Advection of nematic liquid crystals by chaotic flow

NASA Astrophysics Data System (ADS)

O'Náraigh, Lennon

2017-04-01

Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau-de Gennes equation coupled to an externally prescribed flow field is the basis for the study: this is solved numerically in a periodic spatial domain. The focus is on a limiting case where the advection is passive, such that variations in the liquid-crystal properties do not feed back into the equation for the fluid velocity. The main tool for analyzing the results (both with and without flow) is the identification of the fixed points of the dynamical equations without flow, which are relevant (to varying degrees) when flow is introduced. The fixed points are classified as stable/unstable and further as either uniaxial or biaxial. Various models of passive shear flow are investigated. When tumbling is present, the flow is shown to have a strong effect on the liquid-crystal morphology; however, the main focus herein is on the case without tumbling. Accordingly, the main result of the work is that only the biaxial fixed point survives as a solution of the Q-tensor dynamics under the imposition of a general flow field. This is because the Q-tensor experiences not only transport due to advection but also co-rotation relative to the local vorticity field. A second result is that all families of fixed points survive for certain specific velocity fields, which we classify. We single out for close study those velocity fields for which the influence of co-rotation effectively vanishes along the Lagrangian trajectories of the imposed velocity field. In this scenario, the system exhibits coarsening arrest, whereby the liquid-crystal domains are "frozen in" to the flow structures, and the growth in their size is thus limited.

Getting Things Sorted With Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team

2014-11-01

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of Lagrangian Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of numerical simulations and laboratory experiments that investigate the behavior of finite size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.

Characterization of mixing in an electroosmotically stirred continuous micro mixer

NASA Astrophysics Data System (ADS)

Beskok, Ali

2005-11-01

We present theoretical and numerical studies of mixing in a straight micro channel with zeta potential patterned surfaces. A steady pressure driven flow is maintained in the channel in addition to a time dependent electroosmotic flow, generated by a stream-wise AC electric field. The zeta potential patterns are placed critically in the channel to achieve spatially asymmetric time-dependent flow patterns that lead to chaotic stirring. Fixing the geometry, we performed parametric studies of passive particle motion that led to generation of Poincare sections and characterization of chaotic strength by finite time Lyapunov exponents. The parametric studies were performed as a function of the Womersley number (normalized AC frequency) and the ratio of Poiseuille flow and electroosmotic velocities. After determining the non-dimensional parameters that led to high chaotic strength, we performed spectral element simulations of species transport and mixing at high Peclet numbers, and characterized mixing efficiency using the Mixing Index inverse. Mixing lengths proportional to the natural logarithm of the Peclet number are reported. Using the optimum non-dimensional parameters and the typical magnitudes involved in electroosmotic flows, we were able to determine the physical dimensions and operation conditions for a prototype micro-mixer.

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2016-01-01

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Magnetic shuffling of coronal downdrafts

NASA Astrophysics Data System (ADS)

Petralia, A.; Reale, F.; Orlando, S.

2017-02-01

Context. Channelled fragmented downflows are ubiquitous in magnetized atmospheres, and have recently been addressed based on an observation after a solar eruption. Aims: We study the possible back-effect of the magnetic field on the propagation of confined flows. Methods: We compared two 3D magnetohydrodynamic simulations of dense supersonic plasma blobs that fall down along a coronal magnetic flux tube. In one, the blobs move strictly along the field lines; in the other, the initial velocity of the blobs is not perfectly aligned with the magnetic field and the field is weaker. Results: The aligned blobs remain compact while flowing along the tube, with the generated shocks. The misaligned blobs are disrupted and merge through the chaotic shuffling of the field lines. They are structured into thinner filaments. Alfvén wave fronts are generated together with shocks ahead of the dense moving front. Conclusions: Downflowing plasma fragments can be chaotically and efficiently mixed if their motion is misaligned with field lines, with broad implications for disk accretion in protostars, coronal eruptions, and rain, for example. Movies associated to Figs. 2 and 3 are available at http://www.aanda.org

Computations of Chaotic Flows in Micromixers

DTIC Science & Technology

2005-01-01

2005 2. REPORT TYPE 3. DATES COVERED 00-00-2005 to 00-00-2005 4. TITLE AND SUBTITLE Computations of Chaotic Flows in Micromixers 5a. CONTRACT...Std Z39-18 215simulation, computing, and modeling 2005 NRL Review Computations of Chaotic Flows In Micromixers FIGURE 6 Schematic of staggered

Management of In-Field Patient Tracking and Triage by Using Near-Field Communication in Mass Casualty Incidents.

PubMed

Cheng, Po-Liang; Su, Yung-Cheng; Hou, Chung-Hung; Chang, Po-Lun

2017-01-01

Near field communications (NFC) is an emerging technology that may potentialy assist with disaster management. A smartphone-based app was designed to help track patient flow in real time. A table-drill was held as a brief evaluation and it showed significant imporvement in both efficacy and accuracy of patient management. It is feasible to use NFC-embedded smartphones to clarify the ambiguous and chaotic patient flow in a mass casualty incident.

Scaling laws and reduced-order models for mixing and reactive-transport in heterogeneous anisotropic porous media

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Karra, S.; Nakshatrala, K. B.

2016-12-01

Fundamental to enhancement and control of the macroscopic spreading, mixing, and dilution of solute plumes in porous media structures is the topology of flow field and underlying heterogeneity and anisotropy contrast of porous media. Traditionally, in literature, the main focus was limited to the shearing effects of flow field (i.e., flow has zero helical density, meaning that flow is always perpendicular to vorticity vector) on scalar mixing [2]. However, the combined effect of anisotropy of the porous media and the helical structure (or chaotic nature) of the flow field on the species reactive-transport and mixing has been rarely studied. Recently, it has been experimentally shown that there is an irrefutable evidence that chaotic advection and helical flows are inherent in porous media flows [1,2]. In this poster presentation, we present a non-intrusive physics-based model-order reduction framework to quantify the effects of species mixing in-terms of reduced-order models (ROMs) and scaling laws. The ROM framework is constructed based on the recent advancements in non-negative formulations for reactive-transport in heterogeneous anisotropic porous media [3] and non-intrusive ROM methods [4]. The objective is to generate computationally efficient and accurate ROMs for species mixing for different values of input data and reactive-transport model parameters. This is achieved by using multiple ROMs, which is a way to determine the robustness of the proposed framework. Sensitivity analysis is performed to identify the important parameters. Representative numerical examples from reactive-transport are presented to illustrate the importance of the proposed ROMs to accurately describe mixing process in porous media. [1] Lester, Metcalfe, and Trefry, "Is chaotic advection inherent to porous media flow?," PRL, 2013. [2] Ye, Chiogna, Cirpka, Grathwohl, and Rolle, "Experimental evidence of helical flow in porous media," PRL, 2015. [3] Mudunuru, and Nakshatrala, "On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method," JCP, 2016. [4] Quarteroni, Manzoni, and Negri. "Reduced Basis Methods for Partial Differential Equations: An Introduction," Springer, 2016.

Chaotic mixing in microchannels via low frequency switching transverse electroosmotic flow generated on integrated microelectrodes.

PubMed

Song, Hongjun; Cai, Ziliang; Noh, Hongseok Moses; Bennett, Dawn J

2010-03-21

In this paper we present a numerical and experimental investigation of a chaotic mixer in a microchannel via low frequency switching transverse electroosmotic flow. By applying a low frequency, square-wave electric field to a pair of parallel electrodes placed at the bottom of the channel, a complex 3D spatial and time-dependence flow was generated to stretch and fold the fluid. This significantly enhanced the mixing effect. The mixing mechanism was first investigated by numerical and experimental analysis. The effects of operational parameters such as flow rate, frequency, and amplitude of the applied voltage have also been investigated. It is found that the best mixing performance is achieved when the frequency is around 1 Hz, and the required mixing length is about 1.5 mm for the case of applied electric potential 5 V peak-to-peak and flow rate 75 microL h(-1). The mixing performance was significantly enhanced when the applied electric potential increased or the flow rate of fluids decreased.

Loading-rate-independent delay of catastrophic avalanches in a bulk metallic glass

DOE PAGES

Chen, S. H.; Chan, K. C.; Wang, G.; ...

2016-02-25

The plastic flow of bulk metallic glasses (BMGs) is characterized by intermittent bursts of avalanches, and this trend results in disastrous failures of BMGs. In the present work, a double-side-notched BMG specimen is designed, which exhibits chaotic plastic flows consisting of several catastrophic avalanches under the applied loading. The disastrous shear avalanches have, then, been delayed by forming a stable plastic-flow stage in the specimens with tailored distances between the bottoms of the notches, where the distribution of a complex stress field is acquired. Differing from the conventional compressive testing results, such a delaying process is independent of loading rate.more » The statistical analysis shows that in the specimens with delayed catastrophic failures, the plastic flow can evolve to a critical dynamics, making the catastrophic failure more predictable than the ones with chaotic plastic flows. Lastly, the findings are of significance in understanding the plastic-flow mechanisms in BMGs and controlling the avalanches in relating solids.« less

Dynamical turbulent flow on the Galton board with friction.

PubMed

Chepelianskii, A D; Shepelyansky, D L

2001-07-16

We study numerically and analytically the dynamics of charged particles on the Galton board, a regular lattice of disk scatters, in the presence of constant external force, magnetic field, and friction. It is shown that under certain conditions friction leads to the appearance of a strange chaotic attractor. In this regime the average velocity and direction of particle flow can be effectively affected by electric and magnetic fields. We discuss the applications of these results to the charge transport in antidot superlattices and the stream of suspended particles in a viscous flow through scatters.

Chaos analysis of viscoelastic chaotic flows of polymeric fluids in a micro-channel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, C. P.; Lam, Y. C., E-mail: myclam@ntu.edu.sg; BioSystems and Micromechanics

2015-07-15

Many fluids, including biological fluids such as mucus and blood, are viscoelastic. Through the introduction of chaotic flows in a micro-channel and the construction of maps of characteristic chaos parameters, differences in viscoelastic properties of these fluids can be measured. This is demonstrated by creating viscoelastic chaotic flows induced in an H-shaped micro-channel through the steady infusion of a polymeric fluid of polyethylene oxide (PEO) and another immiscible fluid (silicone oil). A protocol for chaos analysis was established and demonstrated for the analysis of the chaotic flows generated by two polymeric fluids of different molecular weight but with similar relaxationmore » times. The flows were shown to be chaotic through the computation of their correlation dimension (D{sub 2}) and the largest Lyapunov exponent (λ{sub 1}), with D{sub 2} being fractional and λ{sub 1} being positive. Contour maps of D{sub 2} and λ{sub 1} of the respective fluids in the operating space, which is defined by the combination of polymeric fluids and silicone oil flow rates, were constructed to represent the characteristic of the chaotic flows generated. It was observed that, albeit being similar, the fluids have generally distinct characteristic maps with some similar trends. The differences in the D{sub 2} and λ{sub 1} maps are indicative of the difference in the molecular weight of the polymers in the fluids because the driving force of the viscoelastic chaotic flows is of molecular origin. This approach in constructing the characteristic maps of chaos parameters can be employed as a diagnostic tool for biological fluids and, more generally, chaotic signals.« less

Unscrambling the Omlette: a New Bubble and Crystal Clustering Mechanism in Chaotically Mixed Magma Flows

NASA Astrophysics Data System (ADS)

Robertson, J.; Metcalfe, G.; Wang, S.; Barnes, S. J.

2014-12-01

The concentration of bubbles, crystals or droplets into small volumes of magma is a key trigger for many interesting magmatic processes. For example, gas slugs driving Strombolian eruptions form from the coalesence of exsolved bubbles within a volcanic conduit, while Ni-Cu-PGE magmatic sulfide deposits require a concentration of dense sulfide droplets from a large volume of magma to form a massive ore body. However the physical mechanism for this clustering remains unresolved - especially since small particles in active magma flows are expected to mostly track flow streamlines rather than clustering. We have uncovered a previously unreported clustering mechanism which is applicable to magmatic flows. This mechanism involves the interaction of particles with two kinds of chaotic flow structure: (a) high-strain regions within the well-mixed chaotic zones of the flow, and (b) unmixed islands of stability within the chaotic flow, known as Kolmogorov-Arnold-Moser (KAM) regions. The first figure shows the difference between chaotic and KAM regions in a chaotic laminar pipe flow. Trapping occurs when particles are scattered from high-strain regions in the chaotic zones and become trapped in the KAM regions, leading to a rapid concentration of particles relative to their original distribution (shown in the second series of figures). Using a combination of these analogue experiments and theoretical analysis we outline the conditions under which this clustering process can occur. We examine the onset of secondary density-related instabilities and the effects of increased particle-particle interaction within the clustered particles, and highlight the impact of particle clustering on the dynamics of magma ascent and emplacement.

Active turbulence in a gas of self-assembled spinners

PubMed Central

Kokot, Gašper; Das, Shibananda; Winkler, Roland G.; Aranson, Igor S.; Snezhko, Alexey

2017-01-01

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air–liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generated advection flows. The same-chirality spinners (clockwise or counterclockwise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. Our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale. PMID:29158382

Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos

NASA Astrophysics Data System (ADS)

Castaño, D.; Navarro, M. C.; Herrero, H.

2016-01-01

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

An investigation of chaotic Kolmogorov flows

NASA Technical Reports Server (NTRS)

Platt, N.; Sirovich, L.; Fitzmaurice, N.

1990-01-01

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Local and Global Bifurcations of Flow Fields During Physical Vapor Transport: Application to a Microgravity Experiment

NASA Technical Reports Server (NTRS)

Duval, W. M. B.; Singh, N. B.; Glicksman, M. E.

1996-01-01

The local bifurcation of the flow field, during physical vapor transport for a parametric range of experimental interest, shows that its dynamical state ranges from steady to aperiodic. Comparison of computationally predicted velocity profiles with laser doppler velocimetry measurements shows reasonable agreement in both magnitude and planform. Correlation of experimentally measured crystal quality with the predicted dynamical state of the flow field shows a degradation of quality with an increase in Rayleigh number. The global bifurcation of the flow field corresponding to low crystal quality indicates the presence of a traveling wave for Ra = 1.09 x 10(exp 5). For this Rayleigh number threshold a chaotic transport state occurs. However, a microgravity environment for this case effectively stabilizes the flow to diffusive-advective and provides the setting to grow crystals with optimal quality.

Flow visualization methods for field test verification of CFD analysis of an open gloveport

DOE PAGES

Strons, Philip; Bailey, James L.

2017-01-01

Anemometer readings alone cannot provide a complete picture of air flow patterns at an open gloveport. Having a means to visualize air flow for field tests in general provides greater insight by indicating direction in addition to the magnitude of the air flow velocities in the region of interest. Furthermore, flow visualization is essential for Computational Fluid Dynamics (CFD) verification, where important modeling assumptions play a significant role in analyzing the chaotic nature of low-velocity air flow. A good example is shown Figure 1, where an unexpected vortex pattern occurred during a field test that could not have been measuredmore » relying only on anemometer readings. Here by, observing and measuring the patterns of the smoke flowing into the gloveport allowed the CFD model to be appropriately updated to match the actual flow velocities in both magnitude and direction.« less

Generation of magnetic fields by chaotic fluid convection - The fast dynamo problem

NASA Technical Reports Server (NTRS)

Finn, John M.

1992-01-01

In the kinematic fast dynamo problem, the underlying nonlinear dynamics of the flow play a critical role in the behavior of a dynamo field. It is presently noted that the two important facets of the problem are the approximately lognormal distribution of vector lengths, and the presence of partial cancellation. It is suggested that these features may be reflected in the magnetic fields observed on the sun.

Chaotic advection and heat transfer in two similar 2-D periodic flows and in their corresponding 3-D periodic flows

NASA Astrophysics Data System (ADS)

Vinsard, G.; Dufour, S.; Saatdjian, E.; Mota, J. P. B.

2016-03-01

Chaotic advection can effectively enhance the heat transfer rate between a boundary and fluids with high Prandtl number. These fluids are usually highly viscous and thus turbulent agitation is not a viable solution since the energy required to mix the fluid would be prohibitive. Here, we analyze previously obtained results on chaotic advection and heat transfer in two similar 2-D periodic flows and on their corresponding 3-D periodic flows when an axial velocity component is superposed. The two flows studied are the flow between eccentric rotating cylinders and the flow between confocal ellipses. For both of these flows the analysis is simplified because the Stokes equations can be solved analytically to obtain a closed form solution. For both 2-D periodic flows, we show that chaotic heat transfer is enhanced by the displacement of the saddle point location during one period. Furthermore, the enhancement by chaotic advection in the elliptical geometry is approximately double that obtained in the cylindrical geometry because there are two saddle points instead of one. We also explain why, for high eccentricity ratios, there is no heat transfer enhancement in the cylindrical geometry. When an axial velocity component is added to both of these flows so that they become 3-D, previous work has shown that there is an optimum modulation frequency for which chaotic advection and heat transfer enhancement is a maximum. Here we show that the optimum modulation frequency can be derived from results without an axial flow. We also explain by physical arguments other previously unanswered questions in the published data.

Nonlinear electrohydrodynamics of a viscous droplet

NASA Astrophysics Data System (ADS)

Salipante, Paul; Vlahovska, Petia

2012-02-01

A classic result due to G.I.Taylor is that a drop placed in a uniform electric field adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. We report an instability and transition to a nonaxisymmetric rotational flow in strong fields, similar to the rotation of solid dielectric spheres observed by Quincke in the 19th century. Our experiments reveal novel droplet behaviors such as tumbling, oscillations and chaotic dynamics even under creeping flow conditions. A phase diagram demonstrates the dependence of these behaviors on drop size, viscosity ratio and electric field strength. The theoretical model, which includes anisotropy in the polarization relaxation, elucidates the interplay of interface deformation and charging as the source of the rich nonlinear dynamics.

