bluuebunny/crossref_metadata_2025 huggingface dataset:
Anatomy of the trace formula for the baker’s map
Authors: Saraceno M. , Voros A.
Published: July 2002

The structure of the trace formula for quantum maps on a compact phase space is analyzed. An explicit expression for the functional determinant in terms of a finite number of traces is derived which is algebraic and independent of any approximation. For the specific case of the baker’s map, its simple structure allows the implementation of a symbolic decomposition of the propagator which is exact and which has the structure of usual semiclassical formulas. The method allows the testing of the accuracy of the individual contribution of each periodic orbit to the functional determinant.
Describing the dynamics with a bi-orthogonal decomposition
Authors: Lima Ricardo
Published: July 2002

A space–time decomposition of a signal into orthogonal temporal modes (chronos) and orthogonal spatial modes (topos) for the analysis of the dynamics of CML closed to a Hopf bifurcation are used. Global energy and entropy as a tool to distinguish different kinds of dynamics in CML are introduced.
Quantum irregular scattering induced by tunneling
Authors: Csordás András , Šeba Petr
Published: July 2002

Irregular behavior in a simple two-dimensional scattering model is investigated in the quantum domain. The scattering potential is composed from Dirac deltas on a stadium shaped curve. The unusual feature of the model is that the irregular patterns disappear in the classical limit because the main mechanism leading to resonances in the cross section data is the quantum tunneling. Calculations for the standard characteristics such as nearest-neighbor distribution of eigenphases of the S-matrix, the distribution of the S-matrix elements and the correlation function of the total cross section are performed. Deviations from the usual predictions for irregular scattering have been found in certain regions, which can be traced back to the fact that the model does not have such a characteristic time like the classical escape rate, which survives the classical limit.
Zigzag and varicose instabilities of a localized stripe
Authors: Hirschberg P. , Knobloch E.
Published: July 2002

A localized stripe solution to a reaction–diffusion equation can lose stability simultaneously to zigzag and varicose perturbations at a codimension-two point. The resulting mode interaction is described by O(2)×Z2 equivariant amplitude equations. Stationary mixed-mode solutions are found which can undergo instabilities to breathing modes or to patterns which travel along the stripe.
Chaotic scattering on a double well: Periodic orbits, symbolic dynamics, and scaling
Authors: Daniels Vincent , Vallières Michel , Yuan Jian-Min
Published: July 2002

We investigate classical scattering of particles by a double-well potential. Irregularity in the scattering functions, such as scattering angle and escape time, appears when the collision energy is lowered below a threshold value. This threshold is closely related to the appearance of periodic orbits with energies above the potential maxima. We study the scattering as a function of the energy and impact parameter. In this initial parameter space the scattering functions consist of regular regions interlaced with chaotic rivers. A symbolic dynamics has been developed to organize these structures and used to reveal their scaling properties.
Symmetric patterns in linear arrays of coupled cells
Authors: Epstein Irving R. , Golubitsky Martin
Published: July 2002

In this note we show how to find patterned solutions in linear arrays of coupled cells. The solutions are found by embedding the system in a circular array with twice the number of cells. The individual cells have a unique steady state, so that the patterned solutions represent a discrete analog of Turing structures in continuous media. We then use the symmetry of the circular array (and bifurcation from an invariant equilibrium) to identify symmetric solutions of the circular array that restrict to solutions of the original linear array. We apply these abstract results to a system of coupled Brusselators to prove that patterned solutions exist. In addition, we show, in certain instances, that these patterned solutions can be found by numerical integration and hence are presumably asymptotically stable.
Traveling waves in lattice models of multidimensional and multicomponent media. II. Ergodic properties and dimension
Authors: Afraimovich V. S. , Pesin Ya. B. , Tempelman A. A.
Published: July 2002

We demonstrate a spatio–temporal chaos in lattice models of multidimensional and multicomponent media on the set of traveling waves solutions running with large enough velocities. We describe stability properties of such solutions, construct invariant measures with ‘‘good’’ ergodic properties concentrated on the above set and study different types of dimensions including the correlation dimension.
Rings: Semicoherent oceanic features
Authors: Flierl Glenn R.
Published: July 2002

Solitary wave or isolated eddy models are often invoked to explain the longevity of strong nonlinear features in oceans and atmospheres. But when we look at the physics in detail, we find that models of isolated eddies often hinge either on an oversimplification of the dynamics or on constraints which are not appropriate for the observed eddies. In a more complete model, as this study demonstrates, rings (and probably other nonlinear geophysical eddies as well) will interact with their surroundings via Rossby wave radiation, primarily in the barotropic mode. Such wave generation leads to a slow decay of the eddy as energy leaks into the wave field.
Distribution of fixed-point energies of a quasiperiodic Hamiltonian flow
Authors: Lowenstein J. H.
Published: July 2002

