Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the err...     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.      

Scaling in Electrical Conductivity Measurements and Rheological Measurements of Monarch 700 Dispersions Stabilized by Polymers

For making stable dispersions of graphitic carbon black (Monarch 700), the effectiveness of three dispersants/polymers (hypermer LP1, hypermer B246, and OLOA 11000) in xylene is investigated. Hypermer LP1 (polyhydroxystearic acid) is a homopolymer and hypermer B246 (PEG 30-dipolyhydroxystearate) is a polyhydroxystearic acid/polyethylene oxide/polyhydroxystearic acid ABA block copolymer, while OLOA 11000 (polyisobutylene succinimide) has a polar head group (polyamine) attached to a hydrocarbon chain (polyisobutylene). Well-dispersed graphitic carbon black dispersions were prepared using dispersants at optimum concentrations. Percolation threshold and rheological threshold were determined by analyzing the variations in electrical conductivity and elastic modulus with concentration of carbon black. Above threshold concentration, scaling law was applied to experimental data of rheology (dynamic measurements) and electrical conductivity measurements to evaluate quality of the system. Effectiveness of polymers was investigated on the basis of value of critical exponent (t and t′, respectively) in scaling power law. Hypermer LP1 was proved to be a poor dispersant for Monarch 700 dispersions while other two polymers were found to be effective stabilizers.     

基于变结构理论的中制导律设计方法研究

对于采用复合制导的空地导弹,中末制导交接班问题是影响命中概率的关键因素。针对这一问题,采用变结构理论设计中制导律。首先建立滑模面,保证滑模面上速度矢量与视线重合,且零化视线角速率,然后设计到达函数,使到达条件得到满足,可以保证交班时刻导弹可靠捕获目标,并为末制导提供最优初始条件。建立了导弹六自由度数学模型和目标捕获模型,进行全系统数字仿真,实验结果表明：在中末制导交接时刻,弹目视线与导弹速度矢量基本重合,误差为0.12°,视线角速度为-0.02°/s,在±20°视场下满足捕获需求,并且为末制导提供最优初始条件。该方法可以满足中末制导交接班要求,具有较强鲁棒性,且中制导段弹道平滑,需用过载小。     

Standing waves for 4‐superlinear Schrödinger‐Kirchhoff equations

We consider standing waves for 4‐superlinear Schrödinger–Kirchhoff equations in with potential indefinite in sign. The nonlinearity considered in this study satisfies a condition that is much weaker than the classical Ambrosetti–Rabinowitz condition. We obtain a nontrivial solution and, in the case of odd nonlinearity, an unbounded sequence of solutions via the Morse theory and the fountain theorem, respectively. Copyright © 2014 John Wiley & Sons, Ltd.