critical slowing down in a randomly biased percolating system at percolation threshold using computer simulation a random walk motion is studied in a random percolating system at percolation threshold in the presence of a random field the rms displacement is found to decrease systematically as a function of field strength and shows a non universal power law dependence on it the long time behaviour seems similar to the critical slowing down recently predicted in an analogous magnetic system the spectral dimensionality varies with the field strength and is found to be lees than

disorder induced transport i simple cubic lattice using a vax 11 780 a random walk motion is studied in a random field disordered system a non monotonic transport behaviour is observed as a function of local field intensity in contrast to the random walk motion in random percolating fractals the root mean square displacement here increases as a function of time faster than that of diffusion a crossover from diffusion to disorder induced transport is discussed and its spectral dimensionality is estimated

critical exponents of self avoiding walks on a family of truncated n simplex lattices the authors have studied self avoiding walks saws on a family of truncated n simplex lattices which provide a family of fractals in which the fractal dimension d can be varied to a wide range while the spectral dimension d is held almost fixed by means of exact renormalisation group transformations they have calculated the critical exponents nu alpha and gamma and the connectivity constant mu of the saws for n 5 and 6 they propose an approximate theory for calculating the critical exponents of the saws on fractals which is expected to be accurate at large values of n they show that the theory gives results which are in good agreement with exact values even for small values of n and leads to simple closed relations for the exponents

frequency analysis of strongly nonlinear generalized duffing oscillators using he s frequency amplitude formulation and he s energy balance method in this paper he s frequency amplitude formulation hfaf and he s energy balance method hebm are employed to solve the generalized duffing equation in the form of x x a 3x 3 a 5x 5 a 7x 7 a nx n 0 for any arbitrary power of n a frequency analysis is carried out and the relationship between the natural frequency and the initial amplitude is obtained in analytical form accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the hfaf hebm and exact integration method numerical simulations are extended for even very strong nonlinearities and very good correlations are achieved between the numerical results

branched polymer approach to the structure of lattice animals and percolation clusters the authors treat the percolation problem as a solution of randomly branched chains and argue that such chains are swollen by a three body repulsion acting only within a connected cluster this type of repulsion should not be subject to the screening effects which inhibit ordinary repulsions the repulsion becomes relevant below six dimensions they estimate its effect on the size of a cluster in analogy with flory s argument for the swelling of linear chains above six dimensions the cluster size scales as mass to the 1 4 power as with isolated branched chains in high dimensions

correction to scaling exponents and amplitudes for the correlation length of linear polymers in two dimensions we consider the scaling behaviour of the radius of gyration for a system of dilute linear polymers we focus on pn the mean square end to end distance of an n step self avoiding walk for which an additional two terms were recently calculated for the close packed triangular lattice combining several extrapolation methods we find that a consistent description of the scaling behaviour exists if and only if the correction to scaling exponent a is roughly half as large as commonly believed we conclude that all data ale consistent with the equation pn an2 1 b na c n where y a a 1 j2 abso 21 and c lo

free energy of magnetic model systems at the fractal to euclidian crossover abstract we prove that the free energy per spin of the nearest neighbour classical n vector spin model situated on the sierpinski gasket sg family of fractals tends to the free energy per spin of the same model situated on the standard triangular lattice when the linear size b of the sg fractal generator tends to infinity this finding can be regarded as the first step in the analytical investigation of the spin system thermodynamics at the fractal to euclidean crossover

geometrical arguments against the alexander orbach conjecture for lattice animals and diffusion limited aggregates geometrical arguments are given which suggest that the alexander orbach conjecture 1982 does not hold for lattice animals in d 2 and for the diffusion limited aggregates for large dimensions

conformal invariance and self avoiding walks in restricted geometries the prediction of conformal invariance for the statistics of self avoiding random walks restricted to both semi infinite and wedge shaped geometries are tested by extrapolating exact enumerations close agreement is found both for the angular distribution of the end to end vector and for the dependence of the critical exponent gamma 2 on the opening angle of the wedge

application of he s amplitude frequency formulation to a nonlinear oscillator with discontinuity in this paper he s amplitude frequency formulation is used to obtain a periodic solution of a nonlinear oscillator with discontinuity the accuracy arrives at 0 73 even when the amplitude tends to infinity

