Power-law Characteristics Research Articles

Properties of asymmetrically evolved community networks

This paper studies a simple asymmetrically evolved community network with a combination of preferential attachment and random properties. An important issue about community networks is to discover the different utility increments of two nodes, where the utility is introduced to investigate the asymmetrical effect of connecting two nodes. On the other hand, the connection of two nodes in community networks can be classified as two nodes belonging to the same or to different communities. The simulation results show that the model can reproduce a power-law utility distribution , which can be obtained by using mean-field approximation methods. Furthermore, the model exhibits exponential behaviour with respect to small values of a parameter denoting the random effect in our model at the low-utility region and a power-law feature with respect to big values of this parameter at the high-utility region, which is in good agreement with theoretical analysis. This kind of community network can reproduce a unique utility distribution by theoretical and numerical analysis.

Quantum stirring in a one-dimensional Bose gas

We propose quantum stirring with a laser beam as a probe of superfluidity in a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles crosses over at a critical velocity from a constant at low velocities to a characteristic power law at high velocities. The critical velocity depends on the size of the ring and vanishes in the thermodynamic limit. Details of this cross-over depend on the interaction strength and on the coupling between the stirring beam and the bosons. Our results are relevant for ongoing experiments on ring-trapped Bose-Einstein condensates.

PMOS breakdown effects on digital circuits – Modeling and analysis

The degradations in the pMOS device due to gate oxide breakdown introduced by voltage stress were investigated experimentally. The stress-induced shifts in gate leakage and I– V characteristics were presented. A combined Verilog-A and sub-circuit model was first time introduced and employed to simulate the pMOS breakdown behaviors. The Verilog-A model can accurately simulate the power law characteristics of breakdown gate leakage current with a fractional coefficient. With the developed model, the simulated results and the measurements have good agreements. The traditional logic circuits, such as the inverter and the latch, have been investigated through Cadence simulations with the improved models. The latch suffers from the gate oxide breakdown significantly. The NULL Convention Logic (NCL) circuit has also been examined and analyzed systematically. The results showed substitute degradations due to the pMOS gate oxide breakdown.

Fragment size distributions from the dynamic fragmentation of brittle solids

Abstract Experimental and theoretical size distributions resulting from dynamic fragmentation are briefly surveyed. The power-law character unique to brittle solids is contrasted to fragment distributions of other materials. The catastrophic fracture of competent brittle solids is shown to have close parallels to hydrodynamic turbulence in fluids. Ideas that emerge from the physical similarities suggest methods for extending an earlier energy-based theory of dynamic fragmentation. Features of this theory are compared with limited fragmentation data for brittle solids.

User Behavior and IM Topology Analysis

The use of Instant Messaging, or IM, has become widely adopted in private and corporate communication. They can provide instant, multi-directed and multi-types of communications which make the message spreading in IM different from those in WWW, Blog and email systems. Groups have great impacts on message spreading in IM. The research demonstrates the power law distribution of groups in MSN with parameter γ ranging from 0.76 to 1.22. Based on an online survey, IM user behavior is analyzed from the aspects of message sending/receiving and contacts maintaining. According to the results, degree distribution of users has a peak value and doesn't present power law character. This may indicate that social networks should be a prospective direction for the research on IM topology.

Steady Shear Response of Carbon Nanotube Networks Dispersed in Poly(ethylene oxide)

The response of fractal networks of dispersed single walled carbon nanotubes in poly(ethylene oxide) to continuous constant-rate shear flow is examined as functions of shear rate and nanotube concentration. The steady shear viscosity values are strong functions of shear rate and follow a power-law shear-thinning character, while the nanotube concentration dependence of the viscosity (at a fixed shear rate) is somewhat weaker than the scaling of the equilibrium modulus values. For dispersions with nanotube concentrations corresponding to the semidilute regime, the stress response to constant-rate continuous shear from rest demonstrates a stress maximum that decays to a steady value at long times. The stress maximum and steady shear behavior can be reconciled in terms of the changing structure at the mesoscale for the fractal networks. On the other hand, the transient development of the stress during the start-up experiments can be qualitatively reconciled in the context of a cluster dynamics model.

Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps

Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/f power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.

