Finite-Size Effects for Anisotropic Bootstrap Percolation: Logarithmic Corrections

In this note we analyse an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.     

Dualities for a Class of Finite Range Probabilistic Cellular Automata in One Dimension

In this paper we study dualities for a class of one-dimensional probabilistic cellular automata with finite range interactions by using a sequence of extended cellular automata.     

Decentralized Cooperation Strategies in Two-Dimensional Traffic of Cellular Automata

We study the two-dimensional traffic of cellular automata using computer simulation. We propose two type of decentralized cooperation strategies, which are called stepping aside (CS-SA) and choosing alternative routes (CS-CAR) respectively. We introduce them into an existing two-dimensional cellular automata (CA) model. CS-SA is designed to prohibit a kind of ping-pong jump when two objects standing together try to move in opposite directions. CS-CAR is designed to change the solution of conflict in parallel update. CS-CAR encourages the objects involved in parallel conflicts choose their alternative routes instead of waiting. We also combine the two cooperation strategies (CS-SA-CAR) to test their combined effects. It is found that the system keeps on a partial jam phase with nonzero velocity and flow until the density reaches one. The ratios of the ping-pong jump and the waiting objects involved in conflict are decreased obviously, especially at the free phase. And the average flow is improved by the three cooperation strategies. Although the average travel time is lengthened a bit by CS-CAR, it is shorten by CS-SA and CS-SA-CAR. In addition, we discuss the advantage and applicability of decentralized cooperation modeling.     

Decentralized Cooperation Strategies in Two-Dimensional Traffic of Cellular Automata

We study the two-dimensional traffic of cellular automata using computer simulation. We propose two type of decentralized cooperation strategies, which are called stepping aside (CS-SA) and choosing alternative routes (CS-CAR) respectively. We introduce them into an existing two-dimensional cellular automata (CA) model. CS-SA is designed to prohibit a kind of ping-pong jump when two objects standing together try to move in opposite directions. CS-CAR is designed to change the solution of conflict in parallel update. CS-CAR encourages the objects involved in parallel conflicts choose their alternative routes instead of waiting. We also combine the two cooperation strategies (CS-SA-CAR) to test their combined effects. It is found that the system keeps on a partial jam phase with nonzero velocity and flow until the density reaches one. The ratios of the ping-pong jump and the waiting objects involved in conflict are decreased obviously, especially at the free phase. And the average flow is improved by the three cooperation strategies. Although the average travel time is lengthened a bit by CS-CAR, it is shorten by CS-SA and CS-SA-CAR. In addition, we discuss the advantage and applicability of decentralized cooperation modeling.     

Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

A Two-Lane Cellular Automata Model with Influence of Next-Nearest Neighbor Vehicle

In this paper, we propose a new two-lane cellular automata model in which the influence of the next-nearest neighbor vehicle is considered. The attributes of the traffic system composed of fast-lane and slow-lane are investigated by the new traffic model. The simulation results show that the proposed two-lane traffic model can reproduce some traffic phenomena observed in real traffic, and that maximum flux and critical density are close to the field measurements.Moreover, the initial density distribution of the fast-lane and slow-lane has much influence on the traffic flow states.With the ratio between the densities of slow lane and fast lane increasing the lane changing frequency increases, but maximum flux decreases. Finally, the influence of the sensitivity coefficients is discussed.     

活性-非活性二元混合体系玻璃化转变的模耦合理论

Collective behaviours of active particle systems have gained great research attentions in recent years. Here we present a mode-coupling theory (MCT) framework to study the glass transition of a mixture system of active and passive Brownian particles. The starting point is an effective Smoluchowski equation, which governs the dynamics of the probability distribution function in the position phase space. With the assumption of the existence of a nonequilibrium steady state, we are able to obtain dynamic equations for the intermediate scattering functions (ISFs), wherein an irreducible memory function is introduced which in turn can be written as functions of the ISFs based on standard mode-coupling approximations. The effect of particle activity is included through an effective diffusion coefficient which can be obtained via short time simulations. By calculating the long-time limit of the ISF, the Debye-Waller (DW) factor, one can determine the critical packing fraction η_c of glass transition. We find that for active-passive (AP) mixtures with the same particle sizes, η_c increases as the partial fraction of active particle x_A increases, which is in agreement with previous simulation works. For system with different active/passive particle sizes, we find an interesting reentrance behaviour of glass transition, i.e., η_c shows a non-monotonic dependence on x_A. In addition, such a reentrance behaviour would disappear if the particle activity is large enough. Our results thus provide a useful theoretical scheme to study glass transition behaviour of active-passive mixture systems in a promising way.     

