maps of intervals with indifferent fixed points thermodynamic formalism and phase transitions we develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points for such systems the formalism yields onedimensional systems with many body infinite range interactions for which the thermodynamics is well defined but gibbs states are not piecewise linear systems of this kind yield the soluble in a sense fisher models we prove that such systems exhibit phase transitions the order of which depends on the behavior at the indifferent fixed points we obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable expanding induced version the technique allows one also to obtain a version of the bowen ruelle formula for the hausdorff dimension of repellers for maps with indifferent fixed points and to generalize fisher results to some nonsoluble models

fundamental mode shape and its derivatives in structural damage localization abstract various techniques for structural damage detection involving modal parameters have widely been used over the past few decades this is because the modal parameters of a structure can easily be obtained from forced free or ambient vibration measurements in many of these techniques mode shape curvature has been used for localization of damage in this paper a mathematical basis is provided to show the correlation between a structural damage and a change in the fundamental mode shape and its derivatives this has been achieved by deriving the expression of a damaged mode shape utilizing a perturbation approach for a cantilever shear beam discretized into a large number of elements this approach demonstrates that the change in the fundamental mode shape due to any damage is an excellent indicator of damage localization as it is found to be discontinuous at the location of damage further the change in higher derivatives i e slope and curvature of the fundamental mode shape is shown to be sensitive enough in damage localization a numerical study involving a shear building and a steel moment resisting frame is conducted to show the effectiveness of the proposed approach in damage localization it has been found from this study that spline fitting of mode shapes in case of a limited number of degrees of freedom which is generally adopted for plotting mode shapes and their derivatives may lead to false detection of damage

the behavior of higher order mode shape derivatives in damaged beam like structures this work considers the effect that damage has upon the higher order derivatives of mode shapes of structures having primarily beam like vibration via numerical investigations the sensitivity of various damage related parameters in inducing changes in these higher order modal derivatives is determined leading to a more complete understanding of what factors make the most contribution to significant changes in these derivatives it is concluded that higher order mode shape derivatives e g modal curvature third derivative and fourth derivative are better indicators of damage than the mode shapes three distinct types of response for the damage induced higher order derivative discontinuities are identified as three key parameters the mass loss stiffness loss and damage radius scale vary from this formal approximations are obtained for the expected forms of the higher order derivative discontinuities based upon the underlying behavior predicted by a simple relation among these three parameters these approximations are checked with numerical simulations and an excellent level of agreement is observed under appropriate conditions finally the potential of these higher order derivative changes for indicating the presence and location of damage in a global setting is examined

stochastic one dimensional lorentz gas on a lattice we stud ya one dimensional stochastic lorentz gas wher ea light particle moves i na fixed array of nonidentical random scatterers arranged i na lattice each scatterer is characterized b ya random transmissionreflection coefficient we consider the case when the transmission coefficients of the scatterers are independent identically distributed random variables a symbolic program is presented which generates the exact velocity autocorrelation functio n vacf in terms of the moments of the transmission coefficients the vacf is found for different types of disorder for times up to 20 collision times we then conside ra specific type of disorder a two state lorentz gas in which two types of scatterers are arranged randomly i na lattice the na lattice point is occupied b ya scatterer whose transmission coefficient is with probability p or with probability 1 p a perturbation expansion with respect to is derived the 2 term in this expansion shows that the vacf oscillates with time the period of oscillation being twice the time of flight from one scatterer to its nearest neighbor the coarse grained vacf decays for long times like t 32 which is similar to the decay of the vacf of the random lorentz gas wit ha single type of scatterer the perturbation results and the exact one s found up to 20 collision times show good agreement

ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2 torus we study generic piecewise linear hyperbolic automorphisms of the 2 torus we explain why the resulting dynamical system is ergodic and mixing and prove the exponential decay of correlations

on applications of generalized functions to beam bending problems using a mathematical approach this paper seeks an eacient solution to the problem of beams bending under singular loading conditions and having various jump discontinuities for two instances the boundary value problem that describes beam bending cannot be written in the space of classical functions in the first instance the beam is under singular loading conditions such as point forces and moments and in the second instance the dependent variable s and its derivatives have jump discontinuities in the most general case we consider both instances first we study singular loading conditions and present a theorem by which the equivalent distributed force of a general class of singular loading conditions can be found as a consequence of obtaining the equivalent distributed force of a distributed moment we find a mathematical explanation for the corner condition in classical plate theory while plate theory is not the focus of this paper this explanation is interesting then beams with various jump discontinuities are considered when beams have jump discontinuities the form of the governing diaerential equations changes we find the governing diaerential equations in the space of generalized functions it is shown that for euler bernoulli beams with jump discontinuities the operator of the diaerential equation remains unchanged only the force term changes so that delta function and its distributional derivatives appear within it but for timoshenko beams with jump discontinuities in addition to changes in the force terms the operator of one of the governing diaerential equations changes we then propose a new method for solving these equations this method which we term the auxiliary beam method is to solve the governing diaerential equations not in the space of generalized functions but rather to solve them by means of solving equivalent boundary value problems in the space of classical functions the auxiliary beam method reduces the number of diaerential equations and at the same time obviates the need to solve these diaerential equations in the space of generalized functions which can be more diacult 7 2000 elsevier science ltd all rights reserved

invariance principles for iterated maps that contract on average we consider iterated function schemes that contract on average using a transfer operator approach we prove a version of the almost sure invariance principle this allows the system to be modelled by a brownian motion up to some error term it follows that many classical statistical properties hold for such systems such as the weak invariance principle and the law of the iterated logarithm

statistical properties of maps with indifferent periodic points in this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points as applications we apply our results to the well known manneville pomeau equation and the inhomogeneous diophantine approximation algorithm

central limit theorem and stable laws for intermittent maps in the setting of abstract markov maps we prove results concerning the convergence of renormalized birkhoff sums to normal laws or stable laws they apply to one dimensional maps with a neutral fixed point at 0 of the form x x1 for 0 1 in particular for 1 2 we show that the birkhoff sums of a holder observable f converge to a normal law or a stable law depending on whether f 0 0 or f 0 0 the proof uses spectral techniques introduced by sarig and wiener s lemma in non commutative banach algebras

statistical properties of lorentz gas with periodic configuration of scatterers in our previous paper markov partitions for some classes of dispersed billiards were constructed using these partitions we estimate the decay of velocity auto correlation function and prove the central limit theorem of probability theory and donsker s invariance principle for lorentz gas with periodic configuration of scatterers

natural modes of bernoulli euler beams with symmetric cracks abstract an approximate galerkin solution to the one dimensional cracked beam theory developed by christides and barr for the free bending motion of beams with pairs of symmetric open cracks is suggested the series of comparison functions considered in the galerkin procedure consists of the mode shapes of corresponding uncracked beam the number of terms in the expansion is determined by the covnergence of the natural frequencies and confirmed by studying the stress concentration profile near the crack this approach allows the determination of the higher natural frequencies and mode shapes of the cracked beam it is found that the christides and barr original solution was not fully converged and that cracks render the convergence of the galerkin s procedure very slow by affecting the continuity characteristics of the solution of the boundary value problem to validate the theoretical results a two dimensional finite element approach is proposed which also allows one to determine the parameter that controls the stress concentration profile near the crack tip in the theoretical formulation without requiring the use of experimental results very good agreement between the theoretical and finite element results is observed

on infinite volume mixing in the context of the long standing issue of mixing in infinite ergodic theory we introduce the idea of mixing for observables possessing an infinite volume average the idea is borrowed from statistical mechanics and appears to be relevant at least for extended systems with a direct physical interpretation we discuss the pros and cons of a few mathematical definitions that can be devised testing them on a prototypical class of infinite measure preserving dynamical systems namely the random walks