CO-OCCURRENCE NETWORK OF REUTERS NEWS

Networks describe various complex natural systems including social systems. We investigate the social network of co-occurrence in Reuters-21578 corpus, which consists of news articles that appeared in the Reuters newswire in 1987. People are represented as vertices and two persons are connected if they co-occur in the same article. The network has small-world features with power-law degree distribution. The network is disconnected and the component size distribution has power-law characteristics. Community detection on a degree-reduced network provides meaningful communities. An edge-reduced network, which contains only the strong ties has a star topology. "Importance" of persons are investigated. The network is the situation in 1987. After 20 years, a better judgment on the importance of the people can be done. A number of ranking algorithms, including Citation count and PageRank, are used to assign ranks to vertices. The ranks given by the algorithms are compared against how well a person is represented in Wikipedia. We find up to medium level Spearman's rank correlations. A noteworthy finding is that PageRank consistently performed worse than the other algorithms. We analyze this further and find reasons.

Magnetic, thermal, and electronic properties of iron-antimony filled skutteruditesMFe4Sb12(M=Na,K,Ca,Sr,Ba,La,Yb)

The magnetic susceptibility, field-dependent heat capacity, and electrical transport properties (resistivity and Hall effect) are investigated for filled skutterudites $M{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$ with $M=\mathrm{Na}$, K, Ca, Sr, Ba, Yb, and La. The specific heat ${c}_{p}(T)$ reveals linear terms $\ensuremath{\gamma}$ ranging from $100\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}200\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}\phantom{\rule{0.2em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$. An Einstein term contributing to ${c}_{p}(T)$ is analyzed and discussed in connection with thermal vibrations of the cations $M$. The Einstein temperatures ${\ensuremath{\Theta}}_{E}=70--105\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are compared with values derived from atomic displacement parameters obtained by x-ray diffraction and other methods. Deviations of the amplitude and frequency of the Einstein term from the expected values are discussed. The paramagnetic susceptibility and the magnetic ground state varies systematically with the cation charge. While $\mathrm{Na}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$ and $\mathrm{K}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$ are nearly half-metallic weak itinerant ferromagnets with ${T}_{C}\ensuremath{\approx}80\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, $\mathrm{Ca}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$, $\mathrm{Sr}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$, $\mathrm{Ba}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$, and $\mathrm{Yb}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$ are nearly ferromagnetic metals with a high Sommerfeld-Wilson ratio and strong ferromagnetic spin fluctuations. $\mathrm{La}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$ is paramagnetic with predominantly antiferromagnetic fluctuations. The decrease of the low-temperature specific heat with magnetic field is investigated. A large positive magnetoresistance is observed for both ferromagnetic and nearly ferromagnetic compounds, while that of the La compound is small. Size and temperature dependence of the Hall coefficient points to a compensation of hole and electron carriers. The temperature dependence of the resistivity displays different characteristic power laws and an anomaly around $80\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. These observations can be explained by details of the electronic structure. A systematic variation of the properties with charge transfer from the cation $M$ to the $[{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}]$ polyanion is recognized.

Double power laws in income and wealth distributions

Close examination of wealth distributions reveal the existence of two distinct power law regimes. The Pareto exponents of the super-rich, identified, for example in rich lists such as provided by Forbes, are smaller than the Pareto exponents obtained for top earners in income data sets. Our extension of the Slanina model of wealth is able to reproduce these double power law features.

Studies of structural, thermal and electrical behavior of polymer nanocomposite electrolytes

Structural, thermal and electrical behavior of polymer-clay nanocomposite electrolytes consisting of polymer (polyethylene oxide (PEO)) and NaI as salt with different concentrations of organically modified Na + montmorillonite (DMMT) filler have been investigated. The formation of nanocomposites and changes in the structural properties of the materials were investigated by X-ray diffraction (XRD) analysis. Complex impedance analysis shows the existence of bulk and material-electrode interface properties of the composites. The relative dielectric constant (er) decreases with increase in frequency in the low frequency region whereas frequency independent behavior is observed in the high frequency region. The electrical modulus representation shows a loss feature in the imaginary component. The relaxation associated with this feature shows a stretched exponential decay. Studies of frequency dependence of dielectric and modulus formalism suggest that the ionic and polymer segmental motion are strongly coupled manifeasting as peak in the modulus (M) spectra with no corresponding feature in dielectric spectra. The frequency dependence of ac (alternating current) conductivity obeys Jon- scher power law feature in the high frequency region, where as the low frequency dispersion indicating the presence of electrode polarization effect in the materials.

Influence of user requirement behaviors on internet collective dynamics

The complex network dynamics of the Internet is mainly influenced by user requirement behaviors, and can be statistic in time series. A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions and small-world phenomena. This paper analyzed the empirical collective behavior of user requirements in a region, and discovered that the frequency and the in-degree distributions of bipartite networks constructed by user visiting web sites follows the power-law, and the exponent is between 1.7 and 1.8. A novel two-tier model, the virtual resource networks (VRN) and physics topology networks (PTN), is proposed to study the influences on the Internet collective behaviors. The mapping process mechanisens of VRN to PTN simulates how the dynamic behaviors of resource network influence the internet physics topology networks. The power-law characteristics of VRN can bring forth the result that the phase transition critical point moves left and network performance is more incapable. The distributed mapping process of VRN to PTN was constructed for the small subset with the high degree nodes, then the phase transition critical point of PTN moves right and the network performance is improved obviously.

Feedback Trading and Intermittent Market Turbulence

This paper studies the potential for complex asset return dynamics in a high-frequency, non-fundamental feedback trading model. Price adjustment is driven by the time-varying price impact of net orderflow. In tranquil times feedback trading has no impact on the price level. Given feedback trading intensities, as asset liquidity declines the market progressively becomes stressed and turbulent. Returns and absolute returns persistence are found to display power-law features, and episodes of turbulence are intermittent.

Reconsidering the significance of genomic word frequencies

By conventional wisdom, a feature that occurs too often or too rarely in a genome can indicate a functional element. To infer functionality from frequency, it is crucial to precisely characterize occurrences in randomly evolving DNA. We find that the frequency of oligonucleotides in a genomic sequence follows primarily a Pareto-lognormal distribution, which encapsulates lognormal and power-law features found across all known genomes. Such a distribution could be the result of completely random evolution by a copying process. Our characterization of the entire frequency distribution of genomic words opens a way to a more accurate reasoning about their over- and underrepresentation in genomic sequences.

Characterization of the chemical degradation of hyaluronic acid during chemical gelation in the presence of different cross-linker agents

Dynamic light scattering (DLS) and rheological experiments have been performed on semidilute aqueous hyaluronic acid (HA) solutions during the chemical cross-linking process with a water-soluble carbodiimide (WSC) to produce a hydrogel. The formation and destruction of the gel are characterized. The results suggest that the gel is cross-linked via ester linkages and at later stage in the process, the omnipresent hydrolysis of interpolymer ester linkages and glycosidic bonds prevails, leading to disruption of the gel. The process of forming and breaking the gel is affected by the cross-linker concentration and pH. The cross-linking of HA with WSC in the presence of l-lysine methyl ester produced a gel with a longer time of gelation and the degradation of the gel was prolonged because of the more stable amide bond formation as the cross-link. By using the Ugi multicomponent condensation reaction, interpolymer cross-linking occurs via the formation of amide linkages and a stable gel evolves, which is only slightly degraded over an extended time window. DLS measurements on HA solutions with WSC show the emergence of a long-time power-law tail in the correlation functions at conditions both before and beyond the viscosity maximum. At a late stage in the gel-breakage regime, the power-law profile of the decay disappears and the long-time tail of the correlation function can be portrayed by a stretched exponential. The findings indicate that the power-law feature is associated with the confinement of chain dynamics and anomalous diffusion in the system. At later times, the connectivity is lost due to fragmentation of the network, and the long-time stretched exponential decay in the correlation function reflects the relaxation of clusters of various sizes.

Recent Progress on the Analysis of Power-law Features in Complex Cellular Networks

Complex interactions between different kinds of bio-molecules and essential nutrients are responsible for cellular functions. Rapid advances in theoretical modeling and experimental analyses have shown that drastically different biological and non-biological networks share a common architecture. That is, the probability that a selected node in the network has exactly k edges decays as a power-law. This finding has definitely opened an intense research and debate on the origin and implications of this ubiquitous pattern. In this review, we describe the recent progress on the emergence of power-law distributions in cellular networks. We first show the internal characteristics of the observed complex networks uncovered using graph theory. We then briefly review some works that have significantly contributed to the theoretical analysis of cellular networks and systems, from metabolic and protein networks to gene expression profiles. This prevalent topology observed in so many diverse biological systems suggests the existence of generic laws and organizing principles behind the cellular networks.

