密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

Demixing of severely overlapped H NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A3 spins in a weakly aligning medium

The increasing scientific and industrial interest towards metabonomics takes advantage from the high qualitative and quantitative information level of nuclear magnetic resonance (NMR) spectroscopy. However, several chemical and physical factors can affect the absolute and the relative position of an NMR signal and it is not always possible or desirable to eliminate these effects a priori. To remove misalignment of NMR signals a posteriori, several algorithms have been proposed in the literature. The icoshift program presented here is an open source and highly efficient program designed for solving signal alignment problems in metabonomic NMR data analysis. The icoshift algorithm is based on correlation shifting of spectral intervals and employs an FFT engine that aligns all spectra simultaneously. The algorithm is demonstrated to be faster than similar methods found in the literature making full-resolution alignment of large datasets feasible and thus avoiding down-sampling steps such as binning. The algorithm uses missing values as a filling alternative in order to avoid spectral artifacts at the segment boundaries. The algorithm is made open source and the Matlab code including documentation can be downloaded from www.models.life.ku.dk.     

Connectivity of a general class of inhomogeneous random digraphs

We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models includes as special cases the directed versions of the Erd?s‐Rényi model, graphs with given expected degrees, the generalized random graph, and the Poissonian random graph. We establish a phase transition for the existence of a giant strongly connected component and provide some other basic properties, including the limiting joint distribution of the degrees and the mean number of arcs. In particular, we show that by choosing the joint distribution of the vertex attributes according to a multivariate regularly varying distribution, one can obtain scale‐free graphs with arbitrary in‐degree/out‐degree dependence.     

Integrable Rosochatius Deformations for an Integrable Couplings of CKdV Equation Hierarchy

We propose a method to construct the integrable Rosochatius deformations for an integrable couplings equations hierarchy. As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy with self-consistent sources and its Lax representation are presented.     

Specific Heat of a Two-Layer Magnetic Superlattice

The specific heats of both a two-layer ferromagnetic superlattice and a two-layer ferrimagnetic one are studied. It is found that the spin quantum numbers, the interlayer and intralayer exchange couplings, the anisotropy, the applied magnetic field, and the temperature all affect the specific heat of these superlattices. For both the ferromagnetic and ferrimagnetic superlattices, the specific heat decreases with increasing the spin quantum number, the absolute value of interlayer exchange coupling, intralayer exchange coupling, and anisotropy, while it increases with increasing temperature at low temperatures. When an applied magnetic field is enhanced, the specific heat decreases in the twolayer ferromagnetic superlattice, while it is almost unchanged in the two-layer ferrimagnetic superlattice at low field range at low temperatures.     

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.     

Synthesis of naturally occurring bioactive butyrolactones: maculalactones A-C and nostoclide I

Starting from citraconic anhydride (13), a simple multistep (9-10 steps) synthesis of naturally occurring butyrolactones maculalactone A (3), maculalactone B (1), maculalactone C (2) and nostoclide I (4) have been described with good overall yields via dibenzylmaleic anhydride (20) and benzylisopropylmaleic anhydride (27). The two anhydrides 20 and 27 were prepared by S_N2′ coupling reactions of appropriate Grignard reagents with dimethyl bromomethylfumarate (14), LiOH-induced hydrolysis of esters to acids, bromination of carbon-carbon double bond, in situ dehydration followed by dehydrobromination and chemoselective allylic substitution of bromoatom in disubstituted anhydrides 19 and 26 with appropriate Grignard reagents. The NaBH₄ reduction of these anhydrides 20 and 27 furnished the desired lactones 21 and 29, respectively. The lactone 21 on Knoevenagel condensation with benzaldehyde, furnished maculalactone B (1), which on isomerization gave maculalactone C (2). Selective catalytic hydrogenation of 1 gave maculalactone A (3). The conversion of lactone 29 to nostoclide I (4) is known.     

Organosulfur compounds: electrophilic reagents in transition-metal-catalyzed carbon-carbon bond-forming reactions

Transition-metal-catalyzed carbon-carbon bond-forming reactions are among the most powerful methods in organic synthesis and play a crucial role in modern materials science and medicinal chemistry. Recent developments in the area of ligands and additives permit the cross-coupling of a large variety of reactants, including inexpensive and readily available sulfonyl chlorides. Their desulfitative carbon-carbon cross-coupling reactions (Negishi, Stille, carbonylative Stille, Suzuki-Miyaura, and Sonogashira-Hagihara-type cross-couplings and Mizoroki-Heck-type arylations) are reviewed together with carbon-carbon cross-coupling reactions with other organosulfur compounds as electrophilic reagents.     

A 1H NMR and theoretical investigation of the conformations of some monosubstituted cyclobutanes

The complete analysis of the complex (1)H NMR spectra of some monosubstituted cyclobutanes was achieved to give all the (1)H chemical shifts and (n)J(HH) (n = 2, 3 and 4) coupling constants in these molecules. The substituent chemical shifts of the substituents in the cyclobutane ring differ significantly from those in acyclic systems. For example, the OH and the NH(2) groups in cyclobutanol and cyclobutylamine produce a large shielding of the hydrogens of the opposite CH(2) group of the ring compared with little effect on the comparable methylene protons of butane. These effects and the other (1)H shifts in the cyclobutanes were modelled successfully in the CHARGE program. The RMS error (calculated vs observed shifts) for the 34 (1)H shifts recorded was 0.053 ppm. The conformational equilibrium in these compounds between the axial and the equatorial conformers was obtained by comparing the observed and the calculated (4)J(HH) couplings. These couplings in cyclobutanes, in contrast to the corresponding (3)J(HH) couplings, show a pronounced orientation dependence; (4)J(eq-eq) is ca 5 Hz and (4)J(ax-ax) ca 0 Hz. The couplings in the individual conformers were calculated at the B3LYP/EPR-III level. The conformer energy differences ΔG(ax-eq) vary from 1.1 kcal mol(-1) for OH to 0.2 kcal mol(-1) for the CH(2)OH substituent. The values of the conformer energy differences are compared with the previous IR data and the corresponding theoretical values from molecular mechanics (MM) and DFT theory. Generally, good agreement is observed although both the MM and the DFT calculations deviate significantly from the observed values for some substituents.     

Application of Liquid Crystalline NMR Solvents to a Mixture of Ketones

A series of dilute liquid crystalline solvents are used to study the effect of slight anisotropy caused by partial alignment on chemical shift and residual dipolar coupling (RDC) in small molecules. The residual dipolar couplings between protons in solutes are found to be almost independent of the local environment. It is also found that the chemical shift does not change over the concentration range observed. A linear relationship between residual dipolar coupling and liquid crystal concentration is observed at relatively low concentrations, but is severely violated at high concentrations.