• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.179-199
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• 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.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.11
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• pp.566-571
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• 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
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• v.34 no.2
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• pp.197-208
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• 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.

• Journal of Korea Water Resources Association
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• v.30 no.6
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• pp.753-759
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• 1997

A new numerical model was doveloped to simulate density-dependent ground water flow and solute transport. Accuracy of a numerical model depends upon how well it simulates advection dominant situations because numerical oscillations can spoil solutions for these situations. Nonlinear oscillation-absorption finite element method. based on the variational principle, was employed. Unlike previous numerical models, this model can easily be expanded for more complex situations. Accuracy of the model is evaluated by comparing with analytical solutions and results of other numerical model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.267-278
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• 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.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.345-355
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• 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
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• v.9
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• pp.109-114
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• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.2
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• pp.27-37
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• 1991

The behavior of a negative buoyant flow flowing into a small reservoir is analysed by experiments and dimensional analysis. The nondimensional plunge point, head velocity, head travel distance and the dilution of density current are dependent on the inflow densimetric Froude number, Fre. The thickness of density current, flow pattern and density difference are different from two cases as follows; before the front of head arrive at the downstream end and after. Before the arrival, the thickness of density current is dependent on Fre and after the arrival, time and Fre. It was found that they can be expressed as power laws.

• Journal of Korean Society of Disaster and Security
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• v.6 no.3
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• pp.1-8
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• 2013

Based on random vibration theory, a procedure for calculating the dynamic response of the tall building to time-dependent random excitation is developed. In this paper, the fluctuating along- wind load is assumed as time-dependent random process described by the time-independent random process with deterministic function during a short duration of time. By deterministic function A(t)=1-exp($-{\beta}t$), the absolute value square of oscillatory function is represented from author's studies. The time-dependent random response spectral density is represented by using the absolute value square of oscillatory function and equivalent wind load spectrum of Solari. Especially, dynamic mean square response of the tall building subjected to fluctuating wind loads was derived as analysis function by the Cauchy's Integral Formula and Residue Theorem. As analysis examples, there were compared the numerical integral analytic results with the analysis fun. results by dynamic properties of the tall uilding.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.4
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• pp.1-5
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• 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.