第一过渡系金属-镝单分子磁体研究进展与展望

第一过渡系中的顺磁性离子Cr^Ⅲ、Mn^Ⅱ/Mn^Ⅲ、Fe^Ⅱ/Fe^Ⅲ、Co^Ⅱ、Ni^Ⅱ和Cu^Ⅱ及抗磁性离子Co^Ⅲ和Zn^Ⅱ均可与Dy^Ⅲ在多齿螯合配体配位下形成单分子磁体配合物。在本文中,我们阐述或汇总了几乎所有的第一过渡系金属-镝单分子磁体。对于由顺磁性第一过渡金属离子和Dy^Ⅲ离子形成的配合物,有2个有趣的现象需要引起人们的注意：一是一些Cr-Dy配合物具有较高的阻塞温度和较大的矫顽场,这可归功于配合物内Cr^Ⅲ离子和Dy^Ⅲ离子之间较强的磁耦合作用（|J|>10 cm^-1）。二是报道的Fe^Ⅱ₂-Dy配合物的能垒可达到319 cm^-1（459 K）,这在第一过渡系金属-镝单分子磁体中也是比较高的。这可能与Fe^Ⅱ₂-Dy中Dy^Ⅲ具有较高的轴向对称性（D_5h）有关,且从头计算表明该配合物中Dy的第一激发态也具有较高的轴向对称性。除了部分Cr-Dy和Fe^Ⅱ-Dy配合物外,其他顺磁性第一过渡金属-Dy的能垒较低,这可能由配合物内顺磁离子间弱的磁耦合造成的。为了消除磁耦合对磁弛豫行为影响,近年来人们关注于使用抗磁性第一过渡金属离子与Dy^Ⅲ构建单分子磁体配合物。相比其他核数的Zn-Dy配合物,三核Zn₂Dy配合物被报道的数目最多且研究得最为深入,这可能与较易调控Zn₂Dy中Dy配位几何对称性有关。最后,我们提出了几点关于进一步提升第一过渡系金属-镝单分子磁体的磁性能的建议,其中最为重要的是控制Dy配位几何的轴向对称性及Dy的基态m_J的电荷分布。对于第一过渡系金属-镝单分子磁体中的Dy^Ⅲ离子,Dy^Ⅲ基态m_J的电荷与配体的电荷之间的静电排斥应该降到最低。     

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.     

Stabilization of novel multi-layer networks with noise-based nonlinear superior couplings via aperiodically adaptive intermittent pinning control

In this paper, novel multi-layer networks with superior couplings are proposed firstly which are established on a non-strongly connected digraph. Within the multi-layer networks, a nonlinear coupling based on white noises is introduced, which is the feature of superior couplings. We adopt aperiodically adaptive intermittent pinning control to stabilize the multi-layer networks. An concrete analysis framework about selecting the target vertex of the control is revealed. Aperiodically adaptive intermittent control is employed on the vertex systems of the first layer networks, to achieve the stabilization of the first layer networks, where the couplings of drift terms are treated as negative effects on stabilization. With the help of noise stabilization, the stabilization of the other layers networks is realized based on the stability of the first layer networks and the characteristics of the superior coupling that is based on white noises. By employing graph theory and the Lyapunov method, an almost sure exponential stabilization criterion of the multi-layer networks is acquired. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators with sufficient conditions being given to ensure their stability. Finally, a numerical example is provided to illustrate the feasibility of the stated theoretical results.     

Characteristic Numbers of Matrix Lie Algebras

A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.     

