Axial instability of double-nanobeam-systems

This Letter considers the axial instability of double-nanobeam-systems. Eringen's nonlocal elasticity is utilized for modelling the double-nanobeam-systems. The nonlocal theory accounts for the small-scale effects arising at the nanoscale. The small-scale effects substantially influence the instability (or buckling) of double-nanobeam-systems. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes than the out-of-phase (asynchronous) buckling modes. The increase of the stiffness of the coupling elastic medium in double-nanobeam-system reduces the small-scale effects during the out-of-phase (asynchronous) buckling modes. Analysis of the scale effects in higher buckling loads of double-nanobeam-system with synchronous and asynchronous modes is also discussed in this Letter. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of complex-nanobeam-system such as complex carbon nanotube system.     

Non-linear buckling for the surface rectangular delamination of laminated piezoelectric shells

An analytical method is presented to study the non-linear buckling characteristic of rectangular local delamination near the surface of fiber-reinforced piezoelectric lamination shells under coupled mechanical and electric loads. The stacking sequence of fiber reinforced lamination shells with piezoelectric layers is considered as symmetry, but the stacking sequence of rectangular local delamination sub-shells is arbitrary. Based on the nonlinear displacement mode of delaminated sub-shells, the effects of electric fields, the geometrical, physical parameters and stacking sequences of piezoelectric laminated shells on the non-linear local buckling for rectangular delamination near the surface of piezoelectric laminated base-shells are solved.     

On the Tutte–Krushkal–Renardy polynomial for cell complexes

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte–Krushkal–Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte–Krushkal–Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte–Krushkal–Renardy polynomial.     

Emergence of density dynamics by surface interpolation in elementary cellular automata

A classic problem in elementary cellular automata (ECAs) is the specification of numerical tools to represent and study their dynamical behaviour. Mean field theory and basins of attraction have been commonly used; however, although the first case gives the long term estimation of density, frequently it does not show an adequate approximation for the step-by-step temporal behaviour; mainly for non-trivial behaviour. In the second case, basins of attraction display a complete representation of the evolution of an ECA, but they are limited up to configurations of 32 cells; and for the same ECA, one can obtain tens of basins to analyse. This paper is devoted to represent the dynamics of density in ECAs for hundreds of cells using only two surfaces calculated by the nearest-neighbour interpolation. A diversity of surfaces emerges in this analysis. Consequently, we propose a surface and histogram based classification for periodic, chaotic and complex ECA.     

有超车规则的交通流的元胞自动机模型

分析和评论了2014年美国大学生数学建模竞赛（MCM）A题,以及获得outstanding winner奖的6篇论文。首先对试题进行分析,并结合已有文献指出A题的主要解题思路;然后,通过评述获奖论文,指出学生论文的优点及存在的问题;最后,对今年赛题的某些问题进行讨论。     

细胞神经网络的指数稳定性

该文研究了具有可变时滞的随机细胞神经网络的指数 稳定性,应用Razumikhin定理与Lyapunov函数,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的两类判据,一类是时滞无关而另一类是时滞相关.     

Lattice games without rational strategies

We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional lattice game whose set of winning positions does not have a rational generating function.     

Evolution of groups with a hierarchical structure

The universal occurrence of a hierarchical structure and its dynamic behavior in various types of group, living or abstract, are discussed. Here the word “group” refers not only to tangible aggregation but also to invisible aggregation of social psychological and of geopolitical meaning. The evolution of these groups is simulated using a model of agents distributed on the lattices of cellular grids. It is assumed that agents, fearing isolation, interact asymmetrically with each other with regard to exchange of “power”. As an indicator of hierarchy, the Gini coefficient is introduced. Example calculations are made for the aggregation, fusion and fission of animal groups, and for the appearance of a powerful empire and the rise and fall of supremacy. It is shown that such abstract objects evolve with time in accordance with the universal rules of groups common to birds and fish.     

The unstable behavior of cellular premixed flames induced by intrinsic instability

The unstable behavior of cellular premixed flames induced by intrinsic instability is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier–Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through the flame front; the diffusive-thermal effect is caused by the preferential diffusion of mass versus heat. A disturbance with several wavelength components is superimposed on a planar flame, and the formation of a cellular flame induced by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the combination and division of cells are observed. The behavior of cellular-flame fronts becomes more unstable when the Lewis number is lower than unity, since the diffusive-thermal effect has a great influence on the unstable behavior. The cell size changes with time, and its average is greater than the critical wavelength and becomes smaller by decreasing the Lewis number. The flame velocity of cellular flames depends strongly on the length of computational domain in the direction tangential to the flame front. As the length of computational domain increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances play an important role in the shape of cellular flames, i.e., in the flame-surface area.