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Numerical analysis of field-modulated electroosmotic flows in microchannels with arbitrary numbers and configurations of discrete electrodes.

PubMed

Chao, Kan; Chen, Bo; Wu, Jiankang

2010-12-01

The formation of an electric double layer and electroosmosis are important theoretic foundations associated with microfluidic systems. Field-modulated electroosmotic flows in microchannels can be obtained by applying modulating electric fields in a direction perpendicular to a channel wall. This paper presents a systematic numerical analysis of modulated electroosmotic flows in a microchannel with discrete electrodes on the basis of the Poisson equation of electric fields in a liquid-solid coupled domain, the Navier-Stokes equation of liquid flow, and the Nernst-Planck equation of ion transport. These equations are nonlinearly coupled and are simultaneously solved numerically for the electroosmotic flow velocity, electric potential, and ion concentrations in the microchannel. A number of numerical examples of modulated electroosmotic flows in microchannels with discrete electrodes are presented, including single electrodes, symmetric/asymmetric double electrodes, and triple electrodes. Numerical results indicate that chaotic circulation flows, micro-vortices, and effective fluid mixing can be realized in microchannels by applying modulating electric fields with various electrode configurations. The interaction of a modulating field with an applied field along the channel is also discussed.

Nonlinear filtering techniques for noisy geophysical data: Using big data to predict the future

NASA Astrophysics Data System (ADS)

Moore, J. M.

2014-12-01

Chaos is ubiquitous in physical systems. Within the Earth sciences it is readily evident in seismology, groundwater flows and drilling data. Models and workflows have been applied successfully to understand and even to predict chaotic systems in other scientific fields, including electrical engineering, neurology and oceanography. Unfortunately, the high levels of noise characteristic of our planet's chaotic processes often render these frameworks ineffective. This contribution presents techniques for the reduction of noise associated with measurements of nonlinear systems. Our ultimate aim is to develop data assimilation techniques for forward models that describe chaotic observations, such as episodic tremor and slip (ETS) events in fault zones. A series of nonlinear filters are presented and evaluated using classical chaotic systems. To investigate whether the filters can successfully mitigate the effect of noise typical of Earth science, they are applied to sunspot data. The filtered data can be used successfully to forecast sunspot evolution for up to eight years (see figure).

Quantification of chaotic strength and mixing in a micro fluidic system

NASA Astrophysics Data System (ADS)

Kim, Ho Jun; Beskok, Ali

2007-11-01

Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in micro fluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. The 'chaotic electroosmotic stirrer' of Qian and Bau (2002 Anal. Chem. 74 3616-25) is utilized as the benchmark case due to its well-defined flow kinematics. Lagrangian particle tracking methods are utilized to study particle dispersion in the conceptual device using spectral element and fourth-order Runge-Kutta discretizations in space and time, respectively. Stirring efficiency is predicted using the stirring index based on the box counting method, and Poincaré sections are utilized to identify the chaotic and regular regions under various actuation conditions. Finite time Lyapunov exponents are calculated to quantify the chaotic strength, while the probability density function of the stretching field is utilized as an alternative method to demonstrate the statistical analysis of chaotic and partially chaotic cases. Mixing index inverse, based on the standard deviation of scalar species distribution, is utilized as a metric to quantify the mixing efficiency. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing time (tm) is characterized as a function of the Pe number, and tm ~ ln(Pe) scaling is demonstrated for fully chaotic cases, while tm ~ Peα scaling with α ≈ 0.33 and α = 0.5 are observed for partially chaotic and regular cases, respectively. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified.

Active turbulence in a gas of self-assembled spinners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kokot, Gasper; Das, Shibananda; Winkler, Roland G.

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air-liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generatedmore » advection flows. The same-chirality spinners (clockwise or counterclock-wise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. As a result, our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale.« less

Active turbulence in a gas of self-assembled spinners

DOE PAGES

Kokot, Gasper; Das, Shibananda; Winkler, Roland G.; ...

2017-11-20

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air-liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generatedmore » advection flows. The same-chirality spinners (clockwise or counterclock-wise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. As a result, our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale.« less

Simple Chaotic Flow with Circle and Square Equilibrium

NASA Astrophysics Data System (ADS)

Gotthans, Tomas; Sprott, Julien Clinton; Petrzela, Jiri

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured).

A new transiently chaotic flow with ellipsoid equilibria

NASA Astrophysics Data System (ADS)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows

NASA Astrophysics Data System (ADS)

Richardson, S. I. Heath; Baggaley, A. W.; Hill, N. A.

2018-02-01

We study the effects of imposed three-dimensional flows on the trajectories and mixing of gyrotactic swimming microorganisms and identify phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor-Green and Arnold-Beltrami-Childress (ABC) flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical "plumelike" structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. Furthermore, studies of Lyapunov exponents reveal that, as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds.

Chaotic dynamics of a microswimmer in Poiseuille flow.

PubMed

Chacón, Ricardo

2013-11-01

The chaotic dynamics of pointlike, spherical particles in cylindrical Poiseuille flow is theoretically characterized and numerically confirmed when their own intrinsic swimming velocity undergoes temporal fluctuations around an average value. Two dimensionless ratios associated with the three significant temporal scales of the problem are identified that fully determine the chaos scenario. In particular, small but finite periodic fluctuations of swimming speed result in chaotic or regular motion depending on the position and orientation of the microswimmer with respect to the flow center line. Remarkably, the spatial extension of chaotic microswimmers is found to depend crucially on the fluctuations' period and amplitude and to be highly sensitive to the Fourier spectrum of the fluctuations. This has implications for the design of artificial microswimmers.

On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Mahmoud, Gamal M.

Dynamical systems described by real and complex variables are currently one of the most popular areas of scientific research. These systems play an important role in several fields of physics, engineering, and computer sciences, for example, laser systems, control (or chaos suppression), secure communications, and information science. Dynamical basic properties, chaos (hyperchaos) synchronization, chaos control, and generating hyperchaotic behavior of these systems are briefly summarized. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. They are also used to describe and simulate the physics of detuned laser and thermal convection of liquid flows, where the electric field and the atomic polarization amplitudes are both complex. Clearly, if the variables of the system are complex the equations involve twice as many variables and control parameters, thus making it that much harder for a hostile agent to intercept and decipher the coded message. Chaotic and hyperchaotic complex systems are stated as examples. Finally there are many open problems in the study of chaotic and hyperchaotic complex nonlinear dynamical systems, which need further investigations. Some of these open problems are given.

Do steady fast magnetic dynamos exist?

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward; Hanson, James D.; Kan, Ittai

1989-01-01

This paper considers the question of the existense of a steady fast kinematic magnetic dynamo for a conducting fluid with a steady velocity field and vanishingly small electrical resistivity. The analysis of examples of steady dynamos, found by considering the zero-resistivity dynamics, indicated that, for sufficiently small resistivity, dynamo action can indeed occur in steady smooth three-dimensional chaotic fluid flows and that fast dynamos should consequently be a typical occurrence for such flows.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strons, Philip; Bailey, James L.

Anemometer readings alone cannot provide a complete picture of air flow patterns at an open gloveport. Having a means to visualize air flow for field tests in general provides greater insight by indicating direction in addition to the magnitude of the air flow velocities in the region of interest. Furthermore, flow visualization is essential for Computational Fluid Dynamics (CFD) verification, where important modeling assumptions play a significant role in analyzing the chaotic nature of low-velocity air flow. A good example is shown Figure 1, where an unexpected vortex pattern occurred during a field test that could not have been measuredmore » relying only on anemometer readings. Here by, observing and measuring the patterns of the smoke flowing into the gloveport allowed the CFD model to be appropriately updated to match the actual flow velocities in both magnitude and direction.« less

Symmetry breaking and chaos in droplet electrohydrodynamics

NASA Astrophysics Data System (ADS)

Salipante, Paul; Vlahovska, Petia

2010-11-01

A classic result due to G.I.Taylor is that a drop placed in a uniform electric field adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, recent studies have revealed an instability and transition to a nonaxisymmetric rotational flow in strong fields, similar to the rotation of solid dielectric particles observed by Quincke in the 19th century. We present an experimental and theoretical study of this phenomenon in DC uniform fields, focusing on nonlinear behavior arising from electromechanial coupling at the fluid-fluid interface. Charge convection by the both rotational and straining flows is included in the our model to explain the dependence of critical electric field on viscosity ratio. Hysteresis in the transition is observed for large low-viscosity drops. At stronger fields, chaotic drop tumbling and sustained shape oscillations are observed.

A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2017-01-01

We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.

Dynamical and fractal properties in periodically forced stretch-twist-fold (STF) flow

NASA Astrophysics Data System (ADS)

Aqeel, Muhammad; Ahmad, Salman; Azam, Anam; Ahmed, Faizan

2017-05-01

The periodically forced stretch-twist-fold (STF) flow is introduced in this article. The nonlinear behavior of the STF flow with periodic force along the y -axis is investigated analytically and numerically. The STF flow is a prototype of the dynamo theory that proposes a mechanism of magnetic field generation continuously. The stability analysis is done by Routh Huwritz criteria and Cardano method. Chasing chaos through numerical simulation is determined to demonstrate the chaotic behavior of the forced STF flow. With the help of fractal processes based on the forced STF flow, a multi-wing forced STF flow is obtained that gives a n -wing forced STF flow system.

Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains)

NASA Astrophysics Data System (ADS)

Kędra, Mariola

2014-02-01

Is the underlying dynamics of river flow random or deterministic? If it is deterministic, is it deterministic chaotic? This issue is still controversial. The application of several independent methods, techniques and tools for studying daily river flow data gives consistent, reliable and clear-cut results to the question. The outcomes point out that the investigated discharge dynamics is not random but deterministic. Moreover, the results completely confirm the nonlinear deterministic chaotic nature of the studied process. The research was conducted on daily discharge from two selected gauging stations of the mountain river in southern Poland, the Raba River.

Dancing disclinations in confined active nematics

NASA Astrophysics Data System (ADS)

Shendruk, Tyler N.; Doostmohammadi, Amin; Thijssen, Kristian; Yeomans, Julia M.

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to achieve structured flows and ordered disclinations is of particular importance in the design and control of active systems. By confining an active nematic fluid within a channel, we find a regular motion of disclinations, in conjunction with a well defined and dynamic vortex lattice. As pairs of moving disclinations travel through the channel, they continually exchange partners producing a dynamic ordered state, reminiscent of Ceilidh dancing. We anticipate that this biomimetic ability to self-assemble organised topological disclinations and dynamically structured flow fields in engineered geometries will pave the road towards establishing new active topological microfluidic devices.

Numerical study of enhanced mixing in pressure-driven flows in microchannels using a spatially periodic electric field

NASA Astrophysics Data System (ADS)

Krishnaveni, T.; Renganathan, T.; Picardo, J. R.; Pushpavanam, S.

2017-09-01

We propose an innovative mechanism for enhancing mixing in steady pressure driven flow of an electrolytic solution in a straight rectangular microchannel. A transverse electric field is used to generate an electroosmotic flow across the cross-section. The resulting flow field consists of a pair of helical vortices that transport fluid elements along the channel. We show, through numerical simulations, that chaotic advection may be induced by periodically varying the direction of the applied electric field along the channel length. This periodic electric field generates a longitudinally varying, three-dimensional steady flow, such that the streamlines in the first half of the repeating unit cell intersect those in the second half, when projected onto the cross-section. Mixing is qualitatively characterized by tracking passive particles and obtaining Poincaré maps. For quantification of the extent of mixing, Shannon entropy is calculated using particle advection of a binary mixture. The convection diffusion equation is also used to track the evolution of a scalar species and quantify the mixing efficiency as a function of the Péclet number.

Numerical study of enhanced mixing in pressure-driven flows in microchannels using a spatially periodic electric field.

PubMed

Krishnaveni, T; Renganathan, T; Picardo, J R; Pushpavanam, S

2017-09-01

We propose an innovative mechanism for enhancing mixing in steady pressure driven flow of an electrolytic solution in a straight rectangular microchannel. A transverse electric field is used to generate an electroosmotic flow across the cross-section. The resulting flow field consists of a pair of helical vortices that transport fluid elements along the channel. We show, through numerical simulations, that chaotic advection may be induced by periodically varying the direction of the applied electric field along the channel length. This periodic electric field generates a longitudinally varying, three-dimensional steady flow, such that the streamlines in the first half of the repeating unit cell intersect those in the second half, when projected onto the cross-section. Mixing is qualitatively characterized by tracking passive particles and obtaining Poincaré maps. For quantification of the extent of mixing, Shannon entropy is calculated using particle advection of a binary mixture. The convection diffusion equation is also used to track the evolution of a scalar species and quantify the mixing efficiency as a function of the Péclet number.

Linking Chaotic Advection with Subsurface Biogeochemical Processes

NASA Astrophysics Data System (ADS)

Mays, D. C.; Freedman, V. L.; White, S. K.; Fang, Y.; Neupauer, R.

2017-12-01

This work investigates the extent to which groundwater flow kinematics drive subsurface biogeochemical processes. In terms of groundwater flow kinematics, we consider chaotic advection, whose essential ingredient is stretching and folding of plumes. Chaotic advection is appealing within the context of groundwater remediation because it has been shown to optimize plume spreading in the laminar flows characteristic of aquifers. In terms of subsurface biogeochemical processes, we consider an existing model for microbially-mediated reduction of relatively mobile uranium(VI) to relatively immobile uranium(IV) following injection of acetate into a floodplain aquifer beneath a former uranium mill in Rifle, Colorado. This model has been implemented in the reactive transport code eSTOMP, the massively parallel version of STOMP (Subsurface Transport Over Multiple Phases). This presentation will report preliminary numerical simulations in which the hydraulic boundary conditions in the eSTOMP model are manipulated to simulate chaotic advection resulting from engineered injection and extraction of water through a manifold of wells surrounding the plume of injected acetate. This approach provides an avenue to simulate the impact of chaotic advection within the existing framework of the eSTOMP code.

Chaotic Mixing in Magmatic Systems: a new experiment

NASA Astrophysics Data System (ADS)

de Campos, C. P.; Perugini, D.; Dingwell, D. B.; Poli, G.; Ertel-Ingrisch, W.; Hess, K.

2007-12-01

Previous studies on magma mixing systems have evidenced that mixing processes could be controlled by chaotic dynamics. These processes are thought to be the source of fractal structures propagating within natural magmatic systems, from meter to the micrometer length scale (Perugini et al., 2006. EPSL, 234: 669-680 and references therein). We have developed a device for experimental studies of chaotic mixing dynamics in silicate melts at high temperatures (up to 1700°C). This device has been inspired by the journal bearing or eccentric cylinder geometry for viscous fluids for the study of chaotic mixing in slow flows (Swanson and Ottino, 1990. J. Fluid Mech., 213:227-249). This geometry is thought to be an ideal system for chaotic studies because a) it is experimentally accessible/feasible for silicate rheologies and b) it is subject to an analytical solution for the stream function. In the journal bearing system the flow region, is confined in the torus between the centers of the two cylinders. Their central axes are parallel but not coincident, i. e. the cylinders are eccentric. In order to generate chaos in a flow, the streamlines must be time dependent, resulting in alternating movements between the two cylinders. This means that at least one of the cylinders has alternating rotation directions. The dimension of this new experimental device follows the required main dimensionless numbers for a chaotic flow. Our first experimental goal is to characterize the mixing process in a prototypical system (haplogranite-haplobasalt)under variable mixing protocols. muenchen.de/

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Cheng

Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.

Vector models and generalized SYK models

DOE PAGES

Peng, Cheng

2017-05-23

Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.

Chaotic flows and fast magnetic dynamos

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward

1988-01-01

The kinematic dynamo problem is considered in the R(m) approaching infinity limit. It is shown that the magnetic field tends to concentrate on a zero volume fractal set; moreover, it displays arbitrarily fine-scaled oscillations between parallel and antiparallel directions. Consideration is given to the relationship between the dynamo growth rate and quantitative measures of chaos, such as the Liapunov element and topological entropy.

Experimental chaotic quantification in bistable vortex induced vibration systems

NASA Astrophysics Data System (ADS)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear out the regularity of periodic responses. For this purpose, a surrogate data test is used in order to check the hypotheses for the presence of chaotic behavior. The analyses from the experimental results support the hypothesis from simulation that chaotic response is likely occur on the real system.

Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.

2017-11-01

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow.

Kinematic dynamo, supersymmetry breaking, and chaos

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Enßlin, Torsten A.

2016-04-01

The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.

State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh-Bénard convection.

PubMed

Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F

2009-03-01

Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.

Chaotic Stochasticity: A Ubiquitous Source of Unpredictability in Epidemics

NASA Astrophysics Data System (ADS)

Rand, D. A.; Wilson, H. B.

