In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscil...In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.展开更多
The onset of Rayleigh-Bnard convection in a fluid layer dispersed with phase-change-material particles was studied numerically by using the linear stability theory.The dimensionless fluctuation of specific heat Q wi...The onset of Rayleigh-Bnard convection in a fluid layer dispersed with phase-change-material particles was studied numerically by using the linear stability theory.The dimensionless fluctuation of specific heat Q with dimensionless temperature T was given as a form of sine-function Q =1+ b sin( ψT ).Two kinds of numerical methods were used separately in the calculation of critical Rayleigh number Ra _ cr and wave number k _ cr .One was the numerical integration method using Simpson 1/3 rule,and the other was the numerical difference method of Runge-Kutta with Newton-Raphson iteration. Both methods showed the same calculation results that the critical Rayleigh number Ra _ cr decreased monotonically with increase in the amplitude b of the sine-function,however,the critical wave number k _ cr did not show much difference with the amplitude b of the sine-function while ψ =π/2,but exponentially increased while ψ =π.展开更多
文摘In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.
文摘The onset of Rayleigh-Bnard convection in a fluid layer dispersed with phase-change-material particles was studied numerically by using the linear stability theory.The dimensionless fluctuation of specific heat Q with dimensionless temperature T was given as a form of sine-function Q =1+ b sin( ψT ).Two kinds of numerical methods were used separately in the calculation of critical Rayleigh number Ra _ cr and wave number k _ cr .One was the numerical integration method using Simpson 1/3 rule,and the other was the numerical difference method of Runge-Kutta with Newton-Raphson iteration. Both methods showed the same calculation results that the critical Rayleigh number Ra _ cr decreased monotonically with increase in the amplitude b of the sine-function,however,the critical wave number k _ cr did not show much difference with the amplitude b of the sine-function while ψ =π/2,but exponentially increased while ψ =π.
