bluuebunny/crossref_metadata_2025 huggingface dataset:
DYNAMICAL INTEGRATION
Authors: BROWN RAY , CHUA LEON O.
Published: November 2004

In this letter we show how to use a new form of integration, called dynamical integration, that utilizes the dynamics of a system defined by an ODE to construct a map that is in effect a one-step integrator. This method contrasts sharply with classical numerical methods that utilize polynomial or rational function approximations to construct integrators. The advantages of this integrator is that it uses only one step while preserving important dynamical properties of the solution of the ODE: First, if the ODE is conservative, then the one-step integrator is measure preserving. This is significant for a system having a highly nonlinear component. Second, the one-step integrator is actually a one-parameter family of one-step maps and is derived from a continuous transformation group as is the set of solutions of the ODE. If each element of the continuous transformation group of the ODE is topologically conjugate to its inverse, then so is each member of the one-parameter family of one-step integrators. If the solutions of the ODE are elliptic, then for sufficiently small values of the parameter, the one-step integrator is also elliptic. In the limit as the parameter of the one-step family of maps goes to zero, the one-step integrator satisfies the ODE exactly. Further, it can be experimentally verified that if the ODE is chaotic, then so is the one-step integrator. In effect, the one-step integrator retains the dynamical characteristics of the solutions of the ODE, even with relatively large step sizes, while in the limit as the parameter goes to zero, it solves the ODE exactly.

We illustrate the dynamical, in contrast to numerical, accuracy of this integrator with two distinctly different examples: First we use it to integrate the unforced Van der Pol equation for large ∊, ∊≥10 which corresponds to an almost continuous square-wave solution. Second, we use it to obtain the Poincaré map for two different versions of the periodically forced Duffing equation for parameter values where the solutions are chaotic. The dynamical accuracy of the integrator is illustrated by the reproduction of well-known strange attractors. The production of these attractors is eleven times longer when using a conventional fourth-order predictor-corrector method. The theory presented here extends to higher dimensions and will be discussed in detail in a forthcoming paper. However, we caution that the theory we present here is not intended as a line of research in numerical methods for ODEs.
ON PERIODIC ORBITS AND HOMOCLINIC BIFURCATIONS IN CHUA’S CIRCUIT WITH A SMOOTH NONLINEARITY
Authors: KHIBNIK ALEXANDER I. , ROOSE DIRK , CHUA LEON O.
Published: November 2004

We present the bifurcation analysis of Chua’s circuit equations with a smooth nonlinearity, described by a cubic polynomial. Our study focuses on phenomena that can be observed directly in the numerical simulation of the model, and on phenomena which are revealed by a more elaborate analysis based on continuation techniques and bifurcation theory. We emphasize how a combination of these approaches actually works in practice. We compare the dynamics of Chua’s circuit equations with piecewise-linear and with smooth nonlinearity. The dynamics of these two variants are similar, but we also present some differences. We conjecture that this similarity is due to the central role of homoclinicity in this model. We describe different ways in which the type of a homoclinic bifurcation influences the behavior of branches of periodic orbits. We present an overview of codimension 1 bifurcation diagrams for principal periodic orbits near homoclinicity for three-dimensional systems, both in the generic case and in the case of odd symmetry. Most of these diagrams actually occurs in the model. We found several homoclinic bifurcations of codimension 2, related to the so called resonant conditions. We study one of these bifurcations, a double neutral saddle loop.
BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR
Authors: SÜNNER T. , SAUERMANN H.
Published: November 2004

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.
NONLINEAR INTERACTIONS BETWEEN TWO WIDELY SPACED MODES — EXTERNAL EXCITATION
Authors: NAYFEH S.A. , NAYFEH A.H.
Published: November 2004

Recent experimental studies indicate that energy can be transferred from high- to low-frequency modes in structures with weak nonlinearity. In each of these experiments, a high-frequency mode was driven near its natural frequency but the response included a large contribution due to the first mode of the structure. In this paper, an analytical study of the response of a two-degree-of-freedom nonlinear system with widely spaced modes to a simple-harmonic excitation near the natural frequency of its high-frequency mode is presented. This system serves as a paradigm for the interaction of high- and low-frequency modes.
“CROSSROAD AREA- DISSYMMETRICAL SPRING AREA — SYMMETRICAL SPRING AREA,” AND “DOUBLE CROSSROAD AREA — DOUBLE SPRING AREA” TRANSITIONS
Authors: ALLAM REZK , MIRA CHRISTIAN
Published: November 2004

In a parameter plane, crossroad areas and spring areas are two typical organizations of fold and flip bifurcation curves centred at a fold cusp point. Till now only spring areas in a “symmetrical” configuration have been described. This letter introduces another type of spring area for which such a “symmetry” does not exist. It is called a dissymmetrical spring area. When a third parameter is varied, qualitative modifications of the parameter plane are considered, and an example of a two-dimensional diffeomorphism is given.
MULTI-ARMED SPIRALS IN A LIGHT-CONTROLLED EXCITABLE REACTION
Authors: STEINBOCK O. , MÜLLER S.C.
Published: November 2004

