transition phenomena in cellular automata rule space abstract we define several qualitative classes of cellular automata ca behavior based on various statistical measures and describe how the space of all cellular automata is organized as a cellular automaton is changed by varying entries in its rule table abrupt changes in qualitative behavior may occur these abrupt changes have the character of bifurcations in smooth dynamical systems or of phase transitions in statistical mechanical systems the most complex ca rules exhibit many of the characteristics of second order transitions suggesting an association between computation complexity and critical phenomena

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

on topological dynamics of turing machines abstract we associate to a turing machine two dynamical systems which we call turing machine with moving tape tmt and turing machine with moving head tmh tmt are equivalent to generalized shifts of moore 1990 and they include two sided full shifts tmh are shift commuting maps of two sided sofic systems in both classes we characterize systems with the shadowing property show that a bijective expansive tmt is conjugate to a subshift of finite type and that topological entropy of every tmh is zero we conjecture that every tmt has a periodic point

uniform norm minimization in three dimensions linear programming is the standard tool for constructing solutions to linear inverse problems which have the smallest possible maximum absolute value or uniform norm for problems in three dimensions however the tableaus are usually so large as to be computationally prohibitive an iterative scheme can replace a single very large linear programming tableau with a sequence of much smaller tableaus making such problems tractable

automated pattern detection an algorithm for constructing optimally synchronizing multi regular language filters in the computational mechanics structural analysis of one dimensional cellular automata the following automata theoretic analogue of the change point problem from time series analysis arises given a string and a collection di offinite automata identify the regions of that belong to each di and in particular the boundaries separating them we present two methods for solving this multi regular language filtering problem the first although providing the ideal solution requires a stack has a worst case compute time that grows quadratically in s length and conditions its output at any point on arbitrarily long windows of future input the second method is to algorithmically construct a finite transducer that approximates the first algorithm in contrast to the stack based algorithm however the transducer requires only a finite amount of memory runs in linear time and gives immediate output for each letter read it is moreover the best possible finite state approximation with these three features

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

limit sets of cellular automata associated to probability measures we introduce the concept of limit set associated to a cellular automaton ca and a shift invariant probability measure this is a subshift whose forbidden blocks are exactly those whose probabilities tend to zero as time tends to infinity we compare this probabilistic concept of limit set with the concepts of attractors both in topological and measure theoretic sense we also compare this notion with that of topological limit set in different dynamical situations

the kink of cellular automaton rule 18 performs a random walk we give an exact characterization of the movement of a single kink in the elementary cellular automaton rule 18 it is a random walk with independent increments as well as independent delay times its statistical parameters are computed to confirm the earlier simulation results by grassberger

evolving cellular automata to perform computations mechanisms and impediments abstract we present results from experiments in which a genetic algorithm ga was used to evolve cellular automata cas to perform a particular computational task one dimensional density classification we look in detail at the evolutionary mechanisms producing the ga s behavior on this task and the impediments faced by the ga in particular we identify four epochs of innovation in which new ca strategies for solving the problem are discovered by the ga describe how these strategies are implemented in ca rule tables and identify the ga mechanisms underlying their discovery the epochs are characterized by a breaking of the task s symmetries on the part of the ga the symmetry breaking results in a short term fitness gain but ultimately prevents the discovery of the most highly fit strategies we discuss the extent to which symmetry breaking and other impediments are general phenomena in any ga search

topological aspects of meshless methods and nodal ordering for meshless discretizations the meshless element free galerkin method efgm is considered and compared to the finite element method fem in particular topological aspects of meshless methods as the nodal connectivity and invertibility of matrices are studied and compared to those of the fe method we define four associated graphs for meshless discretizations of efgm and investigate their connectivity the ways that the associated graphs for coupled fe efg models might be defined are recommended the associated graphs are used for nodal ordering of meshless models in order to reduce the bandwidth profile maximum frontwidth and root mean square wavefront of the corresponding matrices finally the associated graphs are numerically compared copyright 2001 john wiley sons ltd