Energy distributions ρ±(E) for the elliptic and hyperbolic fixed points of the Hamiltonian H(x,y)=∑k=04 cos [x cos(2πk/5)+y sin(2πk/5)] are calculated as integrals over a one-dimensional manifold ℳ(E) in five-dimensional space. Singular points of ℳ(E) produce three logarithmic singularities of ρ±(E), and vanishing of connected components of ℳ(E) gives rise to three discontinuities. The strengths of the singularities and discontinuities of ρ±(E) are determined analytically, and the distributions are evaluated numerically for representative points in the nonsingular intervals. The calculation provides an explicit realization of general theorems concerning the critical points of infinitely smooth functions defined on an n-dimensional torus and restricted to a k-dimensional linear subset. Formally the calculation resembles the determination of the density of states of a dynamical system with one degree of freedom on a 2-torus, but with important differences due to topology and symmetry.
The Ginzburg–Landau approach to oscillatory media
Authors: Kramer L. , Hynne F. , Graae So/renson P. , Walgraef D.
Published: July 2002

Close to a supercritical Hopf bifurcation, oscillatory media may be described, by the complex Ginzburg–Landau equation. The most important spatiotemporal behaviors associated with this dynamics are reviewed here. It is shown, on a few concrete examples, how real chemical oscillators may be described by this equation, and how its coefficients may be obtained from the experimental data. Furthermore, the effect of natural forcings, induced by the experimental realization of chemical oscillators in batch reactors, may also be studied in the framework of complex Ginzburg–Landau equations and its associated phase dynamics. We show, in particular, how such forcings may locally transform oscillatory media into excitable ones and trigger the formation of complex spatiotemporal patterns.
Modeling excitable media by a one variable cellular automaton: Application to the cardiac case
Authors: Giaquinta A. , Boccaletti S. , Tellini L. , Arecchi F. T.
Published: July 2002

The dynamics of an assembly of cardiac cells is modeled by a simple cellular automaton that reduces to a single variable the two variable competition of the standard models of excitable media. Furthermore, a short superexcitability period is introduced, as suggested by the dynamics of the single cardiac miocyte. The model reproduces several pathological cardiac behaviors as, e.g., the fast transition from normal behavior to fibrillation, showing how this latter one can either occur over the whole spatial domain or can be confined within a limited region.
Chaotic behavior of channeling particles
Authors: Chen Ling , Kaloyeros Alain E. , Wang Guang-hou
Published: July 2002

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E0 and incident angle ψ0, the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles’ chaotic motion.
Finite-dimensional behavior in dissipative partial differential equations
Authors: Robinson J. C.
Published: July 2002

Dissipative partial differential equations have applications throughout the sciences: models of turbulence in fluids, chemical reactions, and morphogenesis in biology can all be written in a general form which allows them to be subjected to a unified analysis. Recent results on these equations show that in many cases they are not as complex as they initially appear, and can be converted into a set of ordinary differential equations. However, most of the relevant references present a bewildering array of terms which can obscure the simple underlying ideas. The main purpose of this paper is to introduce this terminology, motivated by several major results, slowly and by example. Detailed proofs are omitted, but it is hoped that this approach will give a good understanding of and intuitive feel for the subject without recourse to technicalities. Nevertheless, sufficient mathematical detail is included to allow application of these results to many examples.
Multiple time scale analysis of two models for the peroxidase–oxidase reaction
Authors: Thompson David R. , Larter Raima
Published: July 2002

A multiple time scale analysis of two four-variable models of the peroxidase–oxidase reaction, the DOP, and the Olsen model, is carried out. It is shown that autonomous limit cycle oscillations are exhibited by the fast subsets of these two models, but only in certain regions of parameter space, confirming the prior suggestion that the slow variable (NADH) is not essential for oscillatory behavior. However, it is found that the slow variable is essential for oscillatory behavior over other ranges of parameter values, and is always essential for complex oscillatory and chaotic behavior. This latter conclusion is based on a study involving driving the fast subset with a sinusoidally varying (NADH). This study suggests the level of coupling between fast and slow variables of an autonomous system necessary to cause the chaos observed in the DOP model. Further study of the driven system allows for the identification of a natural period of the nonoscillatory but bistable fast subsystem and a set of rules for applying a parametric driving in such a way as to generate a more complete Farey sequence from a truncated Farey sequence. These conclusions are used to compare the very similar DOP and Olsen models, which, nevertheless, exhibit quite different Farey sequences and routes to chaos.
The nonlinear decay of complex signals in dissipative media
Authors: Gurbatov S. N. , Crighton D. G.
Published: July 2002

