the cellular automata approach to simulating fluid flows in porous media abstract the modeling of fluid flows in porous media using cellular automata is discussed efficient methods for simulating these models on scalar vector and parallel computers are presented results for two dimensional systems with up to 200 million particles show finite size effects which may be interpreted as arising from the mean free path of the fluid particles empirically these finite size effects are found to be proportional to 1 7 r where r is the characteristic size of the system using this information the dependence of the permeability on the porosity of a 2d porous medium can be estimated as e6 5 1

a cellular automaton fluid model with simple rules in arbitrarily many dimensions a new cellular automaton model for fluid dynamics is introduced unlike the conventional fhp type models the model uses easily implementable deterministic pair interaction rules which work on arbitrary dimensional orthogonal lattices the statistical and hydrodynamic theory of the model is developed and the navier stokes like hydrodynamic equations that describe the macroscopic behavior of the model are derived it turns out that the unwanted anisotropic convection behavior can be eliminated in the incompressible limit by suitable choice of the mass density an explicit expression for the viscosity tensor is calculated from a boltzmann type approximation unfortunately the viscosity turns out to be anisotropic which is a drawback as against the conventional fhp and fchc models nevertheless the new model could become interesting for fluid dynamic problems with additional variables e g free surfaces especially in two dimensions since its simple rules could relatively easily be extended for such cases

fragmentation of random trees we study fragmentation of a random recursive tree into a forest by repeated removal of nodes the initial tree consists of n nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly selected existing node as nodes are removed from the tree one at a time the tree dissolves into an ensemble of separate trees namely a forest we study statistical properties of trees and nodes in this heterogeneous forest and find that the fraction of remaining nodes m characterizes the system in the limit we obtain analytically the size density of trees of size s the size density has power law tail with exponent therefore the tail becomes steeper as further nodes are removed and the fragmentation process is unusual in that exponent increases continuously with time we also extend our analysis to the case where nodes are added as well as removed and obtain the asymptotic size density for growing trees

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

simulation of flow through a two dimensional random porous medium the cellular automata approximation of two dimensional hydrodynamics is used to model flow between randomly placed partially overlapping circles the flow resistance is first roughly proportional to the number of circles and then increases more strongly for higher numbers of such obstacles

partition of networks into basins of attraction we study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree each node is associated with or attracted to its neighbor of maximal degree as long as the degree is increasing a node that has no neighbors of higher degree is a peak attracting all the nodes in its basin maximally random scale free networks exhibit different behavior based on their degree distribution exponent gamma for small gamma broad distribution networks are dominated by a giant basin whereas for large gamma narrow distribution there are numerous basins with peaks attracting mainly their nearest neighbors we derive expressions for the first two moments of the number of basins we also obtain the complete distribution of basin sizes for a class of hierarchical deterministic scale free networks that resemble random nets finally we generalize the problem to regular networks and lattices where all degrees are equal and thus the attractiveness of a node must be determined by an assigned weight rather than the degree we derive the complete distribution of basins of attraction resulting from randomly assigned weights in one dimensional chains

random networks with tunable degree distribution and clustering we present an algorithm for generating random networks with arbitrary degree distribution and clustering frequency of triadic closure we use this algorithm to generate networks with exponential power law and poisson degree distributions with variable levels of clustering such networks may be used as models of social networks and as a testable null hypothesis about network structure finally we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network and on the size of the giant component some analysis of these effects is presented

viscous drag by cellular automata a simple method to compute the drag coefficient of two dimensional bodies with arbitrary shapes is presented the procedure is based on cellular automata as an extreme idealization of the molecular dynamics of a viscous fluid we verify the algorithm by examples and obtain results in quantitative agreement with experiments even when eddies behind the obstacle are formed

rate equation approach for correlations in growing network models we propose a rate equation approach to compute two vertex correlations in scale free growing network models based on the preferential attachment mechanism the formalism based on previous work of szabo et al fphys rev e 67 056102 s2002dg for the clustering spectrum measuring three vertex correlations is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k with an appropriate boundary condition we study the properties of both two and three vertex correlations for linear preferential attachment models and also for a model yielding a large clustering coefficient the expressions obtained are checked by means of extensive numerical simulations the rate equation proposed can be generalized to more sophisticated growing network models and also extended to deal with related correlation measures as an example we consider the case of a recently proposed model of weighted networks for which we are able to compute a weighted two vertex correlation function taking into account the strength of the interactions between connected vertices

permeability of thin random media we present the results of calculations using cellular automata of the particle flow through a porous material in our model the material is made of n equal 4 to 12 layers of the same density each layer is independently constructed of interacting monomers and dimers we estimate the dependence of permeability on the porosity of the medium its structure and the external force speeding up the flow we also estimate the range of the parameters for which the relation between the permeability and the porosity is linear we show that the structure of the layers and the external field have stronger effect for sparse and thin barriers than for thick and dense material

