SPECIAL TOPIC—Statistical physics and complex systems
编者按：
从 20 世纪中叶至今, 复杂系统研究迅速发展, 成为了引人注目并具有广泛应用的新领域. 复杂系统要么具有结构的复杂性, 要么具有演化的复杂性, 在多数情况下二者兼具. 不同于传统物理学通常处理的规则介质, 许多复杂系统具有复杂结构, 近年来受到极大关注的复杂网络结构就是其中最典型的代表. 同时复杂系统也可表现为演化行为的多样性和复杂性. 即便系统结构并不复杂, 系统中的非线性相互作用可能产生复杂的演化行为, 包括: 形形色色的不稳定性; 丰富的斑图动力学; 各种各样的自组织、涌现及进化行为等等.物理学从一开始就深深进入了复杂系统研究领域, 其中统计物理无疑是研究和理解复杂系统最主要的工具.
复杂系统研究紧密联系着当前科学发展的两大趋势. 一是不同学科的交叉和融合. 近年来物理学和数学越来越深入地进入其他学科领域, 特别是生物学和社会科学, 使这些传统大多以定性描述为主的学科开始了以数据为依托的定量研究, 而这些交叉领域研究几乎都处于复杂系统的研究范畴. 二是大数据科学的迅猛发展和应用. 基于互联网和物联网数据采集和存储技术的突飞猛进, 现在可利用的数据量正在爆炸性的增长. 这些数据中包含了极大量对自然和社会的有用信息, 能合理利用会带来巨大并不断增长的财富. 但产生这些数据的系统和可能被这些数据所影响的系统, 往往都是复杂系统, 其行为具有高度的不可预测性,使这笔财富并不容易获取. 深入研究复杂系统, 发展有效的数据分析手段是成功使用这笔潜在财富的关键和核心.
要研究和处理所有以上困难和问题, 统计物理是强有力的手段. 长期以来统计物理在处理各种不可确切预见的轨道和状态中发展了丰富的思想、方法和技术手段, 这些必然将会和已经为复杂系统的研究提供了强有力的工具. 同时复杂系统由于结构和行为的大量新特点又为统计物理的创新发展提供强大推动.
本专题邀请了在领域前沿活跃工作的专家学者撰写了 18 篇研究和综述论文, 介绍了作者们在该领域的最新进展和成果. 内容包括对物理领域以及生物、经济、工业和其他交叉领域的复杂系统的研究; 既有宏观经典系统的讨论, 也有量子系统复杂行为的探索; 有论文讨论了复杂系统行为的基础统计理论, 也有论文分析了复杂系统演化的同步化、斑图动力学及其调控. 专题中多篇论文涉及复杂网络问题: 有关于网络结构形成和稳定性分析, 也有利用网络产生的数据分析网络结构, 网络上信息传播, 网络结构下人文活动, 经济演化, 社会运行规律等等. 统计物理和复杂系统是一个内涵宏大的领域, 专题论文都是作者兴趣所在的课题研究成果和心得, 只涉及领域中的点点滴滴. 但我们期望专题中介绍的成果能加强国内学者在这一领域的交流, 吸引对该领域有兴趣的青年学者和学生进来钻研, 推动我国在这一领域的研究水平更上一层.
2020, 69 (8): 080502.
doi: 10.7498/aps.69.20191968
Abstract +
Rhythmic behaviors, i.e. temporally periodic oscillations in a system, can be ubiquitously found in nature. Interactions among various rhythms can lead to self-organized behaviors and synchronizations. This mechanism is also responsible for many phenomena such as nonlinear waves, spatiotemporal patterns, and collective behaviors in populations emerging in complex systems. Mathematically different oscillations are described by limit-cycle oscillators (pacemakers) with different intrinsic frequencies, and the synchrony of these units can be described by the dynamics of coupled oscillators. Studies of microscopic dynamics reveal that the emergence of synchronization manifests itself as the dimension reduction of phase space, indicating that synchrony can be considered as no-equilibrium phase transition and can be described in terms of order parameters. The emergence of order parameters can be theoretically explored based on the synergetic theory, central manifold theorem and statistical physics. In this paper, we discuss the order-parameter theory of synchronization in terms of statistical physics and set up the dynamical equations of order parameters. We also apply this theory to studying the nonlinear dynamics and bifurcation of order parameters in several typical coupled oscillator systems.