The dynamics and geometry of multi-armed spirals in the light-sensitive ruthenium-catalyzed Belousov-Zhabotinsky reaction were investigated experimentally. The patterns were generated by a novel technique based on laser illumination, which allows the formation, control and annihilation of spiral waves. The rotation of n-armed spirals (n≤6) is stabilized by an unexcitable disk, created by a green laser beam. After switching off the laser, the central disk region becomes excitable again and individual cores are formed for each spiral arm. A symmetric collision structure appears periodically in the central region. Spiral arms are not attached to specific cores, but continuously passed on to the adjacent one. The geometry of multi-armed spirals is analyzed in polar coordinates and single arms are compared with a simple Archimedian shape.
PERIODIC WINDOW AND PERIOD SUBTRACTING IN AN ION-BEAM PLASMA SYSTEM
Authors: SARMA B.K. , BURAGOHAIN A. , CHUTIA JOYANTI
Published: November 2004

Observation of different sequences of bifurcations in an ion-beam plasma system excited by an external sinusoidal signal is reported. Under the influence of an external periodic oscillation applied to the anode of the source chamber of a double plasma device, periodic windows are observed with the variation of theamplitude of the external signal when the frequency of the applied signal is at the edge of the total suppressed position of the internal oscillation. On the other hand, period subtracting phenomena are observed with the variation of the amplitude of the applied signal, when the frequency of the applied signal is lowered but fixed within the suppression range of the internal oscillation and with low modulation depth.
CONTROLLING CHAOS WITHOUT FEEDBACK AND CONTROL SIGNALS
Authors: KAPITANIAK T. , KOCAREV LJ. , CHUA L.O.
Published: November 2004

We describe an effective method for controlling chaos by coupling a main chaotic system to a new but simple system with easily changeable parameters. The method is applied to Duffing’s oscillator (numerical and analytical study) and to Chua’s circuit (experimental study). The effectiveness of our method in controlling noisy systems, as well as an illustrative application in a mechanical and an electrical system, are discussed.
TOPOLOGICAL ANALYSIS OF LASER WITH SATURABLE ABSORBER IN EXPERIMENTS AND MODELS
Authors: FIORETTI A. , MOLESTI F. , ZAMBON B. , ARIMONDO E. , PAPOFF F.
Published: November 2004

The chaotic behavior of the output radiation of a CO 2 laser with intracavity saturable absorber (LSA) is investigated, theoretically as well as experimentally, through the topological properties of the related 3D phase space flow of the system. By examining the unstable periodic orbits, we can reconstruct the topological organisation (links) of these orbits and show that, in some cases, the topological entropy of the flow is positive, i.e., the flow is chaotic. A comparison with return-time return maps analysis is also performed.
STATISTICAL MECHANICS OF BIOLOGICAL AND OTHER COMPLEX EXPERIMENTAL TIME SERIES: ASSESSING GEOMETRICAL AND DYNAMICAL PROPERTIES
Authors: PAULUS MARTIN P. , KADTKE JAMES B. , MENKELLO FREDERICK V.
Published: November 2004

Biological and other experimental time series often exhibit complex and possibly chaotic behavior that may not be completely deterministic or completely random. Particularly problematic is the fact that measures of chaos such as the dynamical or geometrical invariants, e.g. the correlation dimension, Lyapunov exponents, or Kolmogorov entropy, often cannot be calculated from short, noisy, and possibly highly discretized experimental time series. Here, it is argued that nonrandom structure in the data may be uncovered by using a conceptual framework based on statistical mechanics and the standard correlation integral as a computational tool. A new use of the generalized correlation integral is proposed to assess statistically the occurrence of nonrandom spatiotemporal patterns in experimental data. We argue that nonrandomness of a time series can be assessed by the statistics of the topology of the reconstructed state space distribution, which we quantify via the generalized correlation integral. This approach provides a simple, graphical tool which can yield immediate information about the length scales and sequence lengths where the data may appear to be different from random, and also may provide a data classification tool based on spatiotemporal patterns. We demonstrate the usefulness of this approach using several numerical examples, including data from experimental biological systems. Finally, we propose that particular characteristics of such patterns imply considerable macroscopic information about the behavior of the generating system, and qualitative changes in the time series.
CROSSOVER BETWEEN THE CONTROL OF PERMANENT AND TRANSIENT CHAOS
Authors: TÉL TAMÁS
Published: November 2004

Characteristics of the OGY method, like the time needed to achieve control or the number of controlled trajectories, as functions of the maximum allowed perturbation, follow completely different scalings for permanent and transient chaos. We derive in this paper the explicit form of how these characteristics cross over smoothly into each other when transient chaos becomes gradually permanent at crisis points. It will be shown that there is a novel quantity, the number of controlled trajectories per unit time, which persists in its power law behavior in the crossover region too.
PARAMETRIC ADAPTIVE CONTROL OF AN NMR LASER MODEL
Authors: VASSILIADIS DIMITRIS
Published: November 2004

The parametric adaptive control method can be used to restore the values of the perturbed parameters of a low-dimensional system. The article illustrates the method by applying it to an NMR laser model.
MEASURING THE PREDICTABILITY OF NOISY RECURRENT TIME SERIES
Authors: WAYLAND R. , PICKETT D. , BROMLEY D. , PASSAMANTE A.
Published: November 2004

