asymptotic stability of densities in coupled map lattices abstract sufficient conditions for the asymptotic stability strong convergence of density evolution in finite dimensional piecewise monotone map lattices with both constant and state dependent coupling are given these conditions are quite useful in numerical work since they allow one to precisely define where one expects to see numerical signatures of asymptotic stability asymptotic stability is illustrated with several examples it is also shown that in constantly coupled lattices the density formed by collapsing the higher dimensional density into one dimension can be approximated by the evolution of densities under the action of an appropriately perturbed one dimensional map

synchronized chaotic intermittent and spiking behavior in coupled map chains we study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type i intermittent behavior two types of parameter distribution linear and random are considered the typical phenomena are the onset and existence of global all to all and cluster partial synchronization with increase of coupling increase of coupling strength can also lead to desynchronization phenomena i e global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states then a regime of a fully incoherent nonsynchronous state spatiotemporal intermittency appears synchronization desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one a chain of coupled maps replicating the spiking behavior of neurobiological networks

adsorbing and collapsing directed animals a model of a self interacting directed animal which also interacts with a solid wall is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition the directed animal is confined to a 45 wedge and it interacts with one of the walls of this wedge the existence of a thermodynamic limit in this model shown and the presence of an adsorption transition is demonstrated by using constructive techniques by comparing this model to a process of directed percolation we show that there is also a collapse or transition in this model we examine directed percolation in a wedge to show that there is a collapse phase present for arbitrary large values of the adsorption activity the generating function of adsorbing directed animals in a half space is found next from which we find the tricritical exponents associated with the adsorption transition a full solution for a collapsing directed animal seems intractible so instead we examine the collapse transition of a model of column convex directed animals with a contact activity next

transition to weak turbulence via spatiotemporal intermittency in the taylor dean system the transition to weak turbulence via spatiotemporal intermittency has been studied in the taylor dean system when the inner cylinder is fixed and only the outer cylinder is rotating the spatiotemporal intermittency regime is characterized by the coexistence of laminar domains and turbulent patches for the same value of the control parameter the transition is supercritical but a particular boundary condition induces an imperfection statistical analysis of the spatiotemporal intermittency shows that the distribution of laminar domains by widths follows a power law decay near the onset while it is exponential for higher values of the control parameter the exponential distribution of the laminar domains has a definite threshold near which the correlation lengths and correlation times of laminar and turbulent domains diverge reinforcing the analogy with second order phase transitions the exponents measured near the critical points in this experiment differ from those observed in other systems thus showing that the spatiotemporal intermittency is not universal in character textcopyright 1996 the american physical society

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

renormalized field theory of collapsing directed randomly branched polymers we present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition we develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition for the swollen phase we find that by choosing model parameters appropriately our stochastic functional reduces to the one describing the relaxation dynamics near the yang lee singularity edge this corroborates that the scaling behavior of swollen branched polymers is governed by the yang lee universality class as has been known for a long time the main focus of our paper lies on the collapse transition of directed branched polymers we show to arbitrary order in renormalized perturbation theory with ensuremath epsilon expansion that this transition belongs to the same universality class as directed percolation

a method to discern complexity in two dimensional patterns generated by coupled map lattices complex patterns generated by the time evolution of a one dimensional digitalized coupled map lattice are quantitatively analyzed a method for discerning complexity among different patterns is implemented the quantitative results indicate two zones in parameter space where the dynamics show the most complex patterns these zones are located on the two edges of an absorbent region where the system displays spatio temporal intermittency

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

modelling the collapse transition in branched polymers abstract we consider a number of lattice animal models for the collapse transition exhibited by branched polymers in dilute solution in all models the collapse is driven by either some kind of near neighbour fugacity or cycle fugacity we describe rigorous upper and lower bounds on the temperature dependence of the limiting free energy and compare these bounds with numerical estimates derived using new exact enumeration data finally we comment on the difficulties associated with the interpretation of results for the specific heat

simple measure for complexity a measure of complexity is proposed based on appropriately defined notions of order and disorder which has a considerable degree of flexibility in its dependence on these concepts the possible functional dependencies which result encompass those of many earlier definitions of complexity the proposed measure is in principle easy to calculate and has the property of an intensive thermodynamic quantity with appropriate choices of parameters it behaves similarly to effective measure complexity for the logistic map it is also a generalization of the normalized complexity of lopez ruiz et al but does not suffer from over universality

