CALCULATING THE MOLECULAR INTERNAL ROTATING STERIC FACTOR OF POLYMERS BY THE RADIATION CROSSLINKING METHOD

In this paper, calculating the molecular internal rotating steric factor of polymers by the radiation crosslinking method is studied and a relationship between the molecular internal rotating steric factor (σ) and crosslinking parameter βis established~([1]) by taking account of the effect of polymer chain flexibility on βvalue, σvalue of polymer obtained by this method is in agreement with that given with other method.     

Struktur‐ und magnetochemische Untersuchungen an KCuGaF6

Structural and Magnetochemical Studies on KCuGaF₆ The crystal structure of KCuGaF₆ was determined on the base of X‐ray single crystal data (wR₂ = 0.084 for 2476 independent reflections). The compound crystallizes with a = 728.56(4), b = 989.51(6), c = 676.27(3) pm, β = 93.120(5)°, Z = 4 in space group P2₁/c of the pyrochlore related KCuCrF₆ type. The octahedral coordinations [GaF₆] and [CuF₆] are slightly resp. strongly distorted (mean values Ga‐F: 188.2 pm resp. Cu‐F: 188.2/200.1/227.6 pm). The longest distances Ga‐F and the shortest ones Cu‐F are found within octahedral chains of these two kinds of atoms, running along [100] and [001], resp., and being mutually bridged as well (M‐F‐M in between 114 and 145°). The magnetic mole susceptibilities measured at powders and at a single crystal follow the isotropic Heisenberg model for S = ¹/₂, if effects of chain disrupture are considered in the form of some paramagnetic portion. No indication of threedimensional magnetic order is observed down to T = 2 K and low magnetic fields H < 100 G. KCuGaF₆ (J/k = —71 K for the powder) is distinguished this way from the chain structure compounds KCuAlF₆ und Na₂CuScF₇ (J/k = —76 resp. —59 K) which were also magnetically studied and yield similar antiferromagnetic exchange constants J/k.     

流体熵相关性质的Monte Carlo模拟新方法

提出了用于计算实际体系熵相关性质的Monte Carlo多级取样分子模拟方法. 应用这一方法, 对硬球流体的化学势及Helmholtz自由能进行了估算, 得到了满意的结果. 计算化学势时, 不存在通常试验粒子方法所遇到的高密度问题. 该方法特别适合规律性的系统研究, 较之普通模拟方法要有效得多. 模拟得到的硬球体系无限稀释组份的超额化学势与对比直径的关系, 在相变区域为一条双凹曲线; 无论是在相变区还是在单相区, Carnahan-Starling公式对这一关系的描述均有较大偏差.     

氢气对氯硅烷功能化非共轭α,ω-双烯烃和丙烯共聚物链结构的影响

基于Ziegler-Natta催化剂的氯硅烷功能化非共轭α,ω-双烯烃与丙烯共聚,在水的引发下脱水缩合可有效地形成长支链结构的聚丙烯树脂.而氢气常作为丙烯聚合中的链转移剂,调控聚丙烯的分子量,基于此,研究了氢气对氯硅烷功能化非共轭α,ω-双烯烃与丙烯共聚物链结构的影响.核磁共振氢谱(~1H-NMR)测试结果表明,氢气抑制了氯硅烷功能化非共轭α,ω-双烯烃的插入,随着氢气用量的增加,共聚物分子链中端基乙烯基含量由0.12 mol%降低到0.05 mol%.熔体流变行为测试结果显示,聚合物熔体的储能模量、损耗模量和零剪切黏度均随着氢气用量增加而降低,这主要是由于相对分子质量减小和长支链密度的减少.     

有限型的首次返回例外集的测度和维数北大核心CSCD

设M=(m_(ij))是一个b×b阶矩阵且m_(ij)∈{0,1},∑_(M)是矩阵M=(m_(ij))诱导产生的有限型,σ是其上左推移算子.本文主要研究的是有限型动力系统(∑_(M),σ)上的首次返回速度问题.令τ_(k)(x)是点x∈∑_(M)首次返回到包含x的k阶柱集时间,且E_(α,β)={x∈∑_(M):lim inf_(k→∞)(logτ_(k)(x))/k=α,lim sup_(k→∞)(logτ_(k)(x))/k=β}.我们证明了:当M是不可约矩阵时,对任意0≤α≤β≤+∞,集合E_(α,β)的Markov测度要么等于0要么等于1并且具有满的Hausdorff维数.     

Set controllability of Markov jump switching Boolean control networks and its applications

In this article, a novel method is proposed for investigating the set controllability of Markov jump switching Boolean control networks (MJSBCNs). Specifically, the switching signal is described as a discrete-time homogeneous Markov chain. By resorting to the expectation and switching indicator function, an expectation system is constructed. Based on the expectation system, a novel verifiable condition is established for solving the set reachability of MJSBCNs. With the newly obtained results on set reachability, a necessary and sufficient condition is further derived for the set controllability of MJSBCNs. The obtained results are applied to Boolean control networks with Markov jump time delays. Examples are demonstrated to justify the theoretical results.     

The nearest neighbor random walk on subspaces of a vector space and rate of convergence

LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV _n overGF(q). A metric may be defined onX by letting

The ground-state energy of the ±J sping glass. A comparison of various biologically motivated algorithms

We compare various evlutionary strategies to determine the ground-state energy of the ±J spin glass. We show that the choice of different evolution laws is less important than a suitable treatment of the free spins of the system At least one combination of these strategies does not give the correct results, but the ground states of the other different strategies coincide. Therefore we are able to extrapolate the infinit-size ground-state energy for the square lattice to –1.401±0.0015 and for the simple cubic lattice to –1.786±0.004.     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Phase separation of symmetrical polymer mixtures in thin-film geometry

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN _A=N _B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT _c (D) of unmixing are located by finite-size scaling methods, and it is shown that , wherev ₃0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as , where ₂ is the critical exponent of the two-dimensional Ising universality class ( ₂=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT _c (D), one observes in practice effective exponents which gradually cross over from ₂ to ₃ with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally.