Line integral methods which preserve all invariants of conservative problems

Recently, the class of Hamiltonian Boundary Value Methods (HBVMs) has been introduced with the aim of preserving the energy associated with polynomial Hamiltonian systems (and, more in general, with all suitably regular Hamiltonian systems). However, many interesting problems admit other invariants besides the Hamiltonian function. It would be therefore useful to have methods able to preserve any number of independent invariants. This goal is achieved by generalizing the line-integral approach which HBVMs rely on, thus obtaining a number of generalizations which we collectively name Line Integral Methods. In fact, it turns out that this approach is quite general, so that it can be applied to any numerical method whose discrete solution can be suitably associated with a polynomial, such as a collocation method, as well as to any conservative problem. In particular, a completely conservative variant of both HBVMs and Gauss collocation methods is presented. Numerical experiments confirm the effectiveness of the proposed methods.     

One-step deterministic multipartite entanglement purification with linear optics

We present a one-step deterministic multipartite entanglement purification scheme for an N-photon system in a Greenberger-Horne-Zeilinger state with linear optical elements. The parties in quantum communication can in principle obtain a maximally entangled state from each N-photon system with a success probability of 100%. That is, it does not consume the less-entangled photon systems largely, which is far different from other multipartite entanglement purification schemes. This feature maybe make this scheme more feasible in practical applications.     

The Lie-group shooting method for solving nonlinear singularly perturbed boundary value problems

A new computational method for solving the second-order nonlinear singularly perturbed boundary value problems (SPBVPs) is provided in this paper. In order to overcome a highly singular behavior very near to the boundary as being not easy to treat by numerical method, we adopt a coordinate transformation from an x-domain to a t-domain via a rescaling technique, which can reduce the singularity within the boundary layer. Then, we construct a Lie-group shooting method (LGSM) to search a missing initial condition through the finding of a suitable value of a parameter r ∈ [0, 1]. Moreover, we can derive a closed-form formula to express the initial condition in terms of r, which can be determined properly by an accurate matching to the right-boundary condition. Numerical examples are examined, showing that the present approach is highly efficient and accurate.     

An improved local error estimator for symmetric time-stepping schemes

We propose a symmetrized version of the defect to be used in the estimation of the local time-stepping error of symmetric one-step methods for the time propagation of linear autonomous evolution equations. Using the anti-commutator of the numerical flow and the right-hand side operator in the definition of the defect of the numerical approximation, a local error estimator is obtained which has higher accuracy asymptotically than an established version using the common defect. This theoretical result is illustrated for a splitting method applied to a linear Schrödinger equation.     

一步处理法制备高水热稳定多级孔ZSM-5分子筛

ZSM-5具有较高的催化活性和独特的择形选择性,因而被广泛用于精细化工和石油炼制等工业过程.但其较小的孔道尺寸导致其在反应中尤其在催化过程中的传质受到影响,从而严重影响催化剂寿命.为了解决反应过程中分子筛中底物及产物的扩散限制问题,近年来关于介微孔复合多级孔道分子筛的研究在分子筛合成领域引起了广泛兴趣,并取得一定进展.但直接合成法存在成本及复杂性问题,因此在量产的分子筛上进行后改性引入介孔表现出明显优势.在这一大类处理过程中,碱处理造介孔因成本低以及可操作性较高而备受青睐.但由于脱硅所形成的介孔往往无序,稳定性较差,因此提高其水热稳定性具有重要意义.文献已有较多报道通过磷元素修饰抑制分子筛在水热环境中脱铝,从而提高分子筛骨架稳定性.但传统的磷元素修饰一般采用后续浸渍法,过程繁琐.本课题组开发了一步法后处理制备高水热稳定多级孔ZSM-5分子筛,将脱硅过程与磷引入过程相结合,以四乙基氢氧化磷(TEPOH)为磷源,直接处理微孔分子筛得到含磷的多级孔分子筛.相比于传统的分子筛磷修饰过程,该磷物种在处理中优先交换分子筛骨架上铝原子附近用来平衡电荷的钠离子,从而增加了磷物种与铝物种相互作用的可能性,提高了稳化骨架的效果.基于此,本文利用氮吸附-脱附、元素分析、X射线粉末衍射(XRD)、扫描电镜(SEM)、透射电镜(TEM)、氨程序升温脱附(NH3-TPD)以及27Al和31P固体核磁(NMR)等一系列表征技术,证明该一步后处理法对分子筛催化性能的作用.SEM和XRD结果表明,分子筛在进行各种处理前后,相对结晶度和分子筛形貌变化不大,说明大部分微孔得到保留.TEM测试表明,经过该一步后处理法得到的分子筛实现了介孔的引入,介孔孔径在10–20 nm.元素分析结果表明,几乎所有的磷源物质在该过程中被引入到分子筛上,实现了介孔和磷物种的同时引入.NH3-TPD测试表明,含磷分子筛在老化前后较无磷分子筛具有更高的酸性位密度保留度,说明磷元素对分子筛上的酸性位起到了稳化作用.孔结构特性数据不仅说明了脱硅过程中成功引入介孔,而且含磷分子筛老化前后的介孔特性数据保留度明显高于无磷样品,实现了磷元素对介孔结构的稳化作用.27Al和31P NMR结果从理论上证明了该样品上磷元素对抑制骨架脱铝的稳化效应,证实了分子筛在处理后水热稳定性的提高.基于前期的研究工作,本文完善了磷元素对分子筛稳化作用的机理过程.TEPBr在水热活化过程中转变成磷酸盐,并修饰分子筛的骨架铝以及部分难以避免的非骨架铝.该过程中形成的磷铝物种在后续的水热老化过程中进一步修饰分子筛骨架铝,使骨架铝得到稳化.而在脱硅过程中存在的"反插铝"过程往往使大部分骨架铝位于介孔孔道中,磷元素与铝元素的相互作用同时也对介孔进行了稳化.通过正辛烯和1,3,5-三异丙苯的裂化测试发现,处理后的分子筛由于其优化后的孔道性能和酸性性质,大大提高了底物分子的转化率以及其自身的容碳能力,从而延长了催化寿命.     

