bluuebunny/crossref_metadata_2025 huggingface dataset:
ENTROPY, TRANSINFORMATION AND WORD DISTRIBUTION OF INFORMATION-CARRYING SEQUENCES
Authors: EBELING WERNER , POSCHEL THORSTEN , ALBRECHT KARL-FRIEDRICH
Published: November 2004

We investigate correlations in information carriers, e.g. texts and pieces of music, which are represented by strings of letters. For information carrying strings generated by one source (i.e. a novel or a piece of music) we find correlations on many length scales. The word distribution, the higher order entropy and the transinformation are calculated. The analogy to strings generated through symbolic dynamics by nonlinear systems in critical states is discussed.
A TEST FOR A BIOLOGICAL SIGNAL ENCODED BY NOISE
Authors: PETRACCHI DONATELLA , BARBI MICHELE , CHILLEMI SANTI , PANTAZELOU ELENI , PIERSON DAVID , DAMES CHRIS , WILKENS LON , MOSS FRANK
Published: November 2004

We consider here a simple example of stimulated sensory neurons operating under the influence of their own internal noise: the hair mechanoreceptor of the crayfish stimulated by a weak, periodic, hydrodynamic signal. Action potential spike trains from the sensory neuron are recorded and assembled into two objects for analysis: the interspike interval histogram (ISIH) and the cycle histogram of the spike density. A time transformation is carried out on the ISIH’s in order to test the hypothesis that the spike train is basically random and that the probability of coherent spike generation is related to the instantaneous stimulus amplitude. Moreover it is shown that the physiological spike train data can be qualitatively mimicked by an electronic Fitzhugh-Nagumo model, operated in the subcritical mode, driven by noise and a weak periodic signal. A discussion of how the Fitzhugh-Nagumo model is properly operated to mimic noisy data from sensory neurons is included.
EXPERIMENTAL DYNAMICS OF A HANGING CABLE CARRYING TWO CONCENTRATED MASSES
Authors: BENEDETTINI FRANCESCO , MOON FRANCIS C.
Published: November 2004

The dynamics of a massless hanging cable with two heavy masses is examined experimentally. The experiment is also a model for a three-dimensional four-bar linkage or two coupled spherical pendulums. The system is subjected to a periodic in-phase and out-of-phase vertical motion of the hanging points. The regions of instability of the planar motion in which the system exhibits prechaotic and chaotic behavior are described by means of the Fourier transform, probability density function, and autocorrelation function. Charts of behavior in the frequency-amplitude excitation parameter plane show regions of periodic, quasiperiodic, and chaotic motions. In the chaotic regime a reconstruction from a scalar time series of the global properties of the attractor is done by means of the delay map technique. An analytical model is developed to compare analytical and numerical results. The structure of the experimental global attractor suggests a Shil’nikov model for the transition to chaotic behavior.
BORDER-COLLISION BIFURCATIONS FOR PIECEWISE SMOOTH ONE-DIMENSIONAL MAPS
Authors: NUSSE HELENA E. , YORKE JAMES A.
Published: November 2004

We examine bifurcation phenomena for continuous one-dimensional maps that are piecewise smooth and depend on a parameter μ. In the simplest case, there is a point c at which the map has no derivative (it has two one-sided derivatives). The point c is the border of two intervals in which the map is smooth. As the parameter μ is varied, a fixed point (or periodic point) Eμ may cross the point c, and we may assume that this crossing occurs at μ=0. The investigation of what bifurcations occur at μ=0 reduces to a study of a map fμ depending linearly on μ and two other parameters a and b. A variety of bifurcations occur frequently in such situations. In particular, Eμ may cross the point c, and for μ<0 there can be a fixed point attractor, and for μ>0 there may be a period-3 attractor or even a three-piece chaotic attractor which shrinks to E0 as μ→0. More generally, for every integer m≥2, bifurcations from a fixed point attractor to a period-m attractor, a 2m-piece chaotic attractor, an m-piece chaotic attractor, or a one-piece chaotic attractor can occur for piecewise smooth one-dimensional maps. These bifurcations are called border-collision bifurcations. For almost every point in the region of interest in the (a, b)-space, we state explicitly which border-collision bifurcation actually does occur. We believe this phenomenon will be seen in many applications.
CHAOTIC BEHAVIOR IN AN ADVERTISING DIFFUSION MODEL
Authors: FEICHTINGER G. , GHEZZI L.L. , PICCARDI C.
Published: November 2004

The paper is concerned with an advertising diffusion model where a firm devotes a fixed proportion of sales to advertising, while customers go through a two-stage adoption process. The model takes the form of a second-order, time-invariant, nonlinear dynamic system, in which a homoclinic bifurcation to infinity is shown to exist. Allowance is subsequently made for a seasonal fluctuation in the firm’s advertising rate. A bifurcation study of the periodic solutions is then accomplished by means of a continuation procedure. Emphasis is placed on the emergence of chaos. Only the chaotic solutions stemming from a cascade of period doublings appear to be economically meaningful.
FLUCTUATIONS IN THE STATE OF CHAOS-CHAOS INTERMITTENCY OF CHUA’S CIRCUIT
Authors: KOCH M. , TETZLAFF R. , WOLF D.
Published: November 2004

