Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Na原子链表面等离激元特性的含时密度泛函研究

本文用含时密度泛函理论研究了线性Na原子链的表面等离激元机理.主要在原子尺度下模拟计算了体系随着原子数增加及原子间距变化的集体激发过程.研究发现线性原子链有一个普遍的特性——存在一个纵模和两个横模.两个横模一般在实验上很难被观测到.纵模随着原子链长度增加,能量红移的同时,该纵模主峰的强度呈线性增长.随着原子个数的增加,端点模式(TE)开始蓝移,能量和偶极强度都逐渐趋向饱和.横模能量被劈裂的原因概括如下:(一)每个位置的电子受到的势不同,在两端的电子受到的势要比在中间的电子受到的势要高,因此两端的电荷积累也比中间多;(二)端点存在悬挂键,所以中间的电子-电子间相互作用与端点的不一样,这两方面又都与原子间距d有关.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了共轭线性算子的一些性质,包括它们的矩阵表示和谱结构等;其次,分别研究了具有共轭线性对称性和完整共轭线性对称性的线性算子,通过它们的矩阵表示,给出了共轭线性对称性和完整共轭线性对称性的等价刻画;作为应用,得到了关于PT-对称及完整PT-对称算子的一些有趣性质,并通过一些具体例子,说明了完整PT-对称性对张量积运算不具有封闭性,同时说明了完整PT-对称性既不是哈密顿算子在某个正定内积下自伴的充分条件,也不是必要条件.     

Modification of Polylactide Nonwovens with Carbon Nanotubes and Ladder Poly(silsesquioxane)

Electrospun nonwovens of poly(L-lactide) (PLLA) modified with multiwall carbon nanotubes (MWCNT) and linear ladder-like poly(silsesquioxane) with methoxycarbonyl side groups (LPSQ-COOMe) were obtained. MWCNT and LPSQ-COOMe were added to the polymer solution before the electrospinning. In addition, nonwovens of PLLA grafted to modified MWCNT were electrospun. All modified nonwovens exhibited higher tensile strength than the neat PLA nonwoven. The addition of 10 wt.% of LPSQ-COOMe and 0.1 wt.% of MWCNT to PLLA increased the tensile strength of the nonwovens 2.4 times, improving also the elongation at the maximum stress.     

Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

Synthesis and Photophysical Properties of a Sc3N@C80‐Corrole Electron Donor–Acceptor Conjugate

Embedding endohdedral metallofullerenes (EMFs) into electron donor–acceptor systems is still a challenging task owing to their limited quantities and their still largely unexplored chemical properties. In this study, we have performed a 1,3‐dipolar cycloaddition reaction of a corrole‐based precursor with Sc₃N@C₈₀ to regioselectively form a [5,6]‐adduct ( 1 ). The successful attachment of the corrole moiety was confirmed by mass spectrometry. In the electronic ground state, absorption spectra suggest sizeable electronic communications between the electron acceptor and the electron donor. Moreover, the addition pattern occurring at a [5,6]‐bond junction is firmly proven by NMR spectroscopy and electrochemical investigations performed with 1 . In the electronically excited state, which is probed in photophysical assays with 1 , a fast electron‐transfer yields the radical ion pair state consisting of the one‐electron‐reduced Sc₃N@C₈₀ and of the one‐electron‐oxidized corrole upon its exclusive photoexcitation. As such, our results shed new light on the practical work utilizing EMFs as building blocks in photovoltaics.     

Synthesis of self‐healing polyurethane urea‐based supramolecular materials

Supramolecular polyurethane ureas are expected to have superior mechanical properties primarily due to the reversible, noncovalent interactions such as hydrogen bonding interactions. We synthesized polyurethane prepolymers from small molecular weight of poly(tetramethylene ether)glycol and isophorone diisocyanates, which were end capped with propylamine to synthesize polyurethane ureas with high contents of urea and urethane groups for hydrogen‐bonding formations to facilitate self‐healing. The effects of polyurethane urea molecular weight (3000 ≤ M_n ≤ 9000), crosslinking, and cutting direction were studied in terms of thermal, mechanical, and morphological properties with an emphasis on the self‐healing efficiency. It was found that the thermal self‐healability was more pronounced as the molecular weight of polyurethane urea decreased, showing a maximum of more than 96% with 3000 M_n when the sample was cut along the stretch direction. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 468–474