Exponent Of Distribution Research Articles

Analysis of topology and routing strategy of container shipping network on “Maritime Silk Road”

In this paper, 706 ports and 2306 container liner routes along the Maritime Silk Road from June to December in 2017 were selected as the sample data of the "Maritime Silk Road" container shipping network. By constructing the network feature set to determine the type of network, argue that the "Maritime Silk Road" shipping network belongs to the scale network and analyze its topological characteristics. By calculating the power law exponent of the network degree distribution, it is concluded that the network belongs to the Barabási-Albert (BA) network. Based on the theory of BA scale network performance improvement, the core parameters of the network are optimized by designing the simulation experiment under different scenarios, and the optimal strategy of improving the capacity of the network is explored. The experimental results show that the congestion of the Maritime Silk Road network is affected by the network node capacity and the network routing strategy. There are different optimal parameter configurations under different conditions. The research results are importance for the "Maritime Silk Road" shipping network’s development.

The principle of least effort and Zipf distribution

”Each individual will adopt a course of action that will involve the expenditure of the probably least average of his work.” This statement was named ”the principle of least effort”. The principle of least effort is often known as a ”deterministic description of human behavior”. In this paper, we present a brief introduction of this principle. Applications of the principle in different fields are also summarized. As the principle of least effort is proposed by Zipf, it is also called Zipf’s law. We then discuss the correlation between three widely considered distributions: Zipf distribution, Pareto distribution and probability distribution. With empirical investigations, it is often stated that, most social behaviors are controlled by the pure Zipf’s law that corresponds to the Zipf distribution of exponent -1. We summarily present the discovery of Zipf’s law in different social behaviors. Some empirical studies are also given as examples, verifying that, in most countries, the distribution of city size by population follows Zipf’s law, and the exponent of Zipf distribution of individual income is about -0.5, the same as Zipf predicted in theory.

Heat and mass transfer phenomena due to a rotating non-isothermal wavy disk

Augmentation in the heat transfer rate through wall roughness is a passive technique which is extensively being used in the modern technologies. For rotating disk geometries its implementation is very rare as the literature does not include any significant works on this topic except a very few. The isothermal rotating wavy disk is available in literature (and has been cited in the introduction part) in which the author reported 15% increase in the rate of heat transfer compared to the flat disk case. Such an increased heat transfer rate can further be increased by assuming certain other flow assumptions. An attempt in this regard has been made in order to acquire the increased heat transfer coefficient when the rotating wavy disk temperature is distributed non-uniformly. The disk temperature is assumed to depend on radial distance in the form of power-law function. In the situation of radially increasing disk temperature following a quatratic variations along the radius up to 110% intensification in the overall heat exchange is observed from the hot wavy disk (with two waves and surface roughness ratio equal to 0.1) to the surrounding quiescent air in comparison to an isothermal flat disk. Apart from this, rate of heat transfer from the wavy disk has also been estimated for a very wide range of Prandtl number (10-2 to 104) in this study. In the current analysis some threshold values of the power-law exponent of the disk temperature distribution have also been captured for which the heat transfer is seized. The invariant threshold value (n∗=-2) of the flat disk is observed to change for a non-flat disk case. However, this variation is found to be small for a variety of fluids. Due to the analogy between convective heat transfer and mass transfer phenomena the obtained findings of this study are two fold as they also characterize the mass transfer rate from a wavy rotating disk with a uniform distribution of mass at the disk surface.

Gene Expression Is Not Random: Scaling, Long-Range Cross-Dependence, and Fractal Characteristics of Gene Regulatory Networks.

Gene expression is a vital process through which cells react to the environment and express functional behavior. Understanding the dynamics of gene expression could prove crucial in unraveling the physical complexities involved in this process. Specifically, understanding the coherent complex structure of transcriptional dynamics is the goal of numerous computational studies aiming to study and finally control cellular processes. Here, we report the scaling properties of gene expression time series in Escherichia coli and Saccharomyces cerevisiae. Unlike previous studies, which report the fractal and long-range dependency of DNA structure, we investigate the individual gene expression dynamics as well as the cross-dependency between them in the context of gene regulatory network. Our results demonstrate that the gene expression time series display fractal and long-range dependence characteristics. In addition, the dynamics between genes and linked transcription factors in gene regulatory networks are also fractal and long-range cross-correlated. The cross-correlation exponents in gene regulatory networks are not unique. The distribution of the cross-correlation exponents of gene regulatory networks for several types of cells can be interpreted as a measure of the complexity of their functional behavior.