The effect of the chosen forecasting method on the measured predictability of a noisy recurrent time series is investigated. Situations where the length of the time series is limited, and where the level of corrupting noise is significant are emphasized. Two simple prediction methods based on explicit nearest-neighbor averages are compared to a more complicated, and computationally expensive, local linearization technique based on the method of total least squares. The comparison is made first for noise-free, and then for noisy time series. It is shown that when working with short time series in high levels of additive noise, the simple prediction schemes perform just as well as the more sophisticated total least squares method.
DETERMINATION OF DIFFERENT CONFIGURATIONS OF FOLD AND FLIP BIFURCATION CURVES OF A ONE OR TWO-DIMENSIONAL MAP
Authors: CARCASSES JEAN-PIERRE
Published: November 2004

Three different configurations of fold and flip bifurcation curves of maps, centered round a cusp point of a fold curve, are considered. They are called saddle area, spring area and crossroad area. For one and two-dimensional maps, this paper uses the notion of contour lines in a parameter plane. A given contour line is related to a constant value of a "reduced multiplier" constructed from the trace and the Jacobian of the matrix associated with a given periodic point. The singularities of such lines define the configuration type of the areas indicated above. When a third parameter varies, the qualitative changes of such areas are directly identified. These singularities also enable the determination of a point of intersection of two bifurcation curves of the same nature (flip or fold), and, when a third parameter varies, the appearance (or disappearance) of a closed fold or flip bifurcation curve.
THE DOVETAIL BIFURCATION STRUCTURE AND ITS QUALITATIVE CHANGES
Authors: MIRA C. , KAWAKAMI H. , ALLAM R.
Published: November 2004

In a parameter plane defined by two parameters of a map, the dovetail bifurcation structure is a bifurcation curve organization, for which two fold cusps have a fold bifurcation segment in common. This gives rise to the association of either a crossroad area with a saddle area or a spring area with a saddle area. This paper describes this structure in the parameter plane for different configurations, and in the corresponding three-dimensional representations of the plane sheets. Then it identifies six different qualitative changes of this structure when a third parameter varies.
THE EFFECTS OF SYMMETRY BREAKING IN CHUA'S CIRCUIT AND RELATED PIECEWISE-LINEAR DYNAMICAL SYSTEMS
Authors: KAHLERT CLAUS
Published: November 2004

The behavior of transfer and return maps in the intermediate region of Chua's circuit and related systems undergoes a number of changes as the symmetry of the dynamics is broken, i.e., the separating planes are moved away from symmetric positions. We employ the technique of maps induced by the flow of the system and construct the critical curves for the maps in the intermediate region of state space. The influence of a broken symmetry on the critical curves and the flow is discussed in depth. We demonstrate that any breaking of symmetry potentially weakens and eventually destroys the chaos producing mechanisms.
CHAOTIC SCATTERING IN CLASSICAL TRIATOMIC MOLECULAR DYNAMICS
Authors: BRUHN B. , KOCH B. P.
Published: November 2004

The classical scattering dynamics of two coupled Morse systems is investigated by analytical and numerical methods. If a McGehee type transformation and the Melnikov method are applied to the invariant manifolds of a nonhyperbolic fixed point at infinity, a proof of the appearance of chaotic scattering is obtained. Furthermore, we study the occurrence of hyperbolic and elliptic periodic orbits under perturbation using the subharmonic Melnikov approach. The analytical predictions regarding the range of the scattering function where chaotic scattering appears are compared with numerical results. Moreover, we investigate the threshold for channel transitions and discuss some mechanisms for this transition.
DEPENDENCE OF HAMILTONIAN CHAOS ON PERTURBATION STRUCTURE
Authors: YANG HUIJUN
Published: November 2004

In this paper, we considered a Hamiltonian dynamical system consisting of a steady wave and a perturbation wave and studied the dependence of spatial patterns of chaos on the perturbation structure (i.e., the wave numbers of the perturbation wave). The system came from the passive wave mixing and transport problem. In order to investigate this dependence, we first did some simple mixing experiments with initially a small blob and calculated the correlation dimensions. Secondly we used Lyapunov exponents to identify the chaotic regions and the invariant tori and computed the histograms or PDFs (Probability Distribution Functions) to characterize the Hamiltonian chaos for different perturbation structure. We found that this dependence was very complicated and the complexity increases with the perturbation structure. This dynamical system became more chaotic with increase in the wave numbers. The fascinating patterns of the Hamiltonian chaos for various perturbation structures were presented. The spatial pattern of chaos on the isentropic surface of the atmosphere was given. Implications of the results of the chaotic wave mixing and transport in climate dynamics, atmospheric chemistry, aeronomy and large scale dynamics of geophysical fluid flows were briefly discussed.
ON A "CROSSROAD AREA–SPRING AREA" TRANSITION OCCURRING IN A DUFFING–RAYLEIGH EQUATION WITH A PERIODICAL EXCITATION
Authors: MIRA CHRISTIAN , QRIOUET MOHAMMED
Published: November 2004

