bluuebunny/crossref_metadata_2025 huggingface dataset:
FINITE TEMPERATURE RESULTS FROM CONSTRAINED FERMIONIZATION IN THE 2-D SPIN 1/2 HEISENBERG ANTIFERROMAGNET I: THE NÉEL PHASE
Authors: DI STASIO M. , TAGLIACOZZO A. , ERCOLESSI E. , MORANDI G.
Published: November 2004

The antiferromagnetic saddle point is studied up to one-loop corrections, including, within the same approximation, the constraint of single site occupancy in the fermionization procedure, at all temperatures. The resulting spin wave spectrum and zero point fluctuations are the same as those of the spin wave theory. The effect of the constraint on the temperature dependence of the specific heat is discussed.
CURRENTS IN THE LOWEST LANDAU LEVEL FIELD THEORY WITH e–e INTERACTIONS
Authors: RAJARAMAN R.
Published: November 2004

We obtain expressions for the electric current in the Lowest Landau Level field theory in the presence of a general (external as well as inter-particle) interaction. This is done in the constrained Lagrangian formulation and is an extension of results obtained by Martinez and Stone for the external force case. However, we work directly with nonlocal field equations rather than convert the Lagrangian into a local one and use Noether's theorem.
HOPPING MAGNETOTRANSPORT IN THE δ-DOPING LAYER
Authors: Koch F.
Published: November 2004

We review the observations on hopping transport in planar arrays of Si donor atoms in GaAs epitaxial layers grown by molecular beam epitaxy. It is shown that properly designed δ-doping layers permit one to unambigously identify interference effects that result from the coherent superposition of the tunneling amplitudes along alternative paths in the plane. Magnetic flux through the area generated by the paths destroys the interference and leads to negative magnetoresistance. We discuss the observed non-monotonic variation of the resistance.
AN EMPIRICAL RELATION BETWEEN MAGNETORESISTANCE AND HALL COEFFICIENT IN INSULATING n-CdSe
Authors: Sarachik M.P. , Zhang Youzhu , Kam Irene
Published: November 2004

We review results obtained for the temperature- and field-dependence of the magnetoresistance and the Hall coefficient of n-type CdSe:In. Based on measurements between 0.05K and 4.2K, an empirical relation valid in magnetic fields between 3T and 9T is proposed between the transverse and longitudinal resistivities, given by ρxy=KHρxx1/2.
1/f NOISE NEAR THE METAL-INSULATOR TRANSITION
Authors: Cohen Oded , Ovadyahu Zvi
Published: November 2004

The 1/f noise level in polycrystalline indium oxide thin films and of zinc oxide accumulation layers is found to be much higher than that usually observed in metals. A systematic study of the flicker noise properties in these systems reveals a correlation between the 1/f noise magnitude and the proximity of the system to the insulating phase. In fact, the noise appears to increase dramatically close to the Anderson transition but when the average transport properties exhibited by the system are still diffusive. For static disorder that exceeds the critical value characterized by KFl≃1 the system exhibits insulating behavior and the noise level saturates at a rather high, but disorder independent value. The similarity of these findings to the behavior of the magnetic-field-induced Conductance Fluctuations in this system will be pointed out to suggest a common physical origin. This leads to the prediction of high levels of 1/f in all electronic systems that are close to the metal-insulator transition.
Hopping Conduction Near the Metal-Insulator Transition in CdMnTe:In and Evidence for a Magnetic Hard Gap in the Density of States
Authors: Terry I. , Penney T. , Molnár S. von , Becla P.
Published: November 2004

A series of resistivity curves is obtained as a function carrier concentration in just one sample of the dilute magnetic persistent photoconductor Cd0.91Mn0.09Te:In. The measurements, made at carrier concentrations approaching the metal-insulator transition, reveal a cross-over from an exp(To/T)1/2 dependence to an exp(EH/T) form when lowering temperature. The exp(To/T)1/2 dependence is characteristic of variable range hopping in the presence of Coulomb interactions, while the energy EH in the activated form is associated with a hard gap in the density of states that is magnetic in origin. All the data are shown to scale onto a single curve. The localization length. ξ, is found to have the same critical dependence on carrier concentration as that of the measured dielectric constant, κ, when approaching the metal-insulator transition. The temperature dependence of the resistivity is interpreted in terms of the orientation of Mn spins by carriers due to the s-d exchange interaction (the formation of magnetic polarons). This model can also account for the large positive and negative magnetoresistance observed in Cd0.91Mn0.09Te:In at low temperatures.
OPTICAL PHASE RELAXATION IN DISORDERED SEMICONDUCTORS DUE TO ELECTRON-PHONON COUPLING
Authors: HEUCKEROTH V. , BENNHARDT D. , THOMAS P. , VAUPEL H.
Published: November 2004

Optical phase coherence can be destroyed by various interaction mechanisms, including scattering by static disorder, electron-phonon interaction and interaction among the optical excitations. The electron-phonon interaction strongly depends on the nature of the electronic states, which in turn is determined by the static disorder. It also gives rise to hopping and phonon-induced delocalization, i.e. to transport. However, there is no one-to-one correspondence between transport processes and dephasing processes in general. Only for strongly localized states can the dephasing rate be identified with the hopping rate. A general formulation of the problem is given and illustrated in terms of a simple model system.
POLARIZATION SPECTROSCOPY OF ns2 IMPURITY IONS IN ALKALI HALIDES
Authors: ZAZUBOVICH SVETLANA
Published: November 2004

