• Honam Mathematical Journal
• /
• v.38 no.2
• /
• pp.305-316
• /
• 2016

In this paper we study general rotational surfaces in the 4-dimensional Euclidean space $\mathbb{E}^4$ and give a characterization of flat general rotational surface with pointwise 1-type Gauss map. Also, we show that a flat general rotational surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.

• Korean Journal of Mathematics
• /
• v.25 no.4
• /
• pp.537-554
• /
• 2017

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

• Journal of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.379-396
• /
• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• KSTLE International Journal
• /
• v.10 no.1_2
• /
• pp.1-5
• /
• 2009

This paper reports an investigation on nanotribological properties of silicon nanochannels coated by a diamond-like carbon (DLC) film. The nanochannels were fabricated on Si (100) wafers by using photolithography and reactive ion etching (RIE) techniques. The channeled surfaces (Si channels) were then further modified by coating thin DLC film. Water contact angle of the modified and unmodified Si surfaces was examined by an anglemeter using the sessile-drop method. Nanotribological properties, namely friction and adhesion forces, of the Si channels coated with DLC (DLC-coated Si channels) were investigated in comparison with those of the flat Si, DLC-coated flat Si (flat DLC), and Si channels, using an atomic force microscope (AFM). Results showed that the DLC-coated Si channels greatly increased hydrophobicity of silicon surfaces. The DLC coating and Si channels themselves individually reduced adhesion and friction forces of the flat Si. Further, the DLC-coated Si channels exhibited the lowest values of these forces, owing to the combined effect of reduced contact area through the channeling and low surface energy of the DLC. This combined modification could prove a promising method for tribological applications at small scales.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1037-1048
• /
• 1997

We show that an asymptotically Euclidean scalar-flat Kahler metric ona complex surface can be smoothly conformally compactified at the infinity point. We discuss some implication of this, characterizing such metrics on $C^2$ blown up at some points.

• Tribology and Lubricants
• /
• v.14 no.1
• /
• pp.54-63
• /
• 1998

In many practical lubricated contacts such as a rough concentrated contact on the sliding of nominally flat surfaces, the fluid may be of molecular (nanometer) scale owing to the asperity interactions on the surfaces. Under this condition, there is insufficient lubricant on the concentrated contact spot to maintain a realistic continuum. Rheological behavior for this kind of concentrated contact has been studied extensively to know whether the application of viscous fluid model is appropriate. The interaction of two rough surfaces is simplified as perfectly flat-rough surfaces contact under certain conditions by "composite topography" and for a nanometer scale fluid film, three kinds of rheological fluid behavior are analyzed in elastohydrodynamic asperity point contact.t contact.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 1997.10a
• /
• pp.173-182
• /
• 1997

In many practical lubricated contacts such as a rough concentrated contact on the sliding of nominally flat surfaces, the fluid may be of molecular (nanometer) scale owing to the asperity interactions on the surfaces. Under this condition, there is insufficient lubricant on the concentrated contact spot to maintain a realistic continuum. Rheological behavior for this kind of concentrated contact was studied to know whether the application of viscous fluid model is appropriate. The interaction of two rough surfaces is simplified as perfectly flat-rough surfaces contact under certain conditions by "composite topography" and for a nanometer scale fluid film, three kinds of rheological fluid behavior are analyzed in elastohydrodynamic asperity point contact.t contact.

• KSTLE International Journal
• /
• v.9 no.1_2
• /
• pp.10-12
• /
• 2008

Silicon micro-patterns were fabricated on Si (100) wafers using photolithography and DRIE (Deep Reactive Ion Etching) fabrication techniques. The patterned shapes included micro-pillars and micro-channels. After the fabrication of the patterns, the patterned surfaces were chemically modified by coating Z-DOL (perfluoropolyether, PFPE) thin films. The surfaces were then evaluated for their micro-friction behavior in comparison with those of bare Si (100) flat, Z-DOL coated Si (100) flat and uncoated Si patterns. Experimental results showed that the chemically treated (Z-DOL coated) patterned surfaces exhibited the lowest values of coefficient of friction when compared to the rest of the test materials. The results indicate that a combination of both the topographical and chemical modification is very effective in reducing the friction property. Combined surface treatments such as these could be useful for tribological applications in miniaturized devices such as Micro/Nano-Electro-Mechanical-Systems (MEMS/NEMS).

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.987-1004
• /
• 2018

In this paper, we get several centroaffine invariant properties for a ruled surface in ${\mathbb{R}}^4$ with centroaffine theories of codimension two. Then by solving certain partial differential equations and studying a centroaffine surface with some centroaffine invariant properties in ${\mathbb{R}}^4$, we obtain such a surface is centroaffinely equivalent to a ruled surface or one of the flat centered cyclic surfaces. Furthermore, some centroaffine invariant properties for centered cyclic surfaces are considered.

• Korean Journal of Mathematics
• /
• v.24 no.4
• /
• pp.613-626
• /
• 2016

In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.