counting lattice animals a parallel attack a parallel algorithm for the enumeration of isolated connected clusters on a regular lattice is presented the algorithm has been implemented on 17 risc based workstations to calculate the perimeter polynomials for the plane triangular lattice up to clustersizes 21 new data for perimeter polynomials ds up tod21 total number of clustersgs up tog22 and coefficientsbr in the low density series expansion of the mean cluster size up tob21 are given

chains null chains and cr geometry a system of distinguished curves distinct from chains is defined on indefinite nondegenerate cr hypersurfaces the new curves are called null chains the properties of these curves are explored and it is shown that two sufficiently nearby points of any nondegenerate cr hypersurface can be connected by either a chain or a null chain

critical probabilities for diversity and number of clusters in randomly occupied square lattices we report the occurrence of critical probabilities associated with the maximum of diversity and the maximum number of fragments clusters on a two dimensional square lattice some scaling relations of these two variables are observed in accordance with work on fragmentation processes

branched polymer approach to the structure of lattice animals and percolation clusters the authors treat the percolation problem as a solution of randomly branched chains and argue that such chains are swollen by a three body repulsion acting only within a connected cluster this type of repulsion should not be subject to the screening effects which inhibit ordinary repulsions the repulsion becomes relevant below six dimensions they estimate its effect on the size of a cluster in analogy with flory s argument for the swelling of linear chains above six dimensions the cluster size scales as mass to the 1 4 power as with isolated branched chains in high dimensions

lattice animals a fast enumeration algorithm and new perimeter polynomials a fast computer algorithm for enumerating isolated connected clusters on a regular lattice and its fortran implementation are presented new perimeter polynomials are calculated for the square the triangular the simple cubic and the square lattice with next nearest neighbors

on the use of nurbs based discretizations in the scaled boundary finite element method for wave propagation problems abstract we discuss the application of non uniform rational b splines nurbs in the scaled boundary finite element method sbfem for the solution of wave propagation problems at rather high frequencies we focus on the propagation of guided waves along prismatic structures of constant cross section comparisons are made between nurbs based discretizations and high order spectral elements in terms of the achievable convergence rates we find that for the same order of shape functions nurbs can lead to significantly smaller errors compared with lagrange polynomials the difference becomes particularly important at very high frequencies where spectral elements are prone to instabilities furthermore we analyze the behavior of nurbs for the discretization of curved boundaries where the benefit of exact geometry representation becomes crucial even in the low frequency range

dynamical model for competing opinions we propose an opinion model based on agents located at the vertices of a regular lattice each agent has an independent opinion among an arbitrary but fixed number of choices and its own degree of conviction the latter changes every time two agents which have different opinions interact with each other the dynamics leads to size distributions of clusters made up of agents which have the same opinion and are located at contiguous spatial positions which follow a power law as long as the range of the interaction between the agents is not too short i e the system self organizes into a critical state short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped when the diversity of opinions is restricted to two a nonconsensus dynamic is observed with unequal population fractions whereas consensus is reached if the agents are also allowed to interact with those located far from them the individual agents convictions the preestablished interaction range and the locality of the interaction between a pair of agents their neighborhood has no effect on the interaction are the main characteristics which distinguish our model from previous ones

cluster size diversity percolation and complex systems diversity of cluster size has been used as a measurement of complexity in several systems that generate a statistical distribution of clusters using monte carlo simulations we present a statistical analysis of the cluster size diversity and the number of clusters generated on randomly occupied lattices for the euclidean dimensions 1 to 6 a tuning effect for diversity of cluster size and critical probabilities associated with the maximum diversity and the maximum number of clusters are reported the probability of maximum diversity is related to the percolation threshold and several scaling relations between the variables measured are reported the statistics of cluster size diversity has important consequences in the statistical description of the universe as a complex system

wave propagation in anisotropic layered media the determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques such computations require great effort the method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices for which the eigenvalues can be found with great speed and accuracy the technique is then illustrated by means of an example involving a cross anisotropic gibson solid