The bifurcation structures considered in this paper are given by a Duffing–Rayleigh equation in the presence of a periodic external excitation. The first one is related to a cascade of fold lips generated by period doubling at subharmonic oscillations, which is obtained in a parameter plane defined by the excitation frequency and its amplitude. When a third parameter (coefficient of the linear approximation of the damping) varies, a qualitative change of the parameter plane occurs. It is related to a new mechanism of "crossroad area–spring area" transition, the areas corresponding to typical arrangements of fold and flip bifurcation curves around a fold cusp.
EXPERIMENTAL OBSERVATION OF ANTIMONOTONICITY IN CHUA'S CIRCUIT
Authors: KOCAREV Lj. , HALLE K. S. , ECKERT K. , CHUA L. O.
Published: November 2004

Two different bifurcation patterns are experimentally observed in Chua's circuit. They show that antimonotonicity — inevitable reversals of period-doubling sequences, is a typical phenomenon in Chua's circuit.
SYNCHRONIZING CHAOS IN DRIVEN CHUA'S CIRCUIT
Authors: MURALI K. , LAKSHMANAN M.
Published: November 2004

In this paper, we report the numerical observations of synchronization in driven Chua's circuit using the criterion of Pecora and Carroll. Also, synchronization behavior of this system is investigated under the influence of Gaussian noise signal and we point out that it is possible to obtain synchronization even in this environment. More interestingly, we also point out the novel possibility of controlling unsynchronized motion using the adaptive control algorithm.
ROBUST CONTROL OF A CHAOTIC VIBRATORY SYSTEM
Authors: YAU CHIN-HORNG , BAJAJ ANIL K. , NWOKAH OSITA D. I.
Published: November 2004

An active robust control system is designed, and is numerically verified, to suppress the undesirable chaotic vibration in a constrained flexible pipe conveying fluid, which exhibits regions of flutter and chaotic motions at sufficiently high flow velocity. The four-dimensional analytical model obtained from the continuous system by Galerkin's method is utilized for designing the control law. Some interesting nonlinear behaviors with the four-dimensional analytical model are discussed as well. Without sensing the flow velocity or gain-scheduling, a robust controller is developed for the system under large flow rate variations by using a newly developed Quantitative Feedback Design (QFD) method. This technique allows the controller to make the closed loop system response meet quantitatively specified performance requirements even though the system has large parameter variations. Numerical simulations validate the effectiveness of the QFD method which yields a remarkable result in stability and performance robustness with respect to flow velocity variations.
DYNAMIC BIFURCATIONS IN A POWER SYSTEM MODEL EXHIBITING VOLTAGE COLLAPSE
Authors: ABED E. H. , WANG H. O. , ALEXANDER J. C. , HAMDAN A. M. A. , LEE H.-C.
Published: November 2004

Dynamic bifurcations, including Hopf and period-doubling bifurcations, are found to occur in a power system dynamic model recently employed in voltage collapse studies. The occurrence of dynamic bifurcations is ascertained in a region of state and parameter space linked with the onset of voltage collapse. The work focuses on a power system model studied by Dobson & Chiang [1989]. The presence of the dynamic bifurcations, and the resulting implications for dynamic behavior, necessitate a re-examination of the role of saddle node bifurcations in the voltage collapse phenomenon. The bifurcation analysis is performed using the reactive power demand at a load bus as the bifurcation parameter. It is determined that the power system model under consideration exhibits two Hopf bifurcations in the vicinity of the saddle node bifurcation. Between the Hopf bifurcations, i.e., in the "Hopf window," period-doubling bifurcations are found to occur. Simulations are given to illustrate the various types of dynamic behaviors associated with voltage collapse for the model. In particular, it is seen that an oscillatory transient may play a role in the collapse.
ON A CLASS OF FRACTAL MATRICES II: DISTRIBUTION AND SCALE-DEPENDENT FRACTAL DIMENSIONS OF THE INTEGER SETS IN EXCESS-MATRICES AND THEIR DISGUISES
Authors: BARBÉ ANDRÉ M.
Published: November 2004

Excess-matrices were defined in a previously published Part I as a special class of integer matrices with multifractal features. The present Part II considers compactifications of an excess-matrix E, i.e., matrices obtained by replacing submatrices of specific sizes in E by a single number according to some prescribed rule. It will be shown how these compactifications can be obtained by a direct mapping from E itself, through the derivation of a set of formulas for the associated mapping sequences (as defined in Part I). Then these formulas are used for characterizing the distribution of certain integer sets over these matrices. The evolution of this distribution over all scales of observation is described by two different fractal-dimension functions, which are scale-dependent extensions of classical practical fractal-dimension measures. Expressions for these functions are derived, and their properties discussed. Exploring the limits of these functions which relate them to the classical small-scale fractal dimension reveals some difficulty in the interpretation of the latter when applied to excess-matrices.
ON THE BIFURCATION PHENOMENA OF THE KURAMOTO–SIVASHINSKY EQUATION
Authors: FEUDEL FRED , FEUDEL ULRIKE , BRANDENBURG AXEL
Published: November 2004

