In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as...In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.展开更多
We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectl...We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.展开更多
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes...In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.展开更多
We report on a forest-like-to-desert-like pattern evolution in the growth of an organic thin film observed by using an atomic force microscope. We use a modified diffusion limited aggregation model to simulate the gro...We report on a forest-like-to-desert-like pattern evolution in the growth of an organic thin film observed by using an atomic force microscope. We use a modified diffusion limited aggregation model to simulate the growth process and are able to reproduce the experimental patterns. The energy of electric dipole interaction is calculated and determined to be the driving force for the pattern formation and evolution. Based on these results, single crystalline films are obtained by enhancing the electric dipole interaction while limiting effects of other growth parameters.展开更多
We have studied the aggregation of particles on a hetero-substrate consisting of two different substrates A and B with finite surface barriers EAB and EBA between the AB and BA boundaries, respectively. With the diffu...We have studied the aggregation of particles on a hetero-substrate consisting of two different substrates A and B with finite surface barriers EAB and EBA between the AB and BA boundaries, respectively. With the diffusion energy limited aggregation （DELA） model, we find that the number of clusters and the mean radius of gyration of the clusters are dependent on the surface barriers EAB and EBA. For the case with a constant of EBA, a series of minima are summarized as EAB ： （E0 - kBAEBA）/kAB with kAB and kBA being two integers, for main minima （kBA = kAB = 1） and two local minima （kBA = kAB and kBA = kAB ＋ 1） between two neighbouring main minima.展开更多
基金Supported by the Natural Science Foundation of China(11001095 and 11001096)
文摘In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.
基金supported partially by NSFC(11671193,11971234)supported partially by the China Postdoctoral Science Foundation(2019M650581).
文摘We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.
基金Supported by the Youth Science Fund for Disaster Prevention and Reduction(201207)Supported by the Teachers’Scientific Research Fund of China Earthquake Administration(20140109)
文摘In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.
基金Project supported by the National Natural Science Foundation of China (Grant No.10774176)the National Basic Research Program of China (Grant No.2006CB806202)
文摘We report on a forest-like-to-desert-like pattern evolution in the growth of an organic thin film observed by using an atomic force microscope. We use a modified diffusion limited aggregation model to simulate the growth process and are able to reproduce the experimental patterns. The energy of electric dipole interaction is calculated and determined to be the driving force for the pattern formation and evolution. Based on these results, single crystalline films are obtained by enhancing the electric dipole interaction while limiting effects of other growth parameters.
基金supported by the Natural Science Foundation of Zhejiang province,China(Grant No Y607142)by the National Natural Science Foundation of China(Grant No 20771092)
文摘We have studied the aggregation of particles on a hetero-substrate consisting of two different substrates A and B with finite surface barriers EAB and EBA between the AB and BA boundaries, respectively. With the diffusion energy limited aggregation （DELA） model, we find that the number of clusters and the mean radius of gyration of the clusters are dependent on the surface barriers EAB and EBA. For the case with a constant of EBA, a series of minima are summarized as EAB ： （E0 - kBAEBA）/kAB with kAB and kBA being two integers, for main minima （kBA = kAB = 1） and two local minima （kBA = kAB and kBA = kAB ＋ 1） between two neighbouring main minima.