monte carlo series analysis of irreversible self avoiding walks i the indefinitely growing self avoiding walk igsaw high precision monte carlo data are used to estimate the exponents which govern the asymptotic behaviour of the recently introduced indefinitely growing self avoiding walk in two dimensions for this walk the exponent gamma is by definition equal to one applying the same methods which are used to extract the exponents from exact series enumeration the authors give an estimate for the exponent nu of 0 567 or 0 003 the leading corrections to this asymptotic behaviour are also calculated

he s parameter expanding methods for strongly nonlinear oscillators ji huan he s work on asymptotic techniques is briefly reviewed and his parameter expanding methods including modified lindstedt poincare method and bookkeeping parameter method are discussed in detail some remarkable virtues of the methods are exploited and their applications are illustrated

dynamic university classes for diffusion limited aggregation and lattice animals a recent application of the real space renormalisation group to the problem of anomalous diffusion on witten sander clusters is generalised and the authors demonstrate that these clusters lie in a distinct dynamic universality class from random lattice animals

an elementary introduction to the homotopy perturbation method this paper is an elementary introduction to the concepts of the homotopy perturbation method particular attention is paid to giving an intuitive grasp for the solution procedure throughout the paper

exact solution for nonlinear schrodinger equation by he s frequency formulation in this work we apply he s frequency formulation to search for the solution to nonlinear schrodinger equation three examples are given and the solutions obtained are in good accordance with wazwaz s solution abdul majid wazwaz a study on linear and nonlinear schrodinger equations by the variational iteration method chaos solitons fractals 37 4 2008 1136 1142 it is shown that he s frequency formulation is of utter straightforward and effective

response of a cantilever model with a surface crack under basal white noise excitation abstract a cantilever with an open surface crack excited by the pedestal movement with the form of the gaussian white noise was modeled in this paper the open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained the dynamical equation governing the transverse motion was gained with the kane s method after sufficient consideration of the geometrical nonlinearity and the axial inertia both quasi conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically the stationary probability density function pdf of the amplitude as well as the joint stationary pdf of the displacement and velocity was investigated for the purpose of exploring the reliability of the cantilever the reliability function was established to avoid the potential fatigue or damage numerical simulations were carried out to vindicate the theoretical analysis the advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary pdf of the amplitude and the joint pdf of displacement and velocity furthermore the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation monte carlo method of the reliability

markov matrix analysis of random walks in disordered continuous media abstract we study by a markov matrix analysis of the equivalent random walks the dynamic properties of continuous media consisting of both correlated and uncorrelated equal size spheres we employ a blind ant random walk model using the rule that a walker jumps among centers of the directly connected spherical particles on an infinite network the dominant eigenvalues and eigenvectors of the transition probability matrix of the random walks are calculated yielding estimates of the spectral dimension d s and the fractal dimension d w of random walks on the continuous network we find that for the present model the estimates are very close to the corresponding lattice percolation values though only after the finite size effects have been carefully taken into account we also show that the finite size scaling of the largest nontrivial eigenvalues holds for our model with the same exponents as for the lattice percolation

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

renormalisation on sierpinski type fractals presents a family of deterministic fractals which generalise the d dimensional sierpinski gaskets and establishes their order of ramification and their fractal and spectral dimensions random walks on these fractals are renormalisable and lead to rational not necessarily polynomial mapping

statistics of the true self avoiding walk in one dimension numerical results of a monte carlo study for the true self avoiding walk in one dimension are presented for any positive value of the strength parameter 0 g infinity the root mean square displacement rn and the range sn of the walk are characterised by two universal exponents nu 2 3 or 0 003 and s 2 3 or 0 01 respectively for negative g self attracting walk both rn and sn exhibit a saturation effect limn to infinity rn rinfinity g and limn to infinity sn sinfinity g with rinfinity g approximately g 1 and sinfinity g approximately g 1 at g or approximately 0 a simple scaling analysis in n and g is proposed and found to be consistent with the monte carlo results

superuniversal spectral dimension for dilute branched polymers the authors introduce the problem of random walks on lattice animals dilute branched polymers and calculate the spectral dimension ds of animals in two and three dimensions by using a two parameter position space renormalisation group method this problem which is a generalisation of the problem of the ant in the labyrinth has been independently proposed and investigated by wilke et al 1984 the spectral dimension is given by ds 2da dw where da is the fractal dimension of the lattice animal and dw the fractal dimension of the random walk on the lattice animal the results indicate that ds may be a superuniversal quantity i e its value is independent of dimension moreover the authors find ds to be close to 4 3 which is the spectral dimension of the largest percolation cluster at the percolation threshold pc as conjectured by alexander and orbach 1982 since both lattice animals and the largest percolation cluster at pc have a homogeneous interior structure the results suggest that the spectral dimension of all such fractals may equal 4 3