series expansions of the percolation probability for directed square and honeycomb lattices we have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices for the square bond problem we have extended the series from 41 terms to 54 for the square site problem from 16 terms to 37 and for the honeycomb bond problem from 13 terms to 36 analysis of the series clearly shows that the critical exponent beta is the same for all the problems confirming expectations of universality for the critical probability and exponent we find in the square bond case qc 0 3552994 or 0 0000010 beta 0 27643 or 0 00010 in the square site case qc 0 294515 or 0 000005 beta 0 2763 or 0 0003 and in the honeycomb bond case qc 0 177143 or 0 000002 beta 0 2763 or 0 0002 in addition we have obtained accurate estimates for the critical amplitudes in all cases we find that the leading correction to scaling term is analytic i e the confluent exponent delta 1

intensive entropic non triviality measure abstract we discuss a way of characterizing probability distributions complementing that provided by the celebrated notion of information measure with reference to a measure of complexity that we call a nontriviality measure our starting point is the lmc measure of complexity advanced by lopez ruiz et al phys lett a 209 1995 321 and its analysis by anteneodo and plastino phys lett a 223 1997 348 an improvement of some of their troublesome characteristics is thereby achieved basically we replace the euclidean distance to equilibrium by the jensen shannon divergence the resulting measure turns out to be i an intensive quantity and ii allows one to distinguish between different degrees of periodicity we apply the cured measure to the logistic map so as to clearly exhibit its advantages

directed animals on two dimensional lattices previously directed animals on square and triangular lattices have been enumerated by area and have been found to have simple generating functions whilst the hexagonal lattice generating function has not been obtained directed animals on several new lattices are enumerated one class of which is solved exactly directed animals by bonds with and without loops are also enumerated in each case an asymptotic growth like n 1 2 mu n is observed and precise estimates for mu are given

dimensional reduction for directed branched polymers dimensional reduction occurs when the critical behaviour of one system can be related to that of another system in a lower dimension we show that this occurs for directed branched polymers dbp by giving an exact relationship between dbp models in d 1 dimensions and repulsive gases at negative activity in d dimensions this implies relations between exponents of the two models d 1 d the exponent describing the singularity of the pressure and d 1 d the correlation length exponent of the repulsive gas it also leads to the relation d 1 1 d where d is the yang lee edge exponent we derive exact expressions for the number of dbp of size n in two dimensions

directed compact percolation cluster size and hyperscaling exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice the corresponding relation for the moment generating function of the length distribution is obtained in closed form whereas in the case of the size distribution only the first three moments are obtained the work is carried out for clusters grown from a seed of arbitrary width on an anisotropic lattice a duality property is shown to exist which relates the moment generating functions on the two sides of the critical curve the moments of both distributions have critical exponents which satisfy a constant gap hypothesis with gap exponents nu 2 and delta 3 corresponding to the scaling length and scaling size respectively the usual hyperscaling relation for directed percolation is found to be invalid for compact clusters and is replaced by delta nu d nu perpendicular to where nu perpendicular to is the exponent corresponding to the cluster width and d is the number of transverse dimensions 1 for the square lattice

spatiotemporal chaos in mixed linear nonlinear two dimensional coupled logistic map lattice abstract we investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2dcml here the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices and the former 2dcml system is only a special case in the proposed system in this paper the criteria such kolmogorov sinai entropy density and universality bifurcation diagrams space amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system furthermore we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2dcml system and the mlncml system theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors which is more suitable for cryptography

topologically massive yang mills a hamilton jacobi constraint analysis we analyse the constraint structure of the topologically massive yang mills theory in instant form and null plane dynamics via the hamilton jacobi formalism the complete set of hamiltonians that generates the dynamics of the system is obtained from the frobenius integrability conditions as well as its characteristic equations as generators of canonical transformations the hamiltonians are naturally linked to the generator of lagrangian gauge transformations

synchronization in coupled map lattices with small world delayed interactions abstract we study the synchronization of coupled map lattices with small world interactions and coupling delays in this paper a stability criterion for the synchronized state is derived numerical examples are presented to demonstrate the correctness of our theoretical result