cylindrical cellular automata a one dimensional cellular automaton with periodic boundary conditions may be viewed as a lattice of sites on a cylinder evolving according to a local interaction rule a technique is described for finding analytically the set of attractors for such an automaton given any one dimensional automaton rule a matrixa is defined such that the number of fixed points on an arbitrary cylinder size is given by the trace ofa n where the powern depends linearly on the cylinder size more generally the number of strings of arbitrary length that appear in limit cycles of any fixed period is found as the solution of a linear recurrence relation derived from the characteristic equation of an associated matrix the technique thus makes it possible for any rule to compute the number of limit cycles of any period on any cylinder size to illustrate the technique closed form expressions are provided for the complete attractor structure of all two neighbor rules the analysis of attractors also identifies shifts as a basic mechanism underlying periodic behavior every limit cycle can be equivalently defined as a set of strings on which the action of the rule is a shift of sizes h i e each string cyclically shifts bys sites inh iterations of the rule the study of shifts provides detailed information on the structure and number of limit cycles for one dimensional automata

correlation analysis of the synchronizing ca landscape abstract a correlation analysis will be applied to subspaces of the fitness landscape generated by the synchronization task for one dimensional cellular automata this results in a stochastic model that can be used to characterize the correlation structure of those subspaces the results show that both subspaces can be characterized by an ar 2 model both for point mutation and crossover

adjoint based optimal control using meshfree discretizations the paper at hand presents a combination of optimal control approaches for pdes with meshless discretizations applying a classical lagrangian type particle method to optimization problems with hyperbolic constraints several adjoint based strategies differing in the sequential order of optimization and discretization of the lagrangian or eulerian problem formulation are proposed and compared the numerical results confirm the theoretically predicted independence principle of the optimization approaches and show the expected convergence behavior moreover they exemplify the superiority of meshless methods over the conventional mesh based approaches for the numerical handling and optimization of problems with time dependent geometries and freely moving boundaries

an algorithm for profile and wavefront reduction of sparse matrices summary an algorithm for reducing the profile and wavefront of a sparse matrix is described the scheme is applicable to any sparse matrix which has a symmetric pattern of zeros and may be used to generate efficient labellings for finite element grids in particular it is suitable for generating efficient labellings for profile and frontal solution schemes empirical evidence obtained from analysis of the 30 test problems collected by everstine suggests that the new algorithm is superior to existing methods for profile and wavefront reduction it is fast requires only a small amount of memory and is simple to program

chaos and diffusion in deterministic cellular automata abstract it is shown that some of the deterministic one dimensional cellular automata studied recently by wolfram exhibit a kind of spontaneous symmetry breaking the associated kinks bloch walls perform annihilating diffusive walks for infinite lattices and large times in addition close analogies between these automata and strange attractors are exhibited by mapping the automata onto dynamical systems defined by iterations of the unit square

turbulent pattern bases for cellular automata abstract unpredictable patterns generated by cellular automata ca can be decomposed with respect to a turbulent positive entropy rate pattern basis the resulting filtered patterns uncover significant structural organization in a ca s dynamics and information processing capabilities we illustrate the decompostion technique by analyzing a binary range 2 cellular automaton having two invariant chaotic domains of different complexities and entropies once identified the domains are seen to organize the ca s state space and to dominate its evolution starting from the domains structures we show how to construct a finite state transducer that performs nonlinear spatial filtering such that the resulting space time patterns reveal the domains and the intervening walls and dislocations to show the statistical consequences of domain detection we compare the entropy and complexity densities of each domain with the globally averaged quantities a more graphical comparison uses difference patterns and difference plumes which trace the space time influence of a single site perturbation we also investigate the diversity of walls and particles emanating from the interface between two adjacent domains