The solution of Burgers’ equation with random initial conditions is often said to describe ‘‘Burgers turbulence.’’ The Burgers equation describes two fundamental effects characteristic of any turbulence—the nonlinear transfer of energy over the spectrum and the dissipation of energy in the small-scale components. Strong interaction between coherent harmonics, associated with the nondispersive nature of the dynamics, leads to the appearance of local self-similar structure. In Burgers’ equation, continuous random initial fields are transformed into sequences of regions with regular behavior, with random locations of the shocks separating them. Moreover, the statistical properties of such random fields are also self-similar. It is already known that the merging of the shocks leads to an increase of the external scale of the turbulence, and because of this the energy of a random signal (‘‘noise’’) decreases more slowly than the energy of simple signals. Here we show that similar behavior takes place for complex regular signals with fractal structure in the coordinate or in the wave-number space. In all these cases, the law of increase of the external scale is determined by the behavior of the structure function of the integral of the initial field—i.e., the structure function of the initial action.
Signatures of deterministic chaos in radar sea clutter and ocean surface winds
Authors: Palmer A. J. , Kropfli R. A. , Fairall C. W.
Published: July 2002

Several time series of wind components and X-band Doppler radar signals, gathered concurrently over a ∼0.01 km2 area of the ocean surface, were examined for evidence of a low-dimensional dynamical attractor with the Grassburger–Procaccia algorithm. Only the vertically polarized radar reflectivity and the horizontal surface wind speed time series suggested the presence of such an attractor. The correlation dimension for these two observables appeared to be nearly the same. This suggested a working hypothesis that the dynamical behavior of both the vertically polarized radar reflectivity and the horizontal surface winds are controlled by a single low-dimensional dynamical system. The hypothesis was further examined by predicting winds from radar reflectivity, using a neural network deterministic model, and comparing the prediction performance with that of the SEASAT statistical algorithm for retrieving surface winds from radar backscatter. It was found that the deterministic model did, in fact, achieve a higher prediction correlation coefficient for a limited time period.
The nonequilibrium Lorentz gas
Authors: Lloyd James , Niemeyer Matthias , Rondoni Lamberto , Morriss Gary P.
Published: July 2002

We study the conductivity of a Lorentz gas system, composed of a regular array of fixed scatterers and a point-like moving particle, as a function of the strength of an applied external field. In order to obtain a nonequilibrium stationary state, the speed of the point particle is fixed by the action of a Gaussian thermostat. For small fields the system is ergodic and the diffusion coefficient is well defined. We show that in this range the Periodic Orbit Expansion can be successfully applied to compute the values of the thermodynamic variables. At larger values of the field we observe a variety of possible dynamics, including the breakdown of ergodic behavior, and later the existence of a single stable trajectory for the largest fields. We also study the behavior of the system as a function of the orientation of the array of scatterers with respect to the external field. Finally, we present a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain. The consequences of this behavior for the ergodicity of the system are explored.
Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H2O2–Cu2+–S2O2−3–NaOH system)
Authors: Strizhak Peter E. , Pojman John A.
Published: July 2002

Dynamic behavior of the pH-regulated oscillations has been studied for the hydrogen peroxide oxidation of thiosulfate ions in the presence of trace amounts of copper(II) ions in a semibatch reactor. A solution of 0.08 M Na2S2O3 and 0.112 M NaOH was flowed at 0.160 mL/min into 300 mL of solution containing the H2O2 and Cu2+ in a vessel. There exists a critical value of the H2O2 or Cu2+ concentrations below which the system does not oscillate. The oscillations appear due to an infinite period bifurcation at low initial concentrations of the H2O2. The initial concentration of Cu2+ may be considered as a bifurcation parameter in this case. Increase of the initial hydrogen peroxide concentration causes the pH-regulated oscillations through a nondegenerate supercritical Hopf bifurcation. The classification of bifurcations is based on the analysis of the behavior of oscillation amplitude and period at different initial concentrations of the H2O2 and Cu2+. Our results show a possibility to distinguish different scenarios for the appearance of transient oscillations in semibatch experiments.
Light induced annihilation and shift of spiral waves
Authors: Agladze K.
Published: July 2002

The light-induced collapse of a pair of spiral waves was studied in a chemically active medium based on the photosensitive Ru(bpy)3—catalyzed Belousov–Zhabotinsky reaction. Spiral waves annihilate only if the light intensity is increased in proper phase relative to the spiral waves’ rotation. Otherwise, the distance between spiral wave cores increases and the pair survives. Computer simulations reveal the mechanism which forces the spiral waves to collide and annihilate. It is based on the shift of a single spiral wave upon an instantaneous decrease of excitability of the medium.
Bifurcation analysis of the travelling waveform of FitzHugh–Nagumo nerve conduction model equation
Authors: Muruganandam P. , Lakshmanan M.
Published: July 2002