chains in cr geometry as geodesics of a kropina metric abstract with the help of a generalization of the fermat principle in general relativity we show that chains in cr geometry are geodesics of a certain kropina metric constructed from the cr structure we study the projective equivalence of kropina metrics and show that if the kernel distributions of the corresponding 1 forms are non integrable then two projectively equivalent metrics are trivially projectively equivalent as an application we show that sufficiently many chains determine the cr structure up to conjugacy generalizing and reproving the main result of 10 the correspondence between geodesics of the kropina metric and chains allows us to use the methods of metric geometry and the calculus of variations to study chains we use these methods to re prove the result of 18 that locally any two points of a strictly pseudoconvex cr manifolds can be joined by a chain finally we generalize this result to the global setting by showing that any two points of a connected compact strictly pseudoconvex cr manifold which admits a pseudo einstein contact form with positive tanaka webster scalar curvature can be joined by a chain

on the phase space approach to complexity we elaborate in some detail on a new phase space approach to complexity due to y c zhang we show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle for a 1d signal we find 1 f noise in accordance with zhang

extension of hoshen kopelman algorithm to non lattice environments abstract we extend the hoshen kopelman hk algorithm for cluster labeling to non lattice environments where sites are placed at random at non lattice points this extension is useful for continuum systems and disordered networks our extension of the hk algorithm relies on several data structures that describe network connectivity regardless of its dimensionality just as for the classic hk algorithm on lattices our extension is completed in a single pass through the sites of the network and cluster relabeling operates on a vector whose size is much smaller than the size of the network our extension of the hk algorithm works for any environment lattice or non lattice of any dimensionality type sites bonds or both and with arbitrary connectivity between the sites the proposed extension is illustrated through a simple network consisting of 16 sites and 24 bonds and applied to a complex network extracted from a 3d micro focused x ray ct image of bentheimer sandstone consisting of 3677 sites and 8952 bonds

global culture a noise induced transition in finite systems we analyze the effect of cultural drift modeled as noise in axelrod s model for the dissemination of culture the disordered multicultural frozen configurations are found not to be stable this general result is proven rigorously in d51 where the dynamics is described in terms of a lyapunov potential in d52 the dynamics is governed by the average relaxation time t of perturbations noise at a rate r t 21 induces monocultural configurations whereasr t 21 sustains disorder in the thermodynamic limit the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence

a high order finite element technique with automatic treatment of stress singularities by semi analytical enrichment abstract this paper presents an approach to the automatic enrichment of finite elements in the vicinity of a stress singularity the enrichment consists of semi analytical singular modes constructed using the scaled boundary finite element method sbfem in contrast to analytical methods the sbfem provides modes for inhomogeneous and anisotropic materials without additional effort the finite element basis can be of arbitrary order and remains unaltered by the enrichment the approach requires enrichment in only one layer of elements around a node due to the compatibility of sbfem with fem there is no need for transitional elements and there are no parasitic terms the approach is tested for several benchmark problems the stress intensity factors are computed based on techniques inspired by the sbfem the proposed procedure is compared to a standard finite element implementation and shows a significant improvement in the error of the displacement field for problems involving singular stresses

dynamic analysis of unbounded domains by a reduced set of base functions the scaled boundary finite element method a semi analytical method based on finite element technology is well suited to model unbounded domains only the boundary is discretized no fundamental solution is necessary general anisotropic material is analyzed without any increase in computational effort the goal of this paper is to increase the computational efficiency of the scaled boundary finite element analysis of large scale problems a reduced set of weighted block orthogonal base functions is introduced the scaled boundary finite element equation is reformulated in generalized coordinates reducing the number of degrees of freedom on boundary the solution procedure in frequency domain is presented to enforce the radiation condition at infinity an asymptotic expansion for displacement at high frequency is developed numerical examples have demonstrated that the computational time is reduced by more than an order of magnitude

thin layer method formulation in the time domain the thin layer method is a semi discrete numerical technique that may be used for the dynamic analysis of laminated solids or fluids in its classical implementation the method is normally formulated in the frequency domain and requires the solution of a complex valued quadratic eigenvalue problem in this paper we present an alternative time domain formulation which can offer advantages in some cases such as avoiding the use of complex algebra the proposed method entails expressing the governing equations in the frequency wavenumber domain solving a linear real valued eigenvalue problem in the frequency variable carrying out an analytical integration over frequencies and performing a numerical transform over wavenumbers this strategy allows obtaining the green s functions for impulsive sources directly in the time domain even when the system has little or no damping we first develop the algorithm in its most general form allowing fully anisotropic materials and arbitrary expansion orders then we consider a restricted class of anisotropic materials for which the required linear eigenvalue problem involves only real narrowly banded symmetric matrices and finally we demonstrate the method by means of a simple problem involving a homogeneous stratum subjected to an antiplane impulsive source

