bluuebunny/crossref_metadata_2025 huggingface dataset:
QUANTUM MECHANICS IS EITHER NONLINEAR OR NON-INTROSPECTIVE
Authors: HÜBSCH TRISTAN
Published: September 2003

The measurement conundrum seems to have plagued quantum mechanics for so long that impressions of an inconsistency amongst its axioms have spawned. A demonstration that such purported inconsistency is fictitious may then be in order and is presented here. An exclusion principle of sorts emerges, stating that quantum mechanics cannot be simultaneously linear and introspective (self-observing). The nonlinearity of this latter approach allows quantum mechanics to describe the entire measuring process, and also to be applied to the entire universe, for which there is no external observer.
INTERACTION ENERGY OF 't HOOFT–POLYAKOV MONOPOLES
Authors: KLEIHAUS B. , KUNZ J. , TCHRAKIAN D. H.
Published: September 2003

The dependence of the energies of axially symmetric monopoles of magnetic charges 2 and 3, on the Higgs self-interaction coupling constant, is studied numerically. Comparing the energy per unit topological charge of the charge-2 monopole with the energy of the spherically symmetric charge-1 monopole, we confirm that there is only one repulsive phase in the interaction energy between like monopoles.
EXTENSION OF SINE–GORDON FIELD THEORY FROM GENERALIZED CLIFFORD ALGEBRAS
Authors: BASEILHAC P. , GRANGÉ P. , RAUSCH DE TRAUBENBERG M.
Published: September 2003

Linearization of homogeneous polynomials of degree n and k variables leads to generalized Clifford algebras. Multicomplex numbers are then introduced in analogy to complex numbers with respect to the usual Clifford algebra. In turn multi-complex extensions of trigonometric functions are constructed in terms of "compact" and "non-compact" variables. It gives rise to the natural extension of the d-dimensional sine–Gordon field theory in the n-dimensional multicomplex space. In two dimensions, the cases n = 1, 2, 3, 4 are identified as the quantum integrable Liouville, sine–Gordon and known deformed Toda models. The general case is discussed.
COSMIC BACKGROUND RADIATION TEMPERATURE ANISOTROPY: POSITION OF FIRST DOPPLER PEAK
Authors: FRAMPTON PAUL H. , NG Y. JACK , ROHM RYAN
Published: September 2003

The purpose of the Cosmic Background Radiation experiments is to measure the temperature anisotropy via the autocorrelation function. The partial wave l1 corresponding to the first Doppler peak caused by baryon–photon oscillations at the surface of last scattering depends on the present density Ω0 and the cosmological constant contribution ΩΛ. We discuss this dependence on the basis of perspicuous figures.
RENORMALON'S CONTRIBUTION TO EFFECTIVE COUPLINGS
Authors: SUZUKI HIROSHI
Published: September 2003

When an asymptotically non-free theory possesses a mass parameter independent of the Λ parameter, the uv renormalon gives rise to nonperturbative contributions, to dimension-four operators and dimensionless couplings, thus has a "dual" effect of the instanton. We illustrate this phenomenon in O(N) symmetric massive λϕ4 model in the 1/N expansion. This effect of uv renormalon is briefly compared with nonperturbative corrections in the magnetic picture of the Seiberg–Witten theory.
EXAMPLES OF D = 11 S-SUPERSYMMETRIC ACTIONS FOR POINT-LIKE DYNAMICAL SYSTEMS
Authors: DERIGLAZOV A. A. , GITMAN D. M.
Published: September 2003

A nonstandard super extensions of the Poincaré algebra (S-algebra1,2), which seems to be relevant for construction of various D = 11 models, are studied. We present two examples of actions for point-like dynamical systems, which are invariant under off-shell closed realization of the S-algebra as well as under local fermionic κ-symmetry. On this ground, an explicit form of the S-algebra is advocated.
TENSIONLESS BRANES AND THE NULL STRING CRITICAL DIMENSION
Authors: BOZHILOV P.
Published: September 2003

BRST quantization is carried out for a model of p-branes with second-class constraints. After extension of the phase space, the constraint algebra coincides with the one of null string when p =1. It is shown that in this case one can or cannot obtain critical dimension for the null string, depending on the choice of the operator ordering and the corresponding vacuum states. When p>1, operator orderings leading to critical dimension in the p=1 case are not allowed. Admissible orderings give no restrictions on the dimension of the embedding space–time. Finally, a generalization to supersymmetric null branes is proposed.
ρ–ω MIXING AT HIGH TEMPERATURE AND DENSITY
Authors: BHATTACHARYYA ABHIJIT
Published: September 2003

The temperature and density dependence of the ρ–ω mixing amplitude has been studied from a purely hadronic model. The in-medium baryon masses and chemical potentials have been obtained at the Mean Field (MF) level and these results have been used to calculate the mixing amplitude. It has been observed that the mixing amplitude changes substantially at high temperature and density.
FIELD-INDUCED AXION EMISSION VIA PROCESS e+e-→a IN PLASMA
Authors: MIKHEEV N. V. , YA. PARKHOMENKO A. , VASSILEVSKAYA L. A.
Published: September 2003