The FitzHugh–Nagumo model for travelling wave type neuron excitation is studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations which the system admits when a specific Z2 symmetry is present and when it is not. Based on a center manifold reduction and normal form analysis, the Hopf normal form is deduced. The condition for the onset of limit cycle oscillations is found to agree well with the numerical results. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli.
The convergence of chaotic integrals
Authors: Bauer Oliver , Mainieri Ronnie
Published: July 2002

We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential.
Adaptive strategies for recognition, noise filtering, control, synchronization and targeting of chaos
Authors: Arecchi F. T. , Boccaletti S.
Published: July 2002

Combining knowledge of the local variation rates with some information on the long time trends of a dynamical system, we introduce an adaptive recognition technique consisting in a sequence of variable resolution observation intervals at which the geometrical positions are sampled. The sampling times are chosen so that the sequence of observed points forms a regularized set, in the sense that the separation of adjacent points is almost uniform. We show how this adaptive technique is able to recognize the unstable periodic orbits embedded within a chaotic attractor and stabilize anyone of them even in the presence of noise, through small additive corrections to the dynamics. These techniques have been applied to the synchronization of three chaotic systems, assuring secure communication between a message sender and a message receiver; furthermore they provide robust solutions to the problems of targeting of chaos and of filtering the noise out of an experimental chaotic data set. Implementation of adaptive methods to chaotic Lorenz, three and four dimensional Roessler models and Mackey-Glass delayed system are reported.
Waves of excitation on nonuniform membrane rings, caustics, and reverse involutes
Authors: Lázár Attila , Försterling Horst-Dieter , Farkas Henrik , Simon Péter , Volford András , Noszticzius Zoltán
Published: July 2002

Chemical wave experiments on concentric nonuniform membrane rings are presented together with their theoretical description. A new technique is applied to create a slow inner and a fast outer zone in an annular membrane. An abrupt qualitative change of the wave profile was observed while decreasing the wave velocity in the inner zone. This phenomenon and all the experimental wave profiles can be adequately described by assuming that waves are involutes of a relevant caustic. A possible connection with recent models of atrial flutter is also set forth.
Complexity lower bounds for polygonal billiards
Authors: Troubetzkoy S.
Published: July 2002

Polygonal billiards have zero topological entropy. Complexity is a finer measure of their asymptotic behavior. In this article we show an explicit quadratic lower bound for the complexity of the billiard in an arbitrary polygon.
Solitary wave solutions of nonlocal sine-Gordon equations
Authors: Alfimov G. L. , Eleonsky V. M. , Lerman L. M.
Published: July 2002

In this paper a nonlocal generalization of the sine-Gordon equation, utt+sin u=(∂/∂x)∫−∞+∞G(x−x′)ux′(x′,t)dx′ is considered. We present a brief review of the applications of such equations and show that involving such a nonlocality can change features of the model. In particular, some solutions of the sine-Gordon model (for example, traveling 2π-kink solutions) may disappear in the nonlocal model; furthermore, some new classes of solutions such as traveling topological solitons with topological charge greater than 1 may arise. We show that the lack of Lorenz invariancy of the equation under consideration can lead to a phenomenon of discretization of kink velocities. We discussed this phenomenon in detail for the special class of kernels G(ξ)=∑j=1Nκje−ηj|ξ|, ηj>0, j=1,2,…,N. We show that, generally speaking, in this case the velocities of kinks (i) are determined unambiguously by a type of kink and value(s) of kernel parameter(s); (ii) are isolated i.e., if c* is the velocity of a kink then there are no other kink solutions of the same type with velocity c∈(c*−ε,c*+ε) for a certain value of ε. We also used this special class of kernels to construct approximations for analytical and numerical study of the problem in a more general case. Finally, we set forth results of the numerical investigation of the problem with the kernel that is the McDonald function G(ξ)∼K0(|ξ|/λ) (λ is a parameter) that have applications in the Josephson junction theory.
Easy-to-implement method to target nonlinear systems
Authors: Baptista Murilo S. , Caldas Iberê L.
Published: July 2002

In this work we present a method to rapidly direct a chaotic system, to an aimed state or target, through a sequence of control perturbations, with few different amplitudes chosen according to the allowed control-parameter changes. We applied this procedure to the one-dimensional Logistic map, to the two-dimensional Hénon map, and to the Double Scroll circuit described by a three-dimensional system of differential equations. Furthermore, for the Logistic map, we show numerically that the resulting trajectory (from the starting point to the target) goes along a stable manifold of the target. Moreover, using the Hénon map, we create and stabilize unstable periodic orbits, and also verify the procedure robustness in the presence of noise. We apply our method to the Double Scroll circuit, without using any low-dimensional mapping to represent its dynamics, an improvement with respect to previous targeting methods only applied for experimental systems that are mapping-modeled.
Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy methods for sums of Lyapunov exponents for dilute gases
Authors: Dorfman J. R. , Latz Arnulf , van Beijeren Henk
Published: July 2002

