critical behavior of sandpile vortices under variable charge in the following we consider a sandpile cellular automaton model height version which also takes account of lattice cyclicity for variable charge of grains projected upon the board the size of the charge or additional grains of sand used to upset the equilibrium and to induce an avalanche is found to affect the distributional forms and in particular the convergence of the estimate for the dynamic exponent exponent estimates show slow variation with lattice dimensionl and some evidence of evolution with charge the scaling region is limited in all cases with noisy decay at all levels of charge results presented extend the work of duarte and goncalves 1990 on the triangular lattice

three mechanisms for power laws on the cayley tree we compare preferential growth critical phase transitions and highly optimized tolerance hot as mechanisms for generating power laws in the familiar and analytically tractable context of lattice percolation and forest fire models on the cayley tree all three mechanisms have been widely discussed in the context of complexity in natural and technological systems this parallel study enables direct comparison of the mechanisms and associated lattice solutions criticality fits most naturally into the category of random processes where power laws are a consequence of fluctuations in an ensemble with no intrinsic scale the power laws in preferential growth can be understood in the context of competing exponential growth and decay processes hot generalizes this functional mechanism involving exponentials of exponentials to a broader class of nonexponential functions which arise from optimization

identifying spatial clustering phenomena in forest fire sequences abstract spatial clustering in fire data recorded from 1997 to 2003 in an area of central italy has been deeply investigated using indices of different type i a topological index the voronoi polygon area ii a statistical index the morishita index iii a dimensional index the fractal dimension our findings reveal the presence of clustering in the spatial distribution of the fire set analysed the knowledge of such property can be very useful to estimate overdensity of fires in those areas where particular prevention and allocation of resources should be assessed

investigation of the forest fire model on a small world network it is shown that the forest fire model of bak et al run on a square lattice network with additional long range interactions in the spirit of a small world network results in a scale free system reminiscent of self organized criticality without recourse to fine tuning as the number of these long range interactions is increased the cluster size distribution exponent is found to decrease in magnitude as the small world regime is entered indicating a change in its universality class it is suggested that such a model could have applicability in the study of disease spreading in human populations

on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

cluster variation approximations for a contact process living on a graph abstract a model classically used for modelling the spread of an infectious diseases in a network is the time continuous contact process which is one simple example of an interacting particles system it displays a non equilibrium phase transition related to the burst of an epidemic within a population in case of an accidental introduction several studies have recently emphasized the role of some geometrical properties of the graph on which the contact process lives like the degree distribution for quantities of interest like the singlet density at equilibrium or the critical value of the infectivity parameter for the emergence of the epidemics but this role is not yet fully understood as the contact process on a graph still cannot be solved analytically even on a 1d lattice some approximations are needed the more naive but well studied approximation is the mean field approximation we explore in this paper the potentiality of a finer approximation the pair approximation used in ecology we give an analytical formulation on a graph of the site occupancy probability at equilibrium depending on the site degree under pair approximation and another dependence structure approximation we point out improvements brought about in the case of realistic graph structures far from the well mixed assumption we also identify the limits of the pair approximation to answer the question of the effects of the graph characteristics we show how to improve the method using a more appropriate order 2 cluster variation method the bethe approximation

message passing approach for recurrent state epidemic models on networks epidemic processes are common out of equilibrium phenomena of broad interdisciplinary interest recently dynamic message passing dmp has been proposed as an efficient algorithm for simulating epidemic models on networks and in particular for estimating the probability that a given node will become infectious at a particular time to date dmp has been applied exclusively to models with one way state changes as opposed to models like sis and sirs where nodes can return to previously inhabited states because many real world epidemics can exhibit such recurrent dynamics we propose a dmp algorithm for complex recurrent epidemic models on networks our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source and thus avoids echo chamber effects where a pair of adjacent nodes each amplify the probability that the other is infectious we demonstrate that this approach well approximates results obtained from monte carlo simulation and that its accuracy is often superior to the pair approximation which also takes second order correlations into account moreover our approach is more computationally efficient than the pair approximation especially for complex epidemic models the number of variables in our dmp approach grows as 2mk where m is the number of edges and k is the number of states as opposed to mk 2 for the pair approximation we suspect that the resulting reduction in computational effort as well as the conceptual simplicity of dmp will make it a useful tool in epidemic modeling especially for high dimensional inference tasks

on the invariant distribution of a one dimensional avalanche process we consider an interacting particle system t t 0 with values in 0 1 z in which each vacant site becomes occupied with rate 1 while each connected component of occupied sites become vacant with rate equal to its size we show that such a process admits a unique invariant distribution which is exponentially mixing and can be perfectly simulated we also prove that for any initial condition the avalanche process tends to equilibrium exponentially fast as time increases to infinity finally we consider a related mean field coagulation fragmentation model we compute its invariant distribution and we show numerically that it is very close to that of the interacting particle system

natural norm a posteriori error estimators for reduced basis approximations we present a technique for the rapid and reliable prediction of linear functional outputs of coercive and noncoercive linear elliptic partial differential equations with affine parameter dependence the essential components are i rapidly convergent global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n judiciously selected points in parameter space ii a posteriori error estimation relaxations of the error residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest and iii offiine online computational procedures methods which decouple the generation and projection stages of the approximation process the operation count for the online stage in which given a new parameter value we calculate the output of interest and associated error bound depends only on n typically very small and the parametric complexity of the problem in this paper we propose a new natural norm formulation for our reduced basis error estimation framework that a greatly simplifies and improves our inf sup lower bound construction offline and evaluation online a critical ingredient of our a posteriori error estimators and b much better controls significantly sharpens our output error bounds in particular through deflation for parameter values corresponding to nearly singular solution behavior we apply the method to two illustrative problems a coercive laplacian heat conduction problem which becomes singular as the heat transfer coefficient tends to zero and a non coercive helmholtz acoustics problem which becomes singular as we approach resonance in both cases we observe very economical and sharp construction of the requisite natural norm inf sup lower bound rapid convergence of the reduced basis approximation reasonable effectivities even for near singular behavior for our deflated output error estimators and significant several order of magnitude online computational savings relative to standard finite element procedures