2020, 69 (8): 080503.
doi: 10.7498/aps.69.20191934
Abstract +
Spiral waves are ubiquitous in diverse physical, chemical, and biological systems. Periodic external fields, such as polarized electric fields, especially circularly polarized electric fields which possess rotation symmetry may have significant effects on spiral wave dynamics. In this paper, control of spiral waves in excitable media under polarized electric fields is reviewed, including resonant drift, synchronization, chiral symmetry breaking, stabilization of multiarmed spiral waves, spiral waves in subexcitable media, control of scroll wave turbulence, unpinning of spiral waves in cardiac tissues, control of spiral wave turbulence in cardiac tissues, etc.
2020, 69 (8): 080505.
doi: 10.7498/aps.69.20200450
Abstract +
Casimir force in quantum electrodynamics is the representation of zero point energy of vacuum. Depending on the type of fluctuation medium, generalized Casimir force covers a wide spectrum of topics in physics, such as, quantum, critical, Goldstone mode, and non-equilibrium Casimir force. In general, long range correlated fluctuations and constraints are two conditions for generating the Casimir force. In this paper, through a survey of the development of Casimir physics, we discuss several types of Casimir forces and several regularization methods. We end the paper with an outlook for the further development of Casimir physics in the future.
2020, 69 (8): 084203.
doi: 10.7498/aps.69.20191721
Abstract +
Pedestrian tracking is a hotspot and a difficult topic in computer vision research. Through the tracking of pedestrians in video materials, trajectories can be extracted to support the analysis of individual or collected behavior dynamics. In this review, we first discuss the difference between pedestrian tracking and pedestrian detection. Then we summarize the development of traditional tracking algorithms and deep learning-based tracking algorithms, and introduce classic pedestrian dynamic models. In the end, typical applications, including intelligent monitoring, congestion analysis, and anomaly detection are introduced systematically. With the rising use of big data and deep learning techniques in the area of computer vision, the research on pedestrian tracking has made a leap forward, which can support more accurate, timely extraction of behavior patterns and then to facilitate large-scale dynamic analysis of individual or crowd behavior.
2020, 69 (8): 088902.
doi: 10.7498/aps.69.20191973
Abstract +
In recent years, the study of partial synchronization of coupled oscillators in complex networks has attracted great attention. The underlying reason is both the extensive existence of the patterns of partial synchronization in brain network and their close relationship to brain functions of cognition and memory. In this paper, we briefly review the research progress in this field. According to the researches by different groups, we classify them as three types, i.e. chimera state, remote synchronization, and clustering synchronization. We mainly discuss the conditions of these three states, as well as their models, detections, and their applications in biology. We discuss the relationship among the three types of states and give some outlooks for future studies.
2020, 69 (8): 088903.
doi: 10.7498/aps.69.20191686
Abstract +
Many spatial mobility of people, goods and information, such as human travel, population migration, commodity trade, information communication, social interaction and scientific cooperation, follow a law similar to Newton’s law of universal gravitation. This law, named social gravity law, is that the flow between two locations is directly proportional to the product of the vitality of these two locations, and inversely proportional to a power function of their distance. The gravity model established by analogy with the gravity law has also been widely used to predict trip distribution, population migration, interregional trade flows, etc. But why do many complex social systems have such a simple law? It is an interesting and valuable issue. This paper reviews the research on exploring the roots of the social gravity law from various perspectives, including statistical physics, microeconomics, and game theory.