critical exponents of the self avoiding walks on a family of finitely ramified fractals the authors have studied the self avoiding walks saw on a family of finitely ramified fractals the first member b 2 of the family is the two dimensional sierpinski gasket while the last member b infinity appears to be a wedge of the homogeneous triangular lattice by means of the exact renormalisation group transformations they have calculated the critical exponents alpha nu and gamma and the connectivity constant mu of saw on each member of a sequence 2 or b or 8 of the studied fractal family the obtained exact results are compared with the recent phenomenological proposals and with the results believed to be exact in the case of a homogeneous two dimensional lattice

connective constant of saws on the sierpinski gasket family using a graph counting technique suitable for regular fractals an exact evaluation of the total number of embeddings of self avoiding walks on the generalized sierpinski gasket is obtained numerical estimates for the connective constants are quoted for the first time where b is the generation parameter of the gaskets it is shown that the number of distinct n step saws per site converges to the triangular lattice values when our analysis indicates that converges to the euclidean value in the same limit and an asymptotic expression is given

counting suffix arrays and strings suffix arrays are used in various applications and research areas like data compression or computational biology in this work our goal is to characterise the combinatorial properties of suffix arrays and their enumeration for a fixed alphabet size and string length we divide the set of all strings into equivalence classes of strings that share the same suffix array for each such equivalence class we count the number of strings contained in it we also give exact formulas for computing the number of equivalence classes our methods yield a lower bound for the compressibility of suffix arrays and build the foundation for the efficient generation of appropriate test data sets for suffix array based algorithms we also show that summing up the elements of all equivalence classes forms a particular instance for some summation identities of eulerian numbers

anomalous diffusion on regular and random models for diffusion limited aggregation families of regular fractal models for witten sander dla clusters in d dimensions are proposed resembling the computer generated aggregates the authors evaluate random walk dimensionalities exactly using resistance scaling ideas the applicability of the conflicting conjectures of alexander orbach 1982 ao dw 3df 2 and aharony stauffer 1984 as dw df 1 to dla is then examined one finds that the dendritic nature of the fractals presented ensures that as is satisfied exactly in all dimensions an rsrg fugacity transformation method is applied to the simplest of the regular fractals in d 2 the result for dw is compared with the exact resistance scaling result to obtain an estimate of the error introduced by the rsrg the rg method is then generalised to treat the random dla problem the resulting estimate for dw is in fortuitously good agreement with as the corresponding monte carlo data and the results above for the regular fractal models

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

monte carlo renormalisation group for the true self avoiding walk following the general ideas by swendsen 1982 a monte carlo renormalisation group mcrg estimation of the end to end exponent nu for the one dimensional true self avoiding walk tsaw has been carried out because the tsaw is known to reach its asymptotic behaviour only very slowly an approximate expression for the fixed point has been determined by monte carlo techniques this approximate fixed point has been used as a starting point for the mcrg the final result for the exponent nu is 0 665 or 0 004

critical behaviour at an edge for the saw and ising model the authors have studied the behaviour of two and three dimensional self avoiding walks confined to a wedge of wedge angle alpha series have been obtained and analysed for the angular dependent critical exponents characterising various edge susceptibilities in terms of a general scaling form for the edge free energy fe approximately t d 2 nu psi e ht y0 nu h1t y1 nu h2t y2 nu they find for the two dimensional case the following scaling indices y0 91 48 y1 3 8 y2 alpha 5 pi 8 alpha they argue that these results are exact from which follow all exponents for the bulk surface and edge problem in three dimensions the authors obtain y0 approximately 2 488 y1 0 65 or 0 02 y2 alpha alpha b pi alpha where a 0 51 or 0 04 b 0 847 or 0 017 which for y2 is precisely of the functional form given by mean field theory y2 alpha 1 2 pi 2 they argue that a 1 2 for all three dimensional o n models this simple angular dependence of y2 is different from that suggested by cardy s one loop epsilon expansion 1983 for the square lattice they have also studied the case in which the wedge is rotated through an angle of pi 4 and find that the various exponents are unchanged for the three dimensional ising model in a wedge analogy with the saw results plus mean field results in conjunction with rg and series work yield y0 approximately 2 485 y1 0 71 or 0 02 and y2 a b pi alpha with a 1 2 and b 0 79 or 0 02

