Fluctuations in network dynamics

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding that for each the coupling of the flux fluctuations with the total flux on individual nodes obeys a unique scaling law. We show that the observed scaling can explain the competition between the system's internal collective dynamics and changes in the external environment, allowing us to predict the relevant scaling exponents.     

Separating internal and external dynamics of complex systems

The observable behavior of a complex system reflects the mechanisms governing the internal interactions between the system's components and the effect of external perturbations. Here we show that by capturing the simultaneous activity of several of the system's components we can separate the internal dynamics from the external fluctuations. The method allows us to systematically determine the origin of fluctuations in various real systems, finding that while the Internet and the computer chip have robust internal dynamics, highway and Web traffic are driven by external demand. As multichannel measurements are becoming the norm in most fields, the method could help uncover the collective dynamics of a wide array of complex systems.     

Scaling of fluctuations in traffic on complex networks

We study the scaling of fluctuations with the mean of traffic in complex networks using a model where the arrival and departure of "packets" follow exponential distributions, and the processing capability of nodes is either unlimited or finite. The model presents a wide variety of exponents between 1/2 and 1 for this scaling, revealing their dependence on the few parameters considered, and questioning the existence of universality classes. We also report the experimental scaling of the fluctuations in the Internet for the Abilene backbone network. We found scaling exponents between 0.71 and 0.86 that do not fit with the exponent 1/2 reported in the literature.     

Thermodynamic properties of an alternating-spin (1/2,1) two-leg ladder

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding evidence of orders of magnitude differences in the fluxes of individual nodes. This dynamical inhomogeneity reflects the emergence of localized high flux regions or hot spots, carrying an overwhelming fraction of the networks activity. We find that each system is characterized by a unique scaling law, coupling the flux fluctuations with the total flux on individual nodes, a result of the competition between the systems internal collective dynamics and changes in the external environment. We propose a method to separate these two components, allowing us to predict the relevant scaling exponents. As high fluctuations can lead to dynamical bottlenecks and jamming, these findings have a strong impact on the predictability and failure prevention of complex transportation networks.Received: 25 October 2003, Published online: 17 February 2004PACS: 89.75.-k Complex systems - 89.75.Da Systems obeying scaling laws - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

A Non-Stationary Poisson Model for the Scaling of Urban Traffic Fluctuations

We investigate the traffic flow volume data on the time dependent activity of Beijing＇s urban road network. The couplings between the average flux and the fluctuations on individual links are shown to follow certain scaling laws and yield a wide variety of scaling exponents between 1/2 and 1. To quantitatively explain this interesting phenomenon, a non-stationary Poisson arriving model is proposed. The scaling property is interpreted as the result of the time- variation of the arriving rate of flux over the network, which nicely explicates the effect of aggregation windows, and provides a concise model for the dependence of scaling exponent on the external/internal force ratio.     

Evolution of Chinese airport network

With the rapid development of the economy and the accelerated globalization process, the aviation industry plays a more and more critical role in today’s world, in both developed and developing countries. As the infrastructure of aviation industry, the airport network is one of the most important indicators of economic growth. In this paper, we investigate the evolution of the Chinese airport network (CAN) via complex network theory. It is found that although the topology of CAN has remained steady during the past few years, there are many dynamic switchings inside the network, which have changed the relative importance of airports and airlines. Moreover, we investigate the evolution of traffic flow (passengers and cargoes) on CAN. It is found that the traffic continues to grow in an exponential form and has evident seasonal fluctuations. We also found that cargo traffic and passenger traffic are positively related but the correlations are quite different for different kinds of cities.     

Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless nonidentical case

We theoretically study the synchronization between collective oscillations exhibited by two weakly interacting groups of nonidentical phase oscillators with internal and external global sinusoidal couplings of the groups. Coupled amplitude equations describing the collective oscillations of the oscillator groups are obtained by using the Ott-Antonsen ansatz, and then coupled phase equations for the collective oscillations are derived by phase reduction of the amplitude equations. The collective phase coupling function, which determines the dynamics of macroscopic phase differences between the groups, is calculated analytically. We demonstrate that the groups can exhibit effective antiphase collective synchronization even if the microscopic external coupling between individual oscillator pairs belonging to different groups is in-phase, and similarly effective in-phase collective synchronization in spite of microscopic antiphase external coupling between the groups.     