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

modified moving least squares with polynomial bases for scattered data approximation one common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes to tackle such problems we present a modified robust moving least squares mls method for scattered data smoothing and approximation the error functional used in the derivation of the classical mls approximation is augmented with additional terms based on the coefficients of the polynomial base functions this allows quadratic base functions to be used with the same size of the support domain as linear base functions resulting in better approximation capability the increased robustness of the modified mls method to irregular nodal distributions makes it suitable for use across many fields the analysis is supported by several univariate and bivariate examples

aperiodicity in one dimensional cellular automata abstract cellular automata are a class of mathematical systems characterized by discreteness in space time and state values determinism and local interaction a certain class of one dimensional binary site valued nearest neighbor automata is shown to generate infinitely many aperiodic temporal sequences from arbitrary finite initial conditions on an infinite lattice the class of automaton rules that generate aperiodic temporal sequences are characterized by a particular form of injectivity in their interaction rules included are the nontrivial linear automaton rules that is rules for which the superposition principle holds certain nonlinear automata with injectivity properties similar to those of linear automata and a wider subset of nonlinear automata whose interaction rules satisfy a weaker form of injectivity together with certain symmetry conditions the evolution of this last subset of automata can be viewed as consisting of multiple domains within which behavior exactly mimics that of a linear automaton a linearization technique is used to establish that these domains coalesce in finite time to produce at most two domains and thereby to assert the aperiodicity of their temporal sequences

a new class of automata networks a new class of automata networks is defined their evolution rules are determined by a probability measure p on the set of all integers z and an indicator function ia on the interval 0 1 it is shown that any cellular automaton rule can be represented by a nonunique rule formulated in terms of a pair p ia this new class of automata networks contains discrete systems which are not cellular automata for a given p a metric can be defined on the space of all rules which induces a metric on the space of all cellular automata rules

a coupled element free galerkin boundary element method for stress analysis of two dimensional solids element free galerkin efg method is a newly developed meshless method for solving partial differential equations using moving least squares interpolants it is however computationally expensive for many problems a coupled efg boundary element be method is proposed in this paper to improve the solution efficiency a procedure is developed for the coupled efg be method so that the continuity and compatibility are preserved on the interface of the two domains where the efg and be methods are applied the present coupled efg be method has been coded in fortran the validity and efficiency of the efg be method are demonstrated through a number of examples it is found that the present method can take the full advantages of both efg and be methods it is very easy to implement and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains

enforcement of essential boundary conditions in meshless approximations using finite elements abstract a technique for easily treating essential boundary conditions for approximations which are not interpolants such as moving least square approximations in the element free galerkin method is presented the technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation in the resulting approximation essential boundary conditions can be treated exactly as in finite elements it is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test numerical studies show that the method retains the high rate of convergence associated with moving least square approximations

intriguing properties of global structure in some classes of finite cellular automata abstract the simplest one dimensional cellular automata introduced recently by wolfram are analyzed particularly the finite cellular automata with two special evolution rules are studied non trivial correspondence in global structure is found between the state transition diagrams under the two rules correspondence of cycle structure basin volume of each cycle and structure of transient trees etc origin of the correspondence is explored on the basis of local properties of the evolution rules it is shown that this correspondence becomes exact in the thermodynamic limit

frictional contact analysis of functionally graded materials with lagrange finite block method summary based on the one dimensional differential matrix derived from the lagrange series expansion the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials in this paper the formulation of the lagrange finite block method with boundary type in the strong form is presented and applied to non conforming contact problems for the functionally graded materials subjected to either static or dynamic loads the first order partial differential matrices are only needed both in the governing equations and in the neumann boundary condition by introducing the mapping technique a block of quadratic type is transformed from the cartesian coordinate of global system to the normalized coordinate with eight seeds time dependent partial differential equations are analyzed in the laplace transformed domain and the durbin s inversion method is applied to determine all the physical values in the time domain conforming and non conforming contacts are investigated by using the iterative algorithm with full load technique illustrative numerical examples are given and comparisons have been made with analytical solutions copyright 2015 john wiley sons ltd

