The coherent scattering function of the reptation model: Simulations compared to theory

We present results of Monte Carlo simulations measuring the coherent structure function of a chain moving through an ordered lattice of fixed topological obstacles. Our computer experiments use chains up to 320 beads and cover a large range of wave vectors and a time range exceeding the reptation time. For additional information we also measured the coherent structure function of internal pieces of the chain. We compare our results i) to the predictions of the primitive chain model, ii) to an approximate form resulting from Rouse motion in a coiled tube, and iii) to our recent evaluation of the full reptation model. i) The primitive chain model can fit the data for times , where T ₂ is the Rouse time of the chain. Besides some phenomenological amplitude factor this fit involves the reptation time T ₃ as a second fit parameter. For the chain lengths measured, the asymptotic behavior is not attained. ii) The model of Rouse motion in a tube, which we have criticized before on theoretical grounds, is shown to fail also on the purely phenomenological level. iii) Our evaluation of the full reptation model yields an excellent fit to the data for both total chains and internal pieces and for all wave vectors and all times, provided specific micro-structure effects of the MC dynamics are negligible. Such micro-structure effects show up for wave vectors of the order of the inverse segment size and enforce the introduction of some phenomenological, wave-vector-dependent prefactor. For the dynamics of the total chain our data analysis based on the full reptation model shows the importance of tube length fluctuations. Universal (Rouse-type) internal relaxation, however, is unimportant. It can be observed only in the form of the diffusive motion of a short central subchain in the tube. Finally, we present a fit formula which in a large range of wave vectors and chain lengths reproduces the numerical results of our theory for the scattering from the total chain.Received: 9 July 2003, Published online: 11 November 2003PACS: 83.10.Kn Reptation and tube theories - 82.35.Lr Physical properties of polymers - 83.10.Rs Computer simulation of molecular and particle dynamics     

Factors influencing the ultrasonic separation of oil-in-water emulsions

Ultrasound may have inherent shortcomings that preclude its ability to coagulate grease from wastewater, yet these may be overcome by the simultaneous application of electrolysis. We studied the role of pH, conductivity, temperature, ultrasound intensity and duration, and electrolysis voltage, current, and duration, in the study treatment. Conductivity was found to be the most significant factor, however interactions among the eight study variables are likely more important than individual factors. The proposed process was capable of removing up to 100% of grease from the studied wastewater.     

Astigmatic coherence sensor for digital imaging

We present a novel sensor that measures the entire spatial coherence function within an aperture by use of a variable astigmatic lens. This sensor permits digital capture and processing of partially coherent fields. We demonstrate the sensor by sampling and computing the coherent modes of a three-dimensional incoherent source.     

Elementary derivation of the universal attractive coulomb term in the interquark potential

We provide a simple derivation of the universal 1/R term in the interquark potential at large distances. We discuss a physical analogy which makes the existence of such a universal term easier to understand. We go on to briefly treat the behavior of the Wilson loop in other regimes, to further illustrate this analogy.     

A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures

A theory of generalized statical bases is developed for usein the flexibility methods as applied to skeletal structuralproblems. It is shown that any maximal linearly independentset of cycles of the integral cycle group of a linear graphmodel of the structure may be used in the formation of a staticalbasis. Such a set of simple cycles is found by embedding thisgraph into a two-dimensional polyhedron. Cell complexes areformed so that the simple cycles bounding the 2-cells correspondto substructures on which a statical basis may be constructed.Two methods are given for the construction of the embeddings.In one a collapsible complex is formed from a union of a setof disks; while in the other the embedding is into an orientablemanifold which is modified to form an admissible complex.     

额尔齐斯河（新疆段）水质评价

对额尔齐斯河1993～1999年的水质污染数据用因子分析的方法进行分析,得到评价额尔齐斯河水质污染的有机污染因子,综合污染因子和金属污染因子,并以此对额尔齐斯河水质污染情况作出较客观的评价。     

向量随机测度关于白噪声的积分的收敛性

本文主要讨论s.i.s.向量随机测度关于白噪声的积分的收敛性,我们得到了如下结果设X是具type2的Banach空间,{Fn}∞n=0是一列被μ所控制的X值s.i.s随机测度,对任意的E∈∑,E[Fn(E)]=0,E‖Fn(E)‖2＜+∞,{Fn(E)}∞n=0是一致W弱可积,且{Fn}∞n=1弱几乎收敛到F0,则(1)对每个n≥0∫FndW是s.i.s向量随机测度;(2)∫FndWwp→∫F0dW.