Bifurcation phenomena of the Kuramoto–Sivashinsky equation have been studied numerically. The solutions considered are restricted to the invariant subspace of odd functions. One possible route to chaos via a period-doubling cascade is investigated in detail: The four-modal steady-state loses its stability through a Hopf bifurcation and a branch of periodic motions is created. After a symmetry breaking the periodic solution undergoes a period-doubling cascade which ends up in two antisymmetric chaotic attractors. A merging of these antisymmetric attractors to a symmetric one is observed. The chaotic branch depending on the bifurcation parameter is characterized by the values of the Lyapunov exponents. Periodic windows within the chaotic region are also detected. Finally, a further increase of the bifurcation parameter leads to a transition from the attractor into transient chaos.
THE BASIN OF ATTRACTION OF A SPIN-ORBIT RESONANCE
Authors: CELLETTI ALESSANDRA , FALCOLINI CORRADO , TEDESCHINI-LALLI LAURA
Published: November 2004

In this paper we investigate the different behaviors of some satellites, subject to a spin-orbit interaction. In particular we compute, in the space of initial data, the basin of attraction of the 3:2 resonance for the Mercury–Sun and Moon–Earth coupling systems.

The results are obtained either by direct integration of the equations of motion or by a numerical implementation of the "straddle" technique to draw the boundary of the basin.
NONLINEAR PHENOMENA IN CIRCULAR PARTICLE ACCELERATORS II: BEAM-BEAM INTERACTION
Authors: ALVES-PIRES RUI , DILÃO RUI
Published: November 2004

We calculate the Poincaré map for the equation of horizontal transverse motion of a test particle in an accelerator under the action of generic nonlinear forces. We particularize to beam-beam type interactions and we study the dynamics of the map. Beam instabilities due to beam-beam interaction are caused by chaotic behavior and not by amplitude growth, as is the case of other nonlinearities due to special purpose machine magnets. There exists a closed region in phase space where the motion is chaotic, even if the central design orbit is unstable. For large amplitudes in phase space the motion is regular and no chaotic behavior or amplitude growth exists. The beam-beam tune as a function of the beam position x is calculated and predictions agree with the numerical values within the maximum relative error of 10%, for beam positions |x| ≤ σ, where σ is the r.m.s. size of the beam. When beams cross at high distances the variation in the tune due to beam-beam effect disappears and the tune value approaches the betatron tune.
THE STABILITY OF SPATIALLY NONHOMOGENEOUS STEADY STATES IN A TUBULAR CHEMICAL REACTOR
Authors: ROTENBERRY JAMES M. , MINZONI ANTONMARIA A.
Published: November 2004

We study the axial heat and mass transfer in a highly diffusive tubular chemical reactor in which a simple reaction is occurring. The steady state solutions of the governing equations are studied using matched asymptotic expansions, the theory of dynamical systems, and by calculating the solutions numerically. In particular, the effect of varying the Peclet and Damköhler numbers (P and D) is investigated. A simple expression for the approximate location of the transition layer for large Peclet number is derived and its accuracy tested against the numerical solution. The stability of the steady states is examined by calculating the eigenvalues and eigenfunctions of the linearized equations. It is shown that a Hopf bifurcation of the CSTR model (i.e., the limit as the P approaches zero) can be continued up to order 1 in the Peclet number. Furthermore, it is shown numerically that for appropriate values of the Peclet number, the Damköhler number, and B (the heat of reaction) these Hopf bifurcations merge with the limit points of an "S–shaped" bifurcation curve in a higher order singularity controlled by the Bogdanov–Takens normal form. Consequently, there must exist a finite amplitude, nonuniform, stable periodic solution for parameter values near this singularity. The existence of higher order degeneracies is also explored. In particular, it is shown for D ≪ 1 that no value of P exists where two pairs of complex conjugate eigenvalues of the steady state solutions can cross the imaginary axis simultaneously.
A TEST FOR STATIONARITY: FINDING PARTS IN TIME SERIES APT FOR CORRELATION DIMENSION ESTIMATES
Authors: ISLIKER HEINZ , KURTHS JÜRGEN
Published: November 2004

We propose a method to identify stationary phases in time series. Stationarity is a necessary condition for many concepts in dynamical systems theory, e.g. deterministic chaos. Therefore, testing for stationarity should necessarily be the first step in any data analysis. Above all, this testing is highly important whenever one deals with systems for which stationarity is not guaranteed by the data acquisition procedure: if only short and unique time series are accessible and if the experimental situation is not or only restrictedly controllable, as for instance in astronomy, economy, or medicine.