We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time-dependent spatial and velocity distribution functions for such systems. We extend the variables in the generalized Boltzmann equation to include a new set of quantities that describe the separation of trajectories in phase space needed for a calculation of the Lyapunov exponents. The method described here is especially suitable for calculating the sum of all of the positive Lyapunov exponents for the system, and may be applied to equilibrium as well as nonequilibrium situations. For low densities we obtain an extended Boltzmann equation, from which, under a simplifying approximation, we recover the sum of positive Lyapunov exponents for hard-disk and hard-sphere systems, obtained before by a simpler method. In addition we indicate how to improve these results by avoiding the simplifying approximation. The restriction to hard-sphere systems in d dimensions is made to keep the somewhat complicated formalism as clear as possible, but the method can be easily generalized to apply to gases of particles that interact with strong short-range forces.
Aperiodic stochastic resonance in chaotic maps
Authors: Krawiecki A. , Sukiennicki A.
Published: July 2002

It is shown by means of numerical simulations that aperiodic stochastic resonance occurs in chaotic one-dimensional maps with various kinds of intermittency. The effect appears in the absence of external noise, as the system control parameter is varied. In the case of input signals slowly varying in time the analytic treatment, using the adiabatic approximation based on the expressions for the mean laminar phase duration, yields the input-output covariance function comparable with numerical results.
Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory
Authors: Pei Xing , Dolan Kevin , Moss Frank , Lai Ying-Cheng
Published: July 2002

The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise.
Chirality dependent component of vortex advection in excitable media
Authors: Voignier V. , Hamm E. , Krinsky V.
Published: July 2002

An advective field induces drift of a vortex in excitable media. The component of the drift velocity C⊥ perpendicular to the field is known to change its sign with the chirality of the vortex. In an experiment with vortices in an electric field in a chemical excitable medium, we have found unexpectedly that C⊥ changes its sign also independently of chirality with changing composition of the medium. We did not succeed to explain this phenomenon by using existing mathematical models of chemical excitable media. The experiment described calls for more realistic models.
Modes selection in polymer mixtures undergoing phase separation by photochemical reactions
Authors: Tran-Cong Qui , Kawai Junji , Endoh Kouichi
Published: July 2002

Phase separation kinetics and morphology of binary polymer mixtures (A/B) in the presence of photochemical reactions were investigated by using phase-contrast optical microscopy combined with digital image analysis. The polymers were chemically designed in such a way that two types of chemical reactions, intermolecular photodimerization and intramolecular photoisomerization, of polymer segments can be induced and controled by irradiation with ultraviolet light. Unlike the conventional case, the phase separation in the presence of these reactions is spontaneously frozen due to the suppression of the long-wavelength instabilities, resulting in stationary spatial structures with intrinsic periodicities. These characteristic length scales are determined by the competition between the two antagonistic interactions: phase separation as a relatively short-range activation and the photochemical reaction as a long-range inhibition. Furthermore, it was found that the spatial symmetry breaking of concentration fluctuations can emerge from the elastic stress associated with the nonhomogeneous kinetics of the reactions. Experimental data obtained with three types of reactions: A-A only cross-link, A-A and B-B simultaneous cross-links and the reversible A⇔B photoisomerization are described. These results do not only indicate that combination of chemical reactions and phase separation could provide a novel method to control the morphology of multiphase polymer materials, but also suggest that photoreactive polymers can be used as a chemical system to study the mode-selection process in polymers far from thermodynamic equilibrium.
Effect of anisotropy on viscous fingering patterns of polymer solutions in linear Hele-Shaw cells
Authors: Kawaguchi Masami , Shimomoto Kohkichi , Shibata Atushi , Kato Tadaya
Published: July 2002

Viscous fingering patterns of hydroxypropyl methyl cellulose (HPMC) solutions were investigated by forcing air in linear geometry isotropic and anisotropic Hele-Shaw cells as functions of HPMC concentration and injection pressure of air. The resulting patterns depended on the HPMC concentration and the cell anisotropy. The characteristic quantities of pattern growth, such as the finger velocity and the finger width, were evaluated. The finger velocity in the anisotropic linear cell was faster than that in the isotropic one, and the finger velocity and the finger width were well correlated with the pattern morphological changes.
Numerical study of chaos based on a shell model
Authors: Yagi M. , Itoh S.-I. , Itoh K. , Fukuyama A.
Published: July 2002