spatio temporal chaos and intermittency in a 1 dimensional energy conserving coupled map lattice abstract the klein gordon equation with cubic nonlinearity the 4 equation is considered and an energy conserving difference scheme is proposed for its solution the scheme extended to finite time increments and spacing is then used to define a coupled map lattice for which an energy like functional is conserved the case of linear instability of the vacuum state is considered when this energy is not positive definite and found to lead under certain additional conditions to spatio temporal chaos the statistical properties of this type of solution such as probability densities and correlation functions are calculated strong intermittency whereby the process wanders between two sub manifolds is found and studied in detail

synchronization and coherence in thermodynamic coupled map lattices with intermediate range coupling in spatially extended systems intermediate range interactions arise naturally in some physical contexts to study them we investigate a model of coupled map lattices cml s with intermediate range coupling and derive analytic conditions for its synchronization we find that in these cml s if the range of coupling is fixed the law of large numbers applies for the mean field the total normalized power in nonzero components of the power spectrum of the mean field goes to zero in the thermodynamic limit we also show that in the same limit the relevant parameter for synchronization and coherence is the fraction of sites coupled and not their number s1063 651x 99 07410 3 pacs number s 05 45 2a the past decade has seen a surge of interest in synchronization and coherence in coupled map lattices cml s 1 10 most work has focused on systems with finite degrees of freedom and short range global or random coupling in this paper we study the synchronization of one and two dimensional 1d and 2d cml s with intermediaterange couplings in the thermodynamic limit this study is related to systems with finite degrees of freedom studied by sinha et al 2 and kozma 10 in these works each site is coupled to a range of neighbors on either side rather than just its nearest neighbors this may be a valid approximation in systems where interaction strength decays slowly with distance just as cml s with nearest neighbor coupling could be considered to be a discretization of partial differential equation cml s with intermediate range coupling could be seen as a discretization of a partial integro differential equation in fact such integro differential equations have often been used in modeling certain physico chemical reactions 11 elimination of rapidly diffusing components in a system of diffusion coupling can also lead to effectively nonlocal coupling in resultant equations 12 cml s in which coupling between two sites separated by distance r decays as power law 1 r a with exponent a have also been considered as models for biological neural networks 6 in the present work we derive the analytic conditions for synchronization in our cml s we find that in the thermodynamic limit the relevant parameter for synchronization is the fraction of sites coupled and not their number we present numerical results which show that for the mean field in the cml s with a fixed range of coupling sites for each site the law of large numbers applies and the total normalized power in nonzero components of the power spectrum goes to zero in the thermodynamic limit this is in sharp contrast with the conjecture of sinha et al 2

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

basic representation of the affine superalgebraa 2 0 1 abstract irreducible modules of the affine superalgebra a 2 0 1 are realized as the tensor product of symmetric and exterior algebras on which a 2 0 1 acts by products of vertex operators and operators of clifford type

involutive constrained systems and hamilton jacobi formalism in this paper we study singular systems with complete sets of involutive constraints the aim is to establish within the hamilton jacobi theory the relationship between the frobenius theorem the infinitesimal canonical transformations generated by constraints in involution with the poisson brackets and the lagrangian point gauge transformations of physical systems

evidence of self organization in brain electrical activity using wavelet based informational tools abstract in the present work we show that appropriate information theory tools based on the wavelet transform relative wavelet energy normalized total wavelet entropy h generalized wavelet complexity c w when applied to tonic clonic epileptic eeg data provide one with valuable insights into the dynamics of neural activity twenty tonic clonic secondary generalized epileptic records pertaining to eight patients have been analyzed if the electromyographic activity is excluded the difference between the ictal and pre ictal mean entropic values h h ictal h pre ictal is negative in 95 of the cases p 0 0001 and the mean complexity variation c w c w ictal c w pre ictal is positive in 85 of the cases p 0 0002 thus during the seizure entropy diminishes while complexity grows this is construed as evidence supporting the conjecture that an epileptic focus in this kind of seizures triggers a self organized brain state characterized by both order and maximal complexity

longitudinal size exponent for square lattice directed animals series expansions for the longitudinal gyration radius of square lattice directed site animals to order n 39 are given this doubles the length of the available series analysis of the series yields the estimate nu sub 0 81722 or 0 00005 which excludes the conjecture nu sub 9 11 based on phenomenological renormalization and shorter series but is consistent with the later phenomenological renormalization estimate of dhar nu sub 0 81733 or 0 00005

