• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.227-245
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• 2016

A generalized constant ratio surface (GCR surface) is defined by the property that the tangential component of the position vector is a principal direction at each point on the surface, see [8] for details. In this paper, by solving some differential equations, a complete classification of Lorentz GCR surfaces in the three-dimensional Minkowski space is presented. Moreover, it turns out that a flat Lorentz GCR surface is an open part of a cylinder, apart from a plane and a CMC Lorentz GCR surface is a surface of revolution.

• Journal of Korean Society for Quality Management
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• v.14 no.1
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• pp.26-32
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• 1986

A class of multi-factor designs for estimating the slope of second order response surfaces is presented. For multi-factor designs the variance of the estimated slope at a point is a function of the direction of measurement of the slope and the design. If we average the variance over all possible directions, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the design origin. This property is called "slope-rotatability over all directions", and the necessary and sufficient conditions for a design to have this property are given and proved. The class of design with this property is mainly discussed.

• Journal of the Korean Statistical Society
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• v.17 no.2
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• pp.121-133
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• 1988

In this paper a class of mixture designs for estimating the slope of second order Scheffe polynomial response surfaces for mixture experiments with q components is presented. The variance of the estimated directional slope at a point is a function of the direction of the slope and the design. If the variance is averaged over all possible directions in the (q-1)-dimensional simplex, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the centroid point. This property is called "slope-rotatability over al directions in the simplex", and the necessary and sufficient conditions for mixture design to have this property are given and proved. The class of designs with this property is compared with other mixture designs and discussed.discussed.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.3
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• pp.27-32
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• 2008

This paper describes a contact atomic force microscope (AFM) that can be used for high-speed precision measurements of microstructured surfaces. The AFM is composed of an air-bearing X stage, an air-bearing spindle with the axis of rotation in the Z direction, and an AFM probe unit. The traversing distance and maximum speed of the X stage are 300 mm and 400 mm/s, respectively. The spindle has the ability to hold a sample in a vacuum chuck with a maximum diameter of 130 mm and has a maximum rotation speed of 300 rpm. The bandwidth of the AFM probe unit in an open loop control circuit is more than 40 kHz. To achieve precision measurements of microstructured surfaces with slopes, a scanning strategy combining constant height measurements with a slope compensation technique is proposed. In this scanning strategy, the Z direction PZT actuator of the AFM probe unit is employed to compensate for the slope of the sample surface while the microstructures are scanned by the AFM probe at a constant height. The precision of such a scanning strategy is demonstrated by obtaining profile measurements of a microstructure surface at a series of scanning speeds ranging from 0.1 to 20.0 mm/s.

• Journal of the Korean Geotechnical Society
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• v.21 no.8
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• pp.107-116
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• 2005

Generally, when the stability of the geosynthetic reinforced soil slopes is analyzed, the required tensile forces of each reinforcement layers are calculated from total reinforcement forces which are necessary to retain the equilibrium state of slip mass in which the slip surfaces are assumed to be a linear or bilinear. It is assumed that the reinforcement forces are increased or constant with depth. However, according to the instrumented field data and laboratory model test results, the maximum tensile strain of reinforcement in a reinforced soil slope is developed in a certain elevation, not a bottom of the slope. In the concept of reinforced soil, postulated failure surfaces are the traces of the position in which the reinforcement tensile forces are maximum in the layer, and the reinforcement tensile forces are related to the stress state on the postulated failure surface. Therefore, in this study, based on the distribution of normal stress on the slip surface, a new method for the evaluation of required tensile forces is suggested and a number of the instrumented field data are analyzed by newly suggested method. As a result, it is shown that the newly suggested method produces relatively accurate reinforcement tension forces.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.2
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• pp.141-151
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• 2020