Gravitational Stability of Circumnuclear Disks in Elliptical Galaxies

A significant fraction of nearby elliptical galaxies are known to have high-density gas disks in their circumnuclear (CN) region (0.1 to a few kpc). Yet ellipticals, especially luminous ones, show little sign of recent star formation. To investigate the possible cause of the dearth of star formation in these systems, we study the gravitational stability of CN gas disks embedded within the gravitational potentials of both the stellar bulge component and the central massive black hole (BH) in elliptical galaxies. We find that CN disks in higher mass galaxies are generally more stable than those in lower mass galaxies, because higher mass galaxies tend to have more massive BHs and more centrally concentrated stellar density profiles. We also consider the case in which the central stellar density profile has a core, which is often observed for ellipticals whose total stellar mass is higher than about 1011 M☉. Such a cored stellar density profile leads to more unstable CN disks than the power-law stellar density profile characteristic of less massive galaxies. However, the more massive BHs in high-mass galaxies act to stabilize the CN disk. Our results demonstrate that the gravitational potentials of both the central BH and the stellar component should be taken into account when studying the properties of CN disks, as their stability is sensitive to both the BH mass and the stellar density profile. Our results could explain the observed trend that less luminous elliptical galaxies have a greater tendency to exhibit ongoing star formation than giant ellipticals.

PowerTrust: A Robust and Scalable Reputation System for Trusted Peer-to-Peer Computing

Peer-to-Peer (P2P) reputation systems are essential to evaluate the trustworthiness of participating peers and to combat the selfish, dishonest, and malicious peer behaviors. The system collects locally-generated peer feedbacks and aggregates them to yield the global reputation scores. Surprisingly, most previous work ignored the distribution of peer feedbacks. We use a trust overlay network (TON) to model the trust relationships among peers. After examining the eBay transaction trace of over 10,000 users, we discover a power-law distribution in user feedbacks. Our mathematical analysis justifies that power-law distribution is applicable to any dynamically growing P2P systems, either structured or unstructured. We develop a robust and scalable P2P reputation system, PowerTrust, to leverage the power-law feedback characteristics. The PowerTrust system dynamically selects small number of power nodes that are most reputable using a distributed ranking mechanism. By using a look-ahead random walk strategy and leveraging the power nodes, PowerTrust significantly improves in global reputation accuracy and aggregation speed. PowerTrust is adaptable to dynamics in peer joining and leaving and robust to disturbance by malicious peers. Through P2P network simulation experiments, we find significant performance gains in using PowerTrust. This power-law guided reputation system design proves to achieve high query success rate in P2P file-sharing applications. The system also reduces the total job makespan and failure rate in large-scale, parameter-sweeping P2P Grid applications.

Preparation and analysis of single-phase Pb(Mn 1/2Nb 1/2)O 3

Single-phase polycrystalline ceramic sample of Pb(Mn 1/2Nb 1/2)O 3 has been prepared through a standard solid-state reaction method. A preliminary structural analysis indicates tetragonal crystal structure. The surface morphology examined through scanning electron microscope (SEM) confirmed single-phase polycrystalline texture of the material in close agreement with the X-ray diffraction (XRD) observation. Electrical properties of the material, investigated using complex impedance spectroscopy (CIS) technique have revealed the presence of both the bulk (grain) and grain-boundary contribution to the overall electrical response. It has been modeled, according to the bricklayer model, as a cascading of parallel combination of the resistive and capacitive elements. Impedance spectrum clearly provides evidence of temperature dependent electrical relaxation in the material occurring at a unique frequency for each temperature. The bulk resistance ( R b) and grain-boundary resistance ( R gb) show strong temperature dependence and conductivity ( σ dc) variation obeys Arrhenius behaviour. The conductivity spectrum has been observed to follow the Jonscher's universal power law feature: σ( ω) = σ dc + Aω n .

Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: Application to polymer melts

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades.