bluuebunny/crossref_metadata_2025 huggingface dataset:
Defect annealing in Cu(In,Ga)Se2 heterojunction solar cells after high-energy electron irradiation
Authors: Jasenek A. , Schock H. W. , Werner J. H. , Rau U.
Published: July 2002

Cu(In,Ga)Se 2 /CdS/ZnO solar cells need at least 1018 cm−2 electrons of an energy of 1 MeV to degrade in their power conversion efficiency by more than 25%. Even after such high irradiation doses, annealing of the irradiated solar cells at temperatures between 130 and 160 °C leads to a full recovery of the device performance. Isochronal annealing experiments unveil that the annealing of the irradiation-induced defects has an activation energy of 1.05 eV.
Deliquescence of small particles
Authors: Russell Lynn M. , Ming Yi
Published: July 2002

The deliquescence of particles smaller than 100 nm in diameter from crystalline form to liquid droplets involves both solvation effects and surface energies. Here we study this phenomenon for the case of salt particles of initial dry diameters from 8 to 100 nm that are exposed to humid conditions from 45 to 95% relative humidity. With a simple thermodynamic equilibrium model for three soluble species (sodium chloride, ammonium sulfate, and a soluble organic compound), we show that the role of surface tension is to increase the relative humidity at which particles will deliquesce. For example, 15 nm dry diameter sodium chloride particles deliquesce at 83%, an 8% increase over the 75% deliquescence relative humidity for supermicron droplets and bulk solution. Many soluble species in air above 45% relative humidity are wetted with multiple layers of water molecules such that the relevant interface is that between the partially dissolved salt crystal and a saturated salt solution rather than between the dry crystal and air. Since surface tensions for this solid/liquid interface are not well known, a range of values have been used from the literature, yielding consistent results. While the existence of unstable equilibria during deliquescence of the system precludes complete experimental verification of the predicted behavior with measurements, a recent experiment suggests indirect agreement with the change in predicted deliquescence relative humidity.
Field emission from porous (100) GaP with modified morphology
Authors: Ichizli V. , Hartnagel H. L. , Mimura H. , Shimawaki H. , Yokoo K.
Published: July 2002

Morphology of n-type porous GaP samples with (100) crystal orientation was modified by postchemical etching for field-emitter application. The structures produced have uniform size and shape distribution and are found to show good emission characteristics. The mechanism of the morphology modification is explained, and a strong correlation between field-emission characteristics and postchemical etching time is shown.
Composition dependence of defect energies and band alignments in the Cu(In1−xGax)(Se1−ySy)2 alloy system
Authors: Turcu M. , Kötschau I. M. , Rau U.
Published: July 2002

The composition dependence of defect energies in polycrystalline Cu(In1−xGax)(Se1−ySy)2 chalcopyrite thin films is investigated by admittance spectroscopy of ZnO/CdS/chalcopyrite heterojunctions. We determine the band alignments within the polycrystalline Cu(In1−xGax)(Se1−ySy)2 semiconductor system using the energy position of the dominant acceptor state as a reference level. Upon alloying CuInSe2 with S the activation energy of the acceptor increases from 300 meV to approximately 380 meV in CuIn(Se0.4S0.6)2. A similar result holds when using Cu(In1−xGax)(Se1−ySy)2 with x≈0.3. In contrast, the acceptor activation energy remains essentially unchanged in the Cu(In1−xGax)Se2 alloy system over the whole composition range 0⩽x⩽1. Taking the acceptor energy as reference, we find a valence band offset ΔEV=−0.23 eV between CuInSe2 and CuInS2. The same valence band offset is found between Cu(In0.7Ga0.3)Se2 and Cu(In0.7Ga0.3)S2. In contrast, the combination CuInSe2/CuGaSe2 displays ΔEV below 0.04 eV. Our results indicate that a bulk reference level exists in the Cu(In1−xGax)(Se1−ySy)2 semiconductors which sets the band structure on a common energy scale, thus establishing the natural band lineups within the alloy system automatically. This conclusion is sustained by our finding that the position of the Fermi level at the CdS/chalcopyrite interface exhibits a constant energy distance to the acceptor level. The concentration of bulk acceptors is in addition correlated to the open circuit voltage losses of heterojunction solar cells.
Convection in chemical fronts with quadratic and cubic autocatalysis
Authors: Vasquez Desiderio A. , Thoreson Erik
Published: July 2002

Convection in chemical fronts enhances the speed and determines the curvature of the front. Convection is due to density gradients across the front. Fronts propagating in narrow vertical tubes do not exhibit convection, while convection develops in tubes of larger diameter. The transition to convection is determined not only by the tube diameter, but also by the type of chemical reaction. We determine the transition to convection for chemical fronts with quadratic and cubic autocatalysis. We show that quadratic fronts are more stable to convection than cubic fronts. We compare these results to a thin front approximation based on an eikonal relation. In contrast to the thin front approximation, reaction–diffusion models show a transition to convection that depends on the ratio between the kinematic viscosity and the molecular diffusivity.
Evolution of spatiotemporal patterns during the electrodissolution of metals: Experiments and simulations
Authors: Jaeger Nils I. , Otterstedt Ralph D. , Bı̂rzu Adrian , Green Brian J. , Hudson John L.
Published: July 2002

