Fourth-order finite-difference method for boundary value problems with two small parameters

We present a finite difference scheme for a class of linear singularly perturbed boundary value problems with two small parameters. The problem is discretized using a Bakhvalov-type mesh. It is proved under certain conditions that this scheme is fourth-order accurate and that its error does not increase when the perturbation parameter tends to zero. Numerical examples are presented which demonstrate computationally the fourth order of the method.     

Boundedness of the anisotropic maximal and anisotropic singular integral operators in generalized Morrey spaces

In this paper we give the conditions on the pair (ω ₁, ω ₂) which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized Morrey space M_p,w1 \mathcal{M}_{p,\omega _1 } to another M_p,w2 \mathcal{M}_{p,\omega _2 }, 1 < p < g8, and from the space M_1,w1 \mathcal{M}_{1,\omega _1 } to the weak space WM_1,w2 W\mathcal{M}_{1,\omega _2 }.     

One‐step boundary knot method for discontinuous coefficient elliptic equations with interface jump conditions

This study makes the first attempt to apply the boundary knot method (BKM), a meshless collocation method, to the solution of linear elliptic problems with discontinuous coefficients, also known as the elliptic interface problems. The additional jump conditions are usually required to be prescribed at the interface which is used to maintain the well‐posedness of the considered problem. To solve the problem efficiently, the original governing equation is first transformed into an equivalent inhomogeneous modified Helmholtz equation in the present numerical formulation. Then the computational domain is divided into several subdomains, and the solution on each subdomain is approximated using the BKM approach. Unlike the conventional two‐step BKM, this study presents a one‐step BKM formulation which possesses merely one influence matrix for inhomogeneous problems. Several benchmark examples with various discontinuous coefficients have been tested to demonstrate the accuracy and efficiency of the present BKM scheme. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1509–1534, 2016     

Anomalous anisotropic magnetoresistance in single-crystalline Co/SrTiO3(001) heterostructures

The anisotropic magnetoresistances (AMRs) in single crystalline Co(6 nm)/SrTiO₃(001) heterostructures from 5 K to 300 K with the current direction setting along either Co[100] or Co[110] are investigated in this work. The anomalous (normal) AMR is observed below (above) 100 K. With the current along Co[100] direction, the AMR shows negative longitudinal and positive transverse magnetoresistances at T< 100 K, while the AMR is inverse with the current along Co[110]. Meanwhile, the amplitude ratio between Co[110] and Co[100] is observed to be as large as 29 at 100 K. A crystal symmetry-adapted model of AMR demonstrates that interplay between the non-crystalline component and crossed AMR component results in the anomalous AMR. Our results may reveal more intriguing magneto-transport behaviors of film on SrTiO₃ or other perovskite oxides.     

Fourth‐order compact scheme with local mesh refinement for option pricing in jump‐diffusion model

The value of a contingent claim under a jump‐diffusion process satisfies a partial integro‐differential equation. A fourth‐order compact finite difference scheme is applied to discretize the spatial variable of this equation. It is discretized in time by an implicit‐explicit method. Meanwhile, a local mesh refinement strategy is used for handling the nonsmooth payoff condition. Moreover, the numerical quadrature method is exploited to evaluate the jump integral term. It guarantees a Toeplitz‐like structure of the integral operator such that a fast algorithm is feasible. Numerical results show that this approach gives fourth‐order accuracy in space. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

Absence of magnetic order in dichloro [1,2-bis(diphenylphosphino)ethane] nickel~(2+) single crystal

Dichloro [1,2-bis(diphenylphosphino) ethane] nickel~(2+)(Ni Cl_2(dppe)) is an organic compound containing C_(26)H_(24)P_2(dppe) molecules and Cl-, Ni~(2+)ions. The large-size Ni Cl_2(dppe) single crystals with longest dimension of4 mm were grown by the method of slow evaporation of organic solution. Single crystal x-ray diffraction spectrum indicates that the single crystal is of high quality. Magnetization results of the Ni Cl_2(dppe) single crystals show an anisotropic paramagnetism behavior and diamagnetic background, which come from Ni~(2+) ions and benzene ring, respectively. However, according to the specific heat results with temperature down to 0.1 K and magnetic field up to 14 T, no expected field-induced quantum phase transition was observed in Ni Cl_2(dppe) single crystals.     

Anisotropic exciton Stark shift in hemispherical quantum dots

The exciton Stark shift and polarization in hemispherical quantum dots(HQDs) each as a function of strength and orientation of applied electric field are theoretically investigated by an exact diagonalization method. A highly anisotropic Stark redshift of exciton energy is found. As the electric field is rotated from Voigt to Faraday geometry, the redshift of exciton energy monotonically decreases. This is because the asymmetric geometric shape of the hemispherical quantum dot restrains the displacement of the wave function to the higher orbital state in response to electric field along Faraday geometry. A redshift of hole energy is found all the time while a transition of electron energy from this redshift to a blueshift is found as the field is rotated from Voigt to Faraday geometry. Taking advantage of the diminishing of Stark effect along Faraday geometry, the hemispherical shapes can be used to improve significantly the radiative recombination efficiency of the polar optoelectronic devices if the strong internal polarized electric field is along Faraday geometry.     

Force-constant-decayed anisotropic network model: An improved method for predicting RNA flexibility

RNA is an important biological macromolecule, which plays an irreplaceable role in many life activities. RNA functions are largely determined by its tertiary structure and the intrinsic dynamics encoded in the structure. Thus, how to effective extract structure-encoded dynamics is of great significance for understanding RNA functions. Anisotropic network model (ANM) is an efficient method to investigate macromolecular dynamical properties, which has been widely used in protein studies. However, the performance of the conventional ANM in describing RNA flexibility is not as good as that on proteins. In this study, we proposed a new approach, named force-constant-decayed anisotropic network model (fcd-ANM), to improve the performance in investigating the dynamical properties encoded in RNA structures. In fcd-ANM, nucleotide pairs in RNA structure were connected by springs and the force constant of springs was decayed exponentially based on the separation distance to describe the differences in the inter-nucleotide interaction strength. The performance of fcd-ANM in predicting RNA flexibility was evaluated using a non-redundant structure database composed of 51 RNAs. The results indicate that fcd-ANM significantly outperforms the conventional ANM in reproducing the experimental B-factors of nucleotides in RNA structures, and the Pearson correlation coefficient between the predicted and experimental nucleotide B-factors was distinctly improved by 21.05% compared to the conventional ANM. Fcd-ANM can serve as a more effective method for analysis of RNA dynamical properties.     

曲边区域上的多边形网格间断有限元离散及其多重网格算法

本文利用多边形网格上的间断有限元方法离散二阶椭圆方程,在曲边区域上,采用多条直短边逼近曲边的以直代曲的策略,实现了高阶元在能量范数下的最优收敛.本文还将这一方法用于带曲边界面问题的求解,同样得到高阶元的最优收敛.此外我们还设计并分析了这一方法的\linebreakW-cycle和Variable V-cycle多重网格预条件方法,证明当光滑次数足够多时,多重网格预条件算法一致收敛.最后给出了数值算例,证实该算法的可行性并验证了理论分析的结果.     

An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.