• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제22권3호
• /
• pp.179-199
• /
• 2018

The paper explores a tri-trophic food chain model with density dependent mortality of intermediate predator. To analyze this aspect, we have worked out the local stability of different equilibrium points. We have also derived the conditions for global stability of interior equilibrium point and conditions for persistence of model system. To observe the global behaviour of the system, we performed extensive numerical simulations. Our simulation results reveal that chaotic dynamics is produced for increasing value of half-saturation constant. We have also observed trajectory motions around different equilibrium points. It is noticed that chaotic dynamics has been controlled by increasing value of density dependent mortality parameter. So, we conclude that the density dependent mortality parameter can be used to control chaotic dynamics. We also applied basic tools of nonlinear dynamics such as Poincare section and Lyapunov exponent to investigate chaotic behaviour of the system.

• 대한전기학회논문지:전기물성ㆍ응용부문C
• /
• 제53권11호
• /
• pp.566-571
• /
• 2004

Pulse modulation technique provide additional controling method for electron temperature and density in rf and microwave processing plasma. Transient characteristics of electron density and temperature have been measured in pulse modulated rf inductively coupled argon plasma using simple probe circuit. Electron temperature relaxation is clearly identified in the after glow stage. Controllability of average electron temperature and density depends on the modulation frequency and duty ratio. Numerical calculation of time-dependent electron density and temperature have been performed based on the global model. It has been shown that simple langmuir probe measurement method used for continuous plasma is also applicable to time-dependent measurement of pulse modulated plasma.

• Geomechanics and Engineering
• /
• 제34권2호
• /
• pp.197-208
• /
• 2023

Rate-dependent mechanical response of sand, subjected to loading of medium to high strain rate range, is of interest for several civilian and military applications. Such rate-dependent response can vary significantly based on the initial density state of the sand, applied confining pressure, considered strain rate range, drainage condition and sand morphology. A numerical study has been carried out employing a recently proposed visco-plastic constitutive model to explore the rate-dependent mechanical behaviour of Toyoura sand under drained triaxial loading condition. The model parameters have been calibrated using the experimental data on Toyoura sand available in published literature. Under strain rates higher than a reference strain rate, the simulation results are found to be in good agreement with the experimentally observed characteristic shearing behaviour of sand, which includes increased shear strength, pronounced post-peak softening and suppressed compression. The rate-dependent response, subjected to intermediate strain rate range, has further been assessed in terms of enhancement of peak shear strength and peak friction angle over varying initial density and confining pressure. The simulation results indicate that the rate-induced strength increase is highest for the dense state and such strength enhancements remain nearly independent of the applied confinement level.

• 한국수자원학회논문집
• /
• 제30권6호
• /
• pp.753-759
• /
• 1997

밀도가 변하는 지하수의 흐름과 용질의 수송 현상을 정확히 모델링할 수 있는 수치모델을 개발하였다. 수치모델의 정확도는 이송이 지배적인 경우에 발생하는 수치진동을 피할 수 있어야 얻을 수 있다. 이를 위하여 변분법에 기초한 비선형 수치진동흡수 유한요소법을 적용하였다. 개발된 수치모델은 기존 수치모델들과 달리 확장성이 뛰어나다. 본 수치모델의 정확도를 해석해와 다른 수치모델 결과와 비교하여 평가하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권4호
• /
• pp.267-278
• /
• 2013

We consider zero range processes with density dependent jump rates g given by $g=g(n,k)=g_1(n)g_2(k/n)$ with $g_1(x)=x^{-\alpha}$ and $$g_2(x)=\{^{x^{-\alpha}\;if\;a&lt;x}_{Mx^{-\alpha}\;if\;x{\leq}a}$$. (0.1) In this case, with 1/2 < a < 1 and ${\alpha}$ > 0, we show that non-complete condensation occurs with maximum cluster size an. More precisely, for any ${\epsilon}$ > 0, there exists $M^*$ > 0 such that, for any 0 < M ${\leq}M^*$, the maximum cluster size is between (a - ${\epsilon}$)n and (a + ${\epsilon}$)n for large n. This provides a simple example of non-complete condensation under perturbation of rates which are deep in the range of perfect condensation (e.g. ${\alpha}$ >> 1) and supports the instability of the condensation transition.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제25권4호
• /
• pp.345-355
• /
• 2018

This paper looks into phase plane behavior of the solution near the positive steady-state for the system with prey density dependent response functions. The positive invariance and boundedness property of the solution to the objective model are proved. The existence result of a positive steady-state and asymptotic analysis near the positive constant equilibrium for the objective system are of interest. The results of phase plane analysis for the system are proved by observing the asymptotic properties of the solutions. Also some numerical analysis results for the behaviors of the solutions in time are provided.

