Theoretical study on the structure and property relationship of the cationic conjugated polyelectrolytes

A theoretical study using density functional theory was performed to understand the structure/property relationship of the cationic conjugated polyelectrolytes, poly[9,9-bis-(6′-N,N,N-trimethylammonium) hexyl] fluorene-alt-4,7-(2,1,3-benzothiadiazole)] (PFBT-X, where X = Br). The torsion angle between the fluorene and benzothiadiazole units in the PFBT monomer was found to substantially affect the structural and electronic properties of the cationic PFBT monomer. The changes of geometrical parameter, HOMO and LUMO energy levels, and band gap, as well as the absorption maximum are discussed in terms of the torsion in the PFBT monomer structure. For comparison, its neutral analogue, the monomer of poly(9,9-di-n-octylfluorene-alt-benzothiadiazole) (F8BT) was also studied. The length of conjugation backbone was also examined.     

Study of Structures and Electronic Properties of Pdn–1Pb and Pdn （n≤8） Clusters

Geometric and electronic properties of Pdn–1Pb and Pdn (n≤8) clusters have been studied by using density functional theory with effective core potentials, focusing on the differences between mono- and bimetallic clusters. The average bond length of Pdn–1Pb (n≤8) bimetallic clusters is longer than that of pure palladium clusters except for n = 2 and 3. The most stable structure of Pdn–1Pb (n≤7) is the singlet where there is at least a Pd or Pb atom on its excited state. The energy gaps of Pd–Pb binary clusters are narrower than those of Pdn clusters, and then the chemical activity is strengthened when Pdn clusters are doped with Pb.     

内含式化合物X@Al12P12的结构与稳定性研究

采用B3LYP/6-31G*方法, 对内含式化合物X@Al₁₂P₁₂ (X＝Li^0/＋, Na^0/＋, K^0/＋, Be^0/2＋, Mg^0/2＋, Ca^0/2＋, H和He)的不同对称性构型进行计算, 讨论其最稳定构型的几何参数、布居分析、偶极矩、电离势、包含能、频率、HOMO-LUMO能隙和自旋密度．发现X@Al₁₂P₁₂化合物中, 客体X＝Na^0/＋, K^0/＋, Mg和He几乎处在笼的中心, Be和Ca^0/2＋处在中心附近0.033 nm的半径内, Li^0/＋, Be^2＋, Mg^2＋和H很大程度上偏离笼的中心位置. 大部分金属内含式化合物的C₃对称性构型稳定．Li^0/＋, Be^0/2＋, Mg^2＋, Ca^2＋和H与其它离子相比更易嵌入笼内形成稳定的内含式化合物.     

弯曲铝合金方管的轴压性能试验研究

为研究带初弯曲度铝合金方管的轴压承载力,完成了8个试件的轴压稳定性试验,并建立了与试验条件一致的有限元模型。通过对比试验和有限元分析结果验证了有限元模型的可靠性。结果表明,带有较大初弯曲度铝合金方管的破坏模式为整体弯曲失稳。最后,根据有限元分析结果拟合得到较大初弯曲度铝合金方管的整体稳定系数计算式,并将拟合计算式结果和数值分析结果及试验结果进行对比,验证了计算式的正确性。     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

Low Mach number limit of inviscid Hookean elastodynamics

The low Mach number limit of inviscid Hookean elastodynamic equations is rigorously proved in bounded domain, whole space and periodic domain, respectively. The uniform existence of smooth solutions and convergence results as the Mach number tends to zero are obtained in three different domains.     

Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Estimates of logarithmic Sobolev constat for finite-volume continuous spin systems

LetM be a compact, connected Riemannian manifold (with or without boundary); we study the logarithmic Sobolev constant for stochastic Ising models on . Let {} be a sequence of cubes inZ ^d ; we show that the logarithmic Sobolev constant for the finite systems onM ^A shrinks at most exponentially fast in ||^(d-1)/d (d2), which is sharp in order for the classical Ising models withM=[–1, 1]. Moreover, a geometrical lemma proved by L. E. Thomas is also improved.     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.