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.     

Thermodynamics of natural selection

It is shown that biological-natural-selection-like behavior can occur, as a general type of time evolution, in a statistical system where detailed balance is violated owing to the presence of metastable energy states. A model of a non-equilibrium phase transition corresponding to the spontaneous origin of self-reproduction in the system is suggested. After a phase transition, the system passes from one quasistationary distribution of self-reproducing subsystems to another, with an increase in the total organization, as long as the growth of the energy flow through the system or a reduction of energy dissipation in the system is possible. The entropy production is calculated for this process in terms of selective values of Eigen's theory for self-organization in autocatalytic systems. Correspondence of the extremal principle of Eigen's theory with the criterion of evolution in Prigogine's thermodynamics is established.     

A DSC-Study of Donor/Acceptor Side-Chain Polymers with Flourinated Taper-Shaped Tails

It is shown that insertion in methacrylic polymers of bulky electron donor/acceptor side-groups with taper-shaped flourinated tails promotes a self-organization of the respective side-chain polymers due to the space demands of the bulky D/A side-groups, leading to a columnar hexagonal mesophase. The presence of an Lc-phase is evidenced by DSC and identified by X-ray analysis. The orientation in the respective copolymers and polymer blends is additionally improved by the CT-interaction between the D/A side-groups. An increased packing effect due to this CT-orientation effect is evidenced in DSC by an increase of the respective transition temperatures. CT-interaction is responsible as well for a preferential polymerization of monomeric D/A-complexes leading to copolymers of alternating structures and for a zip-like arrangement along the main chain of the A/D-complexes between the interacting side-groups in polymer blends. Formation of mesophases is even observed in CT-interacting blends between the Lc-D/A side-chain polymethacrylates and the respective amorphous D/A side-chain polysiloxanes.This revised version was published online in November 2005 with corrections to the Cover Date.     

Two-Dimensional Supramolecular from the Self-Assembly of Dissymmetrical Oxamidato-Bridged Heterometallic Trinuclear Building Blocks: Synthesis, Crystal Structure, and Magnetic Properties

Two heterometallic trinuclear complexes {[Cu(oxbp)]₂Co(H₂O)₂}1.5DMF0.5H₂O (complex 1) and {[Cu(oxbm)]₂Co(H₂O)₂}2DMF (complex 2) were obtained from the self-organization of two new dissymmetrical oxamidato-bridged copper(II) building blocks [Cu(oxbp)]^– and [Cu(oxbm)]^–[H₃oxbp=N-benzoato-N'-(3-aminopropyl)oxamido, H₃oxbm=N-benzoato-N'-(2-amino-2-methylethyl)oxamido, DMF=dimethylformamide]. The crystal structure of complex 1 has been determined. Complex 1 crystallize in triclinic system, space group P-1, a=8.0609(16) Å, b=10.661(2) Å, c=22.279(5) Å, =85.32(3), =86.64(3), =70.90(3), and Z=1. The crystal structure of complex 1 consists of neutral trinuclear complex units, and hydrogen bond involved DMF and water molecules. Through the hydrogen bonds, weak coordination and CuCu weak interactions, complex 1 features a 2-D supramolecular structure. Magnetic susceptibility measurements (5–100 K) indicate that the central Co(II) and terminal copper metal ions are antiferromagnetically coupled with J=–28.09 and J=–29.70 cm^–1 for complex 1 and 2, respectively.     

Assembled structures of nanocrystals in polymer/calcium carbonate thin-film composites formed by the cooperation of chitosan and poly(aspartate)

Assembled structures of calcium carbonate (CaCO₃) nanocrystals have been examined for polymer/CaCO₃ thin-film composites synthesized through a self-organization process inspired by biomineralization. For the crystallization of CaCO₃, a thin-film matrix of chitosan has been used as a polymeric substrate. When the matrix is immersed into a supersaturated aqueous solution of CaCO₃ containing 1.4 × 10⁻³ wt % poly(aspartate) (PAsp), thin-film crystals of CaCO₃ are formed spontaneously. Three kinds of disklike films have been observed under a polarizing optical microscope. Electron diffraction analyses of each film have revealed that one is aragonite, displaying radial orientation of the c axes, and the others are vaterite, exhibiting different orientations. Detailed observation by scanning electron microscopy has clarified that these films are assemblies of crystalline particles 10–20 nm in size. The thin-film composites have been obtained over a PAsp concentration range of 4.4 × 10⁻⁴ to 1.0 × 10⁻² wt %. Vaterite formation becomes dominant when the concentration of PAsp is increased. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5153–5160, 2006     

Pattern dynamics in cellular perception

By using a giant amoeboid cell of the Physarum plasmodium, changes in the intracellular distribution of chemical components are studied in relation to information processing in cell behavior. Various kinds of metabolites oscillate, and so the protoplasm should be a collection of chemical oscillators. Spatially, characteristic chemical patterns are self-organized for different cell shapes, and hence cell behavior. New phase waves propagate throughout the cell upon local stimulation, their direction being opposite for attraction and repulsion. Locomotion is inhibited when the coherence of the oscillators breaks. Thus, pattern dynamics is correlated with information processing in the amoeboid cell.     

Influence of the degree of ionization on the growth mechanism of poly(diallyldimethylammonium)/poly(acrylic acid) multilayers

pH‐dependent growth laws of the mass coverage Γ(n) of poly(diallyldimethylammonium) chloride and poly(acrylic acid) (PAA) layer‐by‐layer films are analyzed by Quartz Crystal Microbalance‐D. (Attenuated Total Reflection)‐FTIR spectroscopy shows a degree of dissociation of acrylic acid groups in the films identical to that in solution. Apart from pH‐regimes of differently pronounced exponential and linear growth, the corresponding kinetics indicate pH‐dependent adsorption, reorganization, and diffusion processes. As the thickest films form with almost uncharged PAA (low pH), the results can only partly be explained by the dissociation degree of PAA in the film. For intermediate and high pH values chain interdiffusion as a mechanism for nonlinear growth is strongly dependent on the charge density of the PAA chains. However, at low pH other types of interactions, most likely ion–dipole interactions, play a major role in the multilayer growth. Furthermore, a change in the symmetry of growth can be observed in the low to intermediate pH range. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 425–434     

Flow-driven Surface Instabilities of Tubular Chitosan Hydrogel

Spatial structures break their symmetry under the influence of shear stress arising from fluid flow. Here, we present surface instabilities appearing on chitosan tubes when an acidic solution of chitosan with various molecular weight is injected into a pool of sodium hydroxide solution. At slow flow rates wrinkle-to-fold transition takes place along the direction of the flow yielding a banded structure. For greater injection rates we observe coexisting modes of wrinkles and folds which are stabilized to periodic wrinkles when the alkaline concentration is increased. The instabilities are characterized by the scaling laws of the pattern wavelength and amplitude with the tube characteristics. Our experimental adaptation of mechanical instabilities provides a new in situ method to create soft biomaterials with the desired surface morphology without the use of any prefabricated templates.     

初始状态对自组织演化过程的影响

从实验上系统研究了在强电场下处于介质中的大量金属小球从不同初始状态通过自组织演化为分形的过程;用Sandbox方法定量分析了最终形成的稳定树枝状分形的维数。结果表明:不同初始状态形成分形的过程完全不同,但最终的树枝状分形的维数基本相同。分析认为,小球之间的相互作用存在临界作用距离,不同初始状态相邻小球之间的平均间距不同,因而演化过程不同;而维数相同正是系统耗散相同的体现。