Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.     

Collective motion of active particles in environmental noise

We study the collective motion of active particles in environmental noise, where the environmental noise is caused by noise particles randomly diffusing in two-dimensional space. We show that active particles in a noisy environment can self organize into three typical phases: polar liquid, band, and disordered gas states. In our model, the transition between band and disordered gas states is discontinuous. Giant number fluctuation is observed in the polar liquid phase. We also compare our results with the Vicsek model and show that the interaction with noise particles can stabilize the band state to very low noise condition. This band structure could recruit most of the active particles in the system, which greatly enhances the coherence of the system. Our findings of complex collective behaviors in environmental noise help us to understand how individuals modify their self-organization by environmental factors, which may further contribute to improving the design of collective migration and navigation strategies.     

Onset of collective and cohesive motion

We study the onset of collective motion, with and without cohesion, of groups of noisy self-propelled particles interacting locally. We find that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. [Phys. Rev. Lett. 75, 1226 (1995)]] for which a nontrivial critical point was previously advocated. We also show that cohesion is always lost near onset, as a result of the interplay of density, velocity, and shape fluctuations.     

自驱动杆状粒子在半柔性弹性环中的集体行为

在生物体系的活性系统中,杆状粒子在弹性半柔性边界中的受限行为极为常见.本文研究了二维情况下,自驱动杆状粒子受限在半柔性弹性环中的集体行为.改变系统的粒子数及噪声强度,系统显示明显的自驱吸附有序态、无序态及中间的过渡态.通过表征弹性环内部粒子的径向极性大小和空间分布的非球度性对这些状态进行了刻画.进一步对弹性环中心附近粒子密度的分析,发现环中心气态粒子分布存在一个与边界高密度区域共存的饱和平台,出现类似吸附转变的粒子分布.在过渡区间,体系内存在较大的涨落会导致弹性环出现异常形变.非对称的粒子分布对弹性环整体的迁移具有重要贡献,系统在过渡区间能获得相对较强的定向迁移.     

Observation of the condensation of a gas of interacting grains

We consider an ensemble of grains that interact through a dipole-dipole interaction. A granular gas is formed by the vertical motion of a piston at the bottom boundary of the system. The interaction between the grains is controlled by an horizontally applied magnetic field. When the speed of the piston is decreased, we observe a transition from a low density to a high density phase. When the interaction between grains is weak, the transition is continuous. It is discontinuous for stronger interaction. The phase diagram displays strong similarities with the ones observed for usual equilibrium phase transitions.     

Phase order in one-dimensional piecewise linear discontinuous map

The phase order in a one-dimensional(1 D) piecewise linear discontinuous map is investigated. The striking feature is that the phase order may be ordered or disordered in multi-band chaotic regimes, in contrast to the ordered phase in continuous systems. We carried out an analysis to illuminate the underlying mechanism for the emergence of the disordered phase in multi-band chaotic regimes, and proved that the phase order is sensitive to the density distribution of the trajectories of the attractors. The scaling behavior of the net direction phase at a transition point is observed. The analytical proof of this scaling relation is obtained. Both the numerical and analytical results show that the exponent is 1, which is controlled by the feature of the map independent on whether the system is continuous or discontinuous. It extends the universality of the scaling behavior to systems with discontinuity. The result in this work is important to understanding the property of chaotic motion in discontinuous systems.     

随机外磁场作用下Ising自旋体系的随机共振

通过采用数字仿真手段，研究了经平均场处理的Ising自旋体系在弱确定性周期外场和随机外场（噪声场）混合驱动下的动态响应行为.着重考察了不同强度混合驱动外场作用下，Is ing自旋体系的非平衡动态转变所表现出区别于单纯确定性周期场作用下的新特征——随机 共振.选定体系非平衡动态转变的动态序参量Q为表征参量，系统模拟计算了混合驱动外场在多种参数组合下体系的动态响应特征，高场低温下的非连续动态转变和低场高温下的连续动态转变.模拟计算表明在适当混合驱动外场的作用下，Ising自旋体系具有随机共振现象，并诱发形成非 关键词： Ising自旋体系 随机共振 动态相变 对称性     

Opinion dynamics on directed small-world networks

In this paper, we investigate the self-affirmation effect on formation of public opinion in a directed small-world social network. The system presents a non-equilibrium phase transition from a consensus state to a disordered state with coexistence of opinions. The dynamical behaviors are very sensitive to the density of long-range-directed interactions and the strength of self-affirmation. When the long-range-directed interactions are sparse and individual generally does not insist on his/her opinion, the system will display a continuous phase transition, in the opposite case with strong self-affirmation and dense long-range-directed interactions, the system does not display a phase transition. Between those two extreme cases, the system undergoes a discontinuous phase transition.     