cluster size entropy in the axelrod model of social influence small world networks and mass media we study the axelrod s cultural adaptation model using the concept of cluster size entropy s c which gives information on the variability of the cultural cluster size present in the system using networks of different topologies from regular to random we find that the critical point of the well known nonequilibrium monocultural multicultural order disorder transition of the axelrod model is given by the maximum of the s c q distributions the width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order by scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q c and the number f of cultural features in two dimensional regular networks we also analyze the effect of the mass media external field on social systems within the axelrod model in a square network we find a partially ordered phase whose largest cultural cluster is not aligned with the external field in contrast with a recent suggestion that this type of phase cannot be formed in regular networks we draw a q b phase diagram for the axelrod model in regular networks

chains on cr manifolds and lorentz geometry we show that two nearby points of a strictly pseudoconvex cr manifold are joined by a chain the proof uses techniques of lorentzian geometry via a correspondence of fefferman the arguments also apply to more general systems of chain like curves on cr manifolds 0 introduction if m is a nondegenerate cr manifold its fefferman metric is a conformal class of pseudo riemannian metrics on a circle bundle over m the various cr invariants of m may be described in terms of the conformal geometry of this metric the description of chains in this setting is especially appealing recently h jacobowitz showed that chains on a strictly pseudo convex cr manifold connect pairs of nearby points this paper presents a new proof of jacobowitz s result which makes use of the fefferman correspondence we hope that this approach will yield new insights into the behavior of chains we begin with a definition of an abstract cr manifold of hypersurface type we then sketch briefly a construction due to lee 15 of the pseudo riemannian fefferman manifold associated to a cr manifold and discuss the special properties of such manifolds much of this discussion applies to a slightly more general class of pseudo riemannian manifolds we then proceed with our proof that chains on a strictly pseudoconvex cr manifold connect pairs of sufficiently nearby points this proof applies also to the pseudochains associated to the more general pseudo riemannian manifolds discussed above finally we discuss an example of a cr manifold with a system of pseudochains which are not chains i cr manifolds and chains an abstract almost cr manifold of hypersurface type is an odd dimensional orientable manifold m2n l which we shall always take to be smooth together with a field of tangent hyperplanes h2n on which a smooth complex structure j j h h linear j2 id ih is given this j is called a cr structure tensor on m an almost cr manifold is called a cr manifold if its nijenhuis torsion tensor n x y jx jy j2 x y j x jy jx y vanishes for x y e h a cr structure satisfying this condition is said to be formally integrable let 0 e t m be a one form which annihilates h a choice of such a one form is called a pseudo hermitian structure on m the almost cr structure on m is said to be nondegenerate if 0 a do a 0 this condition is independent of the choice of 0 received by the editors april 28 1987 1980 mathematics subject classification 1985 revision primary 32f25 secondary 53c50 d1988 american mathematical society 0002 9947 88 1 00 25 per page

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

a versatile entropic measure of grey level inhomogeneity abstract an entropic measure for the analysis of grey level inhomogeneity gli is proposed as a function of length scale it allows us to quantify the statistical dissimilarity of the actual macrostate and the maximizing entropy of the reference one the maximums minimums of the measure indicate those scales at which higher lower average grey level inhomogeneity appears compared to neighbour scales even a deeply hidden statistical grey level periodicity can be detected by the equally distant minimums of the measure the striking effect of multiple intersecting curves mics of the measure has been revealed for pairs of simulated patterns which differ in shades of grey or symmetry properties only in turn for evolving photosphere granulation patterns the stability in time of the first peak position has been found interestingly the third peak is dominant at initial steps of the evolution this indicates a temporary grouping of granules at a length scale that may belong to the mesogranulation phenomenon this behaviour has similarities with that reported by consolini berrilli et al g consolini f berrilli a florio e pietropaolo l a smaldone astron astrophys 402 2003 1115 f berrilli d del moro s russo g consolini th straus astrophys j 632 2005 677 for binarized granulation images of a different data set

