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[en] We have considered the Abelian sandpile model on a small-world network. To obtain a small-world network, we have added a few long-ranged bonds to an ordinary square lattice. It is observed that the probability distribution of the avalanches has two distinct power-law regimes: one corresponding to the ordinary BTW model and another that emerges because of the small-world structure of the network. (paper)
[en] Full text: The paper deals with the results of the investigation of tenzometric properties of layer-chain semiconductor crystals Tlse-TLInSe2 in static regime.Tenzoresistive characteristics of crystals Tlse-TLLnSe2 has been measured at deformation along the tetragonal axis .The electro conductivity of Tlse -TLLnSe2.sharply decreases for crystal tension along this axis , and increases at compression in the same direction.The coefficient tenzosensibility in the direction of tetragonal axis TISe-TLLnSe2 has positive value.The technology of tenzodetectors for supersmall deformation is described in detail.
[en] Highlights: •Cooperation macrocosmically refers to the overall cooperation rate, while reputation microcosmically records individual choices. •Therefore, reputation should be preferred in order to investigate how individual choices evolve. •Both the mean and standard deviation of reputation follow clear patterns, and some factors have quadratic effects on them. -- Abstract: Cooperation is vital for our society, but the temptation of cheating on cooperative partners undermines cooperation. The mechanism of reputation is raised to countervail this temptation and therefore promote cooperation. Reputation microcosmically records individual choices, while cooperation macrocosmically refers to the group or averaged cooperation level. Reputation should be preferred in order to investigate how individual choices evolve. In this work, we study the distribution of reputation to figure out how individuals make choices within cooperation and defection. We decompose reputation into its mean and standard deviation and inspect effects of their factors respectively. To achieve this goal, we construct a model where agents of three groups or classes play the prisoners’ dilemma game with neighbors on a square lattice. It indicates in outcomes that the distribution of reputation is distinct from that of cooperation and both the mean and standard deviation of reputation follow clear patterns. Some factors have negative quadratic effects on reputation's mean or standard deviation, and some have merely linear effects
[en] In the evolution of cooperation, the motion of players plays an important role. In this paper, we incorporate, into an evolutionary prisoner dilemma's game on networks, a new factor that cooperators and defectors move with different probabilities. By investigating the dependence of the cooperator frequency on the moving probabilities of cooperators and defectors, μc and μd, we find that cooperation is greatly enhanced in the parameter regime of μc<μd. The snapshots of strategy pattern and the evolutions of cooperator clusters and defector clusters reveal that either the fast motion of defectors or the slow motion of cooperators always favors the formation of large cooperator clusters. The model is investigated on different types of networks such as square lattices, Erdoes-Renyi networks and scale-free networks and with different types of strategy-updating rules such as the richest-following rule and the Fermi rule. The numerical results show that the observed phenomena are robust to different networks and to different strategy-updating rules.
[en] This experimental study demonstrates intensity maps of far-field focusing using a two-dimensional triangular lattice sonic crystal and intensity maps of near-field focusing using a two-dimensional square lattice sonic crystal for various scatter materials. Besides, the paper presents an experimental method to estimate the effective refraction index of far-field flat lenses. The author introduces the experimental setup developed for the research and discusses the results obtained
[en] We consider configurations of n walkers each of which starts at the origin of a directed square lattice and makes the same number t of steps from node to node along the edges of the lattice. Bose walkers are not allowed to cross, but can share edges. Fermi walk configurations must satisfy the additional constraint that no two walkers traverse the same path. Since, for given t, there are only a finite number of t-step paths, there is a limit nmax on the number of walkers allowed by the Fermi condition. The value of nmax is determined for six types of boundary conditions. The number of Fermi configurations of nmax walkers is also determined using a bijection to standard Young tableaux. In four cases there is no constraint on the endpoints of the walks and the relevant tableaux are shifted.
[en] We investigate the emergence of target waves in a cyclic predator-prey model incorporating a periodic current of the three competing species in a small area situated at the center of a square lattice. The periodic current acts as a pacemaker, trying to impose its rhythm on the overall spatiotemporal evolution of the three species. We show that the pacemaker is able to nucleate target waves that eventually spread across the whole population, whereby three routes leading to this phenomenon can be distinguished depending on the mobility of the three species and the oscillation period of the localized current. First, target waves can emerge due to the synchronization between the periodic current and oscillations of the density of the three species on the spatial grid. The second route is similar to the first, the difference being that the synchronization sets in only intermittently. Finally, the third route toward target waves is realized when the frequency of the pacemaker is much higher than that characterizing the oscillations of the overall density of the three species. By considering the mobility and frequency of the current as variable parameters, we thus provide insights into the mechanisms of pattern formation resulting from the interplay between local and global dynamics in systems governed by cyclically competing species.
[en] We study several models of staircase polygons on the rotated square lattice, which interact with an impenetrable surface while also being pushed towards or pulled away from the surface by a force. The surface interaction is governed by a fugacity a and the force by a fugacity y. Staircase polygons are simplifications of more general self-avoiding polygons, a well-studied model of interacting ring polymers. For this simplified case we are able to exactly determine the limiting free energy in the full a-y plane, and demonstrate that staircase polygons exhibit four different phases, including a ‘mixed’ adsorbed-ballistic phase. (paper)
[en] The family of models on the square lattice includes a dilute loop model, a -vertex model and, at roots of unity, a family of RSOS models. The fused transfer matrices of the general loop and vertex models are shown to satisfy -type fusion hierarchies. We use these to derive explicit - and -systems of functional equations. At roots of unity, we further derive closure identities for the functional relations and show that the universal -system closes finitely. The RSOS models are shown to satisfy the same functional and closure identities but with finite truncation. (paper: quantum statistical physics, condensed matter, integrable systems)
[en] We obtain exact densities of contractible and non-contractible loops in the O(1) model on a strip of the square lattice rolled into an infinite cylinder of finite even circumference L. They are also equal to the densities of critical percolation clusters on 45 degree rotated square lattice rolled into a cylinder, which do not or do wrap around the cylinder respectively. The results are presented as explicit rational functions of L taking rational values for any even L. Their asymptotic expansions in the large L limit have irrational coefficients reproducing the earlier results in the leading orders. The solution is based on a mapping to the six-vertex model and the use of technique of Baxter’s T–Q equation. (letter)