Generating multi-scaling networks with two types of vertices

A variety of scale-free networks have been created since the pioneer work by Barabási and Albert [Science 286 (1999) 509]. Most of these models are homogeneous since they are composed of the same kind of nodes. In the realistic world, however, elements (nodes or vertices) in the network may play different roles or have different functions. In this work, we develop an alternative way of vertex classification other than the ordinary modularity method by introducing two types of vertices. The interaction between two neighbor vertices is dependent on their types. It is found that the vertex degree exhibits a multi-scaling law distribution with the scaling exponent of each types of vertex adjustable. This network model may exhibit some interesting properties concerning the dynamical processes on it.     

Effects of the screening breakdown in the diffusion-limited aggregation model

Several models based on the diffusion-limited aggregation (DLA) model were proposed and their scaling properties explored by computational and theoretical approaches. In this paper, we consider a new extension of the on-lattice DLA model in which the unitary random steps are replaced by random flights of fixed length. This procedure reduces the screening for particle penetration present in the original DLA model and, consequently, generates new pattern classes. The patterns have DLA-like scaling properties at small length of the random flights. However, as the flight size increases, the patterns are initially round and compact but become fractal for sufficiently large clusters. Their radius of gyration and number of particles at the cluster surface scale asymptotically as in the original DLA model. The transition between compact and fractal patterns is characterized by wavelength selection, and 1/k noise was observed far from the transition.Received: 2 March 2004, Published online: 14 December 2004PACS: 05.40.Fb Random walks and Levy flights - 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 05.10.Ln Monte Carlo methods     

Applications of Reflection Amplitudes in Toda-Type Theories

Reflection amplitudes are defined as two-point functions of certain class of conformal field theories where primary fields are given by vertex operators with real couplings. Among these, we consider (Super-) Liouville theory and simply and non-simply laced Toda theories. In this paper we show how to compute the scaling functions of effective central charge for the models perturbed by some primary fields which maintains integrability. This new derivation of the scaling functions are compared with the results from conventional TBA approach and confirms our approach along with other non-perturbative results such as exact expressions of the on-shell masses in terms of the parameters in the action, exact free energies. Another important application of the reflection amplitudes is a computation of one-point functions for the integrable models. Introducing functional relations between the one-point functions in terms of the reflection amplitudes, we obtain explicit expressions for simply-laced and non-simply-laced affine Toda theories. These nonperturbative results are confirmed numerically by comparing the free energies from the scaling functions with exact expressions we obtain from the one-point functions.     

Corrections to finite-size-scaling in two dimensional Potts models

High resolution Monte Carlo simulations are used to examine the finite size behavior of Q-state Potts models in two dimensions. For Q = 3 we find that at the critical point bulk properties are subject to much larger corrections to finite size scaling than were previously realized. For Q = 4 we find that corrections to finite size scaling are subtle and that the multiplicative logarithmic correction is insufficient to correct the dominant terms.     

Topological properties of phylogenetic trees in evolutionary models

The extent to which evolutionary processes affect the shape of phylogenetic trees is an important open question. Analyses of small trees seem to detect non-trivial asymmetries which are usually ascribed to the presence of correlations in speciation rates. Many models used to construct phylogenetic trees have an algorithmic nature and are rarely biologically grounded. In this article, we analyze the topological properties of phylogenetic trees generated by different evolutionary models (populations of RNA sequences and a simple model with inheritance and mutation) and compare them with the trees produced by known uncorrelated models as the backward coalescent, paying special attention to large trees. Our results demonstrate that evolutionary parameters as mutation rate or selection pressure have a weak influence on the scaling behavior of the trees, while the size of phylogenies strongly affects measured scaling exponents. Within statistical errors, the topological properties of phylogenies generated by evolutionary models are compatible with those measured in balanced, uncorrelated trees.     

Fractal patterns of fluid domains for displacement processes in porous media

Percolation invasion displacement of a compressible defender is examined for two cases: when only the smallest accessible site is entered at each step and when all accessible sites less than the size given by a reducing back pressure are entered at each time step. Although the fractions of invading fluid are different, their scaling properties are equivalent. The effect of limited control of a back pressure in a real displacement and the effect of viscosity in a real time displacement are examined. In these cases the scaling properties of a percolation process at breakthrough are removed. As a result, one should expect that realistic displacement models will not have the singular properties usually attributed to percolation processes.     

Modeling network growth with assortative mixing

We propose a model of an underlying mechanism responsible for the formation of assortative mixing in networks between “similar” nodes or vertices based on generic vertex properties. Existing models focus on a particular type of assortative mixing, such as mixing by vertex degree, or present methods of generating a network with certain properties, rather than modeling a mechanism driving assortative mixing during network growth. The motivation is to model assortative mixing by non-topological vertex properties, and the influence of these non-topological properties on network topology. The model is studied in detail for discrete and hierarchical vertex properties, and we use simulations to study the topology of resulting networks. We show that assortative mixing by generic properties directly drives the formation of community structure beyond a threshold assortativity of r ∼0.5, which in turn influences other topological properties. This direct relationship is demonstrated by introducing a new measure to characterise the correlation between assortative mixing and community structure in a network. Additionally, we introduce a novel type of assortative mixing in systems with hierarchical vertex properties, from which a hierarchical community structure is found to result. Electronic supplementary material Supplementary Online Material     

Growth of rough surfaces

The growth of objects with rough surfaces is a common phenomenon. We describe several models used in the study of the temporal evolution of fluctuating interfaces and then we explain the dynamical scaling in this class of growth models with self-affine surfaces. The recent progress in this field is reviewed. Much emphasis is put on roughness properties and in particular on a possible kinetic roughening transition — a nonequilibrium analog of the thermal roughening transition. Both analytical and numerical results for scaling exponents are summarized and indications of a phase transition in some models are discussed.     