Building and analyzing the US airport network based on en-route location information

From a complex network perspective, this study sets out two aims around the US airport network (USAN) which is built from en-route location information of domestic flights in the US. First, we analyze the structural properties of the USAN with respect to its binary and weighted graphs, and second we explore the airport patterns, which have wide-ranging implications. Results from the two graphs indicate the following. (1) The USAN exhibits scale-free, small-world and disassortative mixing properties, which are consistent with the mainstream perspectives. Besides, we find (2) a remarkable power relationship between the structural measurements in the binary graph and the traffic measurements in the weighted counterpart, namely degree versus capacity and attraction versus volume. On the other hand, investigation of the airport patterns suggests (3) that all the airports can be classified into four categories based on multiple network metrics, which shows a complete typology of the airports. And it further indicates (4) that there is a subtle relationship between the airport traffic and the geographical constraints as well as the regional socioeconomic indicators.     

Dispersion and scaling of fluctuating vehicles through a sequence of traffic lights

We study the dynamical behavior of vehicles moving with fluctuating speed through a sequence of traffic lights which are controlled by the synchronized strategy. The dynamics of fluctuating vehicular traffic controlled by traffic lights is described in terms of the stochastic nonlinear map. We study two kinds of traffic: case (A) in which vehicles are allowed to pass other vehicles freely and case (B) in which vehicles are inhibited to pass other vehicles. Vehicles move together (without dispersion) for specific values of cycle time, while vehicles extend over the road for other values of cycle time. Then, vehicular traffic exhibits the dispersion. When the dispersion of vehicles occurs, the variance of arrival time shows the scaling behavior. The scaling properties are derived. The scaling form and exponents are discussed by comparing with those of dynamic scaling of rough surface.     

Self-organized structures in a superorganism: do ants “behave” like molecules?

While the striking structures (e.g. nest architecture, trail networks) of insect societies may seem familiar to many of us, the understanding of pattern formation still constitutes a challenging problem. Over the last two decades, self-organization has dramatically changed our view on how collective decision-making and structures may emerge out of a population of ant workers having each their own individuality as well as a limited access to information. A variety of collective behaviour spontaneously outcome from multiple interactions between nestmates, even when there is no directing influence imposed by an external template, a pacemaker or a leader. By focussing this review on foraging structures, we show that ant societies display some properties which are usually considered in physico-chemical systems, as typical signatures of self-organization. We detail the key role played by feed-back loops, fluctuations, number of interacting units and sensitivity to environmental factors in the emergence of a structured collective behaviour. Nonetheless, going beyond simple analogies with non-living self-organized patterns, we stress on the specificities of social structures made of complex living units of which the biological features have been selected throughout the evolution depending on their adaptive value. In particular, we consider the ability of each ant individual to process information about environmental and social parameters, to accordingly tune its interactions with nestmates and ultimately to determine the final pattern emerging at the collective level. We emphasize on the parsimony and simplicity of behavioural rules at the individual level which allow an efficient processing of information, energy and matter within the whole colony.     

Estimating the model-specific uncertainty of aircraft noise calculations

Aircraft noise contours are estimated with model calculations. Due to their impact, e.g., on land use planning, calculations need to be highly accurate, but their uncertainty usually remains unaccounted for. The objective of this study was therefore to quantify the uncertainty of calculated average equivalent continuous sound levels (L_Aeq) of complex scenarios such as yearly air operations, and to establish uncertainty maps. The methodology was developed for the simulation program FLULA2. In a first step, the partial uncertainties of modelling the aircraft as a sound source and of modelling sound propagation were quantified as a function of aircraft type and distance between aircraft and receiver. Then, these uncertainties were combined for individual flights to obtain the uncertainty of the single event level (L_AE) at a specified receiver grid. The average L_Aeq of a scenario results from the combination of the L_AE of many single flights, each of which has its individual uncertainties. In a last step, the uncertainties of all L_AE were therefore combined to the uncertainty of the L_Aeq, accounting also for uncertainties of the number of movements and of prognoses. Uncertainty estimations of FLULA2 calculations for Zurich and Geneva airports revealed that the standard uncertainty of the L_Aeq ranges from 0.5 dB (day) to 1.0 dB (night) for past-time scenarios when using radar data as input, and from 1.0 dB (day) to 1.3 dB (night) for future scenarios, in areas where L_Aeq ⩾ 53 dB (day) and L_Aeq ⩾ 43 dB (night), respectively. Different uncertainty values may result for other models and/or airports, depending on the model sophistication, traffic input data, available sound source data, and airport peculiarities such as the specific aircraft fleet or prevailing departure and arrival procedures. The methodology, while established for FLULA2 on Zurich and Geneva airports, may be applied to other models and/or airports, but the partial uncertainties have to be specifically re-established to account for individual models and underlying sound source data.     

