bluuebunny/crossref_metadata_2025 huggingface dataset:
THEORETICAL STUDY OF STRUCTURAL AND LATTICE DYNAMICAL PROPERTIES OF MgF2 USING A PAIR-POTENTIAL MODEL
Authors: JIN KIM HYO , KIL CHOO WOONG
Published: November 2004

A two-body interatomic potential model for magnesium difluoride ( MgF 2) is constructed from the known crystal structure and elastic constants. The reliability of this potential model is critically evaluated through the calculation of structural and lattice dynamical properties of MgF 2 in sellaite phase with rutile structure. Energy minimization techniques have been used to predict the lattice parameters and structural properties of MgF 2 both at ambient and elevated pressure conditions. It was found that the calculated structural properties are in excellent agreement with the experimental results. Harmonic lattice dynamical calculations have been performed on the equilibriated structure corresponding to the potential energy minimum. The computed phonon frequencies are in good agreement with experimental data and phonon dispersion curves are reproduced just as well. Frequencies calculated throughout the Brillouin zone have been used to construct a frequency distribution function and harmonic contribution to the specific heat is also calculated.
THERMOMECHANICAL PROPERTIES OF 3d TRANSITION METALS
Authors: KARAOGLU B. , MUJIBUR RAHMAN S.M.
Published: November 2004

We have investigated the density variation of the Einstein temperatures and elastic constants of the 3d transition metals. In this respect we have employed the transition metal (TM) pair potentials involving the sp contribution with an appropriate exchange and correlation function, the d-band broadening contribution and the d-band hybridization term. These calculations are aimed at testing the TM pair potentials in generating the aforesaid quasilocal and local thermomechanical properties.
NONERGODIC BEHAVIOR IN FRUSTRATED SQUARE ICE
Authors: FUCHIZAKI K.
Published: November 2004

A frustrated vertex model is proposed to elucidate some essential properties in proton glass. The frustration mechanism is clarified which arises from the geometric constraint, the so-called ice rule, rather than competing ferroelectric and antiferroelectric interactions. By comparing two order parameters which are obtained by exact thermal averaging and by Monte Carlo sampling, broken ergodicity as well as broken symmetry is examined. Estimation of the diffusion constant in a diffusion process in relevant configuration space allows us to discuss the ergodic convergence property in connection with the free energy surface structure.
η-PAIRING SUPERCONDUCTIVITY IN THE NEGATIVE-U HUBBARD MODEL: EFFECT OF FLUCTUATIONS AND DISORDER
Authors: STEIN JÜRGEN
Published: November 2004

We have studied the influence of singular fluctuations around the mean-field solution as well as higher order contributions to the geometry controlled asymptotic expansion of the propagators on η-pairing superconductivity in the strong coupling negative-U Hubbard model in the presence of unpaired electrons. The modifications of the mean-field results due to the introduction of disorder and allowance for finite U are also calculated. Besides the singularities already present in the O(2) nonlinear σ-model we find a filling-depending singular depression of the repulsive effective pair-hopping interaction which strongly alters the mean-field phase diagram and appears to suppress the η-pairing phase near the band edges.
ELECTRICAL TRANSPORT PROPERTIES OF DIPHASIC AMORPHOUS-MICROCRYSTALLINE SILICON CARBON ALLOYS
Authors: DEMICHELIS F. , PIRRI C.F. , TRESSO E.
Published: November 2004

The dark conductivity of undoped diphasic amorphous-microcrystalline silicon carbon alloy films deposited by plasma-enhanced chemical vapor deposition has been studied as a function of temperature in the range 50–450 K, taking into account their composition, optical and structural properties. From electrical measurements the transport properties were examined and interpreted in terms of a band structure model which includes three mechanisms of carrier transport in different ranges of temperature. The comparison with experiments indicates that the results are consistent with the mechanisms and the model proposed.
DIFFUSION IN THE FRENKEL–KONTOROVA MODEL WITH ANHARMONIC INTERATOMIC INTERACTIONS
Authors: BRAUN OLEG M. , ZELENSKAYA IRINA I. , KIVSHAR YURI S.
Published: November 2004

Low-temperature diffusion and transport properties of the generalized Frenkel–Kontorova model are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weaklyinteracting quasiparticles (kinks). The model takes into account realistic (anharmonic) interaction of particles subjected into a periodic substrate potential, and such a generalization leads to a series of novel effects which we expect are related to the experimentally-observed phenomena in several quasi-one-dimensional systems. Analysing the concentration dependences in the framework of the kink phenomenology, we use the renormalization procedure when the atomic structure with a complex unit cell is treated as (more simple) periodic structure of kinks. Using phenomenology of the ideal kink gas, the low-temperature states of the chain are described as those consisting of "residual" kinks supplemented by thermally-excited kinks. This approach allows us to describe the ground states of the chain as a hierarchy of "melted" kink lattices. Dynamical and diffusion properties of the system are then described in terms of the kink dynamics and kink diffusion. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. Susceptibility, conductivity, self-diffusion and chemical diffusion coefficients of the chain are calculated as functions of the kink diffusion coefficient. In this way, we qualitatively analyze, for the first time to our knowledge, dependence of the different diffusion coefficients on the concentration of atoms in the chain. The results are applied to describe peculiarities in conductivity and diffusion coefficients of quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces which were earlier investigated experimentally.
THEORY OF SPONTANEOUS RADIATION BY BOSONS IN QUASI-CLASSICAL TRAJECTORY-COHERENT APPROXIMATION
Authors: BELOV V. V. , BOLTOVSKY D. V. , YU. TRIFONOV A.
Published: November 2004