synchronization of integrate and fire oscillators with global coupling we study the behavior of globally coupled assemblies of a large number of integrate and fire oscillators with excitatory pulselike interactions on some simple models we show that the additive effects of pulses on the state of integrate and fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators this synchronization occurs in two forms depending on the system either the oscillators evolve en bloc at the same phase and therefore relax together or the oscillators do not remain in phase but their relaxations occur always in stable avalanches we prove that synchronization can occur independently of the convexity or concavity of the oscillator evolution function furthermore the presence of disorder up to some level is not only compatible with synchronization but removes some possible degeneracy of identical systems and allows new mechanisms towards this state textcopyright 1996 the american physical society

forest fire model with immune trees abstract we present a generalization of the forest fire model of p bak et al by including the immunity g which is the probability that a tree is not ignited although one of its neighbors is burning when g reaches a critical value gc p which depends on the tree growth rate p the fire cannot survive any more i e a continuous phase transition takes place from a steady state with fire to a steady state without fire we present results of computer simulations and explain them by analytic calculations the fire spreading at the phase transition represents a new type of percolation which is called fluctuating site percolation

aftershocks in coherent noise models the decay pattern of aftershocks in the so called coherent noise models m e j newman and k sneppen phys rev e54 6226 1996 is studied in detail analytical and numerical results show that the probability to nd a large event at timet after an initial major event decreases as t for smallt with the exponent ranging from 0 to values well above 1 this is in contrast to sneppen und newman who stated that the exponent is about 1 independent of the microscopic details of the simulation numerical simulations of an extended model c wilke t martinetz phys rev e56 7128 1997 show that the power law is only a generic feature of the original dynamics and does not necessarily appear in a more general context finally the implications of the results to the modeling of earthquakes are discussed

power laws from randomly sampled continuous time random walks abstract it has been shown by reed that random sampling a wiener process x t at times t chosen out of an exponential distribution gives rise to power laws in the distribution p x t x t we show both theoretically and numerically that this power law behaviour also follows by random sampling levy flights as continuous time random walks having fourier distribution w k e k with the exponent

crossover behavior in driven cascades we propose a model which explains how power law crossover behavior can arise in a system which is capable of experiencing cascading failure in our model the susceptibility of the system to cascades is described by a single number the propagation power which measures the ease with which cascades propagate physically such a number could represent the density of unstable material in a system its internal connectivity or the mean susceptibility of its component parts to failure we assume that the propagation power follows an upward drifting brownian motion between cascades and drops discontinuously each time a cascade occurs cascades are described by a continuous state branching process with distributional properties determined by the value of the propagation power when they occur in common with many cascading models pure power law behavior is exhibited at a critical level of propagation power and the mean cascade size diverges this divergence constrains large systems to the subcritical region we show that as a result crossover behavior appears in the cascade distribution when an average is performed over the distribution of propagation power we are able to analytically determine the exponents before and after the crossover

self organized criticality in a forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f 0 provided that the time scales of free growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system there is evidence that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

an inverse cascade model for self organized critical behavior we introduce an inverse cascade model to explain self organized critical behavior this model is motivated by the forest re model in the forest re model trees are randomly planted on a grid sparks are also dropped on the grid resulting in res in which trees are lost in the inverse cascade model single trees are introduced and these combine to form larger and larger clusters this is the inverse cascade and gives a power law fractal frequency size distribution of clusters model res eliminate trees from all cluster sizes but signicant numbers of trees are lost only from the largest clusters and this loss terminates the power law scaling finally our model illustrates important dierences between critical and self organized critical behavior c 1999 elsevier science b v all rights reserved

three level description of the domino cellular automaton motivated by the approach of kinetic theory of gases a three level description microscopic mesoscopic and macroscopic of cellular automaton is presented to provide an analytical treatment a simple domino cellular automaton with avalanches is constructed formulas concerning exact relations for density clusters avalanches and other parameters in a stationary state are derived some relations approximately valid for deviations from the stationary state are found and the adequate ito equation is constructed it provides the time evolution description of the density on the macroscopic level the results support an idea of application of the ito equation to some natural time series

system size independence of a large deviation function for frequency of events in a one dimensional forest fire model with a single ignition site it is found that a large deviation function for the frequency of events of a size not equal to the system size in the one dimensional forest fire model with a single ignition site at an edge is independent of the system size by using an exact decomposition of the modified transition matrix of a master equation an exchange in the largest eigenvalue of the modified transition matrix may not occur in the model

on a self organized critical forest fire model the author studies a forest fire model introduced in a paper by drossel and schwabl 1992 by means of simulations with high statistics and very close to the critical point in this way he can correct some statements made in that paper in particular he finds that the critical exponents are not the classical ones proposed by drossel and schwabl in spite of scaling laws with anomalous exponents the typical states of the system are not critical in the sense of being marginally stable locally

