• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.811-819
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• 2023

In this research we have used the definition of standard fractional vector cross product to obtain fractional curl and fractional field of a standing wave, a travelling wave, a transverse wave, a vector field in xy plane, a complex vector field and an electric field. Fractional curl and fractional field for a complex order are also discussed. We have supported the study with calculation of impedance at γ = 0, 0 < γ < 1, γ = 1. The formula discussed in this paper are useful for study of polarization, reflection, impedance, boundary conditions where fractional solutions have applications.

• Journal of Computational Design and Engineering
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• v.2 no.2
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• pp.88-95
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• 2015

Recently, fiber composite materials have been attracting attention from industry because of their remarkable material characteristics, including light weight and high stiffness. However, the costs of products composed of fiber materials remain high because of the lack of effective manufacturing and designing technologies. To improve the relevant design technology, this paper proposes a novel simulation method for deforming fiber materials. Specifically, given a 3D model with constant thickness and known fiber orientation, the proposed method simulates the deformation of a model made of thick fiber-material. The method separates a 3D sheet model into two surfaces and then flattens these surfaces into two dimensional planes by a parameterization method with involves cross vector fields. The cross vector fields are generated by propagating the given fiber orientations specified at several important points on the 3D model. Integration of the cross vector fields gives parameterization with low-stretch and low-distortion.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.09a
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• pp.11-18
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• 2005

Filament inversion routines are highly effective for target definition whenever total-field DHTEM vectors can be obtained using three-component logging tools. However most cross-hole components contain significant noise related to sensor design and errors in observation of probe rotation. Standard stacking methods can be used to improve data quality but additional statistical methods based on cross-correlation and spatial averaging of orthogonal components may be required to ensure a consistent vector migration path. Apart from assisting with spatial averaging, multiple filaments generated for successive time-windows can provide additional imaging information relating to target geometry and current migration. New digital receiver systems provide additional time-windows to provide better tracking options necessary for high-resolution imaging of this type.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.410-416
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• 2001

An algorithm of 3-D particle image velocimetry(3D-PIV) was developed for the measurement of 3-D velocity field of complex flows. The measurement system consists of two or three CCD camera and one RGB image grabber. In this study, stereo photogrammetty was applied for the 3-D matching of tracer particles. Epipolar line was used to decect the stereo pair. 3-D CFD data was used to estimate algorithm. 3-D position data of the first frame and the second frame was used to find velocity vector. Continuity equation was applied to extract error vector. The algorithm result involved error vecotor of about 0.13 %. In Pentium III 450MHz processor, the calculation time of cross-correlation for 1500 particles needed about 1 minute.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.38-43
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• 2022

In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.

• Journal of Ocean Engineering and Technology
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• v.24 no.1
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• pp.47-52
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• 2010

This study presents a modified scheme for the radar image simulation of sea waves. A simulated radar image was obtained by taking into account the dot product of the directed vector from the radar and the normal vector of the sea surface. Moreover, to calculate the radar image, we used the radar received power and radar cross section. To demonstrate the effectiveness of the proposed scheme, the wave spectrum from field data was utilized to obtain the simulated sea waves. The radar image was simulated using numerically generated sea waves. The wave statistics from the simulation agrees comparatively with those of the original field data acquired by real radar measurements.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.726-735
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• 2003

A Process of 3-D Particle image velocimetry, called here, as '3-D volume PIV' was developed for the full-field measurement of 3-D complex flows. The present method includes the coordinate transformation from image to camera, calibration of camera by a calibrator based on the collinear equation, stereo matching of particles by the approximation of the epipolar lines, accurate calculation of 3-D particle positions, identification of velocity vectors by 3-D cross-correlation equation, removal of error vectors by a statistical method followed by a continuity equation criterior, and finally 3-D animation as the post processing. In principle, as two frame images only are necessary for the single instantaneous analysis 3-D flow field, more effective vectors are obtainable contrary to the previous multi-frame vector algorithm. An Experimental system was also used for the application of the proposed method. Three analog CCD camera and a Halogen lamp illumination were adopted to capture the wake flow behind a bluff obstacle. Among 200 effective particle s in two consecutive frames, 170 vectors were obtained averagely in the present study.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.1
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• pp.21-28
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• 2000