We studied the power spectrum of the normalized voltage across the capacitor parallel to a piecewise-linear resistor of Chua’s circuit in the “chaos-chaos intermittency” state [Anishchenko et al., 1992]. The investigations included various initial conditions and circuit parameter values without and with external excitation. In all cases we found spectra showing a 1/ω2-decay over more than four decades.
OBSERVATION OF SOME NEW PHENOMENA INVOLVING PERIOD TRIPLING AND PERIOD DOUBLING
Authors: GOSWAMI BINOY KRISHNA
Published: November 2004

We report the observation of some new phenomena in the nonlinear dynamics of periodically driven, damped oscillators. We have observed period tripling in the form of saddle node bifurcation in the neighborhood of the original period which remains stable. Period tripling is found to be as generic as period doubling. As a consequence, the dynamics involving period tripling and doubling exhibit a new self similarity. These observations are obtained from the numerical simulation of a periodically forced class B laser.
ON THE GENERATION OF SCROLL WAVES IN A THREE-DIMENSIONAL DISCRETE ACTIVE MEDIUM
Authors: PIVKA LADISLAV , ZHELEZNYAK ALEXANDER L. , WU CHAI WAH , CHUA LEON O.
Published: November 2004

This paper reports on the simulation, in three-dimensional cellular-neural-network (CNN) arrays of Chua’s circuits, of basic three-dimensional scroll wave patterns observed previously from other media. Among the simulated patterns are the straight scroll wave, twisted scroll wave in both homogeneous and inhomogeneous media, as well as the scroll ring. These types of waves have been obtained for only one set of circuit parameters by varying the initial conditions.
RETRIEVING DYNAMICAL INVARIANTS FROM CHAOTIC DATA USING NARMAX MODELS
Authors: AGUIRRE LUIS ANTONIO , BILLINGS S.A.
Published: November 2004

This paper is concerned with the estimation of dynamical invariants from relatively short and possibly noisy sets of chaotic data. In order to overcome the difficulties associated with the size and quality of the data records, a two-step procedure is investigated. Firstly NARMAX models are fitted to the data. Secondly, such models are used to generate longer and cleaner time sequences from which dynamical invariants such as Lyapunov exponents, correlation dimension, the geometry of the attractors, Poincaré maps and bifurcation diagrams can be estimated with relative ease. An additional advantage of this procedure is that because the models are global and have a simple structure, such models are amenable for analysis. It is shown that the location and stability of the fixed points of the original systems can be analytically recovered from the identified models. A number of examples are included which use the logistic and Hénon maps, Duffing and modified van der Pol oscillators, the Mackey-Glass delay system, Chua’s circuit, the Lorenz and Rössler attractors. The identified models of these systems are provided including discrete multivariable models for Chua’s double scroll, Lorenz and Rössler attractors which are used to reconstruct the trajectories in a three-dimensional state space.
A PRACTICAL METHOD FOR THE MEASUREMENTS OF THE CHAOTICITY OF ELECTRIC AND MAGNETIC BRAIN ACTIVITY
Authors: KOWALIK ZBIGNIEW J. , ELBERT THOMAS
Published: November 2004

The degree of complexity of the cortical processes related to different cognitive actions should logically produce an image in the electric and magnetic signals of the human brain. Hence, those measures of chaoticity will depend on the particular task being investigated. In many cases, the duration of a brain process does not allow for the generated signal to be treated as stationary. Therefore, the application of the standard method of nonlinear system theory is often questionable. The chaoticity of the process has to characterize the predictability of future state of the system. In the stationary case, such a quantity can be directly expressed by the largest Lyapunov exponent or by K-S entropy.

In this study, we performed a test for the applicability of the local Lyapunov exponent for the description of the chaoticity of the brain processes measured in EEG and MEG experiments. We demonstrate an algorithm for computation of chaoticity based on the local Lyapunov exponent and present possible applications of this method for specific cases with a diagnosis of schizophrenia or of tinnitus. We also show that chaoticity is able to detect critical transitions (phase-transition-like phenomena) which occur in the dynamics of neural mass activity at a specific point in time.
SOLITON TRAINS AND I–V CHARACTERISTICS OF LONG JOSEPHSON JUNCTIONS
Authors: MAKSIMOV A.G. , NEKORKIN V.I. , RABINOVICH M.I.
Published: November 2004

Soliton dynamics in a perturbed sine-Gordon equation modeling a long Josephson junction is investigated. Solitons are found to exist in both simple and chaotic forms. Soliton synchronization by an alternating magnetic field is analysed. Current-voltage characteristics of Josephson junction are plotted.
ON THE EFFECT OF FLUCTUATIONS ON AN INTERMITTENT LAMINAR MOTION
Authors: AGOUDOV N.V. , MALAKHOV A.N.
Published: November 2004

This paper is concerned with the effect of external fluctuations on the type 1 intermittency considered in detail by Hirsch et al. [1982]. The exact average path length of the regular (or laminar) regime is derived on the basis of the solution of the Fokker-Planck equation for one particular example. This average path length is shown to increase with noise intensity growth under certain values of system parameters and noise intensity. The causes of this phenomenon and its origin are discussed, and the maximal value of the average path length and corresponding value of noise intensity are estimated.
CHAOTIC SYNCHRONIZATION OF MUTUALLY-COUPLED GENERATORS WITH FREQUENCY-CONTROLLED FEEDBACK LOOP
Authors: ALEXEYEV A.A. , SHALFEEV V.D.
Published: November 2004