Amplification of intrinsic fluctuations by the Lorenz equations

Macroscopic systems (e.g., hydrodynamics, chemical reactions, electrical circuits, etc.) manifest intrinsic fluctuations of molecular and thermal origin. When the macroscopic dynamics is deterministically chaotic, the intrinsic fluctuations may become amplified by several orders of magnitude. Numerical studies of this phenomenon are presented in detail for the Lorenz model. Amplification to macroscopic scales is exhibited, and quantitative methods (binning and a difference-norm) are presented for measuring macroscopically subliminal amplification effects. In order to test the quality of the numerical results, noise induced chaos is studied around a deterministically nonchaotic state, where the scaling law relating the Lyapunov exponent to noise strength obtained for maps is confirmed for the Lorenz model, a system of ordinary differential equations.     

Correlated dynamics determining x-ray diffuse scattering from a crystalline protein revealed by molecular dynamics simulation

The dynamical origin of the x-ray diffuse scattering by crystals of a protein, Staphylococcal nuclease, is determined using molecular dynamics simulation. A smooth, nearly isotropic scattering shell at originates from equal contributions from correlations in nearest-neighbor water molecule dynamics and from internal protein motions, the latter consisting of -helix pitch and inter--strand fluctuations. Superposed on the shell are intense, three-dimensional scattering features that originate from a very small number of slowly varying (>10 ns) collective motions. The individual three-dimensional features are assigned to specific collective motions in the protein, and some of these explicitly involve potentially functional active-site deformations.     

Noise abatement measures at airports: Contributing factors and mutual dependence

Airports are known to cause noise-related environmental concerns, mostly because significant environmental impact correlated with operation of airports arises from aircraft generated noise. In order to address this concern, many airports have applied a variety of actions that alleviate negative effects of noise i.e. noise abatement measures (NAMs). Although there are similarities between airports applying some of the NAMs, numbers and types of applied measures are quite different among them. This paper focuses on finding statistical evidence to support the hypothesis that there is a significant correlation between applied NAMs and specific characteristics related to airports. To determine the reasons why airports apply NAMs, a logistic regression method was used on the data set for 246 European airports. As predictor variables, five specific characteristics related to airports (number of runways, number of aircraft movements, distance from the city, population of the city it serves, per capita gross domestic product (GDP) of the country an airport is located in), and ten NAMs based on their mutual dependencies were used. The results demonstrate a significant correlation between the applied NAMs and particular airport-related characteristics, but also between NAMs themselves. These findings can be used to determine the likelihood of applying a particular NAM to any airport, based on the characteristics that show a significant correlation with the corresponding NAM.     

Scaling breakdown in flow fluctuations on complex networks

We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of three factors, respectively, of dynamical, topological and statistical nature. In particular, we demonstrate that the existence of a power-law scaling characterizing the flow fluctuations at every node in the network cannot be claimed. We show the validity of this scaling breakdown under quite general topological and dynamical situations by means of different traffic algorithms and by analyzing real data.     

Robust dynamical effects in traffic and chaotic maps on trees

In the dynamic processes on networks collective effects emerge due to the couplings between nodes, where the network structure may play an important role. Interaction along many network links in the nonlinear dynamics may lead to a kind of chaotic collective behavior. Here we study two types of well-defined diffusive dynamics on scale-free trees: traffic of packets as navigated random walks, and chaotic standard maps coupled along the network links. We show that in both cases robust collective dynamic effects appear, which can be measured statistically and related to non-ergodicity of the dynamics on the network. Specifically, we find universal features in the fluctuations of time series and appropriately defined return-time statistics.      

Self-folding mechanics of graphene tearing and peeling from a substrate

Understanding the underlying mechanism in the tearing and peeling processes of graphene is crucial for the further hierarchical design of origami-like folding and kirigami-like cutting of graphene. However, the complex effects among bending moduli, adhesion, interlayer interaction, and local crystal structure during origami-like folding and kirigami-like cutting remain unclear, resulting in challenges to the practical applications of existing theoretical and experimental findings as well as to potential manipulations of graphene in metamaterials and nanodevices. Toward this end, classical molecular dynamics (MD) simulations are performed with synergetic theoretical analysis to explore the tearing and peeling of self-folded graphene from a substrate driven by external force and by thermal activation. It is found that the elastic energy localized at the small folding ridge plays a significant role in the crack trajectory. Due to the extremely small bending modulus of monolayer graphene, its taper angle when pulled by an external force follows a scaling law distinct from that in case of bilayer graphene. With the increase in the initial width of the folding ridge, the self-folded graphene, motivated by thermal fluctuations, can be self-assembled by spontaneous self-tearing and peeling from a substrate. Simultaneously, the scaling law between the taper angle and adhesive energy is independent of the motivations for thermal activation-induced self-assembly and external force tearing, providing effective insights into the underlying physics for graphene-based origami-like folding and kirigami-like cutting.