The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.
THE ROLE OF SUSPENSION STRUCTURE IN THE DYNAMIC RESPONSE OF ELECTRORHEOLOGICAL SUSPENSIONS
Authors: PARTHASARATHY M. , AHN K. H. , BELONGIA B. M. , KLINGENBERG D. J.
Published: November 2004

The dynamic response of electrorheological (ER) suspensions has received little attention relative to the effort devoted to the study of the steady shear response. We report on simulation and experimental investigations of the dynamic oscillatory response of ER suspensions, in particular focusing on the relationship between suspension structure and the rheological response. We consider the response of monodisperse and polydisperse suspensions under linear deformation, as well as the response in the nonlinear regime. Dimensional analysis of the equations of motion predict that the linear rheological response obeys a time-field strength superposition principle, which is confirmed by experiment. The response is found to exhibit a sharp dispersion that is only broadened slightly by polydispersity. Nonlinear deformation is found to significantly broaden the observed dispersion.
FLUID FLOW AND FALLING BALL EXPERIMENTS IN ER FLUIDS
Authors: ZITTER R. N. , CHEN T. J. , ZHANG X. , TAO R.
Published: November 2004

The ability of the induced dipole–dipole model to predict various properties of an electrorheological fluid is tested in a series of experiments: the deformation of a single particle chain under fluid flow, the velocity of a falling ball at various electric fields, particle sizes, and concentrations, and flow valves operating at either constant pressure differential or constant flow rate. Analyses of these rather different experimental situations show that with proper application, the induced dipole model can give a fairly accurate description of observed characteristics.
ON-OFF EXCITATION SWITCH FOR ER DEVICES
Authors: TOZER R. C. , ORRELL C. T. , BULLOUGH W. A.
Published: November 2004

A very important part of any ER fluids based system is the provision of excitation; this is particularly so since the electrical load is conductive and highly capacitive. In this environment the surge current at switch on is large and there are problems in dumping the charge to effect a rapid reduction of the voltage level. This paper describes a voltage switch which when linked to a steady state supply can be used to effect on-off control. The arrangement is somewhat analogous to the ER catch concept insomuch as it switches one of the ER controller electrodes either to high potential or to earth rails, the other electrode being permanently connected to earth (just as the catch attaches to a steady input motion or a brake). If the supply has a low output impedance then the excitation can be rapidly slewed in both ongoing and offgoing directions. The circuit and its operation is described in detail and brief performance characteristics are shown for the switch when connected to a typical, contemporary ER device.
CONTROLLABLE FLUIDS: THE TEMPERATURE DEPENDENCE OF POST-YIELD PROPERTIES
Authors: WEISS KEITH D. , DUCLOS THEODORE G.
Published: November 2004

This paper represents the first detailed description of the affect of temperature on the properties exhibited by state-of-the-art electrorheological (ER) and magnetorheological (MR) fluids. In particular, shear stress versus shear strain rate curves, dynamic and static yield stress values, zero-field viscosity data, and current density measurements are discussed. Specific comments concerning the stability of both mechanical and electrical properties over broad temperature ranges are provided. Finally, insight into the advantages associated with using electrorheological and magnetorheological fluids in a controllable device is provided.
EXACT SOLUTION OF AN ELECTRONIC MODEL OF SUPERCONDUCTIVITY
Authors: EßLER FABIAN H.L. , KOREPIN VLADIMIR E. , SCHOUTENS KARELJAN
Published: November 2004

We study the exact solution of a superconducting model of strongly correlated electrons in 1+1 dimensions. We explain the method of solution and explicitly derive the fundamental Bethe equations that determine the physical properties of the model in the thermodynamic limit. We also give explicit expressions for the conserved quantum integrals of motion in the model and prove a lowest weight theorem for the Bethe Ansatz states.
LINEAR ELECTRIC-DIPOLE POLARIZABILITIES
Authors: BONIN KEITH D. , KADAR-KALLEN MICHAEL A.
Published: November 2004

This article reviews the main theoretical methods and experimental techniques for determining electric-dipole polarizabilities. This review only considers the lowest-order polarizability which describes the linear response of a particle to an electric field, i.e. the induced electric-dipole moment depends linearly on the applied electric field. The scope of the review is broad: it encompasses atomic, molecular and cluster polarizabilities. Both static and dynamic polarizabilities are covered.