Although commercial PIV systems have been widely used for the non-intrusive velocity field measurement of fluid flows, they are still under development and have considerable room for improvement. In this study, a single-frame double-exposure PIV system using a high-resolution CCD camera was developed. A pulsed Nd:Yag laser and high-resolution CCD camera were synchronized by a home-made control circuit. In order to resolve the directional ambiguity problem encountered in the single-frame PIV technique, the second particle image was genuinely shifted in the CCD sensor array during the time interval dt. The velocity vector field was determined by calculating the displacement vector at each interrogation window using cross-correlation with 50% overlapping. In order to check the effect of spatial resolution of CCD camera on the accuracy of PIV velocity field measurement, the developed PIV system with three different resolution modes of the CCD camera (512 ${\times}$ 512, lK ${\times}$ IK, 2K ${\times}$ 2K) was applied to a turbulent flow which simulate the Zn plating process of a steel strip. The experimental model consists of a snout and a moving belt. Aluminum flakes about $1{\mu}m$ diameter were used as scattering particles for the liquid flow in the zinc pot and the gas flow above the zinc surface was seeded with atomized olive oil with an average diameter of 1-$3{\mu}m$. Velocity field measurements were carried out at the strip speed $V_s$=1.0 m/s. The 2K ${\times}$ 2K high-resolution PIV technique was significantly superior compared to the smaller pixel resolution PIV system. For the cases of 512 ${\times}$ 512 and 1K ${\times}$ 1K pixel resolution PIV system, it was difficult to get accurate flow structure of viscous flow near the wall and small vortex structure in the region of large velocity gradient.

• Geophysics and Geophysical Exploration
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• v.5 no.3
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• pp.199-205
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• 2002

In the resistivity method, the potential difference between two grounded electrodes is measured and this can be positive or negative. The apparent resistivity and the potential difference have the same polarity. Since the electric field is the gradient of the potential, the polarity of the potential difference depends on the direction of the electric field. If the direction of the vector connecting two grounded electrodes is the same to that of the electric field, the measured potential difference and the apparent resistivity become positive. If the opposite is the case, they become negative. In general, the primary electric field and the vector connecting two potential electrodes have the same direction in a surface resistivity method. In this case, the measured potential difference is always positive because the primary electric field is greater than the secondary field. Therefore, the apparent resistivity is always positive if noise is free and topography is flat. The secondary field component, however, can be greater than the primary field component along the vector connecting two potential electrodes in the cross-hole resistivity method. Furthermore, if the secondary electric field and the vector connecting two potential electrodes have an opposite direction, the apparent resistivity become negative. Consequently, the apparent resistivity may be negative in the region where the primary electric field component along the vector connecting two potential electrodes is very small.

• Journal of KSNVE
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• v.7 no.1
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• pp.43-53
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• 1997

This paper investigated the practical use for measuring the structural intensity (power flow per width of cross section) in a uniform semi-infinite beam in flexural vibration. The structural intensity is obtained as a vector at a measurement point, One-dimensional structural intensity can be obtained from 4-point cross spectral measurement, or 2-point measurement on the assumption of far field. The measurement errors due to finite difference approximation and phase mismatch of accelerometers are examined. For precise measurements, it would be better to make the value of k$\delta$(wave number x space between accelerometers) between 0.5 and 1.0. Formulation of the relation between bending waves in structures and structural intensity makes it possible to separate the wave components by which one can get a state of the vibration field. Experimental results are obtained from 2- and 4-point measurement performed at 200mm (near field) and 400mm (far field) apart from excitation point in random excitation. the results are compared with the theoretical values and measured values of input power spectrum in order to verify the accuracy of structural intensity method, 2-point method is suggested as the practical structural intensity method.