measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

variational principles and membrane finite elements with drilling rotations for geometrically non linear elasticity reference epfl article 102735view record in web of science record created on 2007 04 23 modified on 2016 08 08

lower and upper bounds for the allocation problem and other nonlinear optimization problems we demonstrate the impossibility of strongly polynomial algorithms for the allocation problem in the comparison model and in the algebraic tree computation model that follow from lower bound results consequently there are no strongly polynomial algorithms for nonlinear concave separable optimization over a totally unimodular constraint matrix this is in contrast to the case when the objective is linear we present scaling based algorithms that use a greedy algorithm as a subroutine the algorithms are polynomial for the allocation problem and its extensions and are also optimal for the sample allocation problem and the generalized upper bounds allocation problem in that the complexity meets the lower bound derived from the comparison model for other extensions of the allocation problem the scaling based algorithms presented here are the fastest known these algorithms are also polynomial time algorithms for solving with e accuracy the allocation problem and its extension in continuous variables

convex separable optimization is not much harder than linear optimization the polynomiality of nonlinear separable convex concave optimization problems on linear constraints with a matrix with small subdeterminants and the polynomiality of such integer problems provided the inteter linear version of such problems ins polynomial is proven this paper presents a general purpose algorithm for converting procedures that solves linear programming problems the conversion is polynomial for constraint matrices with polynomially bounded subdeterminants among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix to integer separable convex programming an algorithm for finding a e accurate optimal continuous solution to the nonlinear problem that is polynomial in log 1 e and the input size and the largest subdeterminant of the constraint matrix is also presented these developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function the practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function only a polynomial number of function evaluations on a prespecified grid

stress resultant geometrically nonlinear shell theory with drilling rotations part ii computational aspects abstract in this work we discuss some details of the numerical implementation of the geometrically nonlinear shell theory presented in part i two possibilities to represent finite rotations with an orthogonal matrix and with a rotation vector are examined in detail along with their mutual relationship in both spatial and material description the issues pertinent to the consistent linearization procedure corresponding to these rotation parameterizations are also carefully considered the geometrically nonlinear method of incompatible modes is extended to the nonlinear shell theory under consideration and used to provide a 4 node shell element with enhanced performance a rather extensive set of numerical examples in nonlinear elastostatics is solved in order to corroborate the non locking performance of the incompatible mode based shell elements the examples include not only analyses of simple shell structures undergoing very large displacements and rotations but also cases of strong practical interest such as non smooth shell structures and shell structures with stiffeners

nonlinear analysis of river flow time sequences within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed in light of these ideas we study the dynamics which control the behavior over time of river flow investigating the existence of a low dimension deterministic component the present article follows the research undertaken in the work of porporato and ridolfi 1996a in which some clues as to the existence of chaos were collected particular emphasis is given here to the problem of noise and to nonlinear prediction with regard to the latter the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown

a deterministic geometric representation of temporal rainfall results for a storm in boston the use of a deterministic fractal multifractal fm representation to model high resolution rainfall time series via projections of fractal interpolating functions weighed by multifractal measures is reported it is shown that the intrinsic shape and variability of an 8 hour boston storm recorded every 15 s on october 25 1980 may be encoded wholistically employing the fractal geometric methodology it is illustrated that the fm methodology provides very faithful descriptions of both major trends and small noisy fluctuations for this storm resulting in preservation of not only classical statistical characteristics of the records but also multifractal and chaotic properties present in them these results and those for other storms suggest that a stochastic framework for rainfall may be bypassed in favor of a deterministic representation based on projections

on implementing a primal dual interior point method for conic quadratic optimization based on the work of the nesterov and todd on self scaled cones an implementation of a primal dual interior point method for solving large scale sparse conic quadratic optimization problems is presented the main features of the implementation are it is based on a homogeneous and self dual model it handles rotated quadratic cones directly it employs a mehrotra type predictor corrector extension and sparse linear algebra to improve the computational efficiency finally the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems this is a novel feature for our implementation computational results are also presented to document that the implementation can solve very large problems robustly and efficiently

separable convex optimization problems with linear ascending constraints separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper an algorithm that explicitly characterizes the optimum point in a finite number of steps is described the optimum value is shown to be monotone with respect to a partial order on the constraint parameters moreover the optimum value is convex with respect to these parameters this work generalizes the existing algorithms of morton von randow and ringwald math programming 32 1985 pp 238 241 and viswanath and anantharam ieee trans inform theory 48 2002 pp 1295 1318 to a wider class of separable convex objective functions computational experiments that compare the proposed algorithm with a standard convex optimization tool are also provided

a kinematically exact finite element formulation of planar elastic plastic frames a finite element formulation of finite deformation static analysis of plane elastic plastic frames subjected to static loads is presented in which the only function to be interpolated is the rotation of the centroid axis of the beam one of the advantages of such a formulation is that the problem of the field consistency does not arise exact non linear kinematic relationships of the finite strain beam theory are used which assume the bernoulli hypothesis of plane cross sections finite displacements and rotations as well as finite extensional and bending strains are accounted for the effects of shear strains and non conservative loads are at present neglected yet they can simply be incorporated in the formulation because the potential energy of internal forces does not exist with elastic plastic material the principle of virtual work is introduced as the basis of the finite element formulation a generalized principle of virtual work is proposed in which the displacements rotation extensional and bending strains and the lagrangian multipliers are independent variables by exploiting the special structure of the equations of the problem the displacements the strains and the multipliers are eliminated from the generalized principle of virtual work a novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation it is shown that n 1 point numerical integration must be employed in conjunction with n node interpolation polynomials for the rotation and the lobatto rule is recommended regarding the integration over the cross section it is demonstrated by numerical examples that due to discontinuous integrands no integration order defined as computationally efficient yet accurate enough could be suggested the theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

chaos in rainfall the question is posed regarding possible chaotic dynamics in the temporal rainfall of storm events chaotic dynamics implies a nonlinear deterministic system very sensitive to initial conditions which yields outputs indistinguishable from a stochastic process by standard techniques the trajectories of these systems in the phase space are characterized by being contained in a strange attractor of fractal dimension a time series of 1990 points of 15 s rainfall for the storm of october 25 1980 in boston is analyzed in detail toward this objective it is found that both the characteristics of the correlation integral and the lyapunov exponents of the historical data give preliminary support to the presence of chaotic dynamics with a strange attractor the implications of these findings for the modeling of storm rainfall and for the limits of predictability of the process are discussed jointly with the research challenges lying ahead in this field

on the role of frame invariance in structural mechanics models at finite rotations in this work we re examine so called geometrically exact models for structures such as beams shells or solids with independent rotation field with respect to invariance under superposed rigid body motion a special attention is given to clarifying the issues pertaining to the finite element implementation which guarantees that the invariance of the continuum problem is preserved by its discrete approximation several numerical simulations dealing with finite rotations of structural models are presented in order to further illustrate and confirm the given theoretical considerations

scaling characteristics in the taiwan stock market some statistical tools including histogram spectral analysis and fractal theory were used on the daily taiwan stock price index tspi from 1987 to 2002 to examine the possible scale invariant behavior and the clustering characteristics in taiwan stock market it was found that the tspi data exhibited the characteristic of right skewed frequency distribution the long term memory and the possibility of scale invariance were roughly identified through the analysis of autocorrelation and power spectrum respectively the monofractal analysis was then performed by the box counting method scale invariance was clearly found in the time series and the box dimension was shown to be a decreasing function of the threshold index level implying multifractal characteristics i e the low and high regions scale differently to test this hypothesis the time series were transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the investigated time series the origin of multifractal phenomena in taiwan stock market might be interpreted in terms of the multiplicative cascade process of stock market information

support vector machines for nonlinear state space reconstruction application to the great salt lake time series 1 the reconstruction of low order nonlinear dynamics from the time series of a state variable has been an active area of research in the last decade the 154 year long biweekly time series of the great salt lake volume has been analyzed by many researchers from this perspective in this study we present the application of a powerful state space reconstruction methodology using the method of support vector machines svm to this data set svm are machine learning systems that use a hypothesis space of linear functions in a kernel induced higher dimensional feature space svm are optimized by minimizing a bound on a generalized error risk measure rather than just the mean square error over a training set under mercer s conditions on the kernels the corresponding optimization problems are convex hence global optimal solutions can be readily computed the svm based reconstruction is used to develop time series forecasts for multiple lead times ranging from 2 weeks to several months unlike previously reported methodologies svm are able to extract the dynamics using only a few past observed data points out of the training examples the reliability of the algorithm in learning and forecasting the dynamics is tested using split sample sensitivity analysis with a particular interest in forecasting extreme states efforts are also made to assess variations in predictability as a function of initial conditions and as a function of the degree of extrapolation from the state space used for learning the model

computational aspects of vector like parametrization of three dimensional finite rotations theoretical and computational aspects of vector like parametrization of three dimensional finite rotations which uses only three rotation parameters are examined in detail in this work the relationship of the proposed parametrization with the intrinsic representation of finite rotations via an orthogonal matrix is clearly identified careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of reissner s non linear beam theory pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2 node three dimensional beam element a number of numerical simulations in three dimensional finite rotation analysis are presented in order to illustrate the proposed approach

