bluuebunny/crossref_metadata_2025 huggingface dataset:
Cantilever effects on the measurement of electrostatic potentials by scanning Kelvin probe microscopy
Authors: Koley G. , Spencer M. G. , Bhangale H. R.
Published: July 2002

Scanning Kelvin probe microscopy (SKPM) is a unique way to measure electrostatic potentials for small geometries. It has numerous applications including characterization of integrated circuits and nanoscale devices. SKPM is attractive because of the quantitative nature of the measurements. In this work, we have examined one of the principal sources of measurement error, the cantilever (which holds the probe tip). The accuracy of measurements of electrostatic potentials on closely spaced regions biased differently is reduced due to a large capacitance gradient associated with the cantilever. However, it is observed that the accuracy of measurements increases as the tip–sample distance is decreased because the capacitance gradient of the tip becomes proportionally larger relative to that of the cantilever. It is further observed that longer tips with smaller cantilever areas measure the electrostatic potentials more accurately as the capacitance gradient of the cantilever is reduced. Scanning probe tips are parametrized by a factor R, which indicates their suitability for SKPM measurements.
Transition from convective to absolute instability in a liquid jet
Authors: O’Donnell B. , Chen J. N. , Lin S. P.
Published: July 2002

The critical Weber number above which a liquid jet is convectively unstable and below which it is absolutely unstable is determined experimentally for various Reynolds numbers. The experimental results compare very well with the theoretical prediction, and provide the first evidence of transition from convective to absolute instability at relatively large Reynolds numbers. Comparisons of the present results with related results are made to expand and clarify the concept of absolute instability in the context of interfacial fluid dynamics.
Multidimensional quantum propagation with the help of coupled coherent states
Authors: Shalashilin Dmitrii V. , Child Mark S.
Published: July 2002

A previous initial value coupled coherent state (CCS) representation is applied to Gaussian wave packet propagation on multidimensional Henon Heiles potentials. Solutions of the time-dependent integro-differential Schrödinger equation are obtained in a basis of trajectory guided Frozen Gaussian Coherent States, with Monte Carlo sampling to ensure a unique capability for propagating multidimensional wave functions. Results, which are obtained for up to 14 D, are compared with those derived by the Herman–Kluk semiclassical initial value representation (IVR) wave packet method.
Single molecule DNA device measured with triple-probe atomic force microscope
Authors: Watanabe Hiroyuki , Manabe Chikara , Shigematsu Taishi , Shimotani Kei , Shimizu Masaaki
Published: July 2002

We have measured the electric properties of a three-terminal single molecule DNA device with a triple-probe atomic force microscope (T-AFM). The T-AFM permits us to connect a single DNA molecule with carbon nanotube (CNT) electrodes as source, drain, and gate terminals. As the gate bias voltage is increased, the voltage gap region decreased in the current–voltage (I–V) curves. Furthermore, we can observe the clear steps in the I–V curve at crossing the DNA molecule and the CNT-gate electrode with gate biased.
Matrix effects on the structural and optical properties of InAs quantum dots
Authors: Chen J. X. , Oesterle U. , Fiore A. , Stanley R. P. , Ilegems M. , Todaro T.
Published: July 2002

InAs quantum dots (QDs) have been grown by molecular-beam epitaxy on different InGaAs or GaAs surface layers to investigate the effect of the matrix on the structural and optical properties of the QDs. The density of QDs directly grown on GaAs is 1.1×1010 cm−2, and increases to 2.3×1010 cm−2 for dots grown on a 1 nm InGaAs layer. Single-mirror light-emitting-diode (SMLED) structures with InAs QDs capped by InGaAs and grown on GaAs and InGaAs layers were fabricated to compare the electroluminescence efficiency between the two structures. The maximum external quantum efficiency for QDs on a GaAs structure is 1.1% while that for QDs on InGaAs is 1.3%. The corresponding radiative efficiency could be deduced to be 17.5% for QDs on GaAs and 21.5% for QDs on InGaAs, respectively.
Planar Dirac electron in Coulomb and magnetic fields: A Bethe ansatz approach
Authors: Chiang Chun-Ming , Ho Choon-Lin
Published: July 2002

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is an example of the so-called quasi-exactly solvable models. The solvable parts of its spectrum were previously solved from the recursion relations. In this work we present a purely algebraic solution based on the Bethe ansatz equations. It is realized that, unlike the corresponding problems in the Schrödinger and the Klein–Gordon cases, here the unknown parameters to be solved for in the Bethe ansatz equations include not only the roots of the wave function assumed, but also a parameter from the relevant operator. We also show that the quasi-exactly solvable differential equation does not belong to the classes based on the algebra sl2.
Chemical profiling of single nanotubes: Intramolecular p–n–p junctions and on-tube single-electron transistors
Authors: Kong Jing , Cao Jien , Dai Hongjie , Anderson Erik
Published: July 2002