The annihilation into axion e+e-→a is investigated in a plasma and an external magnetic field. This process via a plasmon intermediate state has a resonant character at a particular energy of the emitted axion. The emissivity by e+e-→a is compared with the axion cyclotron emissivity.
THE GAUGE HIERARCHY PROBLEM AND HIGHER-DIMENSIONAL GAUGE THEORIES
Authors: HATANAKA HISAKI , INAMI TAKEO , LIM C. S.
Published: September 2003

We report on an attempt to solve the gauge hierarchy problem in the framework of higher-dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to be vanished. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space S2 even the finite mass correction vanishes.
PROPERTIES OF QUANTUM HALL SKYRMIONS FROM ANOMALIES
Authors: BAEZ S. , BALACHANDRAN A. P. , TRAVESSET A. , STERN A.
Published: September 2003

In this letter, we introduce Fractional Quantum Hall Effect (FQHE) Skyrmions in the Chern–Simons effective field theory description, and we present a new derivation of the FQHE Skyrmions properties, namely charge and spin, which results from considerations at the edge of the Hall sample. At the boundary, we demand anomaly cancellation for the chiral edge currents, as well as, allow for the possibility of Skyrmion creation and annihilation. For the Skyrmion charge and spin, we get the values eνN Sky and νN Sky /2, respectively, where e is electron charge, ν is the filling fraction and N Sky is the Skyrmion winding number. We also add terms to the action so that the classical spin fluctuations in the bulk satisfy the standard equations of a ferromagnet and find that spin waves propagate with the classical drift velocity of the electron.
VERTEX OPERATOR EXTENSION OF CASIMIR WAN ALGEBRAS
Authors: ÖZER H. T.
Published: September 2003

We give an extension of Casimir WAN algebras including a vertex operator which depends on non-simple roots of AN-1.
PARTICLE MASSES IN KALUZA–KLEIN–GORDON THEORY AND THE REALITY OF EXTRA DIMENSIONS
Authors: LIU HONGYA , WESSON PAUL S.
Published: September 2003

To see how the effective 4-D mass of a particle is affected by the geometry of an ND space, we take the Klein–Gordon equation in 5-D and evaluate it in 4-D using two exact solutions of 5-D Kaluza–Klein theory. The mass (squared) turns out to be complex if the theory is independent of the extra coordinate, but can be made real if the wave function depends on an extra dimension which is physical. These results have significant implications for 10-D superstring theory.
CAN QUANTUM-CORRECTED BTZ BLACK HOLE ANTI-EVAPORATE?
Authors: NOJIRI SHIN'ICHI , ODINTSOV SERGEI D.
Published: September 2003

Kaluza–Klein reduction of 3-D gravity with minimal scalars leads to 2-D dilaton-Maxwell gravity with dilaton coupled scalars. Evaluating the one-loop effective action for dilaton coupled scalars in large-N and s-wave approximation, we apply it to study quantum evolution of BTZ black hole. It is shown that quantum-corrected BTZ BH may evaporate or else anti-evaporate which is similar to 4-D Nariai BH as is observed by Bousso and Hawking. Instable higher modes in the spectrum also indicate the possibility of proliferation of BTZ BH.
QUADRUPOLE DEFORMATION IN NUCLEI AT FINITE TEMPERATURE
Authors: COLE B. J. , MILLER H. G. , QUICK R. M.
Published: September 2003

The intrinsic quadrupole deformation has been calculated at finite temperature in 20 Ne both in the mean-field approximation and using an exact shell model diagonalization. The results support the view that the phase transition seen at finite temperature in mean-field calculations is not due to the change in nuclear shape from deformed to spherical, but rather is a collective-to-non-collective transition. Both calculations indicate that the average deformation of 20 Ne changes from β rms ≈0.31 at zero temperature to just over β rms =0.2 at T=3.0 MeV. The calculations also suggest that, in the mean-field approximation, the square of the quadrupole operator, Q[2]·Q[2], is a better indicator of shape changes than Q[2] itself.
CONFORMAL TRANSFORMATIONS AND QUANTUM GRAVITY
Authors: SHOJAI FATIMAH , SHOJAI ALI , GOLSHANI MEHDI
Published: September 2003

Recently,1 it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space–time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e. changing the metric), or by making a conformal transformation (i.e. changing all physical quantities). These two ways are investigated and compared. Also, it is argued that, the ultimate formulation of such a quantum gravity theory should be in the framework of the scalar–tensor theories.
FURTHER COMMENTS ON THE DYNAMICS OF EXTENDED OBJECTS
Authors: KHANAL U.
Published: September 2003

The equation of motion of the internal coordinates of a p-brane, arising from the stationarity of the world space Einstein–Hilbert action, is discussed. Assuming the Einstein equation of general relativity, with the energy–momentum tensor of a perfect fluid having positive energy density, it is shown that the governing equation, in matter dominated regions with positive pressure is a (p+1)-dimensional elliptic differential equation which reduces to the (p+1)-dimensional Laplace equation for constant density and pressure. The EOM becomes a hyperbolic p-dimensional wave equation in conducto-dispersive medium only in regions of world space, like those dominated by vacuum, where the total pressure is negative. The Green's function of the matter dominated, elliptic potential problem presented here for p=3, can be analytically continued into the complexified time domain to make contact on the imaginary axis with the Green's function of the wave equation for vacuum domination. Such considerations will allow the study of the matter–vacuum interface using complex time, whence matter domination with positive pressure would be represented on the real axis, vacuum domination with negative pressure on the imaginary axis, and the transition represented by the complex region.
ABELIAN LANDAU–POMERANCHUK–MIGDAL EFFECTS
Authors: DREMIN I. M. , LAM C. S.
Published: September 2003

