• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.137-152
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• 2014

In this paper, we prove, in the spirit of [3, 12, 20, 22, 23], the existence of infinitely many small solutions to the following quasilinear elliptic equation $-{\Delta}_{p(x)}u+{\mid}u{\mid}^{p(x)-2}u={\mid}u{\mid}^{q(x)-2}u+{\lambda}f(x,u)$ in a smooth bounded domain ${\Omega}$ of ${\mathbb{R}}^N$. We also assume that $\{q(x)=p^*(x)\}{\neq}{\emptyset}$, where $p^*(x)$ = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents. The proof is based on a new version of the symmetric mountainpass lemma due to Kajikiya [22], and property of these solutions are also obtained.

• Journal of the Korean Society of Mechanical Technology
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• v.13 no.4
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• pp.125-130
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• 2011

Technological mode progress demands the use of materials at high temperature and pressure. Constant load creep tests have been carried out over the range of stresses at high temperatures. One of the most critical factors in considering such applications as the most critical one is the creep behavior. In order to investigate the creep behavior in this study, the stress exponents during creep were determined over the temperature range of $275^{\circ}C$ to $325^{\circ}C$ and the stress range of 36MPa to 72MPa. The applicability of modified Monkman-Grant relationship was also discussed.

• Korean Journal of Materials Research
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• v.21 no.9
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• pp.477-481
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• 2011

Composites of insulating polyethylene and carbon black are widely used in switching elements, conductive paint, and other applications due to the large gap of resistance value. This research addresses the critical exponent of dielectric breakdown strength of polymer matrix composites (PMC) made with carbon black and polyethylene below the percolation threshold (Pt) for the first time. Here, Pt means the volume fraction of carbon black of which the resistance of the PMC is transferred from its sharp decrease to gradual decrease in accordance with the increase of carbon-black-filled content. First, the Pt is determined based on the critical exponents of resistivity and relative permittivity. Although huge cohesive bodies of carbon black are formed in case of being less than the Pt, a percolation path connecting the conducting phases is not formed. The dielectric breakdown strength (Dbs) of the PMC below Pt is measured by using an impulse voltage in the range from 10 kV to 40 kV to avoid the effect of joule heating. Although the observed Dbs data seems to be well fitted to a straight line with a slope of 0.9 on a double logarithm of (Pt-$V_{CB}$) and Dbs, the least squares method gives a slope of 0.97 for the PMC. It has been found that finite carbon-black clusters play an important role in dielectric breakdown.

• Polymer(Korea)
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• v.34 no.2
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• pp.97-103
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• 2010

PMMA was grafted on MWCNT surface in order to prepare conducting film composed of 6FDAbased polyimide/MWCNT. The electrical conductivity of 6FDA-based polyimide/PMMA-g-MWCNT was investigated as a function of PMMA-g-MWCNT content. Dispersion of MWCNT in 6FDA-based polyimide composite film was better than the pristine MWCNT due to the interaction force between PMMA and 6FDA-based polyimide. Electrical conductivity was interpreted by percolation threshold theory. As a result, 6FDA-6FpDA/PMMA-g-MWCNT which have high critical exponents and low critical concentration showed better dispersion than polyimide composite material that contains DABA(diamino benzoic acid).

• Korea-Australia Rheology Journal
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• v.20 no.3
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• pp.165-173
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• 2008

Multiple particle tracking microrheology is used to characterize the viscoelastic properties of biomaterial and synthetic polymer gels near the liquid-solid transition. Probe particles are dispersed in the gel precursors, and their dynamics are measured as a function of the extent of reaction during gel formation. We interpret the dynamics using the generalized Stokes-Einstein relationship (GSER), using a form of the GSER that emphasizes the relationship between the probe particle mean-squared displacement and the material creep compliance. We show that long-standing concepts in gel bulk rheology are applicable to microrheological data, including time-cure superposition to identify the gel point and critical scaling exponents, and the power-law behavior of incipient network's viscoelastic response. These experiments provide valuable insight into the rheology, structure, and kinetics of gelling materials, and are especially powerful for studying the weak incipient networks of dilute gelators, as well as scarce materials, due to the small sample size requirements and rapid data acquisition.

