We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data. We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the measurement is far away from the obstacle. The imaginary part of the cross-correlation imaging functional always peaks on the boundary of the obstacle. Numerical experiments are included to illustrate the powerful imaging quality

In situ nano-TiB2 reinforced ultrafine-grained (UFG) Al composites were prepared via combined processes of flux-assisted synthesis (FAS) and asymmetrical rolling (ASR). The UFG Al composite with an ASR reduction ratio of 97% exhibits an average matrix grain size of 380 nm and an average TiB2 particulate size of 50 nm. Dislocation density in the composites is higher than that corresponding to the high purity (99.99 wt%) Al under identical processing conditions. The yield and ultimate tensile strength values of the UFG Al composites processed with an ASR reduction ratio of 97% are approximately 9 and 5 times higher relative to those of the initial coarse-grained Al, respectively. Moreover, the UFG Al composite with an ASR reduction ratio of 97% exhibits a higher elongation than that corresponding to the UFG pure Al under identical processing conditions, suggesting that nanoparticulates contribute to the overall plastic deformation when the matrix grains are refined to the UFG regime. Moreover, analysis of the strengthening behavior reveals no clear evidence that Orowan strengthening contributes significantly to the overall yield strength of the Al nanocomposites studied herein.

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The details of STDDM is given for each extension. Numerical results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.

A technique of controlling growth gas flow rate for adjusting crystal resistivity is presented in this paper. The experimental results showed that high growth gas flow rate could affect SiC crystal resistivity remarkably. The SiC crystal resistivity would get higher and higher with increasing growth gas flow rate. The purifying effect of gas flow rate was contributing to resistivity increase at a relatively low flow rate range. As for the high gas flow rate, increase of resistivity might be explained by the well-known site competition effect. Then, one explanation for reducing nitrogen content in the crystal via increasing gas flow rate was put forward. Namely, the Si component in the gas species may more easily go through the graphite crucible at the initial stage to make the growth ambient C-rich when the gas flow rate is ∼800 sccm or more and hence suppress nitrogen incorporation into carbon site to increase crystal resistivity. This result is very helpful to grow high purity high resistivity SiC ingots.

The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori error estimates are derived for both unknowns θ and χ, which exhibit the correct asymptotic order in terms of ε, h and τ. This result circumvents the use of duality, which does not even apply in this context. Several numerical experiments illustrate the reliability of the estimators and document the excellent performance of the ensuing adaptive method.

In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.

The Lawrence–Doniach model for superconducting layered compounds in which the Ginzburg–Landau order parameters in adjacent layers are coupled by Josephson tunneling is considered. The main purpose of this paper is to demonstrate that the time-dependent Ginzburg–Landau model is the limit of the Lawrence–Doniach model as the layer spacing goes to zero.