• 대한설비공학회지:설비저널
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• 제7권1호
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• pp.4-12
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• 1978

At Grashof numbers $10^{10},\;5{\times}10^{10}$, and $10^{11}$ nonlinear partial differential equations for two dimensional thermal circulation of air in a rectangular enclosure heated from below are solved numerically by finite difference explicit methood in time-dependent form. Two vertical walls and ceiling are held at low temperature and floor at high temperture. Results are compared with From's numerical solutions at $10^9{\lesssim}\;N_{Gr}\;<10^{13}$. The effective draft temperature fields are also obtained to examine cold draft problem, there included a line of constant effective draft temperature $-1.667^{\circ}C$ which is essentially Houghten's $80\%$ comfort data.

• Steel and Composite Structures
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• 제49권3호
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• pp.349-359
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• 2023

Dynamic response and economic of a laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the sinusoidal shear deformation theory (SSDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Geomechanics and Engineering
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• 제36권4호
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• pp.407-416
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• 2024

Dynamic response of a rock tunnels by laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the exponential shear deformation theory (ESDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• 대한수학회지
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• 제61권4호
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.321-331
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• 2024

We consider the numerical treatment of blow-up problems having non-monotonic singular solutions that tend to infinity at some point in the domain. The use of standard numerical methods for solving problems with blow-up solutions can lead to significant errors. The reason being that solutions of such problems have singularities whose positions are unknown in advance. To be able to integrate such non-monotonic blow-up problems, we describe and use a method of non-local transformations. To show the efficiency of the method, we present a comparison of exact and numerical solutions in addition to some comparison with the work of other authors.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

• 대한토목학회논문집
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• 제32권5A호
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• pp.255-266
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• 2012

현수교 주케이블은 완성시 교량의 구조적 건전성을 나타내는 중요한 지표이다. 주케이블은 가설완료시 자유 매달림(free hanging) 상태의 형상이 되며 교량완성시 행어, 보강형 등의 고정하중을 지지하여 가설완료시 형상과는 차이가 발생한다. 따라서, 주케이블의 가설완료시 형상이 교량완성시 형상에 직접적인 영향을 미치므로 가설중 형상관리가 매우 중요하다. 주케이블의 가설중 형상관리는 중앙 및 측경간은 새그조정으로, 정착경간은 장력조정으로 수행된다. 새그조정은 새그조절량에 대한 스트랜드 길이 조절량을 나타내는 산정값인 새그민감도가 필요하며 장력조정은 온도변화에 대한 장력변화량을 나타내는 장력민감도가 필요하다. 이에 본 연구에서는 케이블 형상가정에 따라 유도된 기본식과 이로부터 도출된 미분 관계식으로부터 새그 및 장력민감도를 산정하는 방법을 제안하였다. 그리고, 다양한 새그변화 요인에 대해 현수선 기본식을 사용한 비선형 수치해석 새그민감도 계산 흐름도를 제안하여 미분관계식을 적용한 새그민감도 결과와 비교하였다. 또한, 각 새그변화 요인이 복합적으로 발생함으로 이를 고려하여 케이블의 최종 새그변화량을 산정하는 방법을 제안하였다. PPWS 공법으로 시공중인 실교량을 대상으로 PPWS의 길이변화 및 온도변화, 경간장변화 등의 다양한 시공여건의 변화에 따른 새그 및 장력민감도를 산정하였다. 본 연구내용이 주케이블 가설중 형상관리 방법에 대한 체계적인 지침이 되기를 바라며, 향후 실교 현장적용 및 실증에 의해 완성도를 높일 것이다.

• The Korean Journal of Physiology and Pharmacology
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• 제15권6호
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• pp.371-382
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• 2011

We performed experiments using Aplysia neurons to identify the mechanism underlying the changes in the firing patterns in response to temperature changes. When the temperature was gradually increased from $11^{\circ}C$ to $31^{\circ}C$ the firing patterns changed sequentially from the silent state to beating, doublets, beating-chaos, bursting-chaos, square-wave bursting, and bursting-oscillation patterns. When the temperature was decreased over the same temperature range, these sequential changes in the firing patterns reappeared in reverse order. To simulate this entire range of spiking patterns we modified nonlinear differential equations that Chay and Lee made using temperature-dependent scaling factors. To refine the equations, we also analyzed the spike pattern changes in the presence of potassium channel blockers. Based on the solutions of these equations and potassium channel blocker experiments, we found that, as temperature increases, the maximum value of the potassium channel relaxation time constant, ${\tau}_n(t)$ increases, but the maximum value of the probabilities of openings for activation of the potassium channels, n(t) decreases. Accordingly, the voltage-dependent potassium current is likely to play a leading role in the temperature-dependent changes in the firing patterns in Aplysia neurons.

• 대한조선학회논문집
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• 제31권3호
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• pp.80-86
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• 1994

자유수면을 항주하는 선박에 의하여 발생되는 비선형 조파현상을 해석하기 위한 수치해석법을 개발하였다. 유동은 비점성, 비압축성으로 가정하고 선체 및 자유수면 형상과 일치하는 좌표계의 생성을 위하여 타원형 편미분방정식을 수치해석하여 물체적합 좌표계를 생성하였으며 변환된 정규격자 물체적합 좌표계에 대한 Euler방정식을 유한차분법(Finite Difference Method)을 이용하여 계산하였다. 수치해석을 위하여 시간에 대한 미분항은 전진차분, 공간에 대한 미분항은 중심차분법으로 이산화하였고 대류항에는 수치계산의 안정을 위해 인위적인 소산(dissipation)항을 첨가하였다. 자유수면의 형상은 매 시간 단계마다 자유수면 경계조건들을 만족하도록 다시 계산되었고 격자점들은 자유수면형상의 변화에 적합하게 다시 생성되도록 하였으며 압력에 대한 Poisson방정식은 반복연산법에 의하여 풀고 그 결과를 이용하여 속도를 외삽하였다. 개발된 수치해석법의 검증을 위해 수식선형인 Wigley 모형에 대한 계산을 Fn=0.250-0.408에 대하여 수행하고, 그 결과를 실험 결과와 비교하여 잘 일치함을 보였다.