Five-parameter crystallographic characteristics of the interfaces formed during ferrite to austenite transformation in a duplex stainless steel

The crystallography of interfaces in a duplex stainless steel having an equiaxed microstructure produced through the ferrite to austenite diffusive phase transformation has been studied. The five-parameter interface character distribution revealed a high anisotropy in habit planes for the austenite–ferrite and austenite–austenite interfaces for different lattice misorientations. The austenite and ferrite habit planes largely terminated on (1 1 1) and (1 1 0) planes, respectively, for the austenite–ferrite interfaces associated with Kurdjumov–Sachs (K–S) and Nishiyama–Wasserman (N–W) orientation relationships. This was mostly attributed to the crystallographic preference associated with the phase transformation. For the austenite–ferrite interfaces with orientation relationships which are neither K–S nor N–W, both austenite and ferrite habit planes had (1 1 1) orientations. Σ3 twin boundaries comprised the majority of austenite–austenite interfaces, mostly showing a pure twist character and terminating on (1 1 1) planes due to the minimum energy configuration. The second highest populated austenite–austenite boundary was Σ9, which tended to have grain boundary planes in the tilt zone due to the geometrical constraints. Furthermore, the intervariant crystallographic plane distribution associated with the K–S orientation relationship displayed a general tendency for the austenite habit planes to terminate with the (1 1 1) orientation, mainly due to the crystallographic preference associated with the phase transformation.     

Variational model for one-dimensional quantum magnets

A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan–Wigner transformation. The ground state is described by a new non-local trial wave function, and the total energy is calculated in an analytic form as a function of two variational parameters. This approach is demonstrated with an example of the XXZ-chain of spin-1/2 under a staggered magnetic field. Generalizations and applications of the variational technique for low-dimensional magnetic systems are discussed.     

Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation

In this paper, we consider an extended Korteweg-de Vries (KdV) equation. Using the consistent Riccati expansion (CRE) method of Lou, the extended KdV equation is proved to be CRE solvable in only two distinct cases. These two CRE solvable models are the KdV-Lax and KdV-Sawada-Kotera (KdV-SK) equations. In addition, applying the nonauto-Bäcklund transformations which are provided by the CRE method, we present the explicit construction for soliton-cnoidal wave interaction solutions which represent a soliton propagating on a cnoidal periodic wave background in the KdV-Lax and KdV-SK equations, respectively.     

连续小波变换定量反演土壤有机质含量

以北京市东部地区96个潮土土样的土壤参数及对应光谱数据为数据源,采用连续小波多尺度分析处理与分析。首先将土壤光谱进行初步处理,生成小波系数,其次将土样的有机质含量与小波分解系数开展相关性分析,提取特征波段,最后采用特征波段建立预测耕层有机质含量的模型。结果表明：经连续小波处理后,光谱对耕层有机质含量的预测能力明显优于传统光谱变换技术;经连续小波分解后,对土壤有机质含量的预测能力随光谱分辨率降低呈先降后升再降的趋势;连续小波分析算法可提升土壤光谱对有机质含量的估测能力,与土壤高光谱反射率相比,基于连续小波变换的土壤有机含量最佳的精度提高19%;由于光谱分辨率为80 nm建立的模型精度较高,其R2达到0.632,这表明在连续小波算法下,光谱分辨率较低的宽波段数据可用于土壤有机质含量的监测。     

Preparation of synthetic rutile from high titanium slag using microwave heating

In this work, we demonstrate a novel synthesis of synthetic rutile from high titanium slag. This rutile TiO₂ was obtained by a simple one-step microwave roasting route. The influence of microwave roasting temperature and duration on the phase transformation of high titanium slag has been assessed. X-ray diffraction (XRD) results indicate that the intensity of anosovite (Fe₃Ti₃O₁₀) phase, which were the major phase of high titanium slag of carbon thermal reduction of ilmenite ores, decreased rapidly while the peaks for rutile TiO₂ phase increased with increase in the microwave roasting temperature. The scanning electron microscope (SEM) images revealed formation and the particle-size distribution of rutile TiO₂ phase. Based on XRD and SEM analysis, confirmed the dependence of phase structure, composition and crystallite size on the process conditions of microwave roasting.     

Residual Symmetry Reduction and Consistent Riccati Expansion of the Generalized Kaup-Kupershmidt Equation

The residual symmetry of the generalized Kaup-Kupershmidt(gKK) equation is obtained from the truncated Painlevé expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Furthermore, the g KK equation is proved to integrable in the sense of owning consistent Riccati expansion and some new B¨acklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given.     

Wavelet processing and digital interferometric contrast to improve reconstructions from X‐ray Gabor holograms

In this work, the application of an undecimated wavelet transformation together with digital interferometric contrast to improve the resulting reconstructions in a digital hard X‐ray Gabor holographic microscope is shown. Specifically, the starlet transform is used together with digital Zernike contrast. With this contrast, the results show that only a small set of scales from the hologram are, in effect, useful, and it is possible to enhance the details of the reconstruction.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

二阶Emden-Fowler型非线性变时滞微分方程的振荡准则

研究了一类具有变时滞的二阶Emden-Fowler型非线性中立型泛函微分方程的振荡性.借助Riccati变换、积分平均技术和微分不等式等技巧,获得了该类方程振荡的新判别准则和比较判别定理,推广、改进并丰富了现有文献中的结果.