The proposed stationarity test is easily workable and easy to implement in the form of a systematically searching loop. It singles out the parts of a time series which are a reasonable input to a dimension estimate algorithm. Thereby, it can ascertain finite correlation dimensions which are not indicative of deterministic behavior; this kind of dimensions can occur in stochastic processes which are nonstationary, e.g. self-affine.
PREDICTABILITY AND THE BUTTERFLY EFFECT IN TURBULENT FLOWS: A SHELL MODEL STUDY
Authors: CRISANTI A. , VULPIANI A. , JENSEN M. H. , PALADIN G.
Published: November 2004

We discuss the dynamical growth of a disturbance in turbulent flows based on numerical calculations of an approximative model of the Navier–Stokes equations, a so-called shell model. A disturbance at small length scales is observed to propagate (and increase) towards large length scales by an inverse cascade of duration T, the predictability time. At increasing Reynolds number Re, the mean predictability time Tt is found to decrease proportionally to Re−0.47. Moreover, the probability distribution of (T − Tt)/Tt changes its shape as Re increases: at relatively small values of Re it has an almost Gaussian shape, while at large Re it gets an exponential tail, indicating the possibility of large excursions for Tt.
WHORF: A HYPERTEXT TOOL FOR SOFTWARE MAINTENANCE
Authors: BRADE K. , GUZDIAL M. , STECKEL M. , SOLOWAY E.
Published: November 2004

Software maintenance programmers face the daunting task of understanding and modifying complex, unfamiliar programs that contain delocalized plans (conceptually related code that is not located contiguously in a program). Our research shows that programmers use an as-needed strategy when searching for the delocalized components which they need to understand. We have developed a maintenance tool, Whorf, that provides explicit support for visualizing and understanding delocalized plans using an as-needed strategy. Whorf supports this strategy through multiple, concurrent views of the software with instant, easy access to additional views. It supports the understanding of delocalized plans by providing hypertext links between views to highlight interactions between physically disparate components. A study comparing the usage of Whorf and paper documentation shows that the dynamic views and structure supported by Whorf provide information more quickly and easily than the static structure of paper documentation.
TRENDS IN STRUCTURE-ORIENTED ENVIRONMENTS
Authors: WHITTLE B.R. , GAUTIER R.J. , RATCLIFFE M.
Published: November 2004

The term Structure Editor (structured environment, structure-oriented environment) is widely used and has been defined, and redefined, many times since the first recognised structure editor, Emily [51]. This paper follows the trends in this field over the last decade in the following areas: environment parameters, environment architectures, tools and the uses of environments, textual manipulation, internal (structure) representation, conceptual programming with its knowledge-based tools, and environment evaluation. The paper contains an historical perspective of technological events shaping this field and concludes with a unifying summary.
THE FUNSOFT NET APPROACH TO SOFTWARE PROCESS MANAGEMENT
Authors: DEITERS WOLFGANG , GRUHN VOLKER
Published: November 2004

Software processes are usually described by guidelines and advices. These guidelines are claimed to be valid for many projects. This understanding leads to software processes which deviate from initial plans and which frequently yield insufficient results. System-atic management of software processes can help to overcome these shortcomings. In this paper, we introduce an incremental approach to software process management. This approach covers the complete life-cycle of software process models, i.e., it deals with software process modeling, software process model analysis, and software process model enaction. It is based on a net-based software process modeling language called FUNSOFT nets. FUNSOFT nets are high-level Petri nets adapted to the application domain of software process management. We model software processes by means of different views onto a software process model. Our approach is implemented in a software process management environment called MELMAC.
SEMAL: A COST LANGUAGE BASED ON THE CALCULUS OF SELF-MODIFIABLE ALGORITHMS
Authors: EBERBACH EUGENIUSZ
Published: November 2004

The design, specification, and preliminary implementation of the SEMAL language, based upon the Calculus of Self-modifiable Algorithms model of computation is presented. A Calculus of Self-modifiable Algorithms is a universal theory for parallel and intelligent systems, integrating different styles of programming, and applied to a wealth of domains of future generation computers. It has some features from logic, rule-based, procedural, functional, and object-oriented programming. It has been designed to be a relatively universal tool for AI similar to the way Hoare’s Communicating Sequential Processes and Milner’s Calculus of Communicating Systems are basic theories for parallel systems. The formal basis of this approach is described. The model is used to derive a new programming paradigm, so-called cost languages and new computer architectures cost-driven computers. As a representative of cost languages, the SEMAL language is presented.
A KNOWLEDGE-BASED FRAMEWORK OF OBJECT-ORIENTED SOFTWARE DEVELOPMENT ENVIRONMENTS
Authors: SOURROUILLE JEAN LOUIS
Published: November 2004

Software development can be seen as a formalization process which, from informal data (problem), leads to a fully formal representation (solution) by successive enrichments and transformations. This paper presents a representation formalism (KLSDE: Knowledge-based representation Language for Software Development Environments) which supports the iterative and evolutionary features of this process. From syntactic and semantic rules described in the domain model and the software process model, the representation is gradually bound by stronger and stronger constraints, according to the degree of formalization.