Electrical transport properties of intramolecular p–n–p junctions formed on individual semiconducting carbon nanotubes are reported. Chemical dopant “profiling” along the length of a nanotube divides the nanotube into two p-doped sections and a central n-doped section. The double p–n junctions formed on the nanotube dictate the electrical characteristics of the system. Well-defined and highly reproducible single-electron transistors with much smaller size than the geometrical length of the nanotube are obtained.
Application of a multi-element Ge detector in laser pump/x-ray probe time-domain x-ray absorption fine structure
Authors: Jennings Guy , Jäger Wighard J. H. , Chen Lin X.
Published: July 2002

The characterization and application of a multi-element Ge solid state detector in time-domain laser pump, x-ray probe (LPXP) x-ray absorption fine structure (XAFS) using a third-generation synchrotron source (Advanced Photon Source or APS) are described. In particular, the following problems are discussed: (1) proper handling of high numbers of x-ray photons within a single pulse or pulse cluster, (2) optimizing the incident number of photons, (3) synchronization of the laser pulse, the x-ray pulse and the detector readout, and (4) shaping time and timing requirements of the detector. Based on the study, we estimate the detector efficiency for LPXP-XAFS experiments and identify the problems and possible solutions.
Molecular dynamics simulations of water wires in a lipid bilayer and water/octane model systems
Authors: Venable Richard M. , Pastor Richard W.
Published: July 2002

A series of classical molecular dynamics simulations of a water wire in a DPPC bilayer yielded lifetimes τ of up to 90 ps, with τ̄=37±8 ps (not including a significant fraction wires that broke during equilibration). This is sufficiently long to conduct protons across the bilayer through a quantum mechanical hopping mechanism, similar to proton conduction in ice. Lifetimes of wires in the octane region of a water/octane/water “sandwich” were qualitatively similar (τ̄=36±3 ps) though wires were rarely lost during equilibration. Hence, the utility of the water/octane system as a membrane surrogate depends on the application.
Integration of a hard x-ray microprobe with a diffractometer for microdiffraction
Authors: Libera J. , Cai Z. , Lai B. , Xu S.
Published: July 2002

A hard x-ray Fresnel zone-plate-based microprobe has been designed and integrated into a Newport kappa diffractometer for microdiffraction studies at the 2ID-D beamline at the Advance Photon Source. The microprobe employs 10 and 40 cm (focal length at 8 keV) zone plates to provide high and moderate focusing power, respectively. Each zone-plate assembly has two identical zone plates stacked together to provide higher focusing efficiency for higher energy (30 keV) applications. The mounting base of the microprobe is supported by the side of the base of the diffractometer at one end and the central table of the diffractometer at the other end, thus minimizing the instability of relative positions between the focal spot and the specimen. A x-ray focal spot size smaller than 360 nm and angular repeatability of the sample circles smaller than 0.001° have been demonstrated with this setup.
Dynamics of relativistic magnetized blast waves
Authors: Lyutikov Maxim
Published: July 2002

The dynamics of a relativistic blast wave propagating through a magnetized medium is considered, taking into account possible inhomogeneities of density and magnetic field and additional energy supply. Under the simplifying assumption of a spherically symmetric explosion in a medium with toroidal magnetic field self-similar solutions for the internal dynamics of the flow are derived. In the weakly magnetized case, when the bulk of the flow may be described by the unmagnetized solutions, there is a strongly magnetized sheath near the contact discontinuity (when it exists). Self-similar solutions inside the sheath are investigated. In the opposite limit of strongly magnetized upstream plasma new analytical self-similar solutions are found. Possible application to the physics of gamma-ray bursts is discussed.
Mechanisms of cooperativity underlying sequence-independent β-sheet formation
Authors: Guo Chinlin , Cheung Margaret S. , Levine Herbert , Kessler David A.
Published: July 2002

We investigate the formation of β-sheet structures in proteins without sequence-dependent side-chain interactions. To accomplish this, we introduce a model which explicitly incorporates both solvation effects and the angular dependence (on the protein backbone) of hydrogen bond formation. The thermodynamics of this model is studied by exploring the density of states for the entire system and the local couplings in a partially folded structure. Our results suggest that solvation dynamics together with the H-bond angular dependence gives rise to a generic cooperativity in this class of systems; this result explains why pathological aggregates involving β-sheet cores can form from many different proteins. Our work provides the foundation for the construction of phenomenological models to investigate topology effects in β-sheet folding and the competition between native folding and nonspecific aggregation.
Angularly resolved measurements of ion energy of vacuum arc plasmas
Authors: Anders André , Yushkov George Yu.
Published: July 2002