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a perturbation method for stochastic meshless analysis in elastostatics a stochastic meshless method is presented for solving boundary value problems in linear elasticity that involves random material properties the material property was modelled as a homogeneous random field a meshless formulation was developed to predict stochastic structural response unlike the finite element method the meshless method requires no structured mesh since only a scattered set of nodal points is required in the domain of interest there is no need for fixed connectivities between nodes in conjunction with the meshless equations classical perturbation expansions were derived to predict second moment characteristics of response numerical examples based on one and two dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method a good agreement is obtained between the results of the proposed method and monte carlo simulation since mesh generation of complex structures can be a far more time consuming and costly effort than the solution of a discrete set of equations the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems copyright 2001 john wiley sons ltd

power spectral density bounds corresp the determination of a power density spectrum from a finite set of correlation samples is an ill posed problem furthermore it is not possible even to bound the values that consistent power density spectra can take on at a particular point a more reasonable problem is to try to determine the total spectral power in some frequency interval although this power cannot be determined exactly upper and lower bounds on its possible values can be determined this observation leads to a unified treatment of certain classical and modern spectral estimation techniques and to new interpretations for two data adaptive spectral estimators maximum likelihood method mlm and data adaptive spectral estimator dase according to these new interpretations mlm and dase provide upper bounds on spectral power in a specified frequency region subject to the assumption that the spectral density is constant in that region these methods make no use of an extendibility constraint that can be used to obtain tight upper bounds as well as nontrivial lower bounds on power cybenko has studied a related problem of bounding windowed power for an arbitrary window with no assumptions about the form of the spectral density a new type of classical resolution limit for these bounds is derived and a numerical example is presented

local information transfer as a spatiotemporal filter for complex systems we present a measure of local information transfer derived from an existing averaged information theoretical measure namely transfer entropy local transfer entropy is used to produce profiles of the information transfer into each spatiotemporal point in a complex system these spatiotemporal profiles are useful not only as an analytical tool but also allow explicit investigation of different parameter settings and forms of the transfer entropy metric itself as an example local transfer entropy is applied to cellular automata where it is demonstrated to be a useful method of filtering for coherent structure more importantly local transfer entropy provides the first quantitative evidence for the long held conjecture that the emergent traveling coherent structures known as particles both gliders and domain walls which have analogs in many physical processes are the dominant information transfer agents in cellular automata

bounds from noisy linear measurements an estimation problem in which a finite number of linear measurements of an unknown function is available and in which the only prior information available concerning the unknown function consists of inequality constraints on its magnitude is ill posed in that insufficient information is available from which point estimates of the unknown function can be made with any reliability even with exact measurements an alternative to point estimation involves the computation of bounds on linear functionals of the unknown function in terms of the measurements a generalization is described of the bounding technique to problems in which the measurements are inexact the bounds are defined in terms of a primal optimization problem a deterministic interpretation of the bounds is given as well as a probabilistic one for the case of additive gaussian measurement noise an unconstrained dual optimization problem is derived that has an interesting data adaptive filtering interpretation and provides an attractive basis for computation several aspects of the primal and dual optimization problems are investigated that have important implications for the reliable computation of the bounds

the calculi of emergence computation dynamics and induction abstract defining structure and detecting the emergence of complexity in nature are inherently subjective though essential scientific activities despite the difficulties these problems can be analyzed in terms of how model building observers infer from measurements the computational capabilities embedded in nonlinear processes an observer s notion of what is ordered what is random and what is complex in its environment depends directly on its computational resources the amount of raw measurement data of memory and of time available for estimation and inference the discovery of structure in an environment depends more critically and subtlely though on how those resources are organized the descriptive power of the observer s chosen or implicit computational model class for example can be an overwhelming determinant in finding regularity in data this paper presents an overview of an inductive framework hierarchical machine reconstruction in which the emergence of complexity is associated with the innovation of new computational model classes complexity metrics for detecting structure and quantifying emergence along with an analysis of the constraints on the dynamics of innovation are outlined illustrative examples are drawn from the onset of unpredictability in nonlinear systems finitary nondeterministic processes and cellular automata pattern recognition they demonstrate how finite inference resources drive the innovation of new structures and so lead to the emergence of complexity

efg approximation with discontinuous derivatives a technique for incorporating discontinuities in derivatives into meshless methods is presented the technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives the special shape functions have compact support which results in banded matrix equations the technique is described in element free galerkin context but is easily applicable to other meshless methods and projections numerical results for problems in one and two dimensions are reported 1998 john wiley sons ltd