Based on object concepts, KLSDE offers both expressive power as well as simplicity and readability. The power, which stems from knowledge representation techniques, is necessary to build various models such as the software process development, the domain or the solution. Readability and simplicity are required so that the language addresses communication needs. For readability, the language is constructed on current metaphors and concepts. It includes a graphic representation and many structuring mechanisms. Finally, KLSDE is at the center of a development environment. It is parameterized by the user methodology and fulfills the needs for the whole life-cycle.
USING MATHEMATICAL INDUCTION IN SYSTEMATIC PROGRAM DEVELOPMENT
Authors: LI JIANXIN , LAKHOTIA ARUN
Published: November 2004

This paper makes a contribution to the calculational paradigm of program development, a paradigm in which programs are calculated from their specifications by applying meaning preserving transformations. It introduces program induction, a technique analogous to mathematical induction, and iteration folding, a refinement rule. Using program induction, a specification is decomposed into a base case and an inductive case and their solutions are sequentially composed to derive the final program. The iteration folding rule is applied to transform potentially infinite nested if statements into a while statement. Our technique and rule augment the existing repertoire of techniques and rules in the calculus of program refinement.
RESTRICTED TRACK ASSIGNMENT WITH APPLICATIONS
Authors: SARRAFZADEH MAJID , LEE D. T.
Published: November 2004

Consider a set of intervals S = {I1, I2, …, In}, where Ii = (li, ri), li, and ri are real numbers, and li < ri. We study a restricted track assignment problem (RTAP): if an interval Ia contains another interval Ib, then Ia must be assigned to a higher track than Ib, and the goal is to minimize the number of tracks used. The problem RTAP is shown to be NP-hard. An approximation algorithm that produces a solution within twice of the optimal is also presented and the bound is shown to be tight. The algorithm runs in O(n log n) time and requires linear space. The proposed approximation algorithm is employed to solve the problem of finding a maximum-weighted independent set in a circle graph, and related problems.
WALKING IN AN ARRANGEMENT TOPOLOGICALLY
Authors: ASANO TETSUO , GUIBAS LEONIDAS J. , TOKUYAMA TAKESHI
Published: November 2004

We present topological walk, an on-line algorithm for computing a walk in an arrangement. Here, a walk is a visit to the cells of an arrangement in an order such that consecutive cells are adjacent to each other. The algorithm can walk in a part of an arrangement efficiently; more precisely, given an arrangement of n lines in a convex region containing K cells, a walk is performed in O(K + n log n) time and O(n) working space. Several optimal-cell-finding problems can be solved efficiently applying the topological walk. Further, a construction of a spanning tree with maximum node degree three of the dual graph of an arrangement is given.
PRODUCTS OF COMMUTATORS AND PRODUCTS OF SQUARES IN A FREE GROUP
Authors: COMERFORD LEO P. , EDMUNDS CHARLES C.
Published: November 2004

A classification of the ways in which an element of a free group can be expressed as a product of commutators or as a product of squares is given. This is then applied to some particular classes of elements. Finally, a question about expressing a commutator as a product of squares is addressed.
FINITE ELEMENT ANALYSIS OF TE AND TM MODES IN NONLINEAR PLANAR WAVEGUIDES
Authors: ZOBOLI M. , SELLERI S.
Published: November 2004

A general approach based on the finite element method for analyzing optical waves guided by dielectric planar waveguides with arbitrary nonlinear media and with arbitrary refractive index distribution is considered. A complete transverse-electric and transverse-magnetic mode analysis is presented and TM polarization solutions are obtained without approximations on the biaxial nature of the nonlinear refractive index. Solution convergence and stability is discussed and both film-guided and surface-guided modes are presented for symmetrical and asymmetrical structures. Bistability and hysteresis phenomena have been investigated for TE as well as for TM modes.
OPTICAL NONLINEAR DEVICES
Authors: CADA M. , HE J. , NORMANDIN R. , DAI H. , JANZ S.
Published: November 2004

Theoretical and experimental results are described of several nonlinear optical structures and devices investigated by our group, that may potentially be usable for certain applications. Three groups of devices are addressed: a multiple quantum well switching device, a bistable semiconductor periodic multilayered structure and an optical harmonic mixer. Conclusions summarize results achieved up to date and point out some possible future paths to device concepts and their implementations, as well as potential applications in optical fiber communications, computing and signal processing.
NONLINEAR OPTICAL STUDIES OF POLYMER INTERFACES
Authors: SHEN Y.R.
Published: November 2004

Second-order nonlinear optical processes can be used as effective surface probes. They can provide some unique opportunities for studies of polymer interfaces. Here we describe two examples to illustrate the potential of the techniques. One is on the formation of metal/polymer interfaces. The other is on the alignment of liquid crystal films by mechanically rubbed polymer surfaces.
TRAVELLING WAVES PRODUCED BY MOVING SOURCES IN A NONLINEAR REACTIVE-CONVECTIVE SYSTEM
Authors: LOGAN J. DAVID , SHORES THOMAS S.
Published: November 2004

We study the existence of travelling waves that are produced by moving sources in a nonlinear reactive-convective model of reactive flow. The analysis leads to a non-autonomous differential-algebraic system and the existence of solutions is proved using a topological theorem on terminal boundary value problems on ℝ. We also consider an inverse-problem and determine a moving source that leads to a given travelling wave in the system. The ad hoc methods developed herein to analyze the nonautonomous system may be applicable to other problems on infinite domains.
NUMERICAL SHAPE OPTIMIZATION FOR RELAXED DIRICHLET PROBLEMS
Authors: VITA S. FINZI
Published: November 2004

We consider the numerical approximation of optimal design problems governed by an elliptic partial differential equation, in the relaxed formulation recently introduced by Buttazzo and Dal Maso. A discrete optimality condition is derived for the solution of the optimization problem in the finite element setting, by means of which a convergent algorithm is generated. We discuss the numerical results of its application on different examples.
THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D
Authors: MARKOWICH PETER A. , MAUSER NORBERT J.
Published: November 2004

Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases.