1991-11-01

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

NASA Astrophysics Data System (ADS)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

Relationship between stirring rate and Reynolds number in the chaotically advected steady flow in a container with exactly counter-rotating lids

NASA Astrophysics Data System (ADS)

Lackey, Tahirih C.; Sotiropoulos, Fotis

2006-05-01

We solve numerically the three-dimensional incompressible Navier-Stokes equations to simulate the flow in a cylindrical container of aspect ratio one with exactly counter-rotating lids for a range of Reynolds numbers for which the flow is steady and three dimensional (300⩽Re⩽850). In agreement with linear stability results [C. Nore et al., J. Fluid Mech. 511, 45 (2004)] we find steady, axisymmetric solutions for Re <300. For Re >300 the equatorial shear layer becomes unstable to steady azimuthal modes and a complex vortical flow emerges, which consists of cat's eye radial vortices at the shear layer and azimuthally inclined axial vortices. Upon the onset of the three-dimensional instability the Lagrangian dynamics of the flow become chaotic. A striking finding of our work is that there is an optimal Reynolds number at which the stirring rate in the chaotically advected flow is maximized. Above this Reynolds number, the integrable (unmixed) part of the flow begins to grow and the stirring rate is shown conclusively to decline. This finding is explained in terms of and appears to support a recently proposed theory of chaotic advection [I. Mezić, J. Fluid Mech. 431, 347 (2001)]. Furthermore, the calculated rate of decay of the stirring rate with Reynolds numbers is consistent with the Re-1/2 upper bound predicted by the theory.

Structure of chaotic magnetic field lines in IR-T1 tokamak due to ergodic magnetic limiter

NASA Astrophysics Data System (ADS)

Ahmadi, S.; Salar Elahi, A.; Ghorannevis, M.

2018-03-01

In this paper we have studied an Ergodic Magnetic Limiter (EML) based chaotic magnetic field for transport control in the edge plasma of IR-T1 tokamak. The resonance created by the EML causes perturbation of the equilibrium field line in tokamak and as a result, the field lines are chaotic in the vicinity of the dimerized island chains. Transport barriers are formed in the chaotic field line and actually observe in tokamak with reverse magnetic shear. We used area-preserving non-twist (and twist) Poincaré maps to describe the formation of transport barriers, which are actually features of Hamiltonian systems. This transport barrier is useful in reducing radial diffusion of the field line and thus improving the plasma confinement.

Computation of Sound Generated by Viscous Flow Over a Circular Cylinder

NASA Technical Reports Server (NTRS)

Cox, Jared S.; Rumsey, Christopher L.; Brentner, Kenneth S.; Younis, Bassam A.

1997-01-01

The Lighthill acoustic analogy approach combined with Reynolds-averaged Navier Stokes is used to predict the sound generated by unsteady viscous flow past a circular cylinder assuming a correlation length of 10 cylinder diameters. The two-dimensional unsteady flow field is computed using two Navier-Stokes codes at a low Mach number over a range of Reynolds numbers from 100 to 5 million. Both laminar flow as well as turbulent flow with a variety of eddy viscosity turbulence models are employed. Mean drag and Strouhal number are examined, and trends similar to experiments are observed. Computing the noise within the Reynolds number regime where transition to turbulence occurs near the separation point is problematic: laminar flow exhibits chaotic behavior and turbulent flow exhibits strong dependence on the turbulence model employed. Comparisons of far-field noise with experiment at a Reynolds number of 90,000, therefore, vary significantly, depending on the turbulence model. At a high Reynolds number outside this regime, three different turbulence models yield self-consistent results.

Turbulent dusty boundary layer in an ANFO surface-burst explosion

NASA Astrophysics Data System (ADS)

Kuhl, A. L.; Ferguson, R. E.; Chien, K. Y.; Collins, J. P.

1992-01-01

This paper describes the results of numerical simulations of the dusty, turbulent boundary layer created by a surface burst explosion. The blast wave was generated by the detonation of a 600-T hemisphere of ANFO, similar to those used in large-scale field tests. The surface was assumed to be ideally noncratering but contained an initial loose layer of dust. The dust-air mixture in this fluidized bed was modeled as a dense gas (i.e., an equilibrium model, valid for very small-diameter dust particles). The evolution of the flow was calculated by a high-order Godunov code that solves the nonsteady conservation laws. Shock interactions with dense layer generated vorticity near the wall, a result that is similar to viscous, no-slip effects found in clean flows. The resulting wall shear layer was unstable, and rolled up into large-scale rotational structures. These structures entrained dense material from the wall layer and created a chaotically striated flow. The boundary layer grew due to merging of the large-scale structures and due to local entrainment of the dense material from the fluidized bed. The chaotic flow was averaged along similarity lines (i.e., lines of constant values of x = r/Rs and y = z/Rs where R(sub s) = ct(exp alpha)) to establish the mean-flow profiles and the r.m.s. fluctuating-flow profiles of the boundary layer.

Chaos in Magnetic Flux Ropes

NASA Astrophysics Data System (ADS)

Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.

2013-12-01

Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2) O. Russo et al., Phys. Rev. Lett., 99, 154102 (2007), J. Maggs, G.Morales, 55, 085015 (2013)

Turbulence transition and the edge of chaos in pipe flow.

PubMed

Schneider, Tobias M; Eckhardt, Bruno; Yorke, James A

2007-07-20

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.

Turbulence and deterministic chaos. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1992-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.

Inertio-elastic mixing in a straight microchannel with side wells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Sun Ok; Cooper-White, Justin J.; School of Chemical Engineering, University of Queensland, St Lucia, 4072 QLD

Mixing remains a challenging task in microfluidic channels because of their inherently small length scale. In this work, we propose an efficient microfluidic mixer based on the chaotic vortex dynamics of a viscoelastic flow in a straight channel with side wells. When the inertia and elasticity of a dilute polymer solution are balanced (i.e., the Reynolds number Re and Weissenberg number Wi are both on the order of 10{sup 1}), chaotic vortices appear in the side wells (inertio-elastic flow instability), enhancing the mixing of adjacent fluid streams. However, there is no chaotic vortex motion in Newtonian flows for any flowmore » rate. Efficient mixing by such an inertio-elastic instability is found to be relevant for a wide range of Re values.« less

On the onset of secondary flow and unsteady solutions through a loosely coiled rectangular duct for large aspect ratio

NASA Astrophysics Data System (ADS)

Shaha, Poly Rani; Rudro, Sajal Kanti; Poddar, Nayan Kumar; Mondal, Rabindra Nath

2016-07-01

The study of flows through coiled ducts and channels has attracted considerable attention not only because of their ample applications in Chemical, Mechanical, Civil, Nuclear and Biomechanical engineering but also because of their ample applications in other areas, such as blood flow in the veins and arteries of human and other animals. In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a loosely coiled rectangular duct of large aspect ratio. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Dean number, Dn, for two types of curvatures of the duct. The main concern of the present study is to find out effects of curvature as well as formation of secondary vortices on unsteady solutions whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn is increased. Time evolution calculations as well as their phase spaces are performed with a view to study the non-linear behavior of the unsteady solutions, and it is found that the steady-state flow turns into chaotic flow through various flow instabilities, if Dn is increased no matter what the curvature is. It is found that the unsteady flow is a steady-state solution for small Dn's and oscillates periodically or non-periodically (chaotic) between two- and twelve-vortex solutions, if Dn is increased. It is also found that the chaotic solution is weak for small Dn's but strong as Dn becomes large. Axial flow distribution is also investigated and shown in contour plots.

On the onset of secondary flow and unsteady solutions through a loosely coiled rectangular duct for large aspect ratio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shaha, Poly Rani; Poddar, Nayan Kumar; Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com

The study of flows through coiled ducts and channels has attracted considerable attention not only because of their ample applications in Chemical, Mechanical, Civil, Nuclear and Biomechanical engineering but also because of their ample applications in other areas, such as blood flow in the veins and arteries of human and other animals. In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a loosely coiled rectangular duct of large aspect ratio. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Dean number, Dn,more » for two types of curvatures of the duct. The main concern of the present study is to find out effects of curvature as well as formation of secondary vortices on unsteady solutions whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn is increased. Time evolution calculations as well as their phase spaces are performed with a view to study the non-linear behavior of the unsteady solutions, and it is found that the steady-state flow turns into chaotic flow through various flow instabilities, if Dn is increased no matter what the curvature is. It is found that the unsteady flow is a steady-state solution for small Dn’s and oscillates periodically or non-periodically (chaotic) between two- and twelve-vortex solutions, if Dn is increased. It is also found that the chaotic solution is weak for small Dn’s but strong as Dn becomes large. Axial flow distribution is also investigated and shown in contour plots.« less

Analysis of Hepatic Blood Flow Using Chaotic Models

PubMed Central

Cohen, M. E.; Moazamipour, H.; Hudson, D. L.; Anderson, M. F.

1990-01-01

The study of chaos in physical systems is an important new theoretical development in modeling which has emerged in the last fifteen years. It is particularly useful in explaining phenomena which arise in nonlinear dynamic systems, for which previous mathematical models produced results with intractable solutions. Analysis of blood flow is such an application. In the work described here, chaotic models are used to analyze hepatic artery and portal vein blood flow obtained from a pulsed Doppler ultrasonic flowmeter implanted in dogs. ImagesFigure 3

Path Planning for Robot based on Chaotic Artificial Potential Field Method

NASA Astrophysics Data System (ADS)

Zhang, Cheng

2018-03-01

Robot path planning in unknown environments is one of the hot research topics in the field of robot control. Aiming at the shortcomings of traditional artificial potential field methods, we propose a new path planning for Robot based on chaotic artificial potential field method. The path planning adopts the potential function as the objective function and introduces the robot direction of movement as the control variables, which combines the improved artificial potential field method with chaotic optimization algorithm. Simulations have been carried out and the results demonstrate that the superior practicality and high efficiency of the proposed method.

A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation

NASA Astrophysics Data System (ADS)

Abdolmohammadi, Hamid Reza; Khalaf, Abdul Jalil M.; Panahi, Shirin; Rajagopal, Karthikeyan; Pham, Viet-Thanh; Jafari, Sajad

2018-06-01

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays (FPGA). In addition, an electronic circuit design for the chaotic system is introduced.

Chaotic coordinates for the Large Helical Device

NASA Astrophysics Data System (ADS)

Hudson, Stuart; Suzuki, Yasuhiro

2014-10-01

The study of dynamical systems is facilitated by a coordinate framework with coordinate surfaces that coincide with invariant structures of the dynamical flow. For axisymmetric systems, a continuous family of invariant surfaces is guaranteed and straight-fieldline coordinates may be constructed. For non-integrable systems, e.g. stellarators, perturbed tokamaks, this continuous family is broken. Nevertheless, coordinates can still be constructed that simplify the description of the dynamics. The Poincare-Birkhoff theorem, the Aubry-Mather theorem, and the KAM theorem show that there are important structures that are invariant under the perturbed dynamics; namely the periodic orbits, the cantori, and the irrational flux surfaces. Coordinates adapted to these invariant sets, which we call chaotic coordinates, provide substantial advantages. The regular motion becomes straight, and the irregular motion is bounded by, and dissected by, coordinate surfaces that coincide with surfaces of locally-minimal magnetic-fieldline flux. The chaotic edge of the magnetic field, as calculated by HINT2 code, in the Large Helical Device (LHD) is examined, and a coordinate system is constructed so that the flux surfaces are ``straight'' and the islands become ``square.''

The Chaotic Terrains of Mercury: A History of Large-Scale Crustal Devolatilization

NASA Astrophysics Data System (ADS)

Rodriguez, J. A. P.; Domingue, D. L.; Berman, D. C.; Kargel, J. S.; Baker, V. R.; Teodoro, L. F.; Banks, M.; Leonard, G.

2018-05-01

Approximately 400 million years after the Caloris basin impact, extensive collapse formed Mercury's chaotic terrains. Collapse likely resulted from regionally elevated heat flow devolatilizing crustal materials along NE and NW extensional faults.

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

PubMed

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

Mixing Silicate Melts with High Viscosity Contrast by Chaotic Dynamics: Results from a New Experimental Device

NASA Astrophysics Data System (ADS)

de Campos, Cristina; Perugini, Diego; Ertel-Ingrisch, Werner; Dingwell, Donald B.; Poli, Giampiero

2010-05-01

A new experimental device has been developed to perform chaotic mixing between high viscosity melts under controlled fluid-dynamic conditions. The apparatus is based on the Journal Bearing System (JBS). It consists of an outer cylinder hosting the melts of interest and an inner cylinder, which is eccentrically located. Both cylinders can be independently moved to generate chaotic streamlines in the mixing system. Two experiments were performed using as end-members different proportions of a peralkaline haplogranite and a mafic melt, corresponding to the 1 atm eutectic composition in the An-Di binary system. The two melts were stirred together in the JBS for ca. two hours, at 1,400° C and under laminar fluid dynamic condition (Re of the order of 10-7). The viscosity ratio between the two melts, at the beginning of the experiment, was of the order of 103. Optical analyses of experimental samples revealed, at short length scale (of the order of μm), a complex pattern of mixed structures. These consisted of an intimate distribution of filaments; a complex inter-fingering of the two melts. Such features are typically observed in rocks thought to be produced by magma mixing processes. Stretching and folding dynamics between the melts induced chaotic flow fields and generated wide compositional interfaces. In this way, chemical diffusion processes become more efficient, producing melts with highly heterogeneous compositions. A remarkable modulation of compositional fields has been obtained by performing short time-scale experiments and using melts with a high viscosity ratio. This indicates that chaotic mixing of magmas can be a very efficient process in modulating compositional variability in igneous systems, especially under high viscosity ratios and laminar fluid-dynamic regimes. Our experimental device may replicate magma mixing features, observed in natural rocks, and therefore open new frontiers in the study of this important petrologic and volcanological process.

Alteration of chaotic advection in blood flow around partial blockage zone: Role of hematocrit concentration

NASA Astrophysics Data System (ADS)

Maiti, Soumyabrata; Chaudhury, Kaustav; DasGupta, Debabrata; Chakraborty, Suman

2013-01-01

Spatial distributions of particles carried by blood exhibit complex filamentary pattern under the combined effects of geometrical irregularities of the blood vessels and pulsating pumping by the heart. This signifies the existence of so called chaotic advection. In the present article, we argue that the understanding of such pathologically triggered chaotic advection is incomplete without giving due consideration to a major constituent of blood: abundant presence of red blood cells quantified by the hematocrit (HCT) concentration. We show that the hematocrit concentration in blood cells can alter the filamentary structures of the spatial distribution of advected particles in an intriguing manner. Our results reveal that there primarily are two major impacts of HCT concentrations towards dictating the chaotic dynamics of blood flow: changing the zone of influence of chaotic mixing and determining the enhancement of residence time of the advected particles away from the wall. This, in turn, may alter the extent of activation of platelets or other reactive biological entities, bearing immense consequence towards dictating the biophysical mechanisms behind possible life-threatening diseases originating in the circulatory system.

Chaos and ion heating in a slow shock

NASA Technical Reports Server (NTRS)

Lin, Y.; Lee, L. C.

1991-01-01

An ion heating mechanism is proposed of slow shocks, which is associated with the chaotic motion of particles in the downstream wave field. For a coherent electromagnetic wave propagating along the downstream magnetic field, corresponding to switch-off shocks, the particle motions are not chaotic. For an oblique wave, the interaction between the particles and the wave field may lead to chaotic particle motions. Such particles may be greatly thermalized within one wavelength after they are incident into the downstream wave field. The results can be used to explain the existence of the critical intermediate Mach number observed in the hybrid simulations.

Bistability and chaos in the Taylor-Green dynamo.

PubMed

Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj

2012-03-01

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

On retrodictions of global mantle flow with assimilated surface velocities

NASA Astrophysics Data System (ADS)

Colli, Lorenzo; Bunge, Hans-Peter; Schuberth, Bernhard S. A.

2016-04-01

Modeling past states of Earth's mantle and relating them to geologic observations such as continental-scale uplift and subsidence is an effective method for testing mantle convection models. However, mantle convection is chaotic and two identical mantle models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated, thus limiting retrodictions (i.e., reconstructions of past states of Earth's mantle obtained using present information) to the recent past. We show with 3-D spherical mantle convection models that retrodictions of mantle flow can be extended significantly if knowledge of the surface velocity field is available. Assimilating surface velocities produces in some cases negative Lyapunov times (i.e., e-folding times), implying that even a severely perturbed initial condition may evolve toward the reference state. A history of the surface velocity field for Earth can be obtained from past plate motion reconstructions for time periods of a mantle overturn, suggesting that mantle flow can be reconstructed over comparable times.

On retrodictions of global mantle flow with assimilated surface velocities

NASA Astrophysics Data System (ADS)

Colli, Lorenzo; Bunge, Hans-Peter; Schuberth, Bernhard S. A.

2015-10-01

Modeling past states of Earth's mantle and relating them to geologic observations such as continental-scale uplift and subsidence is an effective method for testing mantle convection models. However, mantle convection is chaotic and two identical mantle models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated, thus limiting retrodictions (i.e., reconstructions of past states of Earth's mantle obtained using present information) to the recent past. We show with 3-D spherical mantle convection models that retrodictions of mantle flow can be extended significantly if knowledge of the surface velocity field is available. Assimilating surface velocities produces in some cases negative Lyapunov times (i.e., e-folding times), implying that even a severely perturbed initial condition may evolve toward the reference state. A history of the surface velocity field for Earth can be obtained from past plate motion reconstructions for time periods of a mantle overturn, suggesting that mantle flow can be reconstructed over comparable times.

The fast kinematic magnetic dynamo and the dissipationless limit

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward

1990-01-01

The evolution of the magnetic field in models that incorporate chaotic field line stretching, field cancellation, and finite magnetic Reynolds number is examined analytically and numerically. Although the models used here are highly idealized, it is claimed that they display and illustrate typical behavior relevant to fast magnetic dynamic behavior. It is shown, in particular, that consideration of magnetic flux through a finite fixed surface provides a simple and effective way of deducing fast dynamo behavior from the zero resistivity equation. Certain aspects of the fast dynamo problem can thus be reduced to a study of nonlinear dynamic properties of the underlying flow.