In this paper we report the results of analog and numerical modelling of dynamics from a system comprised of two mutually-coupled generators, each of which has a local feedback loop of frequency control. It is shown that the partial system—single generator with a controlled loop can exhibit a significantly rich variety of dynamical regimes, including stochastic regimes. As one of our main results we consider the effect of mutual stochastic synchronization observed in an ensemble of two such generators coupled symmetrically for definite values of the coupling parameter and parameters of generators.
CONTROLLING CHAOS OF AN UNCERTAIN LOZI SYSTEM VIA ADAPTIVE TECHNIQUES
Authors: GONZÁLEZ GRACIELA ADRIANA
Published: November 2004

A case on the control of chaotic dynamical systems is presented. The chaotic Lozi system is taken with the aim to drive its trajectories to certain given reference points even when there are uncertainties on the parameters of the system. The control objective is reached by applying adaptive control laws.
MECHANICAL STICK-SLIP VIBRATIONS
Authors: GALVANETTO U. , BISHOP S.R. , BRISEGHELLA L.
Published: November 2004

In this paper we consider the behavior of a two degree-of-freedom mechanical system incorporating static and dynamic friction, assumed to be a decreasing function of the relative sliding velocity. The model consists of two blocks linked by springs, which ride upon a moving belt. The dynamics of the system are described within a four-dimensional phase space. A three-dimensional Poincaré map is discussed together with a simpler one-dimensional map of a scalar variable. Considering the one-dimensional map it is possible to study all the attractors of the system for small belt velocities including the construction of one-dimensional basins of attraction. Thus, albeit in a partial zone of the control-phase space, the global dynamics of the system can be characterized displaying periodic, quasi-periodic and chaotic oscillations.
SECONDARY BIFURCATIONS AND SYMMETRY BREAKING AS A ROUTE TOWARDS SPATIOTEMPORAL DISORDER
Authors: PROCTOR M.R.E. , LEGA J.
Published: November 2004

We analyse an equation describing long-wavelength transverse instabilities of a roll-like periodic pattern that has solutions which undergo a series of transitions between states with different symmetries as the order parameter is changed. The transitions appear when the solutions are already chaotic and so are not bifurcations of the usual type. We investigate the first of these transitions in detail, and relate the results to those of a simple low order truncation of the governing p.d.e.’s.
COMPARISON OF EEG TIME SERIES FROM RAT OLFACTORY SYSTEM WITH MODEL COMPOSED OF NONLINEAR COUPLED OSCILLATORS
Authors: KAY LESLIE , SHIMOIDE KOJI , FREEMAN WALTER J.
Published: November 2004

The so-called “spontaneous,” background, or “basal” time series of electroencephalographic (EEG) data from rat olfactory cortex are compared with those generated by a model of the ol-factory system, denoted KIII, composed of nonlinear coupled second order ODEs with feedback delay. Each ODE (KO) represents a neural mass having either excitatory or inhibitory output to the ODEs to which it connects. Connected mutually inhibitory or mutually excitatory pairs represent populations of similar neurons interacting to form one structure (KI set). A connected set (KII set) of excitatory and inhibitory KI sets (KIe and KIi) represents the activity of a gross structure in the olfactory system (the olfactory bulb—OB, anterior olfactory nucleus—AON, and prepyriform cortex—PPC or PC). The set of KII sets connected with dispersion-delay feedback pathways (KIII set) form a model of the first central stage of olfactory perceptual processing upon olfactory stimulation, with transition on receptor input from a self-sustained basal state of activity to an induced burst.

Both basal and stimulated states are studied using amplitude histograms, power spectra, attractor reconstruction, visual inspection of traces, and correlation. A comparison shows that the two systems are similar, having broad spectra, correlation functions that rapidly go to zero, and gaussian amplitude histograms. Activity is nearly periodic and higher amplitude in the excited state and aperiodic, lower amplitude in the basal state with close to 1/f falloff. Cross spectra between OB and PPC show wide frequency bands of coherent high frequency activity in both the model and rat. The excited state nearly periodic frequencies differ between the KIII model and rat (30–60 Hz in KIII, 50–100 Hz in rat EEG), because the KIII model was developed for the cat and the rabbit, which have lower frequencies than the rat. These benchmarks may be used to evaluate the physiological validity of the output produced by a proposed model, as all components of the system and its connectivity were derived from or evaluated by physiological data.
THE CONLEY INDEX AND GLOBAL BIFURCATIONS I: CONCEPTS AND THEORY
Authors: KAPPOS EFTHIMIOS
Published: November 2004

The Morse index is defined for a hyperbolic equilibrium point of a vector field as the dimension of its unstable manifold. This paper presents the theory of the Conley index, which is a farreaching generalization of the Morse index. It also outlines how this new index can be used to solve global bifurcation problems. In fact, we shall argue that the Conley index methods constitute the most appropriate and natural set of tools for studying global aspects of flows. The reason for this is that we have known since the time of Poincaré that global questions have always involved topological considerations. (A typical elementary question involving topology is the following: in what subsets of Euclidean space is it possible to define a "potential function" if we are given its "gradient" — in the form of a smooth vector field, say?)

