• 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 the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.579-593
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• 2007

In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the II-W and the II-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.4
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• pp.193-200
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• 1985

In the reflection and transmission of a plane wave(TE) from a dielectric plane surface oscillating sinusoidally perpendicular to its surface, one could assume that the boundary moves with a uniform velocity equal to the instantaneous oscillating velocity. The reflected and the transmitted fields are obtained as the function of the incident angles, the dielecri'c permittivity, and the oscillating velocities according to the extended Lorentz transform.

• Progress in Superconductivity and Cryogenics
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• v.12 no.4
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• pp.13-16
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• 2010

The Lorentz force distribution of a high $T_c$ superconducting tape with increasing transport currents in magnetic field ($H_a$) was visualized. The external magnetic field was applied normally to the coated conductor tape surface after zero-field cooling, and the transport current ($I_a$) was increased stepwise from 0 to 90 % of the values of the critical current ($I_c$ ($H_a$)) at applied filed, Ha. The field distribution (H(x)) near the sample surface across the tape width (2w) was measured using the scanning Hall probe method. Applying an inversion to the measured field distribution, we obtained the underlying current distribution (J(x)), from which the magnetic induction, B(x) was calculated with Biot-Savart law. Then Lorentz force per unit length was calculated using F(x)=J(x)${\times}$B(x), which appears to be very inhomogeneous along the tape width due to the complicated distributions of J(x) and B(x).

• International Journal of Aeronautical and Space Sciences
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• v.15 no.1
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• pp.82-90
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• 2014

In this paper, the effect of Lorentz force on the stability of attitude orientation of a charged spacecraft moving in an elliptic orbit in the geomagnetic field is considered. Euler equations are used to derive the equations of attitude motion of a charged spacecraft. The equilibrium positions and its stability are investigated separately in the pitch, roll and yaw directions. In each direction, we use the Lorentz force to identify an attitude stabilization parameter. The analytical methods confirm that we can use the Lorentz force as a stabilization method. The charge-to-mass ratio is the main key of control, in addition to the components of the radius vector of the charged center of the spacecraft, relative to the center of mass of the spacecraft. The numerical results determine stable and unstable equilibrium positions. Therefore, in order to generate optimum charge, which may stabilize the attitude motion of a spacecraft, the amount of charge on the surface of spacecraft will need to be monitored for passive control.

• East Asian mathematical journal
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• v.33 no.1
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• pp.115-121
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• 2017

The purpose of this paper is to show how to represent a maximal spacelike surface in $L^n$ in terms of its generalized Guass map.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.6
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• pp.371-378
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• 1986

In the reflection and transmission of a transverse magnetic wave(TM wave) from a dielectric plane osillating sinusoidally perpendicular to ist surface, one could assume that the boundary moves with a uniform nelocity equal to the instantaneous socillating velodity. According to the extended Lorentz transform, the reflected and the transmitted field are obatained as the function of the dielectric permittivity, the oscillating velocities, and the incident angles. The above results are analyzed graphically.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.10 s.175
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• pp.195-201
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• 2005

A laterally driven electromagnetic microactuator (LaDEM) is presented, and a micro-optical switch is designed and fabricated as a possible application. LaDEM provides parallel actuation of the microactuator to the silicon substrate surface (in-plane mode) by the Lorentz force. Poly-silicon-on-insulator (Poly-SOI) wafers and a reactive ion etching (RIE) process were used to fabricate high-aspect-ratio vertical microstructures, which allowed the equipment of a vertical micro mirror. A fabricated arch-shaped leaf spring has a thickness of $1.8{\mu}m$, width of $16{\mu}m$, and length of $800{\mu}m$. The resistance of the fabricated structure fer the optical switch was approximately 5$\Omega$. The deflection of the leaf springs increases linearly up to about 400 mA and then it demonstrates a buckling behavior around the current value. Owing to this nonlinear phenomenon, a large displacement of $60{\mu}m$ could be measured at 566 mA. The displacement-load relation and some dynamic characteristics are analyzed using the finite element simulations.

• Proceedings of the Optical Society of Korea Conference
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• 2008.07a
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• pp.215-216
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• 2008

Electricity unified field is described based on magnetic theory. Maxwell Einstein Lorentz Equation & pair particle photon model was introduced for Photonics. Refractive index is calculated as deceleration and deflection of photon due to photo-induced surface magnetism. MEL equation was proved with magneto-jet assumption.