Streaming instability of multiple particle species in protoplanetary disks

The radial drift and diffusion of dust particles in protoplanetary disks affect both the opacity and temperature of such disks, as well as the location and timing of planetesimal formation. In this paper, we present results of numerical simulations of particle-gas dynamics in protoplanetary disks that include dust grains with various size distributions. We have considered three scenarios in terms of particle size ranges, one where the Stokes number τs = 10−1−100, one where τs = 10−4−10−1, and finally one where τs = 10−3−100. Moreover, we considered both discrete and continuous distributions in particle size. In accordance with previous works we find in our multispecies simulations that different particle sizes interact via the gas and as a result their dynamics changes compared to the single-species case. The larger species trigger the streaming instability and create turbulence that drives the diffusion of the solid materials. We measured the radial equilibrium velocity of the system and find that the radial drift velocity of the large particles is reduced in the multispecies simulations and that the small particle species move on average outwards. We also varied the steepness of the size distribution, such that the exponent of the solid number density distribution, dN∕da ∝ a−q, is either q = 3 or q = 4. Overall, we find that the steepness of the size distribution and the discrete versus continuous approach have little impact on the results. The level of diffusion and drift rates are mainly dictated by the range of particle sizes. We measured the scale height of the particles and observe that small grains are stirred up well above the sedimented midplane layer where the large particles reside. Our measured diffusion and drift parameters can be used in coagulation models for planet formation as well as to understand relative mixing of the components of primitive meteorites (matrix, chondrules and CAIs) prior to inclusion in their parent bodies.

Quantifying market efficiency of China’s regional carbon market by multifractal detrended analysis

An efficient carbon market is important for mitigating carbon emissions. We investigate the efficiency of Chinese carbon market using Multifractal Detrended Fluctuation Analysis. Data samples are based on the return series of seven pilots in the Chinese carbon market. We find asymmetric distributions of carbon prices and general Hurst exponent in the return series, both of which suggest a lack of efficiency in the carbon markets under study. We then define an inefficiency indicator based on the generalized Hurst exponents, in which a zero value means efficient and a higher value less efficient. The inefficiency values of the carbon markets pilots are all greater than one, indicating ubiquitous inefficiencies among them. But there is evidence that the efficiencies had been slightly improved as the markets developed except for the Tianjin pilot. The efficiency ranking of the pilot markets varies when using different time windows for the analysis. For time scales shorter than a month, the Chongqing pilot generally ranks the highest and the Hubei pilot the lowest; for time scales longer than a month, the Beijing pilot performs the best while Tianjin the worst. Regression results further show that the inefficiency is positively correlated with market activity in the short run while negatively in the long run. Policy suggestions for improving the trading activities are also discussed based on the findings.

Consistency of Hill estimators in a linear preferential attachment model

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Practical analyses on the tail exponent of the power-law degree distribution use the Hill estimator as one of the key summary statistics, whose consistency is justified mostly for iid data. The major goal in this paper is to answer the question whether the Hill estimator is still consistent when applied to non-iid network data. To do this, we first derive the asymptotic behavior of the degree sequence via embedding the degree growth of a fixed node into a birth immigration process. We also need to show the convergence of the tail empirical measure, from which the consistency of Hill estimators is obtained. This step requires checking the concentration of degree counts. We give a proof for a particular linear preferential attachment model and use simulation results as an illustration in other choices of models.

The modeling of anomalous transport in the diffusion-ballistic regime

The anomalous transport of a point-like particle within the disordered heterogeneous medium with accelerating traps was investigated using Monte Carlo simulation within the CTRW model. Outside the traps a particle moves according to the diffusion regime of motion. Inside the traps the ballistic regime takes place. Results of the Monte Carlo simulation shows that the final distribution of particle jumps belongs to the class of the stable distributions which corresponds to the anomalous diffusion regime. It is shown that the characteristic exponent of the stable distribution depends on the trap density and particle velocity inside the traps.

Classification of cryptocurrency coins and tokens by the dynamics of their market capitalizations.

We empirically verify that the market capitalizations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values for the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth and death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrat's Law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being ‘entrenched incumbents’ and tokens as an ‘explosive immature ecosystem’, largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.

The agglomeration phenomenon influence on the scaling law of the scientific collaboration system

This paper presents a scientific collaboration hypernetwork evolution model with adjustable clustering coefficient in which the authors are regarded as nodes and the hyperedges are the cooperative articles. Firstly, we build the scientific cooperation hypernetwork through the real paper data which comes from the database of arxive. The empirical results show that the node's hyperdegree follows the power law distribution, but the hyperedge's node-degree has the exponent distribution. In addition, we establish the scientific collaboration clustering hypernetwork evolution model by employing the Poisson process theory and the continuous method for studying the agglomeration phenomenon of scientific cooperation system. The theoretical analysis shows that the node's hyperdegree distribution has scale-free characteristics. The power index of our model is independent of the clustering coefficient, and the theoretical analyses agree with the conducted numerical simulations. Moreover, our model not only describes the scale-free property, but also depicts the phenomenon of agglomeration. Both the properties are usually coexist in the scientific cooperation, our model is more actual.

