• 한국전산유체공학회:학술대회논문집
• /
• 2008.03a
• /
• pp.355-358
• /
• 2008

In order to investigate the physical mechanism of the energy cascade in homogeneous isotropic turbulence, we introduce Galilean-invariant energy and its transfer rate in the real space as a function of position, time and scale. By using a database of direct numerical simulations (DNS) of homogeneous isotropic turbulence, it is shown that (i) fully developed turbulence consists of multi-scale coherent vortices of tubular shapes, (ii) the energy at each scale is mainly confined in vortex tubes with the radii of the same order of the length scale, and (iii) the energy transfer takes place around pairs (especially, anti-parallel pairs) of such vortex tubes. Based on these observations, it is suggested that the energy cascade can be caused, in the real space, by the process of the stretching and creation of smaller (i.e. thinner) vortex tubes by the straining field around pairs of larger (i.e. fatter) vortex tubes. Indeed, it is quite easy to find such events (in our DNS fields) which strongly support this scenario of the energy cascade.

• 한국전산유체공학회:학술대회논문집
• /
• 2008.10a
• /
• pp.355-358
• /
• 2008

In order to investigate the physical mechanism of the energy cascade in homogeneous isotropic turbulence, we introduce Galilean-invariant energy and its transfer rate in the real space as a function of position, time and scale. By using a database of direct numerical simulations (DNS) of homogeneous isotropic turbulence, it is shown that (i) fully developed turbulence consists of multi-scale coherent vortices of tubular shapes, (ii) the energy at each scale is mainly confined in vortex tubes with the radii of the same order of the length scale, and (iii) the energy transfer takes place around pairs (especially, anti-parallel pairs) of such vortex tubes. Based on these observations, it is suggested that the energy cascade can be caused, in the real space, by the process of the stretching and creation of smaller (i.e. thinner) vortex tubes by the straining field around pairs of larger (i.e. fatter) vortex tubes. Indeed, it is quite easy to find such events (in our DNS fields) which strongly support this scenario of the energy cascade.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.259-264
• /
• 2007

In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was mode1ed as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the sealing center and the power function of the radial direction. By use of the mapping type infinite element, the consistent e1ements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.4 no.2
• /
• pp.91-107
• /
• 1992

A numerical formulation is developed to solve the linear three-dimensional hydrodynamic equations which describes wind induced flows in a homogeneous shelf sea. The hydmdynamic equations are at the outset separated into two systems. namely, an equation containing the gradient of sea surface elevation and the mean flow (external mode) and an equation describing the deviation from the mean flow (internal mode). The Galerkin method is then applied to the internal mode equation. The eigenvalues are determined from the eigenvalue problem involving the vertical eddy viscosity subject to a homogeneous boundary condition at the surface and a sheared boundary condition at the sea bed. The model is tested in a one-dimensional channel with uniform depth under a steady, uniform wind. The analytical velocity profile by Cooper and Pearce (1977) using a constant vertical eddy viscosity in channels of infinite and finite length is chosen as a benchmark solution. The model is also tested in a homogeneous, rectangular basin with constant depth under a steady, uniform wind field (the Heaps' Basin of the North Sea scale).

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.365-376
• /
• 2004

The purpose of this study is to show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met. In particular, as a basis function, we are interested in using a conditionally positive definite function $\Phi$ whose generalized Fourier transform is of the form $\Phi(\theta)\;=\;F(\theta)$\mid$\theta$\mid$^{-2m}$ with a bounded function F > 0.

• Journal of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1379-1410
• /
• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.625-633
• /
• 1995

Classical Fatous' theorem asserts that the non-tangential limit of the Poisson integral of an integrals function on $[\pi, \pi]$ exists a.e.

• Communications of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.789-797
• /
• 2020

By considering a certain univalent function in the open unit disk 𝕌, that maps 𝕌 onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We determine the coefficient bounds for functions in this new class. Relevant connections of some of the results obtained with those in earlier works are also provided.

• East Asian mathematical journal
• /
• v.21 no.1
• /
• pp.41-48
• /
• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• Kyungpook Mathematical Journal
• /
• v.50 no.2
• /
• pp.297-306
• /
• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.