• Wind and Structures
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• v.14 no.1
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• pp.35-53
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• 2011

Spherical object in wind is a common scenario in daily life and engineering practice. The main challenge in understanding the aerodynamics in turbulent wind lies in the multi-aspect of turbulence. This paper presents a wind tunnel study, which focuses on the role of turbulence integral length scale ${\Lambda}$ on the drag of a sphere. Particular turbulent flow conditions were achieved via the proper combination of wind speed, orifice perforated plate, sphere diameter (D) and distance downstream from the plate. The drag was measured in turbulent flow with $2.2{\times}10^4{\leq}Re{\leq}8{\times}10^4$, $0.043{\leq}{\Lambda}/D{\leq}3.24$, and turbulence intensity Tu up to 6.3%. Our results confirmed the general trends of decreasing drag coefficient and critical Reynolds number with increasing turbulence intensity. More interestingly, the unique role of the relative integral length scale has been revealed. Over the range of conditions studied, an integral length of approximately 65% the sphere diameter is most effective in reducing the drag.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1023-1032
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• 1997

This paper deals with certain conditions under which irreducibility of a 3-manifold is preserved under attaching a 2-handle along a simple closed curve (and then, if necessary, capping off a 2-sphere boundary component by a 3-ball).

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.41-51
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• 2001

We show that an n-dimensional unit sphere in the 2n-dimensional de Sitter space can be associated to a solution of a partial differential equation on a Lorentzian Grassmannian system coming from the integrable system theory.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.365-371
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• 1997

We prove some relation of volume with the covering radius of Riemannian manifolds and reprove well-known sphere rigidity theorems by using it.

• Honam Mathematical Journal
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• v.4 no.1
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• pp.75-84
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• 1982

Let M be a complete and orientable hypersurface of an odd-dimensional sphere $S^{2n+1}$ with quasi-integrable $(f,\;g,\;u,\;{\nu},\;{\lambda})$ -structure. The purpose of the present paper is to prove the following two theorems. (I) If the scalar curvature of M is constant and the function $\lambda$ is not locally constant, then M is a great sphere $S^{2n}$(1) or a product of two spheres with the same dimension $S^{n}(1/\sqrt{2}){\times}S^{n}(1/\sqrt{2})$. (II) Suppose that the sectional curvature of the section $\gamma(u,\;{\nu})$ spanned by u and $\nu$ is constant on M and M is compact. If the second fundamental tensor H of M is positive semi-definite and satisfies trace $$^{t}HH{\leq_-}{2n}$$, then M is a great sphere $S^{2n}$ (1) or a product of two spheres $S^{n}{\times}S^{n}$ or $S^{p}{\times}S^{2n-p}$, p being odd.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.777-787
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• 2005

In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface $$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$ for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• Journal of the Korean Ceramic Society
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• v.44 no.2 s.297
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• pp.84-88
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• 2007

CdSe hollow spheres with the diameter of about 30-50 nm were synthesized after ultrasonic irradiation in the presence of $Cd(NO_3)_2,\;Na_2SeSO_3$, and polyvinylalcohol(PVA). The characteristics of CdSe hollow spheres were analyzed using X-ray diffraction(XRD), transmission electron microscopy(TEM), UV-vis measurement and PL spectrometer. The characteristics of solvent as water and water-1-propanol mixture in the system played important roles on the controlled synthesis of hollow sphere. Based on the observation of morphological difference of CdSe, the possible mechanism of CdSe hollow sphere formation will be discussed.

• Analytical Science and Technology
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• v.22 no.2
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• pp.141-147
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• 2009

A laser induced breakdown spectroscopy (LIBS) measurement was carried out to derive an optimized measurement condition with a high reproducibility and to grow a plasma sphere to 20 mm high under a 600 mtorr vacuum in order to improve an accuracy of measurement. The measurement of the plasma was taken at a 6.0 mm distance, in the direction of a plasma sphere, from a sample. This location belongs to the outer sphere region in the plasma. The calibration curve of 'Ni' and 'Cu' was acquired by the signal intensity ratio and the atomic ratio for the samples, and linear regression of 'Cu' was $R^2$=0.9886, and the linear regression of 'Ni' was $R^2$=0.9988. The accuracy of LIBS was improved pre-existence as the measurement error of 'Ni' was 0.78%.