Since it was first studied in 1980, solar energy analysis model for geographic information systems has been used to determine the approximate spatial distribution of terrain. However, the spatial pattern was not able to be grasped in 3D (three-dimensional) space with low accuracy due to the limitation of input data. Because of computational efficiency, using a constant value for the brightness of the sky caused the simulation results to be less reliable especially when the slope is high or buildings are crowded around. For the above reasons, this study proposed a model that predicts solar energy of vertical surfaces of buildings with four stages below. Firstly, CIE (Commission Internationale de l'Eclairage) luminance distribution model was used to calculate the brightness distribution of the sky using NREL (National Renewable Energy Laboratory) solar tracking algorithm. Secondly, we suggested a method of calculating the shadow effect using ray tracing. Thirdly, LOD (Level of Detail) 3 of 3D spatial data was used as input data for analysis. Lastly, the accuracy was evaluated based on the atmospheric radiation data collected through the ground observation equipment in Daejeon, South Korea. As a result of evaluating the accuracy, NMBE was 5.14%, RMSE 11.12, and CVRMSE 7.09%.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.107-113
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• 1990

A series of cubical triaxial tests with independent control of the three principal stresses were performed on a compressible sand. All specimens which were formed by depositing the fine sand loosely, were used. It was found that slope of the stress-strain curve increased with increased b value, and the major principal strain at failure first remains approximetely constant for b values smaller than about 0.3 for drained condition and 0.6 for undrained condition respectively, and thereafter decreases with increasing value of b. The test results showed that the direction of the strain increments at failure form acute angles with the failure surfaces for both the drained and undrained condition. The results are thus not in agreement with the normality criterion from classic plasticity theory. However, it was found that the projections of the plastic strain increment vectors on the octahedral plane are perpendicular to the faiure surface in that plane.

• Tribology and Lubricants
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• v.11 no.5
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• pp.128-135
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• 1995

Atomic force microscopy/friction force microscopy (AFM/FFM) techniques are increasingly used for tribological studies of engineering surfaces at scales, ranging from atomic and molecular to microscales. These techniques have been used to study surface roughness, adhesion, friction, scratching/wear, indentation, detection of material transfer, and boundary lubrication and for nanofabrication/nanomachining purposes. Micro/nanotribological studies of single-crystal silicon, natural diamond, magnetic media (magnetic tapes and disks) and magnetic heads have been conducted. Commonly measured roughness parameters are found to be scale dependent, requiring the need of scale-independent fractal parameters to characterize surface roughness. Measurements of atomic-scale friction of a freshly-cleaved highly-oriented pyrolytic graphite exhibited the same periodicity as that of corresponding topography. However, the peaks in friction and those in corresponding topography were displaced relative to each other. Variations in atomic-scale friction and the observed displacement has been explained by the variations in interatomic forces in the normal and lateral directions. Local variation in microscale friction is found to correspond to the local slope suggesting that a ratchet mechanism is responsible for this variation. Directionality in the friction is observed on both micro- and macro scales which results from the surface preparation and anisotropy in surface roughness. Microscale friction is generally found to be smaller than the macrofriction as there is less ploughing contribution in microscale measurements. Microscale friction is load dependent and friction values increase with an increase in the normal load approaching to the macrofriction at contact stresses higher than the hardness of the softer material. Wear rate for single-crystal silicon is approximately constant for various loads and test durations. However, for magnetic disks with a multilayered thin-film structure, the wear of the diamond like carbon overcoat is catastrophic. Breakdown of thin films can be detected with AFM. Evolution of the wear has also been studied using AFM. Wear is found to be initiated at nono scratches. AFM has been modified to obtain load-displacement curves and for nanoindentation hardness measurements with depth of indentation as low as 1 mm. Scratching and indentation on nanoscales are the powerful ways to screen for adhesion and resistance to deformation of ultrathin fdms. Detection of material transfer on a nanoscale is possible with AFM. Boundary lubrication studies and measurement of lubricant-film thichness with a lateral resolution on a nanoscale have been conducted using AFM. Self-assembled monolyers and chemically-bonded lubricant films with a mobile fraction are superior in wear resistance. Finally, AFM has also shown to be useful for nanofabrication/nanomachining. Friction and wear on micro-and nanoscales have been found to be generally smaller compared to that at macroscales. Therefore, micro/nanotribological studies may help def'me the regimes for ultra-low friction and near zero wear.