Spatiotemporal patterns including accelerating fronts, rotating waves, and homogeneous oscillations evolve during the electrodissolution of metals like cobalt and iron that exhibit passivity under potentiostatic control. The nature of the patterns is determined by long-range (nonlocal) coupling through the electric field which in turn is influenced by the geometry of the electrochemical cell, the applied potential, and the conductivity of the electrolyte. A two-variable model in a three-dimensional geometry is presented which is able to simulate the essential features of the experimental system.
Chaotic maps derived from trajectory data
Authors: Boyarsky Abraham , Góra Paweł
Published: July 2002

We assume that we have the following information from observed trajectory data about a discrete time dynamical process: (1) a rough graph of the phase plot, (2) the probability density function and (3) the metric entropy. We describe a method for constructing a nonlinear map whose graph is “within” the rough graph of the phase plot, and which has the observed probability density function and entropy.
Polymorphous transformations in alkaline-earth silicates
Authors: Liu Jianjun , Duan Chun-gang , Mei W. N. , Smith R. W. , Hardy J. R.
Published: July 2002

Structural phase transitions in Ca2SiO4 and Sr2SiO4 are investigated by molecular dynamics simulations. The simulations are based on the potentials calculated from the Gordon–Kim modified electron gas formalism extended to molecular ions. We successfully reproduced the transition γ−αH′−α and β−αL′−αH′−α in Ca2SiO4, and the transition β−α′ in Sr2SiO4. We find that the αL′ phase of Ca2SiO4 is an a×3b×c superstructure of the αH′ phase, while the αH′ phase has a β-K2SO4 structure, and the α phase of Ca2SiO4 has a disordered structure with space group P63/mmc.
Parametric crossover model and physical limit of stability in supercooled water
Authors: Kiselev S. B. , Ely J. F.
Published: July 2002

The two-critical point (TCP) scenario for supercooled water was tested against experimental data with the crossover equation of state (CR EOS) based on the fundamental results of the fluctuation theory of critical phenomena. The CR EOS predicts a second critical point, CP2, in supercooled water with the parameters Tc2=188 K, ρc2=1100 kg⋅m−3, Pc2=230 MPa, and represents the experimental values of the isothermal compressibility in liquid and supercooled water with an average absolute deviation (AAD) of about 1.7% in the pressure range P=0.1–190 MPa, the liquid densities with an AAD of about 0.1%, and the heat capacity with an AAD of about 1.0% in the temperature range 245 K⩽T⩽300 K. The CR EOS also allows calculation of the physical limit of stability in supercooled water—the kinetic spinodal, TKS. At all pressures P<190 MPa, the kinetic spinodal calculated with the CR EOS lies below the homogeneous nucleation temperature, TH, thus satisfying a physically obvious condition TKS⩽TH. We show that the CP2 is always lying in the region where no thermodynamic state is possible—the “nonthermodynamic habitat” for supercooled water; therefore, we consider our result as a strong argument for the TCP scenario, but with the unphysical—“virtual,” rather than real physical, CP2.
First results from cryogenic target implosions on OMEGA
Authors: Stoeckl C. , Chiritescu C. , Delettrez J. A. , Epstein R. , Glebov V. Yu. , Harding D. R. , Keck R. L. , Loucks S. J. , Lund L. D. , McCrory R. L. , McKenty P. W. , Marshall F. J. , Meyerhofer D. D. , Morse S. F. B. , Regan S. P. , Radha P. B. , Roberts S. , Sangster T. C. , Seka W. , Skupsky S. , Smalyuk V. A. , Sorce C. , Soures J. M. , Town R. P. J. , Frenje J. A. , Li C. K. , Petrasso R. D. , Séguin F. H. , Fletcher K. , Paladino S. , Freeman C. , Izumi N. , Lerche R. , Phillips T. W.
Published: July 2002

Initial results from direct-drive spherical cryogenic target implosions on the 60-beam OMEGA laser system [T. R. Boehly, D. L. Brown, R. S. Craxton et al., Opt. Commun. 133, 495 (1997)] are presented. These experiments are part of the scientific base leading to direct-drive ignition implosions planned for the National Ignition Facility (NIF) [W. J. Hogan, E. I. Moses, B. E. Warner et al., Nucl. Fusion 41, 567 (2001)]. Polymer shells (1-mm diam with walls <3 μm) are filled with up to 1000 atm of D2 to provide 100-μm-thick ice layers. The ice layers are smoothed by IR heating with 3.16-μm laser light and are characterized using shadowgraphy. The targets are imploded by a 1-ns square pulse with up to ∼24 kJ of 351-nm laser light at a beam-to-beam rms energy balance of <3% and full-beam smoothing. Results shown include neutron yield, secondary neutron and proton yields, the time of peak neutron emission, and both time-integrated and time-resolved x-ray images of the imploding core. The experimental values are compared with 1-D numerical simulations. The target with an ice-layer nonuniformity of σrms=9 μm showed 30% of the 1-D predicted neutron yield. These initial results are encouraging for future cryogenic implosions on OMEGA and the NIF.
Fabrication of palladium-based microelectronic devices by microcontact printing
Authors: Wolfe Daniel B. , Love J. Christopher , Paul Kateri E. , Chabinyc Michael L. , Whitesides George M.
Published: July 2002