Calculational techniques discussed in detail include variational perturbational theory, the local density approximation, and semi-empirical additivity methods. Special attention is paid to basis sets used in polarizability calculations—especially the increasingly popular Gaussian basis sets. Extensive tabulations of polarizability calculations are provided for helium and sodium atoms, the diatomic nitrogen molecule, the fullerene C60, and sodium and potassium clusters. For each of these cases, the most reliable experimental results are also provided for comparison to theory.

Many traditional experimental techniques are reviewed including dielectric constant, refractive index, Rayleigh scattering, electro-optic Kerr effect, beam deflection, E—H gradient balance, and the beam resonance technique. New experimental methods for determining polarizabilities such as the light-force method and atom interferometry are also extensively discussed. In addition, a novel detection scheme that is elegant and universal—the position-sensitive time-of-flight spectrometer—is thoroughly described.
COMPUTER SIMULATION STUDY OF A THREE-DIMENSIONAL LATTICE SPIN MODEL WITH ANTI-NEMATIC INTERACTIONS
Authors: ROMANO S.
Published: November 2004

We have considered a classical system, consisting of cylindrically symmetric particles, associated with a three-dimensional simple cubic lattice, and interacting via the nearest neighbor pair potential [Formula: see text] here P2 is the second-order Legendre polynomial, ∈ is a positive constant setting the temperature and energy scales, and uk denote the unit vectors defining particle orientations. This potential model was proposed a few years ago [G. Kohring and R.E. Shrock, Nucl. Phys. B295, 36 (1988)] as a system involving ground-state disorder but no frustration, and was found to possess a continuous ordering transition at [Formula: see text]. We report here a more detailed study, using Monte Carlo simulation, molecular field, and two-site cluster treatments, and especially address the structural properties. Comparison shows that the two-site cluster approximation yields results in fair agreement with simulation, and produces a significant improvement over molecular field theory.
NON-HERMITIAN TRICRITICALITY IN THE BLUME-CAPEL MODEL WITH IMAGINARY FIELD
Authors: GEHLEN G. VON
Published: November 2004

Using finite-size-scaling methods, we study the quantum chain version of the spin-1-Blume-Capel model coupled to an imaginary field. The aim is to realize simple non-unitary minimal conformal field theories in an Ising-type spin model. We find that the first ground-state level crossing in the high-temperature phase leads to a second-order phase transition of the Yang-Lee universality class (central charge c=−22/5). The Yang-Lee transition region ends at a line of a new type of tricriticality, where the three lowest energy levels become degenerate. The analysis of the spectrum at two points on this line gives good evidence that this line realizes the universality class of the ℳ2,7-conformal theory with c=−68/7.
A CRITICAL ISING MODEL ON THE LABYRINTH
Authors: BAAKE M. , GRIMM U. , BAXTER R.J.
Published: November 2004

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual couplings are determined. Furthermore, we analyze the subclass of exactly solvable models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspond to the critical points which, as expected, belong to the Onsager universality class.
QUANTUM SUPERSPIN CHAINS
Authors: BAKER T.H. , JARVIS P.D.
Published: November 2004

Supersymmetric formulations of spin-½ quantum chains, associated with integrable models, are considered. One class of super-extensions, based on low-dimensional classical and exceptional superalgebras containing sl(2), is illustrated with the case of osp(1/2). A more radical generalization, in which the algebra of Pauli matrices is identified with the algebra of supersymmetric quantum mechanics, is also presented, and some of its algebraic properties discussed.
q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE-BOND GROUND STATES
Authors: BATCHELOR M.T. , YUNG C.M.
Published: November 2004

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighboring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-½ Majumdar-Ghosh model.
PHENOMENOLOGY OF THE VALENCE-FLUCTUATION PAIRING MECHANISM: Tc SYSTEMATICS OF CUPRATES, AND EVIDENCE FOR THIS MECHANISM IN OTHER SUPERCONDUCTORS
Authors: BRANDOW B.H.
Published: November 2004

The phenomenology of the cuprate superconductors is unconventional in many respects, in addition to the high Tc’s. A number of these features have recently been explained, qualitatively and even semi-quantitatively, by means of a valence-fluctuation mechanism. We now examine the extent to which this mechanism can account, at a qualitative level, for the Tc systematics of the many known cuprate superconductors. We find that this mechanism is consistent with some major features of the Tc systematics: the strong dependence on the hole-doping concentration x, the strong correlation with the Madelung potential of the apical oxygens, and a strong dependence on the number of apical oxygens per planar copper ion. We also argue that the same mechanism should be operating (together with phonons) in a number of other superconductors, in particular in the other “exotic” superconductors of Uemura. The evidence is that typical features of these exotics include extremely short coherence length, very high (and often T2) normalstate resistivity, a highly anomalous form of Hc2(T), a large London penetration depth, and an often obvious suitability for representation by an Anderson lattice form of model Hamiltonian. The frequently-encountered cluster and/or reduced-dimensionality aspects are argued to be features which help to justify the latter form of model Hamiltonian.
GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
Authors: XIANG GUANGHUI , HAN MAOAN
Published: November 2004

