• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2077-2081
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• 2005

A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1123-1148
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• 2016

The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Earthquakes and Structures
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• v.3 no.2
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• pp.97-115
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• 2012

The energy-transmitting boundary, which is used in the well-known finite element method (FEM) program FLUSH, is quite efficient for the earthquake response analysis of buildings considering soil-structure interaction. However, it is applicable only in the frequency domain. The author proposed methods for transforming frequency dependent impedance into the time domain, and studied the time domain transform of the boundary. In this paper, first, the estimation methods for both the halfspace condition under the bottom of the soil model and the pseudo three-dimensional effect were studied with the time domain transmitting boundary. Next, response behavior when using the boundary was studied in detail using a practical soil and building model. The response accuracy was compared with those using viscous boundary, and the boundary that considers the excavation force. Through these studies, the accuracy and efficiency of the proposed time domain transmitting boundary were confirmed.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Geomechanics and Engineering
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• v.28 no.2
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• pp.107-116
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• 2022

The steady state of unsaturated soil takes a long time to achieve. The soil seepage behaviours and hydraulic properties depend highly on the wetting/drying rate. It is observed that the soil-water characteristic curve (SWCC) is dependent on the wetting/drying rate, which is known as the dynamic effect. The dynamic effect apparently influences the scanning curves and will substantially affect the seepage behavior. However, the previous models commonly ignore the dynamic effect and cannot quantitatively describe the hysteresis scanning loops under dynamic conditions. In this study, a dynamic hysteresis model for SWCC is proposed considering the dynamic change of contact angle and the moving of the contact line. The drying contact angle under dynamic condition is smaller than that under static condition, while the wetting contact angle under dynamic condition is larger than that under static condition. The dynamic contact angle is expressed as a function of the saturation rate according to the Laplace equation. The model is given by a differential equation, in which the slope of the scanning curve is related to the slope of the boundary curve by means of contact angle. Empirical models can simulate the boundary curves. Given the two boundary curves, the scanning curve can be well predicted. In this model, only two parameters are introduced to describe the dynamic effect. They can be easily obtained from the experiment, which facilitates the calibration of the model. The proposed model is verified by the experimental data recorded in the literature and is proved to be more convenient and effective.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.1
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• pp.93-101
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• 2008

It is difficult for a MWR(Missile Warning Radar) to perform a threat decision accurately since there is no tracking part which gives more accurate threat information to the MWR. In this paper, the threat decision algorithm is proposed using an azimuth angular rate to improve the accuracy. The azimuth angular rate is dependent upon the direction of an approaching target. The target is classified into a threat or non-threat using a boundary condition of the azimuth angular rate. The boundary condition is determined using the Monte-Carlo simulation. The performance of the proposed algorithm is evaluated using this condition at field tests of MWR. The efficiency of the proposed method for the threat decision is proved by comparing the results of field tests with the simulation results.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• Phonetics and Speech Sciences
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• v.10 no.4
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• pp.77-89
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• 2018

Speech articulators are coordinated for the purpose of segmental constriction in terms of a task. In particular, vertical jaw movements repeatedly contribute to consonantal as well as vocalic constriction. The current study explores vertical jaw movements in conjunction with bilabial constriction in bilabial stop /p/ in the context /a/-to-/a/. Revisiting kinematic data of /p/ collected using the electromagenetic midsagittal articulometer (EMMA) method from seven (four female and three male) speakers of Seoul Korean, we examined maximum vertical jaw position, its relative timing with respect to the upper and lower lips, and lip aperture minima. The results of those dependent variables are recapitulated in terms of linguistic (different word boundaries) and paralinguistic (different speech rates) factors as follows. Firstly, maximum jaw height was lower in the across-word boundary condition (across-word < within-word), but it did not differ as a function of different speech rates (comfortable = fast). Secondly, more reduction in the lip aperture (LA) gesture occurred in fast rate, while word-boundary effects were absent. Thirdly, jaw raising was still in progress after the lips' positional extrema were achieved in the within-word condition, while the former was completed before the latter in the across-word condition. Lastly, relative temporal lags between the jaw and the lips (UL and LL) were more synchronous in fast rate, compared to comfortable rate. When these results are considered together, it is possible to posit that speakers are not tolerant of lenition to the extent that it is potentially realized as a labial approximant in either word-boundary condition while jaw height still manifested lower jaw position in the across-word boundary condition. Early termination of vertical jaw maxima before vertical lower lip maxima across-word condition may be partly responsible for the spatial reduction of jaw raising movements. This may come about as a consequence of an excessive number of factors (e.g., upper lip height (UH), lower lip height (LH), jaw angle (JA)) for the representation of a vector with two degrees of freedom (x, y) engaged in a gesture-based task (e.g., lip aperture (LA)). In the task-dynamic application toolkit, the jaw angle parameter can be assigned numerical values for greater weight in the across-word boundary condition, which in turn gives rise to lower jaw position. Speech rate-dependent spatial reduction in lip aperture may be able to be resolved by means of manipulating activation time of an active tract variable in the gestural score level.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.281-295
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• 2022

This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.