The luminescence of the alkali halides doped with ns2 ions is studied in a wide temperature region by the methods of time-resolved polarization spectroscopy with the use of magnetic and electric fields. It is established that the structure and properties of relaxed excited states (RES) of all the centers investigated may be adequately described in terms of a theory which considers a strong Jahn-Teller effect as the main interaction in the RES. Very interesting effects and processes are also observed, which are caused by some weaker interactions: by spin-orbit, hyperfine and vibronic interactions that mix different excited states of the center; by the influence of the defect associated with an ns2 ion, etc. This paper is based mainly on the experimental results obtained by the author and her co-workers during the last 15 years.
HYDROGEN IN CRYSTALLINE SEMICONDUCTORS: PART II–III–V COMPOUNDS
Authors: PEARTON S.J.
Published: November 2004

The properties of hydrogen in III–V semiconductors are reviewed. Atomic hydrogen is found to passivate the electrical activity of shallow donor and acceptor dopants in virtually all III–V materials, including GaAs, Alx Ga1−x As, InP, InGaAs, GaP, InAs, GaSb, InGaP, AlInAs and AlGaAsSb. The passivation is due to the formation of neutral dopant-hydrogen complexes, with hydrogen occupying a bond-centered position in p-type semiconductors and an anti-bonding site in n-type materials. The dopants are reactivated by annealing at ≤400° C. The neutral hydrogen-dopant complexes have characteristic vibrational bands, around 2000cm−1 for stretching modes and 800cm−1 for wagging modes. Deep levels such as EL2, DX and metallic impurities are also passivated by hydrogen. The diffusivity of hydrogen is high in III–V semiconductors and unintentional incorporation can occur during epitaxial growth, annealing in H2, dry etching, water boiling, wet etching or chemical vapor deposition processes, Surface passivation by (NH4)xS or NH3 plasma treatment is also effective in lowering surface recombination velocities in many III-V semiconductors.
DLTS AS A LOCAL PROBE OF CONCENTRATION AND DEPTH OF TRAP LEVELS
Authors: NÁDAŽDY V. , THURZO I.
Published: November 2004

Complementarity of the capacitance and charge deep level transient spectroscopy (DLTS) is the idea which led us to an advanced method for profiling trap levels in semiconductors. This unifying approach to the space-charge spectroscopy, on grounds of applying the small-amplitude-filling pulse mode and evaluating the trapped charge balance, allows one to implement it in practice while using currently available instrumentation. A simple formalism is sufficient to obtain the demanded trap level depth. The usefulness of this method is demonstrated on bulk traps found in two different metal-insulator-semiconductor (MIS) capacitors. We propose also a new experimental technique providing the option of a direct determination of the trap depth from a single temperature scan. In addition, we found an expression for the relative detection sensitivity of the capacitance DLTS and justified quantitatively the earlier reported improved relative sensitivity of the charge transient spectroscopy.
THEORY OF CHEMISORPTION ON METAL SURFACES AT FINITE SUBMONOLAYER COVERAGES
Authors: TARANKO EWA , TARANKO RYSZARD
Published: November 2004

A chemisorption theory of hydrogen-like atoms on metal surfaces at submonolayer coverages, based on the generalized Anderson-Newns Hamiltonian and Green’s Function formalism, is presented. A very general Hamiltonian with the terms proportional to three and four adion number operators was derived. The utility of this Hamiltonian in the context of the lattice gas model of the chemisorbed layer with non-additive lateral interactions is discussed. The coverage-dependence of the electronic structure of chemisorbed adlayer is investigated. It is shown, that the adatom ionization level’s self-energy is evidently coverage dependent as opposite to this one corresponding to the affinity level.
EFFECTIVE THEORY OF BOSONIC SUPERFLUIDS
Authors: SCHAKEL ADRIAAN M.J.
Published: November 2004

We discuss the effective theory of a bosonic superfluid whose microscopic behavior is described by a nonrelativistic, weak-coupling Φ4 theory in the phase with broken particle number symmetry, both at zero temperature and in the vicinity of the phase transition. In the zero-temperature regime, the theory is governed by the gapless Goldstone mode resulting from the broken .symmetry. Although this mode is gapless, the effective theory turns out to be Gallilei invariant. The regime just below the critical temperature is approached in a high-temperature expansion which is shown to be consistent with the weak-coupling assumption of the theory. We calculate the critical temperature, the co-efficients of the Landau theory, and the finite-temperature sound velocity. A comparison with BCS theory is given.
HIERARCHICAL PHASE TRANSITIONS AND VIBRATIONAL MODES LOCALISATION IN QUASICRYSTALS
Authors: JANOT CHRISTIAN
Published: November 2004

The dynamical response function S (q, ω) measured around Bragg reflections in quasicrystals exhibits phonon-like behavior in the long-wavelength limit, but broadens and progressively smears out when the vibration frequency increases. Dynamical coherence lengths of the order of 10 Å are also determined in relation with the existence of localisation effects. This is explained by the self-similar structure of the quasicrystals which forces the vibrational modes to be essentially critical at 0° K. Phason-assisted mechanisms generate hierarchically extended modes and hierarchical phase transition as the temperature increases.
EFFECT OF ELECTROMAGNETIC FLUCTUATIONS ON ELECTRON TRANSPORT IN QUANTUM WIRES
Authors: ODINTSOV A. A. , HEKKING F. W. J.
Published: November 2004