Also, for every phase-space density in [Formula: see text] (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.
THE SWITCHING BEHAVIOR OF A ONE-DIMENSIONAL PN-DIODE IN LOW INJECTION
Authors: SCHMEISER C. , UNTERREITER A. , WEISS R.
Published: November 2004

The switching of a semiconductor PN-diode from forward to reverse bias is studied. A mathematical model is derived from a one-dimensional version of the standard drift diffusion equations by formal asymptotics. The simplifying assumptions amount to vanishing space charge, low injection, “long” devices and strongly asymmetric doping. The model is equivalent to a nonlinear Volterra integral equation of the second kind for the current through the device. Existence, uniqueness, analyticity and monotonicity of the solution are proved.

In typical situations the integral equation is singularly perturbed. A rigorous perturbation analysis shows that the model is able to reproduce the experimentally observed switching behavior.
FREQUENCY DOMAIN TREATMENT OF ONE-DIMENSIONAL SCALAR WAVES
Authors: DOUGLAS JIM , SANTOS JUAN E. , SHEEN DONGWOO , BENNETHUM LYNN SCHREYER
Published: November 2004

A naturally parallelizable numerical method for approximating scalar waves in a single space variable is developed by going to a frequency domain formulation. General forms of attenuation are permitted. Convergence is established and numerical results are presented.
EXISTENCE AND POSITIVITY RESULTS FOR THE φ−θ AND A MODIFIED k−ε TWO-EQUATIONTURBULENCE MODELS
Authors: LEWANDOWSKI ROGER , MOHAMMADI BIJAN
Published: November 2004

In this work, we consider the k−ε two-equation turbulence model from the point of view of mathematical and numerical analysis. We introduce a new equivalent two-equation model based on a new set of variables. In the first part, we study this model with a constant eddy viscosity. In this model, the coupling between the equations is done only through the right-hand side. In the second part, we consider the complete model with a nonlinear viscosity. Finally, the impact of this new change of variables on the numerical computations with the k−ε model is shown and a robust algorithm which preserves the positivity of the variables is given.
A DECOMPOSITION OF L2(Ω)3 AND AN APPLICATION TO MAGNETOSTATIC EQUATIONS
Authors: CIARLET PATRICK
Published: November 2004

The domain Ω considered in the following is an open, bounded and connected subset of R3. The purpose of this paper is to find a decomposition of the space of functions L2(Ω)3 of the form grad P⊕ curl W and then to apply this result to the magnetostatic set of equations. Moreover, we prove that if the spaces P and W are chosen correctly, a function u of L2(Ω)3 can be written as grad p+curl w, p∈P and w∈W being unique (up to a constant for p). In the case of the magnetostatic equations, we provide a characterization of the magnetic field solution of these equations.
A SINGULAR PERTURBATION APPROACH TO VARIATIONAL PROBLEMS IN FRACTURE MECHANICS
Authors: BRAIDES ANDREA , COSCIA ALESSANDRA
Published: November 2004

We consider functionals of the form I(u, S)=∫Ω\S W(Du)dx+∫S ɸ(u+, u−)dℋn−1, with ɸ(u,v)~|u–v| for small values of |u–v|, which are related to the variational formulation of static or quasi-static phenomena in damage and fracture mechanics. Here ℋn–1 denotes the (n−1)-dimensional Hausdorff measure, Ω is the reference configuration, the function u represents the displacement, which is differentiable outside the “discontinuity surface” S, and u+, u− are the traces of u on both sides of S. The latter can be interpreted as a crack or a plasticity surface. The functions W and ϕ represent the bulk and surface energy densities respectively. These functionals in general are not lower semicontinuous in their natural topology. Hence we may have minimizing sequences with unbounded discontinuity surfaces, and in the limit we could obtain in general a diffuse zone of “non-differentiability.” In order to assure that we obtain solutions whose “fracture” remain confined only on a surface at most, we propose a singular perturbation approach. We approximate the functional I with a sequence of functionals of the form Iε(u, S)=∫Ω\S W(Du)dx+∫S ɸε(u+, u−)dℋn−1. We show that in the model case of ɸ(u, v)=|u−v|, if ɸε(u, v)~|u−v|+εϕ1(u, v) the limits of the minimizers of Iε not only minimize the corresponding problems for I, but also minimize a “first order” problem involving only an appropriate “surface energy density.”
THE FREE STREAMING OPERATOR WITH MAXWELL TYPE BOUNDARY CONDITIONS IN ASYMMETRIC SOBOLEV SPACES
Authors: TOTARO SILVIA
Published: November 2004

Some properties of the free streaming operator T with Maxwell type boundary conditions are studied in this paper.

The domain D(T) is assumed to be contained in a suitable asymmetric Sobolev space. The norm of the element f is defined in such a space by the sum [Formula: see text], where ‖ ‖1 is the usual L1 norm and c is a constant.

It is proved that T generates a contraction semigroup, which preserves positivity.