Influence of the Comonomer on the Dissociation of Some Alternating Maleic Acid Copolymers

Five alternating copolymers of maleic acid with N-vinylpyrrolidone, vinyl acetate, styrene, 2-vinylnaphthalene, and vinyl cyclohexane were used in order to study the influence of the comonomer on the polyelectrolyte behavior. The dissociation of the maleic acid copolymers was investigated by electrochemical methods in pure water and in the presence of supporting electrolytes. The conformational modifications during the dissociation were directly investigated by viscosimetry and fluorescence probing. The shape of the potentiometric and conductometric titration curves was influenced by the comonomer structure. In salt-free solution, only the first dissociation step was observed. The addition of univalent counterions permitted the evidencing of the second ionization step only for the copolymers with hydrophilic comonomers, but the addition of divalent counterions permitted the evidencing of the second ionization step for all five copolymers. The apparent dissociation constants increase with the increase of the comonomer hydrophobicity. A conformational transition was evidenced especially in the case of the maleic acid-2-vinylnaphthalene copolymer.     

Spectral methods for the simulation of incompressible flows in spherical shells

A spatial discretization of the incompressible Navier–Stokes equation is presented in which the velocity is decomposed using poloidal and toroidal scalars whose spatial dependence is given in terms of spherical harmonics and Chebychev polynomials. The radial resolution needs to be large enough at any given angular resolution in order to avoid instability in the simulation of rotating flows. Several semi‐implicit time steps are discussed. The most accurate scheme is an integrating factor technique. Copyright © 1999 John Wiley & Sons, Ltd.     

Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics

Numerical experiments are performed on a 36,000-atom protein–DNA–water simulation to ascertain the effectiveness of two devices for reducing the time spent computing long-range electrostatics interactions. It is shown for Verlet-I/r-RESPA multiple time stepping, which is based on approximating long-range forces as widely separated impulses, that a long time step of 5 fs results in a dramatic energy drift and that this is reduced by using an even larger long time step. It is also shown that the use of as many as six terms in a fast multipole algorithm approximation to long-range electrostatics still fails to prevent significant energy drift even though four digits of accuracy is obtained. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1785–1791, 1997     

Distinct Growth Phenomena Observed on Zinc Cadmium Thiocyanate Crystals by Atomic Force Microscopy

Atomic force microscopy is used to investigate the surface morphology of the prismatic (100) face of ZCTC crystal grown at 30°C at a supersaturation of 0.16. This surface is distinctly formed by periodic “macrosteps” that advance along different directions and join with each other leading to the interlaced growth layers with an inclination of about 137°. These two “macrostep” trains well correspond to the pyramidal faces of (0 ) and (01 ) in orientation, therefore they probably propagate from the edges of these faces. The “macrosteps” are practically formed by highly dense steps at the front with regular elementary steps in between. The alternation of “macrosteps” and elementary steps vividly reflects Chernov's “kinematic waves of steps” theory (Chernov , (1984)) on a nanometer scale. Wide indentations and long clefts are generated at the “macrosteps”. The former is generated by twodimensional nucleation growth at a relatively faster growth rate than that of the underlying layer. The latter is probably caused by step trains generated by individual growth sources that have not merged.     

Escape of a Uniform Random Walk from an Interval

We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [−a,a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a function of the starting point. As a decreases, first-passage properties approach those of continuum diffusion, but non-diffusive effects remain because of residual discreteness effects. PACS: 02.50.C2, 05.40.Fb     

Capillarity-Induced Surface Morphologies

Surface energetics is reviewed including expressions for the chemical potential of a curved surface element and the Legendre transform relation between the projected surface free energy as a function of orientation and the Wulff equilibrium shape. A well known equation is derived describing surface evolution by surface diffusion, assuming local equilibrium. Solutions are reviewed including a decaying sinusoid and a developing thermal groove. Breakdown of local equilibrium is considered. The structure, energetics and dynamics of steps on a vicinal surface are discussed. Facet sizes on the Wulff shape and the surface profile at the edge of a facet are related to the step self and interaction free energies respectively. Fourier analysis of step fluctuations is described, revealing the underlying transport processes. Analysis of the decay of a sinusoidal profile on a vicinal surface in terms of step behavior is given. Finally, examples are reviewed of surface evolution below the roughening temperature T _R in which case facets move by the lateral spreading of steps. Results differ greatly from those of the continuum theory applicable above T _R.     

NUMERICAL METHOD FOR THREE-DIMENSIONAL NONLINEAR CONVECTION-DOMINATED PROBLEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.     

Some Properties of Nonstar Steps in Addition Chains and New Cases Where the Scholz Conjecture Is True

Let ℓ(n) be the smallest possible length of addition chains for a positive integer n. Then Scholz conjectured that ℓ(2ⁿ − 1) ≤ n + ℓ(n) − 1, which still remains open. It is known that the Scholz conjecture is true when ν(n) ≤ 4, where ν(n) is the number of 1's in the binary representation of n. In this paper, we give some properties of nonstar steps in addition chains and prove that the Scholz conjecture is true for infinitely many new integers including the case where ν(n) = 5.     

四段式有限元法分析热耦合的流体-固体相互作用问题

给出了一种流(体)-热-结构综合的分析方法,固体中的热传导耦合了粘性流体中的热对流,因而在固体中产生热应力.应用四段式有限元法和流线逆风Petrov-Galerkin法分析热粘性流动,应用Galerkin法分析固体中的热传导和热应力.应用二阶半隐式Crank-Nicolson格式对时间积分,提高了非线性方程线性化后的计算效率.为了简化所有有限元公式,采用3节点的三角形单元,对所有的变量:流体的速度分量、压力、温度和固体的位移,使用同阶次的插值函数.这样做的主要优点是,使流体-固体介面处的热传导连接成一体.数个测试问题的结果表明,这种有限元法是有效的,且能加深对流(体)-热-结构相互作用现象的理解.