family size variability grows with collapse rate in a birth death catastrophe model forest fire and avalanche models support the notion that frequent catastrophes prevent the growth of very large populations and as such prevent rare large scale catastrophes we show that this notion is not universal a new model class leads to a paradigm shift in the influence of catastrophes on the family size distribution of subpopulations we study a simple population dynamics model where individuals as well as a whole family may die with a constant probability accompanied by a logistic population growth model we compute the characteristics of the family size distribution in steady state and the phase diagram of the steady state distribution and show that the family and catastrophe size variances increase with the catastrophe frequency which is the opposite of common intuition frequent catastrophes are balanced by a larger net growth rate in surviving families leading to the exponential growth of these families when the catastrophe rate is further increased a second phase transition to extinction occurs when the rate of new family creations is lower than their destruction rate by catastrophes

dynamics of driven interfaces near isotropic percolation transition we consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold in particular we study simple discrete forest fire lattice models through monte carlo simulations in two and three spatial dimensions an interface generated in the models is found to display complex behavior away from the percolation transition the interface is self affine with asymptotic dynamics consistent with the kardar parisi zhang universality class however in the vicinity of the percolation transition there is a different behavior at earlier times by scaling arguments we show that the global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying percolation cluster our numerical results are in good agreement with theory however we demonstrate that at the depinning transition the interface as defined in the models is no longer self affine finally we compare these results with those obtained from a more realistic reaction diffusion model of slow combustion s1063 651x 98 08708 x

measuring the dimension of partially embedded networks a b s t r a c t scaling phenomena have been intensively studied during the past decade in the context of complex networks as part of these works recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks in this paper we pro pose a new dimension measurement method for networks which does not require global knowledge on the embedding of the nodes instead it exploits link wise information link lengths link delays or other physical quantities our method can be regarded as a general ization of the spectral dimension that grasps the network s large scale structure through local observations made by a random walker while traversing the links we apply the pre sented method to synthetic and real world networks including road maps the internet infrastructure and the gowalla geosocial network we analyze the theoretically and empir ically designated case when the length distribution of the links has the form p 1 we show that while previous dimension concepts are not applicable in this case the new dimension measure still exhibits scaling with two distinct scaling regimes our observa tions suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks and we show that the proposed measure provides information that complements other known measures

a combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves abstract the inverse problem of material characterization is formulated as a parameter identification problem in which a set of parameters corresponding to the material property can be found by minimizing error functions formulated using the measured displacement response and the one computed by a forward solver based on projected candidates of parameters a hybrid numerical method is employed as the forward solver to calculate the dynamic displacement response on the surface of the composite plate for given material property a combined method is used as the inverse operator to determine the material property of composite plate in this method genetic algorithm is first used to select a set of better solutions close to the optima then the nonlinear least squares method is applied using these better solutions as the initial guesses finally the identification results can be determined from the solutions of nonlinear least squares method by comparing their corresponding error function values actual material characterizations of composites demonstrate the higher efficiency of the present method

multifractal behavior of wild land and forest fire time series in brazil abstract we examine statistical properties of a daily hot pixel time series recorded in brazil during the period 1998 2006 using multifractal detrended fluctuation analysis mf dfa we find that generalized scaling exponent h q is a decreasing function of q indicating multifractal behavior of hot pixel dynamics we also calculate multifractal spectra f and use fourth degree polynomial regression to estimate complexity parameters that describe the degree of multifractality of the underlying process after july 2002 when a significant increase of the number of hot pixel observations is recorded the complexity of the series is reduced manifested by the reduction of width of the f spectrum while small fluctuations increase their dominance over large scale fluctuations manifested by the increase of skew parameter r these results should be taken into account when devising ecological and climatic models for brazil that contemplate the phenomena of wild land and forest fires

exact results for the one dimensional self organized critical forest fire model we present the analytic solution of the self organized critical soc forest fire model in one dimension proving soc in systems without conservation laws by analytic means under the condition that the system is in the steady state and very close to the critical point we calculate the probability that a string of ital n neighboring sites is occupied by a given configuration of trees the critical exponent describing the size distribution of forest clusters is exactly tau 2 and does not change under certain changes of the model rules computer simulations confirm the analytic results

bak tang wiesenfeld model on the square site percolation lattice the bak tang wiesenfeld btw model is considered on the site diluted square lattice tuned by the occupancy probability p various statistical observables of the avalanches are analyzed in terms of p e g the fractal dimension of their exterior frontiers gyration radius loop lengths and green s function the model exhibits critical behavior for all amounts of p and the exponents of the statistical observables are analyzed we find a distinct universality class at which is unstable towards a p 1 btw fixed point this universality class displays some common features such as a two dimensional 2d ising universality class e g the fractal dimension of loops in the thermodynamic limit is which is compatible with the fractal dimension of geometrical spin clusters of the 2d critical ising model with

mean field frozen percolation we define a modification of the erd s renyi random graph process which can be regarded as the mean field frozen percolation process we describe the behavior of the process using differential equations and investigate their solutions in order to show the self organized critical and extremum properties of the critical frozen percolation model we prove two limit theorems about the distribution of the size of the component of a typical frozen vertex

continuous time random walks in periodic systems fluid limit and fractional differential equations on the circle in this paper the continuous time random walk on the circle is studied we derive the corresponding generalized master equation and discuss the effects of topology especially important when levy flights are allowed then we work out the fluid limit equation formulated in terms of the periodic version of the fractional riemann liouville operators for which we provide explicit expressions finally we compute the propagator in some simple cases the analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions

formation of space time structure in a forest fire model we present a general stochastic forest fire model which shows a variety of different structures depending on the parameter values the model contains three possible states per site tree burning tree empty site and three parameters tree growth probability p lightning probability f and immunity g we review analytic and computer simulation results for a quasideterministic state with spiral shaped fire fronts for a percolation like phase transition and a self organized critical state possible applications to excitable systems are discussed