convergence and aperiodicity in fuzzy cellular automata revisiting rule 90 abstract in this paper we consider a continuous version of cellular automata fuzzy ca obtained by fuzzification of the disjunctive normal form which describes the corresponding boolean rule we concentrate on fuzzy rule 90 whose boolean version deserves some attention for the complex patterns it generates we show that the behavior of fuzzy rule 90 is very simple in that the system always converges to a fixed point in the case of finite support configurations we also show aperiodicity of every temporal sequences extending and complementing jen s result on aperiodicity of boolean rule 90 we finally show and analyze the remarkable fact that depending on the level of state discreteness used to visualize the dynamics of fuzzy rule 90 the display might show after a transient the well known complex boolean behavior instead of the correct convergence to a fixed point the results of the analysis lead not only to a caveat on the dangers of visualization but also an unexpected explanation of the dynamics of boolean rule 90

uniform norm minimization for two signed solutions in an earlier paper huestis 1986 i gave an iterative algorithm for efficient linear programming construction of the minimum uniform norm solution of a linear inverse problem in such a problem d data values ei are linear functionals of the unknown solution m r usually expressible as integrals over an appropriate domain v ei vgi r m r dr ei i 1 d the gi are known functions and ei allows for measurement error

idb2 a fortran program for computing extremal bounds in gravity data interpretation it is well known that the interpretation of gravity anomaly data suffers from a fundamental nonuniqueness no matter how complete a gravity data set may be there are an unlimited number of subsurface density solutions compatible with it this generally remains true even when the class of mathematically acceptable solutions is limited by imposed constraints based on physical or geologic arguments the common practice constructing a single solution fitting or only approximately fitting the anomaly data is therefore of limited value

upper bound on the products of particle interactions in cellular automata abstract particle like objects are observed to propagate and interact in many spatially extended dynamical systems for one of the simplest classes of such systems one dimensional cellular automata we establish a rigorous upper bound on the number of distinct products that these interactions can generate the upper bound is controlled by the structural complexity of the interacting particles a quantity which is defined here and which measures the amount of spatio temporal information that a particle stores along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata thereby elucidating why that approach is of general utility the upper bound is tested against several relatively complex domain particle cellular automata and found to be tight

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

automatic filters for the detection of coherent structure in spatiotemporal systems most current methods for identifying coherent structures in spatially extended systems rely on prior information about the form which those structures take here we present two approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures one local sensitivity filtering is a modification of the local lyapunov exponent approach suitable to cellular automata and other discrete spatial systems the other local statistical complexity filtering calculates the amount of information needed for optimal prediction of the system s behavior in the vicinity of a given point by examining the changing spatiotemporal distributions of these quantities we can find the coherent structures in a variety of pattern forming cellular automata without needing to guess or postulate the form of that structure we apply both filters to elementary and cyclical cellular automata eca and cca and find that they readily identify particles domains and other more complicated structures we compare the results from eca with earlier ones based upon the theory of formal languages and the results from cca with a more traditional approach based on an order parameter and free energy while sensitivity and statistical complexity are equally adept at uncovering structure they are based on different system properties dynamical and probabilistic respectively and provide complementary information

defect particle kinematics in one dimensional cellular automata let a z be the cantor space of bi infinite sequences in a finite alphabet a and let s be the shift map on a z a cellular automaton is a continuous s commuting self map f of a z and a f invariant subshift is a closed f s invariant subset s a z suppose a a z is s admissible everywhere except for some small region we call a defect it has been empirically observed that such defects persist under iteration of f and often propagate like particles we characterize the motion of these particles and show that it falls into several regimes ranging from simple deterministic motion to generalized random walks to complex motion emulating turing machines or pushdown automata one consequence is that some questions about defect behaviour are formally undecidable

gravity ideal bodies the interpretation of gravity anomaly data suffers from a fundamental nonuniqueness even when the solution set is bounded by physical or geologic constraints therefore constructing a single solution that fits or approximately fits the data is of limited value consequently much effort has been applied in recent years to developing inverse techniques for rigorous deduction of properties common to all possible solutions to this end parker developed the theory of an ideal body which characterizes the extremal solution with the smallest possible maximum density gravity ideal body analysis is an excellent reconaissance exploration tool because it is especially well suited for handling sparse data contaminated with noise for finding useful rigorous bounds on the infinite solution set and for predicting accurately what data need to be collected in order to tighten those bounds we present a practical three dimensional gravity ideal body computer code idb that can optimize a mesh with over 105 cells

improved xfem an extra dof free well conditioning and interpolating xfem abstract although its unprecedentedly success in approximating the singular field around a crack tip independent of mesh discretization xfem still has been long hindered in engineering applications by its ill conditioning and the difficulty in mass lumping corresponding to extra dofs an improved xfem i xfem is developed to overcome those difficulties from three aspects 1 to eliminate the linear dependence and the ill conditioning issues of the standard and the corrected xfems 2 to get rid of extra dofs in crack tip enrichment to facilitate optimal mass lumping in dynamic analyses 3 to be interpolating at enriched nodes to enable direct essential contact boundary treatments the core of i xfem is a globally interpolating approximation based on local least squares fitting the new method is numerically examined with comprehensive comparisons with the standard xfem and the corrected xfem fries 2008 the new method s excellent performance in terms of accuracy convergence and conditioning stability are demonstrated

local structure theory for cellular automata abstract the mean field theory for cellular automata wolfram and schulman and seiden is generalized to the local structure theory the local structure theory is a sequence of finitely parameterized models of the statistical features of a cellular automaton s evolution the n th model in the sequence takes into account correlations in terms of the probability of blocks of n states a class of measures the n block measures is introduced the local structure operator of order n maps n block measures to n block measures in a manner which reflects the cellular automaton map on blocks of states the fixed points of the map on measures approximate the invariant measures of the cellular automaton the ability of the local structure theory to model evolution from uncorrelated initial distributions is studied the theory gives exact results in simple cases in more complex cases monte carlo numerical experiments suggest that an accurate statistical portrait of cellular automaton evolution is obtained the invariant measures of a cellular automaton and the stability of these measures may be obtained from the local structure theory the local structure theory appears to be a powerful method for characterization and classification of cellular automata nearest neighbor cellular automata with two states per cell are studied using this method

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

computational mechanics of cellular automata an example abstract we illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space time behavior of elementary one dimensional cellular automaton rule 54 the dominant regular domain of the cellular automation is identified and a domain filter is constructed to locate and classify defects in the domain the primary particles are identified and a range of interparticle interactions is studied the deterministic equation of motion of the filtered space time behavior is derived filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher level defects particle interactions and secondary domains we define the emergence time at which the space time behavior condenses into configurations consisting only of domains particles and particle interactions taken together these techniques serve as the basis for the investigation of pattern evolution and self organization in this representative system

a two step approach to finite element ordering abstract a two step approach to finite element ordering is introduced the scheme involves ordering of the finite elements first based on their adjacency followed by a local numbering of the nodal variables the ordering of the elements is performed by the cuthill mckee algorithm this approach takes into consideration the underlying structure of the finite element mesh and may be regarded as a natural finite element ordering scheme the experimental results show that this two step scheme is more efficient than the reverse cuthill mckee algorithm applied directly to the nodes in terms of both execution time and the number of fill in entries particularly when higher order finite elements are used in addition to its efficiency the two step approach increases modularity and flexibility in finite element programs and possesses potential application to a number of finite element solution methods author

replication in one dimensional cellular automata abstract in a cellular automaton ca replication is the ability to indefinitely generate copies of a finite collection of patterns starting from finite seeds a transparent feature of additive ca replication mechanisms are less clear in the absence of additivity this paper investigates such dynamics through several examples for the 1 or 2 rule and its generalizations replication is inevitable and we investigate self organization properties in the perturbed exactly 1 rule we study frequency of replicators and the new phenomenon is called quasireplication the last ca is the extended 1 or 3 rule which allows for replication on different backgrounds we employ a mixture of rigorous and empirical techniques

the use of linear programming in the construction of extremal solutions to linear inverse problems while a finite collection of data does not specify a unique solution to a linear inverse problem it can allow bounds to be placed on certain nonlinear solution functionals using the dirichlet problem for the unit disc as an example this note demonstrates the use of linear programming in constructing extremal solutions associated with a variety of such bounds