Chaotic Motions in the Real Fuzzy Electronic Circuits

DTIC Science & Technology

2012-12-30

field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be...Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended ...model. The overall fuzzy model of the system is achieved by fuzzy blending of the linear system models. Consider a continuous-time nonlinear dynamic

Analysis of coherent dynamical processes through computer vision

NASA Astrophysics Data System (ADS)

Hack, M. J. Philipp

2016-11-01

Visualizations of turbulent boundary layers show an abundance of characteristic arc-shaped structures whose apparent similarity suggests a common origin in a coherent dynamical process. While the structures have been likened to the hairpin vortices observed in the late stages of transitional flow, a consistent description of the underlying mechanism has remained elusive. Detailed studies are complicated by the chaotic nature of turbulence which modulates each manifestation of the process and which renders the isolation of individual structures a challenging task. The present study applies methods from the field of computer vision to capture the time evolution of turbulent flow features and explore the associated physical mechanisms. The algorithm uses morphological operations to condense the structure of the turbulent flow field into a graph described by nodes and links. The low-dimensional geometric information is stored in a database and allows the identification and analysis of equivalent dynamical processes across multiple scales. The framework is not limited to turbulent boundary layers and can also be applied to different types of flows as well as problems from other fields of science.

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

DOE PAGES

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; ...

2015-10-30

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

Lyapunov exponents, covariant vectors and shadowing sensitivity analysis of 3D wakes: from laminar to chaotic regimes

NASA Astrophysics Data System (ADS)

Wang, Qiqi; Rigas, Georgios; Esclapez, Lucas; Magri, Luca; Blonigan, Patrick

2016-11-01

Bluff body flows are of fundamental importance to many engineering applications involving massive flow separation and in particular the transport industry. Coherent flow structures emanating in the wake of three-dimensional bluff bodies, such as cars, trucks and lorries, are directly linked to increased aerodynamic drag, noise and structural fatigue. For low Reynolds laminar and transitional regimes, hydrodynamic stability theory has aided the understanding and prediction of the unstable dynamics. In the same framework, sensitivity analysis provides the means for efficient and optimal control, provided the unstable modes can be accurately predicted. However, these methodologies are limited to laminar regimes where only a few unstable modes manifest. Here we extend the stability analysis to low-dimensional chaotic regimes by computing the Lyapunov covariant vectors and their associated Lyapunov exponents. We compare them to eigenvectors and eigenvalues computed in traditional hydrodynamic stability analysis. Computing Lyapunov covariant vectors and Lyapunov exponents also enables the extension of sensitivity analysis to chaotic flows via the shadowing method. We compare the computed shadowing sensitivities to traditional sensitivity analysis. These Lyapunov based methodologies do not rely on mean flow assumptions, and are mathematically rigorous for calculating sensitivities of fully unsteady flow simulations.

Local and nonlocal parallel heat transport in general magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Chacon, Luis

2011-01-01

A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.

Route to broadband chaos in a chaotic laser diode subject to optical injection.

PubMed

Wang, An-Bang; Wang, Yun-Cai; Wang, Juan-Fen

2009-04-15

We experimentally and numerically demonstrate a route to bandwidth-enhanced chaos that is induced by an additional optical injection for a chaotic laser diode with optical feedback. The measured and calculated optical spectra consistently reveal that the mechanism of bandwidth enhancement is the interaction between the injection and chaotic laser field via beating. The bandwidth can be maximized only when the injected light is detuned into the edge of the optical spectrum of the chaotic laser field and the beating frequency exceeds the original bandwidth. The simulated dynamics maps indicate that 20 GHz broadband chaos can be obtained by commonly used laser diodes.

Distribution of self-propelled organisms in fluid flows

NASA Astrophysics Data System (ADS)

Neufeld, Zoltan

2006-11-01

We study the distribution of microorganisms represented as self-propelled particles in a moving fluid medium. The particles are advected by the flow and, in addition, they swim in a direction controlled by external factors. Two cases are considered: 1. passive spheroidal particles, that swim with constant speed but the swimming direction is reoriented by the viscous torque acting on the spheroid due to the local velocity field, and 2. chemotactic particles, whose swimming speed is oriented and proportional to the gradient of the concentration of a chemoattractant. We show that the combined effects of chaotic mixing and chemotaxis or flow reorientation leads to aggregation of the particles along a complex manifold. We analyse the properties of the aggregates and the efficiency of chemotaxis in flows with strongly non-uniform fluctuating distribution of the chemottractant.

Oscillatory/Chaotic Thermocapillary Flow Induced by Radiant Heating

NASA Technical Reports Server (NTRS)

DeWitt, Kenneth J.

1998-01-01

There is a continuing need to understand the fluid physics occurring under low gravity conditions in processes such as crystal growth, materials processing, and the movement of bubbles or droplets. The fluid flow in such situations is often caused by a gradient in interfacial tension. If a temperature gradient is created due to a heat source, the resulting flow is called thermocapillary flow, a special case of Marangoni Convection. In this study, an experimental investigation was conducted using silicone oil in cylindrical containers with a laser heat source at the free surface. It was desired to determine the conditions under which steady, axisymmetrical thermocapillary flow becomes unstable and oscillatory three-dimensional flow states develop. The critical Marangoni number for each observed oscillatory state was measured as a function of the container aspect ratio and the dynamic Bond number, a measure of buoyant force versus ii thermocapillary force. Various oscillatory modes were observed during three- dimensional convection, and chaotic flow was reached in one test condition. The critical Marangoni numbers are compared with those measured in previous studies, and the power spectra and phase trajectories of the instantaneous surface temperature distributions are used to characterize the routes of transitions to the chaotic flow state. Results show that only superharmonic modes appear in the routes to chaos while infinite number of subharmonic modes occur in flow transitions for pure Rayleigh convection.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

NASA Astrophysics Data System (ADS)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

The chaotic regime of D-term inflation

NASA Astrophysics Data System (ADS)

Buchmüller, W.; Domcke, V.; Schmitz, K.

2014-11-01

We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of `chaotic inflation'.

Computer design of microfluidic mixers for protein/RNA folding studies.

PubMed

Inguva, Venkatesh; Kathuria, Sagar V; Bilsel, Osman; Perot, Blair James

2018-01-01

Kinetic studies of biological macromolecules increasingly use microfluidic mixers to initiate and monitor reaction progress. A motivation for using microfluidic mixers is to reduce sample consumption and decrease mixing time to microseconds. Some applications, such as small-angle x-ray scattering, also require large (>10 micron) sampling areas to ensure high signal-to-noise ratios and to minimize parasitic scattering. Chaotic to marginally turbulent mixers are well suited for these applications because this class of mixers provides a good middle ground between existing laminar and turbulent mixers. In this study, we model various chaotic to marginally turbulent mixing concepts such as flow turning, flow splitting, and vortex generation using computational fluid dynamics for optimization of mixing efficiency and observation volume. Design iterations show flow turning to be the best candidate for chaotic/marginally turbulent mixing. A qualitative experimental test is performed on the finalized design with mixing of 10 M urea and water to validate the flow turning unsteady mixing concept as a viable option for RNA and protein folding studies. A comparison of direct numerical simulations (DNS) and turbulence models suggests that the applicability of turbulence models to these flow regimes may be limited.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

PubMed

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Statistics of Advective Stretching in Three-dimensional Incompressible Flows

NASA Astrophysics Data System (ADS)

Subramanian, Natarajan; Kellogg, Louise H.; Turcotte, Donald L.

2009-09-01

We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421-432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376-380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^{-1/2} . However, it is observed that stretching becomes exponential log S˜ t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^{-1/2} . This behavior is consistent with a random multiplicative stretching process.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding.

PubMed

Lin, Po-Cheng; I, Lin

2016-02-01

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding

NASA Astrophysics Data System (ADS)

Lin, Po-Cheng; I, Lin

2016-02-01

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.; Wang, Qiqi

2018-02-01

Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic systems, including simulations of chaotic vortex shedding and homogeneous isotropic turbulence. However, this gradient information comes at a very high computational cost. This paper presents multiple shooting shadowing (MSS), a more computationally efficient shadowing approach than the original LSS approach. Through an analysis of the convergence rate of MSS, it is shown that MSS can have lower memory usage and run time than LSS.

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet Speech: Where will the future go? M. J. Feigenbaum.

Fluid elasticity and the transition to chaos in thermal convection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khayat, R.E.

1995-01-01

The influence of fluid elasticity on the onset of aperiodic or chaotic motion of an upper-convected Maxwellian fluid is examined in the context of the Rayleigh-Benard thermal convection problem. A truncated Fourier representation of the flow and temperature fields leads to a four-dimensional dynamical system that constitutes a generalization of the classical Lorenz system for Newtonian fluids. It is found that, to the order of the present truncation and above a critical value of the Deborah number De[sup [ital c

Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Tang, G. H.; Li, Zhuo; Wang, J. K.; He, Y. L.; Tao, W. Q.

2006-11-01

Understanding the electroosmotic flow in microchannels is of both fundamental and practical significance for the design and optimization of various microfluidic devices to control fluid motion. In this paper, a lattice Boltzmann equation, which recovers the nonlinear Poisson-Boltzmann equation, is used to solve the electric potential distribution in the electrolytes, and another lattice Boltzmann equation, which recovers the Navier-Stokes equation including the external force term, is used to solve the velocity fields. The method is validated by the electric potential distribution in the electrolytes and the pressure driven pulsating flow. Steady-state and pulsating electroosmotic flows in two-dimensional parallel uniform and nonuniform charged microchannels are studied with this lattice Boltzmann method. The simulation results show that the heterogeneous surface potential distribution and the electroosmotic pulsating flow can induce chaotic advection and thus enhance the mixing in microfluidic systems efficiently.

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

NASA Astrophysics Data System (ADS)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

PubMed

Fromhold, T M; Patanè, A; Bujkiewicz, S; Wilkinson, P B; Fowler, D; Sherwood, D; Stapleton, S P; Krokhin, A A; Eaves, L; Henini, M; Sankeshwar, N S; Sheard, F W

2004-04-15

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

Transition to chaos of a vertical collapsible tube conveying air flow

NASA Astrophysics Data System (ADS)

Castillo Flores, F.; Cros, A.

2009-05-01

"Sky dancers", the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.

Inertial objects in complex flows

NASA Astrophysics Data System (ADS)

Syed, Rayhan; Ho, George; Cavas, Samuel; Bao, Jialun; Yecko, Philip

2017-11-01

Chaotic Advection and Finite Time Lyapunov Exponents both describe stirring and transport in complex and time-dependent flows, but FTLE analysis has been largely limited to either purely kinematic flow models or high Reynolds number flow field data. The neglect of dynamic effects in FTLE and Lagrangian Coherent Structure studies has stymied detailed information about the role of pressure, Coriolis effects and object inertia. We present results of laboratory and numerical experiments on time-dependent and multi-gyre Stokes flows. In the lab, a time-dependent effectively two-dimensional low Re flow is used to distinguish transport properties of passive tracer from those of small paramagnetic spheres. Companion results of FTLE calculations for inertial particles in a time-dependent multi-gyre flow are presented, illustrating the critical roles of density, Stokes number and Coriolis forces on their transport. Results of Direct Numerical Simulations of fully resolved inertial objects (spheroids) immersed in a three dimensional (ABC) flow show the role of shape and finite size in inertial transport at small finite Re. We acknowledge support of NSF DMS-1418956.

Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

Security Analysis of Some Diffusion Mechanisms Used in Chaotic Ciphers

NASA Astrophysics Data System (ADS)

Zhang, Leo Yu; Zhang, Yushu; Liu, Yuansheng; Yang, Anjia; Chen, Guanrong

As a variant of the substitution-permutation network, the permutation-diffusion structure has received extensive attention in the field of chaotic cryptography over the last three decades. Because of the high implementation speed and nonlinearity over GF(2), the Galois field of two elements, mixing modulo addition/multiplication and Exclusive OR becomes very popular in various designs to achieve the desired diffusion effect. This paper reports that some diffusion mechanisms based on modulo addition/multiplication and Exclusive OR are not resistant to plaintext attacks as claimed. By cracking several recently proposed chaotic ciphers as examples, it is demonstrated that a good understanding of the strength and weakness of these crypto-primitives is crucial for designing more practical chaotic encryption algorithms in the future.

Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Vastano, John A.; Moser, Robert D.

1991-01-01

The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.

Low Reynolds number numerical solutions of chaotic flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

1989-01-01

Numerical computations of two-dimensional flow past an airfoil at low Mach number, large angle of attack, and low Reynolds number are reported which show a sequence of flow states leading from single-period vortex shedding to chaos via the period-doubling mechanism. Analysis of the flow in terms of phase diagrams, Poincare sections, and flowfield variables are used to substantiate these results. The critical Reynolds number for the period-doubling bifurcations is shown to be sensitive to mesh refinement and the influence of large amounts of numerical dissipation. In extreme cases, large amounts of added dissipation can delay or completely eliminate the chaotic response. The effect of artificial dissipation at these low Reynolds numbers is to produce a new effective Reynolds number for the computations.

Passive scalars chaotic dynamics induced by two vortices in a two-layer geophysical flow with shear and rotation

NASA Astrophysics Data System (ADS)

Ryzhov, Eugene

2015-11-01

Vortex motion in shear flows is of great interest from the point of view of nonlinear science, and also as an applied problem to predict the evolution of vortices in nature. Considering applications to the ocean and atmosphere, it is well-known that these media are significantly stratified. The simplest way to take stratification into account is to deal with a two-layer flow. In this case, vortices perturb the interface, and consequently, the perturbed interface transits the vortex influences from one layer to another. Our aim is to investigate the dynamics of two point vortices in an unbounded domain where a shear and rotation are imposed as the leading order influence from some generalized perturbation. The two vortices are arranged within the bottom layer, but an emphasis is on the upper-layer fluid particle motion. Point vortices induce singular velocity fields in the layer they belong to, however, in the other layers of a multi-layer flow, they induce regular velocity fields. The main feature is that singular velocity fields prohibit irregular dynamics in the vicinity of the singular points, but regular velocity fields, provided optimal conditions, permit irregular dynamics to extend almost in every point of the corresponding phase space.

Synchronization in node of complex networks consist of complex chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Qiang, E-mail: qiangweibeihua@163.com; Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024

2014-07-15

A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Non-linear dynamics and alternating 'flip' solutions in ferrofluidic Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Altmeyer, Sebastian

2018-04-01

This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined between two concentric independently rotating cylinders. We detected alternating 'flip' solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion.

Chaotic coordinates for the Large Helical Device

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hudson, S. R., E-mail: shudson@pppl.gov; Suzuki, Y.

The theory of quadratic-flux-minimizing (QFM) surfaces is reviewed, and numerical techniques that allow high-order QFM surfaces to be efficiently constructed for experimentally relevant, non-integrable magnetic fields are described. As a practical example, the chaotic edge of the magnetic field in the Large Helical Device (LHD) is examined. A precise technique for finding the boundary surface is implemented, the hierarchy of partial barriers associated with the near-critical cantori is constructed, and a coordinate system, which we call chaotic coordinates, that is based on a selection of QFM surfaces is constructed that simplifies the description of the magnetic field, so that fluxmore » surfaces become “straight” and islands become “square.”.« less

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progressionmore » by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.« less

Characterizing Strength of Chaotic Dynamics and Numerical Simulation Relevant to Modified Taylor-Couette Flow with Hourglass Geometry

NASA Astrophysics Data System (ADS)

Hou, Yu; Kowalski, Adam; Schroder, Kjell; Halmstad, Andrew; Olsen, Thomas; Wiener, Richard

2006-05-01

We characterize the strength of chaos in two different regimes of Modified Taylor-Couette flow with Hourglass Geometry: the formation of Taylor Vortices with laminar flow and with turbulent flow. We measure the strength of chaos by calculating the correlation dimension and the Kaplan-Yorke dimension based upon the Lyapunov Exponents of each system. We determine the reliability of our calculations by considering data from a chaotic electronic circuit. In order to predict the behavior of the Modified Taylor-Couette flow system, we employ simulations based upon an idealized Reaction-Diffusion model with a third order non-linearity in the reaction rate. Variation of reaction rate with length corresponds to variation of the effective Reynolds Number along the Taylor-Couette apparatus. We present preliminary results and compare to experimental data.

Chaotic behavior in electro-rotation

NASA Astrophysics Data System (ADS)

Lemaire, E.; Lobry, L.

2002-11-01

We study the dynamics of an insulating cylinder in a weakly conducting liquid when submitted to a DC electric field. The cylinder is free to rotate along its long axis which is perpendicular to the applied field. Above a threshold value of the electric field, the cylinder rotates in either direction with constant angular velocity. This instability is known as Quincke rotation and can be easily understood by considering the polarization induced by the free charges accumulation on the cylinder surface. Here we present preliminary experimental results which exhibit a chaotic dynamics of the cylinder for higher electric fields: the velocity is no longer constant and the rotation direction changes randomly. By taking into account the finite Maxwell-Wagner polarization relaxation time, we show that this chaotic behavior can be described by the Lorenz equations.

