Weighted enumeration of spanning subgraphs in locally tree‐like graphs

Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}$. To the best of our knowledge, this is the first time that correlation inequalities and unimodularity are combined together to yield a general proof of uniqueness of Gibbs measures on infinite trees. We believe that a similar argument is applicable to other Gibbs measures than those over spanning subgraphs considered here. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

球面角锥棱镜非稳腔钕玻璃激光器

为了将虚共焦非稳腔输出光束质量高和角锥棱镜谐振腔具有免调试的优点结合到一起,提出了用球面角锥棱镜构成虚共焦非稳腔的方案。利用已有虚共焦非稳腔钕玻璃激光器,设计加工了一球面角锥棱镜非稳腔钕玻璃激光器。模拟计算了两谐振腔输出光束的模式分布,然后对两钕玻璃激光器进行了实验对比研究。结果表明:实验得到的模式分布与模拟计算结果相吻合,球面角锥棱镜非稳腔钕玻璃激光器与虚共焦非稳腔钕玻璃激光器分别获得了最大2176.9J和2340.6J的能量输出,二者的电光效率与束散基本相同,分别为4.3%,0.30mrad和4.6%,0.26mrad。     

半导体超常媒质矩形谐振腔(英文)

设计并研究了两个有不同各向异性参数的半导体超常媒质矩形谐振腔,其中填充了部分右手半导体超常媒质和部分左手半导体超常媒质。通过作图法研究了充满非色散的右手半导体超常媒质和色散的左手半导体超常媒质的谐振腔中谐振模式的解。结果显示,谐振腔的谐振模式取决于半导体超常媒质的色散关系。讨论了每种谐振腔中包含的六种情况,分别表示两个区域的传播常数为实数和虚数的不同的组合,并且揭示了构建具有无相差特性的谐振腔的几何参数要求。     

A novel scheme of hybrid entanglement swapping and teleportation using cavity QED in the small and large detuning regimes and quasi-Bell state measurement method

We outline a scheme for entanglement swapping based on cavity QED as well as quasi-Bell state measurement(quasiBSM) methods. The atom–field interaction in the cavity QED method is performed in small and large detuning regimes.We assume two atoms are initially entangled together and, distinctly two cavities are prepared in an entangled coherent–coherent state. In this scheme, we want to transform entanglement to the atom-field system. It is observed that, the fidelities of the swapped entangled state in the quasi-BSM method can be compatible with those obtained in the small and large detuning regimes in the cavity QED method(the condition of this compatibility will be discussed). In addition, in the large detuning regime, the swapped entangled state is obtained by detecting and quasi-BSM approaches. In the continuation,by making use of the atom–field entangled state obtained in both approaches in a large detuning regime, we show that the atomic as well as field states teleportation with complete fidelity can be achieved.     

Study of a magnetic alloy-loaded cavity for compact synchrotrons

Magnetic alloy(MA)-loaded cavities have been widely used in compact proton and heavy-ion synchrotrons,and the MA core is the key issue in their development.Chinese-produced MA has never yet been adopted as core material for an MA-loaded cavity.To use Chinese-produced MA as the core material,it is necessary to study its properties,and compare with MA material produced elsewhere.In this paper,the properties of several MA cores made of Chinese-produced material are measured.Based on the measured results,a schematic design is produced for a cavity which could obtain 1 kV gap voltage with less than 1.5 kW power dissipation in the frequency range of0.5-7 MHz.The difference between resonant frequencies obtained from simulation and analytical results is less than10%.     

波瓣波导谐振腔太赫兹回旋管的研究

以电子回旋脉塞非线性理论为基础, 结合三维电磁仿真软件, 通过导入高频场数值解替代理论解析的方法, 对波瓣波导谐振腔高次谐波太赫兹回旋管进行了理论和模拟研究. 给出了该类回旋管的起振电流、耦合系数以及注波互作用效率等重要参数, 并在此基础上设计了一只工作频率为0.4 THz, 工作模式TE₃₃模三次谐波波瓣波导谐振腔回旋管, 其电子注参数为1.0 A, 40.5 kV, 横纵速度比1.5,互作用区引导磁场为5.09 T, 输出功率达到3.3 kW.     