A shell model is introduced to study a turbulence driven by the thermal instability (Rayleigh–Bénard convection). This model equation describes cascade and chaos in the strong turbulence with high Rayleigh number. The chaos is numerically studied based on this model. The characteristics of the turbulence are analyzed and compared with those of the Gledzer–Ohkitani–Yamada (GOY) model. Quantities such as a mean value of total fluctuation energy, it’s standard deviation, time averaged wave spectrum, probability distribution function, frequency spectrum, the maximum instantaneous Lyapunov exponent, distribution of instantaneous Lyapunov exponents, are evaluated. The dependences of these quantities on the error of numerical integration are also examined. There is not a clear correlation between the numerical accuracy and the accuracy of these quantities, since the interaction between a truncation error and an intrinsic nonlinearity of the system exists. A finding is that the maximum Lyapunov exponent is insensitive to a truncation error.
Bifurcations and selection of equilibria in a simple cosymmetric model of filtrational convection
Authors: Govorukhin V. N. , Yudovich V. I.
Published: July 2002

A three-dimensional set of ordinary differential equations that constitutes a simple abstract model of Darcy convection is investigated. The model reproduces a number of effects that are typical for dynamic systems with nontrivial cosymmetry. Nontrivial cosymmetry can give rise to a continuous family of equilibria where, in this case, the equilibrium stability spectrum varies along the family. The family of equilibria and its stability are examined analytically, and special bifurcations that occur in the system are investigated. It is shown that discrete and continual symmetries, called “flash symmetries,” can be present in the system for certain parameter values. Computer experiments on the selection of equilibria in the symmetric and cosymmetric cases have been carried out. They showed that, for initial points that are far enough from a cycle of equilibria, the neighborhood of a single equilibrium is established in the case of cosymmetry, but all the equilibria are equivalent in the case of symmetry. The authors hope that these results, as well as the formulation of the problems and the approach to their solution, will serve as a sample in the investigation of more complex systems in mathematical physics.
Introduction to the focus issue on granular materials
Authors: Behringer Robert , Jaeger Heinrich , Nagel Sidney
Published: July 2002

In a review paper [H. M. Jaeger, S. R. Nagel, and R. P. Behringer, “Granular solids, liquids and gases,” Rev. Mod. Phys. 68, 1259–1273 (1996)] a few years ago, we wrote about granular material as a distinctive form of matter that exhibits behavior rather different from that of ordinary solids, liquids, or gases. We traced this distinction to three characteristic properties. First, the individual particles making up a granular material are typically large so that thermal energy is irrelevant compared to gravitational energy. Consequently, concepts from equilibrium statistical mechanics are often not applicable. Second, the interactions between particles are frictional and can be mobilized to different degrees depending on the preparation history, giving rise to memory effects, i.e., a static pile will remember how it was formed. Third, when particles collide they do so inelastically so that a “gas” of particles will slow down and come to rest in clumps. In the intervening years, the research on granular matter has progressed rapidly and this may be a good time to ask what we have learned since that article was written. In this spirit, the present special issue of the journal Chaos assembles a spectrum of papers discussing recent developments in the field.
Chaotic mixing of granular material in slowly rotating containers as a discrete mapping
Authors: Elperin T. , Vikhansky A.
Published: July 2002

Chaotic mixing of granular material in a two-dimensional slowly rotating noncircular container in the absence of granular diffusivity is studied analytically and numerically as a discrete mapping. The noncircularity of a drum produces a time periodic disturbance and chaotization of the flow field. The location of the fixed points of the mapping and the separatrices of the hyperbolic points are determined in a closed analytical form.
Massively parallel computer simulation of plane-strain elastic–plastic flow via nonequilibrium molecular dynamics and Lagrangian continuum mechanics
Authors: Hoover William G. , De Groot Anthony J. , Hoover Carol G.
Published: July 2002

Application of massively parallel low-cost computers to the simulation of plane-strain elastic-plastic flow is discussed. Two different approaches, atomistic molecular dynamics and continuum mechanics, are applied to this problem. A hybrid scheme combining the two is also discussed.
Mössbauer studies of Fe2O3 antiferromagnetic small particles
Authors: Dormann J. L. , Cui Ji Ren , Sella C.
Published: July 2002

Granular films consisting of finely dispersed Fe2O3 grains in an Al2O3 matrix have been studied by means of Mössbauer spectroscopy and magnetization measurements. The temperature dependence of the relaxation time is coherent with the superparamagnetism model only if in the τ0 calculation, the noncompensated moment of the antiferromagnetic particles, is considered. This moment is proportional to (n)1/2, n being the number of magnetic atoms in the particle.
Explanation of the influence on the oscillation spectrum of diode lasers for a change of facet reflectivity
Authors: Cassidy Daniel T.
Published: July 2002

A simple, theoretical analysis of the effects on the steady-state oscillation spectrum of diode lasers for a change of the facet reflectivity of the lasers is given. It is shown that the effects can be understood by considering the amount of spontaneous emission which is produced as the facet reflectivity is altered.
Effect of resonance excitation due to dielectronic capture on the gain coefficients of selected transitions in Fe XVII
Authors: Doschek G. A. , Feldman U. , Seely J. F.
Published: July 2002