This letter demonstrates the patterning of thin films of metallic palladium by microcontact printing (μCP) of octadecanethiol, and the use of the patterned films in the fabrication of a functional sensor. This technique was also used to prepare templates of palladium for the electroless deposition of copper. The resistivity of the palladium and copper microstructures was 13.8 and 2.8 μΩ cm, respectively; these values are approximately 40% larger than the values for the pure bulk metals. Palladium patterned into serpentine wires using μCP functioned as a hydrogen sensor with sensitivity of 0.03 vol % H2 in N2, and a response time of ∼10 s (at room temperature).
Magnetic field induced alignment of cyanine dye J-aggregates
Authors: Shklyarevskiy I. O. , Boamfa M. I. , Christianen P. C. M. , Touhari F. , van Kempen H. , Deroover G. , Callant P. , Maan J. C.
Published: July 2002

High magnetic fields were used for the alignment of J-aggregates of cyanine dyes in solution leading to strongly polarized optical properties, yielding a maximum dichroic ratio of 13. The aligned aggregates were fixed by gelation resulting in samples that are stable at room temperature and exhibit strongly polarized absorption and emission spectra.
Gravitational oscillations of a liquid column in a pipe
Authors: Lorenceau Élise , Quéré David , Ollitrault Jean-Yves , Clanet Christophe
Published: July 2002

We report gravity oscillations of a liquid column partially immersed in a bath of liquid. We stress some peculiarities of this system, namely (i) the fact that the mass of this oscillator constantly changes with time; (ii) the singular character of the beginning of the rise, for which the mass of the oscillator is zero; (iii) the sources of dissipation in this system, which is found to be dominated at low viscosity by the entrance (or exit) effects, leading to a long-range damping of the oscillations. We conclude with some qualitative descriptions of a second-order phenomenon, which is the eruption of a jet at the beginning of the rise.
Influence of the orientation of liquid crystalline poly(9,9-dioctylfluorene) on its lasing properties in a planar microcavity
Authors: Virgili T. , Lidzey D. G. , Grell M. , Bradley D. D. C. , Stagira S. , Zavelani-Rossi M. , De Silvestri S.
Published: July 2002

We present a study of optically pumped laser emission from a microcavity containing an oriented layer of the liquid crystalline conjugated polymer poly(9,9-dioctylfluorene). The birefringence of the oriented polymer results in the definition of two cavity modes with electric vectors polarized perpendicular and parallel to the alignment direction. At high excitation density, the emission intensity from the cavity mode polarized parallel to the orientation direction increases rapidly compared to the orthogonal polarized mode and its linewidth narrows from 8 to 2 nm. We identify the parallel-polarized emission as laser action with a threshold excitation density of 7.8×1019 cm−3.
The concept of minimal attractor and maximal attractors of partial differential equations of the Kuramoto–Sivashinsky type
Authors: Il’yashenko Ju. S.
Published: July 2002

The first part of the paper is devoted to definition of the smallest set that may be regarded as the attractor of the dissipative system. Simple properties of this set are discussed. In the second part some geometrical facts concerning attractors of the partial differential equations are revealed. They include well-known results for the two-dimensional Navier–Stokes equation and new ones for the Kuramoto–Sivashinsky and similar equations.
Classical chaos and nonlinear dynamics of rays in inhomogeneous media
Authors: Abdullaev S. S.
Published: July 2002

An investigation is made of the classical nonlinear resonance and the classical stochastic dynamics of rays in waveguide media with irregular inhomogeneities. Analytic and numerical methods are used to study the characteristics of the ray trajectories, their confinement in a nonlinear resonance, and the development of chaotic behavior in waveguides with longitudinal periodic inhomogeneities. It is established that the localization of the rays has fractal properties; in particular, the cycle length of a ray and the time and velocity of propagation of a signal depend on the initial parameters of the ray in the form of a ‘‘devil’s staircase.’’ A waveguide with an inhomogeneous index of refraction and a periodically corrugated wall is considered.
Quantum chaos in the Wigner representation
Authors: Berman G. P. , Kolovskiĭ A. R. , Izrailev F. M. , Iomin A. M.
Published: July 2002

The dynamics of a familiar model of stochastic behavior−the quantum kicked rotator−is analyzed in the Wigner representation. Exact nonlocal maps defined on a discrete phase space are derived. The basic dynamics of a quantum kicked rotator can be described satisfactorily by means of a simplified map that incorporates only the discrete nature of the phase space.
Menopausal hot flashes: Randomness or rhythmicity
Authors: Kronenberg Fredi
Published: July 2002

