Behavior of ZnO-coated alumina dielectric barrier discharge in atmospheric pressure air

A complete investigation of the discharge behavior of dielectric barrier discharge device using ZnO-coated dielectric layer in atmospheric pressure is made. Highly conductive ZnO film was deposited on the dielectric surface. Discharge characteristic of the dielectric barrier discharge are examined in different aspects. Experimental result shows that discharge uniformity is improved definitely in the case of ZnO-coated dielectric barrier discharge. And relevant theoretical models and explanation are presented to describing its discharge physics.Comment: 4 pages,10 figures,1 tabl

Nitsche-XFEM for optimal control problems governed by elliptic PDEs with interfaces

For the optimal control problem governed by elliptic equations with interfaces, we present a numerical method based on the Hansbo's Nitsche-XFEM. We followed the Hinze's variational discretization concept to discretize the continuous problem on a uniform mesh. We derive optimal error estimates of the state, co-state and control both in mesh dependent norm and L2 norm. In addition, our method is suitable for the model with non-homogeneous interface condition. Numerical results confirmed our theoretical results, with the implementation details discussed

A Nitsche-eXtended finite element method for distributed optimal control problems of elliptic interface equations

This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and apply a Nitsche-eXtended finite element method to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around the interface are enriched into the standard linear element space. Optimal error estimates of the state, co-state and control in a mesh-dependent norm and the $L^2$ norm are derived. Numerical results are provided to verify the theoretical results

Numerical analysis of a semilinear fractional diffusion equation

This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Gr\"onwall's inequality and its discrete version are proposed. By the two inequalities, error estimates in three Sobolev norms are derived for a spatial semi-discretization and a full discretization, which are optimal with respect to the regularity of the solution. A sharp temporal error estimate on graded temporal grids is also rigorously established. In addition, the spatial accuracy $\scriptstyle O(h^2(t^{-\alpha} + \ln(1/h)\!)\!)$ in the pointwise $\scriptstyle L^2(\Omega)$-norm is obtained for a spatial semi-discretization. Finally, several numerical results are provided to verify the theoretical results

Analysis of a time-stepping discontinuous Galerkin method for fractional diffusion-wave equation with nonsmooth data

This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretization and continuous piecewise linear functions in the spatial discretization. Nearly optimal convergence rate with respect to the regularity of the solution is established when the source term is nonsmooth, and nearly optimal convergence rate $\ln(1/\tau)(\sqrt{\ln(1/h)} h^2+\tau)$ is derived under appropriate regularity assumption on the source term. Convergence is also established without smoothness assumption on the initial value. Finally, numerical experiments are performed to verify the theoretical results

Numerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equations

Two numerical methods with graded temporal grids are analyzed for fractional evolution equations. One is a low-order discontinuous Galerkin (DG) discretization in the case of fractional order $0<\alpha<1$, and the other one is a low-order Petrov Galerkin (PG) discretization in the case of fractional order $1<\alpha<2$. By a new duality technique, pointwise-in-time error estimates of first-order and $(3-\alpha)$-order temporal accuracies are respectively derived for DG and PG, under reasonable regularity assumptions on the initial value. Numerical experiments are performed to verify the theoretical results

Analysis of the L1 scheme for fractional wave equations with nonsmooth data

This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate is obtained, and the temporal accuracy $\mathcal O(\tau^{3-\alpha})$ is derived for the nonsmooth initial data. In addition, a modified L1 scheme is proposed, and stability and temporal accuracy $\mathcal O(\tau^2)$ are derived for this scheme with nonsmooth initial data. The convergence of the two schemes in the inhomogeneous case is also established. Finally, numerical experiments are performed to verify the theoretical results

Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation

This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed into singular and regular parts, and some growth estimates are obtained for the singular parts. Following the variational discretization concept, a full discretization is applied to the corresponding state and co-state equations by using linear conforming finite element method in space and piecewise constant discontinuous Galerkin method in time. By the growth estimates, error estimates are derived with non-smooth initial data. In particular, graded temporal grids are used to obtain the first-order temporal accuracy. Finally, numerical experiments are performed to verify the theoretical results

An interface-unfitted finite element method for elliptic interface optimal control problem

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an interface-unfitted finite element method due to [A. Hansbo and P. Hansbo. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg., 191(47-48): 5537-5552, 2002] to discretize corresponding state and adjoint equations, where piecewise cut basis functions around interface are enriched into standard conforming finite element space. Optimal error estimates in both $L^2$ norm and a mesh-dependent norm are derived for optimal state, co-state and control under different regularity assumptions. Numerical results verify the theoretical results

Superconductivity induced by U-doping in the SmFeAsO system

Through partial substitution of Sm by U in SmFeAsO, a different member of the family of iron-based superconductors was successfully synthesized. X-ray diffraction measurements show that the lattice constants along the a and c axes are both squeezed through U doping, indicating a successful substitution of U at the Sm site. The parent compound shows a strong resistivity anomaly near 150 K, associated with spin-density-wave instability.U doping suppresses this instability and leads to a transition to the superconducting state at temperatures up to 49 K. Magnetic measurements confirm the bulk superconductivity in this system. For the sample with a doping level of x = 0.2, the external magnetic field suppresses the onset temperature very slowly, indicating a rather high upper critical field. In addition, the Hall effect measurements show that U clearly dopes electrons into the material.Comment: 5 pages,5 figure