In this paper, we study the number of limit cycles in a family of polynomial systems. Using bifurcation methods, we obtain the maximal number of limit cycles in global bifurcation.
CLASSIFICATION OF CHAOTIC SEQUENCES WITH OPEN-LOOP ESTIMATOR — OPTIMAL DESIGN FOR NOISY ENVIRONMENTS
Authors: SCHIMMING THOMAS , BIZZARRI FEDERICO , STORACE MARCO , HASLER MARTIN
Published: November 2004

In this paper, an approach based on ergodic properties for classifying chaotic sequences is given. It is particularly robust due to the open-loop structure of the detector. Unlike previous works in this direction, such as those concerning the inverse system approach, the detector is not uniquely determined by the transmitter (identical or subsystem thereof), but instead depends on the measurement noise model. The classification is optimized under such imperfect observation conditions. The method is introduced in general for the case of chaotic sequences generated by ergodic maps, and a special case is analyzed in detail to illustrate the method. This special example resorts to Tchebychev maps and some additional symmetries to make up a simple signaling scheme which is low in complexity on both transmitter and receiver sides, while at the same time relatively robust, due to the open-loop structure of the detector.
DYNAMICAL EFFECTS FROM ASTEROID BELTS FOR PLANETARY SYSTEMS
Authors: JIANG ING-GUEY , YEH LI-CHIN
Published: November 2004

The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.
PHASE SYNCHRONIZATION IN A MODULATED CHAOTIC LASER ARRAY
Authors: DESHAZER DAVID J. , BREBAN ROMULUS , OTT EDWARD , ROY RAJARSHI
Published: November 2004

Phase synchronization and entrainment of a linear array of loss modulated Nd:YAG lasers are experimentally investigated. The temporally shifting nature of phase synchronization with increasing modulation depth is studied. Chaotic intensity dynamics changes dramatically with increasing modulation, and exhibit entrainment to the modulation signal. Frequency filtered phase variables, defined from the laser intensity time series, uncover phenomena of phase synchronization and competition for phase synchronization that are otherwise hidden.
IMPULSIVE CONTROL OF N-SCROLL GRID ATTRACTORS
Authors: SUN JITAO , ZHANG YINPING
Published: November 2004

This paper derives some sufficient conditions for the stabilization and synchronization of n-scroll attractors via impulsive control with varying impulsive intervals. Some sufficient conditions for the stabilization and synchronization of n-scroll attractors are obtained. The results are illustrated to be efficient through a numerical example and simulation results.
EXCITABLE CHEMICAL MEDIUM CONTROLLER FOR A ROBOTIC HAND: CLOSED-LOOP EXPERIMENTS
Authors: YOKOI HIROSHI , ADAMATZKY ANDY , DE LACY COSTELLO BEN , MELHUISH CHRIS
Published: November 2004

We discuss the experimental implementation of a chemical controller for a robotic hand. In the present case study, we have designed a closed system where a Belousov–Zhabotinsky (BZ) thin layer chemical reactor was linked to the robotic hand via an array of photo-sensors and the fingers of the hand were able to stimulate the excitation dynamics in the BZ medium via the local addition of an activator species. A principal working loop of the chemo-robotic system is that oxidation wave fronts traveling in the medium are detected by photo-sensors and cause (via a microcontroller) the fingers of the hand to bend. When a finger bends, it is set up to apply a small quantity of colloid silver to the reaction and thus causes an additional excitation wave. The traveling and interacting waves stimulate further movements of the fingers and patterns of behavior are observed. These patterns of behavior have been modeled using a cellular automaton. In the paper, we offer an experimental set-up, including algorithms and interfacing, for an experimental chemical robotic hand controller, which contributes to the fields of nonclassical computation, nonlinear physics, and unconventional robotics.
BIFURCATION AND CHAOS IN A COMPLEX MODEL OF DISSIPATIVE MEDIUM
Authors: DANCA MARIUS-F. , CHEN GUANRONG
Published: November 2004

In this paper, we carefully reexamine the chaotic RF model, first studied by Rabinovich and Fabrikant [1979], and have found many new and rich complex dynamics of the model that were mostly not reported before. The chaotic RF model has proved to be a great challenge to classical numerical methods, in the sense that most classical numerical methods have not been very successful in the study of complex dynamics of this special RF model. Therefore, in this paper, we present and apply a special numerical method, the Local Iterative Linearization (LIL) method, along with a special Turbo Pascal code based on this accurate LIL algorithm, for a careful numerical study of this complex RF model. Many interesting new findings are summarized and reported in this paper.
CHAOTIFYING FUZZY HYPERBOLIC MODEL USING ADAPTIVE INVERSE OPTIMAL CONTROL APPROACH
Authors: ZHANG HUAGUANG , WANG ZHILIANG , LIU DERONG
Published: November 2004

In this paper, the problem of chaotifying the continuous-time fuzzy hyperbolic model (FHM) is studied. By tracking the dynamics of a chaotic system, a controller based on inverse optimal control and adaptive parameter tuning methods is designed to chaotify the FHM. Simulation results show that for any initial value the FHM can track a chaotic system asymptotically.
SUPPRESSION OF JAMMING IN EXCITABLE SYSTEMS BY APERIODIC STOCHASTIC RESONANCE
Authors: LAI YING-CHENG , LIU ZONGHUA , NACHMAN ARJE , ZHU LIQIANG
Published: November 2004