Menopausal hot flashes are episodes of flushing, increased heart rate, skin blood flow and skin temperature, and a sensation of heat. The thermoregulatory and cardiovascular concomitants of hot flashes are associated with peaks in the levels of various hormones and neurotransmitters in the peripheral circulation. Although hot flashes affect about 75% of women, and are the primary reason that women at menopause seek medical attention, the mechanism of hot flashes is still not understood. Hot flashes vary in frequency and intensity both within and between individuals, and have been thought of as occurring randomly. Yet, some women report that their hot flashes are worse at a particular time of day or year. Initial examination of subjects’ recordings of their hot flashes showed diurnal patterns of hot flash occurrence. There also seems to be a diurnal rhythm of hot flash intensity. Continuous physiological monitoring of hot flashes is facilitating the analysis of these patterns, which is revealing circadian and ultradian periodicities. The occurrence of hot flashes can be modulated by external and internal factors, including ambient temperature and fever. Rhythms of thermoregulatory and endocrine functions also may influence hot flash patterns. Examination of the interrelationships between the various systems of the body involved in hot flashes, and a multidisciplinary approach to the analysis of hot flash patterns, will aid our understanding of this complex phenomenon.
Transient dynamics in motor control of patients with Parkinson’s disease
Authors: Beuter Anne , Labrie Christiane , Vasilakos Konstantinon
Published: July 2002

Experimental observations of movement disorders including tremor and voluntary microdisplacements recorded in patients with Parkinson’s disease (PD) during a simple visuomotor tracking task are analyzed. The performance of patients with PD having a very large amplitude tremor is characterized either by the intermittent appearance of transient dynamics or by the presence of sudden transitions in the amplitude or frequency of the signal. The need to develop new tools to characterize changes in dynamics (i.e., transitions) and to redefine neurological degeneration, such as Parkinson’s disease, in terms of qualitative changes in oscillatory behaviors is emphasized.
Marginal singularities, almost invariant sets, and small perturbations of chaotic dynamical systems
Authors: Blank M. L.
Published: July 2002

For a class of piecewise monotone locally noncontracting maps f:X→X with small ‘‘traps’’ Yε⊆X (diam(Yε)≤ε), the existence of smooth conditionally f-invariant measures με are proved, corresponding to a limit as n→∞ conditional probabilities that fn+1x∈X\Yε if x,fx,...,fnx∈X\Yε and the point x is chosen at random. Also proven is the convergence of με to smooth f-invariant measures as ε→0. By means of this construction, the numerical phenomenon of the convergence of histograms of trajectories of maps with marginal singularities to densities of nonfinite smooth invariant measures in the computer modeling was investigated.
Dynamical systems in the theory of solitons in the presence of nonlocal interactions
Authors: Alfimov G. L. , Eleonsky V. M. , Kulagin N. E.
Published: July 2002

The behavior of solitons in models which take into account complex dispersion or nonlocal interaction of nonlinear waves is examined. A method is proposed to reduce this problem to one involving special trajectories (homoclinic and heteroclinic) of the dynamic system. This method involves replacing the nonlinear integrodifferential equation with the differential equations which link the original nonlinear field with the auxiliary linear fields. The interaction of fields in such a model is a local interaction. The number of introduced linear fields is determined by the Laplace transform of the integral operator kernel of the basic integrodifferential equation. The problem involving topological solitons for the nonlocal generalization of the Klein–Gordon equation is considered. Nonlocal interactions are found to lead to a number of singularities (unrestricted increase in the slope of the topological soliton front, break in the solutions, and other singularities).
Some new systems that generate a uniform stochastic web
Authors: Yu L. Y. , Parmenter R. H.
Published: July 2002

Evidence is given that many classes of periodically kicked Hamiltonian system with 1.5 degree of freedom generate infinite, uniform stochastic webs. The kick term in the Hamiltonian or the equation of motion need not be purely sinusoidal or some small perturbation of a sinusoidal function. For the resonance condition q=4 the structure of the web can be different from a square lattice; However, remarkably symmetric patterns of chaos are still present throughout the whole phase space. Examples are given for the square wave function and sawtooth function in the kick term of the equation of motion. The sensitive dependence on initial conditions of those systems is investigated.
Space–time renormalization at the onset of spatio–temporal chaos in coupled maps
Authors: Alstro/m Preben , Stassinopoulos Dimitris
Published: July 2002

The transition regime to spatio–temporal chaos via the quasiperiodic route as well as the period-doubling route is examined for coupled-map lattices. Space–time renormalization-group analysis is carried out and the scaling exponents for the coherence length, the Lyapunov exponent, and the size of the phase fluctuations are determined. Universality classes for the different types of coupling at various routes to chaos are identified.
Coupled maps and pattern formation on the Sierpinski gasket
Authors: Cosenza Mario G. , Kapral Raymond
Published: July 2002

The bifurcation structure of coupled maps on the Sierpinski gasket is investigated. The fractal character of the underlying lattice gives rise to stability boundaries for the periodic synchronized states with unusual features and spatially inhomogeneous states with a complex structure. The results are illustrated by calculations on coupled quadratic and cubic maps. For the coupled cubic map lattice bistability and domain growth processes are studied.
Interpolating Hamiltonians for a stochastic-web map with quasicrystalline symmetry
Authors: Lowenstein J. H.
Published: July 2002

A systematic Hamiltonian approximation scheme is developed for a stochastic-web map with fivefold quasicrystalline symmetry. Interpolating Hamiltonians are calculated up to tenth order in the control parameter a. The higher order Hamiltonians are used to provide bounds for closed invariant curves of the map, and to investigate the structural evolution of map’s phase portrait for a≤0.6.
Applications of periodic-orbit theory
Authors: Sieber M.
Published: July 2002