effect of external fields in axelrod s model of social dynamics the study of the effects of spatially uniform fields on the steady state properties of axelrod s model has yielded plenty of counterintuitive results here we reexamine the impact of this type of field for a selection of parameters such that the field free steady state of the model is heterogeneous or multicultural analyses of both one and two dimensional versions of axelrod s model indicate that the steady state remains heterogeneous regardless of the value of the field strength turning on the field leads to a discontinuous decrease on the number of cultural domains which we argue is due to the instability of zero field heterogeneous absorbing configurations we find however that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model we argue that the dimensionality has a significant impact on the stability of the field free homogeneous steady state

superuniversal spectral dimension for dilute branched polymers the authors introduce the problem of random walks on lattice animals dilute branched polymers and calculate the spectral dimension ds of animals in two and three dimensions by using a two parameter position space renormalisation group method this problem which is a generalisation of the problem of the ant in the labyrinth has been independently proposed and investigated by wilke et al 1984 the spectral dimension is given by ds 2da dw where da is the fractal dimension of the lattice animal and dw the fractal dimension of the random walk on the lattice animal the results indicate that ds may be a superuniversal quantity i e its value is independent of dimension moreover the authors find ds to be close to 4 3 which is the spectral dimension of the largest percolation cluster at the percolation threshold pc as conjectured by alexander and orbach 1982 since both lattice animals and the largest percolation cluster at pc have a homogeneous interior structure the results suggest that the spectral dimension of all such fractals may equal 4 3

global interactions information flow and chaos synchronization we investigate the relationship between the emergence of chaos synchronization and the information flow in dynamical systems possessing homogeneous or heterogeneous global interactions whose origin can be external driven systems or internal autonomous systems by employing general models of coupled chaotic maps for such systems we show that the presence of a homogeneous global field either external or internal for all times is not indispensable for achieving complete or generalized synchronization in a system of chaotic elements complete synchronization can also appear with heterogeneous global fields it does not requires the simultaneous sharing of the field by all the elements in a system we use the normalized mutual information and the information transfer between global and local variables to characterize complete and generalized synchronization we show that these information measures can characterize both types of synchronized states and also allow us to discern the origin of a global interaction field a synchronization state emerges when a sufficient amount of information provided by a field is shared by all the elements in the system on the average over long times thus the maximum value of the top down information transfer can be used as a predictor of synchronization in a system as a parameter is varied

enumeration of directed site animals on two dimensional lattices studies the problem of directed site animals on the square triangular and hexagonal lattices closed form expressions are proposed for a s the number of animals of size s on the square and triangular lattices these expressions have been checked for s or 33 and s or 10 for the square and triangular lattices respectively by explicit enumeration they imply that a s varies as lambda 2 s 0 for large s where lambda 3 for the square lattice and lambda 4 for the triangular and theta 1 2 for both for the hexagonal lattice a s is found for s or 48 the results are consistent with lambda 2 0252 or 0 0005 and theta 1 2

on the number of lattice animals embeddable in the square lattice enumeration of lattice animals embeddable in a square lattice has been extended to 24 cell animals by redelmeier 1981 it is shown that the number of animals per site an approximately 0 317 4 0626 nn 1 exp 0 465 n 0 87 to a high degree of accuracy

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

effects of the underlying topology on perturbation spreading in the axelrod model for cultural dissemination abstract we study the effects of the underlying topologies on a single feature perturbation imposed to the axelrod model of consensus formation from the numerical simulations we show that there are successive updates which are similar to avalanches in many self organized criticality systems when a perturbation is imposed we find that the distribution of avalanche size satisfies the finite size scaling fss ansatz on two dimensional lattices and random networks however on scale free networks with the degree exponent 3 we show that the avalanche size distribution does not satisfy the fss ansatz the results indicate that the disordered configurations on two dimensional lattices or on random networks are still stable against the perturbation in the limit n network size however on scale free networks with 3 the perturbation always drives the disordered phase into an ordered phase the possible relationship between the properties of phase transition of the axelrod model and the avalanche distribution is also discussed