Ni(0) catalyzed one step synthesis of benzo[b][1,8] naphthyridin-5-ones from silyl-α-ketoalkynes in water

One-step synthesis of new benzo[b][1,8]naphthyridin-5-ones using a Ni(0) catalytic system in aqueous medium with mild conditions of pressure and temperature is described. It is very interesting to note that Ni(0) catalyst increases the rate of condensation of several α-ketoalkynes with 2-amino-4(1H)-quinolinone obtaining benzo[b][1,8]naphthyridin-5-ones in very high yield. In the absence of catalyst this condensation reaction takes 24 h with a product yield of <10%.     

Hydrophobic octadecylamine-polyphenol film coated slow released urea via one-step spraying co-deposition

Polymer coated fertilizer has been designed for gradual release of nutritional content of fertilizer to improve the utilization efficiency. However, the better slow release property of the coated fertilizer and simplified preparation process are still a huge challenge. The hydrophobic ODA-polyphenol film coated urea was prepared by one-step spraying for excellent nutrient release performance. Octadecylamine (ODA) was used to modify poly(tannic acid) (PTA) and poly(pyrogallol) (PPG) coating on substrates and prepare the hydrophobic ODA-PTA and ODA-PPG coated urea granules. The nutrient release rate of ODA-PTA and ODA-PPG coated fertilizers was much slower than PTA and PPG coated fertilizers in water and soil. The N release longevities of ODA-PTA coated fertilizers will be extended from 2 h to 30 days compared with PTA coated fertilizers. Moreover, pot experiments showed that coated fertilizer could effectively promote plant growth. This work will provide one-step spraying co-deposition approach to fabricate hydrophobic ODA-polyphenol film coated urea to improve the N release longevity, which can shine a light on the development of new slow release fertilizers (SRFs).     

由苯-1,2,4-三羧酸-1,2-酐和二乙醇胺合成结构非对称超支化聚(酰胺-酯)

通过准发散法和一步法由苯 1 ,2 ,4 三羧酸 1 ,2 酐 (BTAA)和二乙醇胺 (DEA)合成了新型水溶性结构非对称超支化聚 (酰胺 酯 ) .聚合物的端基可通过BTAA与DEA的加料比来调节 .产物结构经FTIR ,1 H NMR和TGA进行了表征 .在一步法中 ,当BTAA于DEA的加料比大于 2 0 4时 ,反应体系不易凝胶 ,当加料比小于 2时 ,体系容易发生交联 .在准发散法中 ,不用中间分离过程 ,采用合成树状大分子发散法相同的加料方式 ,可得到大分子产物     

从核心天线到反应中心分子传能研究

利用飞秒时间分辨光谱技术研究了PSⅡ核心复合物内β-Car分子和Chla分子传递光能到反应中心的时间特性.实验测得,在CP47中的β-Car分子用了150 ps,Chla分子用了15 ps;在CP43中β-Car分子用了160 ps,Chla分子用了20 ps.利用超快光谱动力学实验曲线,理论计算出在核心天线中β-Car分子到Chla 662之间的能量传递速率为1.18×10¹²s^-1,β-Car分子到相邻β-Car分子之间按速率 1.14×10¹²s^-1传递能量.理论研究得出,在核心天线中β-Car分子接收到光能,以Dexter电子交换机制和Frster共振传能机制进行激发能传递,最后由Chla分子把能量传递到反应中心,在CP47中用了139 ps,在CP43中用了152 ps.理论研究表明,在核心天线中,Chla分子接收到光能之后,以随机转移方式将能量迅速传递到反应中心P680,在CP47中用了16.8 ps,在CP43中用了18 ps.理论研究与实验研究基本符合.