power law for the permeability in a two dimensional disordered porous medium abstract we report numerical calculations of the permeability as a function of porosity for a two dimensional disordered porous medium this medium is modeled using the well known swiss cheese model the fluid is simulated using a cellular automata algorithm we find that for relatively high porosities the permeability decays exponentially with the density of obstacles as a consequence of this exponential behavior a power law dependence of the permeability as a function of the porosity is obtained for this model system we find that the power law exponent is given by the ratio between two characteristic scales one scale is given by the inverse of the area of one obstacle and is approximately equal to the density of obstacles necessary to reach the percolation threshold the other scale is equal to the average change in the density of obstacles necessary for the permeability to be reduced to about 1 e of its original value

calculation of the permeability of porous media using hydrodynamic cellular automata the permeability of two dimensional porous media is calculated numerically as a function of porosity using the hydrodynamic cellular automata lattice gas approach results are presented for systems with up to 22 million sites 8192 2688 for randomly distributed solid obstacles whose macroscopic dimensions are much longer than the mean free path of particles in the fluid the permeability varies with porositye as e 0 6 1 e fore 0 7 when the solid obstacles are much smaller than the mean free path of particles in the fluid i e when they form a dust of point objects then such a relationship no longer holds and the permeability is more than an order of magnitude smaller than for the former case the program used for the simulations is discussed and a listing is presented in the appendix which achieved a sustained speed of 185 million sites updated per second on a single processor of the cray ymp on a sun sparc workstation the same program ran about 100 times slower

the evolutionary game of pressure or interference resistance and collaboration in this paper we extend the framework of the evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions to address the pressure executed by the major player or principal on the large group of small players who can resist this pressure or collaborate with the major player we prove rigorous results on the convergence of various markov decision models of interacting small agents including evolutionary growth i e pairwise in groups and by coalition formation to a deterministic evolution on the distributions of the state spaces of small players paying main attention to situations with an infinite state space of small players we supply precise rates of convergence the theoretical results of the paper are applied to the analysis of the processes of inspection corruption cyber security counter terrorism banks and firms merging strategically enhanced preferential attachment and many other

evolutionary mixed games in structured populations cooperation and the benefits of heterogeneity evolutionary games on networks traditionally involve the same game at each interaction here we depart from this assumption by considering mixed games where the game played at each interaction is drawn uniformly at random from a set of two different games while in well mixed populations the random mixture of the two games is always equivalent to the average single game in structured populations this is not always the case we show that the outcome is in fact strongly dependent on the distance of separation of the two games in the parameter space effectively this distance introduces payoff heterogeneity and the average game is returned only if the heterogeneity is small for higher levels of heterogeneity the distance to the average game grows which often involves the promotion of cooperation the presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin and they also emphasize the importance of the population structure in amplifying facilitators of cooperation

greedy connectivity of geographically embedded graphs we introduce a measure of greedy connectivity for geographical networks graphs embedded in space and where the search for connecting paths relies only on local information such as a node s location and that of its neighbors constraints of this type are common in everyday life applications greedy connectivity accounts also for imperfect transmission across established links and is larger the higher the proportion of nodes that can be reached from other nodes with a high probability greedy connectivity can be used as a criterion for optimal network design

a mathematical model for generating bipartite graphs and its application to protein networks complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology most of these systems can be organized into networks composed of nodes and interacting edges here we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes we then use this model to investigate protein domain networks a protein can be composed of up to hundreds of domains each domain represents a conserved sequence segment with specific functional tasks we analyze the distribution of domains in homo sapiens and arabidopsis thaliana organisms and the statistical analysis shows that while a the number of domain types shared by k proteins exhibits a power law distribution b the number of proteins composed of k types of domains decays as an exponential distribution the proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of a power law and b exponential distributions our theoretical and computational results show that this model requires 1 growth process and 2 copy mechanism

cluster growth in two growing network models we analyse a simple model for growing tree networks and find that although it never percolates there is an anomalously large cluster at finite size we study the growth of both the maximal cluster and the cluster containing the original vertex and find that they obey power laws this property is also observed through simulations in a nonlinear model with loops and a true percolating phase

zero pearson coefficient for strongly correlated growing trees we obtained pearson s coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by m edges we found that the pearson coefficient is exactly zero in the infinite network limit for the recursive trees m 1 if the number of connections of new vertices exceeds one mg1 then the pearson coefficient in the infinite networks equals zero only when the degree distribution exponent ensuremath gamma does not exceed 4 we calculated the pearson coefficient for finite networks and observed a slow power law like approach to an infinite network limit our findings indicate that pearson s coefficient strongly depends on size and details of networks which makes this characteristic virtually useless for quantitative comparison of different networks

vectorized multisite coding for hydrodynamic cellular automata simulating eight lattices for pomeau s cellular automata simultaneously through bit per bit operations a vectorized fortran program reached 30 million updates per second and per cray ymp processor we give the full innermost loops

on global periodicity of difference equations abstract in this research we consider a difference equation of order k 2 of the following form y n 1 f y n y n k 1 n 0 1 2 we develop necessary and or sufficient conditions on f so that every solution of the above mentioned difference equation is periodic of the same period p