2020, 69 (8): 088904.
doi: 10.7498/aps.69.20192000
Abstract +
In real life, most of the infrastructure networks closely related to the national economy and people's livelihood do not exist independently, but are interconnected with or dependent on each other, so the multilayer network model is proposed to study the independent complex systems and infrastructures. When the nodes in the multilayer network suffer initial failure or attack, the cascade occurs due to the interaction between the “intra-layer” and “inter-layer”, and the failure can propagate in the network layer and across the layers iteratively, so that the scale of the failures is enlarged gradually. As a result, many multilayer networks are more fragile than single networks. The cascading failure of multilayer network usually brings very serious catastrophes to our society. So, conducting the research on preventing the multilayer network from cascading failure and recovering is of great significance. As far as the prevention of cascading failure is concerned, what are mainly included are the strategies such as the fault detection, the protection of important nodes, the optimization of the coupling method of networks, and the backup of nodes. As for the recovery of multi-layer network, included mainly are the strategies such as common boundary node recovery, the idle connected link recovery, the link addition, the priority recovery of important nodes, the topology perturbation, and the repairing of localized attack and adaptive link.
2020, 69 (8): 088906.
doi: 10.7498/aps.69.20200001
Abstract +
Open complex systems far from equilibrium widely exist in the nature and the fields of society and technology, which are the main research objects of complexity science. Through the exchange of energy and material with the outside world, complex systems can form a variety of internal structures, orders and laws by self-organization behaviors, which poses an arduous challenge to the understanding and predicting complex systems. With the improvement of experimental technology and the progress of science and technology, the data reflecting the mechanism of various complex systems are increasing exponentially, thereby providing new opportunities for studying complex systems. Revealing the structures and dynamics of complex systems from the measured data is an inverse problem in the field of physics, which is the premise of understanding complex systems, predicting the evolution of system state, and regulating system state. However, it is very difficult to solve this inverse problem due to the diversity and complexity of complex system. Therefore, we need to fully mine the hidden knowledge and deep mechanism in the data with the help of interdisciplinary integration. In this paper we briefly review the research results of complex system in recent years, especially the reconstruction of complex network structures, hoping to inspire the innovation to the inverse problem of complex systems. Meanwhile, we hope that researchers in different fields can pay much attention to the inverse problems of complex systems, promote the cross and integration of nature, society, economy, biology and technology, and solve the scientific problems that we are facing.
2020, 69 (8): 088907.
doi: 10.7498/aps.69.20191954
Abstract +
With the development of power electronic technology and requirement for clean energy, the traditional power systems which are dominated by synchronous generators are gradually changing into the power-electronic-based power systems with diversified power electronic equipment. The power systems are facing a great revolution in their primary equipment, and this has not happened in the past one hundred years. In recent years, with great increasing penetration of power electronic devices into power grids, the large-scale blackouts caused by power electronic devices have been reported, which seriously threatens the safe and stable operation of power systems. Under the above background, in this paper we first introduce several methods of analyzing the traditional power system transient stability from the equal area criterion for the single machine infinite bus system to several Lyapunov function based direct methods for multi-machine systems. Then we introduce some of our recent work on the nonlinear modeling and analysis of a key component of power-electronic-based power systems, voltage source converter (VSC), and propose a multiple machine system model including power electronic equipment and traditional synchronous machines. Finally, we illustrate the transient characteristics of the power electronic devices, and summarize the basic problems and challenges for the transient stability of power-electronic-based power systems. We hope that these basic problems in power-electronic-based power system dynamics including nonlinearity, multi-time-scale, and complexity could arouse the general interest of researchers in the fields of complex systems and statistical mechanics.
2020, 69 (8): 088908.
doi: 10.7498/aps.69.20191776
Abstract +
With the rapid development of mobile communication and Internet technologies, online live streaming has gradually become popular for information communication and entertainment in the new media environment. Live streaming has been widely used in teaching, reality show, E-sports games and events, brand marketing and other aspects. With the active participation of millions of streamers and hundreds of millions of viewers, massive online crowd behavior activity data are generated, which offers rich experimental scenarios for large-scale crowd behavior dynamics research, live streaming channel recommendation and online community evolution. In this paper, we summarize the relevant research literature of live streaming, and review current studies from a comprehensive list of aspects: workload pattern, viewers and streamers behavior, community network discovery and analysis, etc. We summarize the temporal and spatial patterns of live streaming platform workload, heavy tailed effect of large-scale crowd behavior in live streaming platform, etc. We believe that the future work on live streaming can be directed in the examination of formation and evolution mechanism of various community networks formed by large-scale users, as well as the recommendation and detection of live streaming content.