soc in a population model with global control abstract we study a plant population model introduced recently by wallinga oikos 74 1995 377 it is similar to the contact process simple epidemic directed percolation but instead of using an infection or recovery rate as control parameter the population size is controlled directly and globally by removing excess plants we show that the model is very closely related to directed percolation dp anomalous scaling laws appear in the limit of large populations small densities and long times these laws associated critical exponents and even some non universal parameters can be related to those of dp as in invasion percolation and in other models where the roles of control and order parameters are interchanged the critical value pc of the wetting probability p is obtained in the scaling limit as singular point in the distribution of removal rates we show that a mean field type approximation leads to a model studied by zhang et al j stat phys 58 1990 849 finally we verify the claim of wallinga that family extinction in a marginally surviving population is governed by dp scaling laws and speculate on applications to human mitochondrial dna

power law distribution of family names in japanese societies abstract we study the frequency distribution of family names from a common data base we count the number of people who share the same family name this is the size of the family we find that i the total number of different family names in a society scales as a power law of the population ii the total number of family names of the same size decreases as the size increases with a power law and iii the relation between size and rank of a family name also shows a power law these scaling properties are found to be consistent for five different regional communities in japan

complexity of some problems from the theory of automata 1 1 given a finite alphabet l the regular events over x are those accepted by a finite state automaton by kleene s theorem a subset w of s is a regular event if and only if it can be constructed from the finiteword sets by boolean operations together with concatenation and operation in some sense the regular events are quite simple because they are accepted by a machine with no storage capacity nevertheless in recent years much attention has been paid to special subclasses of the class of regular events in this paper we shall be concerned with star free events events of dot depth one and piecewise testable events star free events are constructed like regular events from the finite word sets but with the restriction that the operation is not allowed events of dot depth one and piecewise testable events are star free of a very simple form and will be defined below star free events have been characterized in the work of schiitzenberger 1965 in terms of their syntactic monoid algebraic characterizations of the other two classes have been given simon 1975 knast 1983 from an algorithmic point of view these algebraic characterizations do not yield efficient procedures because computing the syntactic monoid of a regular event given e g by an automaton is obviously time consuming in this paper we investigate the complexity of three problems which we now describe in the style of garey and johnson 1979 we refer the reader to aho hopcroft and ullman 1983 garey and johnson 1979 for standard concepts of complexity theory

rapid inverse parameter estimation using reduced basis approximation with asymptotic error estimation this paper presents a rapid and reliable approach to solve inverse problems of parameter estimation for structural systems using reduced basis method rbm a reduced basis model is first developed with asymptotic error estimation and is used for fast computation of solving forward mechanics problems of solids and structures a genetic algorithm ga is then used in the inverse search procedure for parameter estimation the approach is applied to a typical inverse problem of estimating the crack location length and orientation inside a cantilever beam the displacements measured at five points on the lower surface of the beam which can also be evaluated by our fast rbm solver are used as inputs for constructing objective functions of error the genetic algorithm is used to search these parameters of the crack inside cantilever beam that minimize the objective function an example has been presented it is found that the estimated results are very accurate and reliable due to the use of rbm forward model with an effective and robust error estimation and detailed sensitivity analysis the present procedure is 460 times faster than the full fem model used inverse procedure

reduced basis approximation and a posteriori error estimation for stress intensity factors we develop reduced basis approximations rigorous a posteriori error bounds and offline online computational procedures for the accurate fast and reliable prediction of stress intensity factors or strain energy release rates for mode i linear elastic crack problems relevant to fracture mechanics we demonstrate the efficiency and rigor of our numerical method in several examples

classifying regular languages by a split game in this paper we introduce the split game a variant of the ehrenfeucht fraisse game from logic which is useful for analyzing the expressive power of classes of generalized regular expressions an extension of the split game to generalized w regular expressions is also established to gain insight into how the split game can be applied to attack the long standing generalized star height 2 problem we propose and solve the omega power problem a similar but tractable problem in the context of w languages namely we show that omega powers together with boolean combinations and concatenations are not sufficient to express the class of w regular languages

highly optimized tolerance and power laws in dense and sparse resource regimes power law cumulative frequency p versus event size l distributions p l similar to l alpha are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics the broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena a discrete highly optimized tolerance hot model referred to as the probability loss resource plr model gives the exponent alpha 1 d as a function of the dimension d of the underlying substrate in the sparse resource regime this agrees well with data for wildfires web file sizes and electric power outages however another hot model based on a continuous dense distribution of resources predicts alpha 1 1 d in this paper we describe and analyze a third model the cuts model which exhibits both behaviors but in different regimes we use the cuts model to show all three models agree in the dense resource limit in the sparse resource regime the continuum model breaks down but in this case the cuts and plr models are described by the same exponent

remark on the star height problem abstract a method is presented which allows to construct general regular expressions of star height 1 for a class of rather complicated regular events general regular expressions include an operation symbol for complement if events of greater general star height exist which is still open they must be more complex than those accessible by this method an event which seems to be of this kind is suggested at the end of the paper

novel position space renormalization group for bond directed percolation in two dimensions abstract a new position space renormalization group approach is investigated for bond directed percolation in two dimensions the threshold value for the bond occupation probabilities is found to be p c 0 6443 correlation length exponents on time parallel and space transverse directions are found to be 1 719 and 1 076 respectively which are in very good agreement with the best known series expansion results

monadic partition logics and finite automata abstract by argumenting first order logic with monadic partition quantifiers we get a new family of extended logics they are strictly weaker in expressive power than monadic second order logic have some good semantic features and offer better specification formalisms for studying finite automata and formal languages

