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连续依赖性
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  continuous dependence
    Spatial Decay Estimates and Continuous Dependence on Time Geometry in Generalized Thermoelasticity
    关于一般热弹性方程的空间衰减估计和对初值几何区域的连续依赖性
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    This paper derives spatial decay bounds and continuous dependence on time geometry in a dynamical problem of linear anisotropic thermoelasticity.
    本文讨论了有关线性、各向异性热弹性方程的动力学问题,得到了该问题的解空间衰减估计及对初始几何区域的连续依赖性
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    This is done by deriving appropriate a priori inequality which displays continuous dependence on the initial time geometry in the weak energy norm.
    我们同时研究了热弹性初边值问题对初值几何区域的连续依赖性,为此,我们建立了一个先验不等式,通过该不等式展示了解对初值几何区域的连续依赖性
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  continuous dependence
In addition, the continuous dependence of the solution of this equation on the linear dispersive coefficient contained in the equation is obtained.
      
Spline approximation of experimental dependences of lnk on P is used to determine the continuous dependence of the activation volume ΔV# on P in the solvents cyclohexane, anisole, toluene, n-nonane, isopropylbenzene, and tert-butylbenzene.
      
Spline approximation of experimental dependences of lnk on P is used to determine the continuous dependence of the activation volume ΔV# on P in the solvents cyclohexane, anisole, toluene, n-nonane, isopropylbenzene, and tert-butylbenzene.
      
Continuous dependence of an element realizing the minimum of a convex functional on the set of admissible elements
      
Existence and continuous dependence of the solution of a system of operator equations
      
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A systematic study has been carried out on the effects of three-dimensional wave forces of vertical pile array, applying method of wave source distribution on arbitrary sectional contour of the piles The piles involved in computation reach up to 100 Some new properties of hydrodynamic interaction among piles are obtained It should be emphasized that the forces on piles shows continuous dependence when the piles number increases over a certain number When the number is very large, forces on the middle...

A systematic study has been carried out on the effects of three-dimensional wave forces of vertical pile array, applying method of wave source distribution on arbitrary sectional contour of the piles The piles involved in computation reach up to 100 Some new properties of hydrodynamic interaction among piles are obtained It should be emphasized that the forces on piles shows continuous dependence when the piles number increases over a certain number When the number is very large, forces on the middle piles are almost uniform whether the number is odd or even For the cases involved in the present paper, we may draw the following conclusions among others, i e 1 In head sea condition, the shielding of the front piles are dominant in relatively shorter waves 2 With the increase of the wave length, the interference effects among piles will gradually become stronger and finally be dominant in the long wave range while the shielding effects are getting weaker 3 There exists a quite narrow wave length range in which the distribution of the wave force amplitudes along a pile array will vary quite sensitive to small changes in wave length both in its configuration and magnitude due to the compatibility between the shielding and interference effects among piles Those new findings, although drawn from arrays of vertical cylinderical piles, would give insight into the hydrodynamic interaction phenomena for multiple objects of general shape in waves These discoveries are significant guidance of the study of hydrodynamic interaction upon other forms of offshore structures

多物体之间的流体动力干扰特性对超大型海洋结构物的设计和研究十分重要用波动源在截面周线上分布的方法,就垂直桩柱间三维流体动力干扰对波浪力的影响进行了系统的研究,桩柱的数目可达100余根得到了柱间流体动力干扰力学机理的若干新的特性尤应指出的是,当桩柱根数超过某一数量后,桩柱上的受力表现出有规律的连续依赖性当柱数很大时,无论柱数是奇数还是偶数,中间大部分的桩柱都将表现出均匀的受力特征这些特性的发现对其他形式多体结构物流体动力干扰的研究也有重要的借鉴和指导意义

Based on the nonlinear Boltzmann model equation, the unified simplified velocity distribution function equations adapted to various flow regimes can be presented. The discrete ordinate method is applied to the reduced distribution functions in order to replace their continuous dependency on the velocity space, and then the kinetic model equation will be cast into hyperbolic conservation laws form with nonlinear source terms. The time splitting method is used to split the distribution function equations into...

Based on the nonlinear Boltzmann model equation, the unified simplified velocity distribution function equations adapted to various flow regimes can be presented. The discrete ordinate method is applied to the reduced distribution functions in order to replace their continuous dependency on the velocity space, and then the kinetic model equation will be cast into hyperbolic conservation laws form with nonlinear source terms. The time splitting method is used to split the distribution function equations into the colliding relaxation equation and the convection movement equations. The NND finite difference method is adopted and extended to solve them. To improve computational efficiency for various Mach number flows, three types of quadrature rules are used to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a simplified unified kinetic algorithm for the gas dynamical problems from various flow regimes has been developed. The computations of the one dimensional shock tube problem and the flows over two dimensional circular cylinder from rarefied transition to continuum indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained.

从非线性模型Boltzmann方程出发 ,引入简化速度分布函数、使用离散速度坐标法对速度空间进行离散、降维 ,去掉分布函数对速度分量的连续依赖性 ;采用时间分裂法 ,将简化速度分布函数松弛变化方程分解为源项碰撞变化方程、对流运动方程 ,进行耦合计算 ,应用NND耗散差分方法直接模拟气体分子速度分布函数 ;发展离散速度数值积分法 ,通过宏观取矩获取物理空间各点的流动参数 ,从而建立一套能有效模拟各流域气动问题的简化的气体运动论统一数值算法。为了证实该数值方法在求解稀薄流到连续流气体动力学问题方面的可靠性 ,本文计算了各流域不同Knudsen数下的一维激波管问题及二维园柱绕流

Based on the BGK-Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be obtained by introducing the colliding relaxation parameters and the local equilibrium distribution function to revise the BGK equation. Based on the principle of probability statistics, the discrete velocity ordinate method is applied to the distribution function equation in order to replace its continuous dependency on the velocity space, the optimum Golden Section...

Based on the BGK-Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be obtained by introducing the colliding relaxation parameters and the local equilibrium distribution function to revise the BGK equation. Based on the principle of probability statistics, the discrete velocity ordinate method is applied to the distribution function equation in order to replace its continuous dependency on the velocity space, the optimum Golden Section method is used to discretize velocity components, and then the equation will be cast into hyperbolic conservation law form with nonlinear source term. The unsteady time-splitting method is used to split the distribution function equations into the colliding relaxation equation and the convection movement equations. The non-oscillatory, containing no free parameters, and dissipative (NND) scheme is employed to solve the convection terms and the colliding relaxation equation is numerically simulated by the aid of the second order Itungc-Kutta method. The gas kinetic finite difference method is constructed for the computation of the discrete velocity distribution function. Four types of quadrature rules, such as the modified Gauss-Hcrmitc formula and the Golden Section number-theoretic integral method based on the thoughts of the Hua-Wang method, are developed and applied to the discretized velocity space to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm based on the nonlinear Boltzmann model equation is established for flows from rarefied transition to continuum. To test the reliability of the present numerical method to solve the gas dynamical problems from rarefied transition to continuum, the one-dimensional shock-tube problems and the flows past two-dimensional circular cylinder and the flows past three-dimensional sphere with various Knudsen numbers are simulated. The computations indicate that both high resolution of the now fields and good qualitative agreement with the theoretical, DSMC, and experimental results can be obtained.

通过引入碰撞松弛参数和当地平衡态分布函数对BGK模型方程进行修正,确定含流态控制参数可描述不同流域气体流动特性的气体分子速度分布函数的简化控制方程.发展和应用离散速度坐标法于气体分子速度空间,利用一套在物理空间和时间上连续而速度空间离散的分布函数来代替原分布函数对速度空间的连续依赖性.基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式,建立直接求解气体分子速度分布函数的气体运动论有限差分数值方法.推广应用改进的 Gauss-Hermite无穷积分法和华罗庚-王元提出的以单和逼近重积分的黄金分割数论积分方法等,对离散速度空间进行宏观取矩获取物理空间各点的气体流动参数,由此发展一套从稀薄流到连续流各流域统一的气体运动论数值算法.通过对不同Knudsen数下一维激波管问题、二维圆柱绕流和三维球体绕流的初步数值实验表明文中发展的数值算法是可行的.

 
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