). This finding was independent of BMI, and significant even in non-obese individuals with body mass index <25 kg/m². Conclusions: MERLOT study demonstrates that IAFA is an independent predictor for new onset of individual components of the metabolic syndrome, even in non-obese healthy Japanese.     

Temperature Characteristics of Vibrating Type Sensor Using Micromachined Optical Fiber-Tip

An optical sensor using a quartz core microcantilever was fabricated by etching clad layer from optical fiber. The temperature dependence of the resonance frequency of this sensor was measured in atmosphere and water. The temperature coefficient of the resonance frequency in water was 1.3×10⁻³/°C, which was about one order larger than that (2.3×10⁻⁴/°C) in atmosphere. This was caused by increase of additional mass due to temperature dependence of the viscosity of water, while, the increase of the resonance frequency in atmosphere was caused by temperature dependence of Young’s modulus of the quartz core. These results were evaluated theoretically using a “string-of-beads” model.