Numerical investigation of flow past 17-cylinder array of square cylinders

NASA Astrophysics Data System (ADS)

Shams-ul-Islam, Nazeer, Ghazala; Ying, Zhou Chao

2018-06-01

In this work, flow past 17-cylinder array is simulated using the two-dimensional lattice Boltzmann method. Effect of gap spacings (0.5 ≤ gx* ≤ 3, 0.5 ≤ gy* ≤ 3) and Reynolds number (Re = 75 - 150) is analyzed in details. Results are presented in the form of vorticity contours plots, time-histories of drag and lift coefficients and power spectrum of lift coefficient. Six distinct flow regimes are identified for different gap spacings and Reynolds numbers: steady flow regime, single bluff body flow regime, non-fully developed flow regime, chaotic flow regime, quasi-periodic-I flow regime and quasi-periodic-II flow regime. Chaotic flow regime is the mostly observed flow regime while the single bluff body flow regime rarely occurs for this configuration. It is observed that drag force along each cylinder in 17-cylinder array decreases in the streamwise direction for fixed Reynold number and gap spacing. C1 and C2 cylinders experience the maximum drag at small gap spacing and Reynolds number. Also the Reynolds number is found to be more effective on flow characteristics as compared to gap spacings.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Parallel heat transport in integrable and chaotic magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Chacon, Luis

2012-01-01

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly chal- lenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), , and the perpendicular, , conductivities ( / may exceed 1010 in fusion plasmas); (ii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates; and (iii) Nonlocal parallel transport in the limit of small collisionality. Motivated by these issues, we present a Lagrangian Green s function method to solve themore » local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geom- etry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island chain), weakly chaotic (devil s staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local closures, is non-diffusive, thus casting doubts on the appropriateness of the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.« less

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations.

PubMed

Chacón, Ricardo

2006-09-15

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative oscillator systems by weak harmonic excitations is presented, including diverse applications, such as chaotic escape from a potential well, chaotic solitons in Frenkel-Kontorova chains and chaotic-charged particles in the field of an electrostatic wave packet.

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

PubMed Central

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

2016-01-01

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

DOE PAGES

Chen, Shuying; Yu, Liping; Ren, Jingli; ...

2016-07-20

Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al 0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, andmore » there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

PubMed

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

2016-07-20

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Akgul, A.; Kaçar, S.; Çavuşoğlu, U.

2018-02-01

Hyperjerk systems have received significant interest in the literature because of their simple structure and complex dynamical properties. This work presents a new chaotic hyperjerk system having two exponential nonlinearities. Dynamical properties of the chaotic hyperjerk system are discovered through equilibrium point analysis, bifurcation diagram, dissipativity and Lyapunov exponents. Moreover, an adaptive backstepping controller is designed for the synchronization of the chaotic hyperjerk system. Also, a real circuit of the chaotic hyperjerk system has been carried out to show the feasibility of the theoretical hyperjerk model. The chaotic hyperjerk system can also be useful in scientific fields such as Random Number Generators (RNGs), data security, data hiding, etc. In this work, three implementations of the chaotic hyperjerk system, viz. RNG, image encryption and sound steganography have been performed by using complex dynamics characteristics of the system.

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field.

PubMed

Wang, C; Wang, F; Cao, J C

2014-09-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Chaos enhancing tunneling in a coupled Bose-Einstein condensate with a double driving.

PubMed

Rong, Shiguang; Hai, Wenhua; Xie, Qiongtao; Zhu, Qianquan

2009-09-01

We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.

A particle tracking method for analyzing chaotic electroosmotic flow mixing in 3D microchannels with patterned charged surfaces

NASA Astrophysics Data System (ADS)

Chang, Chih-Chang; Yang, Ruey-Jen

2006-08-01

This paper presents a numerical simulation investigation into electroosmotic flow mixing in three-dimensional microchannels with patterned non-uniform surface zeta potentials. Three types of micromixers are investigated, namely a straight diagonal strip mixer (i.e. the non-uniform surface zeta potential is applied along straight, diagonal strips on the lower wall of the mixing channel), a staggered asymmetric herringbone strip mixer and a straight diagonal/symmetric herringbone strip mixer. A particle tracing algorithm is used to visualize and evaluate the mixing performance of the various mixers. The particle trajectories and Poincaré maps of the various mixers are calculated from the three-dimensional flow fields. The surface charge patterns on the lower walls of the microchannels induce electroosmotic chaotic advection in the low Reynolds number flow regime, and hence enhance the passive mixing effect in the microfluidic devices. A quantitative measure of the mixing performance based on Shannon entropy is employed to quantify the mixing of two miscible fluids. The results show that the mixing efficiency increases as the magnitude of the heterogeneous zeta potential ratio (|ζR|) is increased, but decreases as the aspect ratio (H/W) is increased. The mixing efficiency of the straight diagonal strip mixer with a length ratio of l/W = 0.5 is slightly higher than that obtained from the same mixer with l/W = 1.0. Finally, the staggered asymmetric herringbone strip mixer with θ = 45°, ζR = -1, l/W = 0.5 and H/W = 0.2 provides the optimal mixing performance of all the mixers presented in this study.

Phase definition to assess synchronization quality of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Freitas, Leandro; Torres, Leonardo A. B.; Aguirre, Luis A.

2018-05-01

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

Phase definition to assess synchronization quality of nonlinear oscillators.

PubMed

Freitas, Leandro; Torres, Leonardo A B; Aguirre, Luis A

2018-05-01

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

The deterministic chaos and random noise in turbulent jet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yao, Tian-Liang; Shanghai Institute of Space Propulsion, Shanghai 201112; Shanghai Engineering Research Center of Space Engine, Shanghai Institute of Space Propulsion, Shanghai 201112

2014-06-01

A turbulent flow is usually treated as a superposition of coherent structure and incoherent turbulence. In this paper, the largest Lyapunov exponent and the random noise in the near field of round jet and plane jet are estimated with our previously proposed method of chaotic time series analysis [T. L. Yao, et al., Chaos 22, 033102 (2012)]. The results show that the largest Lyapunov exponents of the round jet and plane jet are in direct proportion to the reciprocal of the integral time scale of turbulence, which is in accordance with the results of the dimensional analysis, and the proportionalitymore » coefficients are equal. In addition, the random noise of the round jet and plane jet has the same linear relation with the Kolmogorov velocity scale of turbulence. As a result, the random noise may well be from the incoherent disturbance in turbulence, and the coherent structure in turbulence may well follow the rule of chaotic motion.« less

Chaotic interactions of self-replicating RNA.

PubMed

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Chaos of energetic positron orbits in a dipole magnetic field and its potential application to a new injection scheme

NASA Astrophysics Data System (ADS)

Saitoh, H.; Yoshida, Z.; Yano, Y.; Nishiura, M.; Kawazura, Y.; Horn-Stanja, J.; Pedersen, T. Sunn

2016-10-01

We study the behavior of high-energy positrons emitted from a radioactive source in a magnetospheric dipole field configuration. Because the conservation of the first and second adiabatic invariants is easily destroyed in a strongly inhomogeneous dipole field for high-energy charged particles, the positron orbits are nonintegrable, resulting in chaotic motions. In the geometry of a typical magnetospheric levitated dipole experiment, it is shown that a considerable ratio of positrons from a 22Na source, located at the edge of the confinement region, has chaotic long orbit lengths before annihilation. These particles make multiple toroidal circulations and form a hollow toroidal positron cloud. Experiments with a small 22Na source in the Ring Trap 1 (RT-1) device demonstrated the existence of such long-lived positrons in a dipole field. Such a chaotic behavior of high-energy particles is potentially applicable to the formation of a dense toroidal positron cloud in the strong-field region of the dipole field in future studies.

Observation of Droplet Size Oscillations in a Two Phase Fluid under Shear Flow

NASA Astrophysics Data System (ADS)

Courbin, Laurent; Panizza, Pascal

2004-11-01

It is well known that complex fluids exhibit strong couplings between their microstructure and the flow field. Such couplings may lead to unusual non linear rheological behavior. Because energy is constantly brought to the system, richer dynamic behavior such as non linear oscillatory or chaotic response is expected. We report on the observation of droplet size oscillations at fixed shear rate. At low shear rates, we observe two steady states for which the droplet size results from a balance between capillary and viscous stress. For intermediate shear rates, the droplet size becomes a periodic function of time. We propose a phenomenological model to account for the observed phenomenon and compare numerical results to experimental data.

Paramagnetic colloids: Chaotic routes to clusters and molecules

NASA Astrophysics Data System (ADS)

Abdi, Hamed; Soheilian, Rasam; Erb, Randall M.; Maloney, Craig E.

2018-03-01

We present computer simulations and experiments on dilute suspensions of superparamagnetic particles subject to rotating magnetic fields. We focus on chains of four particles and their decay routes to stable structures. At low rates, the chains track the external field. At intermediate rates, the chains break up but perform a periodic (albeit complex) motion. At sufficiently high rates, the chains generally undergo chaotic motion at short times and decay to either closely packed clusters or more dispersed, colloidal molecules at long times. We show that the transition out of the chaotic states can be described as a Poisson process in both simulation and experiment.

Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban

2017-01-01

Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

Separation of Trend and Chaotic Components of Time Series and Estimation of Their Characteristics by Linear Splines

NASA Astrophysics Data System (ADS)

Kryanev, A. V.; Ivanov, V. V.; Romanova, A. O.; Sevastyanov, L. A.; Udumyan, D. K.

2018-03-01

This paper considers the problem of separating the trend and the chaotic component of chaotic time series in the absence of information on the characteristics of the chaotic component. Such a problem arises in nuclear physics, biomedicine, and many other applied fields. The scheme has two stages. At the first stage, smoothing linear splines with different values of smoothing parameter are used to separate the "trend component." At the second stage, the method of least squares is used to find the unknown variance σ2 of the noise component.

Effect of exercise on patient specific abdominal aortic aneurysm flow topology and mixing

PubMed Central

Arzani, Amirhossein; Les, Andrea S.; Dalman, Ronald L.; Shadden, Shawn C.

2014-01-01

SUMMARY Computational fluid dynamics modeling was used to investigate changes in blood transport topology between rest and exercise conditions in five patient-specific abdominal aortic aneurysm models. Magnetic resonance imaging was used to provide the vascular anatomy and necessary boundary conditions for simulating blood velocity and pressure fields inside each model. Finite-time Lyapunov exponent fields, and associated Lagrangian coherent structures, were computed from blood velocity data, and used to compare features of the transport topology between rest and exercise both mechanistically and qualitatively. A mix-norm and mix-variance measure based on fresh blood distribution throughout the aneurysm over time were implemented to quantitatively compare mixing between rest and exercise. Exercise conditions resulted in higher and more uniform mixing, and reduced the overall residence time in all aneurysms. Separated regions of recirculating flow were commonly observed in rest, and these regions were either reduced or removed by attached and unidirectional flow during exercise, or replaced with regional chaotic and transiently turbulent mixing, or persisted and even extended during exercise. The main factor that dictated the change in flow topology from rest to exercise was the behavior of the jet of blood penetrating into the aneurysm during systole. PMID:24493404

Experimental test of scaling of mixing by chaotic advection in droplets moving through microfluidic channels

PubMed Central

Song, Helen; Bringer, Michelle R.; Tice, Joshua D.; Gerdts, Cory J.; Ismagilov, Rustem F.

2006-01-01

This letter describes an experimental test of a simple argument that predicts the scaling of chaotic mixing in a droplet moving through a winding microfluidic channel. Previously, scaling arguments for chaotic mixing have been described for a flow that reduces striation length by stretching, folding, and reorienting the fluid in a manner similar to that of the baker’s transformation. The experimentally observed flow patterns within droplets (or plugs) resembled the baker’s transformation. Therefore, the ideas described in the literature could be applied to mixing in droplets to obtain the scaling argument for the dependence of the mixing time, t~(aw/U)log(Pe), where w [m] is the cross-sectional dimension of the microchannel, a is the dimensionless length of the plug measured relative to w, U [m s−1] is the flow velocity, Pe is the Péclet number (Pe=wU/D), and D [m2s−1] is the diffusion coefficient of the reagent being mixed. Experiments were performed to confirm the scaling argument by varying the parameters w, U, and D. Under favorable conditions, submillisecond mixing has been demonstrated in this system. PMID:17940580

Enhancing emerging organic compound degradation: applying chaotic flow to managed aquifer recharge

NASA Astrophysics Data System (ADS)

Rodríguez-Escales, Paula; Fernandez-Garcia, Daniel; Drechsel, Johannes; Folch, Albert; Sanchez-Vila, Xavier

2017-04-01

The coupling of Managed Aquifer Recharge with soil aquifer remediation treatment, by placing a reactive layer containing organic matter at the bottom of the infiltration pond, is a promising technology to improve the rate of degradation of EOCs. Its success is based on assuming that recharged water and groundwater get well mixed, which is not always true. It has been demonstrated that mixing can be enhanced by inducing chaotic advection through extraction-injection engineering. In this work we analyze how chaotic advection might enhance the spreading of redox conditions with the final aim of improving degradation of a mix of benzotriazoles: benzotriazole, 5-methyl-benzotriazole, and 5-chloro-benzotriazole. The first two compounds are better degraded under aerobic conditions whereas the third one under nitrate reducing conditions. We developed a reactive transport model that describes how a recharged water rich in organic matter mixes with groundwater, how this organic matter is oxidized by different electron acceptors, and how the benzotriazoles are degraded attending for the redox state. The model was tested in different scenarios of recharge, both in homogenous and in heterogenous media. It was found that chaotic flow increases the spreading of the plume of recharged water. Consequently, different redox conditions coexist at a given time within the area affected by recharge, facilitating the degradation of EOCs.

Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence

NASA Technical Reports Server (NTRS)

Abedian, B.; Hyers, R. W.; Curreri, Peter A. (Technical Monitor)

2002-01-01

When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.

Monodomain dynamics for rigid rod and platelet suspensions in strongly coupled coplanar linear flow and magnetic fields. II. Kinetic theory

NASA Astrophysics Data System (ADS)

Forest, M. Gregory; Sircar, Sarthok; Wang, Qi; Zhou, Ruhai

2006-10-01

We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional rate parameters). We solve the Smoluchowski equation of the reduced model to explore: (i) the effect of introducing a coplanar magnetic field on each sheared monodomain attractor of the Doi-Hess kinetic theory and (ii) the coupling of coplanar extensional flow and magnetic fields. For (i), we show each sheared attractor (steady and unsteady, with peak axis in and out of the shearing plane, periodic and chaotic orbits) undergoes its own transition sequence versus magnetic field strength. Nonetheless, robust predictions emerge: out-of-plane degrees of freedom are arrested with increasing field strength, and a unique flow-aligning or tumbling/wagging limit cycle emerges above a threshold magnetic field strength or modified geometry parameter value. For (ii), irrotational flows coupled with a coplanar magnetic field yield only steady states. We characterize all (generically biaxial) equilibria in terms of an explicit Boltzmann distribution, providing a natural generalization of analytical results on pure nematic equilibria [P. Constantin, I. Kevrekidis, and E. S. Titi, Arch. Rat. Mech. Anal. 174, 365 (2004); P. Constantin, I. Kevrekidis, and E. S. Titi, Discrete and Continuous Dynamical Systems 11, 101 (2004); P. Constantin and J. Vukadinovic, Nonlinearity 18, 441 (2005); H. Liu, H. Zhang, and P. Zhang, Comm. Math. Sci. 3, 201 (2005); C. Luo, H. Zhang, and P. Zhang, Nonlinearity 18, 379 (2005); I. Fatkullin and V. Slastikov, Nonlinearity 18, 2565 (2005); H. Zhou, H. Wang, Q. Wang, and M. G. Forest, Nonlinearity 18, 2815 (2005)] and extensional flow-induced equilibria [Q. Wang, S. Sircar, and H. Zhou, Comm. Math. Sci. 4, 605 (2005)]. We predict large parameter regions of bi-stable equilibria; the lowest energy state always has principal axis aligned in the flow plane, while another minimum energy state often exists, with primary alignment transverse to the coplanar field.

Gauge Fields in Homogeneous and Inhomogeneous Cosmologies

NASA Astrophysics Data System (ADS)

Darian, Bahman K.

Despite its formidable appearance, the study of classical Yang-Mills (YM) fields on homogeneous cosmologies is amenable to a formal treatment. This dissertation is a report on a systematic approach to the general construction of invariant YM fields on homogeneous cosmologies undertaken for the first time in this context. This construction is subsequently followed by the investigation of the behavior of YM field variables for the most simple of self-gravitating YM fields. Particularly interesting was a dynamical system analysis and the discovery of chaotic signature in the axially symmetric Bianchi I-YM cosmology. Homogeneous YM fields are well studied and are known to have chaotic properties. The chaotic behavior of YM field variables in homogeneous cosmologies might eventually lead to an invariant definition of chaos in (general) relativistic cosmological models. By choosing the gauge fields to be Abelian, the construction and the field equations presented so far reduce to that of electromagnetic field in homogeneous cosmologies. A perturbative analysis of gravitationally interacting electromagnetic and scalar fields in inhomogeneous cosmologies is performed via the Hamilton-Jacobi formulation of general relativity. An essential feature of this analysis is the spatial gradient expansion of the generating functional (Hamilton principal function) to solve the Hamiltonian constraint. Perturbations of a spatially flat Friedman-Robertson-Walker cosmology with an exponential potential for the scalar field are presented.

Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system

NASA Astrophysics Data System (ADS)

Lai, Qiang; Zhao, Xiao-Wen; Rajagopal, Karthikeyan; Xu, Guanghui; Akgul, Akif; Guleryuz, Emre

2018-01-01

This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.