The periodic-orbit theory of Gutzwiller is applied in various ways by using generalized periodic-orbit sum rules. Numerical evaluations are carried out for the hyperbola billiard, a strongly chaotic system. The most efficient semiclassical determination of quantum energies is achieved by a quantization condition, which is formulated in terms of a zeta function by using a functional equation.
Chaotic behavior in transverse-mode laser dynamics
Authors: Kaige Wang , Abraham N. B. , Albano A. M.
Published: July 2002

We analyze chaotic behavior found in numerical simulations of the transverse pattern dynamics of a laser demonstrating that in some cases chaos originates in phase dynamics and is of low dimension. Investigations of both a Ginzburg–Landau equation for the complex field amplitude of the laser output and a Kuramoto–Sivashinsky-type equation for only the phase of that complex field equation find the same behavior. Both equations can be expanded in terms of spatial modes and in the chaotic regime the behavior of the modal amplitudes seems relatively independent. However, the fluctuations of the modal amplitudes are sufficiently correlated so that the spatiotemporal dynamics is a form of low dimensional chaos rather than a more complex turbulent behavior or even one that might merit the term spatiotemporal chaos.
Chaotic scattering in the gravitational three-body problem
Authors: Boyd Patricia T. , McMillan Stephen L. W.
Published: July 2002

We summarize some results of an ongoing study of the chaotic scattering interaction between a bound pair of stars (a binary) and an incoming field star. The stars are modeled as point masses and their equations of motion are numerically integrated for a large number of initial conditions. The global features of the resulting initial-value space maps are presented, and their evolution as a function of system parameters is discussed. We find that the maps contain regular regions separated by rivers of chaotic behavior. The probability of escape within the chaotic regions is discussed, and a straightforward explanation of the scaling present in these regions is reviewed. We investigate a statistical quantity of interest, namely the cross section for temporarily bound interactions, as a function of the third star’s incoming velocity and mass. Finally, a new way of considering long-lived trajectories is presented, allowing long data sets to be qualitatively analyzed at a glance.
A method of investigation of the evolution of a nonlinear system driven by pulsed noise
Authors: Mersov G. A. , Moiseev S. S. , Nezlina Yu. M.
Published: July 2002

A numerical method is proposed for determining the evolution of nonlinear systems subjected to noise. The method is based on a recurrence equation for the probability density which has been obtained analytically due to the choice of noise in the form of discrete series of random pulses. The method is applied to a dynamical system which describes the motion of a particle in a plane-wave field. The evolution of the probability density in phase and energy space is obtained. It is shown that because of noise effects, the region in phase space where particles can be found rapidly reaches the separatrix and then spreads over the phase space, mainly along the separatrix. In the energy spectrum a new peak appears at the separatrix’s energy. This peak grows in time, while the main peak corresponding to the initial energy drops in time and shifts to lower energy. The moments of motion were analyzed. The character of their evolution indicates a high rate of chaotization. The growth of the fraction of energetic particles is very rapid (exponential at the beginning), whereas the mean energy grows linearly.
Implications of recording strategy for estimates of neocortical dynamics with electroencephalography
Authors: Nunez Paul L. , Srinivasan Ramesh
Published: July 2002

Neocortical dynamics evidently involves very complex, nonlinear processes including top-down and bottom-up interactions across spatial scales. The dynamics may also be strongly influenced by global (periodic) boundary conditions. The primary experimental measure of human neocortical dynamics at short time scales (∼few ms) is the scalp electroencephalogram (EEG). It is shown that different recording and data analysis strategies are sensitive to different parts of the spatial spectrum. Thus experimental measures of system dynamics (e.g., correlation dimension estimates) can generally be expected to depend on experimental method. These ideas are illustrated in two ways: a large scale, quasilinear theory of neocortical dynamics in which standing wave phenomenon occur with predicted frequencies in the general range of EEG, and a relatively simple nonlinear physical system consisting of a linear string with attached nonlinear springs. The string/springs system is integrated numerically to illustrate transitions from periodic to chaotic behavior as mesoscopic nonlinear influences dominate macroscopic linear effects. The implications of these results for new theories of neocortical dynamics, experimental estimates of dynamic properties, and cognitive EEG studies are considered.
New cases of quasiperiodic motions in reversible systems
Authors: Sevryuk M. B.
Published: July 2002

A theorem on the existence of invariant D-dimensional tori in reversible mappings near surfaces foliated into invariant tori of dimension d is announced, where d≤D and the phase space dimension is no less than 2D. This result and its analog for reversible differential equations present a bridge between the so-called global and local lower dimensional reversible Kolmogorov–Arnold–Moser theorems.
Dynamical systems in the theory of nonlinear waves with allowance for nonlocal interactions (the Whitham–Benjamin equation)
Authors: Eleonsky V. M. , Korolev V. G. , Kulagin N. E. , Shil’nikov L. P.
Published: July 2002