It is shown that the high-energy expansion of the scattering amplitude calculated from Feynman diagrams factorizes in such a way that it can be reduced to the eikonalized form up to the terms of inverse power in energy in accordance with results obtained by solving the Klein–Gordon equation. Therefore the two approaches when applied to the suppression of the emission of soft photons by fast charged particles in dense matter should give rise to the same results. A particular limit of thin targets is briefly discussed, and it is shown that the correction to the Bethe–Heitler regime is determined by the ratio of the target thickness to the mean free path. If the same is true in QCD, the nuclear LPM effect could be noticeable.
THE ONE-LOOP DIVERGENCES OF THE LINEAR GRAVITY WITH THE TORSION TERMS IN TETRAD APPROACH
Authors: YU. KALMYKOV M. , PRONIN P. I.
Published: September 2003

In this letter we discuss the connection between the geometric and tetrad approaches in the quantum affine-metric gravity. The corresponding transition formulas are obtained at the one-loop level. As an example, the one-loop counterterms are calculated in the tetrad formalism in the theory with terms quadratic in the torsion field. This model possesses the extra local symmetries connected with transformation of the connection field. It is shown that the special gauge can be chosen so that the corresponding additional ghosts do not contribute to the one-loop divergent terms.
THE DEGENERATE SECTOR OF ASHTEKAR'S PHASE SPACE
Authors: MA YONGGE , LIANG CANBIN
Published: September 2003

We study the phase space of Ashtekar's (3+l)-gravity which involves degenerate triads. A new first-class constraint system is found, which describes a degenerate sector of the phase space. The implications of this constraint system in the dynamics of degenerate triads are also discussed.
OFF-SHELL AMPLITUDES FOR NONORIENTED CLOSED STRINGS
Authors: CAPPIELLO LUIGI , MAROTTA RAFFAELE , PETTORINO ROBERTO , PEZZELLA FRANCO
Published: September 2003

In the context of the bosonic closed string theory, by using the operatorial formalism, we give a simple expression of the off-shell amplitude with an arbitrary number of external massless states inserted on the Klein bottle.
ON GAUGE-EQUIVALENT FORMULATIONS OF N=4 SKdV HIERARCHY
Authors: IVANOV E.
Published: September 2003

We point out that the N=4 supersymmetric KdV hierarchy, when written through the prepotentials of the bosonic chiral and antichiral N=2 supercurrents, exhibits a freedom related to the possibility to choose different gauges for the prepotentials. Some implications of this property are presented. In particular, we give the prepotential form of the "small" N=4 superconformal algebra, the second Hamiltonian structure algebra of the N=4 SKdV hierarchy, for two choices of gauge.
CONFORMAL FIELD THEORY ON Zk-SURFACES WITH EXCHANGE INTERACTIONS
Authors: MAROTTA VINCENZO , SCIARRINO ANTONINO
Published: September 2003

We consider a class of conformal field theories on Riemann surfaces represented as a Zk invariant covering of the sphere. The introduction of exchange interactions among couples of sheets generate effective parafermions. The outgoing theory can be seen as a fractional supersymmetry conformal field theory.
STRUCTURELESS COMPOSITENESS AND THE LEP W+W- DATA
Authors: LEMKE E. H.
Published: September 2003

We specify the electroweak scenario of structureless compositeness (SC) put forward previously to the case of identical masses m(W±)=m(Φ±) and m(Z)=m(Φ0). The resulting quantum-mechanical interference will exhibit a vector–scalar phase interlocking of exactly π. We calculate the total cross-section of e+e-→ W+W- in this scenario and compare with the SM. The experimental data is found not to rule out any of the four scenarios SM, κ an =0, SC at κ=1 and 0. Pronounced differences between these four cases show up for the σ tot contribution of the W L W L final state. The effects are illustrated in plots free of the trivial phase-space factor.
SCALAR–TENSOR THEORIES AND QUANTUM GRAVITY
Authors: SHOJAI FATIMAH , SHOJAI ALI , GOLSHANI MEHDI
Published: September 2003

Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space–time metric. So both gravity and quantum are geometrical features. Gravity determines the causal structure of the space–time, while quantum determines the scale of the space–time. In this letter, it is shown that it is possible to use the scalar-tensor framework to build a unified theory in which both quantum and gravitational effects are present.
THE DIRAC PARTICLE ON CENTRAL BACKGROUNDS AND THE ANTI-DE SITTER OSCILLATOR
Authors: COTĂESCU ION.
Published: September 2003

It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific form of the radial scalar product. As an example, we analytically solve the anti-de Sitter oscillator giving the formula of the energy levels and the form of the corresponding eigenspinors.
NONLOCAL EFFECTS IN QUANTUM GRAVITY
Authors: SHOJAI ALI , SHOJAI FATIMAH , GOLSHANI MEHDI
Published: September 2003

Recently,2 a new quantum gravity theory was presented in which the quantum effects were represented by the conformal degree of freedom of the space–time metric. In this letter we show that in the framework of this theory, quantum gravity is nonlocal.
SUPERSYMMETRY IN A STANDARD-LIKE MODEL
Authors: DEO B. B.
Published: September 2003