We study electron transport through a multi-mode quantum wire with small localized potential inhomogeneities in the framework of a microscopic approach. We find that due to electromagnetic fluctuations the conductance per mode decreases below the universal value 2e2/h although it remains finite. Simultaneously, the I–V characteristic of the wire shows nonlinearity. Both effects manifest a coexistence of elastic and inelastic channels of electron transport. Quantitatively, the electromagnetic fluctuations can be characterized by an effective impedance which shows a quadratic dispersion at low frequencies, Re Z eff (ω) ∝ ω2.
DIPOLE SQUEEZING OF THE ATOM IN A TWO-ATOM SYSTEM: EFFECTS OF THE SUPERPOSITION STATES
Authors: MIR MUBEEN A.
Published: November 2004

Dipole squeezing of the atom in the presence of another atom is investigated for the one-photon and two-photon transition mechanism with the initial atoms in the two-atom squeezed state and the field in a vacuum, a coherent, or a squeezed state. For a vacuum input, the degree of squeezing is shown to depend on the photon multiplicity 'm' and the superposition angles of the atoms, θ1 and θ2. One of the quadratures of the atomic polarization is found to exhibit permanent squeezing only for some nonzero values of θ1, as well as θ2. The effect of θ2 on the dipole squeezing, however, is found to be negligible for the initial field in a coherent or a squeezed state. A comparison with the dipole squeezing of a single atom is also presented.
SCALING AND UNIVERSALITY IN POLYMER REACTION KINETICS
Authors: FRIEDMAN BARRY , O'SHAUGHNESSY BEN
Published: November 2004

This review highlights recent developments in the theory of reacting polymer solutions and melts, where reactive groups are attached to macromolecules. Reaction kinetics of this type govern the evolution of many polymerizations and have been extensively measured using photophysical techniques. Three related theoretical approaches are described and illustrated with examples: (1) simple scaling arguments, (2) renormalization group methods and (3) the self-consistent method of Wilemski and Fixman. AM three approaches predict that two distinct universality classes of reaction kinetics exist, with different scaling laws for rate constants k: mean field (MF) and diffusion-controlled (DC). Increasing chain length or time drives kinetics to one behavior or the other, depending only on the regime of polymer concentration ϕ. Dilute solutions (good solvents) obey MF kinetics because a pair of reactive groups in close proximity is unlikely to react; the mean number of collisions is very small. This is universally true, independently of the group chemistry. In melts, by contrast, reaction is very likely because many collisions occur and thus kinetics are intrinsically DC. In semi-dilute solutions, as ϕ increases from dilute towards the melt a transition occurs, from MF to DC kinetics. At the transition point k is peaked. A range of experimental studies are discussed and their findings compared with theory.
THE CAPACITANCE MODEL FOR PERSISTENT CURRENTS IN MESOSCOPIC METAL RINGS
Authors: KOPIETZ PETER
Published: November 2004

We review recent theoretical work on persistent currents in mesoscopic normal-metal rings and present a detailed discussion the generalized capacitance model.20(a) This model provides a natural explanation for the surprisingly large experimentally observed currents in the diffusive regime. We pay particular attention to the problem of screening in a thin mesoscopic ring, and argue that screening corrections to the flux-dependent part of the Hartree energy are negligible provided the condition [Formula: see text] is satisfied. Here e2/C0 is the classical charging energy for adding one electron to the system, and [Formula: see text] is the average number of energy levels within an interval of width E c below the Fermi energy µ, where E c is the Thouless energy. This condition is equivalent with (k F l)(L⊥/L)2 ≪ 1 (where l is the elastic mean free path, L is the circumference and L⊥ is the transverse thickness of the ring), and shows that the ring geometry plays an important role. In thin rings the mesoscopic persistent current is universal in precisely the same sense as the variance of the conductance.
EFFECTIVE LAGRANGIAN, CASIMIR ENERGY AND CONFORMAL FIELD THEORY DESCRIPTION OF THE QUANTUM HALL EFFECT
Authors: CRISTOFANO G. , GIULIANO D. , MAIELLA G.
Published: November 2004

By using the Girvin–MacDonald effective Lagrangian for the Hall fluid system at filling ν = 1 we are able to evaluate the ground-state energy for a cylinder of infinite length. That is done by using the topological properties of the edge vacuum in the thermodynamic limit, Ne → ∞, ν = 1 fixed,

From the vacuum energy we extract the value of the Casimir energy for both filling ν = 1 and ν = 1/m. The results obtained fix the central charge c of the underlying 2D Conformal Field Theory at c = 1.

This correspondence is further analyzed by using the bosonic realization of the Kac–Moody algebra on the edge vacuum. Then the off-diagonal long-range order of the effective theory can be seen as an equivalent description of the topological order typical of the 2D CFT.
SIMULATION OF SOLID STRUCTURE FORMATION IN AN ELECTRORHEOLOGICAL FLUID
Authors: TAO R. , JIANG QI
Published: November 2004

The temporal evolution of three-dimensional structure in an electrorheological (ER) fluid is examined by a computer simulation. A parameter B characterizing the ratio of the Brownian force to the dipolar force is introduced. For a wide range of B, the ER fluid was a rapid chain formation followed by aggregation of chains to form thick columns, which has a body-centered tetragonal (bct) lattice structure. The Peierls–Landau instability of single chains helps the formation of thick columns. If B is very small, the ER system will be trapped in some local energy-minimum state.
ELECTRIC-FIELD-INDUCED PHASE SEPARATION IN ELECTRORHEOLOGICAL FLUIDS
Authors: TANG XIN-LU , ZHU KE-QIN , GUAN E. , WU XIAO-PING
Published: November 2004

The phase separation into a high-density and a low-density phase, which occurs after a strong electric field is applied to an ER fluids, is demonstrated in terms of the Coulomb interaction energy of the system. The phase separation is manifested by two-dimensional pattern observed in the field direction by means of a pair of transparent glass (TG) electrodes. The development of phase separation with an increasing field is recorded by a computer image processing system consisting of a CCD video camera. The patterns are irregular and their characteristic sizes are determined by two-dimensional auto-correlation approach. The dependency of those patterns on external electric field is analyzed based on statistical methods. Two critical fields are presented to characterize the electric-field-induced phase separation process in the ER fluid.
PRESSURE COUPLING IN THE ELECTRICAL RESPONSE OF ELECTRO-RHEOLOGICAL VALVES
Authors: WHITTLE M. , FIROOZIAN R. , BULLOUGH W. A. , PEEL D. J.
Published: November 2004

An earlier model describing the electrical characteristics of an electrorheological (ER) valve is refined to include the effects of coupling to the pressure response. Expressions including additional linear terms in the pressure and time differential of the pressure are considered and it is found that a single term in the time derivative with a small time delay is quite a sufficient description of the data on the basis of goodness of fit.
ELECTRO-RHEOLOGICAL CATCH/CLUTCH: INERTIAL SIMULATIONS
Authors: JOHNSON A. R. , MAKIN J. , BULLOUGH W. A.
Published: November 2004

A high-speed reciprocating mechanism is described in order to provide the basis of a general investigation into the required properties of electro-rheological fluids and associated materials for use in flexible, inertial mechanisms. The dynamic model of this, when run for realistic existing machine requirements clearly illustrates the need for a fully integrated approach to high speed machinery design. The work sets quantified targets and draws attention to the need for the continuing development of improved electro-rheological fluids which will have high yield stresses with acceptable viscosities and the conditions they must operate under: high shear rates, centrifugal loadings and accelerations.
BINGHAM PLASTIC ANALYSIS OF ER VALVE FLOW
Authors: PEEL D. J. , BULLOUGH W. A.
Published: November 2004

Yield shear stresses and shear rates at a valve wall are derived from experimental results on a series of concentric cylinder valves. The fluid constitutive equation used for this purpose is that of a Bingham Plastic. Valve plates (which are such that the radial gap is small compared to its mean pitch) are taken to be parallel so far as the derivation of the flow ν's pressure ν's geometry model is concerned. A range of electrode separations from 0.5 to 1.0mm are used with flow velocities being limited to the region where the viscous pressure drop component is below that caused by the electro stress. Results show that (away from the region of low shear rates and high voltages) the wall stresses for equivalent conditions are comparable for different valves, for a range of applied field strengths and mean flow velocities. Thus, provided the hysteretic region is avoided the fluid can be treated as a Bingham continuum with some stated reservations. However, this is only applied with precision for the truly corresponding situations defined in the paper.
COMPOSITION DEPENDENCE OF THE TRANSITION TEMPERATURE AND ENERGY GAP OF SUPERCONDUCTING ALLOYS WITH NONMAGNETIC IMPURITIES
Authors: BANERJEE S. , ROY S. K.
Published: November 2004

Analytic expressions of superconducting transition temperature (T c ) and maximum energy gap (Δ0) of alloys with nonmagnetic impurities are obtained in terms of the alloy composition and the modified normal state electron density of states (DOS), assuming a Lorentzian DOS in the unalloyed state. The calculations were performed within the framework of the BCS theory.

As expected, both T c and Δ0 are modified significantly from the BCS expressions. However, the nature of change depends on whether the width of the electron DOS is greater or less than the Debye energy of the alloy.
ν-DIMENSIONAL IDEAL QUANTUM q-GAS: BOSE-EINSTEIN CONDENSATION AND λ-POINT TRANSITION
Authors: R-MONTEIRO M. , RODITI ITZHAK , RODRIGUES LIGIA M.C.S.
Published: November 2004

We consider an ideal quantum q-gas in ν spatial dimensions and energy spectrum ωiα pα Departing from the Hamiltonian H=ω[N], we study the effect of the deformation on thermodynamic functions and equation of state of that system. The virial expansion is obtained for the high temperature (or low density) regime. The critical temperature is higher than in non-deformed ideal gases. We show that Bose-Einstein condensation always exists (unless when ν/α=1) for finite q but not for q=∞. Employing numerical calculations and selecting for v/α the values 3/2, 2 and 3, we show the critical temperature as a function of q, the specific heat CV and the chemical potential µ as functions of [Formula: see text] for q=1.05 and q=4.5. CV exhibits a λ-point discontinuity in all cases, instead of the cusp singularity found in the usual ideal gas. Our results indicate that physical systems which have quantum symmetries can exhibit Bose-Einstein condensation phenomenon, the critical temperature being favored by the deformation parameter.
QUANTUM HAMILTONIANS AND SELF-ORGANISED CRITICALITY
Authors: CARDY JOHN
Published: November 2004