In previous papers, U. Feldman, J. F. Seely, and A. K. Bhatia [J. Appl. Phys. 56, 2475 (1984)] and A. K. Bhatia, U. Feldman, and J. F. Seely [At. Data Nucl. Data Tables (in press)] have calculated atomic data and gain coefficients for ions of the Ne I isoelectronic sequence. Their calculations of electron impact excitation rates were carried out in the distorted wave approximation. They did not include the effect of resonance excitation, i.e., dielectronic capture by a Ne-like ion followed by autoionization leaving the Ne-like ion in an excited state. In this paper, we use the recent calculations of this process by B. W. Smith, J. C. Raymond, J. B. Mann, and R. D. Cowan [Astrophys. J. (in press)] to explore the effect of resonance excitation on gain coefficient calculations for the ion Fe XVII. We find substantial differences (factors of about 1.3–3) between gain coefficient calculations with and without the inclusion of resonances at low temperatures. However, these effects are not important at the temperatures considered by Feldman, Seely, and Bhatia for Fe XVII.
Effects of frequency on optical emission, electrical, ion, and etching characteristics of a radio frequency chlorine plasma
Authors: Donnelly Vincent M. , Flamm Daniel L. , Bruce Richard H.
Published: July 2002

The effects of excitation frequency (10 kHz–25 MHz) on plasma etching, voltage-current characteristics, emission spectra, and ion densities and energies in the sheath of chlorine plasmas, have been studied at 0.3 Torr using several techniques. Emission spectra and mass spectral analysis of ions extracted from the sheath region show a dramatic increase in the Cl+ signal as frequency is lowered through the ion–transit frequency near ∼1 MHz. Concurrently, the voltage at constant power and energy of ions impinging on the electrodes increase dramatically, while the etch rate of poly-Si increases due to ion-enhanced reactions. The Cl+2 ion density and degree of Cl2 dissociation to Cl atoms were found to be roughly frequency independent.
Longitudinal dynamic stress measurements with in-material piezoresistive gauges
Authors: Rosenberg Z. , Partom Y.
Published: July 2002

The response of piezoresistance gauges to dynamic stress loading is analyzed in a general framework which is based on the elasto-plastic properties of the gauge material. This analysis is then applied to manganin transducers on which a relatively large number of empirical calibration curves has been determined in the past 20 years. It is shown that most of the apparent discrepancies between these calibrations can be accounted for by considering the different stress and strain states for wire gauges and foil gauges. We also show how the low stress calibration for manganin wire can be accounted for by considering the nonhydrostatic nature of the material in which the gauge is embedded.
Rutherford backscattering studies of plasma-etched silicon
Authors: Oehrlein Gottlieb S.
Published: July 2002

Near-surface modifications of Si induced by reactive ion etching (RIE), such as surface residues and a disordered Si near-surface region, have been studied by He ion channeling. The dependence of the surface residue layer thickness/composition and the Si surface disorder intensity on the etching gas (mixture) used, the plasma exposure time, and the applied rf power density were investigated. For the case of SiO2/Si selective etching (Si etch rate low), thicker surface residue layers were formed and the Si near-surface disorder was more intensive than for a nonselective RIE process. In selective SiO2/Si etching, both Si substrate disorder and surface residue layer thickness increase initially with plasma exposure time of the substrate. The intensity of Si substrate disorder was found to increase with greater self-bias voltage (caused by more rf power) applied during etching. A thermal annealing study showed that the observed Si disorder must be due to several distinct silicon defect states and is not equivalent to amorphized Si. The deposited C,F-layer thickness was found to depend on the ion bombardment possible during reactive ion etching; above a certain ion energy threshold C,F-layer deposition is suppressed. Various approaches to recover high-quality Si surfaces following RIE were evaluated. Due to the complexity of the near-surface modifications caused by plasma exposure of a Si specimen, simple thermal annealing is ineffective in restoring the surface properties. Promising recovery techniques for device-quality surfaces were found to be O2 RIE and O2 annealing post-RIE treatments. Possible difficulties of the channeling method in the characterization of dry-etched Si were demonstrated by the observation of ion-beam-induced surface impurity desorption and surface-roughness-related Si surface peak areal density changes.
The activation energy of copper shallow acceptors in mercury cadmium telluride
Authors: Chen M. C. , Tregilgas J. H.
Published: July 2002

The thermal activation energy (E0) of isolated copper shallow acceptors in bulk Hg0.8Cd0.2Te has been determined using variable-temperature Hall measurements on samples with 77-K carrier concentrations ranging between 1015 and 1017 cm−3. It was found that the decrease of the activation energy with the increasing hole concentration can be adequately described by the screening of the acceptor potential by free carriers. The measured E0 (11.5 meV) also agrees well with that predicted by the effective-mass theory.
Corrosion characteristics of RE-Fe-B permanent magnets
Authors: Willman C. J. , Narasimhan K. S. V. L.
Published: July 2002

