Chaos Nameplat
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

You Tube Flickr Twitter UniPHY Group iResearch App Facebook

Search Issue | RSS Feeds RSS
Next Issue

Mar 1999

Volume 9, Issue 1, pp. 1-253

Page 1 of 2 Pages Next Page | Jump to Page
back to top
RSS Feeds

Editorial: Nonlinear science in chemical engineering

John L. Hudson and Yannis G. Kevrekidis

Chaos 9, 1 (1999); http://dx.doi.org/10.1063/1.166375 (2 pages)

Full Text: | Download PDF

Abstract Unavailable
Show PACS
05.45.-a Nonlinear dynamics and chaos
01.10.-m Announcements, news, and organizational activities
82.90.+j Other topics in physical chemistry and chemical physics (restricted to new topics in section 82)

On some dynamical diagrams of chemical reaction engineering

Rutherford Aris

Chaos 9, 3 (1999); http://dx.doi.org/10.1063/1.166376 (10 pages) | Cited 1 time

Full Text: | Download PDF

Show Abstract
A brief historical survey of some of the influential types of diagrams that have been used in chemical reaction engineering is given. These include the phase plane, the simple autocatalytic diagram, and the stroboscopic phase plane. © 1999 American Institute of Physics.
Show PACS
82.40.Bj Oscillations, chaos, and bifurcations
05.45.-a Nonlinear dynamics and chaos
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces

Bifurcation analysis of chemical reactors and reacting flows

Vemuri Balakotaiah, Sandra M. S. Dommeti, and Nikunj Gupta

Chaos 9, 13 (1999); http://dx.doi.org/10.1063/1.166377 (23 pages) | Cited 6 times

Full Text: | Download PDF

Show Abstract
In this work we review the local bifurcation techniques for analyzing and classifying the steady-state and dynamic behavior of chemical reactor models described by partial differential equations (PDEs). First, we summarize the formulas for determining the derivatives of the branching equation and the coefficients in the amplitude equations for the most common singularities. We also illustrate the procedure for the numerical computation of these coefficients. Next, the application of these local results to various reactor models described by PDEs is discussed. Specifically, we review the recent literature on the bifurcation features of convection-reaction and convection-diffusion-reaction models in one and more spatial dimensions, with emphasis on the features introduced due to coupling between the flow, heat and mass diffusion and chemical reaction. Finally, we illustrate the use of dynamical systems concepts in developing low dimensional (effective or pseudohomogeneous) models of reactors and reacting flows, and discuss some problems of current interest. © 1999 American Institute of Physics.
Show PACS
05.45.-a Nonlinear dynamics and chaos
82.40.Bj Oscillations, chaos, and bifurcations
47.70.Fw Chemically reactive flows
05.60.-k Transport processes
47.27.T- Turbulent transport processes
82.20.-w Chemical kinetics and dynamics

Temperature patterns on a hollow cylindrical catalytic pellet

J. Annamalai, M. A. Liauw, and D. Luss

Chaos 9, 36 (1999); http://dx.doi.org/10.1063/1.166378 (7 pages) | Cited 5 times

Full Text: | Download PDF

Show Abstract
The atmospheric oxidation of a mixture containing 6 vol % carbon monoxide was carried out on a hollow cylindrical catalytic pellet. The catalyst was held in a conical reactor which enabled simultaneous measurement of the temperature patterns on the top and side of the pellet by an IR imager. Upon a decrease in the reactor temperature the fully ignited, high temperature state of the pellet is transformed to a nonuniform one with temperature fronts separating high and low temperature regions. The transition and the resulting states are rather intricate and are strongly influenced by the nonuniformity of the catalyst and the transport to and from it, as well as the global coupling, which stabilizes temperature fronts and patterns, which would not exist in its absence. Intricate pulse splitting and extinction were observed both on the top and the side of the pellet. Highly irregular motions and conversions were obtained following a decrease in the reactor temperature. © 1999 American Institute of Physics.
Show PACS
82.30.Vy Homogeneous catalysis in solution, polymers and zeolites
05.45.-a Nonlinear dynamics and chaos