length scales and power laws in the two dimensional forest fire model abstract we re examine a two dimensional forest fire model via monte carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two point correlation function of trees we check resp improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode we also investigate the possibility of describing the critical point in terms of a distribution of the global density we find that some qualitative features such as a temporal oscillation and a power law of the cluster size distribution can nicely be obtained from such a model that discards the spatial structure

unstable supercritical discontinuous percolation transitions percolation is a pervasive concept 1 which has applications in a wide variety of natural technological and social systems 2 3 4 5 ranging from conductivity of composite materials 6 7 and polymerization 8 to epidemic spreading 9 10 11 and information diffusion 12 13

application of a nonlinear evolution model to fire propagation the numerical simulation of fire in forest has been an important objective in recent researches the rate of spread and shape of a forest fire front is af8ecte d by many factors the most important of these are as follows fuel type and moisture content wind velocity and variability forest topography fire spread mechanism fuel continuity and the amount of spotting cf l 21 the development of geographic information systems allows the incorporation of these data to the developed models the first models took into account constant factors continuous uniform fuel type constant wind velocity moisture and slope under these conditions a fire ignited at a single point reaches a quasi steady state and progresses toward the down wind direction and expands at a constant rate these data cannot give precise predictions under variable conditions but are very useful in order to the intuition of the fire controller models capable of being incorporated into the computer simulations of fires under variable conditions have been developed based on cellular automata cf 3 7 and stochastic process 8 these models can give useful indicators as to fire behavior under such conditions combustion phenomena has been extensively studied 9 unsteady flame propagation has been analyzed lo models based on combustion theories are very difficult to develop because of the diversity of the fuel type and varied chemical composition within a given fuel type because of the complexity of the problem models based rigorously on combustion theory have not been completely developed in this preliminary work a first attempt is done to design a computer code for numerical simulation of forest fire spread in landscapes basically a convection diffusion model for temperature and a mass consistent model for wind field simulation will be assumed a two steps chemical mechanism is simplified in order to obtain the heat source this proposed 2 d model take into account the convection phenomena due to temperature gradients in vertical direction a numerical solution of the former model is presented using a finite difference method together with the study of stability this numerical method is contrasted with an adaptive finite element method using reflnementiderefinement techniques cf 1 1 143

avalanche duration time in a simple heterogeneous olami feder christensen model abstract a modified version of the olami feder christensen model has been introduced to consider the difference between avalanche duration distribution the duration time of our model well demonstrates the power law behavior and finite size scaling relationship between earthquake duration time and average size has been discussed it gives a power law behavior and provides a new evidence of self organized criticality we have investigated foreshock and aftershock and discovered that the probability of middle size earthquake in the aftershock was significantly greater than others the real data of sichuan earthquake is in alignment with our model

an online coupled state input parameter estimation approach for structural dynamics abstract in many practical structural applications unknown states inputs and parameters are present however most methods require one or more of these variables to be known in order to estimate the other s in this research an estimation technique which employs physical models is proposed to perform coupled state input parameter estimation in order to obtain a modeling technique which allows the estimation of a wide range of parameters in a generic fashion at a minimal computational cost even real time the use of a parametric model reduction technique is proposed the reduced model is coupled to an extended kalman filter ekf with augmented states for the unknown inputs and parameters this leads to a very efficient framework for estimation in structural dynamics problems special attention is also given to the measurement requirements in order to obtain an adequate observability of all unknown quantities and the necessity for at least one displacement level measurement is shown the proposed methodology is validated numerically and experimentally the approach is shown to be easy to tune and provides good results with different measurement methods

a novel reduced basis method with upper and lower bounds for real time computation of linear elasticity problems abstract this paper presents a novel reduced basis method for analyzing problems of linear elasticity in a systematical rapid and reliable fashion for solutions with both upper and lower bounds to the exact solution in the form of energy norm or compliance output the lower bound of the solution output is obtained form the well known reduced basis method based on the galerkin projection used in the finite element method which is termed as gp rbm for the upper bound a new reduced basis approach is developed by the combination of the reduced basis method and a smoothed galerkin projection used in the linearly conforming point interpolation method and it is thus termed as sgp rbm to examine the present sgp rbm we first conduct a theoretical study on the very important upper bound property reduced basis models for both gp rbm and sgp rbm are constructed with the aid of an asymptotic error estimation and greedy adaptive procedure the gp rbm and the newly proposed sgp rbm are applied to analyze a cantilever beam with an oblique crack to verify the proposed rbm technique in terms of accuracy convergence bound properties and computational savings both theoretical analysis and numerical results have demonstrated that the present method is a very efficient method for real time solutions providing exact output bounds

a damage model based on failure threshold weakening abstract a variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions involving either critical phenomena or spinodal nucleation here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding we introduce a failure threshold weakening parameter into the cellular automaton slider block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event we show that a critical point is reached beyond which the probability of a system wide event scales with this weakening parameter we provide a mapping to the percolation transition and show that the values of the scaling exponents approach the values for mean field percolation spinodal nucleation as lattice size l is increased for fixed r we also examine the effect of the weakening parameter on the frequency magnitude scaling relationship and the ergodic behavior of the model

critical properties of the one dimensional forest fire model abstract a one dimensional forest fire model including lightnings is studied numerically and analytically for the tree correlation function a new correlation length with critical exponent v 5 6 is found by simulations a hamiltonian formulation is introduced which enables one to study the stationary state close to the critical point using quantum mechanical perturbation theory with this formulation also the structure of the low lying relaxation spectrum and the critical behaviour of the smallest complex gap are investigated numerically finally it is shown that critical correlation functions can be obtained from a simplified model involving only the total number of trees although such simplified models are unable to reproduce the correct off critical behaviour

