• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.559-580
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• 2024

In this paper, we aim to prove coupled and common coupled fixed point theorems for contractive type conditions in the context of partial metric spaces by means of a control function, and to provide some corollaries of the established results. This paper presents a number of results that generalize and extend previous work in the field. In order to better illustrate the process, we provide examples.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.3
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• pp.227-241
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• 2017

In this study, a Volterra system for the variations of metacentric height (GM) in waves is employed to simulate the parametric roll phenomena of ships in head sea condition. Using the present Volterra system, the transfer function of each harmonic component in the GM variation is computed for different ship models, including mathematical models and a real containership, and the results are validated through the comparison with the values obtained using the direct calculations based on a weakly nonlinear time-domain method. Then, a semi-analytic approach employing a 1-degree of freedom equation for roll motion is developed to simulate the parametric roll motions in irregular waves. In the derived approach, the nonlinear and time-varying restoring forces in the waves are approximated using the Volterra system. Through simulations of the parametric roll for different sea states, the effects of the 1st and 2nd-order harmonic components of the variations in the occurrence and amplitude of the parametric roll motions are investigated. Because of the strong nonlinearities in the phenomena, a stochastic analysis is conducted to examine the statistical properties of the roll motions in consideration of the sensitivities and uncertainties in the computations.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.07a
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• pp.410-414
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• 2001

The microstructure, V-I characteristics, and stability of ZnO-Pr$_{6}$O$_{11}$-CoO-Cr$_2$O$_3$-Y$_2$O$_3$based vairstors were investigated with cooling rate in the range of 2~8$^{\circ}C$/min. The cooling rate relatively weakly affected the microstructure, and the varistor voltage and the leakage current in the V-I chracteristics. But the nonlinear exponent relatively strongly affected by cooling rate. And the cooling rate also greatly affected the stability for DC stress. In gross, the varistors cooled with 4$^{\circ}C$/min exhibited the highest performance in the densification, nonlinearity, and stability. Especially, they exhibited a high stability, in which the variation rate of the varistor voltage and the nonlinear exponent is -1.44% and -4.85%, respectively, under more severe DC stress such as (0.80 V$_{1mA}$9$0^{\circ}C$/12 h)+(0.85 V$_{1mA}$115$^{\circ}C$/12 h)\`(0.90 V$_{1mA}$12$0^{\circ}C$/12 h)+(0.95 V$_{1mA}$1$25^{\circ}C$/12 h)+(0.95 V$_{1mA}$15$0^{\circ}C$/12 h). It should be emphasized that the stability of these varistors is much superior to that of others.s.of others.s.

• Ocean Systems Engineering
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• v.8 no.4
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• pp.381-407
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• 2018

This paper presents a hybrid numerical approach, which combines a two-phase Navier-Stokes model (NS) and the fully nonlinear potential theory (FNPT), for modelling wave-structure interaction. The former governs the computational domain near the structure, where the viscous and turbulent effects are significant, and is solved by OpenFOAM/InterDyMFoam which utilising the finite volume method (FVM) with a Volume of Fluid (VOF) for the phase identification. The latter covers the rest of the domain, where the fluid may be considered as incompressible, inviscid and irrotational, and solved by using the Quasi Arbitrary Lagrangian-Eulerian finite element method (QALE-FEM). These two models are weakly coupled using a zonal (spatially hierarchical) approach. Considering the inconsistence of the solutions at the boundaries between two different sub-domains governed by two fundamentally different models, a relaxation (transitional) zone is introduced, where the velocity, pressure and surface elevations are taken as the weighted summation of the solutions by two models. In order to tackle the challenges associated and maximise the computational efficiency, further developments of the QALE-FEM have been made. These include the derivation of an arbitrary Lagrangian-Eulerian FNPT and application of a robust gradient calculation scheme for estimating the velocity. The present hybrid model is applied to the numerical simulation of a fixed horizontal cylinder subjected to a unidirectional wave with or without following current. The convergence property, the optimisation of the relaxation zone, the accuracy and the computational efficiency are discussed. Although the idea of the weakly coupling using the zonal approach is not new, the present hybrid model is the first one to couple the QALE-FEM with OpenFOAM solver and/or to be applied to numerical simulate the wave-structure interaction with presence of current.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.83-91
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• 2004

Nonlinear system responses of an impact system under randomly perturbed harmonic excitations are predicted in the probability domain by adopting the semi-analytical procedure previously developed. The semi-analytical procedure is obtained by solving the Fokker-Planck equation corresponding to the stochastic differential equation of the given impact system by utilizing the path-integral solution. The evolutionary joint probability density functions are generated by using the method, and the characteristics of nonlinear dynamic response behaviors of the system are examined. Noise effects on the responses are also examined. It Is found that the semi-analytical method can provides the accurate information of the responses via the joint probability functions for the impact system. It is found that the noises weaken and eventually terminate the chaos in the responses, but it is also found that the chaotic signatures reside in the presence of the external noise with relatively high intensity. The joint probability density function shows that the ensemble of the system responses are weakly stationary.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.97.1-97.1
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• 2014