To suppress undesirable noise (jamming) associated with signals is important for many applications. Here we explore the idea of jamming suppression with realistic, aperiodic signals by stochastic resonance. In particular, we consider weak amplitude-modulated (AM), frequency-modulated (FM), and chaotic signals with strong, broad-band or narrow-band jamming, and show that aperiodic stochastic resonance occurring in an array of excitable dynamical systems can be effective to counter jamming. We provide formulas for quantitative measures characterizing the resonance. As excitability is ubiquitous in biological systems, our work suggests that aperiodic stochastic resonance may be a universal and effective mechanism for reducing noise associated with input signals for transmitting and processing information.
APPLICATION OF COHEN'S CLASS TIME-FREQUENCY DISTRIBUTIONS IN THE BELOUSOV–ZHABOTINSKY REACTION ANALYSIS
Authors: DAROWICKI K. , FELISIAK W.
Published: November 2004

The systematic study of application of Cohen's class time-frequency representations in the analysis of periodic BZ oscillations generated in batch reactor has been presented. Several distributions belonging to Cohen's class have been applied in the analysis of selected signal being the register of bromide selective electrode. Among them were Wigner–Ville, Choi–Williams and cone-shaped distributions. The application of mentioned methods allow instantaneous power spectra to be obtained and simultaneously give the possibility of observing evolution of frequency composition of investigated oscillations. The systematic filtering of signal, using so-called kernel functions, allows to eliminate undesirable cross terms and finally leads to the selection of a suitable method for chemical oscillations decomposition. The results presented in the form of three-dimensional pictures, illustrate the decrease in frequency of oscillations of exponential character. On the basis of the obtained results the cone-shaped distribution for kernel function parameter α=1 has been selected as the best method for Belousov–Zhabotinsky oscillations analysis in joint time-frequency domain.
A “SHOOTING” APPROACH TO CHAOS
Authors: HASTINGS S.P.
Published: November 2004

Toplogical shooting is a method for proving existence of solutions to certain types of problems in ordinary differential equations. We show how one-dimensional shooting provides an elementary proof that particular equations have solutions which exhibit properties associated with “chaos.” After an introductory illustration of how the method works for a forced pendulum equation, we outline a proof that the Lorenz equations have behavior typical of chaotic systems. Until 1993, there had been no rigorous proof that the Lorenz equations have any kind of chaotic behavior.
THE NONLINEAR MATHIEU EQUATION
Authors: NORRIS J.W.
Published: November 2004

The purpose of this paper is to classify the different sequences of bifurcation that can occur for small amplitude solutions to the nonlinear Mathieu equation near to the Mathieu regions of instability. We do this by using the Lindstedt-Poincare perturbation method to construct a vector field which interpolates the successive iterations of the Poincare map. These vector fields are then analysed to determine the sequence of bifurcations.
VALIDATING IDENTIFIED NONLINEAR MODELS WITH CHAOTIC DYNAMICS
Authors: AGUIRRE LUIS A. , BILLINGS S.A.
Published: November 2004

This paper investigates the effectiveness of several criteria for validating models which exhibit chaotic dynamics. Embedded trajectories, Poincaré sections, bifurcation diagrams, the largest Lyapunov exponent and correlation dimension are considered. The Duffing-Ueda equation and four identified models are used as examples. The results show that models with similar invariants such as Poincaré sections, the largest Lyapunov exponent and correlation dimension may have very different bifurcation behaviours. This suggests that the requirement that an identified model should reproduce the bifurcation pattern of the original system is a very exacting criterion which is well suited for validation purposes.
FAST AND ACCURATE CALCULATION OF LYAPUNOV EXPONENTS FOR PIECEWISE-LINEAR SYSTEMS
Authors: CHIALINA SILVANO , HASLER MARTIN , PREMOLI AMEDEO
Published: November 2004

An efficient and accurate method for computing the Lyapunov exponents of piecewise-linear systems is presented. Circuit examples are given which show the time dependence of the finite-time estimate of the Lyapunov exponents.
EFFECT OF PERTURBATION ON THE AREA PRESERVATION MAP
Authors: WOO H.-J. , LEE E.-K. , KIM Y.I.
Published: November 2004

Subharmonic bifurcation patterns in area-preserving maps change their forms dramatically under dissipative perturbation. The studies of such changes are done by the use of the normal form theory and the Lyapunov-Schmidt reduction method where the eigenvalues of the linearized map move along a circle of radius (1−∊)1/2 in the complex plane. The results are: (i) one set of three-cycle branches, which is hyperbolic, becomes separated from the origin under the dissipative perturbation; (ii) a pair of four-cycle branches, which can be hyperbolic for both branches, or hyperbolic for one branch and stable for the other one depending on the condition, is separated from the origin also under the same perturbation; (iii) one set of n-cycle (n≥5) branches, which is elliptic for the area-preserving case, is retained under the perturbation for sufficiently small ∊.
CONNECTIVITY AND THE DYNAMICS OF INTEGRATE-AND-FIRE NEURAL NETWORKS
Authors: CHU PO HSIANG , MILTON JOHN G. , COWAN JACK D.
Published: November 2004