structural damage detection based on the reconstructed phase space for reinforced concrete slab experimental study in this paper a parameter based on geometry changes of the reconstructed multidimensional phase space of the measured vibration signals for structural damage identification is proposed the choice of the proper delay time steps and embedding dimensions for phase space reconstruction of linear systems is discussed using the determined delay time and embedding dimensions an index changes of phase space topology cpst with multiple embedding dimensions is calculated and then used to identify the structural damage to demonstrate the reliability of the proposed method vibration test data corresponding to different damage states of a continuous reinforced concrete slab is used to calculate the cpst value for damage identification the results indicate that except the measurement points at structural supports the cpst values at all the measurement points on the structure increase with structural damage level irrespective of the damage location indicating that using a single or a minimum number of measurement points and their cpst value can effectively identify damage existence in the structure the traditional modal based indices are also calculated using the same vibration data for comparison it is found that the proposed method with cpst is the most sensitive to structural damage than any modal based index the results demonstrate that the proposed method with cpst value is very effective in identifying damage existence in the structure although it cannot quantify the damage it can be a good candidate for continuous structural health monitoring because it needs only a few sensors to detect damage existence in the entire structure

an invariance principle for maps with polynomial decay of correlations we give a general method of deriving statistical limit theorems such as the central limit theorem and its functional version in the setting of ergodic measure preserving transformations this method is applicable in situations where the iterates of discrete time maps display a polynomial decay of correlations

a numerical study of the eigenparameters of a damaged cantilever abstract when a structure is subjected to damage its dynamic response changes characterized by shifts in the eigenvalues and modifications of the eigenvectors considerable effort has been put into investigating the relationship between the damage location the damage size and the corresponding changes in the eigenparameters in most cases emphasis has been on using the shift in eigenvalues as a means of determining the damage location and the information derived from the change in eigenvectors has largely remained obscure in this paper a systematic study is presented of the relationship between damage location damage size and the changes in the eigenvalues and eigenvectors of a cantilever when subjected to damage a finite element model of a uniform cross sectioned cantilever was chosen to provide data for analysis the changes in the eigenvalues and eigenvectors are shown to follow a definite trend in relation to the location and extent of damage

almost sure invariance principle for nonuniformly hyperbolic systems we prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems discrete time systems and flows are covered by this result in particular the result applies to the planar periodic lorentz flow with finite horizon statistical limit laws such as the central limit theorem the law of the iterated logarithm and their functional versions are immediate consequences

subexponential decay of correlations we describe a method for proving subexponential lower bounds for correlations functions and apply it to study decay of correlations for maps with countable markov partitions one result is that ls young s upper estimates y2 are optimal in many situations our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on banach spaces which we apply to the iterates of the transfer operator

closed form solutions of euler bernoulli beams with singularities abstract the problem of the integration of the static governing equations of the uniform euler bernoulli beam with discontinuities is studied in particular two types of discontinuities have been considered flexural stiffness and slope discontinuities both the above mentioned discontinuities have been modeled as singularities of the flexural stiffness by means of superimposition of suitable distributions generalized functions to a uniform one dimensional field closed form solutions of governing differential equation requiring the knowledge of the boundary conditions only are proposed and no continuity conditions are enforced at intermediate cross sections where discontinuities are shown the continuity conditions are in fact embedded in the flexural stiffness model and are automatically accounted for by the proposed integration procedure finally the proposed closed form solution for the cases of slope discontinuity is compared with the solution of a beam having an internal hinge with rotational spring reproducing the slope discontinuity

from dynamical systems to the langevin equation abstract it is shown that some dynamical systems which in microscopic time are fully deterministic exhibit a long time stochastic behavior governed by the langevin equation the limit in which this becomes a precise statement is obtained by an appropriate scaling of time and force the results are exemplified by a computer experiment

markov approximations and decay of correlations for anosov flows we develop markov approximations for very general suspension flows based on this we obtain a stretched exponential bound on time correlation functions for 3 d anosov flows that verify uniform nonintegrability of foliations these include contact anosov flows and geodesic flows on compact surfaces of variable negative curvature our bound on correlations is stable under small smooth perturbations

