Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry＇s theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.

Coexistence and Extinction Pattern of Asymmetric Cyclic Game Species in a Square Lattice

The co-evolutionary dynamics of a cyclic game system is investigated in a two-dimensional square lattice with the asymmetrical rates for three species. Different with the well-mixed system, coexistence and extinction emerge alternately in the system, where a ＂zero-one＂ behavior is robust for a small population size, whereas, the system is predominated by coexistence for a big population one. We study in detail the influence about the fluctuation to the change of the state, and find that the difference between the maximal amplitude about the fluctuation and the average intensity determines which state the system is ultimately. In addition, we introduce Ports energy to explain the reason of the ＂zero-one＂ behavior. It is shown that the average Ports energy per site is the distance to the ＂zero-one＂ behavior in the model.

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.

Nonlinear Waves in Two-Dimensional (2D) Square Lattice Frenkel-Kontorova (FK) System

A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.

Effect of Strategy-Homogeneity on the Prisoner’s Dilemma Game in a Square Lattice

We investigate the effect of strategy-homogeneity on the prisoner’s dilemma game in a square lattice. Strategy-homogeneity means that the population contains at least one connected group in which individuals maintain the same strategy at each iteration and may update according to updating rule at next iteration. The simulation results show that the introduction of strategy-homogeneity increases the cooperation in the evolutionary stable state. For any value of temptation to defect, the density of cooperators in equilibrium state increases firstly and then decreases as the level of strategy-homogeneity increases constantly, and there exists an appropriate level of strategy-homogeneity, maximizing the density of cooperators. The results may be favorable for comprehending cooperative behaviors in societies composed of connected groups with coherent strategy.

Propagation and Interaction of Edge Dislocation(Kink) in the Square Lattice

The propagation of kink or edge dislocations in the underdamped generalized two-dimensional Frenkel-Kontorova model with harmonic interaction is studied with numerical simulations. The obtained results show that exactly one line of atoms can be inserted into the lattice, which remains at standstill However, if more than one line of atoms are inserted into the lattice, then they will split into several lines with α= 1, where a presents the atoms inserted. In other words, only the kink with α= 1 is stable, while the other kinks are unstable, and will split into α =1 kinks, which remain at standstill.

Spin waves and phase transition on a magnetically frustrated square lattice with long-range interactions

We investigate the effects of long-range interactions on the spin wave spectra and the competition between magnetic phases on a frustrated square lattice with large spin S.Applying the spin wave theory and assisted with symmetry analysis,we obtain analytical expressions for spin wave spectra of competing Neel and(π,0)stripe states of systems containing anyorder long-range interactions.In the specific case of long-range interactions with power-law decay,we find surprisingly that the staggered long-range interaction suppresses quantum fluctuation and enlarges the ordered moment,especially in the Neel state,and thus extends its phase boundary to the stripe state.Our findings illustrate the rich possibilities of the roles of long-range interactions,and advocate future investigations in other magnetic systems with different structures of interactions.

Design and analysis of superlens based on complex two-dimensional square lattice photonic crystal

We theoretically demonstrate the imaging properties of a complex two-dimensional(2D) face-centered square lattice photonic crystal(PC) made from germanium cylinders in air background. The finitedifference time-domain(FDTD) method is employed to calculate the band structure and simulate image construction. The band diagram of the complex structure is significantly compressed. Negative refraction occurs in the second energy band with negative phase velocity at a frequency of 0.228(2πc/a), which is lower than results from previous studies. Lower negative refraction frequency leads to higher image resolution. Numerical results show that the spatial resolution of the system reaches 0.7296λ, which is lower than the incident wavelength.

Crystal growth of CeMn_(0.85)Sb_(2):Absence of magnetic order of Ce-sublattice

Single crystals of CeMn_(0.85)Sb_(2) have been successfully synthesized by using the Bi as flux.Analysis of single crystal x-ray diffraction data confirms that CeMn_(0.85)Sb_(2) crystallizes in the HfCuSi_(2)-type structure with the space group P4/nmm(No.129).In the case of H‖c,CeMn_(0.85)Sb_(2) displays a robust antiferromagnetic transition at~160 K for Mn-sublattice,and there is no sign of magnetic order regarding Ce-sublattice.In the case of the Mn-sublattice shows signs of magnetic order at 160 K and 116 K,indicating a possible spin reorientation.There is no sign of magnetic order for the Cesublattice either,but,alternating current magnetic susceptibility measurements reveal a spin glass state below 18 K in the case of H⊥c.Isothermal magnetization curves measured below magnetic order with H⊥c show saturation and even large hysteresis at 2 K,indicating the presence of a ferromagnetic component.In addition,a field-induced spin-flop transition is observed in the case of H⊥c,indicating a field-induced spin reorientation of Mn spins.Electrical resistivity measurements indicate a metallic nature for CeMn_(0.85)Sb_(2) and large anisotropy which is consistent with its quasi-two-dimensional layered structure.

