The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by ...The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by using parameter-dependent change of measure.展开更多
This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and t...This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.展开更多
For the growth of large synthetic diamond crystals by temperature gradient method （TGM）, the grit sizes of seed crystals have great effects on the growth rate and quality of large grown crystals. Because of the limi...For the growth of large synthetic diamond crystals by temperature gradient method （TGM）, the grit sizes of seed crystals have great effects on the growth rate and quality of large grown crystals. Because of the limited area of seed surfaces, the maximum diffusion flux of carbon source, which could be absorbed by the seed, is related to the seed size. And with increasing the seed sizes, the growth rates also increase markedly. However, the seed sizes should be lower than a certain value, which determines the crystal quality directly. For example, with NiMnCo alloy as the metal solvent, when the seed size increases from 0.5 to 1.8 mm, the growth rate increases greatly from about 1.1 to 3.2 mg/h; when the size is beyond 2.0 mm, more and more metal inclusions would be incorporated into the grown crystals, and the crystal quality is destroyed heavily. Finite element analysis （FEA） shows that, due to the special assembly of growth cell, the diffusion of carbon source in the metal solvent is very inhomogeneous, which could be substantiated directly by the appearances and shapes of large grown crystals and the remains of carbon source. And this inhomogeneous diffusion of carbon source would be very harmful to the growth of large diamond crystals, especially when large-size seed crystals are used.展开更多
The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonl...The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.展开更多
基金Supported by National Natural Science Foundation of China （Grant No. 10871153）
文摘The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by using parameter-dependent change of measure.
文摘This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.
基金supported by the National Natural Science Foundation of China under grant No.50172018.
文摘For the growth of large synthetic diamond crystals by temperature gradient method （TGM）, the grit sizes of seed crystals have great effects on the growth rate and quality of large grown crystals. Because of the limited area of seed surfaces, the maximum diffusion flux of carbon source, which could be absorbed by the seed, is related to the seed size. And with increasing the seed sizes, the growth rates also increase markedly. However, the seed sizes should be lower than a certain value, which determines the crystal quality directly. For example, with NiMnCo alloy as the metal solvent, when the seed size increases from 0.5 to 1.8 mm, the growth rate increases greatly from about 1.1 to 3.2 mg/h; when the size is beyond 2.0 mm, more and more metal inclusions would be incorporated into the grown crystals, and the crystal quality is destroyed heavily. Finite element analysis （FEA） shows that, due to the special assembly of growth cell, the diffusion of carbon source in the metal solvent is very inhomogeneous, which could be substantiated directly by the appearances and shapes of large grown crystals and the remains of carbon source. And this inhomogeneous diffusion of carbon source would be very harmful to the growth of large diamond crystals, especially when large-size seed crystals are used.
基金supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
文摘The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.