percolation with constant freezing we introduce and study a model of percolation with constant freezing pcf where edges open at constant rate 1 and clusters freeze at rate alpha independently of their size our main result is that the infinite volume process can be constructed on any amenable vertex transitive graph this is in sharp contrast to models of percolation with freezing previously introduced where the limit is known not to exist our interest is in the study of the percolative properties of the final configuration as a function of alpha we also obtain more precise results in the case of trees surprisingly the algebraic exponent for the cluster size depends on the degree suggesting that there is no lower critical dimension for the model moreover even for alpha alpha c it is shown that finite clusters have algebraic tail decay which is a signature of self organised criticality partial results are obtained on mathbb z d and many open questions are discussed

determination of the kardar parisi zhang equation from experimental data with a small number of configurations abstract we introduce an inverse method to determine the parameters of the kardar parisi zhang equation corresponding to an evolving interface which requires a small number of configurations as input data our approach presents advantages for applications in real world scenarios since it does not require small time intervals between fronts the method is applied to a restricted solid on solid model and a stochastic cellular automata model for fire front propagation

a self adjusted monte carlo simulation as a model for financial markets with central regulation abstract properties of the self adjusted monte carlo algorithm applied to 2d ising ferromagnet are studied numerically the endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random walk of the temperature that converges to criticality without an external tuning the robustness of a stationary regime with respect to partial accessibility of the information is demonstrated several statistical and scaling aspects have been identified which allow to establish an alternative spin lattice model of the financial market it turns out that our model alike model suggested by bornholdt int j mod phys c 12 2001 667 may be described by levy type stationary distribution of feedback variations with unique exponent 1 3 3 however the differences reflected by hurst exponents suggest that resemblances between the studied models seem to be non trivial

renormalization scheme for forest fire models we introduce a renormalization scheme for forest fire models in order to characterize the nature of the critical state and its scale invariant dynamics we study one and two dimensional models defining a characterization of the phase space that allows us to describe the evolution of the dynamics under a scale transformation we show the existence of a relevant critical parameter associated with a repulsive fixed point in the phase space from the renormalization group point of view these models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality this general scheme allows us to calculate analytically the critical exponent which describes the approach to the critical point along the repulsive direction and the exponent that characterizes the distribution of forest clusters at the critical point we obtain and respectively for the one and two dimensional cases in very good agreement with exact and numerical results

scaling and correlations in the dynamics of forest fire occurrence forest fire waiting times defined as the time between successive fires above a certain size in a given region are obtained for italy the probability densities of the waiting times are found to verify a scaling law despite that fact that the distribution of fire sizes is not a power law the meaning of such behavior in terms of the possible self similarity of the process in a nonstationary system is discussed we find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a nontrivial instantaneous scaling law sustained by the correlations of the process as a consequence the nonstationary poisson process model does not account for all the complexity of the structure of fire occurrence

asymptotics of one dimensional forest fire processes we consider the so called one dimensional forest fire process at each site of z a tree appears at rate 1 at each site of z a fire starts at rate 0 immediately destroying the whole corresponding connected component of trees we show that when is made to tend to 0 with an appropriate normalization the forest fire process tends to a uniquely defined process the dynamics of which we precisely describe the normalization consists of accelerating time by a factor log 1 and of compressing space by a factor log 1 the limit process is quite simple it can be built using a graphical construction and can be perfectly simulated finally we derive some asymptotic estimates when 0 for the cluster size distribution of the forest fire process

more languages of generalised star height 1 abstract suppose that membership of a word w in a language l is specified in terms of the number modulo some integer k of occurrences of a fixed word w as a factor of w then the language obtained for any m by adding arbitrary numbers of copies of a m anywhere in the words of l has generalized star height at most 1

spatio temporal self organization in a model of disease spreading abstract we investigate an extended version of the probabilistic forest fire model conceived as a model of disease spreading we show that the model self organizes spatially and temporally from random initial conditions into a well defined state with a characteristic length and time scale the time scale has a power law dependence on the correlation length i e z with a non trivial exponent of 0 83 in d 2 we show that stochastic input of susceptible individuals is essential for this behaviour a mean field approximation is presented predicting an exponent of z 1 2

shuffle on positive varieties of languages we show there is a unique maximal positive variety of languages which does not contain the language ab this variety is the unique maximal positive variety satisfying the two following conditions it is strictly included in the class of rational languages and is closed under the shuffle operation it is also the largest proper positive variety closed under length preserving morphisms the ordered monoids of the corresponding variety of ordered monoids are characterized as follows for every pair a b of mutually inverse elements and for every element z of the minimal ideal of the submonoid generated by a and b abzab ab in particular this variety is decidable

kinetics of ring formation we study reversible polymerization of rings in this stochastic process two monomers bond and as a consequence two disjoint rings may merge into a compound ring or a single ring may split into two fragment rings this aggregation fragmentation process exhibits a percolation transition with a finite ring phase in which all rings have microscopic length and a giant ring phase where macroscopic rings account for a finite fraction of the entire mass interestingly while the total mass of the giant rings is a deterministic quantity their total number and their sizes are stochastic quantities the size distribution of the macroscopic rings is universal although the span of this distribution increases with time moreover the average number of giant rings scales logarithmically with system size we introduce a card shuffling algorithm for efficient simulation of the ring formation process and we present numerical verification of the theoretical predictions

a second order phase transition in the complete graph stochastic epidemic model abstract a stochastic model for epidemic spread in a set of individuals placed upon the sites of a complete graph of relations is investigated the model is defined by three parameters the number of individuals or sites n the probability that an infected site transmits the disease to a susceptible site and the probability of recovery of infected sites both referred to the unit of time we show that this system evolves towards a approximately gaussian stationary distribution of infected sites whose mean and variance can be analytically estimated also we find that the average fraction of infected sites x is zero for transmission probabilities below the critical value c 1 e n and grows linearly with for 0 c 1 a sharp peak observed in monte carlo simulations of the variance of the number of infected sites as a function of allows us to classify this dynamical phase transition as second order with x playing the role of an order parameter some consequences of this model to the dynamics of highly connected complex systems such as the brain cortex are also discussed

