Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

排名聚合算法在少量长列表聚合中的性能比较分析

排名聚合将多个排名列表聚合成一个综合排名列表,可应用于推荐系统、链路预测、元搜索、提案评选等.当前已有工作从不同角度对不同排名聚合算法进行了综述、比较,但存在算法种类较少、数据统计特性不清晰、评价指标不够合理等局限性.不同排名聚合算法在提出时均声称优于已有算法,但是用于比较的方法不同,测试的数据不同,应用的场景不同,因此何种算法最能适应某一任务在很多情况下仍不甚清楚.本文基于Mallows模型,提出一套生成统计特性可控的不同类型的排名列表的算法,使用一个可应用于不同类型排名列表的通用评价指标,介绍9种排名聚合算法以及它们在聚合少量长列表时的表现.结果发现启发式方法虽然简单,但是在排名列表相似度较高、列表相对简单的情况下,能够接近甚至超过一些优化类方法的结果;列表中平局数量的增长会降低聚合排名的一致性并增加波动;列表数量的增加对聚合效果的影响呈现非单调性.整体而言,基于距离优化的分支定界方法 (FAST)优于其他各类算法,在不同类型的排名列表中表现非常稳定,能够很好地完成少量长列表的排名聚合.     

The effects of resource limitation and consensual incentives on cooperation

Exploring the evolution of cooperation has been one of the most challenging topics and attracted increasing attention in various realms. Hereby, we institute an analytic model where the relationship between the common benefits and contributions is the typical saturation nonlinearity. We investigate the evolutionary dynamics of cooperation with and without consensual incentives respectively. The population always evolves to full defection when the incentives are absent. Cooperation, however, can be promoted by consensual incentives when the degree of cooperators' preferences for incentives is great. There exists an intermediate amount of resources at which the positive effect of consensual incentives on cooperation is minimized. Furthermore, there is a U-shape relationship between the degree of cooperators' preference for an incentive and the evolution of cooperation. A greater basin of full cooperation can be induced when the cooperators' preference for reward is more pronounced than that for punishment.     

Norbornene derivatives from a metal‐free,strain‐promoted cycloaddition reaction: New building blocks for ring‐opening metathesis polymerization reactions

The preparation of new ring opening metathesis polymerization (ROMP) monomers using a 1,3‐dipolar cycloaddition between aryl azides and norbornadiene is described. Various norbornenetriazolines, obtained through a solvent‐and catalyst‐free reaction, can subsequently be incorporated into polymer backbones through ROMP reactions. Furthermore, thermal decomposition of the triazoline moiety can allow for further polymer functionalization. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2357–2362     

砂岩方梁断裂过程区范围的实验确定方法

裂纹前端的断裂过程区是引起岩石非线性断裂及尺寸效应的主要原因。利用数字图像相关技术对砂岩开展了三点弯曲梁实验,获得观测区域高精度的全场位移和应变数据,根据断裂韧带区域水平位移和水平应变的分布特征,结合裂尖岩石颗粒变化的微观分析,提出采用裂纹尖端水平位移波动性和水平应变突变性所得到的波动系数和水平应变突变值,确定断裂过程区形状和临界尺寸的方法。结果表明:砂岩断裂过程区的形状为不规则的狭长带状区域,断裂过程区的临界长度为11~13mm,临界宽度为1.58~2.36mm。断裂过程区区域内形变在趋向裂尖时呈指数增加,但其单位区域内的形变增量呈波动状态。该方法能够更加准确判断岩石断裂过程区的范围,有助于分析岩石的非线性断裂特性。     

Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.