spectra of complex networks we propose a general approach to the description of spectra of complex networks for the spectra of networks with uncorrelated vertices and a local treelike structure exact equations are derived these equations are generalized to the case of networks with correlations between neighboring vertices the tail of the density of eigenvalues ensuremath rho ensuremath lambda at large ensuremath lambda is related to the behavior of the vertex degree distribution p k at large k in particular as p k ensuremath sim k ensuremath ensuremath gamma ensuremath rho ensuremath lambda ensuremath sim ensuremath lambda 1 ensuremath 2 ensuremath gamma we propose a simple approximation which enables us to calculate spectra of various graphs analytically we analyze spectra of various complex networks and discuss the role of vertices of low degree we show that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real world networks e g of the internet

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

evolution of a social network the role of cultural diversity we present a simple deterministic and based on local rules model of evolving social network which leads to a network with the properties of a real social system e g small world topology and assortative mixing the state of an individual si is characterized by the values of q cultural features drawn from gaussian distribution with variance sigma the other control parameter is sociability ti which describes the maximal number of connections of an individual the state of individuals and connections between them evolve in time as results from numerical computations an initial diversity of cultural features in a community has an essential influence on an evolution of social network it was found that for a critical value of control parameter sigma c q there is a structural transition and a hierarchical network with small world topology of connections and a high clustering coefficient emerges the emergence of small world properties can be related to the creation of subculture groups in a community the power law relation between the clustering coefficient of a node and its connectivity c k approximately k beta was observed in the case of a scale free distribution of sociability ti and a high enough cultural diversity in a population

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

clustering of tag induced subgraphs in complex networks abstract we study the behavior of the clustering coefficient in tagged networks the rich variety of tags associated with the nodes in the networks we considered provide additional relevant information about the entities represented by the nodes such specific features can be important for practical applications like searching in the networks here we examine how the clustering coefficient changes when narrowing the network to a subgraph associated with a given tag and how it correlates with various other properties of the subgraph a further question addressed in our paper is how the clustering coefficient of the individual nodes is affected by the tags on the node we argue that this kind of analysis can be useful when one is aimed at a detailed description of the structure of large complex systems

local affinity in heterogeneous growing networks abstract in this paper we present a study of the influence of local affinity in heterogeneous preferential attachment pa networks heterogeneous pa models are a generalization of the barabasi albert model to heterogeneous networks where the affinity between nodes biases the attachment probability of links threshold models are a class of heterogeneous pa models where the affinity between nodes is inversely related to the distance between their states we propose a generalization of threshold models where network nodes have individual affinity functions which are then combined to yield the affinity of each potential interaction we analyze the influence of the affinity functions in the topological properties averaged over a network ensemble the network topology is evaluated through the distributions of connectivity degrees clustering coefficients and geodesic distances we show that the relaxation of the criterion of a single global affinity still leads to a reasonable power law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions we also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks

integration of elastic multibody systems by invariant conserving dissipating algorithms ii numerical schemes and applications abstract this work presents a novel methodology for the dynamic analysis of general non linear multibody systems composed of rigid and deformable bodies the latter under the small strain assumption in part i we developed the 6 d compact representation and parameterization of motion for constrained bodies part ii is devoted to the design of a class of modified runge kutta rk methods dedicated to non linear dynamics these are capable of integrating on the configuration manifold and of preserving linear and angular momenta within this class of methods two second order algorithms are designed under the requirement of attaining non linear unconditional stability the energy preserving ep and energy decaying ed methods these schemes are associated with an algorithmic law of conservation and dissipation respectively of the total mechanical energy of the system together with the vanishing of the algorithmic work done by ideal time independent constraints their performances are assessed with the aid of some representative numerical applications which confirm the non conventional properties predicted in the analysis

