Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

OUH体系的结构和分析势能函数

采用密度泛涵B3LYP方法优化出了OUH分子的各种结构，确定了最稳定构型和离解能，以及它们的谐性力常数，并导出双原子分子UH,UO的Murrell-Sorbie势能函数及其光谱数据。采用多体项展式方法，导出OUH(X^4A')基态分子的分析势能函数，获得OUH(X^4A')体系的势能面，考察了这个势能函数的基本性质，正确地复现出OUH分子的平衡结构特征，结果表明：U+OH,O+UH,H+UO的反应均为无阈能的放热能反应。为进一步探讨OUH体系的反应动力学过程打下了基础。     

Structure and Phase Transitions of SnP2O7

SnP₂O₇ is a member of the ZrP₂O₇ family of materials, several of which show unusual thermal expansion behavior over certain temperature ranges and which show a number of displacive phase transitions on cooling from high temperature. Here we describe the structural properties of SnP₂O₇ from 100 to 1243 K as determined by X-ray and neutron powder diffraction. These studies reveal that SnP₂O₇ shows two phase transitions in this temperature range. At room temperature the material has a pseudo-cubic 3×3×3× superstructure. Electron diffraction studies show that the symmetry of this structure is P2₁3 or lower. On warming to ∼560 K it undergoes a phase transition to a structure in which the subcell reflections show a triclinic distortion; above 830 K the subcell reflections show a rhombohedral distortion. Significant hysteresis in cell parameters is observed between heating and cooling. The structure of SnP₂O₇ is discussed with references to other members of the AM₂O₇ family of materials.     

The Dowd-Beckwith ring expansion: a theoretical study

UB3LYP/6-311++G(d,p) and ROMP2/6-311++G(d,p)//UB3LYP/6-311++G(d,p) calculations including the effect of benzene solvent through the PCM-UAHF method render a concerted mechanism without fragmentation as the most favourable one for the Dowd-Beckwith radical ring expansion of the bromomethyl adduct of methyl cyclopentanone-2-carboxylate to yield methyl cyclohexanone-3-carboxylate. The corresponding concerted TS is a bicyclic alcoxy radical.     

Palladium-catalyzed ring expansion reaction of 1-alkynylcyclobutanols with aryl iodides: an efficient route to 2-disubstituted methylenecyclopentanones

The reaction of 1-alkynylcyclobutanols with aryl iodides in the presence of Pd(OAc)₂ and Et₃N in acetonitrile at 80°C for 24 h gives 2-disubstituted methylenecyclopentan-1-ones in modest to good yields. The tandem insertion-ring expansion process proceeds via the formation of an alkynyl π-complex, followed by migration of a carbon-carbon bond of the tert-alkanol to form the cyclopentanones stereoselectively.     

Stereoselective synthesis of the octahydroisobenzofuran skeleton of the eunicellins

A de novo asymmetric synthesis of the octahydroisobenzofuran skeleton contained within the eunicellin family of natural products has been completed. The key transformations involve the convergent assembly of a tetrasubstituted tetrahydrofuran by condensation of a functionalised allylsiloxane with an aldehyde; controlled epimerisation of a C4 aldehyde by intramolecular trapping; installation of the isopropyl substituent by stereoselective Michael addition to a 5,5-bicyclic enone; and ring expansion of the 5,5-system to the target structure by radical-mediated cyclopropane fragmentation.     

二硫化锡基钠离子电池负极材料的研究进展

二硫化锡由于其理论容量高、氧化还原电位合适，而成为钠离子电池负极材料的研究热点之一。从纯二硫化锡、二硫化锡/碳复合物和二硫化锡/石墨烯复合物等3个方面对二硫化锡负极材料在近5年的发展进行了概述。     

Role of resonances in building cross sections: Comparison between the Mittag–Leffler and the T‐matrix Green function expansion approaches

Peaks in collision cross sections are often interpreted as resonances. The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S‐matrix and the associated Green function. The performance of the Mittag–Leffler expansion and T‐matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s‐wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag–Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S‐matrix residue. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007