13C NMR investigations of molecular order of rod-like,bent-core,and thiophene mesogens

In this review, methods to obtain the orientational order of topologically variant molecular mesogens using by one- and two-dimensional (2D) solid-state ¹³C nuclear magnetic resonance (NMR) spectroscopy are described. Besides ¹³C chemical shifts, the ¹³C─¹H dipolar couplings measured from 2D-separated local field (SLF) technique are used for computing the order parameters of a variety of mesogens. The investigated molecules are composed of a variable number of rings in the core, that is, core ranging from simply one ring to five rings. Among the mesogens investigated, a special focus has been placed on mesogens with thiophene rings, which are gaining popularity as liquid crystalline organic semiconductors. The replacement of a phenyl ring by thiophene in the core has a dramatic influence on molecular topology, as observed from the measured order parameters. The review highlights the advantages of the 2D SLF method for understanding the local dynamics and for mapping the topology of mesogens through the measured order parameters. SLF NMR studies of as many as 24 molecular mesogens that vary in terms of the molecular structure as well as topology are covered in the review. Order parameters of the rings have been estimated from the ¹³C─¹H dipolar couplings in the nematic, smectic A, smectic C, and tilted hexatic phases as well as in B₁ and B₂ mesophases of various mesogens. It is anticipated that, in the years to come, the 2D SLF method would provide advanced molecular information on structurally complex mesogens that are emerging in liquid crystal science through the incessant efforts of synthetic chemists. The mini review covers the orientational order of topologically variant molecular mesogens determined by 1D and 2D solid-state ¹³C NMR spectroscopy. Accordingly, rod-like, bent-core, and thiophene mesogens were subjected to 2D SLF measurements to get the order parameters from which the topology was established. The replacement of phenyl ring by thiophene and its influence on order parameters as well as on molecular topology is also discussed.     

Network dynamics and its relationships to topology and coupling structure in excitable complex networks

All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend or/network topologies are tasks of both great theoretical importance and broad practical significance. In this paper we study the oscillatory behaviors of excitable complex networks （ECNs） and find some interesting dynamic behaviors of ECNs in oscillatory probability, the multiplicity of oscillatory attractors, period distribution, and different types of oscillatory patterns （e.g., periodic, quasiperiodic, and chaotic）. In these aspects, we further explore strikingly sharp differences among network dynamics induced by different topologies （random or scale-free topologies） and different interaction structures （symmetric or asymmetric couplings）. The mechanisms behind these differences are explained physically.     

Transverse magnetization transfer under planar mixing conditions in spin systems consisting of three coupled spins 1/2

Polarization transfer under planar mixing conditions is a widely used tool in modern NMR-experiments. In the case of two coupled spins 1/2 or a chain of three or more spins 1/2 with only nearest neighbor couplings, it is only possible to transfer a single magnetization component (longitudinal magnetization in the principle axis system of the planar coupling tensors). However, if all couplings in a three-spin system are non-zero, it turns out that all magnetization components can be efficiently transferred even under strictly planar mixing conditions. In this article a detailed theoretical analysis is presented based on analytical transverse coherence transfer functions and on the underlying commutator algebra. In addition, transverse magnetization transfer is demonstrated experimentally. The results show that in highly coupled spin systems, as for example in the case of partially aligned samples with many residual dipolar couplings, special care has to be taken to avoid phase distortions if planar mixing steps are used.     

残留偶极耦合及其在蛋白质结构研究中的应用

近年来溶液中残留偶极耦合常数被用来获取生物大分子化学键之间相对取向等长程构象约束条件,用于计算或优化蛋白质及其复合物的三维空间结构. 介绍了用异核多维NMR技术测量残留偶极耦合常数的方法,及其在蛋白质结构计算中的一些应用：优化蛋白质溶液结构,评价蛋白质结构质量,确定蛋白质结构域取向,获取有关配体的构象和取向的信息,在缺乏NOE数据时构建蛋白质结构等.      

Strong ergodicity of the regime-switching diffusion processes

We provide criteria for the strong ergodicity of regime-switching diffusion processes. Our conditions are imposed on the coefficients of the processes. Particularly, we show that for regime-switching diffusions on the half line, if the corresponding diffusion on each fixed environment is strongly ergodic, then the regime-switching diffusion is strongly ergodic as well, which does not depend on the changing rate of the environment. Moreover, the converse is not always true, which is shown by an example. For transience, recurrence and positive recurrence, there is no such good consistency [R. Pinsky and M. Scheutzow, Some remarks and examples concerning the transience and recurrence of random diffusions, Ann. Inst. Henri. Poincaré 28 (1992) 519–536].