On the Dynamics of the Glass Transition on Bethe Lattices

The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transition upon decreasing the temperature or increasing the degree of constrainedness. Our analysis is based upon a detailed study of large scale rearrangements which control the slow dynamics of the system close to the dynamical transition. Particular attention is devoted to the neighborhood of a zero temperature tricritical point. Both the approach and several key results are conjectured to be valid in a considerably more general context. PACS Numbers:75.50.Lk (Spin glasses), 64.70.Pf (Glass transitions), 89.20.Ff (Computer science     

丙三醇浓溶液玻璃化转变与结构松弛参数DSC分析

利用差示扫描量热仪研究了5种高浓度丙三醇水溶液(60%、70%、80%、90%、100%)的玻璃化转变行为,以考察水分含量和升降温速率对其玻璃化转变行为和结构松弛参数的影响.采用4种线性升降温速率(10、15、20、25K/min)获得玻璃化转变的相关参数.利用GordonTaylor方程对玻璃化转变温度的分析结果表明,水对丙三醇增塑常数的计算结果与升降温速率和玻璃化转变温度的读取方法有很大关系.玻璃化转变过程的比热容变化不仅随水分含量的增加而增加,而且与升降温速率也有一定的依赖关系.结构松弛活化能的计算结果表明,随体系水分含量的增加,体系的结构松弛活化能和动力学脆度都逐渐降低.随水分含量的变化,热力学脆度和动力学脆度表现出相反的变化趋势.     

A new Cellular Automata Model including a decelerating damping effect to reproduce Kerner’s three-phase theory

Most of the conventional traffic Cellular Automaton (CA) models based on the Nagel-Schreckenberg model (NaSch model) have two problems: an unrealistic deceleration dynamics when a vehicle agent collides with a preceding vehicle in a stopping event, and the problem with reproducing the synchronized flow in Kerner’s three-phase theory. In this paper, a revised stochastic Nishinari-Fukui-Schadschneider (S-NFS) model, belonging to the class of NaSch models, is presented. The proposed CA model, where a random braking effect is improved by considering the dependency on the velocity difference and heading distance with a preceding vehicle, is confirmed to overcome the two above-mentioned drawbacks.     

Two-spin-majority cellular automaton as a model of 2D cluster and interface growth

A new probabilistic cellular automaton model is introduced to simulate cluster and interface growth in two dimensions. The dynamics of this model is an extension to higher dimensions of the compact directed percolation studied by Essam. Numerical results indicate that the two-dimensional cluster coarsening and growth can be described only approximately by the conventional cluster size scaling due to a crossover in the growth mode. The spreading of the initially flat interface follows a purely diffusional,t ^1/2, law.     

A New Nano Design for Implementation of a Digital Comparator Based on Quantum-Dot Cellular Automata

International Journal of Theoretical Physics - Quantum-dot is the result of elastic relaxation which has a straight relationship with the optical and electronic aspects of the quantum-dot-based...     

Bonding at Compatible and Incompatible Amorphous Interfaces of Polystyrene and Poly(Methyl Methacrylate) Below the Glass Transition Temperature