The corrosion characteristics of RE-Fe-B magnets in elevated temperature and/or high humidity and salt-containing environments are reported. Magnetic properties, magnet integrity, and corrosion product were evaluated. Methods of improving the corrosion resistance of RE-Fe-B magnets were also investigated. Epoxy-type coatings were found to be successful for many applications.
An improved deep level transient spectroscopy method
Authors: Hjalmarson Harold P. , Samara G. A. , Farmer John W.
Published: July 2002

An examination of the DLTS (deep level transient spectroscopy) technique suggests a new method for analyzing data for DLTS signal intensity S(T) as a function of temperature T. It is shown that the low-temperature asymptotic slope of a plot of ln S(T) vs 1/T yields the activation energy for deep level emission rates. Thus, in the new method, deep level energies are obtained from one run at a given rate window in contrast with traditional DLTS for which several runs at various rate windows are needed to obtain the same information.
Photothermal wave imaging of metal-oxide-semiconductor field-effect transistor structures
Authors: Mandelis Andreas , Williams Andrew , Siu Edwin K. M.
Published: July 2002

A photothermal wave imager has been assembled and used to generate thermal-wave images of an active metal-oxide-semiconductor field-effect and related inactive microelectronic structure fabricated on a silicon chip. The imager, which monitors the thermoelastic surface deformation due to absorption of a highly focused, intensity-modulated heating laser beam, has proven to be capable of producing images of subsurface features related to processing steps (thermal-wave depth profiling) at open circuit, as well as current flow sensitive images related to electronic processes in the active transistor (plasma-wave depth profiling).
High current, small divergence electron beams produced by laser-induced surface photoelectric effect
Authors: Charalambidis D. , Hontzopoulos E. , Fotakis C. , Farkas Gy. , Tóth Cs.
Published: July 2002

The potential application of the laser induced linear surface photoelectric effect for high current and small divergence electron beam formation is examined. The temporal evolution of the current pulses and the angular distribution of the photoelectrons produced following KrF laser irradiation of a gold surface is studied as a function of laser intensity. A threshold laser intensity of (140±20) MW/cm2 was determined, below which the single photon photoeffect dominates any laser induced thermionic emission process. Electron current measurements for vertical and horizontal polarization of the incident laser radiation showed that the current contribution from the surface photoeffect is about three times larger than that from the volume photoeffect. Under these conditions, an angular distribution of the produced electrons of 17°±2° was determined. The estimated normalized transverse beam emittance is 20π mm mrad.
Properties of metal clusters in polymerized hydrocarbon versus fluorocarbon matrices
Authors: Laurent C. , Kay E.
Published: July 2002

The ability to produce transition-metal clusters dispersed in a polymeric matrix by metal sputtering and plasma polymerization in a rf capacitively coupled diode reactor svstem was investigated. An in situ plasma diagnostic technique, i.e., optical emission spectroscopy, was used to predict the metal concentration of the film. Characterization of metal-containing plasma-polymerized propane thin films was realized using x-ray photoelectron spectroscopy, x-ray fluorescence, Raman spectroscopy, transmission electron microscopy, and electron diffraction. Evidence is given that the metal is present in its metallic state in the organic matrix and in the form of uniformly dispersed small particles. The shape and size of gold and cobalt particles at equivalent volume fractions are shown to be different, which is reflected in different electrical percolation threshold values for the two systems.
Separation of surface and volume absorption by photothermal deflection
Authors: Nie Y.-X. , Bertrand L.
Published: July 2002

A complete theoretical treatment of sine-wave photothermal deflection spectroscopy in a sample that includes surface absorption and bulk absorption is given. The results can be used to separate surface absorption from bulk absorption, and the surface absorption by almost all optical coatings can be measured by this method. The theoretical results have been verified experimentally.
Liquid junctions for characterization of electronic materials. II. Photoreflectance and electroreflectance of n-Si
Authors: Shen Wu-Mian , Fantini M. C. A. , Tomkiewicz Micha , Gambino J. P.
Published: July 2002

We compare the photoreflectance of the n-Si/air interface with the electrolyte-electroreflectance and electrolyte-photoreflectance of the n-Si/methanol interface. We observe reversible changes in line shape and in peak position of the photoreflectance signals, upon introduction of the electrolyte. The methanol proved to be the constituent that drives these changes. We have interpreted the effect of the electrolyte to be due to modifications of the kinetics of equilibration between the surface states and the space-charge layer. This is supported by the frequency dispersion experiments in which we have demonstrated that the presence of the methanolic electrolyte causes a decrease in the relaxation time of the surface states by more than an order of magnitude.