Lattice Boltzmann simulation of a laminar square jet in cross flows

A three-dimensional, nineteen-velocity(D3Q19) Lattice Boltzmann Method(LBM) model was developed to simulate the fluid flow of a laminar square jet in cross flows based on the single relaxation time algorithm. The code was validated by the mathematic solution of the Poiseuille flow in a square channel, and was further validated with a previous well studied empirical correlation for the central trajectory of a jet in cross flows. The developed LBM model was found to be able to capture the dominant vortex, i.e. the Counter-rotating Vortex Pair(CVP) and the upright wake vortex. Results show that the incoming fluid in the cross flow channel was entrained into the leeside of the jet fluid, which contributes to the blending of the jet. That the spread width of the transverse jet decreases with the velocity ratio. A layer-organized entrainment pattern was found indicating that the incoming fluid at the lower position is firstly entrained into the leeside of the jet, and followed by the incoming fluid at the upper position.

L(1, 2)-edge-labelings for lattices

For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.

A Solvable Decorated Ising Lattice Model

A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-nelghbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2= -0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.

L(s,t) edge spans of trees and product of two paths

L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assignment of integers to the vertices of G such that adjacent vertices receive integers which differ by at least s, and vertices that are at distance of two receive integers which differ by at least t. Given an L（s, t） -labeling f of a graph G, the L（s, t） edge span of f, βst （ G, f） = max { ｜f（u） -f（v）｜： （ u, v） ∈ E（G） } is defined. The L（ s, t） edge span of G, βst（G）, is minβst（G,f）, where the minimum runs over all L（s, t）-labelings f of G. Let T be any tree with a maximum degree of △≥2. It is proved that if 2s≥t≥0, then βst（T） =（ [△/2 ] - 1）t ＋s; if 0≤2s 〈 t and △ is even, then βst（T） = [ （△ - 1） t/2 ] ; and if 0 ≤2s 〈 t and △ is odd, then βst（T） = （△ - 1） t/2 ＋ s. Thus, the L（s, t） edge spans of the Cartesian product of two paths and of the square lattice are completely determined.

Edge span of L(d,1)-labeling on some graphs

Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.

Monte Carlo Study of CO-NO Catalytic Surface Reaction Including CO-CO Repulsion

The CO-NO reaction on a catalytic surface is studied by using Langmuir-Hinshclwood thermal mechanism with Monte Carlo computer simulation. In this model, a novel concept of CO CO repulsion is introduced, which has experimental evidence due to the formation of dipoles when these molecules are chemisorbed on the surface. The system is investigated by applying two approaches of NO dissociation. In the first ca.se, NO always decomposes into N and O before adsorption on the surface, In the second case, NO adsorbs on the surface molecularly and then dissociates into N and O if a vacancy is present in its adjacent neighbourhood. The steady state reactive window （i.e. the continuous production of CO2 and N2） is obtained only with the diffusion of N-atoms on the surface, which extends with CO-CO repulsion in the first, case. Itowever, in the second case, reactive window is obtained with CO-CO repulsion alone, The reactive window width in this case is reasonably large. The first-order phase transition is eliminated in both the cases with CO-CO repulsion.

Effect of Precursor Mechanism on CO-NO Catalytic Reaction on Body-Centred Cubic Structure： Monte Carlo Simulation

The CO-NO catalytic reaction on body-centred cubic （bcc） lattice is studied by Monte Carlo simulation. The simple Langmuir-Hinshelwood （LH） mechanism yields a steady reactive window, which is separated by continuous and discontinuous irreversible phase transitions. The effect of precursor mechanism on the phase diagram of the system is also studied. According to this mechanism, the precursor motion of CO molecules is considered only on the surface of bcc lattice. Some interesting observations are reported.

Discrete breathers in a model with Morse potentials

Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft （Morse） and hard （quartic） on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter к.

THE CORRELATION EFFECT ON THE CHAIN MOTION CONTRIBUTION TO IONIC TRANSPORT IN POLYMER ELECTROLYTES

The ionic transport process in polymer electrolytes (such as polyethylene oxide) wassimulated numerically on a two dimensional square lattice where charge carriers areaccommodated by the lattice sites connected randomly with available bonds to represent theamorphous chain configuration. Following the dynamic bond percolation theory(DBPT),the chainmotion contribution to the ionic conduction was incorporated via periodical renewal of the randombond configuration. To check and extend the prediction made by DBPT employing global abruptbond renewal,spatial correlation of the bond reassignment was introduced to the system by: 1)regional bond renewal and 2) organized bond motion. It is found that the difference between thediffusivities simulated involving regional bond renewal and those of DBPT becomes negligiblewhen the bond renewal rate approaches the carrier hopping rate.

EVOLUTIONARY PUBLIC GOODS GAMES BASED ON HISTORICAL PAYOFFS

We investigate the evolution of cooperation in public goods game based on individuals' historical payoffs. In particular, the fitness of individuals are characterized by two types of payoffs, which are obtained by acting as cooperators and defectors, respectively. Both of payoffs are the linear combination of the current payoffs and the cumulative historical payoffs. The results show that cooperation is enhanced by an increasing memory effect with a wide range of related factors. To explain this phenomenon, we plot some representative snapshots of the population and scrutinize the mean fitness of cooperators and defectors along the boundary. It is found that increasing memory effect induces a positive feedback mechanism for cooperators to expand their districts. Defectors can just survive through forming narrower clusters to exploit cooperators more widely. The threshold values for cooperators and defectors vanishing under the influence of noise are also investigated.