Abstract

Films of high‐molecular‐weight amorphous polystyrene (PS, M _w = 225 kg/mol, M _w/M _n = 3, T _g‐bulk = 97°C, where T _g‐bulk is the glass transition temperature of the bulk sample) and poly(methyl methacrylate) (PMMA, M _w = 87 kg/mol, M _w/M _n = 2, T _g‐bulk = 109°C) were brought into contact in a lap‐shear joint geometry at a constant healing temperature T _h, between 44°C and 114°C, for 1 or 24 hr and submitted to tensile loading on an Instron tester at ambient temperature. The development of the lap‐shear strength σ at an incompatible PS–PMMA interface has been followed in regard to those at compatible PS–PS and PMMA–PMMA interfaces. The values of strength for the incompatible PS–PMMA and compatible PMMA–PMMA interfaces were found to be close, both being smaller by a factor of 2 to 3 than the values of σ for the PS–PS interface developed after healing at the same conditions. This observation suggests that the development of the interfacial structure at the PS–PMMA interface is controlled by the slow component, i.e., PMMA. Bonding at the three interfaces investigated was mechanically detected after healing for 24 hr at T _h = 44°C, i.e., well below T _g‐bulks of PS and PMMA, with the observation of very close values of the lap‐shear strength for the three interfaces considered, 0.11–0.13 MPa. This result indicates that the incompatibility between the chain segments of PS and PMMA plays a negligible negative role in the interfacial bonding well below T _g‐bulk.     

元胞自动机模拟痕量铅离子在硅油-碳糊电极上吸附富集的动力学

利用元胞自动机原理,在SCILAB自由数学计算工具软件平台上设计并完成了铅在硅油-石墨粉碳糊电极上吸附过程的动力学模拟和等温吸附曲线的模拟。获得的吸附速率常数与实验结果完全一致,并表明其吸附机理遵从朗格缪单分子层吸附机理,为实验研究结果提供了理论依据。     

Critical behaviour of thin films with quenched impurities

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method to the one-loop order within the framework of the n-component φ⁴-model. The finite-size crossover in impure films has been considered on the basis of the fundamental relationship between the effective dimensionality D_eff and the characteristic lengths of the system. The fixed points, their stability properties and the critical exponents are obtained and analyzed, using an -expansion near the effective spatial dimensionality D_eff of the fluctuation modes in D-dimensional hyperslabs with two types of quenched impurities: point-like impurities with short-range random correlations and extended (linear) impurities with infinite-range random correlations along the small-size spatial direction. The difference between the critical properties of infinite systems and films is demonstrated and investigated. A new critical exponent, describing the scaling properties of the thickness of films with extended impurities has been derived and calculated. A special attention is paid to the critical behaviour of real impure films (D=3).     

New Insights into the Effects of Physical Aging on Glass Transition of Polystyrene by FTIR

A new method to detect the glass transition was used to investigate the effects of physical aging on the glass transition of polystyrene by Fourier transform infrared (FTIR) spectroscopy. The results showed that the onset point of the glass transition shifted to higher temperature with aging, but the end point didn't change. It was demonstrated that this method was of great use in determining the glass transition temperature of aged polymeric samples. For each aged sample, the four bands assigned to the vibrational modes of the main chain groups and the side groups of polystyrene showed the same transition regions, indicating that the main chain and the side groups were aging synchronously. The rates of increase of the relative peak areas for the four investigated bands during the glass transition decreased with aging with the increased rates of the relative peak areas for the two bands assigned to side group decreasing less than those of main chain, which seemed to indicate the dominance of the side group in aging process.     

Simple form of the stationary distribution for 3D cellular automata in a special case

3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise-and this is the case we tackle-the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero-one borders within the configuration.     

A Monte Carlo study of ant traffic in a uni-directional trail

In this study, we aim to investigate ant traffic in the uni-directional ant trail. We consider two types of ants moving in the trail: one of which smells well and the other does not. The theoretical base of the study is similar to that of the Nagel–Schreckenberg (NaSch) model, but we do not use the exclusion rule, the asymmetrical exclusion rule is employed instead. Ants are placed on the trail as mixed. By keeping the number of ‘poor-smelling ants’ constant, the traffic in the trail is studied as a function of the number of “good-smelling” ants and the evaporation rate probability of pheromone f$f$. The fundamental physical quantities, i.e., mean speed V$V$ and flux F$F$, interestingly show non-monotonic density dependence for some values of f$f$ at some densities.     

Discontinuous Condensation Transition and Nonequivalence of Ensembles in a Zero-Range Process

We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of a condensation transition. In contrast to previous results, the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases. This leads to a richer phase diagram, including nonequivalence of ensembles in certain phase regions. The paper is motivated by results from granular clustering, where these features have been observed experimentally. An erratum to this article can be found at