The presentation we give is elementary and is addressed to those with no more than a passing acquaintance with the problems and methods of topology. The aim will be to motivate the concepts introduced, to give a number of examples and to only present the theory that is needed for applications. A second part will present illustrative applications in greater detail.
A NECESSARY AND SUFFICIENT CONDITION TO HAVE r PAIRS OF COMPLEX MULTIPLIERS WITH MODULUS EQUAL TO UNITY IN THE CASE OF AN n-DIMENSIONAL MAP
Authors: CARCASSES JEAN-PIERRE
Published: November 2004

Considering a cycle (or periodic point) of an n-dimensional map, a bifurcation occurs when at least one of its multipliers crosses the unit circle in the complex.plane. This paper presents a necessary and sufficient condition for the bifurcations occurring when r pairs of complex multipliers cross the unit circle. Among this kind of bifurcations, the most known is the Neimark's bifurcation corresponding to the case when r is equal to one. From the established condition, an algorithm to trace out these bifurcation curves in a parameter plane of the considered map is displayed.
CHAOTIC MEMORY DYNAMICS IN A RECURRENT NEURAL NETWORK WITH CYCLE MEMORIES EMBEDDED BY PSEUDO-INVERSE METHOD
Authors: NARA SHIGETOSHI , DAVIS PETER , KAWACHI MASAYOSHI , TOTSUJI HIROO
Published: November 2004

It is shown that hierarchical bifurcation of chaotic intermittency among memories can be induced by reducing neural connectivity when sequences of similar patterns are stored in a recurrent neural network using the pseudo-inverse method. This chaos is potentially useful for memory search and synthesis.
LOW-DIMENSIONAL CHAOS IN A PERTURBED KORTEWEG–DE VRIES EQUATION
Authors: TIAN X. , GRIMSHAW R. H. J.
Published: November 2004

Spatial chaos has been observed in the steady state from a numerical study of a perturbed Korteweg–de Vries equation. The onset of chaos is due to a subharmonic bifurcation sequence. A second route to chaos is also observed via a period-doubling sequence generated from each fundamental subharmonic state.

In this paper, the question of determining low-dimensional chaos in this perturbed KdV equation is addressed. The dimension of this system in the steady state is estimated from the corresponding ordinary differential equation via the Lyapunov spectrum, and also from a numerical investigation via a reconstructed attractor using a spatial series.
EXPERIMENTS ON SPEECH AND MUSIC SIGNALS TRANSMISSION USING CHAOS
Authors: DMITRIEV A. S. , PANAS A. I. , STARKOV S. O.
Published: November 2004

This letter presents experimental evidence of how to use Chua's circuit for creating a system transmitting complex analog signals such as speech and music. In comparison with other proposed systems our system has the advantage of being operational over a wide dynamic range of information to chaotic signal ratios.
BIFURCATIONS IN HEART RHYTHMS
Authors: CHAY TERESA REE
Published: November 2004

Heart rhythms exhibit the following interesting phenomena: First, rhythmic cells such as sinus node cells cease their rhythmic activity when a single brief current pulse of the right magnitude is given to the cell at the right time. Second, a premature pulse can initiate a tachycardia (i.e., reentrant arrhythmia) from a quiescent atrial tissue. This tachycardia can be sustained for hours until another brief current pulse is given. Third, ECG recording sometimes shows alternans in electrical activity prior to ventricular tachycardia. Some suggested that this alternans is the first bifurcation in a period doubling sequence. Fourth, a certain class of antiarrhythmic drugs may increase the chance of sudden cardiac death for patients with a history of myocardial infarction. Fifth, when an "adjustable" tricuspid ring is shortened, the conduction velocity of a reentrant wave becomes oscillatory. When the ring size is shortened further, reentry terminates after several oscillatory cycles. Sixth, sustained reentry arises in a tricuspid ring when Class IC drugs (i.e., which exclusively block the sodium channel) are added. On the other hand, Class III (which exclusively blocks the potassium channel) can terminate sustained reentry in the tricuspid ring. In this tutorial review, we explain how one can utilize a bifurcation analysis to explain all these interesting phenomena involved in heart rhythms.
SPIRALS IN SCALAR REACTION–DIFFUSION EQUATIONS
Authors: DELLNITZ MICHAEL , GOLUBITSKY MARTIN , HOHMANN ANDREAS , STEWART IAN
Published: November 2004

Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes "spiral" boundary conditions (ur = muθ). Spiral boundary conditions are motivated by assuming that a solution is infinitesimally an Archimedian spiral near the boundary. It follows from a bifurcation analysis that for this form of spirals there are no singularities in the spiral pattern (technically there is no spiral tip) and that at bifurcation there is a steep gradient between the "red" and "blue" arms of the spiral.
NONLINEAR TIME SERIES ANALYSIS OF THE STOCK EXCHANGE: THE CASE OF AN EMERGING MARKET
Authors: PAPAIOANNOU G. , KARYTINOS A.
Published: November 2004

The extent to which daily return data from the Athens' Stock Exchange Index exhibits non-linear and chaotic characteristics is investigated by employing multiple tests from both the Economics' and the Natural Sciences' fields. The BDS test and Rescale Range (R/S) analysis provide evidence for non-linearity and fractality due to noisy chaos, respectively, while methods of chaotic dynamics, like correlation dimension and related tests, as well as, Lyapunov exponents, give consistent results, which do not rule out the possibility of deterministic chaos. The occurrence of a simple low-dimensional attractor, is not supported. However, noise filtered data by the use of SVD analysis and FIR filters, gives reliable evidence for the existence of an underlying dynamical system with a limited number of degrees-of-freedom.
CONSTRUCTING LORENZ TYPE ATTRACTORS THROUGH SINGULAR PERTURBATIONS
Authors: DENG BO
Published: November 2004

