Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling

We study the synchronization transition in the Kuramoto model by considering a unidirectional coupling with a chain structure. The microscopic clustering features are characterized in the system. We identify several clustering patterns for the long-time evolution of the effective frequencies and reveal the phase transition between them. Theoretically, the recursive approach is developed in order to obtain analytical insights; the essential bifurcation schemes of the clustering patterns are clarified and the phase diagram is illustrated in order to depict the various phase transitions of the system. Furthermore, these recursive theories can be extended to a larger system. Our theoretical analysis is in agreement with the numerical simulations and can aid in understanding the clustering patterns in the Kuramoto model with a general structure.     

Small-world network effect in competing Glauber- and Kawasaki-type dynamics

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.Received: 11 October 2003, Published online: 30 January 2004PACS: 89.75.-k Complex systems - 64.60.Ht Dynamic critical phenomena - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 64.60.Fr Equilibrium properties near critical points, critical exponents     

Quantum phase transitions and vortex dynamics in superconducting networks

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of low-capacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) superconductor–insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum–vortex experiments and theoretical treatments of their quantum dynamics.     

Complete phase diagram of DNA unzipping: eye, Y fork, and triple point

We study the unzipping of double stranded DNA by applying a pulling force at a fraction s (0< or =s < or =1) from the anchored end. From exact analytical and numerical results, the complete phase diagram is presented. The phase diagram shows a strong ensemble dependence for various values of s. In addition, we show the existence of an eye phase and a triple point.     

Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interaction that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.     

Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies

The well-known Ising model used in statistical physics was adapted to a social dynamics context to simulate the adoption of a technological innovation. The model explicitly combines (a) an individual’s perception of the advantages of an innovation and (b) social influence from members of the decision-maker’s social network. The micro-level adoption dynamics are embedded into an agent-based model that allows exploration of macro-level patterns of technology diffusion throughout systems with different configurations (number and distributions of early adopters, social network topologies). In the present work we carry out many numerical simulations. We find that when the gap between the individual’s perception of the options is high, the adoption speed increases if the dispersion of early adopters grows. Another test was based on changing the network topology by means of stochastic connections to a common opinion reference (hub), which resulted in an increment in the adoption speed. Finally, we performed a simulation of competition between options for both regular and small world networks.     

表面催化反应模型中关联噪声诱导非平衡相变

建立含有关联噪声的双分子-单分子(DM)表面催化反应延迟反馈模型,该模型能同时显示一级和二级非平衡动力学相变,即在一级和二级非平衡动力学相变之间的反应窗口展现.讨论双分子在DM延迟反馈模型中两种吸附机制,即局域和随机吸附模型.研究结果表明:1)外部噪声及两噪声关联性致使反应窗口的宽度收缩;2)内部噪声对非平衡动力学相变行为的影响依赖两噪声关联性,即当两噪声负关联,内部噪声致使反应窗口的宽度变宽;而当两噪声正关联时,内部噪声致使反应窗口的宽度收缩;3)关联噪声致使反应窗口变化对DM模型中一级和二级非平衡动力学相变研究具有重要的科学意义.     

Artificial gauge fields for the Bose-Hubbard model on a checkerboard superlattice and extended Bose-Hubbard model

We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid-alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.     

Anti-parity-time symmetric phase transition in diffusive systems

Parity-time (PT) symmetry/anti-parity-time (APT) symmetry in non-Hermitian systems reveal profound physics andspawn intriguing effects. Recently, it has been introduced into diffusive systems together with the concept of exceptionalpoints (EPs) from quantum mechanics and the wave systems. With the aid of convection, we can generate complex thermalconductivity and imitate various wavelike dynamics in heat transfer, where heat flow can be “stopped” or moving against thebackground motion. Non-Hermitian diffusive systems offer us a new platform to investigate the heat wave manipulation.In this review, we first introduce the construction of APT symmetry in a simple double-channel toy model. Then we showthe phase transition around the EP. Finally, we extend the double-channel model to the four-channel one for showing thehigh-order EP and the associated phase transition. In a general conclusion, the phase difference of adjacent channels isalways static in the APT symmetric phase, while it dynamically evolves or oscillates when the APT symmetry is broken.     

Multicritical dynamical phase diagrams of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling in an oscillating field

We study, within a mean-field approach, the stationary states of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling under the presence of a time-varying (sinusoidal) magnetic field. We employ the Glauber-type stochastic dynamics to construct set of dynamic equations of motion. The behavior of the time dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as functions of the reduced temperature are investigated. The dynamic phase transition points are calculated and phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The dynamical transition from one regime to the other can be of first- or second order depending on the region in the phase diagram. According to the values of the crystal field interaction or single-ion anisotropy constant and biquadratic exchange constant, we find 20 fundamental types of phase diagrams which exhibit many dynamic critical points, such as tricritical points, zero-temperature critical points, double critical end points, critical end point, triple point and multicritical point. Moreover, besides a disordered and ordered phases, seven coexistence phase regions exist in the system.     

Kinetic theory of situated agents applied to pedestrian flow in a corridor

A situated agent-based model for simulation of pedestrian flow in a corridor is presented. In this model, pedestrians choose their paths freely and make decisions based on local criteria for solving collision conflicts. The crowd consists of multiple walking agents equipped with a function of perception as well as a competitive rule-based strategy that enables pedestrians to reach free access areas. Pedestrians in our model are autonomous entities capable of perceiving and making decisions. They apply socially accepted conventions, such as avoidance rules, as well as individual preferences such as the use of specific exit points, or the execution of eventual comfort turns resulting in spontaneous changes of walking speed. Periodic boundary conditions were considered in order to determine the density-average walking speed, and the density-average activity with respect to specific parameters: comfort angle turn and frequency of angle turn of walking agents. The main contribution of this work is an agent-based model where each pedestrian is represented as an autonomous agent. At the same time the pedestrian crowd dynamics is framed by the kinetic theory of biological systems.     

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase transition is studied.By analysing the microscopic behaviour of the traffic flow,we obtain analytical results on the phase transition dynamics.Our results can describe the detailed time evolution of the system during phase transition,while they provide good approximation for the numerical simulation data.These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.     

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Spontaneous synchronisation is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronisation. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre stage of research in the field of non-linear dynamics and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronisation phenomenon it exhibits, we summarise recent results on the study of a generalised Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalised model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalised Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.     

Delocalization in one-dimensional tight-binding models with fractal disorder

In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states based on the normalized localization length by controlling the correlation and the disorder strength of the potential. In addition, the transition of the diffusive property of wavepacket dynamics is shown around the critical point.     

Notes on Black Hole Phase Transitions

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios or mechanisms by which these transitions could take place. We begin with a review of the thermodynamics of a black hole system and emphasize that the phase transition is driven by the large entropy of the black hole horizon. Our first theme is illustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz–Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and antivortex topological defects. Finally, we compare the black hole phase transition to another transition driven by an (exponentially) increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory the Hagedorn transition is linked by the Maldacena conjecture to the Hawking–Page black hole phase transition in Anti-de Sitter (AdS) space, as observed by Witten. Thus, the dynamics of the Hagedorn transition may yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within the dynamics of classical string systems. Our third theme points to carrying out a full nonperturbative and nonequilibrium analysis of the large N behavior of classical SU(N) gauge theories to understand its Hagadorn transition. By invoking the Maldacena conjecture we can then gain valuable insight into black hole phase transitions in AdS space.     

The quantum compass chain in a transverse magnetic field

We study the magnetic behaviors of a spin-1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the field-induced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Ising-type phase transition happens in a finite field. In another region, we have identified two quantum phase transitions (QPT)s in the ground state magnetic phase diagram. These quantum phase transitions belong to the universality class of the commensurate-incommensurate phase transition. We also present a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. In particular, we show that the intermediate state (h _c1 < h < h _c2) is gapful, describing the spin-flop phase.     

Deceleration in advance in the Nagel-Schreckenberg traffic flow model

Based on the Nagel-Schreckenberg model, we study the impact of deceleration in advance on the dynamics of traffic flow. In the process of deceleration in advance, the effect of reaction delay and the effect of expectation are considered respectively. The traffic flow properties are studied by analyzing the fundamental diagram, spatio-temporal patterns, distance headway distribution and car accidents. The simulation results show that reaction delay brings complex traffic flow patterns and expectation makes the serious car accidents rarely happen.     

Expanding the thermodynamical potential and analysis of the possible phase diagram of deconfinement in the FL model

Deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

The Improved Subregular Model and the Phase Diagram of a Binary System

In thia paper an improved subregular model is proposed. Using the thermodynamic theory the equations describing liquid-solid phase equilibrium curve are obtained. For some typical phase diagrams of a binary system we give their predictive criteria of the phase diagram type. We enumerate 4 binary alkali halide systems, their phase diagrams are calculated respectively, this improved model is tested. The results calculated show that the agreement between the theoretical phase diagram and its corresponding experimental points is good.