Departing from an analytical phase transformation model, a new analytical approach to deduce transformed fraction for non-isothermal phase transformation was developed. In the new approach, the effect of the initial t...Departing from an analytical phase transformation model, a new analytical approach to deduce transformed fraction for non-isothermal phase transformation was developed. In the new approach, the effect of the initial transformation temperature and the accurate ＂temperature integral＂ approximations are incorporated to obtain an extended analytical model. Numerical approach demonstrated that the extended analytical model prediction for transformed fraction and transformation rate is in good agreement with the exact numerical calculation. The new model can describe more precisely the kinetic behavior than the original analytical model, especially for transformation with relatively high initial transformation temperature. The kinetic parameters obtained from the new model are more accurate and reasonable than those from the original analytical model.展开更多
A model of monolithic transformers is presented, which is analyzed with characteristic functions. A closed- form analytical approach to extract all the model parameters for the equivalent circuit of Si-based on-chip t...A model of monolithic transformers is presented, which is analyzed with characteristic functions. A closed- form analytical approach to extract all the model parameters for the equivalent circuit of Si-based on-chip transformers is proposed. A novel de-coupling technique is first developed to reduce the complexity in the Y parameters for the transformer, and the model parameters can then be extracted analytically by a set of characteristic functions. Simulation based on the extracted parameters has been carried out for transformers with different structures, and good accuracy is obtained compared to a 3-demensional full-wave numerical electro- magnetic field solver. The presented approach will be very useful to provide a scalable and wide-band compact circuit model for Si-based RF transformers.展开更多
In this paper, the analytical solutions of Schrodinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential f...In this paper, the analytical solutions of Schrodinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker-P1anck equation known as the Klein-Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr6dinger equation. The anaiytical results obtained from the two different methods agree with each other well The double well potentiai is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.展开更多
基金Projects (09-QZ-2008, 24-TZ-2009) supported by the Free Research Fund of State Key Laboratory of Solidification Processing, ChinaProject (B08040) supported by the Program of Introducing Talents of Discipline to Universities, China+3 种基金Projects (51071127, 51134011) supported by the National Natural Science Foundation of ChinaProject (JC200801) supported by the Fundamental Research Fund of Northwestern Polytechnical University, ChinaProject (51125002) supported by the National Science Foundation for Distinguished Young Scholars, ChinaProject (2011CB610403) supported by the National Basic Research Program of China
文摘Departing from an analytical phase transformation model, a new analytical approach to deduce transformed fraction for non-isothermal phase transformation was developed. In the new approach, the effect of the initial transformation temperature and the accurate ＂temperature integral＂ approximations are incorporated to obtain an extended analytical model. Numerical approach demonstrated that the extended analytical model prediction for transformed fraction and transformation rate is in good agreement with the exact numerical calculation. The new model can describe more precisely the kinetic behavior than the original analytical model, especially for transformation with relatively high initial transformation temperature. The kinetic parameters obtained from the new model are more accurate and reasonable than those from the original analytical model.
文摘A model of monolithic transformers is presented, which is analyzed with characteristic functions. A closed- form analytical approach to extract all the model parameters for the equivalent circuit of Si-based on-chip transformers is proposed. A novel de-coupling technique is first developed to reduce the complexity in the Y parameters for the transformer, and the model parameters can then be extracted analytically by a set of characteristic functions. Simulation based on the extracted parameters has been carried out for transformers with different structures, and good accuracy is obtained compared to a 3-demensional full-wave numerical electro- magnetic field solver. The presented approach will be very useful to provide a scalable and wide-band compact circuit model for Si-based RF transformers.
基金Supported by National Natural Science Foundation of China under Grant Nos.51276104,51476191
文摘In this paper, the analytical solutions of Schrodinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker-P1anck equation known as the Klein-Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr6dinger equation. The anaiytical results obtained from the two different methods agree with each other well The double well potentiai is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.