a survey on the continuous nonlinear resource allocation problem our problem of interest consists of minimizing a separable convex and differentiable function over a convex set defined by bounds on the variables and an explicit constraint described by a separable convex function applications are abundant and vary from equilibrium problems in the engineering and economic sciences through resource allocation and balancing problems in manufacturing statistics military operations research and production and financial economics to subproblems in algorithms for a variety of more complex optimization models this paper surveys the history and applications of the problem as well as algorithmic approaches to its solution the most common techniques are based on finding the optimal value of the lagrange multiplier for the explicit constraint most often through the use of a type of line search procedure we analyze the most relevant references especially regarding their originality and numerical findings summarizing with remarks on possible extensions and future research 2006 elsevier b v all rights reserved

a decomposition algorithm for nested resource allocation problems we propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions in the presence of either continuous or integer variables no assumption of strict convexity or differentiability is needed the method solves a hierarchy of resource allocation subproblems whose solutions are used to convert constraints on sums of resources into new bounds for variables at higher levels the resulting time complexity for the integer problem is o n log m log b n and the complexity of obtaining an epsilon approximate solution for the continuous case is o n log m log b epsilon n being the number of variables m the number of ascending constraints such that m leq n epsilon a desired precision and b the total resource this algorithm matches the best known complexity when m n and improves it when log m o log n extensive experimental analyses are presented with four recent algorithms on various co

long term stable time integration scheme for dynamic analysis of planar geometrically exact timoshenko beams abstract in this paper an energy momentum method for geometrically exact timoshenko type beam is proposed the classical time integration schemes in dynamics are known to exhibit instability in the non linear regime the so called timoshenko type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known bernoulli type model the treatment of the bernoulli model has been recently addressed by the authors in this present work we extend our approach of using the strain rates to define the strain fields to in plane geometrically exact timoshenko type beams the large rotational degrees of freedom are exactly computed the well known enhanced strain method is used to avoid locking phenomena conservation of energy momentum and angular momentum is proved formally and numerically the excellent performance of the formulation will be demonstrated through a range of examples

thick shell and solid finite elements with independent rotation fields thick shell and solid elements presented in this work are derived from variational principles employing independent rotation fields both elements are built on a special hierarchical interpolation and both possess six degrees of freedom per node performance of the elements is evaluated on a set of problems in elastostatics however the formulation presented herein is also suitable for transient and non linear problems

on finite element implementation of geometrically nonlinear reissner s beam theory three dimensional curved beam elements abstract finite element implementation of the three dimensional finite strain beam theory of reissner is considered in this work in contrast with some earlier works on the subject discussed here are the beam elements whose reference axes are arbitrary space curved lines we have shown that an improved representation of curved reference geometry significantly increases the accuracy of the results however it also makes the choice of non locking finite element interpolations somewhat more delicate a hierarchical displacement interpolation proposed here is proved to be capable of eliminating both shear and membrane locking phenomena a very satisfying non locking performance is demonstrated for a set of problems in nonlinear elasto statics

explanation and elimination of shear locking and membrane locking with field consistence approach abstract in this paper in the context of beam elements shear locking and membrane locking are explained and cured in a unified way with a field consistence approach in the view of field consistence approach when transverse displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are adopted shear locking will occur similarly when in plane displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are used membrane locking will happen the beam elements derived by field consistence approach are not only free of shear locking and membrane locking but also highly efficient compared with their isoparametric counterparts although theoretically the internal forces generalized strains in mixed variational principles can vary independently they are neither independent to each other nor independent of displacement fields from the point of view of the field consistence approach

geometrically non linear method of incompatible modes in application to finite elasticity with independent rotations reference epfl article 102720view record in web of science record created on 2007 04 23 modified on 2016 08 08

finite element analysis of linear and non linear planar deformations of elastic initially curved beams reference epfl article 102719view record in web of science record created on 2007 04 23 modified on 2016 08 08

stress resultant geometrically non linear shell theory with drilling rotations part iii linearized kinematics a consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non linear shell theory considered in parts i and ii of this work it was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three dimensional geometrically non linear continuum with independent rotation field in the finite element implementation of the presented shell theory relying on the modified method of incompatible modes we were able to construct a four node shell element which delivers a very high level performance in order to simplify finite element implementation a shallow reference configuration is assumed over each shell finite element this approach does not impair the element performance for the present four node element the results obtained herein match those obtained with the state of the art implementations based on the classical shell theory over the complete set of standard benchmark problems