soliton like behavior in automata abstract we propose a new kind of automaton that uses newly computed site values as soon as they are available we call them filter automata fa they are analogous to infinite impulse response iir digital filters whereas the usual cellular automata ca correspond to finite impulse response fir digital filters it is shown that as a class the fa s are equivalent to ca s in the sense that the same array of space generation values can be produced they must be generated in a different order however a particular class of irreversible totalistic fa s are described that support a profusion of persistent structures that move at different speeds and these particle like patterns collide in nondestructive ways they often pass through one another with nothing more than a phase jump much like the solitons that arise in the solution of certain nonlinear differential equations histograms of speed displacement and period are given for neighborhood radii from 2 to 6 and particles with generators up to 16 bits wide we then present statistics for neighborhood radii 2 to 9 which show that collisions which preserve the identity of particles are very common

combination of the meshless finite difference approach with the monte carlo random walk technique for solution of elliptic problems abstract this paper proposes a stochastic approach for the fast and effective numerical analysis of the second order elliptic differential equations it is based upon the well known monte carlo mc method with a random walk rw technique carried out on the grid of points this method allows for accurate estimation of the solution of the differential equation at selected point s of the domain and or its boundary it extends the standard formulation of the monte carlo random walk mc rw approach by means of its appropriate combination with the meshless version of the finite difference method in this manner the proposed approach may deal with elliptic equations in more general non homogeneous form as well as boundary conditions of both essential and natural types moreover arbitrarily irregular clouds of nodes may be used with no a priori imposed nodes structure therefore the meshless mc rw approach may be applied to the significantly wider class of problems with more complex geometry this concept was examined on variety of 2d boundary value problems selected numerical results are presented and discussed a simple matlab code is included as well

a coupled interpolating meshfree method for computing sound radiation in infinite domain summary in this paper the coupling of the improved interpolating element free galerkin iiefg method and the variable order infinite acoustic wave envelope element wee method is studied a coupled iiefg wee method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages the coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the iiefg and wee domains in the iiefg domain the improved interpolating moving least squares iimls method is employed to form the shape functions satisfying the kronecker delta condition while nonsingular weight functions can be used the impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated the numerical results show that the coupled iiefg wee method can take full advantage of both the iiefg and wee methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the wee the experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain this article is protected by copyright all rights reserved

a novel meshless scheme for solving surface integral equations with flat integral domains numerical solutions for electromagnetic em integral equations rely on the discretization of integral domains and the use of meshes for geometric description meshing geometries is very tedious especially for complicated structures with many details tiny parts and geometric discontinuities corners or edges and remeshing could be required in many scenarios to reduce the costs of generating quality meshes meshless or mesh free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in em community the meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally in this work we first address the traditional meshless scheme for solving em integral equations based on the moving least square mls approximation for unknown currents and the use of background meshes for integrations and then develop a novel meshless scheme by applying the green s lemma to the em surface integral equations with flat domains the novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain since only the domain boundaries are discretized and no background meshes are needed the scheme is truly meshless numerical examples for em scattering by flat surface objects are presented to demonstrate the effectiveness of the novel scheme

interpolating element free galerkin method for the regularized long wave equation and its error analysis abstract combining the simplified interpolating moving least squares imls method with the galerkin weak form an interpolating element free galerkin iefg method is presented for the numerical study of the regularized long wave rlw equation the trial function in the imls method has one less unknown coefficient than in the traditional mls approximation and the shape functions satisfy the interpolating property at nodes then the iefg method can apply the essential boundary conditions naturally and directly and has high computational accuracy and then this paper studies the error estimates of the iefg method for rlw equation the error estimate of the semi discrete iefg method for the rlw equation on the influence domain radius is first studied and then the convergence rate of the full discrete scheme of the method on the influence domain radius and time step is studied the theoretical results show that the iefg method for rlw equation has good convergence rate for the purpose of demonstration three selected numerical examples are given to demonstrate the method and the mathematical theory of this paper