The dynamics following periodic stimulation at a single point with uniform initial conditions, of an excitatory network of identical integrate-and-fire neurons is investigated as a function of interconnectivity. It is shown that propagating spiral waves as well as other forms of self-maintained activity can arise provided that the probability of neural interconnectivity is an exponentially decreasing function of interneuronal distance. Other forms of connectivity, e.g. nearest neighbor, step function, do not produce spirals.
DYNAMICAL PORTRAIT OF A MODEL OF THERMAL INSTABILITY: CASCADES, CHAOS, REVERSED CASCADES AND INFINITE PERIOD BIFURCATIONS
Authors: FRANKEL MICHAEL L. , ROYTBURD VICTOR
Published: November 2004

The paper presents results of numerical simulations on a model free boundary problem which is qualitatively equivalent to the free interface problems describing solid combustion and exothermic phase transitions. The model problem has been recently shown to exhibit transition to chaotic oscillations via a sequence of period doubling, assuming an Arrhenius type boundary kinetics. In the present paper we demonstrate that for a slightly different class of kinetics the behavior pattern, while retaining the above scenario, may undergo a drastic change. This behavior is characterized by slowly expanding oscillations followed by a powerful burst, after which the system returns to near equilibrium and the scenario is repeated periodically. As the bifurcation parameter approaches the stability threshold, the total period tends to infinity due to an increasingly prolonged “accumulation phase.” Additional scenarios corresponding to increasing supercriticality of the bifurcation parameter include finite period doubling sequences that return to simple periodic regime via a reversed cascade, infinite sequences followed by an interval of chaos and reversed sequences, or a combination of period doubling, chaos and “Shilnikov type” orbits. Our observations suggest that major dynamical patterns are qualitatively kinetics independent and, moreover, may be essentially finite-dimensional. We argue that for a deeper understanding of the mechanisms responsible for the formation of various patterns a further analytical study (including perhaps a reduction to a finite-dimensional model) of the free boundary problem is desirable.
BIFURCATIONAL PRECEDENCES FOR PARAMETRIC ESCAPE FROM A SYMMETRIC POTENTIAL WELL
Authors: CLIFFORD M.J. , BISHOP S.R.
Published: November 2004

Bifurcational precedences are obtained for systems which permit escape from a potential well by considering the three striped horseshoe formed by the invariant manifolds of the hilltop saddles. Considerable information regarding the bifurcational structure is obtained by considering the crossings of periodic orbits in an idealised suspension of the flow in terms of this three striped horseshoe.
OPTICAL VORTEX INTERACTION IN LASERS
Authors: JEFFERY MARK , D’ANGELO E.J.
Published: November 2004

The Maxwell-Bloch equations describing the transverse modes of a large aspect ratio homogeneously broadened single-longitudinal-mode laser are solved numerically. The solutions are visualized by color-coding the intensity and phase of the transverse electric field at each time step and a video showing the detailed time evolution has been made. As the gain is increased optical vortices, or defects, are observed. These vortices interact and for very high gain optical turbulence exists. The orbits of the single- and two-defect solutions are analyzed and the effective force law coupling the defects is numerically calculated. The best fit force is a modified Bessel function which is proportional to r−1/2 exp (−r/α) at large distances and ln(α/r) at close range where α is approximately 2. This interaction force law for optical defects is similar to the force law between Abrikosov vortices in a superconductor.
GENERATION OF PSEUDO-CHAOTIC SEQUENCES
Authors: KILIAS T.
Published: November 2004

This paper deals with the spectral properties of pseudo-random signals generated in maximum-length shift registers. It is shown that infinitely long registers are comparable in behavior with one-dimensional discrete-time chaotic maps. Therefore the theory, results and tools developed for chaotic systems can be applied to the design of the spectral properties of maximum-length shift register sequences.
SYNTHESIZING SELF-SYNCHRONIZING CHAOTIC ARRAYS
Authors: CUOMO KEVIN M.
Published: November 2004

A systematic approach is developed for synthesizing dissipative chaotic arrays that possess the self-synchronization property. The ability to synthesize high-dimensional chaotic arrays further enhances the usefulness of synchronized chaotic systems for communications, signal processing, and modeling of physical processes.
NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
Authors: CHAMPNEYS A.R. , KUZNETSOV Yu. A.
Published: November 2004