Parameter estimation for chaotic systems using improved bird swarm algorithm

NASA Astrophysics Data System (ADS)

Xu, Chuangbiao; Yang, Renhuan

2017-12-01

Parameter estimation of chaotic systems is an important problem in nonlinear science and has aroused increasing interest of many research fields, which can be basically reduced to a multidimensional optimization problem. In this paper, an improved boundary bird swarm algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the good global convergence and robustness of the bird swarm algorithm and the exploitation capability of improved boundary learning strategy. Experiments are conducted on the Lorenz system and the coupling motor system. Numerical simulation results reveal the effectiveness and with desirable performance of IBBSA for parameter estimation of chaotic systems.

Onset of chaos in helical vortex breakdown at low Reynolds number

NASA Astrophysics Data System (ADS)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Turbulent Dynamics of Epithelial Cell Cultures

NASA Astrophysics Data System (ADS)

Blanch-Mercader, C.; Yashunsky, V.; Garcia, S.; Duclos, G.; Giomi, L.; Silberzan, P.

2018-05-01

We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.

Numerical investigation of turbulence in reshocked Richtmyer-Meshkov unstable curtain of dense gas

NASA Astrophysics Data System (ADS)

Shankar, S. K.; Lele, S. K.

2014-01-01

Moderate-resolution numerical simulations of the impulsive acceleration of a dense gas curtain in air by a Mach 1.21 planar shock are carried out by solving the 3D compressible multi-species Navier-Stokes equations coupled with localized artificial diffusivity method to capture discontinuities in the flow field. The simulations account for the presence of three species in the flow field: air, and acetone (used as a tracer species in the experiments). Simulations at different concentration levels of the species are conducted and the temporal evolution of the curtain width is compared with the measured data from the experimental studies by Balakumar et al. (Phys Fluids 20:124103-124113, 2008). The instantaneous density and velocity fields at two different times (prior and after the reshock) are compared with experimental data and show good qualitative agreement. The reshock process is studied by re-impacting the evolving curtain with the reflected shock wave. Reshock causes enhanced mixing and destroys the ordered velocity field causing a chaotic flow. The unsteady flow field is characterized by computing statistics of certain flow variables using two different definitions of the mean flow. The average profiles conditioned on the heavy gas (comprising and acetone) and the corresponding fluctuating fields provide metrics which are more suitable to comparing with experimentally measured data. Mean profiles (conditioned on the heavy gas) of stream-wise velocity, variance of stream-wise velocity, and turbulent kinetic energy and PDF (probability distribution function) of fluctuating velocity components are computed at two different times along the flow evolution and are seen to show trend towards grid convergence. The spectra of turbulent kinetic energy and scalar energy (of mass fraction of heavy gas) show the existence of more than half decade of inertial sub-range at late times following reshock. The Reynolds stresses in the domain are reported while identifying the term that is dominant in its contribution to the Reynolds stresses.

Hypothesis on the Origin of Chaotic Pulse Train in Dart Leader

NASA Astrophysics Data System (ADS)

Pu, Y.; Qie, X.; Sun, Z.; Jiang, R.; Liu, M.; Zhang, H.

2017-12-01

The origin of chaotic pulse train (CPT) during the dart leader propagation remains debatable. Based on previous observations, the `chaotic' dart leader is featured by chaotic electric fields, large charge transfer and high energetic radiation. In some cases, the cause of CPT was attributed to the concurrent branches or upward connecting leader. In this presentation, after carefully examining the simultaneous optical, electrical and VHF location data of triggered lightning in SHATLE and some results in other literature, we found the close relationship between the upper luminous leader segment and CPT. It is hypothesized that the CPT originates from the luminous corona zone around the upper leader channel beyond the leader tip. The fast, sufficient supply of negative charge from the cloud can result in a net negative charge layer around the ionized channel surface. Then new diffuse discharge can make a corona zone outside the channel and radiates in a chaotic way. The cloud charge reservoir and the speed of charge transfer, which can be indicated by the speed of the leader, are determinative to the generation of CPT. Using VHF location technique, we also estimated the speed evolution of the leader and link it with electric field change.

Universal Hitting Time Statistics for Integrable Flows

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Marklof, Jens; Strömbergsson, Andreas

2017-02-01

The perceived randomness in the time evolution of "chaotic" dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the Poisson law for the times at which a particle with random initial data hits a small set. This was proved in various settings for dynamical systems with strong mixing properties. The key result of the present study is that, despite the absence of mixing, the hitting times of integrable flows also satisfy universal limit laws which are, however, not Poisson. We describe the limit distributions for "generic" integrable flows and a natural class of target sets, and illustrate our findings with two examples: the dynamics in central force fields and ellipse billiards. The convergence of the hitting time process follows from a new equidistribution theorem in the space of lattices, which is of independent interest. Its proof exploits Ratner's measure classification theorem for unipotent flows, and extends earlier work of Elkies and McMullen.

Nonlinear modeling of chaotic time series: Theory and applications

NASA Astrophysics Data System (ADS)

Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.

We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.

Mathematical embryology: the fluid mechanics of nodal cilia

NASA Astrophysics Data System (ADS)

Smith, D. J.; Smith, A. A.; Blake, J. R.

2011-07-01

Left-right symmetry breaking is critical to vertebrate embryonic development; in many species this process begins with cilia-driven flow in a structure termed the `node'. Primary `whirling' cilia, tilted towards the posterior, transport morphogen-containing vesicles towards the left, initiating left-right asymmetric development. We review recent theoretical models based on the point-force stokeslet and point-torque rotlet singularities, explaining how rotation and surface-tilt produce directional flow. Analysis of image singularity systems enforcing the no-slip condition shows how tilted rotation produces a far-field `stresslet' directional flow, and how time-dependent point-force and time-independent point-torque models are in this respect equivalent. Associated slender body theory analysis is reviewed; this approach enables efficient and accurate simulation of three-dimensional time-dependent flow, time-dependence being essential in predicting features of the flow such as chaotic advection, which have subsequently been determined experimentally. A new model for the nodal flow utilising the regularized stokeslet method is developed, to model the effect of the overlying Reichert's membrane. Velocity fields and particle paths within the enclosed domain are computed and compared with the flow profiles predicted by previous `membrane-less' models. Computations confirm that the presence of the membrane produces flow-reversal in the upper region, but no continuous region of reverse flow close to the epithelium. The stresslet far-field is no longer evident in the membrane model, due to the depth of the cavity being of similar magnitude to the cilium length. Simulations predict that vesicles released within one cilium length of the epithelium are generally transported to the left via a `loopy drift' motion, sometimes involving highly unpredictable detours around leftward cilia [truncated

Computation of Vortex Shedding and Radiated Sound for a Circular Cylinder

NASA Technical Reports Server (NTRS)

Cox, Jared S.; Brentner, Kenneth S.; Rumsey, Christopher L.; Younis, Bassam A.

1997-01-01

The Lighthill acoustic analogy approach combined with Reynolds-averaged Navier Stokes is used to predict the sound generated by unsteady viscous flow past a circular cylinder assuming a correlation length of ten cylinder diameters. The two- dimensional unsteady ow field is computed using two Navier-Stokes codes at a low Mach number over a range of Reynolds numbers from 100 to 5 million. Both laminar ow as well as turbulent ow with a variety of eddy viscosity turbulence models are employed. Mean drag and Strouhal number are examined, and trends similar to experiments are observed. Computing the noise within the Reynolds number regime where transition to turbulence occurs near the separation point is problematic: laminar flow exhibits chaotic behavior and turbulent ow exhibits strong dependence on the turbulence model employed. Comparisons of far-field noise with experiment at a Reynolds number of 90,000, therefore, vary significantly, depending on the turbulence model. At a high Reynolds number outside this regime, three different turbulence models yield self-consistent results.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Time-delayed chameleon: Analysis, synchronization and FPGA implementation

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Jafari, Sajad; Laarem, Guessas

2017-12-01

In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter space. A novel adaptive modified functional projective lag synchronization algorithm is derived for synchronizing identical time-delayed chameleon systems with uncertain parameters. The proposed time-delayed systems and the synchronization algorithm with controllers and parameter estimates are then implemented in FPGA using hardware-software co-simulation and the results are presented.

Consequences of wave-particle interactions on chaotic acceleration

NASA Technical Reports Server (NTRS)

Schriver, David; Ashour-Abdalla, Maha

1991-01-01

The recent model of Ashour-Abdalla et al. (1991) has proposed that the earth's plasma sheet can be formed by chaotic acceleration in a magnetotail-like field configuration. The ion velocity distributions created by chaotic acceleration have unstable features and represent robust free energy sources for kinetic plasma waves that can modify the original distributions. In the plasma sheet boundary layer, field-aligned ion beamlets are formed which drive a host of instabilities creating a broadbanded noise spectrum and cause thermal spreading of the beamlets. In addition, there is strong heating of any cold background plasma that may be present. In the central plasma sheet, ion antiloss cone distributions are created which are unstable to very low frequency waves that saturate by filling the antiloss cone.

Chaotic dynamics in premixed hydrogen/air channel flow combustion

NASA Astrophysics Data System (ADS)

Pizza, Gianmarco; Frouzakis, Christos E.; Mantzaras, John

2012-04-01

The complex oscillatory behaviour observed in fuel-lean premixed hydrogen/air atmospheric pressure flames in an open planar channel with prescribed wall temperature is investigated by means of direct numerical simulations, employing detailed chemistry descriptions and species transport, and nonlinear dynamics analysis. As the inflow velocity is varied, the sequence of transitions includes harmonic single frequency oscillations, intermittency, mixed mode oscillations, and finally a period-doubling cascade leading to chaotic dynamics. The observed modes are described and characterised by means of phase-space portraits and next amplitude maps. It is shown that the interplay of chemistry, transport, and wall-bounded developing flow leads to considerably richer dynamics compared to fuel-lean hydrogen/air continuously stirred tank reactor studies.

Linear and nonlinear dynamo properties of time-dependent ABC flows

NASA Astrophysics Data System (ADS)

Brummell, N. H.; Cattaneo, F.; Tobias, S. M.

2001-04-01

The linear and nonlinear dynamo properties of a class of periodically forced flows is considered. The forcing functions are chosen to drive, in the absence of magnetic effects (kinematic regime), a time-dependent version of the ABC flow with A= B= C=1. The time-dependence consists of a harmonic displacement of the origin along the line x= y= z=1 with amplitude ɛ and frequency Ω. The finite-time Lyapunov exponents are computed for several values of ɛ and Ω. It is found that for values of these parameters near unity chaotic streamlines occupy most of the volume. In this parameter range, and for moderate kinetic and magnetic Reynolds numbers, the basic flow is both hydrodynamically and hydromagnetically unstable. However, the dynamo instability has a higher growth rate than the hydrodynamic one, so that the nonlinear regime can be reached with negligible departures from the basic ABC flow. In the nonlinear regime, two distinct classes of behaviour are observed. In one, the exponential growth of the magnetic field saturates and the dynamo settles to a stationary state whereby the magnetic energy is maintained indefinitely. In the other the velocity field evolves to a nondynamo state and the magnetic field, following an initial amplification, decays to zero. The transition from the dynamo to the nondynamo state can be mediated by the hydrodynamic instability or by magnetic perturbations. The properties of the ensuing nonlinear dynamo states are investigated for different parameter values. The implications for a general theory of nonlinear dynamos are discussed.

Lagrangian transport near perturbed periodic lines in three-dimensional unsteady flows

NASA Astrophysics Data System (ADS)

Speetjens, Michel

2015-11-01

Periodic lines formed by continuous strings of periodic points are key organizing entities in the Lagrangian flow topology of certain three-dimensional (3D) time-periodic flows. Such lines generically consist of elliptic and/or hyperbolic points and thus give rise to 3D flow topologies made up of families of concentric closed trajectories embedded in chaotic regions. Weak perturbation destroys the periodic lines and causes said trajectories to coalesce into families of concentric tubes. However, emergence of isolated periodic points near the disintegrating periodic lines and/or partitioning of the original lines into elliptic and hyperbolic segments interrupt the tube formation. This yields incomplete tubes that interact with the (chaotic) environment through their open ends, resulting in intricate and essentially 3D flow topologies These phenomena have been observed in various realistic flows yet the underlying mechanisms are to date only partially understood. This study deepens insight into the (perturbed) Lagrangian dynamics of these flows by way of a linearized representation of the equations of motion near the periodic lines. Predictions on the basis of this investigation are in full (qualitative) agreement with observed behavior in the actual flows

Gravitational dynamos and the low-frequency geomagnetic secular variation.

PubMed

Olson, P

2007-12-18

Self-sustaining numerical dynamos are used to infer the sources of low-frequency secular variation of the geomagnetic field. Gravitational dynamo models powered by compositional convection in an electrically conducting, rotating fluid shell exhibit several regimes of magnetic field behavior with an increasing Rayleigh number of the convection, including nearly steady dipoles, chaotic nonreversing dipoles, and chaotic reversing dipoles. The time average dipole strength and dipolarity of the magnetic field decrease, whereas the dipole variability, average dipole tilt angle, and frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large-amplitude dipole secular variation with maximum power at frequencies corresponding to a few cycles per million years on Earth. Their external magnetic field structure, dipole statistics, low-frequency power spectra, and polarity reversal frequency are comparable to the geomagnetic field. The magnetic variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy fluctuations. A constant energy dissipation theory accounts for this inverse energy correlation, which is shown to produce conditions favorable for dipole drift, polarity reversals, and excursions.

Gravitational dynamos and the low-frequency geomagnetic secular variation

PubMed Central

Olson, P.

2007-01-01

Self-sustaining numerical dynamos are used to infer the sources of low-frequency secular variation of the geomagnetic field. Gravitational dynamo models powered by compositional convection in an electrically conducting, rotating fluid shell exhibit several regimes of magnetic field behavior with an increasing Rayleigh number of the convection, including nearly steady dipoles, chaotic nonreversing dipoles, and chaotic reversing dipoles. The time average dipole strength and dipolarity of the magnetic field decrease, whereas the dipole variability, average dipole tilt angle, and frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large-amplitude dipole secular variation with maximum power at frequencies corresponding to a few cycles per million years on Earth. Their external magnetic field structure, dipole statistics, low-frequency power spectra, and polarity reversal frequency are comparable to the geomagnetic field. The magnetic variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy fluctuations. A constant energy dissipation theory accounts for this inverse energy correlation, which is shown to produce conditions favorable for dipole drift, polarity reversals, and excursions. PMID:18048345

The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-dimensional Study of Nonlinear Evolution

NASA Astrophysics Data System (ADS)

Ryu, Dongsu; Jones, T. W.; Frank, Adam

2000-12-01

We investigate through high-resolution three-dimensional simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. As in our earlier work, we have considered periodic sections of flows that contain a thin, transonic shear layer but are otherwise uniform. The initially uniform magnetic field is parallel to the shear plane but oblique to the flow itself. We confirm in three-dimensional flows the conclusion from our two-dimensional work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in three dimensions by this work because it shows how field-line bundles can be stretched and twisted in three dimensions as the quasi-two-dimensional Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of 2 over the two-dimensional effect. If, by these developments, the Alfvén Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest that magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations, the regime in three dimensions for such reorganization is 4<~MAx<~50, expressed in terms of the Alfvén Mach number of the original velocity transition and the initial Alfvén speed projected to the flow plan. When the initial field is stronger than this, the flow either is linearly stable (if MAx<~2) or becomes stabilized by enhanced magnetic tension as a result of the corrugated field along the shear layer before the Cat's Eye forms (if MAx>~2). For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a three-dimensional nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterward. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows becomes magnetohydrodynamic. Decay of the magnetohydrodynamic turbulence is enhanced by dissipation accompanying magnetic reconnection. Hence, in three dimensions as in two dimensions, very weak fields do not modify substantially the character of the flow evolution but do increase global dissipation rates.

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

NASA Astrophysics Data System (ADS)

Tantet, Alexis; Lucarini, Valerio; Dijkstra, Henk A.

2018-02-01

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

NASA Astrophysics Data System (ADS)

Tantet, Alexis; Lucarini, Valerio; Dijkstra, Henk A.

2017-12-01

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

Solving Partial Differential Equations in a data-driven multiprocessor environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Chaotic electron transport in semiconductor devices

NASA Astrophysics Data System (ADS)

Scannell, William Christian

The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q, that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of DF values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high DF values are shown to de-correlate at smaller increments of field than the FCF with lower DF values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated.

An easily fabricated three-dimensional threaded lemniscate-shaped micromixer for a wide range of flow rates

PubMed Central

Rafeie, Mehdi; Welleweerd, Marcel; Hassanzadeh-Barforoushi, Amin; Asadnia, Mohsen; Olthuis, Wouter; Ebrahimi Warkiani, Majid

2017-01-01

Mixing fluid samples or reactants is a paramount function in the fields of micro total analysis system (μTAS) and microchemical processing. However, rapid and efficient fluid mixing is difficult to achieve inside microchannels because of the difficulty of diffusive mass transfer in the laminar regime of the typical microfluidic flows. It has been well recorded that the mixing efficiency can be boosted by migrating from two-dimensional (2D) to three-dimensional (3D) geometries. Although several 3D chaotic mixers have been designed, most of them offer a high mixing efficiency only in a very limited range of Reynolds numbers (Re). In this work, we developed a 3D fine-threaded lemniscate-shaped micromixer whose maximum numerical and empirical efficiency is around 97% and 93%, respectively, and maintains its high performance (i.e., >90%) over a wide range of 1 < Re < 1000 which meets the requirements of both the μTAS and microchemical process applications. The 3D micromixer was designed based on two distinct mixing strategies, namely, the inducing of chaotic advection by the presence of Dean flow and diffusive mixing through thread-like grooves around the curved body of the mixers. First, a set of numerical simulations was performed to study the physics of the flow and to determine the essential geometrical parameters of the mixers. Second, a simple and cost-effective method was exploited to fabricate the convoluted structure of the micromixers through the removal of a 3D-printed wax structure from a block of cured polydimethylsiloxane. Finally, the fabricated mixers with different threads were tested using a fluorescent microscope demonstrating a good agreement with the results of the numerical simulation. We envisage that the strategy used in this work would expand the scope of the micromixer technology by broadening the range of efficient working flow rate and providing an easy way to the fabrication of 3D convoluted microstructures. PMID:28798843

An easily fabricated three-dimensional threaded lemniscate-shaped micromixer for a wide range of flow rates.