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

fluctuating fronts as correlated extreme value problems an example of gaussian statistics in this paper we view fluctuating fronts made of particles on a one dimensional lattice as an extreme value problem the idea is to denote the configuration for a single front realization at time t by the set of co ordinates k i t identical with k 1 t k 2 t k n t t of the constituent particles where n t is the total number of particles in that realization at time t when k i t are arranged in the ascending order of magnitudes the instantaneous front position can be denoted by the location of the rightmost particle i e by the extremal value k f t max k 1 t k 2 t k n t t due to interparticle interactions k i t at two different times for a single front realization are naturally not independent of each other and thus the probability distribution p k f t based on an ensemble of such front realizations describes extreme value statistics for a set of correlated random variables in view of the fact that exact results for correlated extreme value statistics are rather rare here we show that for a fermionic front model in a reaction diffusion system p k f t is gaussian in a bosonic front model however we observe small deviations from the gaussian

connectivity degrees in the threshold preferential attachment model abstract in this paper we present a study of the connectivity degrees of the threshold preferential attachment model a generalization of the barabasi albert model to heterogeneous complex networks the threshold model incorporates the states of the nodes in its preferential linking rule and assumes that the affinity between network nodes follows an inverse relationship with the distance between their states we numerically analyze the connectivity degrees of the model studying the influence of the main parameters on the distribution of connectivity degrees and its statistics the average degree and highest degree of the network we show that such statistics exhibit markedly different behaviors in the dependence on the model parameters particularly as regards the interaction threshold nevertheless we show that the two statistics converge in the limit of null threshold and often exhibit scaling that can be described by power laws of the model parameters

coevolution of glauber like ising dynamics and topology we study the coevolution of a generalized glauber dynamics for ising spins with tunable threshold and of the graph topology where the dynamics takes place this simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model the threshold and the rewiring probability the diagram displays phase transitions of different types spin ordering percolation and connectedness at variance with traditional coevolution models in which all spins of each connected component of the graph have equal value in the stationary state we find that for suitable choices of the parameters the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like signed spins mean field calculations enable one to estimate some features of the phase diagram

noetherian quotients of the algebra of partial difference polynomials and grobner bases of symmetric ideals abstract in this paper we develop a grobner bases theory for ideals of partial difference polynomials with constant or non constant coefficients in particular we introduce a criterion providing the finiteness of such bases when a difference ideal contains elements with suitable linear leading monomials this can be explained in terms of noetherianity of the corresponding quotient algebra among these noetherian quotients we find finitely generated polynomial algebras where the action of suitable finite dimensional commutative algebras and in particular finite abelian groups is defined we obtain therefore a consistent grobner bases theory for ideals that possess such symmetries

dynamics of efficiency a simple model we propose a simple model that describes the dynamics of efficiencies of competing agents agents communicate leading to increase of efficiencies of underachievers and an efficiency of each agent can increase or decrease irrespectively of other agents when the rate of deleterious changes exceeds a certain threshold the system falls into a stagnant phase in the opposite situation the average efficiency improves with asymptotically constant rate and the efficiency distribution has a finite width the leading algebraic corrections to the asymptotic growth rate are also computed

coauthorship networks and patterns of scientific collaboration by using data from three bibliographic databases in biology physics and mathematics respectively networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper we use these networks to answer a broad variety of questions about collaboration patterns such as the numbers of papers authors write how many people they write them with what the typical distance between scientists is through the network and how patterns of collaboration vary between subjects and over time we also summarize a number of recent results by other authors on coauthorship patterns

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

localized growth and branching random walks with time correlations we generalize a model of growth over a disordered environment to a large class of it processes in particular we study how the microscopic properties of the noise influence the macroscopic growth rate the present model can account for growth processes in large dimensions and provides a bed to understand better the tradeoff between exploration and exploitation an additional mapping to the schrodinger equation readily provides a set of disorders for which this model can be solved exactly this mean field approach exhibits interesting features such as a freezing transition and an optimal point of growth which can be studied in detail and gives yet another explanation for the occurrence of the zipf law in complex well connected systems