We consider a stochastic particle model which has been proposed to exhibit the essential features of self-organised criticality. The master equation is reformulated as a one-dimensional quantum system of interacting bosons. The hydrodynamic behavior of the system is recovered as the classical limit of the quantum system, and the problem of fluctuations, important for the critical behavior, is discussed.
SCALAR KINKS
Authors: VEGA H.J. DE , MEZINCESCU LUCA , NEPOMECHIE RAFAEL I.
Published: November 2004

We determine the excitations and S matrix of an integrable isotropic antiferromagnetic quantum spin chain of alternating spin 1/2 and spin 1. There are two types of gapless one-particle excitations: the usual spin 1/2 (“spinor”) kink, and a new spin 0 (“scalar”) kink. Remarkably, the scalar-spinor scattering is nontrivial, yet the spinor-spinor scattering is the same as for the Heisenberg chain. Moreover, there is no scalar-scalar scattering.
FUSION OF A-D-E LATTICE MODELS
Authors: ZHOU YU-KUI , PEARCE PAUL A.
Published: November 2004

Fusion hierarchies of A-D-E face models are constructed. The fused critical D, E and elliptic D models yield new solutions of the Yang-Baxter equations with bond variables on the edges of faces in addition to the spin variables on the corners. It is shown directly that the row transfer matrices of the fused models satisfy special functional equations. Intertwiners between the fused A-D-E models are constructed by fusing the cells that intertwine the elementary face weights. As an example, we calculate explicitly the fused 2×2 face weights of the 3-state Potts model associated with the D4 diagram as well as the fused intertwiner cells for the A5-D4 intertwiner. Remarkably, this 2×2 fusion yields the face weights of both the Ising model and 3-state CSOS models.
ON ALGEBRAIC DIAGONALIZATION OF THE XXZ CHAIN
Authors: MARTIN PAUL , SALEUR HUBERT
Published: November 2004

The purpose of this note is to comment on the diagonalization of the XXZ chain Hamiltonian (and others such as the Potts model), using the abstract Temperley-Lieb algebra relations, following the paper by Dan Levy1 where the idea was first developed.
THE TENSOR PRODUCT OF TENSOR OPERATORS OVER QUANTUM ALGEBRAS: SOME APPLICATIONS TO QUANTUM SPIN CHAINS
Authors: SCHEUNERT M.
Published: November 2004

The present work is a direct sequel to a recent article by the author, in which he has analysed the tensor product of tensor operators over quantum algebras. Here the results obtained there are summarized and then specialized and extended to prepare possible applications to quantum spin chains. In particular, certain invariant two-point operators are introduced (whose expectation values yield the invariant two-point correlation functions) and their multiplicative properties are derived.
QUASI-RATIONAL FUSION PRODUCTS
Authors: NAHM WERNER
Published: November 2004

Fusion is defined for arbitrary lowest weight representations of W-algebras, without assuming rationality. Explicit algorithms are given. A category of quasi-rational representations is defined and shown to be stable under fusion. Conjecturally, it may coincide with the category of representations of finite quantum dimensions.
STATISTICAL PROPERTIES OF EIGENFUNCTIONS OF RANDOM QUASI 1D ONE-PARTICLE HAMILTONIANS
Authors: FYODOROV YAN V. , MIRLIN ALEXANDER D.
Published: November 2004

The article reviews recent analytical results concerning statistical properties of eigenfunctions of random Hamiltonians with broken time reversal symmetry describing a motion of a quantum particle in a thick wire of finite length L. It is demonstrated that the problem is equivalent to the study of properties of large Random Banded Matrices in the limit of large width of the band. Matrices of this class are relevant for a number of problems in Solid State physics and in the domain of Quantum Chaos.

We find the analytical expressions for the distribution of the following quantities: i) the eigenfunction amplitude |ψ(r)|2 at given point of the sample; ii) spatial extent of the eigenfunction measured by the “inverse participation ratio” P=∫V dr|ψ(r)|4; iii) the quantity R=|ψ(r)ψ(r′)|2, points r and r′ belonging to the opposite ends of the sample. For a long sample the quantity –(ln R)/L characterizes the decay rate of a localized eigenfunction (Lyapunov exponent).

Relation with available numerical results is discussed.
MULTI-INPUT AND MULTI-OUTPUT NONLINEAR SYSTEMS: INTERCONNECTED CHUA'S CIRCUITS
Authors: DUAN ZHISHENG , WANG JINZHI , HUANG LIN
Published: November 2004

In this paper, a class of MIMO nonlinear systems are studied. Some frequency domain conditions are established for the property of dichotomy. These kinds of systems can also be viewed as a class of interconnected systems composed of SISO systems through some linear and nonlinear interconnections. A class of nonlinear input and output interconnections are presented. The corresponding condition for testing dichotomy is given. Furthermore, Chua's circuit and interconnected Chua's circuit are studied to illustrate the theoretical results.
ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF AN IMPACTING OSCILLATOR WITH TWO FENDERS
Authors: CZOLCZYNSKI KRZYSZTOF , KAPITANIAK TOMASZ
Published: November 2004

A system that consists of a damped oscillator impacting two immovable fenders has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable.
BORDER COLLISION BIFURCATION CONTROL OF CARDIAC ALTERNANS
Authors: HASSOUNEH MUNTHER A. , ABED EYAD H.
Published: November 2004