In this paper we briefly present a general approach to the description of the nonlinear and nonlocal Whitham–Benjamin model, based on the introduction of a system of auxiliary fields that interact locally with the initial nonlinear field. In the case of stationary waves a corresponding dynamical system is defined that admits of a Hamiltonian representation. Some results are presented of a qualitative and numerical analysis of the stationary solitary waves of the Whitham–Benjamin equation with a rapidly decreasing oscillatory kernel. An investigation is made into a phenomenon related to the loss of smoothness of the solution of the original equation and the noncontinuability of these solutions when the structural parameters of the system are changed (this phenomenon is analogous to the formation of limiting Stokes waves).
Pattern formation and competition in photorefractive oscillators
Authors: Arecchi F. T. , Boccaletti S. , Puccioni G. P. , Ramazza P. L. , Residori S.
Published: July 2002

We introduce a general model of pattern formation in optical systems made of a cavity with an active medium as a photorefractive crystal fed by a pump. The model is based on the interplay of a diffractive equation for the optical field and a diffusive equation for the medium refractivity. The aim of the model is to describe a series of experiments which have shown mode competition (periodic or chaotic alternation) for low Fresnel numbers (F) and mode coexistence, leading to short range space correlations, for high F. For low F, a linear stability analysis provides the set of modes above threshold as a function of the transverse wave number. Due to the interplay of the optical and the diffusive interactions, different behaviors result depending on the thickness of the medium as compared to the optical absorption length and diffusion length. Including the leading nonlinearities compatible with the symmetry constraints, we introduce normal form equations which describe the time-dependent mode competition. In the case of a large number of modes (high F), nonlinear mode–mode interaction is equivalent to a self-induced noise. In this limit, the relevant feature to be compared with the experiment is the power spectrum.
Chaotic capture of vortices by a moving body. II. Bound pair model
Authors: Luithardt Harry H. , Kadtke James B. , Pedrizzetti Gianni
Published: July 2002

Previously, we have presented a simple model for the interaction of a fluid vortex structure with a moving bluff body, and demonstrated the existence of a trapping mechanism related to chaotic scattering. This single point vortex model required explicit perturbation to generate chaos and the subsequent complex dynamics. Here, we present a model which attempts to introduce internal degrees-of-freedom in the vortex structure in the simplest manner, by replacing the single vortex with a like-signed pair. We show that this model exhibits chaotic trapping without the need of explicit perturbation, however, the region of parameter space for which trapping occurs is exceedingly small due to the spatially dependent form of the perturbation. We claim that this result explains some the behavior observed in Navier–Stokes simulations of the same vortex–body system, where we find close correspondence between the dynamics of an extended vorticity distribution and the single vortex model. Finally, we generalize the model to unequal strength vortex pairs, and find more complex behavior which includes ‘‘partial’’ capture of the weaker vortex by the body.
Fractal structure of large-scale variability of wind-driven waves according to laser-scanning data
Authors: Zosimov V. V. , Naugol’nykh K. A.
Published: July 2002

Results are presented for experimental laser-scanning investigations of the statistical characteristics of wind-driven ocean waves. The method involves counting the number of specular points during scanning of the sea surface by a narrow laser beam on a moving ship. The data analyzed are the set of specular points recorded along a track traced out by the laser beam as a result of the motion of the ship and the scanning beam. A prominent feature is the large-scale variability of the number of specular points and the self-similar nature of the process over a rather wide range of spatial scales. A fractal analysis of the process shows a clear power-law interval in the spatial spectrum of the distribution of specular points.
Phase resetting and dynamics in isolated atrioventricular nodal cell clusters
Authors: Kunysz Arkady M. , Munk Andrew A. , Shrier Alvin
Published: July 2002

In the heart, the AV node is the primary conduction pathway between the atria and ventricles and subserves an important function by virtue of its rate-dependent properties. Cell clusters isolated from the rabbit atrioventricular (AV) node beat with a stable rhythm (cycle length: 300–520 ms) and are characterized by slow action potential upstroke velocities (7 to 30 V/s). The goal of this study is to better characterize the phase resetting and the rhythms during periodic stimulation of this slow inward current system. Single or periodic depolarizing pulses (20 ms in duration) were injected into AV nodal cell clusters using glass microelectrodes. Phase resetting curves of both strong, weak as well as discontinuous types were obtained by applying single current pulses of different intensities and latencies following every ten action potentials. Graded responses were elicited in a wide range of stimulus phases and amplitudes. A single premature stimulus caused a transient prolongation of the cycle length. Sustained periodic stimulation, at rates faster than the intrinsic beat rate, resulted in various N:M (stimulus frequency: action potential frequency) entrainment rhythms as well as periodic or irregular changes in action potential morphology. The changes in action potential characteristics were evaluated by computing the area under the action potential trace and above a fixed threshold (−45 mV). We show that the variations in action potential morphology play a major role in the onset of complicated dynamics observed in this experimental preparation. In this context, the prediction of entrainment rhythms using techniques based on the iteration of phase resetting curves (PRCs) is inadequate since the PRC does not carry information directly related to the changes in action potential morphology. This study demonstrates the need to consider graded events which, though not propagated, have important implications in the understanding of dynamical diseases of the heart.
Nonlinear dynamical analysis of turbulence in a stable cloud layer
Authors: Palmer A. J.
Published: July 2002