eden model on the manhattan lattice the authors study the eden growth model on the square manhattan lattice sml for this purpose it has been necessary to extend the standard eden model in such a way that each act of growing is conceived as a directional process by applying the position space renormalisation group technique they find that the eden processes on the sml and on the ordinary square lattice are in different universality classes this finding and corresponding fractal dimensions are compared with results obtained for similar models of irreversible kinetic processes

solution of nonlinear equations by an ancient chinese algorithm in this paper we re study an ancient chinese algorithm the ying buzu shu in about second century bc known as the rule of double false position in west after 1202 ad the method can powerfully applied to solve nonlinear equations some examples are given

statistical mechanics of polymer chains grafted to adsorbing boundaries of fractal lattices embedded in three dimensional space abstract we study the adsorption problem of linear polymers immersed in a good solvent when the container of the polymer solvent system is taken to be a member of the sierpinski gasket sg family of fractals embedded in the three dimensional euclidean space members of the sg family are enumerated by an integer b 2 b and it is assumed that one side of each sg fractal is impenetrable adsorbing boundary we calculate the surface critical exponents 11 1 and s which within the self avoiding walk model saw of polymer chain are associated with the numbers of all possible saws with both one and no ends grafted to the adsorbing surface adsorbing boundary respectively by applying the exact renormalization group method for 2 b 4 we have obtained specific values for these exponents for various types of polymer conformations to extend the obtained sequences of exact values for surface critical exponents we have applied the monte carlo renormalization group method for fractals with 2 b 40 the obtained results show that all studied exponents are monotonically increasing functions of the parameter b for all possible polymer states we discuss mutual relations between the studied critical exponents and compare their values with those found for other types of lattices in order to attain a unified picture of the attacked problem

renormalisation of the true self avoiding walk it is shown that the renormalisation of the true self avoiding walk of amit et al 1982 is its upper critical dimensionality two involves at least two possibly three coupling constants fixed points to first order in epsilon 2 d are identified and the asymptotic behaviour at d 2 is discussed

on the size of the smallest alphabet for lyndon trees abstract we consider the problem of reverse engineering the lyndon tree i e given a full binary ordered tree t with n leaves as input we are to compute a string w of length n of which lyndon tree is isomorphic to the input tree t hereby we call such a string a solution string although the problem is easily solvable in linear time for binary alphabets and unbounded size alphabets it is not known how to efficiently find the smallest alphabet size for a solution string in this paper we show several new observations concerning this problem namely we show that 1 for any positive integer n there exists a full binary ordered tree t with n leaves s t the smallest alphabet size of a solution string for t is n 2 1 2 for any full binary ordered tree t with n leaves there exists a solution string w over an alphabet of size at most n 2 1 3 for any full binary ordered tree t there exists a solution string w over an alphabet of size at most h 1 where h is the height of t 4 for any complete binary ordered tree t with 2 k leaves there exists a solution string w over an alphabet of size at most 4

homogeneity and spectral dimension of aggregation fractals the fracton or spectral dimension ds of two sutherland type ghost aggregation fractals is obtained for high space dimension by a scaling argument if as seems probable these fractals are homogeneous the results ds 2ln2 ln3 and ds 4 square root 17 1 support recent conjectures that ds is close to 4 3 for all homogeneous fractals however they are not consistent with the stronger conjecture that ds is exactly 4 3 for all such fractals

ideal chain on a two dimensional critical percolation cluster the authors study the statistics of the ideal chain or equally weighted trajectories for the first time on a two dimensional critical percolation cluster they discuss the asymptotic behaviour of the mean end to end distance and the number of chains for the long chain limit by exact enumeration the results strongly suggest that this problem does not belong to the same universality class as the random walk or kinetically weighted trajectories on the same fractal cluster

cluster renormalisation study of site lattice animals in two and three dimensions the author studies site lattice animals using the cluster renormalisation cr approach previously applied to bond animals the exponent v characterising the asymptotic behaviour of the mean square radius of gyration of site animals and the fractal dimension df 1 v are determined in two and three dimensions he finds v 0 649 or 0 009 and v approximately 0 51 in two and three dimensions respectively in addition he studies restricted valence site animals on a triangular lattice using a single parameter cr approach

growing partially directed self avoiding walks a partially directed self avoiding walk model with the kinetic growth weighting is solved exactly on the square lattice and for two restricted strip geometries some finite size effects are examined

response to the comment on eden model on the manhattan lattice the authors respond to the numerical simulation result obtained by botet ibid vol 19 p 2233 1986 which implies that the eden aggregates should be compact objects and comment on the validity of the renormalisation group approach to the same problem