Spin-1 Bose–Hubbard model with two- and three-body interactions

We investigated the ground state of spin-1 bosons interacting under local two- and three-body interactions in one dimension by means of the density matrix renormalization group method. We found that the even–odd asymmetry will be obtained or not depending on the relative values of the two- and three-body interactions. The Mott insulator lobes are spin isotropic, the first showing a dimerized pattern and the second being composed of singlets. The three-body interactions disfavor a longitudinal polar superfluid and a quantum phase transition to a transverse polar superfluid occurs, which could be continuous or discontinuous.     

Jamming percolation and glass transitions in lattice models

A new class of lattice gas models with trivial interactions but constrained dynamics is introduced. These models are proven to exhibit a dynamical glass transition: above a critical density rhoc ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and time scales diverge as exp[C(rhoc-rho)-mu]. Dynamic correlations display two-step relaxation similar to glass formers and jamming systems.     

Dynamical quorum sensing and synchronization in collections of excitable and oscillatory catalytic particles

We present experimental studies of interacting excitable and oscillatory catalytic particles in well-stirred and spatially distributed systems. A number of distinct paths to synchronized oscillatory behavior are described. We present an example of a Kuramoto type transition in a well-stirred system with a collective rhythm emerging on increasing the number density of oscillatory particles. Groups of spatially distributed oscillatory particles become entrained to a common frequency by organizing centers. Quorum sensing type transitions are found in populations of globally and locally coupled excitable particles, with a sharp transition from steady state to fully synchronized behavior at a critical density or group size.     

Incommensurate-commensurate phase transitions in an anisotropic antiferromagnetic model on triangular lattice

An anisotropic antiferromagnetic model on a triangular lattice with competing interactions is investigated by the cluster transfer-matrix method. A phase diagram with ferrimagnetic, incommensurate, and disordered phases is found. Three order parameters are introduced. At commensurate-incommensurate and incommensurate-disorder phase transition lines two of them change in continuous and one in discontinuous way.     

Gregarious versus individualistic behavior in Vicsek swarms and the onset of first-order phase transitions

The standard Vicsek model (SVM) is a minimal non-equilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven continuous order–disorder phase transition. In this work, we extend the SVM by introducing a parameter α$\alpha$ that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%$10\%$) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the α$\alpha$-extended model preserves the O(n)$O\left(n\right)$ symmetry and the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first order), an intriguing manifestation of the richness of the non-equilibrium flocking/swarming phenomenon.     

Collective transport in locally asymmetric periodic structures

In this paper we give an overview of the cooperative effects in fluctuation driven transport arising from the interaction of a large number of particles. (i) First, we study a model with finite-sized, overdamped Brownian particles interacting via hard-core repulsion. Computer simulations and theoretical calculations reveal a number of novel cooperative transport phenomena in this system, including the reversal of direction of the net current as the particle density is increased, and a very strong and complex dependence of the average velocity on both the size and the average distance of the particles. (ii) Next, we consider the cooperation of a collection of motors rigidly attached to a backbone. This system possesses dynamical phase transition allowing spontaneous directed motion even if the system is spatially symmetric. (iii) Finally, we report on an experimental investigation exploring the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits complex collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. (c) 1998 American Institute of Physics.     

Phase behavior and collective excitations of the Morse ring chain

Using primarily numerical methods we study clustering processes and collective excitations in a one-dimensional ring chain. The ring chain is constituted by N identical point particles with next neighbors interacting via nonlinear Morse springs. If the system is coupled to a heat bath (Gaussian white noise and viscous friction), then depending on the particle density and the bath temperature different phase-like states can be distinguished. This will be illustrated by means of numerically calculated phase diagrams. In order to identify collective excitations activated by the heat bath we calculate the spectrum of the normalized dynamical structure factor (SDF). Our numerical results show that the transition regions between different phase-like states are typically characterized by a 1/f-type SDF spectrum, reflecting the fact that near critical points correlations on all length and time scales become important. In the last part of the paper we also discuss a non-equilibrium effect, which occurs if an additional nonlinearly velocity-dependent force is included in the equations of motions. In particular it will be shown that such additional dissipative effects may stabilize cluster configurations.Received: 27 June 2003, Published online: 2 October 2003PACS: 05.70.Fh Phase transitions: general studies - 05.70.Ln Non-equilibrium and irreversible processes - 05.40.-a Fluctuation phenomena, random processes, noise and Brownian motion     

