Stability of Runge-Kutta methods for delay differential systems with multiple delays

The stability of Runge-Kutta methods for systems of delay differentialequations (DDEs) with multiple delays is considered. The stabilityregions of explicit and implicit Runge-Kutta methods are discussedwhen they are applied to asymptotically stable linear DDEs withmultiple delays. A simple estimate on the stability regionsof explicit Runge-Kutta methods is presented. It is shown thatthe stable step-size for numerical integration of DDEs withmultiple delays can be easily selected by means of the estimate.     

All the Bell Inequalities

Bell inequalities are derived for any number of observers, any number of alternative setups for each one of them and any number of distinct outcomes for each experiment. It is shown that if a physical system consists of several distant subsystems, and if the results of tests performed on the latter are determined by local variables with objective values, then the joint probabilities for triggering any given set of distant detectors are convex combinations of a finite number of Boolean arrays, whose components are either 0 or 1 according to a simple rule. This convexity property is both necessary and sufficient for the existence of local objective variables. It leads to a simple graphical method which produces a large number of generalized Clauser-Horne inequalities corresponding to the faces of a convex polytope. It is plausible that quantum systems whose density matrix has a positive partial transposition satisfy all these inequalities, and therefore are compatible with local objective variables, even if their quantum properties are essentially non-local.     

过渡金属类立方烷原子簇化合物电子结构和二阶非线性光学性质的密度泛函理论研究

采用基于第一原理的含时密度泛函理论(TDDFT)对一系列具有类立方烷簇芯结构的过渡金属簇合物二阶非线性光学性质进行了研究。结果证明, 由于簇芯结构的对称性的影响, 这一类簇分子的二阶非线性光学系数的数值要小于三核欠完整类立方烷体系。通过对电子结构的分析, 发现二阶非线性光学性质主要是由簇芯内电荷的迁移造成的。轨道分析显示, -S原子对于电荷的迁移起主要的传递作用。定域化轨道分析证明簇分子中存在的多中心键有利于簇芯内电荷的迁移。分子模拟的研究表明:虽然类立方烷结构簇分子的值比较小, 但是通过合理的配体设计, 获得具有较大值非线性光学晶体是可能的。     

Sub-micrometer polarimetry of chiral surfaces using near-field scanning optical microscopy

In this work we have studied the optical activity of chiral crystal surfaces with polarized near-field scanning optical microscopy (NSOM); our studies clearly demonstrated that polarized NSOM can be utilized to determine chirality at crystal surfaces.     

Novel semi‐IPN through vinyl silane polymerization and crosslinking within PVC films

Novel semi‐IPN (interpenetrating polymer networks) were synthesized through vinyl silane modification of unplasticized poly(vinyl chloride) (PVC) films using relatively low temperatures, relatively high vinyl silane contents, and several different processing routes. A free‐radical initiator was used to promote reaction of the vinyl groups, and an aqueous acetic acid solution was used to promote the methoxysilane hydrolysis and condensation (HC) reactions for siloxane crosslink formation. A gel consisting of silane alone was formed prior to the HC process, indicating the formation of a semi‐IPN. The gel content following the HC process far exceeded the silane content, indicating a significant amount of PVC was entrapped by the silane network. This conclusion is supported by the homogeneous molecular structure and morphology of the films. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 8–22, 2001     

不同生长期当归1H NMR指纹图谱的研究

利用¹H NMR法测定27个不同生长期的当归提取物,对当归的主要活性成分阿魏酸、藁本内酯、当归多糖进行了初步归属,用特征峰相对峰面积表示3种活性成分的相对含量,并对它们在生长过程中的含量变化进行分析. 数据分析显示,当归中阿魏酸、藁本内酯、当归多糖的含量在第1年变化较为平稳,第2年和第3年变化相对较为活跃,而在当归的生长周期内,当归多糖的含量变化明显大于其他两种活性成分,为参与代谢活动的主要活性成分. 结果证实,通过对照¹H NMR指纹图谱, 将相对含量法与主成分分析法相结合,能对不同生长期的当归药材中的活性成分进行宏观评价和分析,可作为植物药材代谢组学的研究方法.     