Lorenz type attractors are constructed by singular perturbations. The technique is based on a new type of fast switching subsystem and the method of Deng [1994]. New attractors of the Lorenz type are found when parameters in the system are varied. The singular limit attractors are also presented in terms of one-dimensional mappings.
SYMMETRY BREAKING BIFURCATIONS OF CHAOTIC ATTRACTORS
Authors: ASTON PHILIP J. , DELLNITZ MICHAEL
Published: November 2004

In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators.
ON BIFURCATIONS IN THE SCHRÖDINGER PROBLEM ADMITTING OF AN EXISTENCE OF NONLINEAR SHIFT OPERATORS
Authors: ELEONSKY V. M. , KOROLEV V. G.
Published: November 2004

The problem of reconstruction of one-dimensional potentials with a given spectrum that is strictly equidistant except for one gap of a specified size and location is solved. This problem leads to a necessity of a nonlinear generalization of spectral shift operators. The solvability condition for an equation for these operators generates a dynamical system for possible potentials.

Two classes of symmetric and regular in ℛ1 potentials obeying this equation are found and investigated in detail. The first class is a countable set of one-parameter families of anharmonic oscillators with a spectrum as described above. The second class is a countable set of two-parameter families of complicated potentials with asymptotics that oscillate with linearly increasing frequency and amplitude. The spectrum of that class is a combination of three strictly equidistant sequences of levels with the ground states shifted arbitrarily relative to each other.

Bifurcations of those potentials under changes of structure parameters as well as bifurcations of corresponding spectra have been studied.
THE ATTITUDE STABILITY OF THE STATIONARY MOTIONS OF A DUMBBELL SATELLITE IN THE CASE OF AIR DRAG
Authors: BÉDA P. B.
Published: November 2004

This letter investigates the effect of the length of an Earth orbiting dumbbell system on the number and the Lyapunov stability of its stationary motions. This effect appears when a weak aerodynamical drag is taken into consideration and being important for low orbit satellites. The equation of motion is obtained as a Lagrange equation. Using analytical methods a critical length can be found causing essential changes in the structure of the set of stationary positions and in the stability properties, too. For longer systems the number of stationary positions is four, for shorter ones it is two. In the critical case the other two positions come together and disappear in a saddle-node bifurcation. The numerical values of the bifurcation point and of the critical length are also presented in a case described in the literature.
A CONTINUED FRACTION TITBIT
Authors: KEANE MICHAEL
Published: November 2004

In 1812 Gauss, in a letter to Laplace, proposed without proof a formula explaining the statistical regularity of continued fractions. There has since been speculation concerning the manner in which Gauss arrived at this formula. In this article we present a plausible explanation, which at the same time gives an elementary proof of the full ergodic nature of the underlying dynamical system. The method seems to be of interest for other number-theoretic expansions.
FRACTALS BY NUMBERS
Authors: BARBÉ ANDRÉ M.
Published: November 2004

We introduce an extension of an earlier defined simple, number-based matrix substitution system for obtaining fractal matrices, by considering cyclic substitutions. The elements of the resulting matrices are related to representations of their addresses in a mixed number base. The Hutchinson operator for the limit form of a geometrical representation of the fractal matrix is derived. It is shown that the class of fractal limit sets obtainable from cyclic substitutions does not extend the class obtainable from the simple substitutions.
WHEN AN INFINITELY-RENORMALIZABLE ENDOMORPHISM OF THE INTERVAL CAN BE SMOOTHED
Authors: TRESSER CHARLES , WILKINSON AMIE
Published: November 2004

Let K be a closed subset of a smooth manifold M, and let f: K→K be a continuous self-map of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism of the ambient space M. We give a necessary condition for the smoothability of the faithfully infinitely interval-renormalizable homeomorphisms of Cantor sets in the unit interval. This class contains, in particular, all minimal homeomorphisms of Cantor sets in the line which extend to continuous maps of an interval with zero topological entropy.
OPTIMAL GEOMETRY IN EQUILIBRIUM AND GROWTH
Authors: ALMGREN FRED , TAYLOR JEAN E.
Published: November 2004

We discuss geometric optimization as a mathematical device with which to model several natural processes involving surface free energy.
SUPER BROWNIAN MOTION IS A FRACTAL MEASURE FOR WHICH THE MULTIFRACTAL FORMALISM IS INVALID
Authors: TAYLOR S. JAMES
Published: November 2004

Whenever Xt is the measure value of super Brownian motion in Rd(d≥3), and [Formula: see text]St is the topological support of Xt it is known7 that there is a positive constant c, depending only on d, such that for every Borel set A, [Formula: see text] There is no such exact measure function for packing measure, but it follows from the precise results in Ref. 16 that the packing dimension as well as the Hausdorff dimension of St is 2. This means that Xt is dimension regular with exact dimension 2. We describe some of the key ideas, written up in Ref. 24, which show that a.s. [Formula: see text] while [Formula: see text] is not empty for 2<β<4. Further Aβ is not dimension regular since dim Aβ=[Formula: see text]. For this reason the multifractal formalism used in Ref. 11 or Ref. 9 is invalid because their function τ(q) cannot exist.
COOPERATIVE STRATEGIES IN FORMATION OF COMPLEX BACTERIAL PATTERNS
Authors: BEN-JACOB ESHEL , SHOCHET OFER , COHEN INON , TENENBAUM ADAM , CZIRÓK ANDRAS , VICSEK TAMAS
Published: November 2004