Chaotic patterns in a coupled oscillator–excitator biochemical cell system

Igor Schreiber, Pavel Hasal, and Miloš Marek

Chaos 9, 43 (1999); http://dx.doi.org/10.1063/1.166400 (12 pages) | Cited 8 times

Full Text: | Download PDF

Show Abstract
In this paper we examine dynamical modes resulting from diffusion-like interaction of two model biochemical cells. Kinetics in each of the cells is given by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the other cell — a fraction of activated cell surface receptors—is varied so that the dynamics in the cell is either excitable or oscillatory or a stable focus. The cells are interacting via mass transfer and dynamics of the coupled system are studied as two parameters are varied—the fraction of activated receptors and the coupling strength. We find that (i) the excitator–excitator interaction does not lead to oscillatory patterns, (ii) the oscillator–excitator interaction leads to alternating phase-locked periodic and quasiperiodic regimes, well known from oscillator–oscillator interactions; torus breaking bifurcation generates chaos when the coupling strength is in an intermediate range, (iii) the focus–excitator interaction generates compound oscillations arranged as period adding sequences alternating with chaotic windows; the transition to chaos is accompanied by period doublings and folding of branches of periodic orbits and is associated with a Shilnikov homoclinic orbit. The nature of spontaneous self-organized oscillations in the focus–excitator range is discussed. © 1999 American Institute of Physics.
Show PACS
87.18.-h Biological complexity
05.45.Xt Synchronization; coupled oscillators
87.10.-e General theory and mathematical aspects

Ripening of surface phases coupled with oscillatory dynamics and self-induced spatial chaos through surface roughening

L. M. Pismen and B. Y. Rubinstein

Chaos 9, 55 (1999); http://dx.doi.org/10.1063/1.166379 (7 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
Some pattern formation processes on single-crystal catalytic surfaces involve transitions between alternative surface phases coupled with oscillatory reaction dynamics. We describe a two-tier symmetry-breaking model of this process, based on nanoscale boundary dynamics interacting with oscillations of adsorbate coverage on microscale. The surface phase distribution oscillates together with adsorbate coverage, and, in addition, undergoes a slow coarsening process due to the curvature dependence of the drift velocity of interphase boundaries. The coarsening is studied both statistically, assuming a circular shape of islands of the minority phase, and through detailed Lagrangian modeling of boundary dynamics. Direct simulation of boundary dynamics allows us to take into account processes of surface reconstruction, leading to self-induced surface roughening. As a result, the surface becomes inhomogeneous, and the coarsening process is arrested way before the thermodynamic limit is reached, leaving a chaotic distribution of surface phases. © 1999 American Institute of Physics.
Show PACS
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces
68.35.B- Structure of clean surfaces (and surface reconstruction)
68.35.Rh Phase transitions and critical phenomena
05.45.-a Nonlinear dynamics and chaos

Pattern selection during electropolishing due to double-layer effects

Vadim V. Yuzhakov, Pavlo V. Takhistov, Albert E. Miller, and Hsueh-Chia Chang

Chaos 9, 62 (1999); http://dx.doi.org/10.1063/1.166380 (16 pages) | Cited 13 times

Full Text: | Download PDF

Show Abstract
We extend our earlier study of nanoscale pattern formation during electropolishing [Nanotechnology 7, 360 (1996); Phys. Rev. B 56, 12 608 (1997)]. The patterns are attributed to preferential adsorption of organic molecules on the convex portion of the electrode due to its enhanced electric field. This local enhancement occurs because of the effect of surface curvature on the double-layer potential drop. By allowing for transport correction to the double-layer potential drop at thermodynamic equilibrium, we estimate this anodic overpotential to be in the realistic mV range and hence verify the Debye–Hückel approximation used in our model. This small anodic overpotential suggests that pattern formation is a generic electropolishing phenomenon whose only requirement is that the polarizability of the organic additive relative to water must lie within a range specified by our theory. We verify this prediction experimentally with a variety of electrolyte solutions. The voltage ranges for specific hexagonal and ridge patterns are well correlated by our model with only a single parameter. © 1999 American Institute of Physics.
Show PACS
81.65.Ps Polishing, grinding, surface finishing
81.07.-b Nanoscale materials and structures: fabrication and characterization
81.16.-c Methods of micro- and nanofabrication and processing
85.35.-p Nanoelectronic devices
05.65.+b Self-organized systems
82.45.-h Electrochemistry and electrophoresis