application of directed lattice animal theory to river networks it is shown that the theory of directed lattice animals is a good candidate for determining the exponents which describe river networks

longitudinal size exponent for two dimensional directed animals using phenomenological renormalisation with strip widths up to size 23 the author has numerically estimated the longitudinal size exponent nu sub for two dimensional directed animals he gets nu sub 0 817 33 or 0 000 05 this rules out the simple fraction 9 11 suggested by earlier numerical data the effective correction to the scaling exponent in the continuous time version of the problem is 1 5 or 0 1

disturbance propagation in chaotic extended systems with long range coupling propagation of initially localized perturbations is investigated in chaotic coupled map lattices with long range couplings decaying as a power of the distance the initial perturbation propagates exponentially fast along the lattice with a rate given by the ratio of the maximal lyapunov exponent and the power of the coupling a complementary description in terms of a suitable comoving lyapunov exponent is also given

exact solution of a directed site animals enumeration problem in three dimensions an exact equivalence is established between the directed site animals enumeration dsae problem in d dimensions and a crystal growth model defined on the same lattice in special cases the latter reduces to the calculation of the free energy of a d ensuremath 1 dimensional lattice gas with extended hard cores the author solves a dsae problem with d 3 exactly by using its equivalence to the hard hexagon problem and shows that the exponent ensuremath theta frac 5 6 a new and simpler solution to the dsae problem on the square and triangular lattices is given

associative memory based on parametrically coupled chaotic elements abstract in this paper we propose an associative memory system based on parametrically coupled chaotic elements the proposed system is obtained by adding a new parameter control to our previously proposed system a chaotic activity in an early association stage makes an efficient association over the memories that are stored by means of autocorrelational learning when the system successfully recalls the target memory the system s motion is dominated by a spatially coherent oscillation while unstable motions remain when the system fails to make the association in addition the system has a large memory capacity a comparison between the proposed system and an approach with a nonmonotonic transfer function is also shown

mean field model of a game for power abstract our aim is to model a game for power equivalent to total energy as a dynamical process where an excess of power possessed by a player allows him to gain even more power such a positive feedback is often termed as the matthew effect analytical and numerical methods allow to identify a set of stationary states i e fixed points of the model dynamics the positions of the unstable fixed points give an insight on the basins of attraction of the stable fixed points the results are interpreted in terms of modeling of coercive power

a fisher gradient complexity in systems with spatio temporal dynamics abstract we define a benchmark for definitions of complexity in systems with spatio temporal dynamics and employ it in the study of collective motion we show that lmc s complexity displays interesting properties in such systems while a statistical complexity model scm based on autocorrelation reasonably meets our perception of complexity however this scm is not as general as desirable as it does not merely depend on the system s probability distribution function inspired by the notion of fisher information we develop a scm candidate which we call the fisher gradient complexity which exhibits nice properties from the viewpoint of our benchmark

potts model formulation of branched polymers in a solvent a potts model formulation of the statistics of branched polymers or lattice animals in a solvent is given the migdal kadanoff renormalisation group is employed to study the critical behaviour or fractal dimension of the branched polymer four different critical behaviours are found corresponding to random animal collapse or theta point percolation and compact cluster the theta point behaviour is described by a tricritical point while percolation corresponds to a higher order critical point where the effect of the solvent on the branched polymer is the same as the screening effect of the other clusters in percolation

conversion of local transient chaos into global laminar states in coupled map lattices with long range interactions abstract spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales characterized by repeated conversions from spatially localized transient chaos into global laminar patterns a simple model yet retaining some features of more complex systems consists of a lattice of a class of tent maps with an escaping region the coupling prescription we adopt in this work considers the interaction of a site with all its neighbors the corresponding strength decaying with the lattice distance as a power law this makes possible to pass continuously from a local nearest neighbor to a global kind of coupling we investigate statistical properties of both the chaotic transient bursts and the periodic laminar states with respect to the coupling parameters