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period-doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period-doubling border collision bifurcation. No smooth period-doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in control laws that quench the bifurcation, and hence result in alternan suppression.
NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS
Authors: BEYN WOLF-JÜRGEN , HÜLS THORSTEN , ZOU YONGKUI
Published: November 2004

This paper contains a survey of numerical methods for connecting orbits in discrete dynamical systems. Special emphasis is put on degenerate cases where either the orbit loses transversality or one of its endpoints loses hyperbolicity. Numerical methods that approximate the connecting orbits by finite orbit sequences are described in detail and theoretical results on the error analysis are provided. For most of the degenerate cases we present examples and numerical results that illustrate the applicability of the methods and the validity of the error estimates.
IMPLICIT CRITERIA OF EIGENVALUE ASSIGNMENT AND TRANSVERSALITY FOR BIFURCATION CONTROL IN FOUR-DIMENSIONAL MAPS
Authors: WEN GUILIN , XU DAOLIN
Published: November 2004

In anti-control of bifurcations, it is common to create different types of bifurcations by adjusting the control parameters. For maps, the type of bifurcation is determined by the eigenvalue assignment on the unit circle at the bifurcation parameter point. Thus, an unavoidable problem in the creation of bifurcations is to desirably assign some eigenvalues at the specified locations on the unit circle, and the others inside the unit circle. However, for relatively complicated and high dimensional maps, the explicit expressions of eigenvalues are usually not available so that the implementation of the eigenvalue assignment becomes very difficult. To solve this problem, we proposed the new criteria of eigenvalue assignment without using eigenvalues. The criteria give implicit conditions to specify the eigenvalue assignments in terms of some simple algebraic equalities and inequalities associated with the elements of Jacobian matrix, i.e. eventually associated with the control parameters. Bifurcation occurs with another critical condition, the transversality condition. The computation of the transversality condition is usually nontrivial in high dimensional maps because it is related to the partial differentiation of the eigenvalues on the unit circle. We also present the implicit expression of the transversality condition in the form of the derivative of the Jacobian matrix and its eigenvectors that are computable at the bifurcation point. The proposed criteria cover most known types of bifurcations in four-dimensional maps and serve as the preferable methods for designing the critical bifurcation conditions in anti-control of bifurcations. The application to a modified Hénon map is illustrated in conjunction with the use of the delayed-feedback control and the washout-filter-aided feedback control.
NEW BOUNDED TRAVELING WAVES OF CAMASSA–HOLM EQUATION
Authors: LIU ZHENGRONG , LI QIXIU , LIN QINGMEI
Published: November 2004

In this paper, the bifurcation method of planar systems and simulation method of differential equations are employed to investigate the bounded traveling waves of the Camassa–Holm equation. Some new bounded traveling waves are found and their implicit expressions are obtained. Both qualitative and numerical results show that they possess the properties of compactons or generalized kink waves.
A TWO-DIMENSIONAL BLAST WAVE IN RELATIVISTIC MAGNETOHYDRODYNAMICS
Authors: VAN PUTTEN MAURICE H.P.M.
Published: November 2004

The blast wave produced by a star-like object in a magnetic field is studied numerically in the approximation of ideal, fully relativistic magnetohydrodynamics (MHD). Waves of this type are observed to evolve along three episodes. At early time an outgoing shock front and an ingoing rarefaction wave is established. The ingoing rarefaction wave steepens, and gives rise to dust formation in the core. The steep rarefaction wave front becomes an ingoing shock. An annular region of high magnetic pressure about the equatorial plane deforms this shock front radially, whereby it becomes prolate along the axis of symmetry. The core is subsequently refilled as this shock front converges. Subsequent collapse in the center gives rise to high pressures, familiar from the well-known converging shock problem in nonrelativistic hydrodynamics, and high densities unique to the relativistic description. The results are compared with spherical blast waves in relativistic hydrodynamics, where a similar three episodes can be found and where collapse of the interior shock at the center constitutes a fluid singularity. It remains an open question whether such fluid singularity persists in the full MHD problem.

The computations employ the covariant equations of constraint-free MHD in divergence form introduced in earlier work. The magnetic field is kept divergence free to within machine round-off error.
CHAOS-CHAOS INTERMITTENCY AND 1/f NOISE IN CHUA’S CIRCUIT
Authors: ANISHCHENKO V.S. , NEIMAN A.B. , CHUA L.O.
Published: November 2004

Statistical and dynamical properties of the “chaos-chaos” type intermittency in Chua’s circuit are studied by numerical simulation methods. It is shown that at the onset of this intermittency phenomenon, the power spectrum of the associated time series has the shape of 1/f noise. The influence of external noise and computer calculation errors on the form of the spectrum and other process characteristics are analyzed. The structure and scaling of the Poincaré map at the transition threshold are also discussed.
GROUP THEORETICAL MODE INTERACTIONS WITH DIFFERENT SYMMETRIES
Authors: GATERMANN KARIN , WERNER BODO
Published: November 2004

In two-parameter systems two symmetry breaking bifurcation points of different types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the inner-connectivity of irreducible representations of supergroup and subgroups. Colored pictures of examples are included.
A NEW STRANGE ATTRACTOR IN THREE DIMENSIONS
Authors: BEDDING STEPHEN
Published: November 2004

We investigate a set of three simple difference equations in three variables with one free parameter.