an attractor in a solar time series a time series analysis of observed solar radio pulsations suggests that there must be a low dimensional attractor the power spectrum cannot be interpreted as a superposition of periodic components estimates of the maximum lyapunov exponent and of the kolmogorov entropy give some indications for a deterministic chaos in order to study the limitations inherent in small data samples we include data from the lorenz model and an artificial noise record consequences for the physical modelling of the pulsation event are discussed

an energy momentum method for in plane geometrically exact euler bernoulli beam dynamics summary nonlinear geometrically exact rod dynamics is of great interest in many areas of engineering in recent years the research was focused towards timoshenko type rod theories where shearing is of importance however in many general model of mechanisms and spatial deformations it is desirable to have a displacement only formulation which brings us back to the classical bernoulli beam while it is well known for linear analysis the bernoulli beam is not as common in geometrically exact models of dynamics especially when we want to incorporate the rotational inertia into the model this paper is about the development of an energy momentum integration scheme for the geometrically exact bernoulli type rod we will show that the task is achievable and devise a general framework to do so copyright 2014 john wiley sons ltd

fractal nature of highway traffic data in this paper we applied a fractal approach to analyze the traffic data collected from the beijing yuquanying the power spectrum the empirical probability distribution function the statistical moment scaling function and the autocorrelation function are used as indicators to investigate the presence of the fractal the results from the fractal identification methods indicate that these data exhibit fractal behavior a fractal framework seemed well suited for description of the data observed here but its suitability for general traffic systems was not clear

predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach 1 perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one even though the sensitivity of initial conditions limits the predictability in chaotic systems an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent all of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions conceptually global models are ineffective in modeling the highly unstable structure of the chaotic attractor this paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters i e embedding dimension and delay time to quantify the uncertainty in initial conditions the ensemble approach is implemented through a local learning wavelet network model with a global feed forward neural network structure for the phase space prediction of chaotic streamflow series quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times the ensemble approach is proved to be 50 more efficient than the single prediction for both local approximation and wavelet network approaches the wavelet network approach has proved to be 30 50 more superior to the local approximation approach compared to the traditional local approximation approach with single initial condition the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times localization property of wavelets utilizing different dilation and translation parameters helps in capturing most of the statistical properties of the observed data the need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated

numerical formulations of elasto viscoplastic response of beams accounting for the effect of shear the finite deformation elasto viscoplastic response of beams is considered from a numerical point of view in this paper formulations in terms of stress resultants are discussed and extended to include viscoplastic material response by introducing rate equations for the evolution of the finite inelastic deformations special attention is given to the objectivity of the rates and to the form of the plastic flow potential an alternative one dimensional formulation obtained by introducing a kinematic constraint and numerically integrating over the cross section of the beam is also presented both formulations account for the effect of warping which arises as a result of shear deformation a numerical algorithm for the time dependent problem is presented in which the numerically integrated nonlinear rate equations are exactly satisfied at each iteration of the newton raphson scheme the implications of the formulations discussed in this paper are illustrated through a set of numerical examples

formulation of geometrically non linear problems in the spatial reference frame this paper presents a new formulation for geometrically non linear problems and their numerical treatment by the p version of the finite element method the formulation is characterized by a weak form based on the spatial representation of the equilibrium equations a deformed geometry mapped by the displacement field a natural description for non conservative loads that keeps the symmetry of the equations and a direct non incremental iterative algorithm to solve the equations the paper is concerned only with problems for which the solution is unique i e the load displacement curves are single valued and the strains are small examples are presented 1997 by john wiley sons ltd

shape optimal design of elastic space frames with non linear response this paper describes an approach to shape optimal design of elastic planar frames with non linear response the foundation of the proposed approach forms an appropriate strategy of shape representation of the structure based on the design element technique a frame structure is treated as to be assembled from several frame design elements which in turn may consist of several appropriately joined beam finite elements the shape of each frame design element is defined by convenient functions involving bezier blending polynomials the original formulation of the beam finite element proposed by saje is modified in order to fit nicely into the context of the frame design element technique the formulation of the shape optimal design problem in a form of a problem of non linear mathematical programming and its solution by employing gradient based methods of mathematical programming are discussed briefly the theory is illustrated with two numerical examples