• Applied Science and Convergence Technology
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• v.25 no.4
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• pp.77-80
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• 2016

The $PbSc_{1/2}Nb_{1/2}O_3$ ceramics at a relatively low temperature of $1300^{\circ}C$ was successful synthesized. Solid state reaction of two-step process is not necessary. The dielectric constant, dielectric loss and admittance of ceramic samples were determined. The pyroelectric characteristics are in good agreement with the dielectric properties. Ferroelectric properties of well-formed the $PbSc_{1/2}Nb_{1/2}O_3$ ceramics are in agreement with broad distribution of relaxation phenomenon. Relatively strong frequency dependent of dielectric constant is observed at about $110^{\circ}C$. The distinct thermal hysteresis was observed in the measurement of the dielectric constant and dielectric loss. The critical exponents of during cooling and heating measurements in the $PbSc_{1/2}Nb_{1/2}O_3$ ceramics were 1.14 and 1.59 at 1 kHz, respectively.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1401-1406
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• 2003

Performance of two vapor pressure correlation equations in a polynomial expression is compared. These are the Wagner-type equation and the Inverted form equation. The equations are fitted to correlate the data in the ASHRAE tables and from NIST Chemistry WebBook for 17 pure substances. Some observations on the exponents in the two polynomial equations are made, which results in a proposal of a new closed form vapor pressure equation. The new equation yields the accuracy comparable to that of the Wagner-type equation and better than that of the Inverted form equation.

• Economic and Environmental Geology
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• v.29 no.4
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• pp.523-528
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• 1996

In Korean topography the behaviors of random fractals and multifractality are analytically and numerically studied on the mountain heights shown between $128{\sim}129^{\circ}E$ and $37{\sim}38^{\circ}N$. The phase transitions on the fractal structure are approximately found at the critical length $N_c=2000m$ from the values of standard deviations that it varies with both the longitudinal and latitudinal lengths. In the multifractal structure we assume that the mountain heights divided by the intervals of 20 m are located on the horizontal plane in two dimensional square lattice, and estimate the values of the generalized dimension and the scaling exponents by using the the box counting method for the three cases of square area ($1{\times}1km^2$, $2{\times}2km^2$, $4{\times}4km^2$).

• Steel and Composite Structures
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• v.32 no.1
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• pp.141-156
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• 2019

This paper presents the flexural behaviour of stainless steel beam-to-tubular column joints with extended endplates subjected to static loading. Moment-rotation relationships were investigated numerically by using Abaqus software with geometric and material nonlinearity considered. The prediction of damages among components was achieved through ductile damage models, and the influence of initial geometric imperfections and residual stresses was evaluated in large fabricated stainless steel joints involving hollow columns and concrete-filled columns. Parametric analysis was subsequently conducted to assess critical factors that could affect the flexural performance significantly in terms of the initial stiffness and moment resistance. A comparison between codes of practice and numerical results was thereafter made, and design recommendations were proposed for further applications. Results suggest that the finite element model can predict the structural behaviour reasonably well with the component damage consistent with test outcomes. Initial geometric imperfections and residual stresses are shown to have little effect on the moment-rotation responses. A series of parameters that can influence the joint behaviour remarkably include the strain-hardening exponents, stainless steel strength, diameter of bolts, thickness of endplates, position of bolts, section of beams and columns. AS/NZS 2327 is more reliable to predict the joint performance regarding the initial stiffness and moment capacity compared to EN 1993-1-8.

• Steel and Composite Structures
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• v.46 no.3
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• pp.385-401
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• 2023

Steel is becoming increasingly popular due to its high strength, excellent ductility, great assembly performance, and recyclability. In reality, steel structures serving for a long time in atmospheric, industrial, and marine environments inevitably suffer from corrosion, which significantly decreases the durability and the service life with the exposure time. For the mechanical properties of corroded steel, experimental studies are mainly conducted. The existing numerical analyses only evaluate the mechanical properties based on corroded morphology at the isolated time-in-point, ignoring that this morphology varies continuously with corrosion time. To solve this problem, the relationships between pit depth expectation, standard deviation, and corrosion time are initially constructed based on a large amount of wet-dry cyclic accelerated test data. Successively, based on that, an in-situ pitting evolution method for evaluating the residual tensile strength of corroded steel is proposed. To verify the method, 20 repeated simulations of mass loss rates and mechanical properties are adopted against the test results. Then, numerical analyses are conducted on 135 models of corrosion pits with different aspect ratios and uneven corrosion degree on two corroded surfaces. Results show that the power function with exponents of 1.483 and 1.091 can well describe the increase in pit depth expectation and standard deviation with corrosion time, respectively. The effect of the commonly used pit aspect ratios of 0.10-0.25 on yield strength and ultimate strength is negligible. Besides, pit number ratio α equating to 0.6 is the critical value for the strength degradation. When α is less than 0.6, the pit number increases with α, accelerating the degradation of strength. Otherwise, the strength degradation is weakened. In addition, a power function model is adopted to characterize the degradation of yield strength and ultimate strength with corrosion time, which is revised by initial steel plate thickness.