To simulate the concrete shrinkage in varying temperature and moisture environments, a simulate procedure comprising an analytical process and a finite element analysis is proposed based on the coupled partial differe...To simulate the concrete shrinkage in varying temperature and moisture environments, a simulate procedure comprising an analytical process and a finite element analysis is proposed based on the coupled partial differential equations describing heat and moisture transfer in a porous medium. Using the Laplace transformation method and transfer function to simplify and solve the coupled equations in Laplace domain, the moisture and temperature distribution in time domain are obtained by inverse Laplace transformation. The shrinkage deformations of concrete are numerically simulated by the finite element method （FEM） based on the obtained temperature and moisture distribution. This approach avoids the complex eigenvalues, coupling difficulty and low accuracy found in other solving methods, and also effectively calculates the moisture induced shrinkage which is almost impossible using familiar FEM software. The validity of the simulation procedure is verified by Hundt＇s test data. The results reveal that the proposed approach can be considered a reliable and efficient method to simulate the coupling moisture and temperature shrinkage of concrete.展开更多
Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following th...Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.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
By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the ...By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.展开更多
Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating...Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating parameters, thus, it is possible to reduce computation time in comparison with numerical methods. In this paper, an alternative procedure is presented. Here is used a hybrid solution based on Green＇s function and real characteristics （discrete data） of the boundary conditions.展开更多
In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponentia...In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponential sums, and give an exact computational formuiu for it.展开更多
Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is...Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.展开更多
基金The National Natural Science Foundation of China(No50539040)the Trans-Century Training Programme Foundation forthe Talents by the State Education Commission (NoNCET-05-0473)
文摘To simulate the concrete shrinkage in varying temperature and moisture environments, a simulate procedure comprising an analytical process and a finite element analysis is proposed based on the coupled partial differential equations describing heat and moisture transfer in a porous medium. Using the Laplace transformation method and transfer function to simplify and solve the coupled equations in Laplace domain, the moisture and temperature distribution in time domain are obtained by inverse Laplace transformation. The shrinkage deformations of concrete are numerically simulated by the finite element method （FEM） based on the obtained temperature and moisture distribution. This approach avoids the complex eigenvalues, coupling difficulty and low accuracy found in other solving methods, and also effectively calculates the moisture induced shrinkage which is almost impossible using familiar FEM software. The validity of the simulation procedure is verified by Hundt＇s test data. The results reveal that the proposed approach can be considered a reliable and efficient method to simulate the coupling moisture and temperature shrinkage of concrete.
文摘Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.
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The project supported by National Natural Science Foundation of China under Grant No. 10575087 and the Natural Science Foundation of Zhejiang Province of China under Grant No. 102053
文摘By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.
文摘Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating parameters, thus, it is possible to reduce computation time in comparison with numerical methods. In this paper, an alternative procedure is presented. Here is used a hybrid solution based on Green＇s function and real characteristics （discrete data） of the boundary conditions.
基金supported by the National Natural Science Foundation of China(Nos.11371291,11471258)the Graduate Independent Innovation Fund of Northwest University(No.YZZ13071)
文摘In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponential sums, and give an exact computational formuiu for it.
基金supported by the National Natural Science Foundation of China(Grant No.50876106)
文摘Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.