Interphase human chromosome exhibits out of equilibrium glassy dynamics

Fingerprints of the three-dimensional organization of genomes have emerged using advances in Hi-C and imaging techniques. However, genome dynamics is poorly understood. Here, we create the chromosome copolymer model (CCM) by representing chromosomes as a copolymer with two epigenetic loci types corresponding to euchromatin and heterochromatin. Using novel clustering techniques, we establish quantitatively that the simulated contact maps and topologically associating domains (TADs) for chromosomes 5 and 10 and those inferred from Hi-C experiments are in good agreement. Chromatin exhibits glassy dynamics with coherent motion on micron scale. The broad distribution of the diffusion exponents of the individual loci, which quantitatively agrees with experiments, is suggestive of highly heterogeneous dynamics. This is reflected in the cell-to-cell variations in the contact maps. Chromosome organization is hierarchical, involving the formation of chromosome droplets (CDs) on genomic scale, coinciding with the TAD size, followed by coalescence of the CDs, reminiscent of Ostwald ripening.

Iso-height lines of multifractal etched silicon rough surfaces

Morphology of etched silicon wafers during anisotropic etching process is investigated utilizing the geometrical exponents of iso-height contour lines. The images obtained from field emission scanning electron microscopy show pyramidal microstructures which disappear in large time scales and porous silicon structures are formed. The morphology of these microstructures is investigated utilizing the data obtained from atomic force microscopy and contour loop analysis. The results show that the anisotropic etching breaks the up-down symmetry in the height fluctuations of etched silicon surfaces. Area of the contour loops increases by enhancement of pyramids sizes. Fractal dimensions of the loops decrease at the beginning of etching process. Distributions of loops and geometrical exponents of iso-height lines in different etching times are determined. The results indicate that in spite of asymmetry in the height fluctuations, the hyperscaling relation and Zipf's law are verified for the multi-affine silicon surfaces during etching process.

Spatiotemporal Organization of Correlated Local Activity within Global Avalanches in Slowly Driven Interfaces

We study the jerky response of slowly driven fronts in disordered media, just above the depinning transition. We focus on how spatially disconnected clusters of internally correlated activity lead to large-scale velocity fluctuations in the form of global avalanches and identify three different ways in which local activity clusters may organize within a global avalanche, depending on the distance to criticality. Ouranalysis provides new scaling relations between the power-law exponents of the statistical distributions of sizes and durations of local bursts and global avalanches. Fluid fronts of imbibition in heterogeneous media are taken as a case study to validate these scaling relations.

Localization of disordered harmonic chain with long-range correlation

In the previous paper (Yamada, (2018)), we investigated localization properties of one-dimensional disordered electronic system with long-range correlation generated by modified Bernoulli (MB) map. In the present paper, we report localization properties of phonon in disordered harmonic chains generated by the MB map. Here we show that Lyapunov exponent becomes positive definite for almost all frequencies ω except ω=0, and the B−dependence changes to exponential decrease for B > 2, where B is a correlation parameter of the MB map. The distribution of the Lyapunov exponent of the phonon amplitude has a slow convergence, different from that of uncorrelated disordered systems obeying a normal central-limit theorem. Moreover, we calculate the phonon dynamics in the MB chains. We show that the time-dependence of spread in the phonon amplitude and energy wave packet changes from that in the disordered chain to that in the periodic one, as the correlation parameter B increases.

Mode-III interfacial crack propagation in heterogeneous media.

We monitor optically the propagation of a slow interfacial mode III crack along a heterogeneous weak interface and compare it to mode I loading. Pinning and depinning of the front on local toughness asperities within the process zone are the main mechanisms for fracture roughening. Geometrical properties of the fracture fronts are derived in the framework of self-affine scale invariance and Family-Vicsek scaling. We characterize the small and large scale roughness exponents ζ_{-}=0.6 and ζ_{+}=0.35, the growth exponent at large scale β_{+}=0.58, and the power-law exponent of the local velocity distribution of the fracture fronts, η=2.55. All these analyzed properties are similar to those previously observed for mode I interfacial fractures. We also observe a common power-law decay of the probability distribution function of avalanche area. We finally observe that amplitude of front fluctuations, local rupture velocity correlation in time, and larger size of events highlight more dynamically unstable behavior of mode III crack ruptures.