PubMed

Rafeie, Mehdi; Welleweerd, Marcel; Hassanzadeh-Barforoushi, Amin; Asadnia, Mohsen; Olthuis, Wouter; Ebrahimi Warkiani, Majid

2017-01-01

Mixing fluid samples or reactants is a paramount function in the fields of micro total analysis system (μTAS) and microchemical processing. However, rapid and efficient fluid mixing is difficult to achieve inside microchannels because of the difficulty of diffusive mass transfer in the laminar regime of the typical microfluidic flows. It has been well recorded that the mixing efficiency can be boosted by migrating from two-dimensional (2D) to three-dimensional (3D) geometries. Although several 3D chaotic mixers have been designed, most of them offer a high mixing efficiency only in a very limited range of Reynolds numbers ( Re ). In this work, we developed a 3D fine-threaded lemniscate-shaped micromixer whose maximum numerical and empirical efficiency is around 97% and 93%, respectively, and maintains its high performance (i.e., >90%) over a wide range of 1 <  Re  < 1000 which meets the requirements of both the μTAS and microchemical process applications. The 3D micromixer was designed based on two distinct mixing strategies, namely, the inducing of chaotic advection by the presence of Dean flow and diffusive mixing through thread-like grooves around the curved body of the mixers. First, a set of numerical simulations was performed to study the physics of the flow and to determine the essential geometrical parameters of the mixers. Second, a simple and cost-effective method was exploited to fabricate the convoluted structure of the micromixers through the removal of a 3D-printed wax structure from a block of cured polydimethylsiloxane. Finally, the fabricated mixers with different threads were tested using a fluorescent microscope demonstrating a good agreement with the results of the numerical simulation. We envisage that the strategy used in this work would expand the scope of the micromixer technology by broadening the range of efficient working flow rate and providing an easy way to the fabrication of 3D convoluted microstructures.

Effect of exercise on patient specific abdominal aortic aneurysm flow topology and mixing.

PubMed

Arzani, Amirhossein; Les, Andrea S; Dalman, Ronald L; Shadden, Shawn C

2014-02-01

Computational fluid dynamics modeling was used to investigate changes in blood transport topology between rest and exercise conditions in five patient-specific abdominal aortic aneurysm models. MRI was used to provide the vascular anatomy and necessary boundary conditions for simulating blood velocity and pressure fields inside each model. Finite-time Lyapunov exponent fields and associated Lagrangian coherent structures were computed from blood velocity data and were used to compare features of the transport topology between rest and exercise both mechanistically and qualitatively. A mix-norm and mix-variance measure based on fresh blood distribution throughout the aneurysm over time were implemented to quantitatively compare mixing between rest and exercise. Exercise conditions resulted in higher and more uniform mixing and reduced the overall residence time in all aneurysms. Separated regions of recirculating flow were commonly observed in rest, and these regions were either reduced or removed by attached and unidirectional flow during exercise, or replaced with regional chaotic and transiently turbulent mixing, or persisted and even extended during exercise. The main factor that dictated the change in flow topology from rest to exercise was the behavior of the jet of blood penetrating into the aneurysm during systole. Copyright © 2013 John Wiley & Sons, Ltd.

Investigation of the mixing efficiency of a chaotic micromixer using thermal lens spectrometry.

PubMed

Ghaleb, Khalil Abbas; Stephan, Khaled; Pittet, Patrick; Ferrigno, Rosaria; Georges, Joseph

2006-05-01

This work investigates the efficiency of a chaotic micromixer using thermal lens spectrometry. The outlet of the mixing device was connected to a thermal lens detection head integrating the probe beam optical fibers and the sample capillary. The chaotic micromixer consisted of a Y-shaped poly(dimethylsiloxane) (PDMS) microchip in which ribbed herringbone microstructures were etched on the floor of the main channel. Due to the solvent composition dependence of the thermal lens response, the photothermal method was shown to be highly sensitive to nonhomogeneous mixing compared to fluorescence detection. The apparatus was applied to the determination of Fe2+ with 1,10-phenanthroline using flow injection analysis; a limit of detection of 11 microg L(-1) of iron was obtained.

Chaotic behavior of the coronary circulation.

PubMed

Trzeciakowski, Jerome; Chilian, William M

2008-05-01

The regulation of the coronary circulation is a complex paradigm in which many inputs that influence vasomotor tone have to be integrated to provide the coronary vasomotor adjustments to cardiac metabolism and to perfusion pressure. We hypothesized that the integration of many disparate signals that influence membrane potential of smooth muscle cells, calcium sensitivity of contractile filaments, receptor trafficking result in complex non-linear characteristics of coronary vasomotion. To test this hypothesis, we measured an index of vasomotion, flowmotion, the periodic fluctuations of flow that reflect dynamic changes in resistances in the microcirculation. Flowmotion was continuously measured in periods ranging from 15 to 40 min under baseline conditions, during antagonism of NO synthesis, and during combined purinergic and NOS antagonism in the beating heart of anesthetized open-chest dogs. Flowmotion was measured in arterioles ranging from 80 to 135 microm in diameter. The signals from the flowmotion measurements were used to derive quantitative indices of non-linear behavior: power spectra, chaotic attractors, correlation dimensions, and the sum of the Lyapunov exponents (Kolmogorov-Sinai entropy), which reflects the total chaos and unpredictability of flowmotion. Under basal conditions, the coronary circulation demonstrated chaotic non-linear behavior with a power spectra showing three principal frequencies in flowmotion. Blockade of nitric oxide synthase or antagonism of purinergic receptors did not affect the correlation dimensions, but significantly increased the Kolmogorov-Sinai entropy, altered the power spectra of flowmotion, and changed the nature of the chaotic attractor. These changes are consistent with the view that certain endogenous controls, nitric oxide and various purines (AMP, ADP, ATP, adenosine) make the coronary circulation more predictable, and that blockade of these controls makes the control of flow less predictable and more chaotic.

Non scale-invariant density perturbations from chaotic extended inflation

NASA Technical Reports Server (NTRS)

Mollerach, Silvia; Matarrese, Sabino

1991-01-01

Chaotic inflation is analyzed in the frame of scalar-tensor theories of gravity. Fluctuations in the energy density arise from quantum fluctuations of the Brans-Dicke field and of the inflation field. The spectrum of perturbations is studied for a class of models: it is non scale-invarient and, for certain values of the parameters, it has a peak. If the peak appears at astrophysically interesting scales, it may help to reconcile the Cold Dark Matter scenario for structure formation with large scale observations.

Nonlinear modeling of chaotic time series: Theory and applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casdagli, M.; Eubank, S.; Farmer, J.D.

1990-01-01

We review recent developments in the modeling and prediction of nonlinear time series. In some cases apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifyingmore » and quantifying low-dimensional chaotic behavior. During the past few years methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics and human speech. 162 refs., 13 figs.« less

Experimental evidence of chaotic mixing at pore scale in 3D porous media

NASA Astrophysics Data System (ADS)

Heyman, J.; Turuban, R.; Jimenez Martinez, J.; Lester, D. R.; Meheust, Y.; Le Borgne, T.

2017-12-01

Mixing of dissolved chemical species in porous media plays a central role in many natural and industrial processes, such as contaminant transport and degradation in soils, oxygen and nitrates delivery in river beds, clogging in geothermal systems, CO2 sequestration. In particular, incomplete mixing at the pore scale may strongly affect the spatio-temporal distribution of reaction rates in soils and rocks, questioning the validity of diffusion-reaction models at the Darcy scale. Recent theoretical [1] and numerical [2] studies of flow in idealized porous media have suggested that fluid mixing may be chaotic at pore scale, hence pointing to a whole new set of models for mixing and reaction in porous media. However, so far this remained to be confirmed experimentally. Here we present experimental evidence of the chaotic nature of transverse mixing at the pore scale in three-dimensional porous media. We designed a novel experimental setup allowing high resolution pore scale imaging of the structure of a tracer plume in porous media columns consisting of 7, 10 and 20 mm glass bead packings. We conjointly used refractive index matching techniques, laser induced fluorescence and a moving laser-sheet to reconstruct the shape of a steady tracer plume as it gets deformed by the porous media flow. In this talk, we focus on the transverse behavior of mixing, that is, on the plane orthogonal to the main flow direction, in the limit of high Péclet numbers (diffusion is negligible). Moving away from the injection point, the plume cross-section turns quickly into complex, interlaced, lamellar structures. These structures elongated at an exponential rate, characteristic of a chaotic system, that can be characterized by an average Lyapunov exponent. We finally discuss the origin of this chaotic behavior and its most significant consequences for upscaling mixing and reactive transport in porous media. Reference:[1] D. R. Lester, G. Metcafle, M. G. Trefry, Physical Review Letters, 111, 174101 (2013) [2] R. Turuban, D. R. Lester, T. Le Borgne, and Y. Méheust (2017), under review.

Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field.

PubMed

Bayindir, Cihan

2016-03-01

In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castillo-Negrete, Diego del; Blazevski, Daniel

2016-04-15

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in three-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands andmore » remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in large helical device and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude of modulated heat pulses.« less

Analytical treatment of particle motion in circularly polarized slab-mode wave fields

NASA Astrophysics Data System (ADS)

Schreiner, Cedric; Vainio, Rami; Spanier, Felix

2018-02-01

Wave-particle interaction is a key process in particle diffusion in collisionless plasmas. We look into the interaction of single plasma waves with individual particles and discuss under which circumstances this is a chaotic process, leading to diffusion. We derive the equations of motion for a particle in the fields of a magnetostatic, circularly polarized, monochromatic wave and show that no chaotic particle motion can arise under such circumstances. A novel and exact analytic solution for the equations is presented. Additional plasma waves lead to a breakdown of the analytic solution and chaotic particle trajectories become possible. We demonstrate this effect by considering a linearly polarized, monochromatic wave, which can be seen as the superposition of two circularly polarized waves. Test particle simulations are provided to illustrate and expand our analytical considerations.

Open problems in active chaotic flows: Competition between chaos and order in granular materials.

PubMed

Ottino, J. M.; Khakhar, D. V.

2002-06-01

There are many systems where interaction among the elementary building blocks-no matter how well understood-does not even give a glimpse of the behavior of the global system itself. Characteristic for these systems is the ability to display structure without any external organizing principle being applied. They self-organize as a consequence of synthesis and collective phenomena and the behavior cannot be understood in terms of the systems' constitutive elements alone. A simple example is flowing granular materials, i.e., systems composed of particles or grains. How the grains interact with each other is reasonably well understood; as to how particles move, the governing law is Newton's second law. There are no surprises at this level. However, when the particles are many and the material is vibrated or tumbled, surprising behavior emerges. Systems self-organize in complex patterns that cannot be deduced from the behavior of the particles alone. Self-organization is often the result of competing effects; flowing granular matter displays both mixing and segregation. Small differences in either size or density lead to flow-induced segregation and order; similar to fluids, noncohesive granular materials can display chaotic mixing and disorder. Competition gives rise to a wealth of experimental outcomes. Equilibrium structures, obtained experimentally in quasi-two-dimensional systems, display organization in the presence of disorder, and are captured by a continuum flow model incorporating collisional diffusion and density-driven segregation. Several open issues remain to be addressed. These include analysis of segregating chaotic systems from a dynamical systems viewpoint, and understanding three-dimensional systems and wet granular systems (slurries). General aspects of the competition between chaos-enhanced mixing and properties-induced de-mixing go beyond granular materials and may offer a paradigm for other kinds of physical systems. (c) 2002 American Institute of Physics.

Magnetic field induced dynamical chaos.

PubMed

Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra

2013-12-01

In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.

Detecting dynamic causal inference in nonlinear two-phase fracture flow

NASA Astrophysics Data System (ADS)

Faybishenko, Boris

2017-08-01

Identifying dynamic causal inference involved in flow and transport processes in complex fractured-porous media is generally a challenging task, because nonlinear and chaotic variables may be positively coupled or correlated for some periods of time, but can then become spontaneously decoupled or non-correlated. In his 2002 paper (Faybishenko, 2002), the author performed a nonlinear dynamical and chaotic analysis of time-series data obtained from the fracture flow experiment conducted by Persoff and Pruess (1995), and, based on the visual examination of time series data, hypothesized that the observed pressure oscillations at both inlet and outlet edges of the fracture result from a superposition of both forward and return waves of pressure propagation through the fracture. In the current paper, the author explores an application of a combination of methods for detecting nonlinear chaotic dynamics behavior along with the multivariate Granger Causality (G-causality) time series test. Based on the G-causality test, the author infers that his hypothesis is correct, and presents a causation loop diagram of the spatial-temporal distribution of gas, liquid, and capillary pressures measured at the inlet and outlet of the fracture. The causal modeling approach can be used for the analysis of other hydrological processes, for example, infiltration and pumping tests in heterogeneous subsurface media, and climatic processes, for example, to find correlations between various meteorological parameters, such as temperature, solar radiation, barometric pressure, etc.

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Granular chaos and mixing: Whirled in a grain of sand.

PubMed

Shinbrot, Troy

2015-09-01

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

Granular chaos and mixing: Whirled in a grain of sand

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shinbrot, Troy, E-mail: shinbrot@rutgers.edu

2015-09-15

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combinesmore » micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.« less

Working Towards Führer: A Chaotic View

NASA Astrophysics Data System (ADS)

Cakar, Ulas

Leadership is a concept that has been discussed since the beginning of history. Even though there have been many theories in the field accepting leadership's role in bringing order, chaotic aspects of leadership are generally neglected. This chapter aims to examine the leadership beyond an orderly interpretation of universe. For this purpose, Third Reich period and leadership during this period will be examined. Ian Kershaw's "Working Towards Führer" concept provides a unique understanding of leadership concept. It goes beyond the dualist depiction of Third Reich, it does not state Adolf Hitler as an all powerful dictator, or a weak one. Rather, he expresses that due to the conditions in the Third Reich, Adolf Hitler was both of this. This complex situation can be understood deeper when it is examined through the lens of chaos theory. This study contributes to the field by being the first in using chaos theory for examining "Working Towards Führer" concept and its development. Seemingly orderly nature of synchronization process and its vortex will be shown. Adolf Hitler's storm spot position in the chaotic system and its dynamics are explained. War's entropic power and its effect on the downfall of the system is crucial in understanding this unique chaotic system. The chaotic pattern of "Working Towards Führer" offers an opportunity to analyze the complexities of the leadership concept.

Chaotic micromixer utilizing electro-osmosis and induced charge electro-osmosis in eccentric annulus

NASA Astrophysics Data System (ADS)

Feng, Huicheng; Wong, Teck Neng; Che, Zhizhao; Marcos

2016-06-01

Efficient mixing is of significant importance in numerous chemical and biomedical applications but difficult to realize rapidly in microgeometries due to the lack of turbulence. We propose to enhance mixing by introducing Lagrangian chaos through electro-osmosis (EO) or induced charge electro-osmosis (ICEO) in an eccentric annulus. The analysis reveals that the created Lagrangian chaos can achieve a homogeneous mixing much more rapidly than either the pure EO or the pure ICEO. Our systematic investigations on the key parameters, ranging from the eccentricity, the alternating time period, the number of flow patterns in one time period, to the specific flow patterns utilized for the Lagrangian chaos creation, present that the Lagrangian chaos is considerably robust. The system can obtain a good mixing effect with wide ranges of eccentricity, alternating time period, and specific flow patterns utilized for the Lagrangian chaos creation as long as the number of flow patterns in one time period is two. As the electric field increases, the time consumption for homogenous mixing is reduced more remarkably for the Lagrangian chaos of the ICEO than that of the EO.

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.

2007-01-01

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

Paradigms of Complexity: Fractals and Structures in the Sciences

NASA Astrophysics Data System (ADS)

Novak, Miroslav M.

