• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

• Journal of Mechanical Science and Technology
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• v.14 no.1
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• pp.84-92
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• 2000

A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.

• Journal of the Korean Physical Society
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• v.73 no.10
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• pp.1541-1545
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• 2018

We study lattice thermal conductivity of $Sb_2Te_3$ using molecular dynamics simulations. The interatomic potentials are fitted to reproduce total energy and elastic constants, and phonon properties calculated using the potentials are in reasonable agreement with first-principles calculations and experimental data. Our calculated lattice thermal conductivities of $Sb_2Te_3$ decrease with temperature from 150 K to 500 K. The in-plane lattice thermal conductivity of $Sb_2Te_3$ is higher than cross-plane lattice thermal conductivity of $Sb_2Te_3$, as in the case of $Bi_2Te_3$, which is consistent with the anisotropy of the elastic constants.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2731-2736
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• 2007

In this paper, incompressible flow over a cylinder near a plane wall using the Immersed Boundary. Finite Difference Lattice Boltzmann Method (IB-FDLBM) is implemented. In this present method, FDLBM is mixed with IBM by using the equilibrium velocity. We introduce IBM so that we can easy to simulate bluff-bodies. With this numerical procedure, the flow past a circular cylinder near a wall is simulated. We calculated the flow patterns about various Reynolds numbers and gap ratios between a circular cylinder and plane wall. So these are enabled to observe for vortex shedding. The numerical results are found to be in good agreement with those of previous studies.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.181-193
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• 1997

The enumeration of various classes of paths in the real plane has an important implications in the area of combinatorics wit statistical applications. In 1887, D. Andre [3, pp. 21] first solved the famous ballot problem, formulated by Berttand [2], by using the well-known reflection principle which contributed tremendously to resolve the problems of enumeration of various classes of lattice paths in the plane. First, it is necessary to state the definition of NSEW-paths in the palne which will be employed throughout the paper. From [3, 10, 11], we can find results concerning many of the basics discussed in section 1 and 2.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.457-468
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• 1999

Autologistic lattice process is used to model binary spatial data. A conditional probability is derived for the incomplete data where the lattice consists of partially yet systematically observed sites. This result, which is interesting in its own right, is in turn applied to area prediction in the plane.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.45-48
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• 2008

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.

• Proceedings of the KSR Conference
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• 2008.11b
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• pp.1403-1406
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• 2008

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.575-580
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• 2000

Recently it is increased by degrees to construct complex and large lattice structure such as bridge, tower and crane structures. It is very important problem to know dynamic properties of such structures. Authors presented new dynamic response analysis algorithm for rectilinear structure already. This analysis algorithm is combined transfer stiffness coefficient method with Newmark method. Presented method improves the computational accuracy remarkably owing to advantage of the transfer stiffness coefficient method. This paper formulates dynamic response analysis algorithm for plane lattice structure expanding rectilinear structures.

• Journal for History of Mathematics
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• v.23 no.2
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• pp.101-121
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• 2010

This article includes an introduction, a history of Pick's theorem on lattice polyhedron and its proof, Reeve's theorem on 3-dimensional lattice polyhedrons extended from the Pick's theorem and Ehrhart polynomial generalized as an n-dimensional lattice polyhedron, and then shows the relationship between the volume of 3-dimensional polyhedron and the number of its lattice points by means of Reeve's theorem. It is aimed to apply the relationship to the visualization of sums in sequences.