2020, 69 (8): 080201.
doi: 10.7498/aps.69.20191584
Abstract +
Rank aggregation aims to combine multiple rank lists into a single one, which has wide applications in recommender systems, link prediction, metasearch, proposal selection, and so on. Some existing studies have summarized and compared different rank aggregation algorithms. However, most of them cover only a few algorithms, the data used to test algorithms do not have a clear statistical property, and the metric used to quantify the aggregated results has certain limitations. Moreover, different algorithms all claim to be superior to existing ones when proposed, the baseline algorithms, the testing samples, and the application scenario are all different from case to case. Therefore, it is still unclear which algorithm is better for a particular task. Here we review nine rank aggregation algorithms and compare their performances in aggregating a small number of long rank lists. We assume an algorithm to generate different types of rank lists with known statistical properties and cause a more reliable metric to quantify the aggregation results. We find that despite the simplicity of heuristic algorithms, they work pretty well when the rank lists are full and have high similarities. In some cases, they can reach or even surpass the optimization-based algorithms in performance. The number of ties in the list will reduce the quality of the consensus rank and increase fluctuations. The quality of aggregated rank changes non-monotonically with the number of rank lists that need to be combined. Overall, the algorithm FAST outperforms all others in three different rank types, which can sufficiently complete the task of aggregating a small number of long rank lists.
2020, 69 (8): 080203.
doi: 10.7498/aps.69.20200170
Abstract +
Brain is a typical complex system with characteristics such as self-adaptation, self-organization, and multistability. The activity of the default mode network (DMN), a crucial functional subnetwork of the human brain in resting state, obeys typical non-equilibrium statistical mechanical processes in which the system continually switches among multiple metastable states. Revealing the underlying dynamical mechanism of these processes has important scientific significance and clinical application prospects. In this paper, according to the blood oxygen level dependent (BOLD) signals obtained from functional magnetic resonance imaging (fMRI), we build an energy landscape, disconnectivity graph and transition network to explore the non-equilibrium processes of DMN switching among different attractors in resting state. Taking the activities of high-level visual and auditory cortices for examples, we verify the intimate relationship between the dynamics of DMN and the activity modes of these external brain regions, through comparing the distributions in state space and the algorithms such as XGBoost and deep neural networks. In addition, we analyze the interaction between various DMN regions in the resting state by using the techniques such as compressive-sensing-based partial correlation and convergence cross mapping. The results in this paper may presnt new insights into revealing the dynamics of the intrinsic non-equilibrium processes of brain in resting state, and putting forward clinically significant biomarkers for brain dysfunction from the viewpoint of dynamics.
2020, 69 (8): 080506.
doi: 10.7498/aps.69.20200360
Abstract +
Quantum scar is an intriguing phenomenon in quantum or wave dynamics that the wavefunction takes an exceptionally large value around an unstable periodic orbit. It has attracted much attention and advances the understanding of the semiclassical quantization. Most of previous researches involving quantum scars focus on hard-wall quantum billiards. Here we investigate the quantum billiard with a smooth confinement potential which possesses complex classical dynamics. We demonstrate that the semiclassical quantization approach works well for both the stable and unstable classical periodic orbit, besides the fact that the shape of the orbits varies as the energy increases or even the stability switches. The recurrence rule of the quantum scars in this complex solf-wall billiard differs from that of the hard-wall nonrelativistic quantum billiard, such as being equally spaced in energy instead of being equally spaced in the square root of energy. These results implement the previous knowledge and may be used for understanding the measurements of density of states and transport properties in two-dimensional electron systems with random long-range impurities.
2020, 69 (8): 080507.
doi: 10.7498/aps.69.20200561
Abstract +
In biological active systems there commonly exist active rod-like particles under elastic confinement. Here in this work, we study the collective behavior of self-propelled rods confined in an elastic semi-flexible ring. By changing the density of particles and noise level in the system, It is clearly shown that the system has an ordered absorbing phase-separated state of self-propelled rods and the transition to a disordered state as well. The radial polar order parameter and asphericity parameter are characterized to distinguish these states. The results show that the gas density near the central region of the elastic confinement has a saturated gas density that co-exists with the absorbed liquid crystal state at the elastic boundary. In the crossover region, the system suffers an abnormal fluctuation that drives the deformation of the elastic ring. The non-symmetric distribution of particles in the transition region contributes significantly to the collective translocation of the elastic ring.