• Current Research on Agriculture and Life Sciences
• /
• 제9권
• /
• pp.109-114
• /
• 1991

The depth and spread of root systems and the density of root branching affect the success and survival of plants subjected to drought. The type and size of root systems are controlled by heredity and soil conditions. There are also important interaction between roots and shoots; roots are dependent on shoots for carbohydrates, growth regulators, and certain vitamins, and shoots are dependent on roots for water, minerals, and certain growth regulators. Pinus thunbergii Parlatore had most of roots in the top 20cm of soil, and had little short of roots in the less than 80cm of soil. Average of root density was $270cm/cm^3$ in the upper soil(0~20cm). Root density of Pinus thunbergii Parlatore was similar to that of Cryptomeria japonica. There is no saying that Pinus thunbergii Parlatore has an advantage over Cryptomeria japonica in the drought. This data will be used to the root density values in the simulation model of black pine stands.

• 대한토목학회논문집
• /
• 제11권2호
• /
• pp.27-37
• /
• 1991

음부력을 갖는 유체가 소규모 저수지로 유입되어 일어나는 밀도류의 거동 및 순환이 차원해석과 수리실험을 이용하여 해석된다. 무차원침강점 및 밀도류전면속도, 밀도류전면이동거리, 머리 뒤의 밀도층내회석 등은 유입밀도후르드수, Fre의 영향을 받으며 밀도층의 두께, 흐름양상 및 저수지내 밀도의 변화는 밀도류전면이 하류단에 도달하여 반사되기 전과 후의 양상이 현저하게 다르다. 밀도층의 두께는 전자의 경우에는 Fre, 후자의 경우는 시간과 Fre의 영향을 받으며 이들은 지수식으로 표현할 수 있다.

• 한국방재안전학회논문집
• /
• 제6권3호
• /
• pp.1-8
• /
• 2013

시간과 공간에 따라 변화하는 난류성분의 변동풍하중을 받는 고층건물의 경량화 및 연성화 현상은 고유진동수와 감쇠비를 적게함으로서 동적으로 매우 불리한 진동문제을 발생하게 되어, 변동풍하중을 받는 도심의 고층건물에 대한 동적해석의 중요성이 인식되고 있다. 본 논문에서는 돌풍과 같이 짧은 시간동안에 통계적 성질이 변화하는 변동풍하중을 나타내기 위하여 정상불규칙 풍하중에 시간에 따라 변화하는 결정적함수(A(t) = 1-exp($-{\beta}t$))를 곱하여 나타냈고, 이러한 변동풍하중을 받는 고층건물에 대한 평균류방향의 동적변위응답해석은 진동이론으로부터 Time-dependent Response Spectral Density함수를 나타냈고, 진동함수를 포함하여 나타내는 Time-dependent Response Spectral Density의 진동수영역에 대한 적분의 해로부터 동적응답을 해석적으로 구하기 위하여 Contour적분에서 Cauchy의 적분정리와 잔유치 정리(residue theorem)에 의한 잔유치 적분으로부터 해석함수를 구했다. 해석 예에서 본 논문에서 구한 해석함수와 기존의 수치해석방법에 따른 결과를 비교 검토했고, 고층건물의 동적 특성에 따른 해석결과도 비교 검토했다.

• 대한전자공학회논문지
• /
• 제13권4호
• /
• pp.1-5
• /
• 1976

Spectrum의 시간기복을 나타내는 시간 및 주파수의 함수 F(w,t,T) 및 W(w,t,T)를 정의하였고, 실례에 적용시켰다. Fourier변환을 f(t)와 Phasor ejwt와의 Correlation으로 정의하였고 그 변환시분이 시간마다의 성분의 합계이어서 t 시각에서의 Spectrum을 그 근거에서의 f(t)값에만 의함을 증명하였다. Two new time functions defining Time Dependent Fourier Transform F(w,t,T) and Time Dependent Spectrum Density W(w,t,T) are deduced. courier transform is defined as the correlation between the time function f(t) and phasor ejwt. Several theorems corncerning the new functions are proved in order to verify the instantaneous cause a effet of the function f(t) and the nuctuating spectrum.