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

goal oriented model constrained optimization for reduction of large scale systems optimization oriented reduced order models should target a particular output functional span an applicable range of dynamic and parametric inputs and respect the underlying governing equations of the system to achieve this goal we present an approach for determining a projection basis that uses a goal oriented model constrained optimization framework the mathematical framework permits consideration of general dynamical systems with general parametric variations and is applicable to both linear and nonlinear systems results for a simple linear model problem of the two dimensional heat equation demonstrate the ability of the goal oriented approach to target a particular output functional of interest application of the methodology to a more challenging example of a subsonic blade row governed by the unsteady euler flow equations shows a significant advantage of the new method over the proper orthogonal decomposition

on the asymptotic density in a one dimensional self organized critical forest fire model consider the following forest fire model where the possible locations of trees are the sites of each site has two possible states vacant or occupied vacant sites become occupied at rate 1 at each site ignition by lightning occurs at ignition rate the parameter of the model when a site is ignited its occupied cluster becomes vacant instantaneously in the literature similar models have been studied for discrete time the most interesting behaviour occurs when the ignition rate approaches 0 it has been stated by drossel clar and schwabl 1993 that then in our notation the density of vacant sites at stationarity is of order 1 log 1 their argument uses a scaling ansatz and is not rigorous we give a rigorous and mathematically more natural proof for our version of the model and point out how it can be modified for the model studied by drossel et al our proof shows that regardless of the initial configuration already after time of order log 1 the density is of the above mentioned order 1 log 1 we also obtain bounds on the cluster size distribution showing that the scaling ansatz of drossel et al needs correction

three state model and chemical reactions a three state model is formulated in terms of raising and lowering operators as an application cyclic chemical reactions with three different species in the solid state are studied the evolution equations for the densities and for the correlation functions can be derived starting from a master equation in a generalized fock space representation on a lattice such a description guarantees the consideration of the excluded volume effect in contrast to the classical kinetic behaviour the system offers stable and unstable regimes depending on the averaged composition ratio

phase transitions with infinitely many absorbing states in complex networks we investigate the properties of the threshold contact process tcp a process showing an absorbing state phase transition with infinitely many absorbing states on random complex networks the finite size scaling exponents characterizing the transition are obtained in a heterogeneous mean field hmf approximation and compared with extensive simulations particularly in the case of heterogeneous scale free networks we observe that the tcp exhibits the same critical properties as the contact process which undergoes an absorbing state phase transition to a single absorbing state the accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a hmf theory is a universal feature of absorbing state phase transitions in complex networks depending only on the locality of the interactions and independent of the number of absorbing states the conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible infected susceptible epidemic spreading model which in fact belongs to a different universality class in complex networks

inverse identification of thermal parameters using reduced basis method a novel computational method is presented to inversely identify heat convection constants for complex engineering systems a reduced basis approach is developed as a forward solver for heat transfer analysis in order to significantly reduce the computational complexity in each forward analysis which is crucial for the inverse analysis of complex systems an intergeneration projection genetic algorithm ip ga is introduced as the inverse procedure to speed up the process of finding the desired global minimum of the fitness function of error that leads to the parameters to be identified as an example identification of the heat convection constants of a typical microelectronic package are performed using the present method and the performance is examined comparing with other inverse identification methods it is found that the reduced basis method combined with the ip ga significantly outperforms the conventional methods the proposed inverse identification method is efficient enough even for online analysis of inverse problems due to both the use of the reduced basis approach and the present inverse procedure

criticality in the dynamic failure model to probe the interplay of different mechanisms for criticality we study the dynamic failure model each element of which is allowed to break or to be healed with given conditional probabilities under an external load the system evolves to the stationary state which may exhibit breakages of various sizes in addition as the healing parameter is varied the system undergoes a discontinuous transition between the functioning state and the failed one in the regimes with appropriate amounts of healing and fluctuations of the surviving fraction scale invariance in spatial and temporal correlations is observed manifested by the power spectrum of the breakage rate of elements and by the cluster size distribution of broken elements

connectivity effects in the dynamic model of neural networks we study via extensive monte carlo calculations the effects of connectivity in the dynamic model of neural networks to observe that the mattis state order parameter increases with the number of coupled neurons such effects appear more pronounced when the average number of connections is increased by introducing shortcuts in the network in particular the power spectra of the order parameter at stationarity are found to exhibit power law behavior depending on how the average number of connections is increased the cluster size distribution of the memory unmatched sites also follows a power law and possesses strong correlations with the power spectra it is further observed that the distribution of waiting times for neuron firing fits roughly to a power law again depending on how neuronal connections are increased

a characterization of regular expressions under bisimulation we solve an open question of milner 1984 we define a set of so called well behaved finite automata that modulo bisimulation equivalence corresponds exactly to the set of regular expressions and we show how to determine whether a given finite automaton is in this set as an application we consider the star height problem

some results on the generalized star height problem abstract we prove some results related to the generalized star height problem in this problem as opposed to the restricted star height problem complementation is considered as a basic operator we first show that the class of languages of star height n is closed under certain operations left and right quotients inverse alphabetic morphisms injective star free substitutions it is known that languages recognized by a commutative group are of star height 1 we extend this result to nilpotent groups of class 2 and to the groups that divide a semidirect product of a commutative group by z 2 z n in the same direction we show that one of the languages that were conjectured to be of star height 2 during the past ten years is in fact of star height 1 next we show that if a rational language l is recognized by a monoid of the variety generated by wreath products of the form m g n where m and n are aperiodic monoids and g is a commutative group the l is of star height 1 finally we show that every rational language is the inverse image under some morphism between free monoids of a language of resticted star height 1