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

diffusion on lattice animals and percolation clusters a renormalisation group approach a position space renormalisation group method is developed to study the scaling properties of random walks on fractals calculations in two dimensions for site lattice animals and site percolation clusters yield numerical results for the critical exponent defined by the asymptotic behaviour of the root mean square displacement of the walker the renormalisation group results are consistent with recent monte carlo calculations

more properties of the fibonacci word on an infinite alphabet abstract recently the fibonacci word w on an infinite alphabet was introduced by zhang et al 2017 13 as a fixed point of the morphism 2 i 2 i 2 i 1 2 i 1 2 i 2 over all i n in this paper we investigate the occurrence of squares palindromes and lyndon factors in this infinite word

novel dynamical scaling in kinetic growth phenomena abstract a novel dynamical scaling characterized by infinitely many growth exponents is presented this new behavior is manifested in the time dependent pair correlation function and therefore is amenable to direct experimental observation an exact analytical solution on the time dependent ginzburg landau model is obtained in the large n limit for a quench at zero temperature which exhibits such multiscaling behavior this new form of behavior reflects a morphological pattern in the growing domains and is expected in other growth phenomena as indicated by preliminary analysis on dla clusters a connection between multiscaling and multifractality is discussed

large cell renormalisation and systems of dimensionality larger than the upper marginal dimension a recent argument dismissing the applicability of large cell renormalisation schemes to systems of dimensionality d larger than the upper marginal dimension dc is critically discussed in this connection new large cell renormalisation results for the random walk for d 3 and 4 are presented which indicate convergence to the correct results

random walks on invasion percolation clusters results are presented of numerical simulations of random walks on invasion percolation clusters in two and three dimensions including simulations on continuum percolation clusters at threshold walks of up to 105 steps were taken the results indicate that the fracton dimension of invasion percolation clusters both on regular lattices and in the continuum is the same within numerical errors as the fracton dimension of ordinary percolation clusters at threshold

cell renormalisation of growth processes true self avoiding walks and growing animals the authors present a generating function formalism for growth processes in general and introduce a new cell renormalisation scheme as examples they treat the true self avoiding walk and the eden process or growing animals in two and three dimensions using small cells the results in both cases indicate a substantial increase in the fractal dimension d compared with their equilibrium counterparts the case of the eden process may however suggest a peculiar convergence behaviour as the cell size b tends to infinity

end to end distance of linear polymers in two dimensions a reassessment recent exact enumeration studies of the two dimensional self avoiding walk have produced evidence in support of non analytic scaling corrections newly extended series for the triangular and square lattices to n 19 and 25 respectively are examined in the light of recent monte carlo results suggesting the absence of corrections of this type using a modified approach to series analysis it is concluded that the end to end distance can best be understood in terms of analytic corrections alone in view of the lack of theoretical support there is little reason to introduce additional kinds of correction in attempting to explain the data

he s frequency amplitude formulation for the duffing harmonic oscillator he s frequency amplitude formulation is used to solve the duffing harmonic oscillator problem the solution procedure is simple and the result obtained is valid for the whole solution domain with high accuracy

asymptotic form of the spectral dimension at the fractal to lattice crossover the authors study the spectral dimension of the sierpinski gasket family of fractals each member of the family is labelled by an integer b 2 or b infinity so that when b to infinity both the fractal and spectral dimension approach the euclidean value 2 the asymptotic law for the spectral dimension was recently suggested to be ds approximately 2 b 1nb beta with b and beta being some constants here the authors demonstrate that this form should be replaced by the asymptotic law ds approximately 2 1n 1nb constant 1nb their analysis is based on the exact calculation of the electric resistances rb for all members of the family up to b 650

he s frequency amplitude formulation for nonlinear oscillators with an irrational force in this paper he s frequency amplitude formulation is applied to determine the periodic solution for a nonlinear oscillator system with an irrational force comparison with the exact solution shows that the result obtained is of high accuracy

