• Journal of the Korean Society for Nondestructive Testing
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• v.37 no.2
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• pp.115-121
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• 2017

The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke's equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at $300^{\circ}C$ for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke's equation. The results showed that the variations in these parameters were in good agreement with each other.

• Journal of information and communication convergence engineering
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• v.13 no.3
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• pp.167-171
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• 2015

A radio over fiber (RoF) system is a kind of analog optical transmission system and considered as a strong candidate for the next-generation fronthaul link in the future mobile network. In RoF systems, nonlinearity compensation is essential to increase the link capacity. In this paper, we propose a nonlinearity detection and compensation scheme using a monitoring channel in RoF systems. A monitoring channel is added at the transmitter site and used for transmitting a reference signal in an RoF transmission. The nonlinearity in the RoF transmission is detected by comparing the received monitoring signal and the original reference signal at the receiver site. Finally, the nonlinearity is compensated at the receiver by giving the reverse function of the detected nonlinearity. Our results show that the proposed scheme can almost remove the error vector magnitude degradation induced by the nonlinearity in the RoF system.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.

• Journal of the Korean Ceramic Society
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• v.36 no.9
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• pp.923-929
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• 1999

The cause of optical nonlinearity induced in thermally poled silica glass is believed to be the space charge polarization. Since the second order optical nonlinearity (electro-optic effect) can be used in optical switches the optical nonlinearity in silica glass has drawn a large attention. Space charge polarization occurs when an ionic conducting material is subjected to dc electric field by the blocking electrode. Thermal poling performed to induce the optical nonlinearity in silica glass is basically identical to the process generating space charge polarization. As a first step to understand the mechanism of space charge polarization in silica glass hence the induced optical nonlinearity the absorption currents as functions of time were measured for various types of silica glasses and analyzed by the theory of space charge polarization. It was found that the electrical relaxation exhibited a step by the space charge polarization in the relatively long time range and dielectric loss peak showed a maximum at a specific temperature which is depending on type of silica glass. It was turned out that this relaxation might be a cause of nonlinearity in electrical conductivity of silica glass.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.9
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• pp.171-178
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• 2001

The nonlinearity of a laser interferometer usually ranges from sub-nanometer to several manometers. This nonlinearity, which has periodic characteristics, limits the accuracy of the interferometer at the sub-nanometer level. The nonlinearity error of the one-frequency homodyne interferometer with quadrature fringe detection results from a number of factors including polarization mixing by imperfect optical elements, unequal gain of photo detectors, lack of quadrature between two signals and misalignment. In this paper, we described a method for measuring and compensating the nonlinearity of homodyne interferometer using the elliptical fitting technique with least-square method. Experimental results demonstrate that $^\pm$3.5 nm nonlinearity can be reduced to $^\pm$0.2 nm level.

• ETRI Journal
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• v.19 no.4
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• pp.389-401
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• 1997

In this paper, we consider the relationship between nonlinearity and correlation immunity of Boolean functions. In particular, we discuss the nonlinearity of correlation immune functions suggested by P. Camion et al. For the analysis of such functions, we present a simple method of generating the same set of functions, which makes it possible to construct correlation immune functions with controllable correlation immunity and nonlinearity. Also, we find a bound for the correlation immunity of functions having maximal nonlinearity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.6
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• pp.751-756
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• 2010

Ultrasonic nonlinearity is very sensitive to changes in material properties. This paper describes the study of the correlation between heat treatment and ultrasonic nonlinearity by taking nonlinear factors into consideration. A modified formula was proposed for ultrasonic velocity. This formula indicated that the changes occurring in nonlinearity during heat treatments cause changes in the ultrasonic velocity. The experimental results show that the relative nonlinearity parameters calculated from the modified ultrasonic velocities and the ratio of amplitudes of the second harmonic and fundamental wave are in good agreement. The experimental results prove that heat treatment can result in changes in material nonlinearity. Moreover, the relative nonlinearity parameter calculated from the modified velocity formula is has a large value. Since this parameter has high sensitivity to changes in nonlinearity, it can be used to represent the relative nonlinearity change calculated in this study by using the modified formula for ultrasonic velocity.

• Journal of the Korean Society for Nondestructive Testing
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• v.36 no.1
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• pp.53-59
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• 2016

Ultrasonic nonlinear evaluation is generally utilized for detection of not only defects but also microdamage such as corrosion and plastic deformation. Nonlinearity is determined by the amplitude ratio of primary wave second harmonic wave, and the results of its comparison are used for evaluation. Owing to the experimental features, the experimental nonlinearity result contains system nonlinearity and material nonlinearity. System nonlinearity is that which is unwanted by the user; hence, it acts as an error and interrupts analysis. In this study, a bulk wave mixing technique is implemented in order to minimize the system nonlinearity and obtain the reliable analysis results. The biggest advantage of this technique is that experimental nonlinearity contains less system nonlinearity than that for the conventional nonlinear ultrasonic technique. Theoretical and experimental verifications are performed in this study. By comparing the results of the bulk wave mixing technique with those of the conventional technique, the strengths, weaknesses, and application validity of the bulk wave mixing technique are determined.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.367-380
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• 2024

Investigations has shown that the correct estimation of the effective amplification period is as important as the amplification value itself. It gets more important in 2D basins. This study presents a quantitative coefficient for consideration of the nonlinearity effect in terms of amplification value and the shift in its period which is missing or ineffectively considered in the previous studies. To attain this goal, by the application of a time domain fully nonlinear method, the deviation of the more common equivalent linear results from the basin nonlinear behavior under strong ground motions is investigated quantitatively. Also, despite the increase in the damping ratio, the possibility of the increase in the amplification due to the increase in motion strength is shown. To make the results useful in engineering practice, by introducing nonlinearity ratio, the effect of the nonlinearity is quantitatively estimated for two soft and stiff clayey basins with three different depths under a set of motions scaled to two target spectrum. Results show that at the 100 m depth soft clayey basin, while the nonlinearity ratio shows a 35% deviation at the basin edge part under DD1 motion level, its effect moves to the central part with 20% effect under DD3 motion level. By the increase in depth to 150 m, the results show a decrease in the overall effect of the nonlinear behavior for both clay types. At this depth, the nonlinearity ratio gives a 30% and 17% difference on a limited distance from outcrop at the soft clayey basin under DD1 and DD3 motion levels, respectively. At the 30 m depth basins, the nonlinearity ratio shows up to 25% difference for different cases. The presented ratio would be introduced as nonlinearity coefficients for consideration of the nonlinearity effects in the codes. The presented quantitative margins will help the designer to have a better understanding of the amplification period change because of nonlinearity over 2D basin surface.