The kinetic energy of ions generated by pulsed vacuum arcs was measured with angular resolution in the interval −90° to +90° with respect to the cathode normal. A current perturbation method in conjunction with drift time measurements was used. Cathode materials included C, Mg, Ti, Cu, Ag, Ta, and Pb with an average arc current of 300 A and 600 μs duration. The measured angular energy distributions are slightly peaked at the cathode normal. Each distribution can be fitted by a superposition of an isotropic component and a cosine function, with the isotropic component dominating. This result is in contrast to plasma jet formation observed by others, which is most likely due to effects of anode geometry and magnetic fields, including the self-field of the current-carrying plasma.
Orbital alignment at p-sexiphenyl and coronene/layered materials interfaces measured with photoemission spectroscopy
Authors: Schroeder P. G. , France C. B. , Parkinson B. A. , Schlaf R.
Published: July 2002

The energy level alignment at the interfaces between para-sexiphenyl/highly oriented pyrolytic graphite (HOPG), coronene/SnS2, and coronene/HOPG were determined using in situ thin film deposition in combination with x-ray photoelectron spectroscopy (XPS) and ultraviolet photoemission spectroscopy (UPS) measurements. The organic thin films were grown in multiple steps by vapor deposition, then sequentially characterized in situ after each growth step. The vacuum cleaved single crystals of SnS2 and HOPG substrates provided clean, atomically flat, and chemically inert surfaces, allowing for the investigation of the phenomena of band bending and interface dipoles without the interference of chemical reactions or morphological problems. Due to the distinctly different work functions of the HOPG (Φ=4.65 eV) and SnS2 (Φ=5.45 eV) substrates, the observed shifts in the binding energies of the organic overlayer related XPS core level emission lines could be associated with band bending resulting from Fermi level equilibration between the organic thin films and substrates. Possible occurrence of screening effects due to the different polarization energies of the two substrates can, however, complicate the ability to precisely measure band bending. Low intensity XPS work function measurements enabled the detection of the overlayer-thickness-dependent onset of charging phenomena in the UPS measurements. This allowed the precise determination of the highest occupied molecular orbital alignment of the organic molecules at the investigated interfaces.
Single crystal silver nanowires prepared by the metal amplification method
Authors: Barbic Mladen , Mock Jack J. , Smith D. R. , Schultz S.
Published: July 2002

We present a method of fabricating single crystal silver nanowires based on the electroless deposition of silver into the pores of the polycarbonate membranes by the metal amplification process. A gold film on one side of the nanoporous membrane is used as the initiation layer for the silver crystal growth, while the pores of the membrane are used for guiding the growth of the silver crystal into a cylindrical nanostructure. Optical microscopy and spectroscopy of individual nanowires, transmission electron microscopy (TEM), and TEM diffraction crystallography were used to characterize the silver nanostructures. The metal amplification technique presents an electroless, simple, and inexpensive solution to the challenge of fabricating silver nanowires for electronic, optical, and biological applications.
Protein-based integrated optical switching and modulation
Authors: Ormos Pál , Fábián László , Oroszi László , Wolff Elmar K. , Ramsden Jeremy J. , Dér András
Published: July 2002

The static and dynamic response of optical waveguides coated with a thin protein film of bacteriorhodopsin was investigated. The size and kinetics of the light-induced refractive index changes of the adlayer were determined under different conditions of illumination. The results demonstrate the applicability of this protein as an active, programmable nonlinear optical material in all-optical integrated circuits.
Limiting probability distribution for a random walk with topological constraints
Authors: Koralov L. B. , Nechaev S. K. , Sinai Ya. G.
Published: July 2002

The joint limiting probability distribution is studied for the two-dimensional random walk with topological constraints, ω(2ns), on Z2 lattice, where 2n is its total length and (0≤s≤1). The expression for the density of finite-dimensional limiting probability distribution π{ξn(s1),ξn(s2),...,ξn(sr)} where ξn(s) = ω(2ns)/n1/4, is described.
The migrating myoelectric complex of the small intestine
Authors: Telford Gordon L. , Sarna Sushil K.
Published: July 2002

Gastric and small intestinal myoelectric and motor activity is divided into two main patterns, fed and fasted. During fasting, the predominant pattern of activity is the migrating myoelectric complex (MMC), a cyclically occurring pattern of electric and mechanical activity that is initiated in the stomach and duodenum almost simultaneously and, from there, propagates the length of the small intestine. Cyclic motor activity also occurs in the lower esophageal sphincter, the gallbladder, and the sphincter of Oddi with a duration that is related to the MMC in the small intestine. Of the possible mechanisms for initiation of the MMC in the small intestine (extrinsic neural control, intrinsic neural control, and hormonal control), intrinsic neural control via a series of coupled is the most likely. The keep this sentence in! hormone motilin also plays a role in the initiation of MMCs. After a meal, in man the MMC is disrupted and replaced by irregular contractions. The physiologic role of the MMC is to clear the stomach and small intestine of residual food, secretions, and desquamated cells and propel them to the colon. Disruption of the MMC cycle is associated with bacterial overgrowth in some patients, an observation that supports the proposed cleansing function of the MMC cycle.
Heat transfer between two degrees of freedom
Authors: Hoover William G. , Craig Errol , Posch Harald A. , Holian Brad Lee , Hoover Carol G.
Published: July 2002

