Evolution of co-operation among mobile agents with different influence

Co-operation is a key factor in understanding the evolution of our society. Inspired by this issue, the individual mobility in game theory has been proved to be a very useful scenario. However, it is not realistic, as described in previous studies, that each agent has the same influence on its neighbour’s movement trait. In this work, we mainly focus on the weighted influence on the mobility of agents in the prisoner’s dilemma game. Here the weight is proportional to its degree with power exponent of λ$\lambda$, where λ$\lambda$ is the adjustable parameter to control the level of heterogeneity among individuals in the network. Through numerous simulations we find that co-operation level is promoted when the heterogeneous influence factor is considered. In particular, there is an intermediate value _λopt≈10${\lambda }_{opt}\approx 10$ to guarantee the optimal evolution of co-operation. Moreover, we also prove that the effect of influence weight on the enhancement of co-operation is only valid when the agent’s interaction radius is within a threshold value. We thus present a viable method of understanding the ubiquitous co-operative behaviour in nature and hope that it will inspire further studies to resolve social dilemmas.     

Global Regularity of the 3D Axi-Symmetric Navier–Stokes Equations with Anisotropic Data

In this paper, we study the 3D axisymmetric Navier–Stokes equations with swirl. We prove the global regularity of the 3D Navier–Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the solution in terms of its initial data in some L ^p norm. Our results also reveal some interesting dynamic growth behavior of the solution due to the interaction between the angular velocity and the angular vorticity fields.     

Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory

The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Kármán type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon–Fletcher–Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces.     

Highly stereoselective synthesis of (Z)-3-methoxy-1-methyleneisoindoles via DMAP catalyzed cyclization of methyl 2-alkynylbenzimidates

A DMAP (4-dimethylaminopyridine) catalyzed cyclization of methyl 2-alkynylbenzimidates has been developed, which affords 3-methoxy-1-methyleneisoindoles with excellent Z-stereoselectivity under mild and transition-metal-free conditions. The (Z)-3-methoxy-1-methyleneisoindole products can be converted to corresponding 3-amino-1-methyleneisoindoles, 3-methoxy-isoindoles, 3-methyleneisoindolinones and isoindolinones with high efficiency.     

NH4I/1,10-phenanthroline catalyzed direct sulfenylation of N-heteroarenes with ethyl arylsulfinates

An efficient synthesis of N-heterocyclic aryl sulfides via NH₄I/1,10-phenanthroline-catalyzed direct sulfenylation reactions was reported. In this reaction, heteroarenes such as indoles, and pyrroles serve as nucleophiles by installing a arylthio group at the C3 and C2 position of heterocycles, respectively. With readily accessible and free of unpleasant odor ethyl arylsulfinates as sulfur reagents, the metal-free-catalyzed direct sulfenylation of N-heteroarenes has been developed. 3-Arylthio-indoles and 2-arylthio-pyrroles derivatives were obtained in moderate to excellent yields, even on gram scale. The reaction was general for a broad scope of substrates and demonstrated good tolerance to a variety of functional groups.     

Nitrogen‐rich Salts based on 3‐Dinitromethyl‐[1,2,4]triazine: Synthesis,Characterization, and Performance

1,1‐Diamino‐2,2‐dinitroethylene (FOX‐7), one of the most well‐known energetic materials, has attracted broad attention around the world. To extend the chemistry of FOX‐7, we present here a series of energetic salts based on 3‐dinitromethyl‐[1,2,4]triazine, which is prepared from FOX‐7. All these salts were fully characterized using ¹H NMR, ¹³C NMR, IR, and elemental analysis. In addition, the potassium salt ( 2 ), ammonium salt ( 5 ), and guanidinium salt ( 7 ) were further confirmed by single‐crystal X‐ray diffraction. Extensive hydrogen bonds were observed in these salts. The salts exhibit moderate densities varying from 1.63 to 1.76 g · cm^–3. All the compounds possess good thermal stability with decomposition temperatures from 118 to 267 °C. The detonation performance for salts were calculated by using EXPLO 5, their detonation velocities are in the range from 6807 to 8614 m · s^–1 and detonation pressures fall between 18.8 to 31.6 GPa. All the salts exhibit very low mechanical sensitivity, which indicates their potential application as insensitive energetic materials.     

Bowl Inversion in an Exo‐type Supramolecule in the Solid State

Bowl inversion is a unique property of buckybowls. The polarity and assembly configuration of buckybowls are reversed after bowl inversion. So far, this unique phenomenon has been studied in solution and on surface, but not in solid state due to spatial constraint. Now a series of exo‐type supramolecular assemblies of trithiasumanene and nanographene are investigated. Tuning the electron density of the nanogaphene component was found to directly affect the binding constant of the complex. Reversible bowl inversion in the solid state was then successfully achieved by subjecting the trithiasumanene–nanographene assembly with the weakest binding strength to repeated heating–cooling cycles, which was unambiguously observed by single crystal X‐ray diffraction.     

BN‐Embedded Tetrabenzopentacene: A Pentacene Derivative with Improved Stability

Considerable efforts have been devoted to achieving stable acene derivatives for electronic applications; however, the instability is still a major issue for such derivatives. To achieve higher stability with minimum structural change, CC units in the acenes were replaced with isoelectronic BN units to produce a novel BN‐embedded tetrabenzopentacene (BNTBP). BNTBP, with a planar structure, is highly stable to air, moisture, light, and heat. Compared with its carbon analogue tetrabenzopentacene (TBP), BN embedment lowered the highest occupied molecular orbital (HOMO) energy level of BNTBP, changed the orbital distribution, and decreased the HOMO orbital coefficients at the central carbon atoms, which stabilize BNTBP molecules upon exposure to oxygen and sunlight. The single‐crystal microribbons of BNTBP exhibited good performance in field‐effect transistors (FETs). The high stability and good mobility of BNTBP indicates that BN incorporation is an effective approach to afford stable large‐sized acenes with desired properties.     

Cations Controlling the Chiral Assembly of Luminescent Atomically Precise Copper(I) Clusters

Chiral assembly and asymmetric synthesis are critically important for the generation of chiral metal clusters with chiroptical activities. Here, a racemic mixture of [K(CH₃OH)₂(18‐crown‐6)]⁺[Cu₅(S^tBu)₆]^? ( 1?CH₃OH ) in the chiral space group was prepared, in which the chiral red‐emissive anionic [Cu₅(S^tBu)₆]^? cluster was arranged along a twofold screw axis. Interestingly, the release of the coordinated CH₃OH of the cationic units turned the chiral 1?CH₃OH crystal into a mesomeric crystal [K(18‐crown‐6)]⁺[Cu₅(S^tBu)₆]^? ( 1 ), which has a centrosymmetric space group, by adding symmetry elements of glide and mirror planes through both disordered [Cu₅(S^tBu)₆]^? units. The switchable chiral/achiral rearrangement of [Cu₅(S^tBu)₆]^? clusters along with the capture/release of CH₃OH were concomitant with an intense increase/decrease in luminescence. We also used cationic chiral amino alcohols to induce the chiral assembly of a pair of enantiomers, [d /l ‐valinol(18‐crown‐6)]⁺[Cu₅(S^tBu)₆]^? ( d /l ‐Cu_5V ), which display impressive circularly polarized luminescence (CPL) in contrast to the CPL‐silent racemic mixture of 1?CH₃OH and mesomeric 1 .