a point interpolation method with least square strain field pim lss for solution bounds and ultra accurate solutions using triangular mesh abstract a point interpolation method with least square strain field pim lss is developed for solid mechanics problems using triangular background mesh in the pim lss pim shape functions are used for displacement field construction that may or may not be compatible and a least square fitting technique is adopted to construct the strain field a strain constructed galerkin sc galerkin weak formulation is then proposed for establishing discretized pim lss models that have a number of special properties we proved theoretically 1 the pim lss provides a softening effect to the fem model and a stiffing effect to the node based smoothed point interpolation method ns pim model 2 the exact solution is bounded from both by pim lss solutions with strain field of zero order fitting and that with higher order fitting 3 there exists a preferred order of fitting for the strain field such that ultra accurate one order higher accuracy solution can be obtained using the pim lss these theorems and properties have been confirmed in numerical examples

theoretical studies of self organized criticality these notes are intended to provide a pedagogical introduction to the abelian sandpile model of self organized criticality and its related models the abelian group the algebra of particle addition operators the burning test for recurrent states equivalence to the spanning trees problem are described the exact solution of the directed version of the model in any dimension is explained the model s equivalence to scheidegger s model of river basins takayasu s aggregation model and the voter model is discussed for the undirected case the solution for one dimensional lattices and the bethe lattice is briefly described known results about the two dimensional case are summarized generalization to the abelian distributed processors model is discussed time dependent properties and the universality of critical behavior in sandpiles are briefly discussed i conclude by listing some still unsolved problems

reduced basis approximation and a posteriori error estimation for a boltzmann model abstract we present a reduced basis approximation and associated rigorous a posteriori output flow rate error bound for a simple linearized bgk boltzmann model for flow in a channel we consider two parameters the knudsen number and the accommodation coefficient the reduced basis approximation is built upon and the reduced basis error is measured relative to a truth mapped weighted spectral discretization of a stabilized petrov galerkin weak formulation we exploit the affine nature of the parametric dependence to provide an offline online computational procedure that decouples the spectral and reduced basis quantities the computational complexity of the online stage in which given a new parameter value we evaluate the reduced basis flow rate prediction and associated error bound depends only on the typically very small dimension of the reduced basis space n and not on the typically very large dimension of the truth spectral approximation n we demonstrate that the reduced basis approximation converges very rapidly with n and that the error estimator effectivities remain bounded albeit somewhat large in the online stage the reduced basis approximation achieves a certifiable relative accuracy of 10 2 with respect to the truth spectral result at only 1 100th the computational effort the method is appropriate in the many query and real time e g parameter estimation contexts in which there is a premium on reduced marginal cost and a tolerance for significant offline pre processing effort

flaw detection in sandwich plates based on time harmonic response using genetic algorithm an inverse identification technique is proposed to assess the presence location size and degree of flaw in the core layer of sandwich plates the time harmonic response of the sandwich plates is used as the input for inverse analysis the responses of the plates in forward analysis are predicted using finite element method fem based on mindlin plate theory the flaw is characterized by a set of parameters the genetic algorithm ga is applied to search the parameters to improve the efficiency of ga in searching for the true solution a two stage searching method is proposed numerical examples are given to illustrate the proposed technique

self organised criticality in base pair breathing in dna with a defect abstract we analyse base pair breathing in a dna sequence of 12 base pairs with a defective base at its centre we use both all atom molecular dynamics md simulations and a system of stochastic differential equations sdes in both cases fourier analysis of the trajectories reveals self organised critical behaviour in the breathing of base pairs the fourier transforms fts of the inter base distances show power law behaviour with gradients close to 1 the scale invariant behaviour we have found provides evidence for the view that base pair breathing corresponds to the nucleation stage of large scale dna opening or melting and that this process is a second order phase transition although the random forces in our sde system were introduced as white noise fts of the displacements exhibit pink noise as do the displacements in the amber md simulations

self organized criticality in forest fire models we review properties of the self organized critical soc forest fire model ffm self organized critical systems drive themselves into a critical state without fine tuning of parameters after an introduction the rules of the model and the conditions for spiral shaped and soc large scale structures are given for the soc state critical exponents and scaling relations are introduced the existence of an upper critical dimension and the universal behavior of the model are discussed the relations and differences between ffm and percolation systems are outlined considering an extension of the ffm into the regions beyond the critical point phase transitions and the various structures found in these regions are illustrated

scaling properties of a model for ruptures in an elastic medium we generalize a model proposed by xu et al for ruptures in an elastic medium subject to shear stress this model is applied to the study of earthquakes we restrict ourselves to one dimensional discretizations of the region on which we focus and consider the effects of disorder degree of stress release and degree of stress nonconservation dissipation the one dimensional systems display power law cumulative size frequency distributions over a certain range of size the power laws cut off due to finite size effects i e the effects of the finite size of the system and the finite size of the basic unit of discretization in addition in the absence of disorder there is a crossover region at small sizes and its origin is explained the scaling properties in the absence of dissipation are characterized by exponents and as well as by a function f dependent on the parameters of the model is associated with the cumulative size frequency distribution in the thermodynamic limit with the finite size of the system and f with the finite size of the basic unit of discretization when stress dissipation is introduced into the model a characteristic earthquake size smaller than system size appears in contrast with the case in which stress dissipation is absent