A particularly simple chaotic nonequilibrium open system with two Cartesian degrees of freedom, characterized by two distinct temperatures Tx and Ty, is introduced. The two temperatures are maintained by Nosé–Hoover canonical-ensemble thermostats. Both the equilibrium (no net heat transfer) and nonequilibrium (dissipative) Lyapunov spectra are characterized for this simple system.
Cantori for the stadium billiard
Authors: Meiss J. D.
Published: July 2002

Although almost all orbits in the stadium billiard are ‘‘chaotic,’’ there are many regular orbits as well−the ordered periodic orbits and cantori. The symmetries of the stadium are exploited to find maximizing and saddle periodic orbits. Cantori are maximizing quasiperiodic orbits; they have caustics. Transport in the stadium should be impeded by cantori, just as in any twist map; this is particularly important for those orbits that are nearly glancing.
Collective behaviors in coupled map lattices with local and nonlocal connections
Authors: Chaté Hugues , Manneville Paul
Published: July 2002

After having recalled the basic properties of the nontrivial collective dynamics exhibited by lattices of maps with local coupling and synchronous updating, we present the behavior of the same models in which all the connections are random. The mean-field, synchronized limit is shown to be reached only for large enough connectivities and sufficiently strong local chaos. Intermediate models, in which only a few of the connections of each site are taken at random, are then considered. Preliminary results indicate that the nontrivial collective behaviors shown by the regularly connected models may be robust to a small proportion of nonlocal, random connections.
Periodic orbits in a two-variable coupled map
Authors: Houlrik Jens M.
Published: July 2002

Periodic orbits are calculated for a linear transformation composed of two coupled tent maps using a symbolic dynamics defined as the direct product of the single-map symbols {0,1,2}. As the coupling strength is increased orbits are pruned and a crossover to one-dimensional behavior is observed. The disallowed binary orbits containing only symbols {0,1} form a connected region in a binary symbol plane. Stable orbits may appear for strong couplings.
Billiard in a barrel
Authors: Zaslavsky George M. , Strauss H. R.
Published: July 2002

Orbits in the three-dimensional billiard of the form of a truncated ellipsoid (‘‘barrel’’) are studied both analytically and numerically. A special form of mapping is proposed to get the expression for Kolmogorov–Sinai entropy, and the transition from strong chaos to weak chaos is obtained.
Pruning of orbits in four-disk and hyperbola billiards
Authors: Hansen Kai T.
Published: July 2002

It is shown that for the four-disk system and the hyperbola billiard it is possible to construct a new symbolic plane preserving the orientation existing in the dynamical space. Physical orbits are mapped into the topological well-ordered plane and it is shown that the forbidden and allowed orbits are separated by a monotone pruning front.
Nonlinear forecasting and iterated function systems
Authors: Mantica Giorgio , Giraud B. G.
Published: July 2002

The theory of dynamical forecasting can be extended to iterated function systems. An unordered set of iterates may be sufficient to construct a simulation of the unknown dynamics. The underlying dynamical system may be nondeterministic: A random element may be allowed in the dynamics, and retrieved by our proposed procedures. A first application of these extensions pertains to the reconstruction of fractal attractors, and allows us to solve the so-called inverse problem in Iterated Functions Systems.
Coupling of the relaxation and resonant elements in the autonomous chaotic relaxation oscillator (ACRO)
Authors: Bernhardt Paul A.
Published: July 2002

If a harmonic oscillator is embedded in a relaxation oscillator, the resulting system may behave like an autonomous chaotic relaxation oscillator (ACRO). The discharge transient of the relaxation oscillator excites sinusoidal oscillations in the harmonic oscillator and these sinusoids affect when the next discharge occurs. This can lead to chaotic intervals in the oscillator periods. A simple electronic model of the ACRO is studied over a wide range of parameters using numerical, analytic, and experimental techniques. The dynamics of the ACRO is found to be determined by three parameters: (1) tuning, (2) coupling, and (3) damping. Complex, intermittent outputs can always be inhibited by increasing the damping of the harmonic oscillator. For weak damping, strong coupling yields chaotic periods. With weak damping and weak coupling, complex behavior only occurs if the relaxation oscillator is tuned near a resonance of the harmonic oscillator. A new path to chaos, called a disruption bifurcation, is the source for intermittency in the ACRO. This bifurcation occurs when the amplitude of internal resonances is excited to the degree that existing limit cycles are disrupted.
Quantum chaotic scattering with CsI molecules
Authors: Blümel R.
Published: July 2002