self avoiding walks attached to triangular and face centred cubic lattice surfaces extended exact enumeration data the analysis of exact enumeration data of self avoiding walks attached to the surfaces of triangular and face centred cubic lattices is consistent with gamma 1 0 718 or 0 008 136 delta pc where delta pc pc 0 0995 in three dimensions and 0 9530 or gamma 1 or 0 9548 in two dimensions where pc for the triangular lattice is assumed to lie in the range 0 240 915 or pc or 0 240 93

diffusion on percolation clusters at criticality the concept of fractal dimensionality is used to study the problem of diffusion on percolation clusters the authors find from monte carlo simulations that the fractal dimensionality of a random walk on a critical percolation cluster in three dimensional space is d 3 3 or 0 1 where the size of the cluster is restricted to be larger than the span of the walk and is d 3 9 or 0 1 for a walk on clusters not subject to this restriction for two dimensional space they find d approximately d approximately 2 7 or p0 1 the exponent d and d is related to the scaling of the average length r of n steps via rd varies as n the fracton dimensionality which is related to the density of states was found to be 1 26 or 0 1 these results are in good agreement with the predictions of alexander and orbach 1982

single random walker on disordered lattices random walks on square lattice percolating clusters were followed for up to 2 10 steps the mean number of distinct sites visited sn gives a spectral dimension of d s 1 30 5 0 03 consistent with superuniversality d s 4 3 but closer to the alternative ds 182 139 based on the low dimensionality correction simulations are also given for walkers on an energetically disordered lattice with a jump probability that depends on the local energy mismatch and the temperature an apparent fractal behavior is observed for a low enough reduced temperature above this temperature the walker exhibits a crossover from fractal to euclidean behavior walks on two and three dimensional lattices are similar except that those in three dimensions are more efficient

flory approximant for self avoiding walks on fractals a flory approximant for the exponent describing the end to end distance of a self avoiding walk saw on fractals is derived the approximant involves the fractal dimensionalities of the backbone and of the minimal path and the exponent describing the resistance of the fractal the approximant yields values which are very close to those available from exact and numerical calculations

true self avoiding walks on fractal lattices above the upper marginal dimension we study by monte carlo simulations the critical behaviour and the cross over scaling of the true self avoiding walks tsaw on fractal lattices above the upper marginal dimension we estimate the flory exponent nu which characterizes the rms end to end distances of saw on a percolation cluster at percolation thresholds both in three and four dimensions and on a dla cluster in three dimensions results were in good agreement with the predictions of the known flory formulae we also discuss the fractal to euclidean and the rw to tsaw cross over scaling monte carlo data appear to collapse in the scaling regions for both cases however we found that the scaling function for the latter is different from that on the regular lattices

comment on transport processes on fractal structures the scaling exponents for the depleted sierpinski gasket derived by havlin and ben avraham ibid vol 16 p l483 7 1983 are shown to differ sharply from those derived by the method of given and mandelbrot ibid vol 16 p l565 9 1983 the discrepancy is analysed and it is shown that the argument used by havlin and ben avraham is incorrect

true self avoiding walks on a percolation cluster the authors investigate by monte carlo simulations the critical behaviour of true self avoiding walks tsaws on a percolation cluster performed very close to the percolation threshold specifically they generate tsaws on a site percolated incipient infinite cluster for various values of the self avoidance parameter g 0 they found that such walks exhibit critical behaviour different from that of ordinary self avoiding walks and also from that of random walks of no constraint the flory exponent obtained was v 0432 or 0 005 for all g 0 which agrees well with the flory type formula suggested by rammal 1984

self avoiding walk model for proteins a real space renormalisation group treatment diffusion on the model for proteins introduced by helman coniglio and tsallis 1984 hct is discussed using real space renormalisation group ideas the authors perform cell to cell transformations in two dimensions for both the hct model and the self avoiding walk the latter system is quasi linear and so they expect trivial diffusive behaviour given by dw 2df 8 3 diffusion on the hct model however is complicated by the possibility of jumps across nearest neighbour hydrogen bond bridges the authors results are not consistent with the prediction that dw 2 for the hct model rather they support the assertion that dwhct is close to but slightly greater than dwsaw

he s variational approach for nonlinear oscillators with high nonlinearity in this paper he s variational approach is applied to the strongly nonlinear oscillators with high nonlinearity some examples are given to illustrate the effectiveness and convenience of this method comparison with the exact solutions is also made revealing that the present method leads to accurate solutions