A numerical procedure is presented for the automatic accurate location of certain codimension-two homoclinic singularities along curves of codimension-one homoclinic bifurcations to hyperbolic equilibria in autonomous systems of ordinary differential equations. The procedure also allows for the continuation of multiple-codimension homoclinic orbits in the relevant number of free parameters. A systematic treatment is given of codimension-two bifurcations that involve a unique homoclinic orbit. In each case the known theoretical results are reviewed and a regular test-function is derived for a truncated problem. In particular, the test-functions for global degeneracies involving the orientation of a homoclinic loop are presented. It is shown how such a procedure can be incorporated into an existing boundary-value method for homoclinic continuation and implemented using the continuation code AUTO. Several examples are studied, including Chua’s electronic circuit and the FitzHugh-Nagumo equations. In each case, the method is shown to reproduce codimension-two bifurcation points that have previously been found using ad hoc methods, and, in some cases, to obtain new results.
WEAK DISSIPATION IN A HAMILTONIAN MAP
Authors: MONDRAGÓN C. RAÚL J. , RICHTER PETER H.
Published: November 2004

The dynamics of a bouncing ball reflected off a harmonic spring is investigated, with weak dissipation of three different types. The phase space is found to be organized into a system of tubes that wind around the branches of the bifurcation tree of periodic orbits of the Hamiltonian system. Instead of attraction towards special periodic orbits we observe a kind of piecewise adiabatic invariance of the tubes, with jumps occurring when the branches penetrate each other.
BIFURCATIONS IN FLAT-TOPPED MAPS AND THE CONTROL OF CARDIAC CHAOS
Authors: GLASS LEON , ZENG WANZHEN
Published: November 2004

A recent experiment in cardiac physiology [Garfinkel et al., 1992] controlled irregular interbeat intervals by delivering a stimulus that was meant to perturb the trajectory to the stable manifold of an unstable fixed point. This paper offers an alternative mechanism for regularizing cardiac rhythms. In analogy with the operation of commercial cardiac pacemakers, we analyze a mechanism for chaos control in which a stimulus is delivered at a fixed delay, provided the preceding interbeat interval lies in a well-defined range. This mechanism can be characterized by maps with flat segments that we analyze using standard methods of symbolic dynamics. This mechanism is compared with a control scheme in which a parameter is perturbed repeatedly to stabilize an unstable fixed point.
RELAXATION BEHAVIOR AND PATTERN FORMATION IN REACTION-DIFFUSION SYSTEMS
Authors: HANUSSE PATRICK , PEREZ-MUÑUZURI VICENTE , GOMEZ-GESTEIRA MONCHO
Published: November 2004

The notions of relaxation oscillation and hard excitation have been extensively used and early recognized as important qualitative features of many nonlinear systems. Nevertheless, there seems to exist so far no clear mathematical definitions of these notions. We consider the description of relaxation behavior in oscillating or excitable systems resulting from symmetry breaking of the rotational symmetry of the velocity vector field of the Hopf normal form. From symmetry considerations we detect the first terms responsible for the relaxation character of the phase dynamics in such systems and show that they provide a good general, if not universal, definition of the relaxation properties. We analyze their consequence in the modeling of spatiotemporal patterns such as spiral waves.
CHARACTERIZATION OF WAVE FRONT INSTABILITIES IN THE BELOUSOV-ZHABOTINSKY REACTION: AN OVERVIEW
Authors: NAGY-UNGVARAI Zs. , MÜLLER S.C.
Published: November 2004

Two types of instability of wave front propagation are compared. Reaction-induced or lateral instability leads to wave front fragmentation in systems having low excitability and high threshold of excitation. On the contrary, diffusion-induced instability was shown theoretically to cause wave front folding in systems with different diffusion of the autocatalyst and the inhibitor. First experiments pointing in this direction are presented. From wavelength λ0, velocity c0 of spiral waves and diffusion coefficient D of the autocatalytic species the dimensionless quantity Q=λ0c0/D is calculated for experimental characterization of lateral instability in different chemical systems. Furtheron, the connection between front curvature and fragmentation is analyzed. Various experimental possibilities to realize unstable wave propagation are summarized.
A WEAKLY NONLINEAR INSTABILITY OF MISCIBLE DISPLACEMENTS IN A RECTILINEAR POROUS MEDIA FLOW
Authors: ZIMMERMAN WILLIAM B.
Published: November 2004

The linear stability theory of Tan & Homsy [1986] is extended to include the effects of weak nonlinear coupling between mass flux and viscous effects when the viscous fingers grow from a slowly diffusing, nearly flat displacement front. A regular perturbation scheme combined with a similarity-separation of variables technique leads to a Landau equation for the amplitude of the disturbance. The Landau constant has a simple pole for a given wavenumber within the linear theory cutoff wavenumber for growth. An argument is given that this pole leads to pairing of fingers while the instability remains small. Comparison of the length scale of the pole of the Landau constant with experimental measurements of finger scale shows good agreement where plausibly finite-amplitude effects might come into play, but with the linear theory otherwise.
SELF-OSCILLATIONS AND OPTICAL CHAOS OF AN INDUCED ABSORBER IN COUPLED CAVITIES
Authors: ZHANG F. , GROHS J. , STEFFEN J. , IßLER H. , KLINGSHIRN C.
Published: November 2004