Using weighted global control for stabilizing patterned states

Vadim Panfilov and Moshe Sheintuch

Chaos 9, 78 (1999); http://dx.doi.org/10.1063/1.166381 (10 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
A general method to control a desired patterned state in reaction–diffusion processes is presented. Weighted global control is aimed to keep weighted spatially averaged properties of state variable at preset values. It is shown that weighted global control creates a stable direction in the global space of system states and affects system dynamics globally. We apply it for a specific two-component reaction–diffusion system and show that the desired pattern is attainable for a wide range of the control parameters. © 1999 American Institute of Physics.
Show PACS
05.60.Cd Classical transport
05.45.Gg Control of chaos, applications of chaos

On the dynamics of nonlinear systems with input constraints

Navneet Kapoor and Prodromos Daoutidis

Chaos 9, 88 (1999); http://dx.doi.org/10.1063/1.166382 (7 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
In this work we deal with the dynamical analysis of nonlinear systems with input constraints. A characterization of the domain of attraction of the region of controllability of an equilibrium point under bounded control is provided and the concept of regions of invariance within such domains of attraction is introduced and characterized. The concepts and results are illustrated through case studies on chemical reactor models. © 1999 American Institute of Physics.  
Show PACS
05.45.Gg Control of chaos, applications of chaos

Reaction network reduction for distributed systems by model training in lumped reactors: Application to bifurcations in combustion

S. Raimondeau, M. Gummalla, Y. K. Park, and D. G. Vlachos

Chaos 9, 95 (1999); http://dx.doi.org/10.1063/1.166383 (13 pages)

Full Text: | Download PDF

Show Abstract
A new methodology is presented to derive reduced reaction mechanisms for distributed reacting flows by model training in a lumped parameter system (a continuous-stirred tank reactor). The method identifies the relevant transport time scales in the reaction zone of a distributed system along with the local composition vector, over a range of operation conditions. A training box in the parameter space of pressure-transport time scale-composition is then identified. Sensitivity and principal component analyses are subsequently performed at bifurcation points in a lumped parameter system at representative conditions of the training box. The most inclusive chemistry derived in the lumped system captures the proper transport–chemistry coupling and is suitable for the distributed reactor. Application to ignition of hydrogen/air and methane/air mixtures is presented and validated for premixed and diffusion flames in a stagnation flow geometry. © 1999 American Institute of Physics.
Show PACS
82.33.Vx Reactions in flames, combustion, and explosions
05.45.-a Nonlinear dynamics and chaos
47.70.Fw Chemically reactive flows

Identification of low order manifolds: Validating the algorithm of Maas and Pope

Carl Rhodes, Manfred Morari, and Stephen Wiggins

Chaos 9, 108 (1999); http://dx.doi.org/10.1063/1.166398 (16 pages) | Cited 18 times

Full Text: | Download PDF

Show Abstract
The algorithm of is presented as a method for identification of invariant reduced-order manifolds for stable systems which exhibit dynamics with a time-scale separation. While this method has been published previously in the literature, theoretical justification for the algorithm was not presented in the original work. Here, it will be shown rigorously that the algorithm correctly identifies the slow manifold. Before the theoretical results are presented, a brief background on the behavior of singularly perturbed systems is presented. The algorithm of is then introduced. This method will be applied to two different examples, a distillation column and a two-phase chemical reactor. For each of these examples, the resulting reduced-order description will be compared to other standard methods of producing reduced-order models. In addition, some preliminary thoughts on how this method can be used to form reduced-order models are presented. © 1999 American Institute of Physics.
Show PACS
05.45.Gg Control of chaos, applications of chaos

A tutorial on the Rayleigh–Marangoni–Bénard problem with multiple layers and side wall effects

Duane Johnson and R. Narayanan

Chaos 9, 124 (1999); http://dx.doi.org/10.1063/1.166384 (17 pages) | Cited 10 times

