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.     

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.     

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.     

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     

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.     

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.     

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...     

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).     

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.     

Design of a Rectangular to Circular Groove Waveguide Transition by Finite Element Method

A rectangular to circular groove waveguide transition is described in millimeter-wave band. The transition maintains a constant cutoff wavelength. Using the Finite Element Method, the size of the variable cross-section throughout the transition are calculated and the transition is designed.     

Activation Energy for the Glass Transition of a Confined Elastomer in HDPE/PP Blends

Blends of two highly crystalline polymers containing an elastomer were prepared to study the glass transition of the confined elastomer. The polymers chosen were high density poly ethylene (HDPE), polypropylene (PP), and two elastomers of a different nature: natural number (NR) and EPDM. The dynamic mechanical analyzer (DMA) technique was used to analyze the storage modulus of blends with elastomer content from 0% to 30% by weight, with the remainder made up of equal amounts of HDPE and PP, and blends with 10% of the elastomer, but varied ratios of polyolefins. We used the differentiation modification of the Arrhenius method in the kinetic analysis assuming an n‐order relaxation mechanism, which allowed detecting the percolation threshold of NR. Results indicate that both temperature and activation energy for glass transition (T _g ) are dependent on the types of polymers in the blend and blend composition. The T _g and E values of the unblended elastomers are higher than those in blends; this behavior is associated with the elastomer confinement and blend morphology.     

The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

We study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces self-sustained activity. Nonlocal connections, or shortcuts, are randomly introduced according to a specified connection probability. There is a range of connection probabilities for which neuron firing occurs, as well as a critical probability for which the firing ceases in the absence of time delay. The critical probability for nonlocal shortcuts depends on the network size according to a power-law. We also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes.     

Finite size scaling of the spontaneous symmetry breaking model of X-chromosome inactivation

X-Chromosome inactivation is the process whereby one of the two X-chromosomes in female cells is silenced to prevent the cell producing too much of any X-linked proteins and RNA. The proposed blocking-factor mechanism of X-inactivation is not well understood and hence is the subject of much current research. In this paper we investigated the nature of the phase transition predicted to exist in the spontaneous symmetry breaking model of X-inactivation proposed by Nicodemi and Prisco [Mario Nicodemi, Antonella Prisco, Symmetry breaking model for x-chromosome inactivation, Phs. Rev. Lett. 98 (2007) 108104]. Finite size effects were investigated by using an on lattice Monte Carlo simulation. From the scaling it is concluded that the transition is in general abrupt. The critical temperature of the system was determined to be 1.68±0.01E₀/k_B in the thermodynamic limit when the concentration C=0.025 blocking-factors per lattice site.