A molecular beam of CsI molecules passed through the electric field created by a pair of charged wires is proposed as a laboratory experiment on quantum chaotic scattering. It is shown that the proposed experiment is realistic.
Critical properties of lattices of diffusively coupled quadratic maps
Authors: van de Water Willem , Bohr Tomas
Published: July 2002

We study the critical properties of lattices of coupled logistic maps in the regime where the individual maps are closely above the onset of chaos. We discuss both spatial and temporal characteristics and especially the link between them. We show that the mutual information function between two points on the lattice decays exponentially with distance. In this way we find support for the relation ξ∼λ−1/2 between the coherence length ξ and the largest Lyapunov exponent λ which is further corroborated by a detailed study of the spreading of small perturbations. Finally we study the structure function of the lattice field variable. It shows that at the onset of chaos the lattice remains smooth.
The triple-twist map: Generator of a four-dimensional uniform stochastic web
Authors: Parmenter R. H. , Yu L. Y.
Published: July 2002

The system consisting of three identical harmonic oscillators impulsively coupled can be described by the four-dimensional triple-twist map. This map is capable of generating a uniform stochastic web, periodic in all four dimensions. Some properties of this web are studied.
Phase space structure and chaotic scattering in near-integrable systems
Authors: Koch B.-P. , Bruhn B.
Published: July 2002

We investigate the bifurcation phenomena and the change in phase space structure connected with the transition from regular to chaotic scattering in classical systems with unbounded dynamics. The regular systems discussed in this paper are integrable ones in the sense of Liouville, possessing a degenerated unstable periodic orbit at infinity. By means of a McGehee transformation the degeneracy can be removed and the usual Melnikov method is applied to predict homoclinic crossings of stable and unstable manifolds for the perturbed system. The chosen examples are the perturbed radial Kepler problem and two kinetically coupled Morse oscillators with different potential parameters which model the stretching dynamics in ABC molecules. The calculated subharmonic and homoclinic Melnikov functions can be used to prove the existence of chaotic scattering and of elliptic and hyperbolic periodic orbits, to calculate the width of the main stochastic layer and of the resonances, and to predict the range of initial conditions where singularities in the scattering function are found. In the second example the value of the perturbation parameter at which channel transitions set in is calculated. The theoretical results are supplemented by numerical experiments.
Truncated horseshoes and formal languages in chaotic scattering
Authors: Troll G.
Published: July 2002

In this paper we study parameter families of truncated horseshoes as models of multiscattering systems which show a transition to chaos without losing hyperbolicity, so that the topological features of the transition are completely describable by a parametrized family of symbolic dynamics. At a fixed parameter value the corresponding horseshoe represents the set of orbits trapped in the scattering region. The bifurcations are a pure boundary effect and no other bifurcations such as saddle center bifurcations occur in this transition scenario. Truncated horseshoes actually arise in concrete potential scattering under suitable conditions. It is shown that a simple scattering model introduced earlier can realize this scenario in a certain parameter range (the ‘‘truncated sawshoe’’). For this purpose, we solve the inverse scattering problem of finding the central potential associated to the sawshoe model. Furthermore, we review classification schemes for the transition to chaos of truncated horseshoes originating from symbolic dynamics and formal language theory and apply them to the truncated double horseshoe and the truncated sawshoe.
Phase-locking for maps of a torus: a computer assisted study
Authors: Galkin Oleg G.
Published: July 2002

In the description of bifurcations in a family of maps of an n-torus it is natural to consider phase-locked regions in the parameter space that correspond approximately to the sets of parameter values for which the maps have invariant tori. The extreme case of phase-locking is resonance, where the torus map has a periodic orbit. We study a family of maps of an n-torus that only differ from a family of torus translations by a small nonlinear perturbation. The widths of the phase-locked regions for this family generally increase linearly with the perturbation amplitude. However, this growth varies to a higher power law for families of maps that are given by trigonometric polynomials (the so-called Mathieu-type maps). The exponent of the asymptotic power law can be found by simple arithmetic calculations that relate the spectrum of the trigonometric polynomial to the unperturbed translation. Perturbation theory and these calculations predict that typical resonance regions for the family of Mathieu-type maps are narrow elliptical annuli. All these results are illustrated in a number of numerical examples.
Motion of defects in rotating fluids
Authors: Millan-Rodriguez Juan , Pérez-García Carlos , Bestehorn Michael , Neufeld Marc , Friedrich Rudolf
Published: July 2002