algebraic construction and numerical behavior of a new s consistent difference scheme for the 2d navier stokes equations abstract in this paper we consider a regular grid with equal spatial spacings and construct a new finite difference approximation difference scheme for the system of two dimensional navier stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity in so doing we use earlier constructed discretization of the system of three equations the continuity equation and the proper navier stokes equations then we compute the canonical grobner basis form for the obtained discrete system it gives one more difference equation which is equivalent to the pressure poisson equation modulo difference ideal generated by the navier stokes equations and thereby comprises a new finite difference approximation scheme we show that the new scheme is strongly consistent besides our computational experiments demonstrate much better numerical behavior of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and with the scheme which is not strongly consistent

optimal transportation network with concave cost functions loop analysis and algorithms transportation networks play a vital role in modern societies structural optimization of a transportation system under a given set of constraints is an issue of great practical importance for a general transportation system whose total cost c is determined by c sigma c i j ij i ij with c ij i ij being the cost of the flow i ij between node i and node j banavar and co workers phys rev lett 84 4745 2000 proved that the optimal network topology is a tree if c ij proportional to parallel to i ij parallel to gamma with 0 1 the same conclusion also holds in the more general case where all the flow costs are strictly concave functions of the flow i ij to further understand the qualitative difference between systems with concave and convex cost functions a loop analysis of transportation cost is performed in the present paper and an alternative mathematical proof of the optimality of tree formed networks is given the simple intuitive picture of this proof then leads to an efficient global algorithm for the searching of optimal structures for a given transportation system with concave cost functions

robust integration schemes for flexible multibody systems a framework for the development of robust time integration schemes for nonlinear flexible multibody systems is presented the proposed schemes are designed to meet four specific requirements nonlinear unconditional stability of the scheme a rigorous treatment of both geometric and material nonlinearities exact satisfaction of the constraints and the presence of high frequency numerical dissipation specific algorithms are presented for rigid bodies cables beams shells and elasto dynamics the kinematic nonlinearities are treated in a rigorous manner for all elements and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function the treatment of the constraint equations associated with the six lower pair joints are presented as well the efficiency and robustness of the proposed approach is demonstrated with specific numerical examples

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

automatic integration of euler lagrange equations with constraints abstract numerical difficulties in the integration of euler lagrange and similar equations are discussed a technique for reducing their index from three to two is introduced and it is shown that variable order variable step bdf methods converge for these index two problems the practical application of this reduction in a numerical setting is examined

numerical simulation of mechanical systems using methods for differential algebraic equations a simple approach to the numerical simulation of mechanical systems consisting of rigid and flexible bodies is presented the mechanical system may consist of rigid bodies different types of flexible bodies joints and actuators and may have arbitrary topological structure with kinematical loops the equations of motion are formulated as a large sparse system of equations in absolute co ordinates as well as relative co ordinates these equations are numerically integrated as a system of differential algebraic equations using modern numerical methods

clustering properties of a generalized critical euclidean network many real world networks exhibit a scale free feature have a small diameter and a high clustering tendency we study the properties of a growing network which has all these features in which an incoming node is connected to its ith predecessor of degree k i with a link of length l using a probability proportional to k beta i l alpha for alpha 0 5 the network is scale free at beta 1 with the degree distribution p k proportional to k gamma and gamma 3 0 as in the barabasi albert model alpha 0 beta 1 we find a phase boundary in the alpha beta plane along which the network is scale free interestingly we find a scale free behavior even for beta 1 for alpha 0 5 where the existence of a different universality class is indicated from the behavior of the degree distribution and the clustering coefficients the network has a small diameter in the entire scale free region the clustering coefficients emulate the behavior of most real networks for increasing negative values of alpha on the phase boundary

extreme value statistics and traveling fronts various applications abstract an intriguing connection between extreme value statistics and traveling fronts has been found recently in a number of diverse problems in this short review we outline a few such problems and consider their various applications

time step size independent conditioning and sensitivity to perturbations in the numerical solution of index three differential algebraic equations we propose a simple preconditioning for the equations of motion of constrained mechanical systems in index three form the scaling transformation is applied to the displacement velocity multiplier and to the reduced displacement multiplier forms the analysis of the transformed system shows that conditioning and sensitivity to perturbations become independent of the time step size as in the case of well behaved ordinary differential equations the new scaling transformation is simple to implement and does not require the rewriting of the system equations as other approaches do the theoretical analysis is confirmed by numerical examples