fluctuation of the entropy production for the lorentz gas under small external forces in this paper we study the physical and statistical properties of the periodic lorentz gas with finite horizon driven to a non equilibrium steady state by the combination of non conservative external forces and deterministic thermostats a version of this model was introduced by chernov eyink lebowitz and sinai and subsequently generalized by chernov and the third author non equilibrium steady states for these models are srb measures and they are characterized by the positivity of the steady state entropy production rate our main result is to establish that the entropy production in this context equal to the phase space contraction satisfies the gallavotti cohen fluctuation relation the main tool needed in the proof is the family of anisotropic banach spaces introduced by the first and third authors to study the ergodic and statistical properties of billiards using transfer operator techniques

renewal sequences and intermittency in this paper we examine the generating function z of a renewal sequence arising from the distribution of return times in the turbulent region for a class of piecewise affine interval maps introduced by gaspard and wang and studied by several authors we prove that it admits a meromorphic continuation to the entire complex z plane with a branch cut along the ray 1 moreover we compute the asymptotic behavior of the coefficients of its taylor expansion at z 0 from this we obtain the exact polynomial asympotics for the rate of mixing when the invariant measure is finite and of the scaling rate when it is infinite

gelfand kirillov dimension of commutative subalgebras of simple inﬁnite dimensional algebras and their quotient division algebras

convergence to equilibrium for intermittent symplectic maps we investigate a class of area preserving non uniformly hyperbolic maps of the two torus first we establish some results on the regularity of the invariant foliations then we use this knowledge to estimate the rate of mixing

an analogue of the conjecture of dixmier is true for the algebra of polynomial integro differential operators abstract let a 1 k x d d x be the weyl algebra and i 1 k x d d x be the algebra of polynomial integro differential operators over a field k of characteristic zero the conjecture problem of dixmier 1968 still open is an algebra endomorphism of the weyl algebra a 1 an automorphism the aim of the paper is to prove that each algebra endomorphism of the algebra i 1 is an automorphism notice that in contrast to the weyl algebra a 1 the algebra i 1 is a non simple non noetherian algebra which is not a domain moreover it contains infinite direct sums of nonzero left and right ideals

nonunitary transformations and hydrodynamic limit in the one dimensional hard point gas abstract the ergodic theoretical formalism of nonunitary transformations is compared with the derivation of kinetic equations by the hydrodynamic scaling limit the one dimensional hard point system is used as an illustration both methods rest on the k mixing property of the physical systems considered we show that the specific form of the operator is important only on the microscopic time scale on the macroscopic scale it acts like a projector with broken time reversal symmetry we also discuss the connection between the kolmogorov sinai k s entropy of the model dynamical system the relative entropy production rate in the nonunitary formalism and the macroscopic entropy production rate

dynamical and transport properties in a family of intermittent area preserving maps we introduce a family of area preserving maps representing a nontrivial two dimensional extension of the pomeau manneville family in one dimension we analyze the long time behavior of recurrence time distributions and correlations providing analytical and numerical estimates we study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments finally the dynamical effects of a stochastic perturbation are considered

the statistics of the trajectory of a certain billiard in a flat two torus we consider a billiard in the punctured torus obtained by removing a small disk of radius 0 from the flat torus 2 with trajectory starting from the center of the puncture in this case the phase space is given by the range of the velocity only let and respectively r denote the first exit time length of the trajectory and respectively the number of collisions with the side cushions when 2 is being identified with 0 1 2 we prove that the probability measures on 0 associated with the random variables and r are weakly convergent as varepsilon rightarrow 0 and explicitly compute the densities of the limits

invariance principles for interval maps with an indifferent fixed point in this note we establish an almost sure invariance principle for a large class of interval maps with indifferent fixed points including the manneville pomeau map this implies a number of well known corollaries including the weak invariance principle and the law of the iterated logarithm