Point defect states of a hollow cylinder in two-dimensional phononic crystal

Point defect states in two-dimensional phononic crystal of a hollow mercury cylinder in a water host are studied.An improved plane expansion method combined with the supercell technique is used to calculate the band gaps and the pressure distribution at the defect position.The sonic pressure of defect modes shows that the waves are localized at or near the defect.As the filing fraction increases,more defect modes appear in the band gaps.     

Methylazacalixpyridines: remarkable bridging nitrogen-tuned conformations and cavities with unique recognition properties

Methylazacalix[n]pyridines (n = 4, 8) and methylazacalix[m]arene[n]pyridines (m = n = 2, 4) have been synthesized by a convenient fragment coupling approach starting from 2,6-dibromopyridine, 2,6-diaminopyridine, and benzene-1,3-diamine. Thanks to the intrinsic electronic nature of nitrogen, which can adopt mainly sp(2) hybridization, allowing it variously to conjugate, partially conjugate, or not conjugate with the adjacent one or two pyridine rings, the resulting nitrogen-bridged calixpyridine derivatives act as a unique class of macrocyclic host molecules with intriguing conformational structures offering fine-tunable cavities and versatile recognition properties. Whilst in solution it is fluxional, in the solid state methylazacalix[4]pyridine adopts a 1,3-alternate conformation with a C(2v) symmetry in which every two bridging nitrogen atoms conjugate with one pyridine ring. After protonation, the methylazacalix[4]pyridinium species has a different conjugation system of its four bridging nitrogen atoms, yielding the similar twisted 1,3-alternate conformations with an approximate S(4) symmetry. The cavity of each protonated methylazacalix[4]pyridine, however, varies finely to accommodate guest species of different size and geometry, such as planar DMF or HO(2)CCO(2) (-) ion, a twisted HO(2)CCO(2) (-) ion, and a tetrahedral ClO(4) (-) ion. As giant macrocyclic hosts, both methylazacalix[8]pyridine and methylazacalix[4]arene[4]pyridine interact efficiently with fullerenes C(60) and C(70) through van der Waals forces. Their ease of preparation, versatile conformational structures, and recognition properties make these multinitrogen-containing calixarenes or cyclophanes unique and powerful macrocyclic hosts in supramolecular chemistry.     

Validation of an empirical RNA-ligand scoring function for fast flexible docking using RiboDock®

We report the design and validation of a fast empirical function for scoring RNA-ligand interactions, and describe its implementation within RiboDock, a virtual screening system for automated flexible docking. Building on well-known protein-ligand scoring function foundations, features were added to describe the interactions of common RNA-binding functional groups that were not handled adequately by conventional terms, to disfavour non-complementary polar contacts, and to control non-specific charged interactions. The results of validation experiments against known structures of RNA-ligand complexes compare favourably with previously reported methods. Binding modes were well predicted in most cases and good discrimination was achieved between native and non-native ligands for each binding site, and between native and non-native binding sites for each ligand. Further evidence of the ability of the method to identify true RNA binders is provided by compound selection ('enrichment factor') experiments based around a series of HIV-1 TAR RNA-binding ligands. Significant enrichment in true binders was achieved amongst high scoring docking hits, even when selection was from a library of structurally related, positively charged molecules. Coupled with a semi-automated cavity detection algorithm for identification of putative ligand binding sites, also described here, the method is suitable for the screening of very large databases of molecules against RNA and RNA-protein interfaces, such as those presented by the bacterial ribosome.     

Fluorescence sensing of Cu within a pseudo 18-crown-6 cavity

We report herein a pseudo-crown based fluorescent receptor (1) for the selective detection of Cu²⁺ cation. Receptor 1 can detect Cu²⁺ even in 5 μM level in acetonitrile-water (9:1 v/v). Compound 1 is very effective for the detection of Cu²⁺ amongst the series of metal ions studied (Li⁺, Na⁺, K⁺, Ca²⁺, Mg²⁺, Ba²⁺, Pb²⁺, Fe³⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, Hg²⁺ and Mn²⁺).