• The Bulletin of The Korean Astronomical Society
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• v.35 no.1
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• pp.72.2-72.2
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• 2010

We use three-dimensional hydrodynamic simulations to investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a massive perturber moving on a circular orbit through a uniform gaseous medium. We assume that the background medium is non-rotating and adiabatic with index 5/3, and represent the perturber using a Plummer potential with softening radius a. This work extends our previous study where we showed that the drag force on a straight-line trajectory is proportional to a0.45 if the perturber is massive enough. This indicates that the orbital decay of supermassive black holes (SMBHs) near galaxy centers may take much longer than the prediction of the linear force formula applicable for low-mass perturbers. For the circular orbits are considered, however, we find that the nonlinear drag force becomes independent of a, but dependent instead on the orbital radius R as $\varpropto$ R0.5. This suggests not only that the choices of large values of a, for resolution issues, in recent numerical experiments for mergers of SMBH, are marginally acceptable, but also that the gaseous drag indeed provides an efficient mean for the orbtial decay of SMBHs.

• Geomechanics and Engineering
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• v.14 no.6
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• pp.571-580
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• 2018

The failure mechanism of tunnel roof is investigated with upper bound theorem of limit analysis. The stochastic settlement and nonlinear failure criterion are considered in the present analysis. For the collapse of tunnel roof, the surface settlement is estimated by the simplified stochastic medium theory. The failure curve expressions of collapse blocks in homogeneous and in layered soils are derived, and the effects of material parameters on the potential range of failure mechanisms are discussed. The results show that the material parameters of initial cohesion, nonlinear coefficient and unit weight have significant influences on the potential range of collapse block in homogeneous media. The proportion of collapse block increases as the initial cohesion increases, while decreases as the nonlinear coefficient and the unit weight increase. The ground surface settlement increases with the tunnel radius increasing, while the possible collapse proportion decreases with increase of the tunnel radius. In layered stratum, the study is investigated to analyze the effects of material parameters of different layered media on the proportion of possible collapse block.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.225-238
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• 2020

This work treats the axisymmetric buckling of functionally graded (FG) porous annular/circular nanoplates based on modified couple stress theory (MCST). The nanoplate is located at the elastic medium which is simulated by Kerr foundation with two spring and one shear layer. The material properties of the porous FG nanostructure are assumed to vary through the nanoplate thickness based on power-law rule. Based on two variables refined plate theory, the governing equations are derived by utilizing Hamilton's principle. Applying generalized differential quadrature method (GDQM), the buckling load of the annular/circular nanoplates is obtained for different boundary conditions. The influences of different involved parameters such as boundary conditions, Kerr medium, material length scale parameter, geometrical parameters of the nanoplate, FG power index and porosity are demonstrated on the nonlinear buckling load of the annular/circular nanoplates. The results indicate that with increasing the porosity of the nanoplate, the nonlinear buckling load is decreased. In addition, with increasing the material length scale parameter to thickness ratio, the effect of spring constant of Kerr foundation on the buckling load becomes more prominent. The present results are compared with those available in the literature to validate the accuracy and reliability. A good agreement is observed between the two sets of the results.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.384-384
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• 2017

In this study, the numerical investigation of nonlinear flow in a porous medium was carried out. The applied numerical model is ANSYS CFX which is a three-dimensional fluid dynamic model, and the verification of this model was carried out by using the experimental data obtained from Mayer et al works(2011). The experimental and numerical results of velocity and Reynolds number-friction coefficient relationship show relatively a good agreement. Based on the experimental results, we analysed numerically the velocity and Reynolds number-friction coefficient relationship with the variation of permeability, dynamic viscosity and porosity and quantitatively the variation by applying the best curve fitting for each case.

• Computers and Concrete
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• v.19 no.6
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• pp.677-687
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• 2017

The nonlinear buckling response of nano composite anti-symmetric functionally graded polymeric microplate reinforced by single-walled carbon nanotubes (SWCNTs) rested on orthotropic elastomeric foundation with temperature dependent properties is investigated. For the carbon-nanotube reinforced composite (CNTRC) microplate, a uniform distribution (UD) and four types of functionally graded (FG) distribution are considered. Based on orthotropic Mindlin plate theory, von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is employed to calculate the non-linear buckling response of the plate. Effects of FG distribution type, elastomeric foundation, aspect ratio (thickness to width ratio), boundary condition, orientation of foundation orthotropy and temperature are considered. The results are validated. It is found that the critical buckling load without elastic medium is significantly lower than considering Winkler and Pasternak medium.

• Earthquakes and Structures
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• v.6 no.4
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• pp.437-455
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• 2014

Some conventional lateral load patterns for pushover analysis, and proposing a new accurate pattern was investigated in present research. The new proposed load pattern has load distribution according weight and stiffness variation in height and mode shape of structure. The assessment of pushover application with mentioned pattern in X type braced steel frames and steel moment resisting frames, with stiffness and mass variation in height, was studied completely and the obtained results were compared with nonlinear dynamic analysis method (including time history analysis). The methods were compared from standpoints of some basic parameters such as displacement, drift and shape of lateral load pattern. It is concluded that proposed load pattern results are closer to nonlinear dynamic analysis (NDA) compared to other pushover load patterns especially in tall and medium-rise buildings having different stiffness and mass during the height.

• Korean Journal of Optics and Photonics
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• v.5 no.1
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• pp.67-73
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• 1994

The simulation code was developed to analyze the amplification properties of the regenerative amplifier, such as gain narrowing, nonlinear effect, and energy saturation. To reduce gain narrowing in the regenerative amplifier, the input pulse with a symmetrical shape and the same center wavelength of the active medium should be amplified in the active medium with a broad fluorescence linewidth. In this respect, Ti:Sapphire with a low nonlinear refractive index, a high saturation fluence, and a broad fluorescence linewidth is the most appropriate medium for the regenerative amplifier. The knowledge and the important parameters were acquired for the optimum design of the regenerative amplifier.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Advances in nano research
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• v.3 no.1
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• pp.29-37
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• 2015

In the current study, the nonlinear vibration properties of an embedded zigzag single-walled carbon nanotube (SWCNT) are investigated. Winkler-type model is used to simulate the interaction of the zigzag SWCNTs with a surrounding elastic medium. The relation between deflection amplitudes and resonant frequencies of the SWCNT is derived through harmonic balance method. The equivalent Young's modulus and shear modulus for zigzag SWCNT are derived using an energy-equivalent model. The amplitude - frequency curves for large-amplitude vibrations are graphically illustrated. The simulation results show that the chirality of zigzag carbon nanolube as well as surrounding elastic medium play more important roles in the nonlinear vibration of the single-walled carbon nanotubes.

• Journal of Biomedical Engineering Research
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• v.16 no.3
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• pp.359-366
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• 1995

The parameter, B/A, quantifies nonlinearity of the pressure-density relationship of propagation medium. This study investigated quantitative evaluation technique for healing fractured bones using this ultrasonic nonlinear parameter, B/A, obtained by the second harmonic amplitude method. A series of fundamental experiments were performed on cylinder phantoms made of aluminium, which demonstrated potential capability of nonlinear parameter B/A in the diagnosis of healing fractured bones using ultrasound.