the cluster structure in collapsing animals in this paper i revisit the connection between edge percolation and the collapse transition in lattice animals it was shown by domb 1976 j phys a math gen 9 l141 that the critical percolation point is a transition in a certain model of self interacting animals i extend this result by showing that the free energy of lattice animals in the cycle contact model is non analytic in contact and cycle activities at points other than the critical percolation point this correspondence between percolation and collapsing animals suggests that the collapse transition in this model may be related to percolation contact collapse in animals is then studied from a percolation of clusters of contacts perspective i first argue that there is a critical activity for percolation of clusters of contacts and then investigate this numerically

evidence for directed percolation universality at the onset of spatiotemporal intermittency in coupled circle maps we consider a lattice of coupled circle maps a popular model for the study of mode locked phenomena we find that the onset of spatiotemporal intermittency sti in this system is analogous to directed percolation dp with the transition being to a unique absorbing state for low nonlinearities and to weakly chaotic absorbing states for high nonlinearities we find that the complete set of static exponents and spreading exponents at all critical points match those of dp very convincingly further hyperscaling relations are fulfilled leading to independent controls and consistency checks of the values of all the critical exponents these results provide an example in support of the conjecture that the onset of sti in deterministic models belongs to the dp universality class nonuniversal spreading exponents are seen only for the cases where the initial state is homogeneous with symmetrically placed seeds leading to strictly symmetric spreading however very small departures from homogeneity are sufficient to restore the dp exponents

universality classes of spatiotemporal intermittency abstract we discuss the spatiotemporal intermittency sti seen in the coupled sine circle map lattice the phase diagram of this system when updated with random initial conditions shows very rich behaviour including synchronised solutions and sti of various kinds these behaviours are organised around the bifurcation boundary of the synchronised solutions as well as an infection line which separates the lower part of the phase diagram into a spreading and a non spreading regime the sti seen at the bifurcation boundary in the spreading regime belongs convincingly to the directed percolation dp universality class in the non spreading regime spatial intermittency si with temporally regular bursts is seen at the bifurcation boundary the laminar length distribution scales as a power law with an exponent which is quite distinct from dp behaviour therefore both dp and non dp universality classes are seen in this system when the coupled map lattice is mapped to a cellular automaton via coarse graining a transition from a probabilistic cellular automaton to a deterministic cellular automaton at the infection line signals the transition from spreading to non spreading behaviour

collapse of two dimensional linear polymers we study the collapse transition of a two dimensional very long polymer the model we consider is a lattice model where the chain is represented by a self avoiding walk with nearest neighbor attraction by using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width we then use finite size scaling to determine the values of the tricritical point exponentsv1 0 55 0 01vu 1 15 0 15 1 v1 1 80 0 05 we compare these results to the other values already proposed in the literature

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

brain electrical activity analysis using wavelet based informational tools ii tsallis non extensivity and complexity measures the processing of information by the brain is reflected in dynamical changes of the electrical activity in i time ii frequency and iii space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the present work complements the efforts described in rosso et al physica a 313 2002 587 devoted to non extensive information measures a la tsallis here we show that the notion of complexity using 1 appropriate information theory tools adapted to a non extensive scenario and 2 scalp eeg data provides one with valuable insights into the dynamics of neural activity in particular using different complexity measures we detect the presence of states characterized by both order and maximal complexity

directed percolation a finite size renormalisation group approach the finite size renormalisation group technique introduced by nightingale 1976 is applied to the directed percolation problem the decay of correlations is anisotropic in this model and finite size scaling is extended to treat such anisotropy precise estimates for critical exponents and percolation probabilities are obtained for site bond and site bond percolation on the square lattice with bonds directed along the positive axes both free boundary conditions for which the results converge linearly with 1 n as n to infinity and helical boundary conditions for which unexpectedly the results converge linearly with 1 n3 are considered

dynamic characterizers of spatiotemporal intermittency we study spatiotemporal intermittency sti in a system of coupled sine circle maps the phase diagram of the system shows parameter regimes where the sti lies in the directed percolation dp class as well as regimes which show pure spatial intermittency where the temporal behavior is regular which do not belong to the dp class thus both dp and non dp behavior can be seen in the same system the signature of dp and non dp behavior can be seen in the dynamic characterizers viz the spectrum of eigenvalues of the linear stability matrix of the evolution equation as well as in the multifractal spectrum of the eigenvalue distribution the eigenvalue spectrum of the system in the dp regimes is continuous whereas it shows evidence of level repulsion in the form of gaps in the spectrum in the non dp regime the multifractal spectrum of the eigenvalue distribution also shows the signature of dp and non dp behavior these results have implications for the manner in which correlations build up in extended systems