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

self avoiding walks with curvature energy on fractals self avoiding walks with a curvature dependent energy are studied with renormalization group methods on some fractal lattices fixed points corresponding to universal and non universal behaviours are generally present however initial conditions of the renormalization group recursions can prevent non universality when universality holds the persistence length is found to diverge much faster than in the periodic lattice as the curvature energy increases

approximate periodic solutions for the helmholtz duffing equation approximate periodic solutions for the helmholtz duffing oscillator are obtained in this paper he s energy balance method hebm and he s frequency amplitude formulation hfaf are adopted as the solution methods oscillation natural frequencies are analytically analyzed error analysis is carried out and accuracy of the solution methods is evaluated

static and dynamic properties for growth models how does one measure static properties in dynamic models the authors propose a basic approach that should help keep the statics and the dynamics of growth models clearly separated their formalism is used to elaborate a large cell renormalisation group scheme which gives very good results for the determination of the fractal dimension of eden and dla models they also propose a dynamic scaling theory for growth models which they verify for both eden and dla models

diffusion on random systems above below and at their percolation threshold in two and three dimensions a detailed monte carlo study is presented for classical diffusion random walks on random l l triangular and l l l simple cubic lattices with l up to 4096 and 256 respectively the speed of a cyber 205 vector computer is found to be about one order of magnitude larger than that of a usual cdc cyber 76 computer to reach the asymptotic scaling regime walks with up to 10 million steps were simulated with about 10 jl steps in total for l 256 at the percolation threshold we review and extend the dynamical scaling description for the distance traveled as function of time the diffusivity above the threshold and the cluster radius below earlier discrepancies between scaling theory and computer experiment are shown to be due to insufficient monte carlo data the conductivity exponent is found to be 2 0 0 2 in three and 1 28 0 02 in two dimensions our data in three dimensions follow well the finite size scaling theory below the threshold the approach of the distance traveled to its asymptotic value is consistent with theoretical speculations and an exponent 2 5 independent of dimensionality the correction to scaling exponent at pc seems to be larger in two than in three dimensions

a quick tour on suffix arrays and compressed suffix arrays suffix arrays are a key data structure for solving a run of problems on texts and sequences from data compression and information retrieval to biological sequence analysis and pattern discovery in their simplest version they can just be seen as a permutation of the elements in 1 2 n encoding the sorted sequence of suffixes from a given text of length n under the lexicographic order yet they are on a par with ubiquitous and sophisticated suffix trees over the years many interesting combinatorial properties have been devised for this special class of permutations for instance they can implicitly encode extra information and they are a well characterized subset of the n permutations this paper gives a short tutorial on suffix arrays and their compressed version to explore and review some of their algorithmic features discussing the space issues related to their usage in text indexing combinatorial pattern matching and data compression

molecular trajectory algorithm for random walks on percolation systems at criticality in two and three dimensions abstract random walk simulations based on a molecular trajectory algorithm are performed on critical percolation clusters the analysis of corrections to scaling is carried out it has been found that the fractal dimension of the random walk on the incipient infinite cluster is d w 2 873 0 008 in two dimensions and 3 78 0 02 in three dimensions if instead the diffusion is averaged over all clusters at the threshold not subject to the infinite restriction the corresponding critical exponent k is found to be k 0 3307 0 0014 for two dimensional space and 0 199 0 002 for three dimensional space moreover in our simulations the asymptotic behaviors of local critical exponents are reached much earlier than in other numerical methods

theory of laplacian fractals diffusion limited aggregation and dielectric breakdown model abstract we describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the laplace equation and a stochastic field this new theory provides a systematic method for the calculation of the fractal dimension d and of the multifractal spectrum of the growth probability a detailed application to the dielectric breakdown model and diffusion limited aggregation in two dimensions is presented our approach exploits the scale invariance of the laplace equation that implies that the structure is self similar both under growth and scale transformation this allows one to introduce a fixed scale transformation instead of coarse graining as in the renormalization group theory that defines a functional equation for the fixed point of the distribution of basic diagrams used in the coarse graining process for the calculation of the matrix elements of this transformation one has to consider an infinite but rapidly convergent number of processes that occurs outside a considered diagram