Chaotic characteristics of pseudoplastic fluid induced by 6PBT impeller in a stirred vessel

Xanthan gum solutions with different mass concentrations were used to study the chaotic characteristics induced by the impeller of perturbed six-bent-blade turbine (6PBT) in a stirred vessel. Based on the velocity time series obtained by the experiment of particle image velocimetry (PIV), with the software MATLAB (R2016a), the distributions of the largest Lyapunov exponent (LLE) and Kolmogorov entropy (K entropy) of the system, as two important parameters for characterizing the chaotic degree, were investigated respectively. Results showed that both of the LLE and K entropy increased with the increasing speed at the beginning. As the speed was up to 200 r·min− 1, the two parameters reached the maximal values meanwhile, corresponding to 0.535 and 0.834, respectively, which indicated that the chaotic degree of the flow field was up to the highest level. When the speed was increased further, both of the LLE and K entropy decreased on the contrary, which meant that the chaotic degree was decreasing. It was also observed that the chaotic characteristics of flow field were hardly affected by the fluid rheology and the detecting positions. The research results will enhance the understanding of the chaotic mixing mechanism and provide a theoretical reference for optimizing impeller structure.

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller (HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257–311 (2004)). By analyzing the distribution of the finite-time Lyapunov exponent (FTLE) along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence

The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed chaos, this statistics is here analyzed assuming that the entropy associated with the fluid kinematic state is maximum. The distribution of the local Lyapunov exponents results in an unsymmetrical uniform function in a proper interval of variation. From this PDF, we determine the relationship between average and maximum Lyapunov exponents and the longitudinal velocity correlation function. This link, which in turn leads to the closure of von Kármán–Howarth and Corrsin equations, agrees with results of previous works, supporting the proposed PDF calculation, at least for the purposes of the energy cascade main effect estimation. Furthermore, through the property that the Lyapunov vectors tend to align the direction of the maximum growth rate of trajectories distance, we obtain the link between maximum and average Lyapunov exponents in line with the previous results. To validate the proposed theoretical results, we present different numerical simulations whose results justify the hypotheses of the present analysis.

Near-infrared scattering as a dust diagnostic

Context. Regarding the evolution of dust grains from diffuse regions of space to dense molecular cloud cores, many questions remain open. Scattering at near-infrared wavelengths, or “cloudshine”, can provide information on cloud structure, dust properties, and the radiation field that is complementary to mid-infrared “coreshine” and observations of dust emission at longer wavelengths. Aims. We examine the possibility of using near-infrared scattering to constrain the local radiation field and the dust properties, the scattering and absorption efficiency, the size distribution of the grains, and the maximum grain size. Methods. We use radiative transfer modelling to examine the constraints provided by the J, H, and K bands in combination with mid-infrared surface brightness at 3.6 μm. We use spherical one-dimensional and elliptical three-dimensional cloud models to study the observable effects of different grain size distributions with varying absorption and scattering properties. As an example, we analyse observations of a molecular cloud in Taurus, TMC-1N. Results. The observed surface brightness ratios of the bands change when the dust properties are changed. However, even a change of ±10% in the surface brightness of one band changes the estimated power-law exponent of the size distribution γ by up to ~30% and the estimated strength of the radiation field KISRF by up to ~60%. The maximum grain size Amax and γ are always strongly anti-correlated. For example, overestimating the surface brightness by 10% changes the estimated radiation field strength by ~20% and the exponent of the size distribution by ~15%. The analysis of our synthetic observations indicates that the relative uncertainty of the parameter distributions are on average Amax, γ ~ 25%, and the deviation between the estimated and correct values ΔQ < 15%. For the TMC-1N observations, a maximum grain size Amax > 1.5μm and a size distribution with γ > 4.0 have high probability. The mass weighted average grain size is ⟨am⟩ = 0.113μm. Conclusions. We show that scattered infrared light can be used to derive meaningful limits for the dust parameters. However, errors in the surface brightness data can result in considerable uncertainties on the derived parameters.

Acoustic emission signatures prior to snow failure

ABSTRACTSnow slab avalanches are caused by cracks forming and propagating in a weak snow layer below a cohesive slab. The gradual damage process leading to the formation of the initial failure within the weak layer (WL) is still not entirely understood. To this end, we designed a novel test apparatus that allows performing loading experiments with large snow samples (0.25 m2) including a WL at different loading rates and simultaneously monitoring the acoustic emissions (AE) response. By analyzing the AE generated by micro-cracking, we studied the evolution of the damage process preceding snow failure. At fast loading rates, the exponent of the AE energy distribution (b-value) gradually changed, and both the energy rate and the inverse waiting time increased exponentially with increasing load. These changes in AE signature indicate a transition from small to large events and an acceleration of the damage processes leading to brittle failure. For the experiments at slow loading rate, these changes in the AE signature were not or only partially present, even if the sample failed, indicating a different evolution of the damage process. The observed characteristics in AE response provide new insights on how to model snow failure as a critical phenomenon.