We study defect motion in a rotating convection cell. We present numerical results of a generalized Swift–Hohenberg equation, which provides a model description of the vertically averaged three-dimensional (3-D) hydrodynamic equations. Our model includes non-Boussinesq effects. It also accounts for the effects of the Coriolis force induced by a rotation of the fluid layer around its vertical symmetry axis. We show that even a slow rotation well below the Küppers–Lortz instability causes defect motion perpendicular to the convective rolls. We derive an analytic estimation of that motion.
Stable heteroclinic cycles and symbolic dynamics
Authors: Alsedà Lluís , Gambaudo Jean Marc , Mumbrú Pere
Published: July 2002

Let S10, S11,...,S1n−1 be n circles. A rotation in n circles is a map f:∪i=0n−1S1i→∪ i=0n−1S1i which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.
Excitability in liquid crystal
Authors: Coullet P. , Frisch T. , Gilli J. M. , Rica S.
Published: July 2002

The spiral waves observed in a liquid crystal submitted to a vertical electric field and a horizontal rotating magnetic field are explained in the framework of a purely mechanical description of the liquid crystal. The originality of the experiment described in this paper is the presence of the vertical electric field which allows us to analyze the spiral waves in the framework of a weakly nonlinear theory.
Regular and chaotic transport of impurities in steady flows
Authors: Vasiliev A. A. , Neishtadt A. I.
Published: July 2002

This paper considers the properties of the transport of impurity particles in steady fluid flows and describes the principal modes of particle motion. An impurity consisting of particles with a lower density than that of the medium is localized at stationary points of the flow, whereas a heavy impurity can perform a spatially unbounded motion. The conditions for the transition from the bounded motion of a heavy impurity to the long-range transport mode, which occurs as a result of a loss of the stability of the heteroclinic trajectory, are obtained for a model two-dimensional flow having an eddy-cell structure. A mode is found in which a particle, after being transported over a long distance, is trapped forever within the confines of one cell. The transition from regular to chaotic particle transport is analyzed. The question of the effect of a small noise (for example, molecular diffusion) on the character of the motion of a heavy impurity is investigated. It is shown that this effect is important at high viscosity and leads to a transition from bounded motion of the impurity particle to diffusion-type chaotic motion.
Discrete-time stimulation of the oscillatory and excitable forms of a FitzHugh–Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone
Authors: Foweraker J. P. A. , Brown D. , Marrs R. W.
Published: July 2002

A model for the pulsatile release of luteinizing hormone releasing hormone (LHRH) can be reduced to a FitzHugh–Nagumo model subject to regular and quasiregular (i.e., with slight random variation in the interstimulus interval), discrete-time stimulation. The relationship of output pulse frequency (OPF) to stimulus frequency is compared between the excitable and oscillatory forms of the model and discussed in the context of results from other pulse-driven model systems. Some examples of the changes in OPF caused by quasiregular and purely Poissonian stimuli are given for the excitable case. The unstimulated system frequently interacts with the stimulation in such a complex manner that the OPF bears little resemblance to the frequency of stimulation or of the unstimulated system. Furthermore, the inability of the oscillatory form of the model to allow complete suppression of output pulses for moderate stimulation frequencies suggests that the LHRH system can be more appropriately described by the excitable form of the model.
On the singularity structure of invariant curves of symplectic mappings
Authors: de la Llave Rafael , Tompaidis Stathis
Published: July 2002

We study invariant curves in standard-like maps conjugate to rigid rotation with complex frequencies. The main goal is to study the analyticity domain of the functions defined perturbatively by Lindstedt perturbation expansions. We argue, based on infinite-dimensional bifurcation theory that the boundary of analyticity should typically consist of branch points of order two and we verify it in some examples using nonperturbative numerical methods. We show that this nature of the singularities of the analyticity domain can explain previously reported numerical results and also suggests other numerical methods.
Involutes: the geometry of chemical waves rotating in annular membranes
Authors: Lázár Attila , Noszticzius Zoltán , Farkas Henrik , Försterling Horst-Dieter
Published: July 2002

According to earlier theories certain parts of a chemical wave front propagating in a 2-D excitable medium with a convex obstacle should be involutes of that obstacle. The present paper discusses a special case where self-sustained chemical waves are rotating around a central obstacle in an annular 2-D excitable region. A simple geometrical model of wave propagation based on the Fermat principle (minimum propagation time) is suggested. Applying this model it is shown that the wave fronts in the case of an annular excitable region should be purely involutes of the central obstacle in the asymptotic state. This theory is supported by experiments in a novel membrane reactor where a catalyst of the Belousov–Zhabotinsky reaction is fixed on a porous membrane combined with a gel medium. Involutes of circular and triangular obstacles are observed experimentally. Deviations from the ideal involute geometry are explained by inhomogeneities in the membrane.
Painleve’ analysis of a variable coefficient Sine-Gordon equation
Authors: Di Garbo Angelo , Fronzoni Leone
Published: July 2002