extremal analytic discs with prescribed boundary data this paper concerns the existence and uniqueness of extremal analytic discs with prescribed boundary data in a bounded strictly linearly convex domain d in cn we prove that for any two distinct points p q in dd respectively p e dd and a vector v such that f lv e tp dd and v p p 2 vji j p 0 where v p is the outward normal to dd at p there exists an extremal analytic disc passing through p q if dd e ck k 3 respectively l p l v if dd e ck k 14 consequently we can foliate d with these extremal analytic discs introduction in this paper we always assume that d is a bounded strictly linearly convex domain in cn see 1 for definitions let u denote the open unit disc in c an extremal analytic disc of d is a holomorphic map from u into d such that the kobayashi distance of any two points in f u is realized by lempert in 6 7 has proved the existence uniqueness and boundary regularity of such maps with data given at interior points following 7 we shall use the term e mapping for the extremal analytic disc it is also known 6 proposition 5 that if dd is of class ck k 3 then any e mapping of d is in ck 2 u

cluster renormalisation study of site lattice animals in two and three dimensions the author studies site lattice animals using the cluster renormalisation cr approach previously applied to bond animals the exponent v characterising the asymptotic behaviour of the mean square radius of gyration of site animals and the fractal dimension df 1 v are determined in two and three dimensions he finds v 0 649 or 0 009 and v approximately 0 51 in two and three dimensions respectively in addition he studies restricted valence site animals on a triangular lattice using a single parameter cr approach

cluster diversity and entropy on the percolation model the lattice animal identification algorithm we present an algorithm to identify and count different lattice animals la s in the site percolation model this algorithm allows a definition of clusters based on the distinction of cluster shapes in contrast with the well known hoshen kopelman algorithm in which the clusters are differentiated by their sizes it consists in coding each unit cell of a cluster according to the nearest neighbors nn and ordering the codes in a proper sequence in this manner a la is represented by a specific code sequence in addition with some modification the algorithm is capable of differentiating between fixed and free la s the enhanced hoshen kopelman algorithm j hoshen m w berry and k s minser phys rev e 56 1455 1997 is used to compose the set of nn code sequences of each cluster using monte carlo simulations on planar square lattices up to 2000x2000 we apply this algorithm to the percolation model we calculate the cluster diversity and cluster entropy of the system which leads to the determination of probabilities associated with the maximum of these functions we show that these critical probabilities are associated with the percolation transition and with the complexity of the system

scaling and critical probabilities for cluster size and la diversity on randomly occupied square lattices using monte carlo simulations we report the behaviour of the total number of clusters the cluster size diversity and the lattice animals la diversity on randomly occupied square lattices the critical probability associated with the maximum of these variables is determined in comparison with the percolation probability pc our simulations indicate that pc and the critical probability of the maximum cluster size diversity pc d s max occur at the same point as indicated in a previous paper tsang i r and tsang i j 1997 j phys a math gen 30 l239 the probability for the maximum number of clusters is obtained at a lower value pc n max 0 27 0 01 we describe the cluster identification algorithm used to count the different la and determined the critical probability for the maximum la diversity pc d f max 0 45 0 02 we derive the exponents characterizing the relation between d s max d f max and n max and several scaling relations between the variables measured the lattice size and the probability of occupation p in addition we show the scaling behaviour of la diversity versus cluster size diversity for each value of p

entropic analysis of random morphologies abstract when the random morphology of ramified or percolating clusters exhibit local fluctuations the framework of the theory of random percolation with its critical exponents and fractal dimension is still not enough to describe the disorder and the optical properties we propose an alternative concept the configuration entropy that we compare to the multifractal analysis on computer simulated morphologies at the percolation threshold the entropy undergoes a maximum and its optimum length a minimum in contrast with the multifractal analysis the configuration entropy gives unambiguous results relatively independent of the finite size of the image

delay enhanced coherent chaotic oscillations in networks with large disorders we study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all to all global topology in the presence of impurities disorder we find that the coupling delay is capable of inducing phase coherent chaotic oscillations in both types of networks thereby enhancing the spatiotemporal complexity even in the presence of 50 of symmetric disorders of both fixed and random types furthermore the coupling delay increases the robustness of the networks up to 70 of disorders thereby preventing the network from acquiring periodic oscillations to foster disorder induced spatiotemporal order we also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated kuramoto order parameter we also explain a possible mechanism for the phenomenon of delay induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications

microstructural sensitivity of local porosity distributions the recently introduced concept of local porosity distributions for the geometric characterization of arbitrary porous media is scrutinized using computer generated pore space images the paper presents the first direct determination of local porosity distributions from digital images pore space images with identical two point correlation functions are employed to analyse the geometrical sensitivity of the local porosity concept the main finding is that local distributions can be used to discriminate between images which are indistinguishable using standard correlation functions we also discuss the question of length scales associated with the local porosity concept

formation and maintenance of complex systems a complex system is often identified by the absence of a characteristic length e g as in a fractal a very large system subject to a fragmentation and or aggregation dynamics passes through such complex configurations we study statistically creation and maintenance of such configurations in space dimensions d 1 to 5 and find that they are easily created maintained for small large d an intermediate d such as d 3 seems to be ideal for the creation and maintenance of complex systems this has consequences in a statistical description of the universe

a semi analytical curved element for linear elasticity based on the scaled boundary finite element method summary this work introduces a semi analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method sbfem this approach adapts the fundamental idea of the sbfem concept to scale a boundary to describe a geometry until now scaling in sbfem has exclusively been performed along a straight coordinate that enlarges shrinks or shifts a given boundary in this novel approach scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction the derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures the resulting elements can be coupled to general sbfem or fem domains for elastodynamic problems computations are performed in the frequency domain results of this work are validated using the global matrix method and standard finite element analysis copyright 2016 john wiley sons ltd

on the game of life population and its diversity abstract one of the most important features of biological life in all levels is its astounding diversity in this work we study the well known game life due to conway analysing the statistics of cluster population n t and cluster diversity d t we have performed simulations on life for dimensions d 1 and 2 starting with an uncorrelated distribution of live and dead sites at t 0 for d 2 we study the effect of different neighbourhood relations in identifying and counting clusters an interesting scaling relation connecting the maxima of n t and d t is found

activity of a social dynamics model axelrod s model was proposed to study interactions between agents and the formation of cultural domains it presents a transition from a monocultural to a multicultural steady state which has been studied in the literature by evaluation of the relative size of the largest cluster in this article we propose new measurements based on the concept of activity per agent to study the axelrod s model on the square lattice we show that the variance of system activity can be used to indicate the critical points of the transition furthermore the frequency distribution of the system activity is able to show a coexistence of phases typical of a first order phase transition finally we verify a power law dependence between cluster activity and cluster size for multicultural steady state configurations at the critical point

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

numerical simulations for fragmentation dynamics a geometrical model for the study of fragmentation dynamics is introduced detailed statistical analysis of the fragment distribution for percolation clusters sierpinski carpets and menger sponges on square and cubic lattices is given and static and dynamic critical exponents are calculated

percolation and cluster structure parameters the enhanced hoshen kopelman algorithm an enhanced hoshen kopelman ehk algorithm for calculating cluster structure parameters is presented for the site percolation problem the ehk algorithm enables efficient calculation of cluster spatial moments perimeters and bounding boxes for very large monte carlo simulated lattices the algorithm is used to compute the squared radius of gyration and internal perimeters of clusters in 3000 ifmmode times else texttimes fi 3000 square simulated lattices the squared radius of gyration was used to calculate the value of the correlation length exponent

on two dimensional percolation we present new series data for both high and low density bond and site percolation on the square lattice the series have been obtained by the finite lattice method and in all cases extend pre existing series an analysis of these series gives refined estimates of critical points critical exponents and amplitudes for bond and site animals and for the percolation probability and mean size exponents

a local high order doubly asymptotic open boundary for diffusion in a semi infinite layer a high order open boundary for transient diffusion in a semi infinite homogeneous layer is developed the method of separation of variables is used to derive a relationship between the modal function and the flux at the near field far field boundary in the fourier domain the resulting equation in terms of the modal impedance coefficient is solved by expanding the latter into a doubly asymptotic series of continued fractions as a result the open boundary condition in the fourier domain is represented by a system of algebraic equations in terms of i w this corresponds to a system of fractional differential equations of degree a 0 5 in the time domain this temporally global formulation is transformed into a local description by introducing internal variables the resulting local high order open boundary condition is highly accurate as is demonstrated by a number of heat transfer examples a significant gain in accuracy is obtained in comparison with existing singly asymptotic formulations at no additional computational cost

