• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.141-154
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• 2023

We study the stability of traveling waves of a certain chemotaxis model. The traveling wave solution is a central object of study in a chemotaxis model. Kim et al. [8] introduced a model on a population and nutrient densities based on a nonlinear diffusion law. They proved the existence of traveling waves for the one dimensional Cauchy problem. Existence theory for traveling waves is typically followed by stability analysis because any traveling waves that are not robust against a small perturbation would have little physical significance. We conduct a numerical nonlinear stability for a few relevant instances of traveling waves shown to exist in [8]. Results against absolute additive noises and relative additive noises are presented.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.607-612
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• 2001

Rotary ultrasonic motors are based on the traveling wave generated by piezo materials attached on the stator. Large scale model of an annular ring was built to understand the fundamental mechanism involved in the rotary ultrasonic motors. Traveling wave on the structure can be generated by superposing two standing waves. Precise matching of the amplitudes and phase shift between two standing waves in time and space is the key to the success of generating a traveling wave.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.661-666
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• 2000

Traveling wave on the structure can be generated by superposing two standing waves. Precise matching of the amplitudes and phase shift between two standing waves in time and space is the key to the success of generating a traveling wave. The principle of generating a traveling wave on the structure is utilized in the construction of linear and rotary type ultrasonic motors. This paper demonstrates experimentally generating a traveling wave on the simply supported beam.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.26 no.2
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• pp.51-60
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• 2012

An improved method for detecting fault distance in overhead transmission lines is described in this paper. Based on single-ended measurement, propagation theory of traveling waves together with the wavelet transform technique is used. In estimating fault location, a simple, but fundamental method using the time difference between the two consecutive peaks of transient signals is considered; however, a new method to enhance measurement sensitivity and its accuracy is sought. The algorithm is developed based on the lattice diagram for traveling waves. Representing both the ground mode and alpha mode of traveling waves, in a lattice diagram, several relationships to enhance recognition rate or estimation accuracy for fault location can be found. For various cases with fault types, fault locations, and fault inception angles, fault resistances are examined using the proposed algorithm on a typical transmission line configuration. As a result, it is shown that the proposed system can be used effectively to detect fault distance.

• Journal of electromagnetic engineering and science
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• v.11 no.4
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• pp.290-297
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• 2011

Recent progresses in the live electrooptic imaging (LEI) technique are reviewed with emphasis on its functionality of real-time visual accesses to traveling electric waves in the GHz range. Together with the principles, configurations, and procedures for the visual observation experiments by an LEI camera system, the following results are described as examples indicating the wide application ranges of the technique; Ku-band waves on arrayed planar antennas, waves on a Gb/s-class digital circuit, W-band waves traveling both in slab-waveguide modes and aerially, backward-traveling wave along composite right/left-handed transmission line, and, waves in monolithic microwave integrated circuit module case.

• Journal of Advanced Marine Engineering and Technology
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• v.27 no.5
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• pp.590-599
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• 2003

In this study. object transport method based on ultrasonic flexural vibration is presented. Ultrasonic vibration generates ultrasonic traveling waves on the surface of elastic medium. Objects are transported through the interaction with traveling waves propagating in medium. Two types of transport methods are studied： frictional drive and acoustic levitation. With frictional drive, objects are transported in contact with the beam in the opposite direction of wave propagation whereas with acoustic levitation, objects are acoustically levitated above the beam surface and transported in the wave propagation direction. Transport characteristics are experimentally investigated using objects of different shapes and sizes. The transition from acoustic levitation mode to frictional drive mode is also examined. and it is found to occur when the ratio of mass to area of an object exceeds the threshold ratio of mass to area. It is envisaged that this feasibility study will serve as a stepping-stone for ultrasonic vibration to become an effective industrial material handling device in the future.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.261-273
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• 2015

We consider the hyperelastic rod equation describing nonlinear dispersive waves in compressible hyperelastic rods. We investigate the existence of certain traveling wave solutions to this equation. We also determine whether two other equations(the b-family equation and the modified Camassa-Holm equation) have our solution type.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.383-395
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• 2010

In the present paper, we construct the traveling wave solutions involving parameters of nonlinear evolution equations in the mathematical physics via the (3+1)- dimensional potential- YTSF equation, the (3+1)- dimensional generalized shallow water equation, the (3+1)- dimensional Kadomtsev- Petviashvili equation, the (3+1)- dimensional modified KdV-Zakharov- Kuznetsev equation and the (3+1)- dimensional Jimbo-Miwa equation by using a simple method which is called the ($\frac{G'}{G}$)- expansion method, where $G\;=\;G(\xi)$ satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.4
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• pp.272-279
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• 2002

The time-dependent frequency and energy of free vibration of the spagetti problem, that is the axially moving continuum with time-varying length, are investigated. Exact expressions for the natural frequency and time-varying vibration energy are derived by dealing with traveling waves. The vibration period increases with increasing length, but the free vibration energy decreases. When the string undergoes retraction, the vibration energy increases with time. The free response of the time-varying string is represented by superposing two traveling waves.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.11
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• pp.2095-2100
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• 2009

Since most of the Extra High Voltage (EHV) transmission lines are untransposed and multi-circuits, errors are occurred inevitably because of the unbalanced impedances of the lines and so on. Therefore, a distance relaying algorithm applicable to the untransposed multi-circuits transmission lines needs to be developed. The proposed algorithm of fault location estimation in the paper uses the fundamental phasor to reduce the effects of the harmonics. This algorithm also analyzes the second-order difference of the phasor to calculate the traveling times of waves generated by faults. The traveling time of the waves generated by faults is derived from the second-order difference of the phasor. Finally, the distance from the relaying point to the faults is estimated using the traveling times. To analyze the performance of the algorithm, a power system with the EHV untransposed double-circuit transmission lines are modeled and simulated under various fault conditions such as several fault types, fault locations, fault inception angles and fault resistances. The results of the simulations show that the proposed algorithm has the capability to estimate the fault locations quickly and accurately.