In nature, bacterial colonies often must cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication channels on all levels. The result is that a profusion of complex patterns are formed during growth of various bacterial strains and for different environmental conditions. Some qualitative features of the complex morphologies may be accounted for by invoking ideas from pattern formation in non-living systems together with a simplified model of chemotactic “feedback”. We present a non-local communicating walkers model to study the effect of local bacterium-bacterium interaction and communication via chemotaxis signaling. The model is an hybridization of the continuous approach (to handle chemicals’ diffusion) and the atomistic approach (each “atom” or “walker” represents 104–105 bacteria). Using the model we demonstrate how communication enables the colony to develop complex patterns in response to adverse growth conditions. Efficient response of the colony requires self-organization on all levels, which can be achieved only via cooperative behavior of the bacteria. It can be viewed as the action of an interplay between the micro-level (the individual bacterium) and the macro-level (the colony) in the determination of the emerging pattern. We show that seemingly unrelated patterns can result from the employment of the same generic strategies.
FRACTAL GROWTH OF BACTERIAL COLONIES
Authors: FAMILY FEREYDOON
Published: November 2004

The dynamics of the growth of three different strains of bacteria, ATCC 25589, Bacillus subtilis and Escherichia coli, was studied under different conditions of low as well as rich nutrient concentrations. We find that within the statistical fluctuations in the experimental data, the mean radius of the bacterial colonies grow with a power of time and the exponent characterizing this power law growth has an anomalous value. We present and discuss a simple phenomenological approach for explaining the existence of anomalous power-law exponents in bacterial growth. This approach may be useful in determining the key mechanisms which control the growth and morphology of bacterial colonies.
A NONLOCAL COMPUTATIONAL BOUNDARY CONDITION FOR DUCT ACOUSTICS
Authors: ZORUMSKI WILLIAM E. , WATSON WILLIE R. , HODGE STEVE L.
Published: November 2004

A nonlocal boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two-dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three-dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new nonlocal boundary condition are shown to be consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.
PARABOLIC EQUATION DEVELOPMENT IN RECENT DECADE
Authors: LEE DING , PIERCE ALLAN D.
Published: November 2004

Numerous contributions have been made in the enhancement of the Parabolic Equation (PE) approximation method, which has been shown to be a useful tool for solving realistic problems in many different scientific fields. Evidence of its usefulness is the application of PE to solve ocean acoustic propagation problems. In early years, when the PE was introduced to the field of underwater acoustics, its main purpose was to predict long-range, low-frequency acoustic propagations in range-dependent environments; thus, there were certain limitations. In the recent decade, these limitations have been relaxed a great deal due to many useful contributions. The time has come to survey and report these important contributions and to discuss how these contributions enhance the capability of the PE method. This paper gives a brief review of what had been done before 1984 and highlights some important PE developments from 1984 to 1994. Also, some applications of the PE to predict ocean acoustic propagation problems will be presented. We shall call attention to a few important issues related to the PE developments and applications. Looking ahead we will discuss what more a PE can do in order to stimulate future research, development, as well as applications.
SOME ASPECTS OF THE PHYSICS AND NUMERICAL MODELING OF BIOT COMPRESSIONAL WAVES
Authors: CARCIONE JOSÉ M. , QUIROGA-GOODE GERARDO
Published: November 2004

We investigate the problem of wave propagation in a porous medium, in the framework of Biot's theory, computing the numerical solution of the differential equations by a grid method. The problems posed by the stiffness of the equations are circumvented by using a partition (or splitting) time integrator which allows for an efficient explicit solution as in the case of nonstiff differential equations. The resulting algorithm possesses fourth-order accuracy in time and "infinite" (spectral) accuracy in space. Alternatively, a second-order algorithm, based on a Crank–Nicolson method, provides similar stability properties, although lower accuracy. The simulations correctly reproduce the wave forms of the fast and slow compressional waves and their relative amplitudes. Moreover, we observe the static slow mode, particularly strong when the source is a bulk perturbation or a fluid volume injection. The numerical results are confirmed by the analytical solution.
EARLY STRUCTURAL STAGES OF METALLIC EPITAXY: THE MODEL CASE OF Fe/Cu (100)
Authors: HEINZ K. , BAYER P. , MÜLLER S.
Published: November 2004

By epitaxial growth of iron on Cu (100) phases of fcc-Fe can be stabilized at room temperature and below. Dependent on coverage the films show various superstructures which we investigate by quantitative analysis of low-energy electron diffraction intensities. There are three coverage regimes, whereby in the first one (Θ≤4 ML ) all iron layers are considerably reconstructed and are fcc(100) layers only on average. Upon further iron deposition (5 ML <Θ<10 ML ) subsurface iron layers flatten and only the top layer is reconstructed. Simultaneously, the epitaxial growth seems to change from pseudomorphic to nonpseudomorphic. At about 10 ML there is a 1. order phase transition fcc (100)⇒ bcc (110), the latter phase being stable at higher coverages. It turns out that the reconstruction of layers always entails an increased atomic volume available for iron atoms involved in the reconstruction. In turn this is consistent with magnetic properties known for the iron films from the literature, i.e., bulk ferromagnetism in the first coverage regime and only surface ferromagnetism in the second. So, magnetic and structural properties are shown to be closely related.
OBSERVATION OF PHASE TRANSITIONS AT THE (100) SURFACE OF Al-3 at.% Ag
Authors: WETLI E. , HOCHSTRASSER M. , PESCIA D. , ERBUDAK M.
Published: November 2004