As the parameter increases from zero, iteration of the equations results in a bifurcation pathway leading to chaos and a strange attractor. The attractor is of the twisted band variety, reminiscent of that of Rössler, though it differs from the latter by the fact that it arises from iteration of a set of pure difference equations, as opposed to a numerical algorithm applied to differential equations.
ASYMPTOTIC POWER SPECTRUM ANALYSIS OF CHAOTIC BEHAVIOR IN FLUIDIZED BEDS
Authors: DING JIANMIN , TAM SHIU-WING
Published: November 2004

The nonlinear behavior of fluidized beds is analyzed quantitatively using an asymptotic power spectrum method. A model based on kinetic theory is used to compute the voidage signals in a two-dimensional bubbling fluidized bed with a fluidization condition of U/Umf=4, where U is the fluidizing velocity and Umf is the minimum fluidizing velocity. The data for power versus frequency in the asymptotic frequency regime are shown to obey a power-law falloff. This means that the bubbling fluidization under such a fluidization condition cannot be a low-dimensional strange attractor. Pressure fluctuation data, obtained from a three-dimensional bubbling fluidized bed, are also analyzed and clearly show the power-law falloff. This is consistent with previous findings in that the correlation dimension for these data cannot be small (i.e., 2 or 3). The differences between our findings and others are discussed.
FRACTIONAL HARMONIC SYNCHRONIZATION IN THE DUFFING-RAYLEIGH DIFFERENTIAL EQUATION
Authors: QRIOUET M. , MIRA C.
Published: November 2004

The considered Duffing-Rayleigh equation is submitted to an external periodic driving force. Bifurcation properties of three families of fractional harmonic (or ultra-subharmonic) solutions are analysed. Notions of irreducible harmonics and reducible harmonics are introduced. They correspond to different properties of the associated periodic solutions.
STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS
Authors: ANISHCHENKO V.S. , SAFONOVA M.A. , CHUA L.O.
Published: November 2004

Using numerical simulation, we establish the possibility of realizing the stochastic resonance (SR) phenomenon in Chua’s circuit when it is excited by either an amplitude-modulated or a frequency-modulated signal. It is shown that the application of a frequency-modulated signal to a Chua’s circuit operating in a regime of dynamical intermittency is preferable over an amplitude-modulated signal from the point of view of minimizing the signal distortion and maximizing the signal-to-noise ratio (SNR).
CONTROLLING CHAOS IN CHUA’S CIRCUIT VIA SAMPLED INPUTS
Authors: DEDIEU HERVÉ , OGORZAŁEK MACIEJ
Published: November 2004

We consider a class of autonomous, continuous time, chaotic dynamical systems the state equations of which can be represented in so-called Lur’e form. In particular we consider Chua’s circuit which is a paradigmatic chaotic system belonging to this class. It is shown that the dynamic behavior of such a system can be influenced in such a way as to obtain out of chaotic behavior a desired periodic orbit corresponding to an unstable periodic trajectory which exists in the system.

This kind of control can be achieved via injection of a single continuous time signal representing the output of the system associated with an unstable periodic orbit embedded in the chaotic attractor.

Further, we investigate the case when this signal is sampled, i.e. we supply to the system the control signal at discrete time moments only. We show via extensive numerical simulations that effective control can be achieved with a low number of samples only. Control proves to be very robust. Despite the presence of scaling of system variables and noise of a significant level introduced by signal quantization and offset, we were still able to control the chosen orbit (although with growing noise level the orbit becomes more and more distorted but maintains the same periodicity). We present a variety of simulation results to support this claim. First laboratory confirmations are also included.

We claim that this method, proved to be functional for controlling chaos in Chua’s circuit, is also applicable to any chaotic system of the Lur’e type with a single nonlinearity.
OPTIMAL CONTROL OF CHAOTIC SYSTEMS
Authors: CHEN GUANRONG
Published: November 2004

A conventional optimal control approach to controlling chaotic systems by minimum parameter perturbation sequences, in the sense of “total control energy,” is suggested in this short letter.
CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS
Authors: SHIL’NIKOV LEONID P.
Published: November 2004

Mathematical problems arising from the study of complex dynamics in Chua’s circuit are discussed. An explanation of the extreme complexity of the structure of attractors of Chua’s circuit is given. This explanation is based upon recent results on systems with homoclinic tangencies. A number of new dynamical phenomena is predicted for those generalizations of Chua’s circuits which are described by multidimensional systems of ordinary differential equations.
NONLINEAR MODELING OF COMPLEX MECHANICAL SYSTEMS
Authors: LESSER MARTIN
Published: November 2004

This article provides an introduction to a technique for formulating nonlinear models of mechanical systems composed of interconnected and constrained rigid body systems such as those encountered in vehicle technology, biomechanics, spacecraft design and robotics. The approach is based on an algorithm developed by Kane to treat nonholonomic systems, for example systems with rolling constraints. The algorithm is interpreted geometrically in terms of tangent vectors to the instantaneous configuration manifold embedded in the space of nonconstrained motions for the system. The level and style of the presentation is intended to be understood by scientifically literate readers with minimal knowledge in mechanics beyond the introductory level. Examples also show how computer algebra can be used to reduce the effort required for treating complex systems. An annotated reference list, which includes a discussion of computer software, is also provided.
PHASE-RESETTING MAP AND THE DYNAMICS OF QUASI-PERIODICALLY FORCED BIOLOGICAL OSCILLATORS
Authors: DING MINGZHOU , KELSO J.A. SCOTT
Published: November 2004