a scaling theory of the collapse transition in geometric cluster models of polymers and vesicles much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk polygon and animal models the crossover exponent phi has been of special interest and sometimes is assumed to obey the relation 2 alpha 1 phi with the alpha the canonical thermodynamic exponent that characterizes the divergence of the specific heat the reasons for the validity of this relation are not widely known the authors present a scaling theory of collapse transitions in such models the free energy and canonical partition functions have finite length scaling forms whilst the grand partition function has a tricritical scaling form the link between the grand and canonical ensembles leads to the above scaling relation they then comment on the validity of current estimates of the crossover exponent for interacting self avoiding walks in two dimensions and propose a test involving the scaling relation which may be used to check these values

synchronization in coupled sine circle maps we study the spatially synchronized and temporally periodic solutions of a one dimensional lattice of coupled sine circle maps we carry out an analytic stability analysis of this spatially synchronized and temporally periodic case and obtain the stability matrix in a neat block diagonal form we find spatially synchronized behavior over a substantial range of parameter space we have also extended the analysis to higher spatial periods with similar results numerical simulations for various temporal periods of the synchronized solution reveal that the entire structure of the arnold tongues and the devil s staircase seen in the case of the single circle map can also be observed for the synchronized coupled sine circle map lattice our formalism should be useful in the study of spatially periodic behavior in other coupled map lattices

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

a transfer matrix study of directed lattice animals and directed percolation on a square lattice we studied the large scale properties of directed lattice animals and directed percolation on a square lattice using a transfer matrix approach on strips of finite widths we generated relatively long sequences of estimates for effective values of critical fugacity percolation threshold and correlation length critical exponents we applied two different extrapolation methods to obtain estimates for infinite systems the precision of our final estimates is comparable to or better than the precision of the best currently available results

synchronous versus asynchronous dynamics in spatially distributed systems abstract many prototypical models of spatially extended systems that are capable of complex spatiotemporal dynamics impose a finite discretization window of space and time for such models it is important to determine to what extent the specific procedure which is used to update local states affects the overall regimes as the latter might turn out to be artifacts due to an unrealistic digitalization of the world the chances of generating spatiotemporal patterns with no counterparts in the physical world are particularly high with granular space time models that rely on a synchronous evolution of distributed states as such synchronous evolution is found in nature most typically in systems governed by evolution laws in the form of partial differential equations we show this possibility to be the case for the regimes produced in coupled map lattices as markedly different dynamics arise when the standard synchronous model is made asynchronous by quantifying the degree of mutual asynchrony in the system signatures of asynchronous spatiotemporal dynamics are unraveled and further characterized in terms of simple stability measures

exponent vperp for 2d directed compact site animals the authors obtain the transverse cluster radius exponent vperp 0 for 2d directed compact animals they find that the exponent vperp takes two different values which depend on definition of the animal width

directed lattice animals and the lee yang edge singularity the exponents nu perpendicular to gamma of directed animals in d dimensions are shown to equal those for the lee yang problem in d 1 dimensions for d 2 the author obtains the exact results nu perpendicular to theta 1 2 and for d or 7 the scaling relation theta d 1 nu perpendicular to

routes to spatiotemporal chaos in the rheology of nematogenic fluids with a view to understanding the rheochaos observed in recent experiments in a variety of orientable fluids we study numerically the equations of motion of the spatiotemporal evolution of the traceless symmetric order parameter of a sheared nematogenic fluid in particular we establish by decisive numerical tests that the irregular oscillatory behavior seen in a region of parameter space where the nematic is not stably flow aligning is in fact spatiotemporal chaos we outline the dynamical phase diagram of the model and study the route to the chaotic state we find that spatiotemporal chaos in this system sets in via a regime of spatiotemporal intermittency with a power law distribution of the widths of laminar regions as in h chate and p manneville phys rev lett 58 112 1987 further the evolution of the histogram of band sizes shows a growing length scale as one moves from the chaotic towards the flow aligned phase finally we suggest possible experiments in which one can observe the intriguing behaviors discussed here