In the bulk binary alloy Al-3 at.% Ag , Ag 2 Al precipitates are formed below 410°C which are reversibly dissolved at elevated temperatures. We have followed this phase transition at a (100) surface as a function of temperature by monitoring the bandwidth of the Ag 4d states in X-ray photoelectron spectroscopy. Since the bandwidth measures the coordination number of the emitting atoms, it directly reveals the short-range order of the Ag atoms at the surface. The measurements show that the dissolution of the Ag -rich clusters starts at temperatures at least 100 K below the bulk transition, and the observed hysteresis behavior is indicative of a first-order phase transition at the surface.
STRUCTURAL ANALYSIS OF THE INITIAL INTERACTION BETWEEN OXYGEN AND A CLEAN Si(100) BY TIME OF FLIGHT AND RECOILING SPECTROSCOPY
Authors: BOUSETTA A. , HSU C.C. , WANG Y.
Published: November 2004

The structure of both Si (100)in situ thermally annealed Si (100) at 1373 K and Si (100) exposed to dry oxygen at room temperature in the range 5 to 1700 Langmuirs, have been studied using time of flight and recoiling spectroscopy (TOF-SARS). Structural analyses were performed by recording the intensities of recoiled oxygen and silicon ions as a function of azimuthal angle. The results show that (1) the clean annealed Si (001) is dimerized, (2) oxygen chemisorbs at the surface at the Si-unsaturated bond, which are left unoccupied after the (2×1) reconstruction, and (3) at 100 L and above the Si surface is reconstructed into a (1×1) structure with the oxygen binding to the broken Si-Si dimer bonds.
THE EFFECT OF DEGRADATION OF DEPTH RESOLUTION ON THE INTERDIFFUSION DATA IN THIN POLYCRYSTALLINE Au-Ag MULTILAYER FILMS
Authors: BUKALUK ANTONI
Published: November 2004

Auger electron spectroscopy (AES) in conjunction with argon-ion sputtering was used to determine the diffusion profiles in the thin-film Au-Ag multilayer system. Interdiffusion coefficients, obtained in the temperature range of 175–250°C, have been derived from the change of the concentration amplitude of the structure and from the variation of the composition at the interface of two consecutive layers of the multilayer system. The influence of the depth resolution on the diffusion data have been analyzed and discussed.
STRUCTURE OF A SINGLE-ATOMIC LAYER OF COBALT ON THE Pt(111) SURFACE: A STUDY BY QUANTITATIVE LOW-ENERGY ELECTRON DIFFRACTION
Authors: ATREI ANDREA , GALEOTTI MONICA , BARDI UGO , TORRINI MARCO , ZANAZZI ERMANNO , ROVIDA GIANFRANCO
Published: November 2004

The atomic structure of the surface formed by depositing a single-atomic layer of cobalt on Pt (111) has been investigated using low-energy electron diffraction (LEED) crystallographic analysis. Cobalt grows at room temperature on the Pt (111) surface forming islands a single-atomic layer thick. The layer is ordered and it forms a 1×1 epitaxial phase where cobalt atoms are in an fcc registry with respect to the substrate.
HIGH-RESOLUTION CORE-LEVEL PHOTOEMISSION INVESTIGATIONS OF ALKALI ON ALUMINUM ADSORPTION SYSTEMS
Authors: ANDERSEN JESPER N.
Published: November 2004

The use of high-resolution core-level photoemission spectroscopy for investigating the geometrical aspects of alkali adsorption on aluminum surfaces is reviewed. Examples are given of the use of the technique for studies of the submonolayer growth modes of alkali overlayers, of the geometry of the strongly reconstructed ordered overlayer structures, and of temperature-induced phase transformations between metastable and stable alkali-induced structures.
ALKALI-METAL ADSORPTION GEOMETRIES ON METAL SURFACES FROM PHOTOELECTRON-DIFFRACTION EXPERIMENTS
Authors: FASEL R. , OSTERWALDER J.
Published: November 2004

The results of recent photoelectron-diffraction investigations of structures formed upon alkali-metal adsorption on metal surfaces are presented. A variety of unexpected phenomena that are in contrast to earlier beliefs is found to occur for many systems. Photoelectron diffraction, in its angle-scanned or energy-scanned mode, is found to provide a powerful and direct tool for the identification and investigation of unanticipated adsorbate geometries such as ontop adsorption, substitutional adsorption, and surface alloy formation.
QUANTUM CHEMICAL STUDY OF THE OXYGEN EVOLUTION ON THE PLATINUM AND RHODIUM OXIDIZED SURFACES
Authors: SHCHEKA OLEG L. , EMELINA TATYNA B. , KLIMENKO OKSANA O.
Published: November 2004