Full Text: | Download PDF

Show Abstract
A brief review in the form of a tutorial is presented on convective instabilities that arise from thermocapillary and buoyancy effects. This tutorial primarily focuses on the effect of multiple layers and side walls on the nature of the convective flows and associated patterns. A comprehensive explanation of the physics of this type of convection is followed by a discussion of the mathematical features of bifurcation associated with the problem and some of the recent experimental studies. © 1999 American Institute of Physics.
Show PACS
47.27.T- Turbulent transport processes
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
05.45.-a Nonlinear dynamics and chaos

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Omar K. Matar and Sandra M. Troian

Chaos 9, 141 (1999); http://dx.doi.org/10.1063/1.166385 (13 pages) | Cited 25 times

Full Text: | Download PDF

Show Abstract
We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air–liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. [Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman (Materials Research Society, Boston, 1996), Vol. 464, p. 237; Phys. Fluids A 9, 3645 (1997); O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998]. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow [Phys. Fluids A 10, 1234 (1998); “Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances,” submitted to Phys. Fluids]. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage. © 1999 American Institute of Physics.
Show PACS
81.15.Lm Liquid phase epitaxy; deposition from liquid phases (melts, solutions, and surface layers on liquids)
68.15.+e Liquid thin films
05.45.-a Nonlinear dynamics and chaos

The sharkskin instability of polymer melt flows

Michael D. Graham

Chaos 9, 154 (1999); http://dx.doi.org/10.1063/1.166386 (10 pages) | Cited 14 times

Full Text: | Download PDF

Show Abstract
Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. © 1999 American Institute of Physics.
Show PACS
47.50.-d Non-Newtonian fluid flows
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.45.Gx Slip flows and accommodation
47.60.-i Flow phenomena in quasi-one-dimensional systems
05.45.-a Nonlinear dynamics and chaos

Contacting and forming singularities: Distinguishing examples

Paul H. Steen and Yi-Ju Chen

Chaos 9, 164 (1999); http://dx.doi.org/10.1063/1.166387 (9 pages) | Cited 4 times

Full Text: | Download PDF

Show Abstract
A thin film bridge breaks in a way that starts at one equilibrium state and ends at another equilibrium state. The dynamical trajectory that carries it from connected to disconnected provides rare evidence regarding the singularity of passage through topological change. This nonequilibrium trajectory, called a “forming” flow, is discussed in an attempt to frame it within the larger class of singularities for which bounding surfaces do not remain material surfaces. As a contrast, the weaker “contacting” singularity is illustrated by a stagnation flow where material points reach the stagnation point in finite time. A classification scheme based on pathology of the nonunique Lagrangian motions is suggested. New results for the disconnection example include healing of surgery in post-disconnection simulations, different dynamical scalings of the just-disconnected components and a comparison of post-disconnection simulation to experiment. © 1999 American Institute of Physics.
Show PACS
05.45.-a Nonlinear dynamics and chaos
46.55.+d Tribology and mechanical contacts
46.50.+a Fracture mechanics, fatigue and cracks

Residence-time distributions for chaotic flows in pipes

Igor Mezić, Stephen Wiggins, and David Betz

Chaos 9, 173 (1999); http://dx.doi.org/10.1063/1.166388 (10 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
In this paper we derive two rigorous properties of residence-time distributions for flows in pipes and mixers motivated by computational results of Khakhar et al. [Chem. Eng. Sci. 42, 2909 (1987)], using some concepts from ergodic theory. First, a curious similarity between the isoresidence-time plots and Poincaré maps of the flow observed in Khakhar et al. is resolved. It is shown that in long pipes and mixers, Poincaré maps can serve as a useful guide in the analysis of isoresidence-time plots, but the two are not equivalent. In particular, for long devices isoresidence-time sets are composed of orbits of the Poincaré map, but each isoresidence-time set can be comprised of many orbits. Second, we explain the origin of multimodal residence-time distributions for nondiffusive motion of particles in pipes and mixers. It is shown that chaotic regions in the Poincaré map contribute peaks to the appropriately defined and rescaled axial distribution functions. © 1999 American Institute of Physics.
Show PACS
47.52.+j Chaos in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems

Design criteria of a chemical reactor based on a chaotic flow

X. Z. Tang and A. H. Boozer

Chaos 9, 183 (1999); http://dx.doi.org/10.1063/1.166389 (12 pages) | Cited 13 times