无机-有机杂化非线性光学晶体材料LAP和d-LAP晶体红外吸收边计算

根据双原子谐振子模型近似,提出了估算分子晶体材料红外吸收边的理论方法,然后利用超分子量子化学从头算,计算了L-精氨酸一水磷酸盐(LAP)晶体和氘化L-精氨酸一水磷酸盐(d-LAP)晶体单元超分子的红外振动光谱,其中LAP晶体超分子计算值与晶体红外光谱实验值吻合,表明超分子计算能有效地模拟无机-有机杂化非线性光学晶体的红外振动光谱。在归属了超分子重要基频线后,分析其红外强度,并估算了泛频频率。根据我们提出的方法,估算了这两种晶体的红外吸收边,结果与实验值较吻合。表明我们建议的理论方法是合理的。此外,通过计算表明,如果非线性光学晶体材料的红外吸收边是由与活泼H有关的伸缩振动泛频频率决定,那么活泼H的氘化是一种改善红外吸收边的有效途径。     

在RHIC的极限碎裂和Φ介子产生(英文)

利用强子和串级联模型LUCIAE研究了PHOBOS的极限碎裂等以及在PHIC进行的Au+Au碰撞中带电粒子多重性的经验标度规律. 对Φ介子的产生机制也通过与带电粒子多重性的比较进行类似的研究. 结果似乎表明在串级碎裂模型中带电粒子和Φ介子有共同的产生机制. 还讨论了PHOBOS经验标度规律的模型依赖性.The PHOBOS’s limiting fragmentation etc. three empirical scaling rules for charged multiplicity in Au+Au collisions at RHIC are investigated by ahadron and string cascade model LUCIAE. Similar studies are performed for the meson exploring its production mechanism via comparing with the charged multiplicity. The LUCIAE results for charged multiplicity are compatible with PHOBOS observations. However, for the  meson the three empirical scaling rules are either kept only or kept better in the LUCIAE calculations without reduction mechanism of the s quark suppression extra introduced for the strangeness in LUCIAE model. These results seem indicating a universal production mechanism for charged particle and  meson in string fragmentation regime. It is discussed that the PHOBOS’s empirical scaling rules are model dependent indeed.     

Net Charge Fluctuation and String Fragmentation

We present the simulation results of the net charge fluctuation in Au Au collisions at /Snn=130 GeV froma dynamic model, JPCIAE, and its revisions. The simulations are done for the quark-gluon matter, the directly producedpions, the pion matter, and the hadron matter. The simulated net charge fluctuation of the quark-gluon matter is closeto the thermal model prediction for the quark-gluon gas. However, the discrepancy exists comparing the simulated netcharge fluctuation for directly produced pions and the pion matter with the thermal model prediction for pion gas andthe resonance pion gas, respectively. The net charge fluctuation of hadron matter from default JPCIAE simulations isnearly 3.5 times larger than quark-gluon matter. A discussion is given for the net charge fluctuation as an evidence ofQGP phase transition.     

Theoretical Studies on the First Hyperpolarizabilities of One-dimensional Donor-bridge-acceptor Chromophores and New Applications of BLA in Determining Molecular First Hyperpolarizabilities

We present a quantum-chemical analysis of the relationship between the bond length alteration （BLA） and the static first hyperpolarizability of a series of one-dimensional （1D） chromophores with donor-bridge-acceptor （D-B-A） structures. The calculated results show that the parameter BLA can be considered as an indicator to evaluate the molecular first hyper- polarizability. Along the direction of molecular ground-state dipole moments, the evolutions of BLA can be classified into three categories： the first is a non-monotonic line, which represents most chromophores; the second is monotonic increasing; and the third, contrarily, is monotonic decreasing. On the whole, the first hyperpolarizabilities of these studied chromophores are the monotonic functions of BLA along the direction of dipole moments. Therefore, the first hyperpolarizability of these 1D chromophores can be preliminarily evaluated in terms of the development of BLA without a rigorous computation. In other words, one can roughly estimate the relative magnitude of the first hyperpolarizability according to the optimized geometry.