The nonempirical discrete-variational method of local-density approximation was used to study the peculiarities of the oxygen evolution reaction on the polycrystalline platinum and rhodium oxidized surfaces. The correlations of the electronic properties and electrocatalytic activity of purely oxidized and N-substituted in part of surfaces were noted. A comparison of the behavior of the platinum and rhodium electrode surface layers in oxygen evolution reaction was carried out. It was found that under the substitution of one oxygen atom in first coordination sphere of metal on the nitrogen atom, the surface electrocatalytic activity of both platinum and rhodium electrodes became identical.
CALCULATION OF CHARGE EXCHANGE IN POTASSIUM IONS/ATOMS SCATTERED FROM METAL SURFACES
Authors: PAN LIMIN , WANG YANSEN , HUANG FAYANG , TANG JIAYONG , YANG FUJIA
Published: November 2004

The charge-exchange processes of K ions/atoms scattered from metal surface are discussed in terms of the time-dependent Newns-Anderson quantum model with intra-atomic Coulomb interaction. The final charge-states distribution is calculated as a function of work function of the surfaces. The calculated results are compared with the experimental data. Furthermore, the probabilities of charge states of the moving K ions/atoms approaching to and leaving from the surface are demonstrated.
A SIMPLE MODEL FOR ORIENTATIONAL ORDERING OF A SILVER MONOLAYER ELECTRODEPOSITED ON A C(0001) SURFACE
Authors: MOLA E.E. , APPIGNANESSI A.G. , VICENTE J.L. , VAZQUEZ L. , SALVAREZZA R.C. , ARVIA A.J.
Published: November 2004

The model for the angular orientational energy (AOE) has been extended to hexagonal submonolayer domains of Ag electrodeposited at a constant overpotential on a C(0001) surface. These domains which are characterized by an epitaxy angle θ=15±5° and an Ag−Ag distance d Ag−Ag =0.330± 0.016 nm, can be considered as precursors of 3D Ag crystal formation, according to a Volmer-Weber type mechanism. Calculations are based upon a simple Hamiltonian evaluated by introducing the concept of the commensurable unit cell. A Fourier series expansion for the substrate potential was used. Results from the model predict the existence of a commensurable cell in agreement with the experimental data derived from STM imaging.
INITIAL STEPS OF ALKALI-METAL-PROMOTED OXIDATION OF THE Al(111) SURFACE
Authors: HUTTEL Y. , SOUKIASSIAN P. , MANGAT P.S. , HURYCH Z.
Published: November 2004

We investigate the initial Na-promoted oxidation of an Al surface at room temperature by core-level photoemission spectroscopy using synchrotron radiation. We bring the first evidence that, in the initial state, adsorbed oxygen atoms break the Na-Al bonds. This leads to the formation of an intermediate oxidation state involving both Na and Al sites with oxygen atom in a bridge-type site. This bonding configuration is shown to result from the Na/Al intermixing and appears as a precursor step playing a key role in the observed promoted oxidation. It is also likely to explain the formation, upon annealing, of Al oxides having a higher oxygen content than Al 2 O 3.
GLOBAL EXISTENCE AND ASYMPTOTIC STABILITY FOR THE NONLINEAR AND GENERALIZED DAMPED EXTENSIBLE PLATE EQUATION
Authors: CAVALCANTI M. M. , DOMINGOS CAVALCANTI V. N. , SORIANO J. A.
Published: November 2004

The nonlinear and damped extensible plate (or beam) equation is considered [Formula: see text] where Ω is any bounded or unbounded open set of Rn, α>0 and f, g are power like functions. The existence of global solutions is proved by means of the Fixed Point Theorem and continuity arguments. To this end we avoid handling the nonlinearity M(∫Ω|∇u|2dx) in the a priori estimates of energy. Furthermore, uniform decay rates of the energy are also obtained by making use of the perturbed energy method for domains with finite measure.
NON WELL POSEDNESS OF PARABOLIC EQUATIONS WITH SUPERCRITICAL NONLINEARITIES
Authors: ARRIETA JOSÉ M. , RODRÍGUEZ-BERNAL ANÍBAL
Published: November 2004

In this paper we show that several known critical exponents for nonlinear parabolic problems are optimal in the sense that supercritical problems are ill posed in a strong sense. We also give an answer to an open problem proposed by Brezis and Cazenave in [9], concerning the behavior of the existence time for critical problems. Our results cover nonlinear heat equations including the case of nonlinear boundary conditions and weigthed spaces settings. In the latter case we show that in some cases the critical exponent is equal to one.
COMBINATORIAL YAMABE FLOW ON SURFACES
Authors: LUO FENG
Published: November 2004

In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial Yamabe flow on the space of all piecewise flat metrics associated to a triangulated surface. We show that the flow either develops removable singularities or converges exponentially fast to a constant combinatorial curvature metric. If the singularity develops, we show that the singularity is always removable by a surgery procedure on the triangulation. We conjecture that after finitely many such surgery changes on the triangulation, the flow converges to the constant combinatorial curvature metric as time approaches infinity.
APPROXIMATIONS WITH VORTICITY BOUNDS FOR THE GINZBURG–LANDAU FUNCTIONAL
Authors: BETHUEL F. , ORLANDI G. , SMETS D.
Published: November 2004

We propose an approximation scheme for complex-valued functions defined on a smooth domain Ω: the approximating functions have a Ginzburg–Landau energy of the same magnitude as the initial function, but they possess moreover improved bounds on vorticity. As an application, we obtain a variant of a Jacobian estimate first established by Jerrard and Soner. This variant was conjectured by Bourgain, Brezis and Mironescu.