Full Text: | Download PDF

Show Abstract
We consider the design criteria of a chemical mixing device based on a chaotic flow, with an emphasis on the steady-state devices. The merit of a reactor, defined as the Q-factor, is related to the physical dimension of the device and the molecular diffusivity of the reactants through the local Lyapunov exponents of the flow. The local Lyapunov exponent can be calculated for any given flow field and it can also be measured in experimental situations. Easy-to-compute formulae are provided to estimate the Q-factor given either the exact spatial dependence of the local Lyapunov exponent or its probability distribution function. The requirements for optimization are made precise in the context of local Lyapunov exponents. © 1999 American Institute of Physics.
Show PACS
47.70.Fw Chemically reactive flows
47.15.-x Laminar flows
02.50.Cw Probability theory
05.45.-a Nonlinear dynamics and chaos

Chaotic mixing of granular materials in two-dimensional tumbling mixers

D. V. Khakhar, J. J. McCarthy, J. F. Gilchrist, and J. M. Ottino

Chaos 9, 195 (1999); http://dx.doi.org/10.1063/1.166390 (11 pages) | Cited 26 times

Full Text: | Download PDF

Show Abstract
We consider the mixing of similar, cohesionless granular materials in quasi-two-dimensional rotating containers by means of theory and experiment. A mathematical model is presented for the flow in containers of arbitrary shape but which are symmetric with respect to rotation by 180° and half-filled with solids. The flow comprises a thin cascading layer at the flat free surface, and a fixed bed which rotates as a solid body. The layer thickness and length change slowly with mixer rotation, but the layer geometry remains similar at all orientations. Flow visualization experiments using glass beads in an elliptical mixer show good agreement with model predictions. Studies of mixing are presented for circular, elliptical, and square containers. The flow in circular containers is steady, and computations involving advection alone (no particle diffusion generated by interparticle collisions) show poor mixing. In contrast, the flow in elliptical and square mixers is time periodic and results in chaotic advection and rapid mixing. Computational evidence for chaos in noncircular mixers is presented in terms of Poincaré sections and blob deformation. Poincaré sections show regions of regular and chaotic motion, and blobs deform into homoclinic tendrils with an exponential growth of the perimeter length with time. In contrast, in circular mixers, the motion is regular everywhere and the perimeter length increases linearly with time. Including particle diffusion obliterates the typical chaotic structures formed on mixing; predictions of the mixing model including diffusion are in good qualitative and quantitative (in terms of the intensity of segregation variation with time) agreement with experimental results for mixing of an initially circular blob in elliptical and square mixers. Scaling analysis and computations show that mixing in noncircular mixers is faster than that in circular mixers, and the difference in mixing times increases with mixer size. © 1999 American Institute of Physics.
Show PACS
47.55.Kf Particle-laden flows
45.70.Mg Granular flow: mixing, segregation and stratification
47.32.-y Vortex dynamics; rotating fluids
64.75.-g Phase equilibria
47.80.-v Instrumentation and measurement methods in fluid dynamics
05.45.-a Nonlinear dynamics and chaos
back to top
RSS Feeds

Observation of structure in the Lorenz map

P.-M. Binder and Diego Laverde

Chaos 9, 206 (1999); http://dx.doi.org/10.1063/1.166391 (2 pages)

Full Text: | Download PDF

Show Abstract
Through massive numerical integration of the Lorenz system, we are able to discern structure in its Poincaré map. We are also able to estimate its capacity dimension; our result is consistent with previous measurements of the correlation dimension of the Lorenz attractor. © 1999 American Institute of Physics.
Show PACS
05.45.Pq Numerical simulations of chaotic systems
02.60.Jh Numerical differentiation and integration
02.30.Cj Measure and integration

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

Thomas Kuruvilla and V. M. Nandakumaran

Chaos 9, 208 (1999); http://dx.doi.org/10.1063/1.166392 (5 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions. © 1999 American Institute of Physics.
Show PACS
42.60.Fc Modulation, tuning, and mode locking
05.45.-a Nonlinear dynamics and chaos