chaotic bursting at the onset of unstable dimension variability dynamical systems possessing symmetries have invariant manifolds according to the transversal stability properties of this invariant manifold nearby trajectories may spend long stretches of time in its vicinity before being repelled from it as a chaotic burst after which the trajectories return to their original laminar behavior the onset of chaotic bursting is determined by the loss of transversal stability of low period periodic orbits embedded in the invariant manifold in such a way that the shadowability of chaotic orbits is broken due to unstable dimension variability characterized by finite time lyapunov exponents fluctuating about zero we use a two dimensional map with an invariant subspace to estimate shadowing distances and times from the statistical properties of the bursts in the transversal direction a stochastic model biased random walk with reflecting barrier is used to relate the shadowability properties to the distribution of the finite time lyapunov exponents

synchronization and cluster periodic solutions in globally coupled maps abstract the purpose of this work is to investigate mechanisms by which synchronization takes place in networks of elements with global couplings we consider a family of globally coupled nonlinear maps and find for each model sufficient conditions for synchronization we also analyze bifurcations of syncrhonized dynamics to other homogeneous and cluster periodic solutions in terms of corresponding low dimensional maps

stabilization of causally and non causally coupled map lattices abstract two dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood the action of the neighborhood on individual maps can be implemented in terms of causal coupling to spatially distant past states or non causal coupling to spatially distant simultaneous states in this contribution we show that globally stable behavior of coupled map lattices is facilitated by causal coupling thus indicating a surprising relationship between stability and causality the influence of causal versus non causal coupling for synchronous and asynchronous updating as a function of coupling strength and for different neighborhoods is analyzed in detail

representation of the affine superalgebras a 4 0 2l a 2 0 2l 1 and their subalgebras a2l 2 a2l 1 2 by vertex operators abstract the structure theory of standard modules of affine lie algebras given by j lepowsky and r l wilson in lw is stated for representations of affine superalgebras as an application the standard modules of level one for the superalgebras a 4 0 2l a 2 0 2l 1 and their affine subalgebras a2l 2 a2l 1 2 are constructed explicitly these modules are realized as the tensor product of symmetric and exterior algebras with an irreducible representation of a certain finite 2 group the affine superalgebra acts on this space by tensor products of vertex operators operators of clifford type and elements of the 2 group as a corollary the spin representations of the lie algebras bl and dl are obtained from the 2 group representation

on directed interacting animals and directed percolation we study the phase diagram of fully directed lattice animals with nearest neighbour interactions on the square lattice this model comprises several interesting ensembles directed site and bond trees bond animals strongly embeddable animals as special cases and its collapse transition is equivalent to a directed bond percolation threshold precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n 17 the crossover region in the vicinity of the collapse transition is analysed in detail and the crossover exponent is determined directly from the singular part of the free energy we show using scaling arguments and an exact relation due to dhar that is equal to the fisher exponent governing the size distribution of large directed percolation clusters

numerical study of transport properties in continuum percolation the authors present numerical simulations of ac conductance for a random resistor capacitor network the conductance obeys a probability density function p g varies as g alpha 0 alpha 1 they use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice at low frequencies they find that for the concentration p of conducting bonds less than the percolation threshold pc the imaginary part of conductance is proportional to frequency im geff approximately omega and the real part of conductance shows an anomalous frequency dependence re geff approximately omega 2 alpha the results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the maxwell garnett approximation they also calculate the non universal dc conductivity exponents in continuum percolation the results are consistent with earlier theoretical predictions and numerical calculations

directed percolation universality in asynchronous evolution of spatiotemporal intermittency we present strong evidence that a coupled map lattice model for spatiotemporal intermittency belongs to the universality class of directed percolation when the updating rules are asynchronous i e when only one randomly chosen site is evolved at each time step in contrast when the system is subjected to parallel updating available numerical evidence suggest that it does not belong to this universality class and that it is not even universal we argue that in the absence of periodic external forcing the asynchronous rule is the more physical

divergence measures based on the shannon entropy a novel class of information theoretic divergence measures based on the shannon entropy is introduced unlike the well known kullback divergences the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved more importantly their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds these bounds are crucial in many applications of divergence measures the measures are also well characterized by the properties of nonnegativity finiteness semiboundedness and boundedness