In this paper we study a variable coefficient Sine-Gordon (vSG) equation given by θtt−θxx+F(x,t)sin θ=0 where F(x,t) is a real function. To establish if it may be integrable we have performed the standard test of Weiss, Tabor, and Carnevale (WTC). We have got that the (vSG) equation has the Painleve’ property (Pp) if the function F(x,t) satisfies a well-defined nonlinear partial differential equation. We have found the general solution of this last equation and, consequently, the functions F(x,t) such that the (vSG) equation possesses the (Pp), are given by F(x,t)=F1(x+t)F2(x−t) where F1(x+t) and F2(x−t) are arbitrary functions. Using this last result we have obtained some particular solutions of the 〈vSG〉 equation.
The dripping faucet revisited
Authors: Néda Z. , Bakó B. , Rees E.
Published: July 2002

High accuracy experimental results on the nonlinear dynamical behaviour of a dripping faucet are presented. The distribution functions for droplet sizes and drip intervals together with return maps are studied for various dripping rates. Increasing this control parameter, chaotic behaviour is obtained and discussed.
Enlarged scaling ranges for the KS-entropy and the information dimension
Authors: Kantz Holger , Schürmann Thomas
Published: July 2002

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data.
Collective patterns arising out of spatio-temporal chaos
Authors: Sasa Shin-ichi
Published: July 2002

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under periodic boundary conditions. Thus the spatial inhomogeneity of the statistical state arises through spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.
Bifurcation analysis of nephron pressure and flow regulation
Authors: Barfred Mikael , Mosekilde Erik , Holstein-Rathlou Niels-Henrik
Published: July 2002

One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats.
Dynamics and kinematics of simple neural systems
Authors: Rabinovich Mikhail , Selverston Allen , Rubchinsky Leonid , Huerta Ramón
Published: July 2002

The dynamics of simple neural systems is of interest to both biologists and physicists. One of the possible roles of such systems is the production of rhythmic patterns, and their alterations (modification of behavior, processing of sensory information, adaptation, control). In this paper, the neural systems are considered as a subject of modeling by the dynamical systems approach. In particular, we analyze how a stable, ordinary behavior of a small neural system can be described by simple finite automata models, and how more complicated dynamical systems modeling can be used. The approach is illustrated by biological and numerical examples: experiments with and numerical simulations of the stomatogastric central pattern generators network of the California spiny lobster.
Chaotic particle motion under linear surface waves
Authors: Bohr Tomas , Hansen Jonas Lundbek
Published: July 2002

We investigate the motion of infinitesimal particles in the flow field inside the fluid under a traveling surface wave. It is shown that, even for two-dimensional waves, a superposition of two or more traveling harmonic waves is enough to generate chaotic particle motion, i.e., Lagrangian chaos.
Control of noisy chaotic motion in a system with nonlinear excitation and restoring forces
Authors: King P. E. , Yim S. C. S.
Published: July 2002

In this study we examine the complex and chaotic oscillations of a dynamical system with nonlinear excitation and restoring forces for the purpose of controlling these oscillatory states. The physical system, modeled as a system of first-order nonlinear ordinary differential equations, takes into account a geometric nonlinearity in the restoring force, a quadratic viscous drag, and a harmonic excitation force. It is controlled using small perturbations about a selected unstable cycle and control is instigated for periodic cycles of varying periodicities. The controller, when applied on the dynamical system with additive random noise in the excitation, successfully controls the system with noise levels in excess of 5% of the total energy, giving the first evidence that (stochastic) control of these systems is possible.
On the chaotic nature of turbulence observed in benchmark analysis of nonlinear plasma simulation
Authors: Yagi Masatoshi , Itoh Sanae-I. , Itoh Kimitaka , Fukuyama Atsushi
Published: July 2002

Simulational results of two dissipative interchange turbulence (Rayleigh–Taylor-type instability with dissipation) models with the same physics are compared. The convective nonlinearity is the nonlinear mechanism in the models. They are shown to have different time evolutions in the nonlinear phase due to the different initial value which is attributed to the initial noise. In the first model (A), a single pressure representing the sum of the ion and electron components is used (one-fluid model). In the second model (B) the ion and electron components of the pressure fields are independently solved (two-fluid model). Both models become physically identical if we set ion and electron pressure fields to be equal in the model (B). The initial conditions only differ by the infinitesimally small initial noise due to the roundoff errors which comes from the finite difference but not the differentiation. This noise grows in accordance with the nonlinear development of the turbulence mode. Interaction with an intrinsic nonlinearity of the system makes the noise grow, whose contribution becomes almost the same magnitude of the fluctuation itself in the results. The instantaneous deviation shows the chaotic characteristics of the turbulence.
Bifurcation of the branching of a cycle in n-parameter family of dynamic systems with cosymmetry
Authors: Kurakin L. G. , Yudovich V. I.
Published: July 2002