2020, 69 (8): 084701.
doi: 10.7498/aps.69.20200362
Abstract +
Polymer microparticles with various compositions and morphologies have recently received much attention. Their surface-roughness significantly affects the physical and chemical properties, which especially counts in regulating the interaction between biological materials and living systems. In this paper, we design a polystyrene microsphere with controllable surface textures. At first, a microfluidic device is used to generate droplets with uniform size containing the hydrophobic polymer and a co-surfactant. During the volatilization of the organic solvent, the shrinking droplets appear to be unstable at the interface. Thus, the surface area increases spontaneously, and microspheres with wrinkles on the surface are obtained after being solidified. The results show that tuning the concentration of the co-surfactant and the rate of solvent evaporation can effectively regulate the surface roughness of the microspheres. Circulating tumor cell capture experiments reveal that this textured structure can facilitate the cell adhesion and increase the number of the captured cells. These features indicate that the coarse microspheres possess a promising application prospect in the field of biomedical analysis.
2020, 69 (8): 086102.
doi: 10.7498/aps.69.20200332
Abstract +
In the B4 phase of bent-core liquid crystals, smectic layers of tilted achiral bent-core molecules are chiral and polar, which, driven by intra-layer structural mismatch, eventually twist into helical nanofilaments. We design a NOBOW/hexadecane organogel system, which is different from traditional organogel system, and the studied organogels show reversible gel-liquid transitions under temperature cycles. At high temperature, the NOBOW molecules dissolve in hexadecane and the storage modulus and viscous modulus show typical liquid characteristics. At low temperature, the mobility of NOBOW molecules decreases and the storage modulus of the organogels increases as the temperature decreases. We conduct a rheology experiment to systematically investigate the viscoelasticity of the organogel to understand the property of the organogel and develop the application in soft matter. The viscoelastic studies of the organogels reveal that the helical nanofilaments are internally strained and their 3D networks are relatively stiff, which provides an in-depth insight into the properties of the organogels and paves the way for their applications in soft matter.
2020, 69 (8): 088901.
doi: 10.7498/aps.69.20191817
Abstract +
Link prediction in complex networks has attracted much attention in recent years and most of work focuses on proposing more accurate prediction algorithms. In fact, “how difficultly the target network can be predicted” can be regarded as an important attribute of the network itself. In this paper it is intended to explain and characterize the link predictability of the network from the perspective of spectrum. By analyzing the characteristic spectrum of the network, we propose the network link predictability index. Through calculating the index, it is possible to learn how difficultly the target network can be predicted before choosing algorithm, and to solve the problem whether the network is unpredictable or the algorithm is inappropriate. The results are useful for the selecting and matching the complex network and link prediction algorithms.
2020, 69 (8): 088905.
doi: 10.7498/aps.69.20191970
Abstract +
In this paper, we propose a new type of relativistic regional innovation index by using the international patent application data. Based on the super-linear relationship between regional innovation and economic development, the new index can eliminate the influence of economic development level on innovation capabilities, and can effectively achieve the comparison of innovation capabilities among economies at different economic development levels. This new index is quite simple, and points out a series of new findings that are sharply different from the traditional cognitive phenomena, e.g. the index shows that the technological innovation capabilities of mainland China are among the highest in the world in 1980s. Moreover, the use of this new index not only can efficiently explain the economic growth of countries in the world at a higher level, but also find that there is a novel 20-year business cycle in the correlation between the index and economic growth rate. These results show that the index, as a simple single indicator, can achieve a higher degree of explanatory ability with minimal data dependence. This new index not only repositions the innovation capacity of world’s economies, but also provides a new insight into an in-depth understanding of the relationship between innovation and economic development, and implies the development potential and application space such a kind of relativistic economic indicator.