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, successfully reproducing the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up proposing new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.     

Distributions and moments of structural properties for percolation clusters

We study numerically and by scaling methods the distributions and moments of several structural properties of percolation clusters in two and three dimensions. The clusters are generated at criticality and properties such as the distribution of the mass as a function of linear size or chemical distance are studied. Our results suggest that the hierarchy of moments can be represented by a single gap exponent. Using a scaling approach, we obtain analytical forms for the different distribution functions which agree very well with the numerical data.     

Atomistic simulation of the transition from atomistic to macroscopic cratering

Using large-scale atomistic simulations, we show that the macroscopic cratering behavior emerges for projectile impacts on Au at projectile sizes between 1000 and 10000 Au atoms at impact velocities comparable to typical meteoroid velocities. In this size regime, we detect a compression of material in Au nanoparticle impacts similar to that observed for hypervelocity macroscopic impacts. The simulated crater volumes agree with the values calculated using the macroscopic crater size scaling law, in spite of a downwards extrapolation over more than 15 orders of magnitude in terms of the impactor volume. The result demonstrates that atomistic simulations can be used as a tool to understand the strength properties of materials in cases where only continuum models have been possible before.     

Scaling and allometry in the building geometries of Greater London

Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal structure. We redress this here by examining scaling relationships in a world city using data on the geometric properties of individual buildings. We first summarise how power laws can be used to approximate the size distributions of buildings, in analogy to city-size distributions which have been widely studied as rank-size and lognormal distributions following Zipf [Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, 1949)] and Gibrat [Les Inégalités économiques (Librarie du Recueil Sirey, Paris, 1931)]. We then extend this analysis to allometric relationships between buildings in terms of their different geometric size properties. We present some preliminary analysis of building heights from the Emporis database which suggests very strong scaling in world cities. The data base for Greater London is then introduced from which we extract 3.6 million buildings whose scaling properties we explore. We examine key allometric relationships between these different properties illustrating how building shape changes according to size, and we extend this analysis to the classification of buildings according to land use types. We conclude with an analysis of two-point correlation functions of building geometries which supports our non-spatial analysis of scaling.     

Vacuum expectation values from fusion of vertex operators

The algebra of fused vertex operators for the ABF model is defined and studied in the free fields approach. Vacuum expectation values of local operators in the scaling theory are reproduced from the matrix elements of the fused vertex operators.     

New method of applying conformal group to quantum fields

Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method(RGM). We start with the renormalization group equation(RGE), in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application,we find out that quite a few interaction vertices are separately invariant under certain transformations(generators) of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.     

Creation of high resolution pattern by nanoscratching

The lithography is a basic microelectronic process which determines properties of fabricated device. The resolution of optical lithography applied nowadays is insufficient for creating high resolution patterns such as gate electrode in transistors. The scaling ability is the major motivation for undertaking experiments to elaborate high resolution lithography techniques. The atomic force microscope (AFM) is commonly used as tool for creation patterns in sub-micrometers resolution. In this paper, the results of simulations of electromagnetic field behavior during passing the gap with a size smaller than the wavelength of the optical lithography light source are presented. Also results of the nanoscratching lithography prepared for various parameters of force that are applied to the tip are summarized.     

Scale properties of sea ice deformation and fracturing

The sea ice cover, which insulates the ocean from the atmosphere, plays a fundamental role in the Earth's climate system. This cover deforms and fractures under the action of winds, ocean currents and thermal stresses. Along with thermodynamics, this deformation and fracturing largely controls the amount of open water within the ice cover and the distribution of ice thickness, two parameters of high climatic importance, especially during fall and winter (no melting). Here we present a scaling analysis of sea ice deformation and fracturing that allows us to characterize the heterogeneity of fracture patterns and of deformation fields, as well as the intermittency of stress records. We discuss the consequences of these scaling properties, particularly for sea ice modelling in global climate models. We show how multifractal scaling laws can be extrapolated to small scales to learn about the nature of the mechanisms that accommodate the deformation. We stress that these scaling properties preclude the use of homogenisation techniques (i.e. the use of mean values) to link different scales, and we discuss how these detailed observations should be used to constrain sea ice dynamics modelling. To cite this article: J. Weiss, D. Marsan, C. R. Physique 5 (2004).     

Scaling properties of geometric parallelization

We present a universal scaling law for all geometrically parallelized computer simulation algorithms. For algorithms with local interaction laws we calculate the scaling exponents for zero and infinite lattice size. The scaling is tested on local (cellular automata, Metropolis Ising) as well as cluster (Swendsen-Wang) algorithms. The practical aspects of the scaling properties lead to a simple recipe for finding the optimum number of processors to be used for the parallel simulation of a particular system.     

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.     

两相流有限穿越可视图演化动力学研究

针对小管径两相流流动特性, 全新优化设计弧形对壁式电导传感器. 通过动态实验在获取传感器测量信号的基础上, 采用有限穿越可视图理论构建对应于不同流型的两相流复杂网络. 通过分析发现, 有限穿越可视图网络异速生长指数和网络平均度值的联合分布可实现对小管径两相流的流型辨识; 有限穿越可视图度分布曲线峰值可有效刻画与泡径大小分布相关的流动物理结构细节特征; 网络平均度值可表征流动结构的宏观特性; 网络异速生长指数对流体动力学复杂性十分敏感, 可揭示不同流型演化过程中的细节演化动力学特性. 两相流测量信号的有限穿越可视图分析为揭示两相流流型的形成及演化动力学机理提供了新途径. 关键词： 两相流 复杂网络 有限穿越可视图 网络异速生长指数