We observe that the bosons and fermions belonging to the group SU(3) × SU(2) × U(1) × U(1) behave like supersymmetric partners of each other. Except for one additional auxiliary vector boson, there are no other SUSY particles.
THE DIRAC PARTICLE ON DE SITTER BACKGROUND
Authors: COTĂESCU ION I.
Published: September 2003

We show that the Dirac equation on de Sitter background can be analytically solved in a special static frame where the energy eigenspinors can be expressed in terms of the usual angular spinors known from special relativity, and a pair of radial wave functions.
LOCAL WZW THEORY ON A MANIFOLD WITH BOUNDARY
Authors: APIKYAN S. A. , OHANYAN V. R.
Published: September 2003

This letter studies a boundary variation of the well-known WZW theory. The corresponding "extended" boundary Ward identity, the analog of the Knizhnik–Zamolodchikov equation, and the boundary structure constants for the group SU(2) are derived.
A GENERALIZED FIELD COSMOLOGY
Authors: DIRAR M. , EL-TAHIR ALI , SHADDAD M. H.
Published: September 2003

The generalized field equation is used to construct a cosmological mode by suggesting a Lagrangian which consists of a quadratic term besides the linear one. Solutions of this model are non-singular and do not possess the horizon, entropy, flatness or the age problem.
TENSOR FORCE AND NN SCATTERING WITH POLARIZED BEAM AND TARGET
Authors: RAMACHANDRAN G. , DEEPAK P. N.
Published: September 2003

Expressing the NN scattering matrix in terms of irreducible tensor amplitudes which are directly related to the central interaction in the singlet channel and the central, spin-orbit and tensor interactions in the triplet channel, we show how incisive information can be gathered about the NN interaction and in particular about tensor interactions at low energies by measuring the differential cross-section employing polarized beam and target with appropriate geometries.
NEGATIVE ENERGY DENSITY IN SPINNING MATTER SOURCES IN WORMHOLE SPACE–TIMES WITH TORSION
Authors: GARCIA DE ANDRADE L. C.
Published: September 2003

Negative energy densities in spinning matter sources of non-Riemannian ultrastatic traversable wormholes require the spin energy density to be higher than the negative pressure or the radial tension. Since the radial tension necessary to support wormholes is higher than the spin density in practice, it seems very unlikely that wormholes supported by torsion may exist in nature. This result corroborates earlier results by Soleng against the construction of the closed time-like curves (CTC) in space–time geometries with spin and torsion. It also agrees with earlier results by Kerlick according to which Einstein–Cartan (EC) gravity torsion sometimes enhance the gravitational collapse instead of avoiding it.
ON LOCAL CONSTRAINTS OF D=4 EUCLIDEAN SUPERGRAVITY IN TERMS OF DIRAC EIGENVALUES
Authors: PAUNA N. , VANCEA ION V.
Published: September 2003

It has recently been shown that in order to have Dirac eigenvalues as observables of Euclidean supergravity, certain constraints should be imposed on the covariant phase space as well as on Dirac eigenspinors. We investigate the relationships among the constraints in the first set and argue that these relationships are not linear. We also derive a set of equations that should be satisfied by some arbitrary functions that enter as coefficients in the equation expressing the linear dependency of the constraints in order that the second set of constraints be linearly independent.
ON THE NUMERICAL CLOSENESS OF THE EFFECTIVE PHENOMENOLOGICAL ELECTROWEAK MIXING ANGLE θ AND THE $\overline{\rm{MS}}$ PARAMETER ${\hat\theta}$
Authors: MALTONI M. , VYSOTSKY M. I.
Published: September 2003

It happens that s2 and ŝ2 are equal with 0.1% accuracy, though they are split by radiative corrections and a natural estimate for their difference is 1%. This degeneracy occurs only for mt value close to 170 GeV, so no deep physical reason can be attributed to it. However, another puzzle of the standard model, the degeneracy of [Formula: see text] and s2, is not independent of the previous one since a good physical reason exists for [Formula: see text] and ŝ2 degeneracy. We present explicit formulas which relate these three angles.
AN EXACTLY SOLVABLE MODEL OF THE CALOGERO TYPE FOR THE ICOSAHEDRAL GROUP
Authors: HASCHKE O. , RÜHL W.
Published: September 2003

We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.
THE HAGEDORN TRANSITION, DECONFINEMENT AND THE AdS/CFT CORRESPONDENCE
Authors: RAMA S. KALYANA , SATHIAPALAN B.
Published: September 2003

A connection between the Hagedorn transition in string theory and the deconfinement transition in (nonsupersymmetric) Yang–Mills theory is made using the AdS/CFT correspondence. We modify the model of zero temperature QCD proposed by Witten by compactifying an additional space–time coordinate with supersymmetry breaking boundary conditions thus introducing a finite temperature in the boundary theory. There is a Hagedorn-like transition associated with winding modes around this coordinate, which signals a topology changing phase transition to a new AdS/Schwarzschild black hole where this coordinate is the time coordinate. In the boundary gauge theory time-like Wilson loops acquire an expectation value above this temperature.
AXIALLY SYMMETRIC SOLUTIONS IN DILATONIC THEORY AND THE SOLAR SYSTEM TESTS
Authors: MATOS TONATIUH , VILLEGAS HUGO , OBREGÓN OCTAVIO
Published: September 2003

