In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated b...In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated by using the methods of the nonlinear dynamical analysis. The time-domain diagram,power spectrum,phase diagram and the largest Lyapunov exponent obtained from the process of the signal propagate through different control module are given. The researches on different control systems demonstrate that: after single-frequency signal goes through the nonlinear controller,it is still non-chaotic although the output contains more frequency components; but with the feedback and the external perturbation,the output is a continuous broadband spectrum and the result shows that there is chaos. The energy of the input signal reduces with some appropriate parameters. Therefore,the control system of the nonlinear feedback is a good way to broaden the spectrum of output with inputting a single-frequency signal.展开更多
Previously we derived equations determining line broadening in ax-ray diffraction profile due to stacking faults. Here, we will consider line broadening due to particle size and strain which are the other factors affe...Previously we derived equations determining line broadening in ax-ray diffraction profile due to stacking faults. Here, we will consider line broadening due to particle size and strain which are the other factors affecting line broadening in a diffraction profile. When line broadening in a diffraction profile is due to particle size and strain, the theoretical model of the sample under study is either a Gaussian or a Cauchy function or a combination of these functions, e.g. Voigt and Pseudovoigt functions. Although the overall nature of these functions can be determined by Mitra’s R(x) test and the Pearson and Hartley x?test, details of a predicted model will be lacking. Development of a mathematical model to predict various parameters before embarking upon the actual experiment would enable correction of significant sources of error prior to calculations. Therefore, in this study, predictors of integral width, Fourier Transform, Second and Fourth Moment and Fourth Cumulant of samples represented by Gauss, Cauchy, Voigt and Pseudovoigt functions have been worked out. An additional parameter, the coefficient of excess, which is the ratio of the Fourth Moment to three times the square of the Second Moment, has been proposed. For a Gaussian profile the coefficient of excess is one, whereas for Cauchy distributions, it is a function of the lattice variable. This parameter can also be used for determining the type of distribution present in aggregates of distorted crystallites. Programs used to define the crystal structure of materials need to take this parameter into consideration.展开更多
基金Sponsored by Basic Research Development Program(Grant No.7131107)the National Natural Science Foundation of China(Grant No.51206101)
文摘In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated by using the methods of the nonlinear dynamical analysis. The time-domain diagram,power spectrum,phase diagram and the largest Lyapunov exponent obtained from the process of the signal propagate through different control module are given. The researches on different control systems demonstrate that: after single-frequency signal goes through the nonlinear controller,it is still non-chaotic although the output contains more frequency components; but with the feedback and the external perturbation,the output is a continuous broadband spectrum and the result shows that there is chaos. The energy of the input signal reduces with some appropriate parameters. Therefore,the control system of the nonlinear feedback is a good way to broaden the spectrum of output with inputting a single-frequency signal.
文摘Previously we derived equations determining line broadening in ax-ray diffraction profile due to stacking faults. Here, we will consider line broadening due to particle size and strain which are the other factors affecting line broadening in a diffraction profile. When line broadening in a diffraction profile is due to particle size and strain, the theoretical model of the sample under study is either a Gaussian or a Cauchy function or a combination of these functions, e.g. Voigt and Pseudovoigt functions. Although the overall nature of these functions can be determined by Mitra’s R(x) test and the Pearson and Hartley x?test, details of a predicted model will be lacking. Development of a mathematical model to predict various parameters before embarking upon the actual experiment would enable correction of significant sources of error prior to calculations. Therefore, in this study, predictors of integral width, Fourier Transform, Second and Fourth Moment and Fourth Cumulant of samples represented by Gauss, Cauchy, Voigt and Pseudovoigt functions have been worked out. An additional parameter, the coefficient of excess, which is the ratio of the Fourth Moment to three times the square of the Second Moment, has been proposed. For a Gaussian profile the coefficient of excess is one, whereas for Cauchy distributions, it is a function of the lattice variable. This parameter can also be used for determining the type of distribution present in aggregates of distorted crystallites. Programs used to define the crystal structure of materials need to take this parameter into consideration.