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

breakdown of interdependent directed networks increasing evidence shows that real world systems interact with one another via dependency connectivities failing connectivities are the mechanism behind the breakdown of interacting complex systems e g blackouts caused by the interdependence of power grids and communication networks previous research analyzing the robustness of interdependent networks has been limited to undirected networks however most real world networks are directed their in degrees and out degrees may be correlated and they are often coupled to one another as interdependent directed networks to understand the breakdown and robustness of interdependent directed networks we develop a theoretical framework based on generating functions and percolation theory we find that for interdependent erd s renyi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions we also find that the percolation behavior of interdependent directed scale free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness the percolation threshold and the integrated size of the giant component during an entire attack process interestingly we find that the in degree and out degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths moreover by applying our theoretical analysis to real interdependent international trade networks we find that the robustness of these real world systems increases with the in degree and out degree correlations confirming our theoretical analysis

phenomenological models of socioeconomic network dynamics we study a general set of models of social network evolution and dynamics the models consist of both a dynamics on the network and evolution of the network links are formed preferentially between similar nodes where the similarity is defined by the particular process taking place on the network the interplay between the two processes produces phase transitions and hysteresis as seen using numerical simulations for three specific processes we obtain analytic results using mean field approximations and for a particular case we derive an exact solution for the network in common with real world social networks we find coexistence of high and low connectivity phases and history dependence

rigid body dynamics in terms of quaternions hamiltonian formulation and conserving numerical integration in the present paper unit quaternions are used to describe the rotational motion of a rigid body the unit length constraint is enforced explicitly by means of an algebraic constraint correspondingly the equations of motion assume the form of differential algebraic equations daes a new route to the derivation of the mass matrix associated with the quaternion formulation is presented in contrast to previous works the newly proposed approach yields a non singular mass matrix consequently the passage to the hamiltonian framework is made possible without the need to introduce undetermined inertia terms the hamiltonian form of the daes along with the notion of a discrete derivative make possible the design of a new quaternion based energy momentum scheme two numerical examples demonstrate the performance of the newly developed method in this connection comparison is made with a quaternion based variational integrator a director based energy momentum scheme and a momentum conserving scheme relying on the discretization of the classical euler s equations

socioeconomic networks with long range interactions we study a modified version of a model previously proposed by jackson and wolinsky to account for communication of information and allocation of goods in socioeconomic networks in the model the utility function of each node is given by a weighted sum of contributions from all accessible nodes the weights parametrized by the variable decrease with distance we introduce a growth mechanism where new nodes attach to the existing network preferentially by utility by increasing the network structure evolves from a power law to an exponential degree distribution passing through a regime characterized by shorter average path length lower degree assortativity and higher central point dominance in the second part of the paper we compare different network structures in terms of the average utility received by each node we show that power law networks provide higher average utility than poisson random networks this provides a possible justification for the ubiquitousness of scale free networks in the real world

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

structural transitions in scale free networks real growing networks such as the world wide web or personal connection based networks are characterized by a high degree of clustering in addition to the small world property and the absence of a characteristic scale appropriate modifications of the barabasi albert preferential attachment network growth capture all these aspects we present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for clustering this is solved for a specific case with the result c k approximately 1 k for the clustering of a node of degree k this mean field exponent agrees with simulations and reproduces the clustering of many real networks

structure of a large social network we study a social network consisting of over 10 4 individuals with a degree distribution exhibiting two power scaling regimes separated by a critical degree k mathrm crit and a power law relation between degree and local clustering we introduce a growing random model based on a local interaction mechanism that reproduces the observed scaling features and their exponents we suggest that the double power law originates from two very different kinds of networks that are simultaneously present in the human social network