on the hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms we reconsider the problem of the hamiltonian interpolation of symplectic mappings following moser s scheme we prove that for any mapping e analytic and e close to the identity there exists an analytic autonomous hamiltonian system he such that its time one mapping he differs from e by a quantity exponentially small in 1 e this result is applied in particular to the problem of numerical integration of hamiltonian systems by symplectic algorithms it turns out that when using an analytic symplectic algorithm of orders to integrate a hamiltonian systemk one actually follows exactly namely within the computer roundoff error the trajectories of the interpolating hamiltonian he or equivalently of the rescaled hamiltonian ke e 1he which differs fromk but turns out to be e5 close to it special attention is devoted to numerical integration for scattering problems

damage identification for beams in noisy conditions based on teager energy operator wavelet transform modal curvature abstract modal curvatures have been widely used in the detection of structural damage attractive features of modal curvature include great sensitivity to damage and instant determination of damage location however an intrinsic deficiency in a modal curvature is its susceptibility to the measurement noise present in the displacement mode shape that produces the modal curvature likely obscuring the features of damage to address this deficiency the teager energy operator together with wavelet transform is tactically utilized to treat modal curvature producing a new modal curvature termed the teager energy operator wavelet transform modal curvature this new modal curvature features distinct capabilities of suppressing noise canceling global trends and intensifying the singular feature caused by damage for a measured mode shape involving noise these features maximize the sensitivity to damage and accuracy of damage localization the proposed modal curvature is demonstrated in several analytical cases of cracked pinned pinned clamped free and clamped clamped beams with emphasis on characterizing damage in noisy conditions and it is further validated by an experimental program using a scanning laser vibrometer to acquire mode shapes of a cracked aluminum beam the teager energy operator wavelet transform modal curvature essentially overcomes the deficiency of conventional modal curvature providing a new dynamic feature well suited for damage characterization in noisy environments the matlab code for implementing teager energy operator wavelet transform modal curvature can be provided by the corresponding author on request

recurrence properties of a special type of heavy tailed random walk in the proof of the invariance principle for locally perturbed periodic lorentz process with finite horizon a lot of delicate results were needed concerning the recurrence properties of its unperturbed version these were analogous to the similar properties of simple symmetric random walk however in the case of lorentz process with infinite horizon the analogous results for the corresponding random walk are not known either in this paper these properties are ascertained for the appropriate random walk this happens to be in the non normal domain of attraction of the normal law as a tool an estimation of the remainder term in the local limit theorem for the corresponding random walk is computed

on the distribution of free path lengths for the periodic lorentz gas consider the domain and let the free path length be defined as the distribution of values of is studied in the limit as for all it is shown that the value is critical for this problem in other words the limiting behavior of depends only on whether is larger or smaller than

krull gelfand kirillov and filter dimensions of simple affine algebras the aim of the paper is to prove the following two results 1 letabe a finitely partitive simple affine algebra with gk a then the krull dimension where gk and fil dim are the gelfand kirillov and the filter dimension respectively 2 letbbe an integral regular domain affine over a field of characteristic zero and let d b be its ring of differential operators the filter dimension fil dim d b 1

damage detection from changes in curvature mode shapes abstract a damage in a structure alters its dynamic characteristics the change is characterized by changes in the eigenparameters i e natural frequency damping values and the mode shapes associated with each natural frequency considerable effort has been spent in obtaining a relationship between the changes in eigenparameters the damage location and the damage size most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the damage in this paper a new parameter called curvature mode shape is investigated as a possible candidate for identifying and locating damage in a structure by using a cantilever and a simply supported analytical beam model it is shown here that the absolute changes in the curvature mode shapes are localized in the region of damage and hence can be used to detect damage in a structure the changes in the curvature mode shapes increase with increasing size of damage this information can be used to obtain the amount of damage in the structure finite element analysis was used to obtain the displacement mode shapes of the two models by using a central difference approximation curvature mode shapes were then calculated from the displacement mode shapes