We clarify the dynamics connecting a solar flare and a coronal mass ejection (CME) based on the results of a magnetohydrodynamic (MHD) simulation starting from a nonlinear force-free field (NLFFF) in Inoue et al. 2014. In previous studies, many authors proposed numerous candidates for triggering processes of a solar flare and the associated CME. Among them, the tether-cutting reconnection or the torus instability has been supported by recent simulations and observations. On the other hand, our MHD simulation in accordance with more realistic situations show that highly twisted field lines are first produced through a tether-cutting reconnection between the twisted field lines in the NLFFF, and then the newly formed, strongly twisted field erupts away from the solar surface because of a loss of equilibrium. This dynamics corresponds to the onset of a solar flare. Furthermore we have found that the strongly twisted erupting field reconnect with the weakly twisted ambient field during the eruption, creating a large flux tube, and then it rises over a critical height of the torus instability to trigger a CME. From these results, we conclude that the coupled process of tether-cutting reconnection and torus instability is important in the flare-CME relationship.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.3
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• pp.187-197
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• 2015

This study aims the development of a semi-analytic method for the parametric roll of large containerships advancing in longitudinal waves. A 1.5 Degree-of-Freedom(DOF) model is proposed to account the change of transverse stability induced by wave elevations and vertical motions (heave and pitch). By approximating the nonlinearity of restoring moment at large heel angles, the magnitude of roll amplitude is predicted as well as susceptibility check for parametric roll occurrence. In order to increase the accuracy of the prediction, the relationship between righting arm(GZ) and metacentric height(GM) is examined in the presence of incident waves, and then a new formula is proposed. Based on the linear approximation of the mean and first harmonic component of GM, the equation of parametric roll in irregular wave excitations is introduced, and the computational results of the proposed model are validated by comparing those of weakly nonlinear simulation based on an impulse-response-function method combined with strip theory. The present semi-analytic doesn’ t require heavy computational effort, so that it is very efficient particularly when numerous sea conditions for the analysis of parametric roll should be considered.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.6
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• pp.348-357
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• 2021

In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

• Atmosphere
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• v.23 no.3
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• pp.293-305
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• 2013

Nonhydrostatic effects on convectively forced mesoscale flows in two dimensions are numerically investigated using a nondimensional model. An elevated heating that represents convective heating due to deep cumulus convection is specified in a uniform basic flow with constant stability, and numerical experiments are performed with different values of the nonlinearity factor and nonhydrostaticity factor. The simulation result in a linear system is first compared to the analytic solution. The simulated vertical velocity field is very similar to the analytic one, confirming the high accuracy of nondimensional model's solutions. When the nonhydrostaticity factor is small, alternating regions of upward and downward motion above the heating top appear. On the other hand, when the nonhydrostaticity factor is relatively large, alternating updraft and downdraft cells appear downwind of the main updraft region. These features according to the nonhydrostaticity factor appear in both linear and nonlinear flow systems. The location of the maximum vertical velocity in the main updraft region differs depending on the degrees of nonlinearity and nonhydrostaticity. Using the Taylor-Goldstein equation in a linear, steady-state, invscid system, it is analyzed that evanescent waves exist for a given nonhydrostaticity factor. The critical wavelength of an evanescent wave is given by ${\lambda}_c=2{\pi}{\beta}$, where ${\beta}$ is the nonhydrostaticity factor. Waves whose wavelengths are smaller than the critical wavelength become evanescent. The alternating updraft and downdraft cells are formed by the superposition of evanescent waves and horizontally propagating parts of propagating waves. Simulation results show that the horizontal length of the updraft and downdraft cells is the half of the critical wavelength (${\pi}{\beta}$) in a linear flow system and larger than ${\pi}{\beta}$ in a weakly nonlinear flow system.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.18 no.1
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• pp.1-12
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• 2013

Acoustic backscatter profiles were measured by Eco-sounder along an east-west section in the mid-eastern Yellow Sea and at an anchoring station in the low salinity region off the Keum River estuary in September 2012, with observing physical water property structure by CTD. Tidal front was established around the sand ridge developed in 50 m depth region. Internal waves measured by Eco-sounder during low tide period in the eastern side of the sand ridge were nonlinear depression waves with wave height of 15 m and mean wavelength of 500 m. These waves were interpreted into tidal internal waves that were produced by tidal current flowing over the sand ridge to the southeast. When weakly non-linear soliton model was applied, propagation speed and period of these internal depression wave were 50 m/s and 16~18 min. Red tides by Dinoflagelates Cochlodinium were observed in the sea surface where strong acoustic scattering layer was raised up to 7 m. Hourly CTD profiles taken at the anchoring station off the Keum River estuary showed the halocline depth change by tidal current and land-sea breeze. When tidal current flowed strongly to the northeast during flood period and land-breeze of 7 m/s blew to the west, the halocline was temporally raised up as much as 2 m and acoustic profile images showed a complex structure in the surface layer within 5-m depth: in tens of seconds the declined acoustic structure of strong and weak scattering signals alternatively appeared with entrainment and intrusion shape. These acoustic profile structures in the surface mixed layer were observed for the first time in the coastal sea of the mid-eastern Yellow Sea. The acoustic profile images and turbidity data suggest that relatively transparent low-layer water be intruded or entrained into the turbid upper-layer water by vertical shear between flood current and land breeze-induced surface current.