虚拟网络行为对互联网整体特性的影响

虚拟网络是一种依赖Internet基础设施所提供的传输能力，但又具有独立拓扑结构和信息传递规则的应用层网络行为逻辑网络.提出了耦合虚拟网络行为与物理节点的抽象模型，对一类典型的虚拟网络逻辑拓扑给互联网整体特性带来的影响进行了分析.研究表明在虚拟网络作用下，节点数据包排队长度存在相变特性，但相变临界点比对规则网络发生了明显左移，网络性能相对恶化.当数据包注入速率小于相变临界速率时，节点数据包排队长度不相关或短程相关；在接近临界速率处，节点数据包排队长度长程相关，幂指数H增大，网络获得更强的长程相关性.同时，在注入速率大于或等于临界速率时，虚拟网络行为使网络呈现出一致的长程相关特性.     

活性Janus粒子体系中的定向运动涌现行为

本文使用过阻尼郎之万方程动力学模拟方法模拟了二维体系中活性Janus粒子的群体动力学行为. 体系随着粒子密度的增加，存在一个活性粒子的定向运动涌现行为. 此现象在无各向异性相互作用或者无活性驱动的体系中无法观察到. 另外涌现行为发生的临界转变密度会随着活性大小和各向异性相互作用强度的增大而减小，且通过调节活性大小和各向异性相互作用强度大小可以控制体系不同状态的转变. 最后借助动力学理论分析，重复出了模拟结果的基本特征. 结果论证了单个粒子层次上的各向异性相互作用足以导致活性体系进入稳定的群体定向运动.     

Dynamic compensation temperatures in a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field

We study the existence of dynamic compensation temperatures in the mixed spin-1 and spin-3/2 Ising ferrimagnetic system Hamiltonian with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice. We employ the Glauber transitions rates to construct the mean-field dynamic equations. We investigate the time dependence of an average sublattice magnetizations, the thermal behavior of the dynamic sublattice magnetizations and the total magnetization. From these studies, we find the phases in the system, and characterize the nature (continuous or discontinuous) of transitions as well as obtain the dynamic phase transition (DPT) points and the dynamic compensation temperatures. We also present dynamic phase diagrams, including the compensation temperatures, in the five different planes. A comparison is made with the results of the available mixed spin Ising systems.     

Collective motion of microspheres in suspensions observed by phase-mode dynamic ultrasound scattering technique

Compared with a nano-sized particle, dynamics of a micron-sized particle in a liquid is often associated with sedimentation (or floating) due to its relatively large mass. The motion of more than two particles is dominated by the hydrodynamic interactions, which are known to persist over a fairly long range, e.g., several millimeters, in suspensions. The particle size may be obtained from the dynamic ultrasound scattering (DSS) technique by the analysis of velocity fluctuations, whose origin is believed to take root in the particle-number fluctuations among temporally formed domains involving collective motion of particles with a certain cut-off length. In this study, such collective particle motion in highly turbid solutions was visualized by means of the phase-mode DSS technique with a single element transducer. Quantitative agreement between the velocity fluctuations obtained by the phase- and conventional amplitude-mode analyses was confirmed, followed by examination of the concentration and the particle size dependences on the dynamic structures induced by the long-ranged interactions. It was found that the phase mode-DSS was a promising method to evaluate the time-dependent structures of the micro-particles in highly turbid suspensions.     

Liquid-liquid critical point: an analytical approach

Theoretical simulations and experimental studies have showed that many systems (like liquid metals) can exhibit two phase transitions: gas-liquid and liquid-liquid. Consequently the fluid phase of these systems presents two critical points, namely the usual gas-liquid (G-L) critical point and the liquid-liquid critical point that results from a phase transition between two liquids of different densities: a low density liquid (LDL) and a high density liquid (HDL). The van der Waals theory for simple fluids [Phys. Rev. E 50, 2913 (1994)] is based on taking a system with purely repulsive forces as a reference, is able to describe two stable first-order phase transitions between fluids of different densities. The particles in our system interact via a total pair potential, which splits into a repulsive V_R and a density-dependent attractive V_A part.