In this paper we investigate the nonlinear dynamics of an induced absorber (CdS) in two coupled, hybrid, optoelectronic ring-cavities. By changing the cw-pumping intensity an inverse successive-subharmonic-oscillation cascade followed by a chaotic oscillation is experimentally observed with a narrow bistable input-output characteristics of the absorber. The related numerical simulations are given. For fixed delayed times a new type of frequency hysteresis is found. In the case of one very short and one very long delay time, a series of mixed self-oscillation modes, which is composed from the modes corresponding to the two delay times, is observed.
STOCHASTIC RESONANCE: TUTORIAL AND UPDATE
Authors: MOSS FRANK , PIERSON DAVID , O’GORMAN DAVID
Published: November 2004

Stochastic resonance is by now a well studied phenomenon whereby certain nonlinear systems, subject to weak input signals, have the property that the presentation of stochastic forcing, or “noise,” can enhance the coherence of the output. Since its introduction in 1981, this curious phenomenon has been the object of much study, yet a number of questions remain. In addition to offering an update to recent reviews, we hope here to set the stage with a brief tutorial, raise some questions and then to offer a speculative look towards the future.
USING COLOR AND ROTATION FOR VISUALIZING FOUR-DIMENSIONAL POINCARÉ CROSS-SECTIONS: WITH APPLICATIONS TO THE ORBITAL BEHAVIOR OF A THREE-DIMENSIONAL HAMILTONIAN SYSTEM
Authors: PATSIS P.A. , ZACHILAS L.
Published: November 2004

The problems encountered in the study of three-dimensional Hamiltonian systems by means of the Poincare cross-sections are reviewed. A new method to overcome these problems is proposed. In order to visualize the four-dimensional “space” of section we introduce the use of color and rotation. We apply this method to the case of a family of simple periodic orbits in a three-dimensional potential and we describe the differences in the orbital behavior between regions close to stable and unstable periodic orbits. We outline the differences between the transition from stability to simple instability and the transition from stability to complex instability. We study the changes in the structure of the 4D “spaces” of section, which occur when the family becomes complex unstable after a DU →Δ or a S →Δ transition. We conclude that the orbital behavior after the transition depends on the orbital behavior before it.
SUBSIDIARY HOMOCLINIC ORBITS TO A SADDLE-FOCUS FOR REVERSIBLE SYSTEMS
Authors: CHAMPNEYS A.R.
Published: November 2004

A dynamical system is said to be reversible if there is an involution of phase space that reverses the direction of the flow. Examples are classical Hamiltonian systems with quadratic kinetic energy. For reversible systems, homoclinic orbits that are invariant under the reversible transformation typically persist as parameters are varied. This paper concerns reversible systems for which a primary homoclinic orbit to a saddle-focus is assumed to exist. The problem under investigation is a characterisation of the subsidiary homoclinic orbits which then exist in a neighbourhood of the primary one. Such orbits have applications as solitary water waves and as buckling solutions of nonlinear struts.

A Shil’nikov-type analysis is performed for four-dimensional linearly reversible systems. It is shown that each subsidiary homoclinic orbit can be labelled by a symmetric string of positive integers. All possible strings of length one, two or three correspond to the existence of a homoclinic orbit, whereas only certain of those of length four or greater do. This situation contrasts with known results if the reversible system is also Hamiltonian. The analysis is supported by performing careful numerical experiments on the equation [Formula: see text] where P and α are parameters; a good agreement with the theory is found.
BIFURCATION AND CHAOS IN THE SIMPLEST DISSIPATIVE NON-AUTONOMOUS CIRCUIT
Authors: MURALI K. , LAKSHMANAN M. , CHUA L.O.
Published: November 2004

We present a detailed investigation of the bifurcation and chaos phenomenon associated with the simplest sinusoidally driven dissipative second-order circuit made up of three linear circuit elements and a Chua’s diode. Unlike other non-autonomous second-order chaotic circuits whose nonlinear element is a nonlinear capacitor/inductor, the Chua’s diode of this circuit is a nonlinear resistor, and is therefore simpler from a circuit theoretic point of view. The chaotic dynamics of this circuit is confirmed both by experiments and by computer simulation of the circuit model.
SOME REMARKS ON STRUCTURE SELECTION FOR NONLINEAR MODELS
Authors: AGUIRRE LUIS ANTONIO
Published: November 2004

This note is concerned with structure selection of nonlinear models. By structure selection it is meant the choice of the model basis prior to parameter estimation. It is argued that the effect of the sampling period and the noise on the data may in some cases preclude adequate structure selection. Other issues which are briefly discussed include the selection of the sampling period and the effectiveness of information criteria in indicating the best size of a nonlinear model.
ARNOL’D TONGUES, DEVIL’S STAIRCASE, AND SELF-SIMILARITY IN THE DRIVEN CHUA’S CIRCUIT
Authors: PIVKA LADISLAV , ZHELEZNYAK ALEXANDER L. , CHUA LEON O.
Published: November 2004

Empirical recurrent relations, governing the structure of the devil’s staircase in the driven Chua’s circuit are given, which reflect the self-similar structure in an algebraic form. In particular, it turns out that the same formulas hold for both winding and period numbers, but with different “initial conditions”.

Some of the finer details such as period-doubling along with numerous coexistence phenomena within staircases of mode-locked states have been revealed by computing high-resolution bifurcation diagrams.