non universality in the collapse of two dimensional branched polymers in this paper we study the complete phase diagram of a model of interacting branched polymers the model we consider is a lattice animal one where the collapse transition can be driven both by a contact fugacity between two occupied nearest neighbours and by a fugacity related to each occupied edge using a potts model formulation of the problem we conjecture the existence of two different universality classes for the theta transitions with thermal exponents nu and phi equal to 1 2 2 3 and 8 15 8 15 separated by a higher order percolation point we also present convincing numerical evidence for these exponent values using a transfer matrix approach we discuss the possibility of a collapse collapse transition and we predict the behaviour of our model when an adsorbing surface is included

semi directed percolation in two dimensions abstract we studied a model of semi directed percolation on finite strips of the square and triangular lattices using the transfer matrix method combined with phenomenological renormalization group approach we obtain good numerical estimates for critical probabilities and correlation lengths critical exponents our results confirm the conjecture that semi directed percolation belongs to the universality class of the usual fully directed percolation model

collapse transitions in animals and vesicles we discuss the relationship between the solvent model of collapse in strongly and weakly embeddable lattice animals and a model recently introduced by vanderzande 1993 and by stella et al 1992 we show that there are important qualitative differences in the behaviour predicted by these two models in the compact regime

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

analytical results for coupled map lattices with long range interactions we obtain exact analytical results for lattices of maps with couplings that decay with distance as r ensuremath ensuremath alpha we analyze the effect of the coupling range on the system dynamics through the lyapunov spectrum for lattices whose elements are piecewise linear maps we get an algebraic expression for the lyapunov spectrum when the local dynamics is given by a nonlinear map the lyapunov spectrum for a completely synchronized state is analytically obtained the critical line characterizing the synchronization transition is determined from the expression for the largest transversal lyapunov exponent in particular it is shown that in the thermodynamical limit such transition is only possible for sufficiently long range interactions namely for ensuremath alpha l ensuremath alpha c d where d is the lattice dimension

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

two dimensional self avoiding walk with hydrogen like bonding phase diagram and critical behaviour the phase diagram for a two dimensional self avoiding walk model on the square lattice incorporating attractive short ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques the model displays a collapse transition in contrast to the standard point model the transition is first order the phase diagram in the full fugacity temperature plane displays an additional transition line when compared to the point model as well as a critical transition at finite temperature in the hamiltonian walk limit

fractal deterministic cracks abstract cracks are grown in an elastic medium submitted to external shear by solving the full equations of motion on a two dimensional lattice one finds that deterministic fracture patterns are in general branched and can be fractal this effect is due to the competition between the direction of global stress and the local growth direction imposed by the lattice anisotropy viscoelastic effects are also discussed

the collapse of directed animals directed animals on a square lattice with attractive nearest neighbour and next nearest neighbour interactions are considered using an equivalence between the collapse problem and the directed site bond percolation problem the bulk free energy per site is calculated exactly in the collapsed phase it shows no singularity as the transition is approached from the collapsed side for the three dimensional directed animals bulk free energy per site in the collapsed phase is calculated exactly if the interaction weights are related by an algebraic equation

two dimensional background field gravity a hamilton jacobi analysis we analyse the constraint structure of the background field model for two dimensional gravity via the hamilton jacobi formalism this analysis consists in finding the complete set of involutive hamiltonians that assure the integrability of the system we then calculate the characteristic equations of the system also establishing the equivalence between these equations and the field equations

statistical complexity measures as telltale of relevant scales in emergent dynamics of spatial systems abstract the definition of complexity through statistical complexity measures scm has recently seen major improvements mostly the effort is concentrated in measures on time series we propose a scm definition for spatial dynamical systems our definition is in line with the trend to combine entropy with measures of structure such as disequilibrium we study the behaviour of our definition against the vectorial noise model of collective motion from a global perspective we show how our scm is minimal at both the microscale and macroscale while it reaches a maximum at the ranges that define the mesoscale in this model from a local perspective the scm is minimum both in highly ordered and disordered areas while it reaches a maximum at the edges between such areas these characteristics suggest this is a good candidate for detecting the mesoscale of arbitrary dynamical systems as well as regions where the complexity is maximal in such systems