An eight mode truncated spectral model based on Burgers’ approximation to the one-dimensional Navier–Stokes equations is used to compute the Lyapunov dimension of the dynamical attractor for turbulence in a stable cloud layer. The model results are compared with the correlation dimension obtained earlier from a time series of radar Doppler and reflectivity signals from a turbulent layer in a marine stratus cloud. The analysis supports a weak coupling explanation for the lower correlation dimension found for the reflectivity time series compared with that for the Doppler time series. Turbulent Prandtl number emerges from the analysis as a flow parameter which can enlarge the dimension of the model’s dynamical attractor, but the attractor dimension computed for the model remains lower than the radar Doppler correlation dimension. Linear stability analysis of the model’s equilibrium states suggests that a nontruncated version of the model will possess an attractor which is also of lower dimension than the radar Doppler correlation dimension.
Wave trains in a model of gypsy moth population dynamics
Authors: Wilder J. W. , Vasquez D. A. , Christie I. , Colbert J. J.
Published: July 2002

A recent model of gypsy moth [Lymantria dispar (Lepidoptera: Lymantriidae)] populations led to the observation of traveling waves in a one-dimensional spatial model. In this work, these waves are studied in more detail and their nature investigated. It was observed that when there are no spatial effects the model behaves chaotically under certain conditions. Under the same conditions, when diffusion is allowed, traveling waves develop. The biomass densities involved in the model, when examined at one point in the spatial domain, are found to correspond to a limit cycle lying on the surface of the chaotic attractor of the spatially homogeneous model. Also observed are wave trains that have modulating maxima, and which when examined at one point in the spatial domain show a quasiperiodic temporal behavior. This complex behavior is determined to be due to the interaction of the traveling wave and the chaotic background dynamics.
Variational principle for periodic trajectories of hyperbolic billiards
Authors: Bunimovich Leonid A.
Published: July 2002

We prove for some classes of hyperbolic billiards that the action functional has only one local minimum or only one local maximum for any finite admissible sequence of regular components of the boundary. This result suggests an effective algorithm for the search of all periodic trajectories of these billiards.
The dynamics of a generalized Heisenberg ferromagnetic spin chain
Authors: Daniel M. , Gutkin Eugene
Published: July 2002

We introduce a generalized Heisenberg ferromagnetic spin chain with a four-dimensional target space, and investigate its continuous limit, the generalized continuous Heisenberg model (GCHM). We reduce the dynamics of the GCHM to a nonlinear evolution of space curves in four dimensions. The space curve evolution is expressed in terms of a system of coupled nonlinear equations for the three curvatures, k1(x),k2(x),k3(x), of a curve in R4. Applying the Painlevé analysis to the stationary equations, we conclude that GCHM, in general, is not integrable, unless k1 is constant. We obtain explicit solutions of the resulting stationary system under the latter condition.
Quantum zeta function for perturbed cat maps
Authors: Creagh Stephen C.
Published: July 2002

The behavior of semiclassical approximations to the spectra of perturbed quantum cat maps is examined as the perturbation parameter brings the corresponding classical system into the nonhyperbolic regime. The approximations are initially accurate but large errors are found to appear in the traces and in the coefficients of the characteristic polynomial after nonhyperbolic structures appear. Nevertheless, the eigenvalues obtained from them remain accurate up to large perturbations.
From Hamiltonian chaos to Maxwell’s Demon
Authors: Zaslavsky George M.
Published: July 2002

The problem of the existence of Maxwell’s Demon (MD) is formulated for systems with dynamical chaos. Property of stickiness of individual trajectories, anomalous distribution of the Poincaré recurrence time, and anomalous (non-Gaussian) transport for a typical system with Hamiltonian chaos results in a possibility to design a situation equivalent to the MD operation. A numerical example demonstrates a possibility to set without expenditure of work a thermodynamically non-equilibrium state between two contacted domains of the phase space lasting for an arbitrarily long time. This result offers a new view of the Hamiltonian chaos and its role in the foundation of statistical mechanics.
A two-parameter study of the extent of chaos in a billiard system
Authors: Dullin Holger R. , Richter Peter H. , Wittek Andreas
Published: July 2002

The billiard system of Benettin and Strelcyn [Phys. Rev. A 17, 773–785 (1978)] is generalized to a two-parameter family of different shapes. Its boundaries are composed of circular segments. The family includes the integrable limit of a circular boundary, convex boundaries of various shapes with mixed dynamics, stadiums, and a variety of nonconvex boundaries, partially with ergodic behavior. The extent of chaos has been measured in two ways: (i) in terms of phase space volume occupied by the main chaotic band; and (ii) in terms of the Lyapunov exponent of that same region. The results are represented as a kind of phase diagram of chaos. We observe complex regularities, related to the bifurcation scheme of the most prominent resonances. A detailed stability analysis of these resonances up to period six explains most of these features. The phenomenon of breathing chaos [Nonlinearity 3, 45–67 (1990)]—that is, the nonmonotonicity of the amount of chaos as a function of the parameters—observed earlier in a one-parameter study of the gravitational wedge billiard, is part of the picture, giving support to the conjecture that this is a fairly common global scenario.
Dynamical behavior of the multiplicative diffusion coupled map lattices
Authors: Wang Wei , Cerdeira Hilda A.
Published: July 2002

We report a dynamical study of multiplicative diffusion coupled map lattices with the coupling between the elements only through the bifurcation parameter of the mapping function. We discuss the diffusive process of the lattice from an initially random distribution state to a homogeneous one as well as the stable range of the diffusive homogeneous attractor. For various coupling strengths we find that there are several types of spatiotemporal structures. In addition, the evolution of the lattice into chaos is studied. A largest Lyapunov exponent and a spatial correlation function have been used to characterize the dynamical behavior.
Formation and control of localized structures in nonlinear optical systems
Authors: Brambilla M. , Lugiato L. A. , Stefani M.
Published: July 2002

Diffractive effects in passive nonlinear optical resonators can lead to pattern-forming instabilities. When the pattern (in our case, a regular hexagonal lattice of intensity peaks) coexists with the homogeneous solution, soliton-like intensity peaks in the transverse plane can be excited. These solutions have the characteristics of localized structures and are highly degenerate with respect to the peak location. By injecting narrow laser pulses, it is possible to turn on such peaks at desired locations and to turn them off selectively. The conditions to ensure independence among the peaks are described as well. These features suggest the possibility of encoding optical information in the structure of the field profile.
Adiabatic chaos in a two-dimensional mapping
Authors: Vainshtein D. L. , Vasiliev A. A. , Neishtadt A. I.
Published: July 2002

A close to identity symplectic mapping describing the dynamics of a charged particle in the field of an infinitely wide packet of electrostatic waves is studied. A region of chaotic dynamics, whose width is large for an arbitrarily small deviation of the mapping from the identity, exists on the phase cylinder. This is explained by the quasirandom change occurring in an adiabatic invariant of the problem when the phase trajectory crosses a resonance curve. An asymptotic formula is derived for the jump in the adiabatic invariant. The width of the chaos region and the density of the set of invariant curves near the boundary of the chaos region are estimated.
Deterministic diffusion in almost integrable systems
Authors: Vega J. L. , Uzer T. , Borondo F. , Ford J.
Published: July 2002

Diffusion processes are usually associated with randomness in the system. In this paper we show that deterministic diffusion processes can also occur in systems with zero entropy that mimic chaos with any precision without being mathematically chaotic. A random walk model is used to predict the behavior of the diffusion coefficient.
Quantum chaos in nano-sized billiards in layered two-dimensional semiconductor structures
Authors: Berggren Karl-Fredrik , Ji Zhen-Li
Published: July 2002

We consider two-dimensional, electron-rich cavities that can be created at a (AlGa)As–GaAs interface. In the modelling of such cavities we include features that are typical for small semiconductor structures or devices, i.e., soft walls representing electrostatic confinement and disorder due to ionized impurities. The introduction of soft walls is found to have a profound effect on the dynamic behaviour. There are situations in which there is a crossover from a Wigner distribution for the nearest level spacing to an effectively Poisson-like one as the confining walls are softened. The crossover occurs in a region which is accessible experimentally. A mechanism for the crossover is discussed in terms of groups of energy levels being separated from each other as walls become soft. The effects of disorder are found to be negligible for high-mobility samples, i.e., the motion of the particles is ballistic. These findings are of a general nature. Chaotic Robnik dots, circular dots with a special ‘‘dent,’’ are also investigated. In this case there is no crossover from Wigner to Poisson distributions. An explanation for this difference is proposed. Finally, the effects of leads are investigated in an elementary way by simply attaching two stubs to a circular dot. For wide stubs, which in our simple model would correspond to open leads, we obtain Wigner statistics indicating a transition to irregular behaviour. A lead-induced transition of this kind appears consistent with recent measurements of the line-shape of the weak localization peak, observed in the low-temperature magnetoresistance of square semiconductor billiards. Finally, implications for conductance fluctuations are briefly commented on.
Chaos in the relativistic Euler problem
Authors: Hock Kai Meng
Published: July 2002

The Euler problem with two fixed point masses and one moving mass is reconsidered in the light of general relativity. The scattering of a particle by two fixed black holes is shown to be strongly chaotic. Two neutral black holes have been used for the study. The particle trajectories have been computed numerically using a modified muffin tin approximation. A plot of the scattering angle against impact parameter showing distinct signs of chaos is presented.
Internal symmetries of cellular automata
Authors: Urías Jesús , Enciso Agustín
Published: July 2002

(Internal) transformations on the space Σ of automaton configurations are defined as bi-infinite sequences of permutations of the cell symbols. A pair of transformations (γ,θ) is said to be an internal symmetry of a cellular automaton f:Σ→Σ if f=θ−1fγ. It is shown that the full group of internal symmetries of an automaton f can be encoded as a group homomorphism F such that θ=F(γ). The domain and image of the homomorphism F have, in general, infinite order and F is presented by a local automaton-like rule. Algorithms to compute the symmetry homomorphism F and to classify automata by their symmetries are presented. Examples on the types of dynamical implications of internal symmetries are discussed in detail.
Dynamics of coupled maps with a conservation law
Authors: Grigoriev R. O. , Cross M. C.
Published: July 2002

A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are calculated for a set of independent order parameters. Numerical evidence is produced suggesting that the singularity in the density of Lyapunov exponents at λ=0 is a reflection of the singularity in the density of Fourier modes (a “Van Hove” singularity) and disappears if the conservation law is broken. Applicability of the Lyapunov dimension to the description of spatiotemporal chaos in a system with a conservation law is discussed.