Dynamic surface elasticity of polymer solutions

The surfaces of surfactant solutions exhibit viscoelastic dilational behavior which may be investigated by modern optical and mechanical methods. The present study focuses on the dynamic dilational properties of the polymer solution — gas interface. Linear flexible polymer chains at the surface are considered as consisting of trains, lying on the surface, and loops and tails that protrude into the liquid. The Rouse model is used to describe the inner dynamics of the trains, whereas their motion relative to their neighbors on the surface can be described with the help of the reptation conception. An expression for the complex dynamic dilational surface elasticity has been derived. Although, in general, the relaxation of the surface tension is characterized by an infinite series of relaxation times, it is shown that for many systems the dynamics of the surface layer can be described approximately by only two main relaxation times. The dispersion equation, which was obtained earlier for solutions of conventional surfactants, is shown to be fulfilled for polymer solutions also.     

苯乙烯－马来酸酐共聚物单分子膜的静、动态性质

对不同分子量的苯乙烯－马来酸酐共聚物（PSM）单分子膜的π－A等温线、微 分曲线进行了研究，讨论了PSM单分子膜成膜过程及分子量对膜相变的影响，并用 动态膜障振动法测定了PSM单分子膜的动态弹性，结果表明，分子链的相互作用（ 如卷曲和缠结）在膜的形成中起着重要的作用，并影响膜的静、动态性质，单分子 膜的动态弹性曲线有双峰，且前者比后者小，随分子量增大，膜的凝聚性、刚性和 稳定性都增强，动态弹性都增大；且分子链的相互作用对PSM单分子性质影响增大 ，压缩过程中单分子膜的相变更明显。     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

Surfactant in the gaseous phase II. Influence on stability of foams and thin liquid films

The influence of the vapors ofn-amyl orn-decyl alcohol on the stability of single thin liquid films, single bubbles, and foam columns was determined. It was found that the presence of surfactant vapors lowered the stability of foams and single foam films. The mechanism of the destabilizing action of the surfactant vapors on wet, dynamic foams under dynamic conditions is discussed. It is shown that the destabilizing action of the surfactant vapors is a further indication that surface elasticity forces are the main factor determining stability of wet, dynamic foams.     

Quantum theory for plasmon-assisted local field enhancement

We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.     

线弹性问题的一个四面体元分析

构造了一个新的locking-free非协调四面体元,研究了单元对三维纯位移弹性问题的一致收敛性,得到了最优的误差估计结果.     

Surface effects in the deformation of an anisotropic elastic material with nano-sized elliptical hole

We examine the effect of surface energy on an anisotropic elastic material weakened by an elliptical hole. A closed-form, full-field solution is derived using the standard Stroh formalism. In particular, explicit expressions for the hoop stress, normal, in-plane tangential and out-of-plane displacement components along the edge of the hole are obtained. These expressions clearly demonstrate the effect of elastic anisotropy of the bulk material on the corresponding field variables. When the material becomes isotropic, the hoop stress agrees with the well-known result in the literature while both the in-plane tangential and out-of-plane displacements vanish and the normal displacement is constant along the entire boundary of the elliptical hole.     

Harnack's inequality for parabolic nonlocal equations

The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive.     

Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with Lp data and applications to nonlinear elasticity

We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$. More precisely, for any $1<q<(p+1)/2$ we construct $W^{1,q}$-bi-Sobolev maps with identity boundary conditions; for $f\in L^{\infty }$, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.