Formation of a Syndiotactic Organic Polymer Inside a MOF by a [2+2] Photo‐Polymerization Reaction

Getting suitable crystals for single‐crystal X‐ray crystallographic analysis still remains an art. Obtaining single crystals of metal–organic frameworks (MOFs) containing organic polymers poses even greater challenges. Here we demonstrate the formation of a syndiotactic organic polymer ligand inside a MOF by quantitative [2+2] photopolymerization reaction in a single‐crystal‐to‐single‐crystal manner. The spacer ligands with trans,trans,trans‐conformation in the pillared‐layer MOF with guest water molecules in the channels, undergo pedal motion to trans,cis,trans‐conformation prior to [2+2] photo‐cycloaddition reaction and yield single crystals of MOF containing two‐dimensional coordination polymers fused with the organic polymer ligands. We also show that the organic polymer in the single crystals can be depolymerized reversibly by cleaving the cyclobutane rings upon heating. These MOFs also show interesting photoluminescent properties and sensing of small organic molecules.     

Transition mechanisms of translational motions of bubbles in an ultrasonic field

The translation behaviors of oscillating bubbles are closely related to the polymerizations and dispersions between them, which are crucial for the ultrasonic cavitation effect. In this study, six types of translational motion of bubbles with a wide range of sizes (2–100 μm) in the R₀₁-R₀₂ plane are investigated. Our results demonstrate that in addition (to the 2nd order harmonic), the 1/2 order subharmonic can change the bubble pairs from the three states of the attraction, stable after attraction, and repulsion to that of the repulsion, coalescence, and attraction, respectively. Furthermore, within the range of the main resonance radius and the 1/2 order subharmonic resonance radius, the chaotic bubble pairs with alternating attractive and repulsive forces appear in the region between the coalescence pairs and stable pairs after attraction. Finally, the corresponding physical mechanisms of the chaotic translational motions are also revealed.     

基于微观粒子运动本质再探核外电子运动的教学设计与实施*

高中选择性必修阶段对核外电子运动再探究需要在学科理解视域下认识核外电子运动的本质规律。通过原子结构模型的演变过程抽提核外电子运动的本原性问题,在本原性问题解决的学习任务中引导学生发展性地建构原子结构模型。基于微观粒子运动的本质认识核外电子的运动特征和描述方式,建构核外电子运动的微观认识视角。     

Mixed Quantum Classical Reaction Rates based on the Phase Space Formulation of the Hierarchical Equations of Motion

In a previous work [J. Chem. Phys. 140 , 174105 (2014)], we have shown that a mixed quantum classical (MQC) rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions. However, the method is based on the high temperature approximation of the hierarchical equation of motion (HEOM) with the Debye-Drude spectral density, and results in a multi-state Zusman type of equation. We now extend this theory to include quantum effects of the bath degrees of freedom. By writing the full HEOM into a multidimensional partial differential equation in phase space, we can define a new reaction coordinate, and the previous method can be generalized to the full quantum regime. The validity of the new method is demonstrated by using numerical examples, including the spin-Boson model, and the double well model for proton transfer reaction. The new method is found to resolve some key problems of the previous theory based on high temperature approximation, including possible numerical instability in long time simulation and wrong rate constant at low temperatures.     

Restriction of Intramolecular Motion(RIM): Investigating AIE Mechanism from Experimental and Theoretical Studies

Mechanistic studies promote scientific development from phenomena to theories.Aggregation-induced emission(AIE),as an unusual photophysical phenomenon,builds the bridge between molecular science and aggregate mesoscience.With the twenty-year development of AIE,restriction of intramolecular motion(RIM)has been verified as the working mechanism of AIE effect.In this review,these mechanistic works about RIM are summarized from experimental and theoretical perspectives.Thereinto,the experimental studies are introduced from three parts:external rigidification,structural modification and structural characterization.In the theoretical part,calculations on the low-frequency motion of AIEgens have been performed to prove the RIM mechanism.By virtue of the theoretical calculations,some new mechanisms are proposed to supplement the RIM,such as restriction of access to conical intersection,suppression of Kasha transition,restriction of access to dark state,etc.It is foreseeable that the RIM mechanism will unify the photophysical theories for both molecules and aggregates,and inspire more progress in aggregate science.     

Continuity in law with respect to the Hurst index of some additive functionals of sub-fractional Brownian motion

In this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub-fractional Brownian motion. We prove that our result can be obtained easily, by using the decomposition in law of the sub-fractional Brownian motion given by Bardina and Bascompte [Collect. Math. 61(2010):191–204] and Ruiz de Chavez and Tudor [Math. Rep. 11(2009):67–74], without using the result of Wu and Xiao [Stoch. Proc. Appl. 119(2009):1823–1844] by connecting the sub-fractional Brownian motion to its stationary Gaussian process through Lamperti’s transform. This decomposition in law leads to a better understanding and simple proof of our result.     

双荷子系统运动的经典解

根据力学理论和经典电磁理论研究双荷子系统的运动.列出双荷子系统的运动微分方程,导出运动积分,说明系统的对称性,包括SO(4)对称性;利用变分法逆问题方法,构造双荷子系统的Lagrange(拉格朗日)函数和Hamilton(哈密顿)函数;解出双荷子系统的运动规律.     

分数扩散模型的参数估计及其应用

研究分数扩散模型的参数估计及其应用问题.分数扩散模型是一类由分数Brownian运动驱动的随机微分方程.主要结果有:(1)利用二次变差方法给出模型中扩散系数的估计量,通过最小二乘法给出模型中漂移系数的估计量;(2)证明这些估计量的一致收敛性和渐近正态性;(3)利用MCMC方法对此估计量进行验证,并通过R软件将上述模型以及参数估计量应用到SHIBOR利率中进行实证研究.     

New algorithm for tensor contractions on multi‐core CPUs,GPUs, and accelerators enables CCSD and EOM‐CCSD calculations with over 1000 basis functions on a single compute node

A new hardware‐agnostic contraction algorithm for tensors of arbitrary symmetry and sparsity is presented. The algorithm is implemented as a stand‐alone open‐source code libxm . This code is also integrated with general tensor library libtensor and with the Q‐Chem quantum‐chemistry package. An overview of the algorithm, its implementation, and benchmarks are presented. Similarly to other tensor software, the algorithm exploits efficient matrix multiplication libraries and assumes that tensors are stored in a block‐tensor form. The distinguishing features of the algorithm are: (i) efficient repackaging of the individual blocks into large matrices and back, which affords efficient graphics processing unit (GPU)‐enabled calculations without modifications of higher‐level codes; (ii) fully asynchronous data transfer between disk storage and fast memory. The algorithm enables canonical all‐electron coupled‐cluster and equation‐of‐motion coupled‐cluster calculations with single and double substitutions (CCSD and EOM‐CCSD) with over 1000 basis functions on a single quad‐GPU machine. We show that the algorithm exhibits predicted theoretical scaling for canonical CCSD calculations, O (N ⁶), irrespective of the data size on disk. © 2017 Wiley Periodicals, Inc.     

The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion

In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short). By means of the G-Lyapunov function method, some criteria on p-th moment stability and p-th moment asymptotical stability for the trivial solutions of IGSDEs are established. An example is presented to illustrate the efficiency of the obtained results.