An analysis of the three classical solar system tests for dilatonic gravity coupled to electromagnetism is discussed using an exact, axially symmetric solution. At the post-Newtonian order there is no difference with general relativity, but a constraint on the coupling constant α is obtained at the next order.
GENERALIZED n-POISSON BRACKETS ON A SYMPLECTIC MANIFOLD
Authors: GRABOWSKI J. , MARMO G.
Published: September 2003

On a symplectic manifold (M,ω) we study a family of generalized Poisson brackets associated with 2k-forms ωk. The extreme cases are related to the Hamiltonian and Liouville dynamics. We show that the Dirac brackets can be obtained in a similar way.
NONLINEAR GRAVITON AS A LIMIT OF sl(N;C) CHIRAL FIELDS AS N→∞
Authors: PRZANOWSKI MACIEJ , FORMAŃSKI SEBASTIAN , TURRUBIATES FRANCISCO J.
Published: September 2003

An example of a sequence of the sl(N;C) chiral fields, for N≥2, tending to the complex heavenly metric (nonlinear graviton) of the type [4]× [-] when N→∞ is given.
TUNNELING IN A COSMOLOGICAL MODEL WITH VIOLATION OF STRONG ENERGY CONDITION
Authors: JAFARIZADEH M. A. , DARABI F. , REZAEI-AGHDAM A. , RASTEGAR A. R.
Published: September 2003

The tunneling rate, with exact prefactor, is calculated to first order in ℏ for a closed FRW universe filled with perfect fluid violating the strong energy condition. The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru–Kleinert path integral.
QUANTUM PLANCK SIZE BLACK HOLE STATES WITHOUT A HORIZON
Authors: OBREGÓN O. , RYAN M. P.
Published: September 2003

A minisuperspace method is used to define a Wheeler–DeWitt equation. By imposing coordinate conditions, the space-like coordinate r is chosen as the foliation parameter. This procedure makes it possible to find "quantum black hole" states. These turn out to be naked singularities, quantum Planck size states without a horizon.
On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency
Authors: Mandal Swapan
Published: September 2003

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.
A Trilinear Three-Body Problem
Authors: Lodge G. , Walsh J. A. , Kramer M.
Published: September 2003

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton's inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful mathematics involved in the study of the three-body problem.
A New Criterion for Chaos Synchronization Using Linear State Feedback Control
Authors: Jiang Guo-Ping , Chen Guanrong , Tang Wallace Kit-Sang
Published: September 2003

This paper studies chaos synchronization between two coupled chaotic systems using linear state feedback control. A new, simple and yet easily applicable criterion is derived for chaos synchronization based on the Lyapunov stability theory and the Linear Quadratic Optimal Control theory. This criterion is given in terms of some simple algebraic inequalities established by the Gerschgorin theorem, and it is easily applicable to a large class of chaotic systems. As an example, the familiar Chua's circuit is simulated for demonstration.
Some New Trajectory Patterns and Periodic Behaviors of Unstable Second-Order Digital Filter with Two's Complement Arithmetic
Authors: Ling Wing-Kuen , Tam Kwong-Shum
Published: September 2003

This Letter shows some counter-intuitive simulation results that for some filter parameters in the extended boundaries of the stability triangle, the state vector will converge to a periodic orbit after some iterations, no matter what the initial conditions. Also, a new pattern, which looks like a rotated letter "X", is found. The center of the rotated letter is located at the origin and the slopes of the "straight lines" of the rotated letter are equal to the values of the pole locations.
Some Analytical Criteria for Local Activity of Three-Port CNN with Four State Variables: Analysis and Applications
Authors: Min Lequan , Wang Jingtao , Dong Xisong , Chen Guanrong
Published: September 2003

This paper presents some analytical criteria for local activity principle in reaction–diffusion Cellular Nonlinear Network (CNN) cells [Chua, 1997, 1999] that have four local state variables with three ports. As a first application, a cellular nonlinear network model of tumor growth and immune surveillance against cancer (GISAC) is discussed, which has cells defined by the Lefever–Erneaux equations, representing the densities of alive and dead cancer cells, as well as the number of free and bound cytotoxic cells, per unit volume. Bifurcation diagrams of the GISAC CNN provide possible explanations for the mechanism of cancer diffusion, control, and elimination. Numerical simulations show that oscillatory patterns and convergent patterns (representing cancer diffusion and elimination, respectively) may emerge if selected cell parameters are located nearby or on the edge of the chaos domain. As a second application, a smoothed Chua's oscillator circuit (SCC) CNN with three ports is studied, for which the original prototype was introduced by Chua as a dual-layer two-dimensional reaction–diffusion CNN with three state variables and two ports. Bifurcation diagrams of the SCC CNN are computed, which only demonstrate active unstable domains and edges of chaos. Numerical simulations show that evolution of patterns of the state variables of the SCC CNN can exhibit divergence, periodicity, and chaos; and the second and the fourth state variables of the SCC CNNs may exhibit generalized synchronization. These results demonstrate once again Chua's assertion that a wide spectrum of complex behaviors may exist if the corresponding CNN cell parameters are chosen in or nearby the edge of chaos.
Biological Pattern Formation as a Complex Dynamic Phenomenon
Authors: Meinhardt Hans
Published: September 2003

Self-enhancement coupled with one or more antagonistic reactions is the crucial element in pattern forming reactions. Depending on the parameter, this can lead to patterns in space and/or in time which can be either extremely robust and reproducible or highly variable. Complex patterns result from a linkage of many pattern forming reactions, one pattern generates the prerequisites for the next. The support these models have obtained recently by molecular-genetic observations give rise to the hope that in the future an interplay between theory and experiment will lead to a still better understanding of this central issue.

Free from functional constraints, the diversity of patterns on the shells of mollusks provide a rich source to study the properties of dynamic systems in general. Everyday, we are confronted by systems that have an inherent tendency to change. The weather, the stock market, or the economic situation are examples in which self-enhancing and antagonistic processes also play a decisive role. The shell patterns are sufficiently complex to be a challenge but also sufficiently simple to be accessible to modeling. Their one-dimensional character and the preservation of the history of their formation provide unusual help for deciphering these patterns. They illustrate the range of behavior that can be generated by modifications of a basic mechanism. They can be regarded as a natural exercise book to study dynamic systems.
Continuous-Time System Identification for Linear and Nonlinear Systems Using Wavelet Decompositions
Authors: Coca D. , Billings S. A.
Published: September 2003

A new approach for estimating linear and nonlinear continuous-time models directly from noisy observations is introduced using wavelet decompositions. Results using both simulated and experimental data are included to demonstrate the performance of the new algorithm.
Generating Chaotic Secure Sequences with Desired Statistical Properties and High Security
Authors: Hong Zhou , Xieting Ling
Published: September 2003

This work proposes a class of one-dimensional analogue chaotic signals which have perfect statistical properties. A non-invertible transformation is introduced to generate a class of binary (symbolic) chaotic sequences with desired distribution function and correlation function. These binary chaotic secure sequences are proven to have near-ideal linear complexity and infinite large discrete correlation dimension, thus they cannot be reconstructed by linear-feedback shift-register (LFSR) techniques or nonlinear dynamics (NLD) forecasting in finite order.
Turbulent Fronts and Self-Fractalizing Ornaments Generated by An Interface Dynamics Equation
Authors: Frankel Michael L.
Published: September 2003

We present results of numerical experimentation with a 2-D version of an equation of surface dynamics that has been derived earlier in the context of flame fronts [Frankel & Sivashinsky, 1987, 1988] and solid-liquid interfaces [Frankel, 1988]. Our observations confirm qualitative predictions of Frankel & Sivashinsky [1987, 1988]: the curves develop chaotic cellular pattern and accelerate while imbedding is sustained. However, if we allow self-intersections, in a different range of parameters the equation gives birth to remarkably complex and beautiful fractal-like structures either entirely chaotic or preserving any symmetry if inherited from the initial configuration. This accumulation of complexity is also manifested in exponential growth of the length while diameter of the set increases linearly which results in increasingly dense covering of the plane. Based on these observations we introduce concepts of self-fractalizing family and asymptotic fractal dimension, which turns out to be equal to two.
Homoclinic Orbits in the Complex Domain
Authors: Lazutkin V. F. , Simó C.
Published: September 2003

We consider the standard map, as a paradigm of area preserving map, when the variables are taken as complex. We study how to detect the complex homoclinic points, which cannot dissappear under a homoclinic tangency. This seems a promising tool to understand the stochastic zones of area preserving maps. The paper is mainly phenomenological and includes theoretical support to the observed phenomena. Several conjectures are stated.
A Causal Bifurcation Sequence Producing a Chaotic Transient Regime
Authors: Foster E. A. D.
Published: September 2003

An organized sequence of codimension-1 bifurcations is investigated. This bifurcation sequence is shown to be generic for a class of noninvertible scalar maps containing symmetry, and is believed to occur commonly in both discrete and continuous dynamical systems.

Particular dynamics are specified initially, in which chaotic sets with symmetry evolve from attracting to transients and back to attracting. The required dynamics limit the bifurcation structures possible, which in turn constrain the functional form of the dynamical system. The canonical scalar map producing these dynamics is determined to be quintic and odd symmetric. Analysis includes a discussion of the structure of the chaotic transient regime, description of the bifurcation sequence corresponding to full dynamics, and a complete classification of bifurcation sequences producing associated partial dynamics.
Positive Topological Entropy of Chua's Circuit: A Computer Assisted Proof
Authors: Galias Zbigniew
Published: September 2003

In this paper we describe a technique for proving that a particular system is chaotic in the topological sense, i.e. that it has positive topological entropy. This technique combines existence results based on the fixed point index theory and computer-assisted computations, necessary to verify the assumptions of the existence theorem. First we present an existence theorem for periodic points of maps, which could be appropriately homotoped with the deformed horseshoe map. As an example we consider Chua's circuit. We prove the existence of infinitely many periodic points of Poincaré map associated with Chua's Circuit. We also show how to use this result to prove that the topological entropy of the Poincaré map and also of the continuous system is positive.
On Control of Coupled Map Lattices: Using Local Dynamics to Predict Controllability
Authors: Mondragón Raúl J. , Arrowsmith David K.
Published: September 2003