the general problem of elastic wave propagation in multilayered anisotropic media exact analytical treatment of the interaction of harmonic elastic waves with n layered anisotropic plates is presented each layer of the plate can possess up to as low as monoclinic symmetry and thus allowing results for higher symmetry materials such as orthotropic transversely isotropic cubic and isotropic to be obtained as special cases the wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle solutions are obtained by using the transfer matrix method according to this method formal solutions for each layer are derived and expressed in terms of wave amplitudes by eliminating these amplitudes the stresses and displacements on one side of the layer are related to those of the other side by satisfying appropriate continuity conditions at interlayer interfaces a global transfer matrix can be constructed which relates the displacements and stresses on one side of the plate to those on the other invoking appropriate boundary conditions on the plates outer boundaries a large variety of important problems can be solved of these mention is made of the propagation of free waves on the plate and the propagation of waves in a periodic media consisting of a periodic repetition of the plate confidence is the approach and results are confirmed by comparisons with whatever is available from specialized solutions a variety of numerical illustrations are included

role of dimensionality in axelrod s model for the dissemination of culture we analyze a model of social interaction in one and two dimensional lattices for a moderate number of features we introduce an order parameter as a function of the overlap between neighboring sites in a one dimensional chain we observe that the dynamics is consistent with a second order transition where the order parameter changes continuously and the average domain diverges at the transition point however in a two dimensional lattice the order parameter is discontinuous at the transition point characteristic of a 4rst order transition between an ordered and a disordered state c

a thermodynamic counterpart of the axelrod model of social influence the one dimensional case abstract we propose a thermodynamic version of the axelrod model of social influence in one dimensional 1d lattices the thermodynamic model becomes a coupled potts model with a bonding interaction that increases with the site matching traits we analytically calculate thermodynamic and critical properties for a 1d system and show that an order disorder phase transition only occurs at t 0 independent of the number of cultural traits q and features f the 1d thermodynamic axelrod model belongs to the same universality class of the ising and potts models notwithstanding the increase of the internal dimension of the local degree of freedom and the state dependent bonding interaction we suggest a unifying proposal to compare exponents across different discrete 1d models the comparison with our hamiltonian description reveals that in the thermodynamic limit the original out of equilibrium 1d axelrod model with noise behaves like an ordinary thermodynamic 1d interacting particle system

further results of enumeration of directed animals on two dimensional lattices in a previous paper we gave enumerations and results of the enumeration of directed animals of three different forms sites bonds and bonds without loops on a variety of two dimensional lattices this letter adds results for site animals without loops and gives an exact solution for the sites no loops kagome lattice which is actually a pair of directed self avoiding walks

a numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method abstract in this paper a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures the formulation is based on the scaled boundary finite element method the through thickness direction of the plate is discretized in the finite element sense while the direction of propagation is described analytically this leads to a standard eigenvalue problem for the calculation of wave numbers the proposed method is not limited to homogeneous plates multi layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation higher order elements have been employed for the finite element discretization leading to excellent convergence for complex structures it is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities

multistable binary decision making on networks we propose a simple model for a binary decision making process on a graph motivated by modeling social decision making with cooperative individuals the model is similar to a random field ising model or fiber bundle model but with key differences on heterogeneous networks for many types of disorder and interactions between the nodes we predict discontinuous phase transitions with mean field theory which are largely independent of network structure we show how these phase transitions can also be understood by studying microscopic avalanches and describe how network structure enhances fluctuations in the distribution of avalanches we suggest theoretically the existence of a glassy spectrum of equilibria associated with a typical phase even on infinite graphs so long as the first moment of the degree distribution is finite this behavior implies that the model is robust against noise below a certain scale and also that phase transitions can switch from discontinuous to continuous on networks with too few edges numerical simulations suggest that our theory is accurate