A method for visualization of invariant sets of dynamical systems based on the ergodic partition

Igor Mezić and Stephen Wiggins

Chaos 9, 213 (1999); http://dx.doi.org/10.1063/1.166399 (6 pages) | Cited 13 times

Full Text: | Download PDF

Show Abstract
We provide an algorithm for visualization of invariant sets of dynamical systems with a smooth invariant measure. The algorithm is based on a constructive proof of the ergodic partition theorem for automorphisms of compact metric spaces. The ergodic partition of a compact metric space A, under the dynamics of a continuous automorphism T, is shown to be the product of measurable partitions of the space induced by the time averages of a set of functions on A. The numerical algorithm consists of computing the time averages of a chosen set of functions and partitioning the phase space into their level sets. The method is applied to the three-dimensional ABC map for which the dynamics was visualized by other methods in Feingold et al. [J. Stat. Phys. 50, 529 (1988)]. © 1999 American Institute of Physics.
Show PACS
05.45.-a Nonlinear dynamics and chaos

Hyperchaotic qualities of the ball motion in a ball milling device

C. Caravati, F. Delogu, G. Cocco, and M. Rustici

Chaos 9, 219 (1999); http://dx.doi.org/10.1063/1.166393 (8 pages) | Cited 6 times

Full Text: | Download PDF

Show Abstract
Ball collisions in milling devices are governed by complex dynamics ruled by impredictable impulsive forces. In this paper, nonlinear dynamics techniques are employed to analyze the time series describing the trajectory of a milling ball in an empty container obtained from a numerical model. The attractor underlying the system dynamics was reconstructed by the time delay method. In order to characterize the system dynamics the calculation of the spectrum of Lyapunov exponents was performed. Six Lyapunov exponents, divided into two terns with opposite sign, were obtained. The detection of the positive tern demonstrates the occurrence of the hyperchaotic qualities of the ball motion. A fractal Lyapunov dimension, equal to 5.62, was also obtained confirming the strange features of the attractor. © 1999 American Institute of Physics.
Show PACS
05.45.Tp Time series analysis
05.45.Df Fractals
05.45.Pq Numerical simulations of chaotic systems
45.40.-f Dynamics and kinematics of rigid bodies

Role of multistability in the transition to chaotic phase synchronization

D. E. Postnov, T. E. Vadivasova, O. V. Sosnovtseva, A. G. Balanov, V. S. Anishchenko, and E. Mosekilde

Chaos 9, 227 (1999); http://dx.doi.org/10.1063/1.166394 (6 pages) | Cited 16 times

Full Text: | Download PDF

Show Abstract
In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples using Rössler systems and model maps are given. © 1999 American Institute of Physics.
Show PACS
05.45.Xt Synchronization; coupled oscillators

The control of high-dimensional chaos in time-delay systems to an arbitrary goal dynamics

M. J. Bünner

Chaos 9, 233 (1999); http://dx.doi.org/10.1063/1.166395 (5 pages)

Full Text: | Download PDF

Show Abstract
We present the control of high-dimensional chaos, with possibly a large number of positive Lyapunov exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control force. In the case of an unknown system, a formula to compute a model-based control force is derived. We give an example by demonstrating the control of the Mackey–Glass system toward a fixed point and a Rössler dynamics. © 1999 American Institute of Physics.
Show PACS
05.45.Jn High-dimensional chaos
05.45.Gg Control of chaos, applications of chaos

Chirality dependent component of vortex advection in excitable media

V. Voignier, E. Hamm, and V. Krinsky

Chaos 9, 238 (1999); http://dx.doi.org/10.1063/1.166396 (4 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
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.© 1999 American Institute of Physics.
Show PACS
82.20.-w Chemical kinetics and dynamics
05.45.-a Nonlinear dynamics and chaos
47.32.C- Vortex dynamics
Page 1 of 2 Pages Next Page | Jump to Page
Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation
  2. Fundamentals of synchronization in chaotic systems, concepts, and applications
  3. Quantitative optical tomography of chemical waves and their organizing centers
  4. Quantitative analysis of heart rate variability
  5. Approximate entropy (ApEn) as a complexity measure
Go to AIP Home
Copyright © American Institute of Physics
close