Computing optimal scalings by parametric network algorithms

Asymmetric scaling of a square matrixA 0 is a matrix of the formXAX ^–1 whereX is a nonnegative, nonsingular, diagonal matrix having the same dimension ofA. Anasymmetric scaling of a rectangular matrixB 0 is a matrix of the formXBY ^–1 whereX andY are nonnegative, nonsingular, diagonal matrices having appropriate dimensions. We consider two objectives in selecting a symmetric scaling of a given matrix. The first is to select a scalingA of a given matrixA such that the maximal absolute value of the elements ofA is lesser or equal that of any other corresponding scaling ofA. The second is to select a scalingB of a given matrixB such that the maximal absolute value of ratios of nonzero elements ofB is lesser or equal that of any other corresponding scaling ofB. We also consider the problem of finding an optimal asymmetric scaling under the maximal ratio criterion (the maximal element criterion is, of course, trivial in this case). We show that these problems can be converted to parametric network problems which can be solved by corresponding algorithms.This research was supported by NSF Grant ECS-83-10213.     

Reaction–Diffusion models: From particle systems to SDE’s

Let $V$ be any finite set and $p(?,?)$ a transition kernel on it. We present a construction of a family of Reaction–Diffusion models that converge after scaling to the solution to the $\left|V\right|$-dimensional SDE: $d{\zeta }_t=\left[{\Delta }_p{\zeta }_t?\beta ?{\zeta }_t^k\right]dt+\sqrt{\alpha ?{\zeta }_t^{?}}d{B}_t$with arbitrary initial condition ${\zeta }_0\in {\mathbb{R}}^V$. Here, ${\Delta }_p$ is the diffusion on $V$ corresponding to $p$, $\alpha$, $\beta$ are positive real numbers and $k$, $?$ are positive integers.     

Turbulence temperature spectra: Scaling theory

Grand canonical Monte Carlo, histogram reweighting and finite-size scaling methods are used to determine the phase transitions of bulk (three-dimensional) and confined (quasi-two-dimensional) neutral colloid–polymer systems. The colloids are modeled as hard spheres and the polymer molecules as hard chains, and the only attractive forces are effective ones induced by depletion effects. In contrast to the predictions of mean field and other approximate theories, the nature of the coexistence phases is found to not depend solely on the polymer-to-colloid size ratio, q, but on the colloid diameter, the polymer radius of gyration, and the polymer monomer size. The threshold values of q for the onset of liquid–liquid phase separation differ significantly from earlier predictions, and depend strongly on the dimensionality of space. Extrapolation to the “protein limit” of very small colloid and very long polymer indicates that immiscibility persists at this limit in three dimensions, while it does not always do so for confined systems.     

Quantum transport phenomena in disordered electron systems with spin–orbit coupling in two dimensions and below

Electron transport phenomena in disordered electron systems with spin–orbit coupling in two dimensions and below are studied numerically. The scaling hypothesis is checked by analyzing the scaling of the quasi-1D localization length. A logarithmic increase of the mean conductance is also confirmed. These support the theoretical prediction that the two-dimensional metal in systems with spin–orbit coupling has a perfect conductivity. Transport through a Sierpinski carpet is also reported.     

描述高能强相互作用的荷电粒子多重性分布

假设:强子-强子碰撞产生n个荷电粒子的概率是Pn=xPn(1)+(1-x),其中适当选择参数1,2,k和x,可成功地描述质心能量GeV处、全相空间的真实多重性分布.利用s=200GeV和900GeV处、质子-反质子的非单绕碰撞实验数据检验这个假设,证实了这假设很好地描述了实际情况.最后,讨论了这个假设的理论根据.     

高价盐对柱状聚电解质刷的效应

应用标度理论研究了外加的高价反离子对柱状聚电解质刷的影响.以外加盐浓度的不同,在单价盐情况下,强和弱聚电解质刷分别有2个和3个标度区域,而在高价盐情况下,柱状聚电解质刷的行为可分为4个区域.第一个区域,盐浓度很低,刷的行为不依赖于外加盐浓度.第二个区域,外加盐浓度对刷的行为开始有影响,刷的厚度随外加盐浓度增大而减小.第三个区域,强聚电解质刷厚度不依赖于外加盐浓度,而弱聚电解质刷厚度反而随外加盐浓度增大而升高.第四个区域,聚电解质刷厚度随外加盐浓度升高而降低,行为类似单价盐情形下的盐刷.这些区域都是链熵弹性与小离子渗透压平衡造成的,与单价和高价反离子在刷内的交换密切相关.新发现的区域尚待实验和计算机模拟的验证.     

模拟地热水中304不锈钢管和镀锌钢管的腐蚀与结垢

采用扫描电子显微镜(SEM)、能谱仪(EDS)、X射线衍射仪(XRD)和电化学测试的方法研究了304不锈钢管和镀锌钢管在模拟地热水(我国中部平原地热水的环境条件)中的腐蚀与结垢行为.结果表明,不锈钢管的结垢产物为"针"状物,其组成主要为CaCO3和MgCO3;镀锌钢管的腐蚀与结垢产物为"球"状物和"针"状物,其组成主要为Zn(OH)2、ZnO和CaCO3;腐蚀产物与结垢产物在晶核的形成生长过程中往往存在相互作用,同时它们在基材表面的分布对镀锌钢管的进一步腐蚀产生一定的抑制作用.     

疏水高分子单链在疏水表面上吸附和扩散过程的分子动力学模拟

采用分子动力学模拟方法研究不同聚合度(N)的聚乙烯(PE)单链在Si(111)表面上的吸附和扩散行为. 分别设置相对介电常数为1和78模拟无溶剂和不良溶剂环境. PE单链的平衡吸附构象均呈现为二维吸附构象, 但在这两种截然不同的环境中呈现不同的构象和动力学特征, 说明溶剂环境对于疏水高分子单链在疏水表面上的吸附和扩散起到了很大的作用. 吸附能与聚合度呈线性关系, 单位链长的平均吸附能是-0.38 kJ·mol^-1. 另外, 扩散系数(D)与聚合度之间的标度关系是D~N^-3/2.