about strongly polynomial time algorithms for quadratic optimization over submodular constraints we present new strongly polynomial algorithms for special cases of convex separable quadratic minimization over submodular constraints the main results are an o nm log n 2 m algorithm for the problemnetwork defined on a network onm arcs andn nodes an o n logn algorithm for thetree problem onn variables an o n logn algorithm for thenested problem and a linear time algorithm for thegeneralized upper bound problem these algorithms are the best known so far for these problems the status of the general problem and open questions are presented as well

is correlation dimension a reliable indicator of low dimensional chaos in short hydrological time series the reliability of the correlation dimension estimation in short hydrological time series is investigated using an inverse approach according to this approach first predictions are made using the phase space reconstruction technique and the artificial neural networks the correlation dimension is estimated next independently and is compared with the prediction results a short hydrological series monthly runoff series of 48 years with a total of only 576 values observed at the coaracy nunes araguari river watershed in northern brazil is studied the correlation dimension results are in reasonably good agreement with the optimal embedding dimension obtained from the phase space method and the optimal number of inputs from the neural networks no underestimation of the correlation dimension is observed due to the small data size rather there seems to be a slight overestimation due to the presence of noise in the data the results indicate that the accuracy of the correlation dimension may not be judged on the basis of the length of the time series but on whether the time series is long enough to reasonably represent the dynamical changes in the system such an observation suggests that the correlation dimension could indeed be a reliable indicator of low dimensional chaos even in short hydrological time series which is certainly encouraging news for hydrologists who often have to deal with short time series less

biases of correlation dimension estimates of streamflow data in the canadian prairies the correlation dimension d2 of the unregulated streamflow data of six rivers in the canadian prairies were estimated using the hill estimate and grassberger procaccia algorithms from both procedures and using an embedding phase space up to 10 the d2 obtained for all cases are found to saturate at 3 0 however the saturated d2 generally increased to between 4 and 6 when the data were first randomly resampled prior to estimating the correlation dimension since the highest embedding dimension d used in this study is 10 theoretically randomly resampled data should have a d2 approximately equal to 10 therefore there is a consistent underestimation of d2 by an amount of 4 6 by accounting for the combined clustering effect of the streamflow data s underlying distribution which is gamma the effect of sample size and possibly the choice of time delay the d2 of the prairie streamflow data should be 7 9 the hypothesis that the clustering effect of unevenly distributed data contributed to the underestimation of d2 was confirmed from the different d2 obtained for random numbers of uniform gamma and poisson distributions in addition analysis of the uniformly distributed random numbers and streamflow data showed that increasing the sample size from say 6500 to 17 000 marginally improved the estimated d2 however for the range of time delay chosen for this study 40 180 days its effect on d2 is less obvious this may be partly because all the streamflow data tested exhibit long term persistence

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

scaling characteristics in aftershock sequence of earthquake abstract the possible scale invariant behavior and the clustering characteristics in aftershock sequence of chi chi taiwan main earthquake asccme that occurred in 1999 9 20 17 47 were investigated by means of some statistical tools histogram spectral analysis and fractal theory the examined data were constructed from the aftershocks that occurred at the locations defined at longitude 120 1 121 3 and latitude 23 3 24 5 during the 1999 9 20 17 47 1999 9 24 08 13 period it was found that the aftershock sequence exhibited the characteristic right skewed frequency distribution and could be well described with the lognormal distribution long term memory and the possibility of scale invariance were first roughly identified through the analysis of autocorrelation and power spectrum respectively scale invariance was clearly revealed with the aid of box counting method and the box dimension was shown to be a decreasing function of the threshold magnitude level i e the weak and intense regions scaled differently to verify the existence of multifractal characteristics the aftershock sequence was transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the examined aftershock sequence the origin of both the pronounced right skewness and multifractal phenomena in aftershock sequence might be interpreted in terms of the multiplicative cascade process of the stress in the earth s crust a simple two scale cantor set with unequal scales and weights was then used to fit the calculated q q plot this model fitted remarkably well the entire spectrum of scaling exponents of the examined asccme

decentralized resource allocation in dynamic networks of agents we consider the problem of n agents that share m common resources the objective is to derive an optimal allocation that maximizes a global objective expressed as a separable concave objective function we propose a decentralized asynchronous gradient descent method that is suitable for implementation in the case where the communication between agents is described in terms of a dynamic network this communication model accommodates situations such as mobile agents and communication failures the method is shown to converge provided that the objective function has lipschitz continuous gradients we further consider a randomized version of the same algorithm for the case where the objective function is nondifferentiable but has bounded subgradients we show that both algorithms converge to near optimal solutions and derive convergence rates in terms of the magnitude of the gradient of the objective function we show how to accommodate nonnegativity constraints on the resources using the results derived ex

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow