Inverse conductivity Problem with Internal Data

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This problem finds applications in multi-wave imaging, greedy methods to approximate parameter-dependent elliptic problems, and image treatment with partial differential equations. We first show that the inverse problem for smooth coefficients can be rewritten as a linear transport equation. Assuming that the coefficient is known near the boundary, we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin method. We propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization parameter. We finally provide numerical examples for the inversion assuming a lower regularity of the coefficient, and using synthetic data.     

A Low Order Nonconforming Mixed Finite Element Method for Non-Stationary Incompressible Magnetohydrodynamics System

A low order nonconforming mixed finite element method (FEM) is established for the fully coupled non-stationary incompressible magnetohydrodynamics (MHD) problem in a bounded domain in 3D. The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field and the magnetic field, in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by $H^1(\Omega)$-conforming finite elements, respectively. The existence and uniqueness of the approximate solutions are shown. Optimal order error estimates of $L^2(H^1)$-norm for the velocity field, $L^2(L^2)$-norm for the pressure and the broken $L^2(H^1)$-norm for the magnetic field are derived.     

Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group

It was proved by Bahouri et al. [9] that the Schrödinger equation on the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason global dispersive estimates cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$     

Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients

The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are considered. Under the conditions that the coefficient is quasi-monotone up to a constant and the meshes are locally refined by using the newest vertex bisection algorithm, some uniform convergence results are proved for the standard multigrid V-cycle algorithm with Gauss-Seidel relaxations performed only on new nodes and their immediate neighbours. The multigrid V-cycle algorithm uses $\mathcal{O}(N)$ operations per iteration and is optimal.     

Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System*

The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper. When the thickness of the diffuse interfacial zone, which is parameterized by ε, goes to zero, they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^∞(L²) ∩ L²(H¹) sense on a uniform time interval independent of the smal...     

High pressure infiltration sintering behavior of WC-Co alloys

In this paper, two average tungsten carbide particle sizes of 2, 0.5?μm are placed respectively, in contact with a WC-16Co substrate, pressed at the pressure of 4.5–5.5?GPa, and heated to temperatures ranging from 1350°C to 1500°C in a large-volume cubic press. During the process Co was forced out of the WC-16Co substrate into the compressed powder. The resulting infiltrated samples were characterized using X-ray diffraction (XRD), scanning electron microscope (SEM), Vickers hardness and cutting performance tests. The results of XRD confirmed that the sintered bulks have WC and Co phases. The scanning electron microscopy (SEM) analysis reveals that the WC grains in well-sintered alloys are round in shape and cobalt with lower content is uniformly dispersed in the WC grain boundaries. The sintered sub-micron WC-Co alloy with a cobalt content of 3.8?wt% exhibits a prominent combination of high hardness value of 23.1?GPa and a large fracture toughness value of 8.6?MPa?m^½. The high-speed cutting tests indicating its cutting performance is significantly superior to the commercial YG6X (WC-6?wt%Co with WC grain size of 0.5?μm).     

经典单色短峰水波理论的三阶完备解

针对经典的有限水深三阶单色短峰波,考虑环境均匀流效应,赋予一新的解析解,从而与原经典解析解构成完备的解析解.这就在第二阶解、第三阶解结构上显示出多种相互作用机制.     

直喷式柴油机燃烧系统均匀优化设计的多维仿真研究

以直喷式柴油机的动力性和经济性为优化目标,对柴油机燃烧系统进行了基于均匀设计的多维仿真研究。通过回归分析的方法,综合考虑了柴油机的进气系统、喷油系统和燃烧室形状等参数,得到了燃烧系统参数的最优组合。结果表明:均匀设计法能以较少的仿真计算次数得到优化结果;通过回归分析和回归方程的分析得出,涡流比、油束夹角,以及涡流比和油束夹角的交互作用对柴油机的动力性和经济性影响最大;均匀设计的优化结果准确可靠,因此均匀设计法可以用于柴油机的多维仿真研究;涡流比和油束夹角的交互作用对油气混合有较大的影响。     

具有时滞食物链系统周期解的存在性和全局渐近稳定性

本文考虑时滞三种群食物链系统,给出周期解存在和全局渐近的充分条件。