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

the embedded projection method a general index reduction procedure for constrained system dynamics abstract the embedded projection method epm is an attempt to eliminate most of the difficulties related to the solution of high index differential algebraic equations daes as those typical of the dynamics of constrained systems the intimate coupling between the algebraic and the differential parts lies at the origin of these difficulties therefore we uncouple these components introduce an unconstrained modified state variable and complement the resulting ordinary differential equation ode by additional algebraic variables as a result a general consistent index reduction from arbitrarily high values to one is obtained allowing the use of any suitable ode integration algorithm without the need for a specialized dae solver the epm solution is intrinsically endowed with greater accuracy and stability than conventional counterparts thus balancing the higher complexity of the procedure we illustrate the epm including some applications of holonomic and non holonomic mechanical systems

a renormalization group theory of cultural evolution abstract we present a theory of cultural evolution based upon a renormalization group scheme we consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment these representations are built around the most important degrees of freedom of their world cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter as the importance of social interactions increases or agents become more intelligent we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society a similar phase transition may explain the so called cultural explosion in human evolution some 50 000 years ago

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

modularity and extreme edges of the internet we study the spectral properties of a diffusion process taking place on the internet network focusing on the slowest decaying modes these modes identify an underlying modular structure roughly corresponding to individual countries for instance in the slowest decaying mode the diffusion current flows from russia to u s military sites quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale free network we propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network for the 100 slowest decaying modes of the internet this fraction is 30 finally we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

integration of elastic multibody systems by invariant conserving dissipating algorithms i formulation abstract this work presents a novel methodology for the dynamic analysis of general non linear flexible multibody systems in part i we develop the 6 d compact representation of motion for those body models which motion may be described by a displacement field plus an independent rotation field this approach explores the fundamental properties of rigid body motion and in particular the coupled nature of linear and angular quantities in both kinematics and dynamics inspiring a novel parameterization technique based on the exponential map using the proposed approach we derive the governing equations for the case of multibody systems composed by rigid bodies and geometrically non linear beams connected by holonomic constraints these equations provide the starting point for the derivation of a class of numerical algorithms characterized by non conventional conservation properties in part ii of this work we develop the algorithms and illustrate their properties with the aid of some numerical applications

early fragmentation in the adaptive voter model on directed networks we consider voter dynamics on a directed adaptive network with fixed out degree distribution a transition between an active phase and a fragmented phase is observed this transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out degree distribution however if a significant number of nodes with low out degree is present then fragmentation can occur even far below the estimated critical point due to the formation of self stabilizing structures that nucleate fragmentation this process may be relevant for fragmentation in current political opinion formation processes

a unified set of single step asymptotic annihilation algorithms for structural dynamics when solving the equations of structural dynamics using direct time integration meth6ds algorithmic damping is useful in controlling spurious high frequency oscillations ideally an algorithm should possess asymptotic annihilation of the highfrequency response i e spurious oscillations in the high frequencies are eliminated after one time step in this paper a new class of asymptotic annihilation algorithms for structural dynamics is presented that possesses little numerical dissipation in the low frequency regime the algorithms are based upon using finite elements in time the displacement and velocity fields are interpolated independently using time discontinuous functions the equations of motion displacement velocity compatibility and the time continuity of displacement and velocity are satisfied weakly asymptotic annihilation is achieved by choosing the displacement and velocity fields to be of equal order algorithms of any desired order of temporal accuracy can be obtained by appropriate choice of the finite element interpolations in time an analysis of the proposed class of algorithms is given proving the asymptotic annihilation property and the spectral equivalence of the algorithms to the upper diagonal of the pad6 approximation table results from finite difference analyses are presented showing the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low frequency regime

designer nets from local strategies we propose a local strategy for constructing scale free networks of arbitrary degree distributions based on the redirection method of krapivsky and redner phys rev e 63 066123 2001 our method includes a set of external parameters that can be tuned at will to match detailed behavior at small degree k in addition to the scale free power law tail signature at large k once achieved the target distribution is maintained throughout the growth of the net the method is local in that addition of a new node requires knowledge of only the immediate environs of the randomly selected node to which it is attached global strategies require information on finite fractions of the growing net