In this paper we study the dynamics of a biological oscillator forced at two incommensurate frequencies which, as our results show, can exhibit a variety of novel dynamical phenomena, including two-frequency quasi-periodicity, three-frequency quasi-periodicity, chaos and, in particular, strange nonchaotic attractors. We discuss the significance and observable signatures of these phenomena, and suggest biological systems in which these phenomena may be experimentally investigated.
COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS
Authors: ZHELEZNYAK A.L. , CHUA L.O.
Published: November 2004

Spatiotemporal dynamics of a one-dimensional cellular neural network (CNN) made of Chua’s circuits which mimics a reaction-diffusion medium is considered. An approach is presented to analyse the properties of this reaction-diffusion CNN through the characteristics of the attractors of an associated infinite-dimensional dynamical system with a matrix phase space. Using this approach, the spatiotemporal correlation dimension of the CNN’s spatiotemporal patterns is computed over various ranges of the diffusion coupling parameter, length of the chain, and initial conditions. It is shown that in a finite-dimensional projection of the matrix phase space of the CNN, both low- and high-dimensional attractors corresponding to different initial conditions coexist.
MATHEMATICAL MODEL OF HUMAN GESTATION AND PARTURITION: IMPLICATIONS FOR EARLY DIAGNOSIS OF PREMATURITY AND POSTMATURITY
Authors: SORNETTE D. , FERRÉ F. , PAPIERNIK E.
Published: November 2004

Knowledge of precursors and predictors of human parturition would be important both for our understanding of the controlling mechanisms and for practical use in the detection and diagnosis of various abnormalities of the birth process. They involve a multitude of genetic, metabolic, nutritional, hormonal and environmental factors. Present research is however hindered by the lack of a clear recognized correlation between the time evolution of these various variables and the initiation of parturition. Here, we propose a coherent logical framework which allows us to rationalize the various laboratory and clinical observations on maturation, the triggering mechanisms of parturition, the existence of various abnormal patterns as well as the effect of external stimuli of various kinds. Within the proposed mathematical model, parturition is seen as a ”critical” instability or phase transition from a state of quietness, characterized by a weak incoherent activity of the uterus in its various parts as a function of time (state of activity of many small incoherent intermittent oscillators), to a state of globally coherent contractions where the uterus functions as a single macroscopic oscillator. Our approach gives a number of new predictions and suggests a strategy for future research and clinical studies, which present interesting potentials for improvements in predicting methods and in describing various abnormal prenatal situations.
APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM I: OBSERVING TRAJECTORIES IN STATE SPACE
Authors: HENG H. , DOERNER R. , HÜBINGER B. , MARTIENSSEN W.
Published: November 2004

A phenomenological introduction to concepts of nonlinear dynamics is given. A driven pendulum is used as an appropriate model to demonstrate characteristic features of the dynamics of nonlinear systems. The mechanical and electronic setup of the pendulum is described and quantified in detail, and different techniques to visualize the motion in state space are discussed. Finally, a “road map” in parameter space is calculated which provides a tool for finding special scenarios by choosing appropriate driving amplitudes and frequencies.
APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM II: ANALYZING CHAOTIC MOTION
Authors: DOERNER R. , HÜBINGER B. , HENG H. , MARTIENSSEN W.
Published: November 2004

Using a driven damped pendulum as a demonstration model we illustrate some fundamental concepts of nonlinear dynamics. We find deterministic chaos in the motion of the pendulum by observing its sensitive dependence on the initial state. We calculate the corresponding Lyapunov exponents from the equation of motion. The largest exponent gives the average predictability time scale. We estimate fractal dimensions of the attractor by determining the Kaplan Yorke dimension. Further we investigate the organization of unstable periodic orbits embedded in the attractor of the pendulum.
DISCRETE RECONSTRUCTION OF STRANGE ATTRACTORS OF CHUA’S CIRCUIT
Authors: AGUIRRE LUIS A. , BILLINGS S.A.
Published: November 2004

This work is concerned with the identification of discrete nonlinear models from time series of strange attractors emerging in Chua’s circuit. The quality of the models is assessed by estimating the largest Lyapunov exponent, the correlation dimension and by comparing the geometry of the reconstructed dynamics to the original attractors. The major aim of the paper is to investigate how parameters such as the discretization period, sampling rate and the number of terms in an estimated model affect the dynamics and to determine if there is any relationship among such parameters. Conclusions in this direction are believed to be especially relevant in determining adequate model structures in identification applications. This is known to be critical in the identification of nonlinear systems.
THE WINDING-NUMBER LIMIT OF PERIOD-DOUBLING CASCADES DERIVED AS FAREY-FRACTION
Authors: ENGLISCH VOLKER , LAUTERBORN WERNER
Published: November 2004

It is shown, that the winding number w∞ at the accumulation point of a period-doubling cascade can be derived as a Farey sum from each two adjacent winding numbers wk and wk+1 of the cascade.
A COUPLED CHAOTIC SYSTEM WITH DIFFERENT TIME SCALES: POSSIBLE IMPLICATIONS OF OBSERVATIONS BY DYNAMICAL SYSTEMS
Authors: OKUDA H. , TSUDA I.
Published: November 2004

We present three curious phenomena in coupled chaotic systems with different time scales: a copy, an itinerant motion, and a “firework.” The phenomena obtained may possibly have implications on the interaction between two macroscopic systems, namely the “observing” and the “observed” systems.