We consider the problem of achieving global stabilisation, using local, non-interacting control of a coupled map lattice at the same unstable fixed point on each site. In particular, a probabilistic model is described for the transition from full controllability to partial controllability as the coupling parameter is increased from zero. The phase transition aspect of this change in the controllability behaviour is recovered by using a statistical model derived from the coupling map. We exemplify our approach by considering coupled map lattices with logistic and Arn'old circle map dynamics. Numerical experiments detecting the phase transition are compared with use of the model developed in this letter.
Using Surrogate Data Analysis for Unmasking Chaotic Communication Systems
Authors: Parlitz U. , Kocarev L.
Published: September 2003

Synchronization-based communication systems are presented using hyperchaotic attractors with Lyapunov dimensions DL = 10.02 and DL = 100.02. The transmitted signal containing the encoded message is subject to surrogate data tests in order to unmask and identify the transmission of informations. Using moderate data sets (16K samples) the tests are able to detect the chaotic carrier in the case of the attractor with DL = 10.02 but not for DL = 100.02. These results thus indicate limits for both, the privacy of chaotic communication systems and surrogate data tests.
The Parameter Space Structure of the Kicked Logistic Map and Its Stability
Authors: Baptista M. S. , Caldas I. L.
Published: September 2003

In this paper, we analyzed the three-dimension parameter space of the Kicked Logistic Map (KLM), which is the Logistic Map perturbed by periodic kicks with constant amplitude. In this space parameter, diagrams are numerically determined, identifying the regions with finite attractors and their topology. For the identified periodic regions, isoperiodic diagrams are also computed. Examples of these diagrams are presented for fixed kick periods. Dynamical properties of the KLM are characterized by the forms observed in these diagrams. Furthermore, the considered map has different basins of attraction. Thus, for the kick period t = 2, an analytical analysis shows the coexistence of two basins of attraction. In addition, for this kick period, a stability diagram is presented for the period-two orbits, without iterating the KLM, reproducing the corresponding regions in the isoperiodic diagrams. Lastly, the coexistence of two basins, one for a periodic and another for a chaotic attractor, causes, in critical regions of the parameter space, the appearance of a type of crisis named transfer crisis.
Bifurcation of Homoclinic Structures.
Authors: Gerling Jürgen , Jürgens Hartmut , Peitgen Heinz-Otto
Published: September 2003

This paper is a continuation of Gerling et al. [1997] and investigates the periodic structure of a specific area-preserving homeomorphism which is generated by the finite difference approximation for a nonlinear boundary value problem. Moreover, these and prior results are extended to further approximation schemes like collocation and finite elements.
Numerical Methods for Steady State/Hopf Mode Interactions
Authors: Amdjadi F. , Aston P. J.
Published: September 2003

Numerical methods for dealing with steady state/Hopf mode interactions using extended systems are considered. In particular, it is shown that such a mode interaction corresponds to a symmetry breaking bifurcation of a Hopf extended system as well as a Hopf bifurcation of a symmetry breaking extended system. Non-degeneracy conditions associated with these bifurcations are derived and interpreted in the context of the mode interaction. The alternative approach of using a single test function instead of a full extended system is considered in detail in one of the cases. Numerical results for a two-parameter version of the Kuramoto–Sivashinsky equation are presented to illustrate the theory.
Mixed Strategy Global Sub-Optimal Feedback Control for Chaotic Systems
Authors: Lee H. W. J. , Paskota M. , Teo K. L.
Published: September 2003

How to perform targeting of chaotic systems in a global sense is an important question. In this paper, we address this problem by introducing a mixed strategy global sub-optimal feedback control scheme. The idea is to partition the state space into 2 parts, namely, the target region and its complement. The proposed controller will take different forms depending on which partition of the state space the system is in. Simulations are also provided to illustrate the proposed scheme.
Impulsive Control and Synchronization of Nonlinear Dynamical Systems and Application to Secure Communication
Authors: Yang Tao , Chua Leon O.
Published: September 2003

Impulsive control is a newly developed control theory which is based on the theory of impulsive differential equations. In this paper, we stabilize nonlinear dynamical systems using impulsive control. Based on the theory of impulsive differential equations, we present several theorems on the stability of impulsive control systems. An estimation of the upper bound of the impulse interval is given for the purpose of asymptotically controlling the nonlinear dynamical system to the origin by using impulsive control laws. In this paper, impulsive synchronization of two nonlinear dynamical systems is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two nonlinear systems by using synchronization impulses. The robustness of impulsive synchronization to additive channel noise and parameter mismatch is also studied. We conclude that impulsive synchronization is more robust than continuous synchronization. Combining both conventional cryptographic method and impulsive synchronization of chaotic systems, we propose a new chaotic communication scheme. Computer simulation results based on Chua's oscillators are given.
Master-Slave Synchronization Using Dynamic Output Feedback
Authors: Suykens J. A. K. , Curran P. F. , Chua L. O.
Published: September 2003

A method of linear dynamic output feedback for master-slave synchronization of two identical Lur'e systems is introduced. In this scheme, synchronization is obtained using one or at least fewer measurement signals and control signals than the number of state variables of the Lur'e system. A sufficient condition for global asymptotic stability of the error system is derived from a quadratic Lyapunov function and is expressed as a matrix inequality. The dynamic controller is designed by solving a constrained nonlinear optimization problem. The method is demonstrated on Chua's circuit and a hyperchaotic circuit consisting of 2-double scroll cells.
Gradient Control of Hènon Map Dynamics
Authors: Guzenko Peter Yu. , Fradkov Alexander L.
Published: September 2003

The paper is devoted to gradient control of the Hènon map — a simple two-dimensional discrete system with complex dynamics. Some gradient-based algorithms are suggested for stabilizing fixed point and model-reference control. Some sufficient system stability conditions are obtained and discussed. Simulation results demonstrating the performance of the suggested algorithms also included for the purpose of illustration.
Chaotic Motion of a Nonhomogeneous Torsional Pendulum
Authors: Yeh Jiin-Po
Published: September 2003

In this paper, the nonlinear oscillations of a nonhomogeneous torsional pendulum are investigated. Chaotic motions are shown to exist in both damped systems with two-well potential and undamped systems with one-well or two-well potential. Autocorrelations of the Poincaré mappings of the motion are presented and shown to be another useful tool to judge whether the system is chaotic. The total energy of the torsional pendulum is explored as well and it is conjectured that the irregularity of the total energy is probably one of the important factors which cause chaos. Lyapunov exponents are used as an indication of chaos in this paper. For systems with two-well potential, the phase-plane trajectories are found to stay in one well if the motion is regular, but jump from one well to another if the motion is chaotic. Making the initial conditions near the local minimum of the two-well potential is proved to be successful in preventing chaos from happening in the undamped systems.
Noise Reduction of Chaotic Systems by Kalman Filtering and by Shadowing
Authors: Walker David M. , Mees Alistair I.
Published: September 2003

We investigate two techniques for filtering signals from noisy nonlinear systems. Both the dynamics and the observed signals may be subject to noise. The first technique is a modified Kalman filter which accounts for the noise-amplification properties of chaotic systems and has less tendency to diverge than the usual Kalman filter. The second is the noise-reduction algorithm of Hammel, based on the concept of shadowing from dynamical systems theory.
Order Function Theory of Macroscopic Phase-Locking in Globally and Weakly Coupled Limit-Cycle Oscillators
Authors: Daido Hiroaki
Published: September 2003

Macroscopic phase-locking in large populations of coupled nonlinear oscillators is an interesting phenomenon analogous to collective behaviors of conventional cooperative systems, being paid increasing attention in diverse fields of science. The behavior of such populations is known to be well described by what is called phase models, provided that both mutual interactions among oscillators and the dispersion of their intrinsic frequencies are comparatively weak. Here reviewed is one of recent developments in the study of macroscopic phase-locking based on phase models, which is the order function theory enabling us to understand and analyze that phenomenon in a general way for such populations that every element is coupled to all the other. With this theory, generic features of macroscopic phase-locking under such coupling will be clarified, in particular, as to scaling behaviors at the onset of macroscopic phase locking.
New Characteristic Relations in Type-II and III Intermittency
Authors: Kim M. O. , Lee Hoyun , Kim Chil-Min , Pang Hyun-Soo , Lee Eok-Kyun , Kwon O. J.
Published: September 2003

We obtained new characteristic relations in Type-II and III intermittencies according to the reinjection probability distribution. When the reinjection probability distribution is fixed at the lower bound of reinjection, the critical exponents are -1, as is well known. However when the reinjection probability distribution is uniform, the critical exponent is -1/2, and when it is of form [Formula: see text], -3/4. On the other hand, if the square root of Δ, which represents the lower bound of reinjection, is much smaller than the control parameter ∊, i.e. ∊ ≫ Δ1/2, critical exponent is always -1, independent of the reinjection probability distribution. Those critical exponents are confirmed by numerical simulation study.
Low Voltage Bifurcations in a Diode Resonator
Authors: Kim Youngtae , Shin Jong Cheol , Kwun Sook-Il
Published: September 2003

We have observed an interesting bifurcation sequence at very low driving voltages applied to a diode resonator. As the driving voltage increases, an ordinary period-doubling bifurcation appears. Further increase of the driving voltage results in a reverse period-doubling bifurcation and a sudden jump of an amplitude of the current oscillation of the diode. The experimental results were compared with the results of numerical simulations of the equivalent circuit of the diode resonator and they were in good agreement. This suggests that these low-voltage bifurcations are due to nonlinearity of the capacitance and current of the diode to the applied voltage. A simple one-dimensional map explaining these low-voltage bifurcations of the diode resonator is introduced and its properties are discussed.
Synchrony and Clustering in Two and Three Synaptically Coupled Hodgkin–Huxley Neurons with a Time Delay
Authors: Lee S. G. , Kim S. , Kook H.
Published: September 2003

Synchrony and clustering in phase dynamics of two and three Hodgkin–Huxley neurons coupled globally by excitatory synapses with a time delay have been studied by numerical simulations and bifurcation analysis. In particular, we have obtained phase diagrams for the synchronous state and various cluster states in the parameter space of the synaptic coupling strength, G syn , and the synaptic time delay, τd, by computing the phase shifts of action potential spikes. In the weak coupling limit the computed phase diagrams are found to be consistent with the results of phase model analysis. The bifurcation analysis shows the phase model predictions break down at G syn ~ 0.3 and new complex phase dynamics appear. For all numbers of neurons explored, the critical time delay at which the nature of synaptic coupling changes completely is found to be typically about 2–4 msec, which may have some implications in modeling cortical dynamics.