the physical modelling of society a historical perspective abstract by seeking to uncover the rules of collective human activities today s statistical physicists are aiming to return to their roots statistics originated in the study of social numbers in the 17th century and the discovery of statistical invariants in data on births and deaths crimes and marriages led some scientists and philosophers to conclude that society was governed by immutable natural laws beyond the reach of governments of which the gaussian error curve became regarded as the leitmotif while statistics flourished as a mathematical tool of all the sciences in the 19th century it provoked passionate responses from philosophers novelists and social commentators social statistics also guided maxwell and boltzmann towards the utilization of probability distributions in the development of the kinetic theory of gases the foundation of statistical mechanics

a matrix function solution for the scaled boundary finite element equation in statics the scaled boundary finite element method is a fundamental solution less boundary element method based on finite elements it leads to semi analytical solutions for displacement and stress fields which permits problems with singularities or in infinite domains to be handled conveniently and accurately however the present eigenvalue method for solving the scaled boundary finite element equation requires additional treatments for multiple eigenvalues with parallel eigenvectors which results from logarithmic terms in the solutions a matrix function solution for the scaled boundary finite element equation in statics is presented in this paper it is numerically stable for multiple or near multiple eigenvalues as it is based on real schur decomposition power functions logarithmic functions and their transitions as occurring in fracture mechanics composites and two dimensional unbounded domains are represented semi analytically no a priori knowledge on the types and orders of singularity are required when simulating stress singularities

the computation of dispersion relations for three dimensional elastic waveguides using the scaled boundary finite element method abstract in this paper a numerical approach for the computation of dispersion relations for three dimensional waveguides with arbitrary cross section is proposed the formulation is based on the scaled boundary finite element method sbfem it is an extension of the approach previously derived for plate structures it is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the z matrix which is well known in the sbfem the hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives the cross section of the waveguide is discretized using higher order spectral elements it is discussed in detail how symmetry axes can be utilized to reduce computational costs in order to sort the solutions at different frequencies a mode tracking algorithm is proposed based on the pade expansion

effects of noise and confidence thresholds in nominal and metric axelrod dynamics of social influence we study the effects of bounded confidence thresholds and of interaction and external noise on axelrod s model of social influence our study is based on a combination of numerical simulations and an integration of the mean field master equation describing the system in the thermodynamic limit we find that interaction thresholds affect the system only quantitatively but that they do not alter the basic phase structure the known crossover between an ordered and a disordered state in finite systems subject to external noise persists in models with general confidence threshold interaction noise here facilitates the dynamics and reduces relaxation times we also study axelrod systems with metric features and point out similarities and differences compared to models with nominal features

mass lumping techniques in the spectral element method on the equivalence of the row sum nodal quadrature and diagonal scaling methods abstract in the context of wave propagation analysis the spectral element method sem in conjunction with a diagonal mass matrix is often the method of choice therefore it is of high importance to investigate the influence of different mass lumping schemes on the accuracy of the numerical results to this end we compare the performance of three established methods including the row sum method the nodal quadrature method and the diagonal scaling method the theoretical analysis of these methods reveals a close connection between them under certain conditions that are discussed in detail in this article we are able to show a direct equivalence between these three approaches in this regard the attainable accuracy of the numerical integration of the mass matrix plays an important role by means of several dynamic benchmark problems we verify the theoretical results and illustrate the convergence properties of the lumped mass matrix sem in comparison to a formulation based on the consistent mass matrix

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

local versus global interactions in nonequilibrium transitions a model of social dynamics a nonequilibrium system of locally interacting elements in a lattice with an absorbing order disorder phase transition is studied under the effect of additional interacting fields these fields are shown to produce interesting effects in the collective behavior of this system both for autonomous and external fields disorder grows in the system when the probability of the elements to interact with the field is increased there exists a threshold value of this probability beyond which the system is always disordered the domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields however the zero field limit is discontinous in the limit of vanishingly small probability of interaction with the field autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone we consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of axelrod s model for cultural dissemination

the existence of negative absolute temperatures in axelrod s social influence model abstract we introduce the concept of temperature as an order parameter in the standard axelrod s social influence model it is defined as the relation between suitably defined entropy and energy functions t s e 1 we show that at the critical point where the order disorder transition occurs this absolute temperature changes in sign at this point which corresponds to the transition homogeneous heterogeneous culture the entropy of the system shows a maximum we discuss the relationship between the temperature and other properties of the model in terms of cultural traits