A study is reported of the bifurcation of the branching of a cycle (Poincaré–Andronov–Hopf bifurcation) from a smooth one-dimensional submanifold of equilibria of a dynamical system that depends on a vector parameter and admits cosymmetry. The paper reports a topological classification of local phase portraits near a known equilibrium, when the system parameter is close to its critical value that corresponds to an oscillatory instability. New phenomena that are not observed in the classical case of an isolated equilibrium include a delay of cycle creation with respect to the system parameter, loss of stability by the family of equilibria without loss of attraction, and the possibility of unstable supercritical self-oscillations.
Sensitive dependence on initial conditions for cellular automata
Authors: Urı́as Jesús , Rechtman Raúl , Enciso Agustı́n
Published: July 2002

The property of sensitive dependence on intial conditions is the basis of a rigorous mathematical construction of local maximum Lyapunov exponents for cellular automata. The maximum Lyapunov exponent is given by the fastest average velocity of either the left or right propagating damage fronts. Deviations from the long term behavior of the finite time Lyapunov exponents due to generation of information are quantified and could be used for the characterization of the space time complexity of cellular automata.
Entropy potential and Lyapunov exponents
Authors: Lepri Stefano , Politi Antonio , Torcini Alessandro
Published: July 2002

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthermore, it is shown that the knowledge of the entropy potential allows determining also Lyapunov spectra in general reference frames where the time-like and space-like axes point along generic directions in the space-time plane. Finally, the existence of an entropy potential implies that the integrated density of positive exponents (Kolmogorov-Sinai entropy) is independent of the chosen reference frame.
Tracking controlled chaos: Theoretical foundations and applications
Authors: Schwartz Ira B. , Carr Thomas W. , Triandaf Ioana
Published: July 2002

Tracking controlled states over a large range of accessible parameters is a process which allows for the experimental continuation of unstable states in both chaotic and non-chaotic parameter regions of interest. In algorithmic form, tracking allows experimentalists to examine many of the unstable states responsible for much of the observed nonlinear dynamic phenomena. Here we present a theoretical foundation for tracking controlled states from both dynamical systems as well as control theoretic viewpoints. The theory is constructive and shows explicitly how to track a curve of unstable states as a parameter is changed. Applications of the theory to various forms of control currently used in dynamical system experiments are discussed. Examples from both numerical and physical experiments are given to illustrate the wide range of tracking applications.
Dynamical ensembles in nonequilibrium statistical mechanics and their representations
Authors: Rondoni Lamberto , Stöcker Sabine
Published: July 2002

The stationary states of driven systems of particles are considered from the point of view of the invariant probability distributions in the phase space which characterize them. The main features of various representations of such distributions are reviewed, and a brief derivation of the one based on orbital measures is given. We mention the limits of the mathematical derivations, and discuss the expected range of applicability beyond such limits.
Near threshold anomalous transport in the standard map
Authors: White R. B. , Benkadda S. , Kassibrakis S. , Zaslavsky G. M.
Published: July 2002

Anomalous transport is investigated near threshold in the standard map. Very long time flights, and a large anomaly in the transport, are shown to be associated with a new form of multi-island structures causing orbit sticking. The phase space structure of these traps, and the exponents of the characteristic long time tails associated with them are determined. In general these structures are very complex, but some cases, consisting of layers of islands, allow simple modeling.
Chaotic evolution of arms races
Authors: Tomochi Masaki , Kono Mitsuo
Published: July 2002

A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson’s model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.
Wave analysis of ray chaos in underwater acoustics
Authors: Sundaram Bala , Zaslavsky G. M.
Published: July 2002

The dispersion of a wave packet in an acoustic medium is considered in the paraxial wave approximation, where the effective potential, due to variation of the speed of propagation, varies both with depth and propagation distance. The analysis of the resulting parabolic equation, similar to the Schrödinger equation, clearly demonstrates the role of ray chaos in enhancing the dispersion of the initial packet. However, wave coherence effects are also seen that suppress the effects of the ray chaos in a manner analogous to the effects of quantum chaos.
Spectral properties of dissipative chaotic quantum maps
Authors: Braun Daniel
Published: July 2002

I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the propagator of the reduced density matrix, and traces of its classical counterpart, the Frobenius–Perron operator, are identical in the limit of ℏ→0. Numerically I find that even for finite ℏ the agreement can be very good. This holds in particular if the classical phase space contains a strange attractor, as long as one stays clear of bifurcations. Traces of the quantum propagator for iterations of the map agree well with the corresponding traces of the Frobenius–Perron operator if the classical dynamics is dominated by a strong point attractor.
Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis
Authors: Fan Aihua , Jiang Yunping
Published: July 2002

It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps.