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System of relaxation equations for materially isolated surfactant solution with spherical and cylindrical micelles


System of relaxation equations for materially isolated surfactant solution with spherical and cylindrical micelles


Preceding studies have overcome the difficulty in solving the onedimensional [13] and two dimensional [4] problems by various techniques, the basic idea being the use of implicit difference schemes for approximating the relaxation equations.


The relaxation equations and the enthalpy equation are integrated numerically along the stream lines.


The wall friction is calculated using the data previously obtained by solving a nonstationary equation of motion simultaneously with relaxation equations for turbulent stress and turbulent viscosity.

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The polarization anisotropy was described in terms of a unit vector whose direction was determined by a relaxation equation.


The closed linearized relaxation equation determining the variations (with time) in the total concentrations of spherical and cylindrical micelles in a materially isolated surfactant solution is derived and solved.


Generalization of the Krook kinetic relaxation equation


The Krook model relaxation equation retains all the features of the Boltzmann equation which are associated with free molecular motion and describes approximately, in a meanstatistical fashion, the molecular collisions.


Careful and thorough study of the model relaxation equation [24], and also solution of several problems for this equation, have aided in providing a deeper understanding of the processes in a rarefied gas.

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 The behavior of electron spin randomization of optically pumped alkaliatoms in the spin temperature limit is treated theoretically in this article. Numerical solutions of the relaxation equation of motion are presented. And a generalized slowing down factor as a funtion of the polarization and nuclear spin is analysed in detail.  本文分析了自旋交换碰撞为主要机制时,光泵硷金属原子的电子自旋弛豫,给出弛豫方程数值解,并对广义减慢因子进行了详细讨论。  The critical phenomena of bistability is discussed on the basis of the relaxation equation of the nonlinear systems with a timedelayed feedback. We find that the critical slowing down at the edges of bistable region possesses consistency with the divergence of the time duration of intermittency. The critica1 exponent is 1/2. We also find that, different from the critical points at the bistable region edges, there are consistencies with the perioddoubling bifurcation points and split bifurcation points at the... The critical phenomena of bistability is discussed on the basis of the relaxation equation of the nonlinear systems with a timedelayed feedback. We find that the critical slowing down at the edges of bistable region possesses consistency with the divergence of the time duration of intermittency. The critica1 exponent is 1/2. We also find that, different from the critical points at the bistable region edges, there are consistencies with the perioddoubling bifurcation points and split bifurcation points at the cusp point (in cusp catastrophe model of bistability). The critical exponent is 1. The abovementioned results possess universal properties. The computer experiments have been made in the liquid crystal hybrid optical bistable device. The results are in agreement with the analyses.  本文以具有反馈时间延迟的非线性系统弛豫方程为出发点,讨论了双稳态临界点的临界现象。发现双稳区边沿的临界慢化与混沌运动中切分叉点附近阵发混沌时间间隔发散具有一致性,临界指数为1/2。在双稳区(尖顶突变模型)的尖顶处,与双稳区边沿临界点不同,它与混沌运动中倍周期分叉点及劈分叉点的临界慢化具有一致性,临界指数为1。上述结果具有普适性。以液晶混合光学双稳系统为例,进行了计算机实验,其结果与分析相一致。  The complex dielectric constant of a PTCR (positive temperature coeffecient of resistance) ceramic material at room temperature is reported as a function of frequency. A dielectric relaxation has been observed at about 25MHz which can be approximately described by the Debye type relaxation equations. At lower frequencies, conductivity dominates the imaginary part of the dielectric constant. From the dielectric measurement, not only the dielectric constant but also the resistivity can be evaluated for grains... The complex dielectric constant of a PTCR (positive temperature coeffecient of resistance) ceramic material at room temperature is reported as a function of frequency. A dielectric relaxation has been observed at about 25MHz which can be approximately described by the Debye type relaxation equations. At lower frequencies, conductivity dominates the imaginary part of the dielectric constant. From the dielectric measurement, not only the dielectric constant but also the resistivity can be evaluated for grains and grainboundaries separately.  研究了一种以钛酸钡为基的PTCR陶瓷在30kHz至300MHz频率范围内的室温介电频谱。该介电响应可近似地用Debye弛豫方程加以描述,但低频时电导率对介电常数虚部起主导作用。根据介电频谱的测量结果,分别得出了晶粒和晶界的电阻率和介电常数。   << 更多相关文摘 
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