diffusion and fracton dimensionality on fractals and on percolation clusters the authors present simulations of diffusion on an exact fractal and on percolation clusters at criticality for two and three dimensions the results for the fractal support the rammal and toulouse proposition 1983 that ds n dn varies as b n s n the results for percolation are in excellent agreement with the alexander and orbach conjecture 1982 that the fracton dimensionality d 4 3

random walk statistics on fractal structures we consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds range renewal theory mean first passage time etc asymptotic behaviors are shown to be controlled by the fractal d and spectral d dimensionalities of the considered structure a simple decimation procedure giving the value of d is outlined and illustrated in the case of the sierpinski gaskets recent results for the trapping problem the self avoiding walk and the true self avoiding walk are briefly reviewed new numerical results for diffusion on percolation clusters are also presented

self avoiding walks on percolation clusters the author studies self avoiding walks saws on percolation clusters a scaling function representation for r the mean end to end distance is proposed which describes a crossover from ordinary saws to saws on fractals he distinguishes between saws on a single cluster for which r approximately nx where x nu 1 and saws on all clusters for which r approximately nz where z nu 2 and n is the number of monomers in the walk he estimates nu 1 d 2 approximately 1 285 and the correction to scaling exponent omega d 2 approximately 1 3 and nu 1 d 3 approximately 1 38 two plausible generalisations of the flory 1953 approximation for nu 1 are investigated and it is argued that none of them provides a satisfactory approximation for nu 1 at all dimensions

multi frequency excitation of stiffened triangular plates for large amplitude oscillations abstract free and forced vibrations of triangular plate are investigated diverse types of stiffeners were attached onto the plate to suppress the undesirable large amplitude oscillations the governing equation of motion for a triangular plate based on the von karman theory is developed and the nonlinear ordinary differential equation of the system using galerkin approach is obtained closed form expressions for the free undamped and large amplitude vibration of an orthotropic triangular elastic plate are presented using the two well known analytical methods namely the energy balance method and the variational approach the frequency responses in the closed form are presented and their sensitivities with respect to the initial amplitudes are studied an error analysis is performed and the vibration behavior as well as the accuracy of the solution methods is evaluated different types of the stiffened triangular plates are considered in order to cover a wide range of practical applications numerical simulations are carried out and the validity of the solution procedure is explored it is demonstrated that the two methods of energy balance and variational approach have been quite straightforward and reliable techniques to solve those nonlinear differential equations subsequently due to the importance of multiple resonant responses in engineering design multi frequency excitations are considered it is assumed that three periodic forces are applied to the plate in three specific positions the multiple time scaling method is utilized to obtain approximate solutions for the frequency resonance cases influences of different parameters namely the position of applied forces geometry and the number of stiffeners on the frequency response of the triangular plates are examined

hamiltonian walks on sierpinski and n simplex fractals we study hamiltonian walks hws on sierpinski and n simplex fractals via numerical analysis of exact recursion relations for the number of hws we calculate the connectivity constant and find the asymptotic behaviour of the number of hws depending on whether or not the polymer collapse transition is possible on a studied lattice different scaling relations for the number of hws are obtained these relations are in general different from the well known form characteristic of homogeneous lattices which has thus far been assumed to also hold for fractal lattices

true self avoiding walk on fractals the authors investigate the true self avoiding walk on fractal spaces the number sn of sites visited during an n step walk and the root mean square displacement rn are calculated via extensive monte carlo simulations on the 2d sierpinski gasket for all positive values of the repulsion parameter g they found the same exponents s 0 815 or 0 001 and nu 0 510 or 0 005 respectively both rn and sn are shown to exhibit a simple scaling behaviour in n and g the authors compare the results with a simple flory like prediction for the exponent nu

critical exponent γ for a class of directed walks at the fractal to euclidean crossover abstract an exact evaluation of the critical exponent associated with the average number of n step walks of the piecewise directed random walks is presented in the case of the complete family of the sierpinski gasket type of fractals

the notion of a strange fractal phenomenon disorder induced walk it is argued that a random system coupled with a walk may cause an unusual phenomenon which shares some of the opposite properties of fractals

statistics of equally weighted random paths on a class of self similar structures we study the statistics of equally weighted random walk paths on a family of sierpinski gasket lattices whose members are labelled by an integer b 2 b 2 mean path end to end distance grows more slowly than any power of its length n we provide arguments for the emergence of usual power law critical behaviour in the limit b when fractal lattices become almost compact