The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic Dynamics of Elastic-Plastic Beams * The Riemann Non-Differentiable Function and Identities for the Gaussian Sums * Revealing the Multifractal Nature of Failure Sequence * The Fractal Nature of wood Revealed by Drying * Squaring the Circle: Diffusion Volume and Acoustic Behaviour of a Fractal Structure * Relationship Between Acupuncture Holographic Units and Fetus Development; Fractal Features of Two Acupuncture Holographic Unit Systems * The Fractal Properties of the Large-Scale Magnetic Fields on the Sun * Fractal Analysis of Tide Gauge Data * Author Index

The Magnetohydrodynamic Kelvin-Helmholtz Instability. III. The Role of Sheared Magnetic Field in Planar Flows

NASA Astrophysics Data System (ADS)

Jeong, Hyunju; Ryu, Dongsu; Jones, T. W.; Frank, Adam

2000-01-01

We have carried out simulations of the nonlinear evolution of the magnetohydrodynamic (MHD) Kelvin-Helmholtz (KH) instability for compressible fluids in 2.5 dimensions, extending our previous work by Frank et al. and Jones et al. In the present work we have simulated flows in the x-y plane in which a ``sheared'' magnetic field of uniform strength smoothly rotates across a thin velocity shear layer from the z-direction to the x-direction, aligned with the flow field. The sonic Mach number of the velocity transition is unity. Such flows containing a uniform field in the x-direction are linearly stable if the magnetic field strength is great enough that the Alfvénic Mach number MA=U0/cA<2. That limit does not apply directly to sheared magnetic fields, however, since the z-field component has almost no influence on the linear stability. Thus, if the magnetic shear layer is contained within the velocity shear layer, the KH instability may still grow, even when the field strength is quite large. So, here we consider a wide range of sheared field strengths covering Alfvénic Mach numbers, MA=142.9 to 2. We focus on dynamical evolution of fluid features, kinetic energy dissipation, and mixing of the fluid between the two layers, considering their dependence on magnetic field strength for this geometry. There are a number of differences from our earlier simulations with uniform magnetic fields in the x-y plane. For the latter, simpler case we found a clear sequence of behaviors with increasing field strength ranging from nearly hydrodynamic flows in which the instability evolves to an almost steady cat's eye vortex with enhanced dissipation, to flows in which the magnetic field disrupts the cat's eye once it forms, to, finally, flows that evolve very little before field-line stretching stabilizes the velocity shear layer. The introduction of magnetic shear can allow a cat's eye-like vortex to form, even when the field is stronger than the nominal linear instability limit given above. For strong fields that vortex is asymmetric with respect to the preliminary shear layer, however, so the subsequent dissipation is enhanced over the uniform field cases of comparable field strength. In fact, so long as the magnetic field achieves some level of dynamical importance during an eddy turnover time, the asymmetries introduced through the magnetic shear will increase flow complexity and, with that, dissipation and mixing. The degree of the fluid mixing between the two layers is strongly influenced by the magnetic field strength. Mixing of the fluid is most effective when the vortex is disrupted by magnetic tension during transient reconnection, through local chaotic behavior that follows.

Local parametric instability near elliptic points in vortex flows under shear deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koshel, Konstantin V., E-mail: kvkoshel@poi.dvo.ru; Institute of Applied Mathematics, FEB RAS, 7, Radio Street, Vladivostok 690022; Far Eastern Federal University, 8, Sukhanova Street, Vladivostok 690950

The dynamics of two point vortices embedded in an oscillatory external flow consisted of shear and rotational components is addressed. The region associated with steady-state elliptic points of the vortex motion is established to experience local parametric instability. The instability forces the point vortices with initial positions corresponding to the steady-state elliptic points to move in spiral-like divergent trajectories. This divergent motion continues until the nonlinear effects suppress their motion near the region associated with the steady-state separatrices. The local parametric instability is then demonstrated not to contribute considerably to enhancing the size of the chaotic motion regions. Instead, themore » size of the chaotic motion region mostly depends on overlaps of the nonlinear resonances emerging in the perturbed system.« less

Applied Chaos: From Oxymoron to Reality.

NASA Astrophysics Data System (ADS)

Ditto, William

1996-11-01

The rapidly emerging field of chaotic dynamics has presented the applied scientist with intriguing new tools to understand and manipulate systems that behave chaotically. An overview will be presented which will answer the questions: What is Chaos? and What can you do with Chaos? Examples of recent applications of chaos theory to the physical and biological sciences will be presented covering applications that range from encryption in communications to control of chaotically beating human hearts. Part A of program listing

Magnetic nanoparticles stimulation to enhance liquid-liquid two-phase mass transfer under static and rotating magnetic fields

NASA Astrophysics Data System (ADS)

Azimi, Neda; Rahimi, Masoud

2017-01-01

Rotating magnetic field (RMF) was applied on a micromixer to break the laminar flow and induce chaotic flow to enhance mass transfer between two-immiscible organic and aqueous phases. The results of RMF were compared to those of static magnetic field (SMF). For this purpose, experiments were carried out in a T-micromixer at equal volumetric flow rates of organic and aqueous phases. Fe3O4 nanoparticles were synthesized by co-precipitation technique and they were dissolved in organic phase. Results obtained from RMF and SMF were compared in terms of overall volumetric mass transfer coefficient (KLa) and extraction efficiency (E) at various Reynolds numbers. Generally, RMF showed higher effect in mass transfer characteristics enhancement compared with SMF. The influence of rotational speeds of magnets (ω) in RMF was investigated, and measurable enhancements of KLa and E were observed. In RMF, the effect of magnetic field induction (B) was investigated. The results reveal that at constant concentration of nanoparticles, by increasing of B, mass transfer characteristics will be enhanced. The effect of various nanoparticles concentrations (ϕ) within 0.002-0.01 (w/v) on KLa and E at maximum induction of RMF (B=76 mT) was evaluated. Maximum values of KLa (2.1±0.001) and E (0.884±0.001) were achieved for the layout of RMF (B=76 mT), ω=16 rad/s and MNPs concentration of 0.008-0.01 (w/v).

Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations

NASA Astrophysics Data System (ADS)

Zhou, Zhi-Rui; Zhang, You-Sheng; Tian, Bao-Lin

2018-03-01

Implicit large eddy simulations of two-dimensional Rayleigh-Taylor instability at different density ratios (i.e., Atwood number A =0.05 , 0.5, and 0.9) are conducted to investigate the late-time dynamics of bubbles. To produce a flow field full of bounded, semibounded, and chaotic bubbles, three problems with distinct perturbations are simulated: (I) periodic sinusoidal perturbation, (II) isolated W-shaped perturbation, and (III) random short-wave perturbations. The evolution of height h , velocity v , and diameter D of the (dominant) bubble with time t are formulated and analyzed. In problem I, during the quasisteady stage, the simulations confirm Goncharov's prediction of the terminal speed v∞=Fr√{A g λ /(1 +A ) } , where Fr=1 /√{3 π } . Moreover, the diameter D at this stage is found to be proportional to the initial perturbation wavelength λ as D ≈λ . This differed from Daly's simulation result of D =λ (1 +A )/2 . In problem II, a W-shaped perturbation is designed to produce a bubble environment similar to that of chaotic bubbles in problem III. We obtain a similar terminal speed relationship as above, but Fr is replaced by Frw≈0.63 . In problem III, the simulations show that h grows quadratically with the bubble acceleration constant α ≡h /(A g t2)≈0.05 , and D expands self-similarly with a steady aspect ratio β ≡D /h ≈(1 +A )/2 , which differs from existing theories. Therefore, following the mechanism of self-similar growth, we derive a relationship of β =4 α (1 +A ) /Frw2 to relate the evolution of chaotic bubbles in problem III to that of semibounded bubbles in problem II. The validity of this relationship highlights the fact that the dynamics of chaotic bubbles in problem III are similar to the semibounded isolated bubbles in problem II, but not to that of bounded periodic bubbles in problem I.

Numerical Study of Sound Emission by 2D Regular and Chaotic Vortex Configurations

NASA Astrophysics Data System (ADS)

Knio, Omar M.; Collorec, Luc; Juvé, Daniel

1995-02-01

The far-field noise generated by a system of three Gaussian vortices lying over a flat boundary is numerically investigated using a two-dimensional vortex element method. The method is based on the discretization of the vorticity field into a finite number of smoothed vortex elements of spherical overlapping cores. The elements are convected in a Lagrangian reference along particle trajectories using the local velocity vector, given in terms of a desingularized Biot-Savart law. The initial structure of the vortex system is triangular; a one-dimensional family of initial configurations is constructed by keeping one side of the triangle fixed and vertical, and varying the abscissa of the centroid of the remaining vortex. The inviscid dynamics of this vortex configuration are first investigated using non-deformable vortices. Depending on the aspect ratio of the initial system, regular or chaotic motion occurs. Due to wall-related symmetries, the far-field sound always exhibits a time-independent quadrupolar directivity with maxima parallel end perpendicular to the wall. When regular motion prevails, the noise spectrum is dominated by discrete frequencies which correspond to the fundamental system frequency and its superharmonics. For chaotic motion, a broadband spectrum is obtained; computed soundlevels are substantially higher than in non-chaotic systems. A more sophisticated analysis is then performed which accounts for vortex core dynamics. Results show that the vortex cores are susceptible to inviscid instability which leads to violent vorticity reorganization within the core. This phenomenon has little effect on the large-scale features of the motion of the system or on low frequency sound emission. However, it leads to the generation of a high-frequency noise band in the acoustic pressure spectrum. The latter is observed in both regular and chaotic system simulations.

Optimizing homogenization by chaotic unmixing?

NASA Astrophysics Data System (ADS)

Weijs, Joost; Bartolo, Denis

2016-11-01

A number of industrial processes rely on the homogeneous dispersion of non-brownian particles in a viscous fluid. An ideal mixing would yield a so-called hyperuniform particle distribution. Such configurations are characterized by density fluctuations that grow slower than the standard √{ N}-fluctuations. Even though such distributions have been found in several natural structures, e.g. retina receptors in birds, they have remained out of experimental reach until very recently. Over the last 5 years independent experiments and numerical simulations have shown that periodically driven suspensions can self-assemble hyperuniformally. Simple as the recipe may be, it has one important disadvantage. The emergence of hyperuniform states co-occurs with a critical phase transition from reversible to non reversible particle dynamics. As a consequence the homogenization dynamics occurs over a time that diverges with the system size (critical slowing down). Here, we discuss how this process can be sped up by exploiting the stirring properties of chaotic advection. Among the questions that we answer are: What are the physical mechanisms in a chaotic flow that are relevant for hyperuniformity? How can we tune the flow parameters such to obtain optimal hyperuniformity in the fastest way? JW acknowledges funding by NWO (Netherlands Organisation for Scientific Research) through a Rubicon Grant.

Coupling between plate vibration and acoustic radiation

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Maestrello, Lucio; Bayliss, Alvin

1992-01-01

A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far-field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far-field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance.

A chaotic micromixer using obstruction-pairs

NASA Astrophysics Data System (ADS)

Park, Jang Min; Duck Seo, Kyoung; Kwon, Tai Hun

2010-01-01

A micromixer is one of the most important components for a chemical and/or diagnostic analysis in microfluidic devices such as a micro-total-analysis-system and a lab-on-a-chip. In this paper, a novel chaotic micromixer is developed in a simple design by introducing obstruction-pairs on the bottom of a microchannel. An obstruction-pair, which is composed of two hexahedron blocks arranged in an asymmetric manner, can induce a rotational flow along the down-channel direction due to the anisotropy of flow resistance. By utilizing this characteristic of the obstruction-pair, four mixing units are designed in such a way that three obstruction-pairs induce three rotational flows which result in a down-welling and a hyperbolic point in the channel cross-section. There can be a variety of micromixer geometries by arranging the mixing units in various sequences along the microchannel, and their mixing performances will differ from each other due to different flow characteristics. In this regard, numerical investigations are carried out to predict and characterize the mixing performances of various micromixers. Also experimental verifications are carried out by a flow visualization technique using phenolphthalein and sodium hydroxide solutions in a polydimethylsiloxane-based micromixer.

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

NASA Astrophysics Data System (ADS)

Ren, Shuili; Panahi, Shirin; Rajagopal, Karthikeyan; Akgul, Akif; Pham, Viet-Thanh; Jafari, Sajad

2018-02-01

Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

Cooling of a magmatic system under thermal chaotic mixing

NASA Astrophysics Data System (ADS)

Petrelli, Maurizio; El Omari, Kamal; Le Guer, Yves; Perugini, Diego

2015-04-01

The cooling of a melt undergoing chaotic advection is studied numerically for a magma with a temperature-dependent viscosity in a 2D cavity with moving boundary. Different statistical mixing and energy indicators are used to characterize the efficiency of cooling by thermal chaotic mixing. We show that different cooling rates can be obtained during the thermal mixing even of a single basaltic magmatic batch undergoing chaotic advection. This process can induce complex temperature patterns inside the magma chamber. The emergence of chaotic dynamics strongly affects the temperature field during time and greatly increases the cooling rates. This mechanism has implications for the lifetime of a magmatic body and may favor the appearance of chemical heterogeneities in igneous systems as a result of different crystallization rates. Results from this study also highlight that even a single magma batch can develop, under chaotic thermal advection, complex thermal and therefore compositional patterns resulting from different cooling rates, which can account for some natural features that, to date, have received unsatisfactory explanations. Among them, the production of magmatic enclaves showing completely different cooling histories compared with the host magma, compositional zoning in mineral phases, and the generation of large-scale compositionally zoning observed in many plutons worldwide.

Chaotic transport and damping from θ-ruffled separatrices.

PubMed

Kabantsev, A A; Dubin, Daniel H E; Driscoll, C F; Tsidulko, Yu A

2010-11-12

Variations in magnetic or electrostatic confinement fields give rise to trapping separatrices, and neoclassical transport theory analyzes effects from collision-induced separatrix crossings. Experiments on pure electron plasmas now quantitatively characterize a broad range of transport and wave damping effects due to "chaotic" separatrix crossings, which occur due to equilibrium plasma rotation across θ-ruffled separatrices, and due to wave-induced separatrix fluctuations.

Noise-enhanced chaos in a weakly coupled GaAs/(Al,Ga)As superlattice.

PubMed

Yin, Zhizhen; Song, Helun; Zhang, Yaohui; Ruiz-García, Miguel; Carretero, Manuel; Bonilla, Luis L; Biermann, Klaus; Grahn, Holger T

2017-01-01

Noise-enhanced chaos in a doped, weakly coupled GaAs/Al_{0.45}Ga_{0.55}As superlattice has been observed at room temperature in experiments as well as in the results of the simulation of nonlinear transport based on a discrete tunneling model. When external noise is added, both the measured and simulated current-versus-time traces contain irregularly spaced spikes for particular applied voltages, which separate a regime of periodic current oscillations from a region of no current oscillations at all. In the voltage region without current oscillations, the electric-field profile consist of a low-field domain near the emitter contact separated by a domain wall consisting of a charge accumulation layer from a high-field regime closer to the collector contact. With increasing noise amplitude, spontaneous chaotic current oscillations appear over a wider bias voltage range. For these bias voltages, the domain boundary between the two electric-field domains becomes unstable and very small current or voltage fluctuations can trigger the domain boundary to move toward the collector and induce chaotic current spikes. The experimentally observed features are qualitatively very well reproduced by the simulations. Increased noise can consequently enhance chaotic current oscillations in semiconductor superlattices.

Noise-enhanced chaos in a weakly coupled GaAs/(Al,Ga)As superlattice

NASA Astrophysics Data System (ADS)

Yin, Zhizhen; Song, Helun; Zhang, Yaohui; Ruiz-García, Miguel; Carretero, Manuel; Bonilla, Luis L.; Biermann, Klaus; Grahn, Holger T.

2017-01-01

Noise-enhanced chaos in a doped, weakly coupled GaAs /Al0.45Ga0.55As superlattice has been observed at room temperature in experiments as well as in the results of the simulation of nonlinear transport based on a discrete tunneling model. When external noise is added, both the measured and simulated current-versus-time traces contain irregularly spaced spikes for particular applied voltages, which separate a regime of periodic current oscillations from a region of no current oscillations at all. In the voltage region without current oscillations, the electric-field profile consist of a low-field domain near the emitter contact separated by a domain wall consisting of a charge accumulation layer from a high-field regime closer to the collector contact. With increasing noise amplitude, spontaneous chaotic current oscillations appear over a wider bias voltage range. For these bias voltages, the domain boundary between the two electric-field domains becomes unstable and very small current or voltage fluctuations can trigger the domain boundary to move toward the collector and induce chaotic current spikes. The experimentally observed features are qualitatively very well reproduced by the simulations. Increased noise can consequently enhance chaotic current oscillations in semiconductor superlattices.

In Situ Self Assembly of Nanocomposites: Competition of Chaotic Advection and Interfacial Effects as Observed by X-Ray Diffreaction

PubMed Central

Ratnaweera, Dilru R.; Mahesha, Chaitra; Zumbrunnen, David A.; Perahia, Dvora

2015-01-01

The effects of chaotic advection on the in situ assembly of a hierarchal nanocomposite of Poly Amide 6, (nylon 6 or PA6) and platelet shape nanoparticles (NPs) were studied. The assemblies were formed by chaotic advection, where melts of pristine PA6 and a mixture of PA6 with NPs were segregated into discrete layers and extruded into film in a continuous process. The process assembles the nanocomposite into alternating pristine-polymer and oriented NP/polymer layers. The structure of these hierarchal assemblies was probed by X-rays as a processing parameter, N, was varied. This parameter provides a measure of the extent of in situ structuring by chaotic advection. We found that all assemblies are semi-crystalline at room temperature. Increasing N impacts the ratio of α to γ crystalline forms. The effects of the chaotic advection vary with the concentration of the NPs. For nanocomposites with lower NP concentrations the amount of the γ crystalline form increased with N. However, at higher NP concentrations, interfacial effects of the NP play a significant role in determining the structure, where the NPs oriented along the melt flow direction and the polymer chains oriented perpendicular to the NP surfaces. PMID:28347015

Architecture of chaotic attractors for flows in the absence of any singular point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Letellier, Christophe; Malasoma, Jean-Marc

2016-06-15

Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain—in the particular case of the Wei system—such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2 × 2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in themore » neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system.« less

Anomalous transport in Charney-Hasegawa-Mima flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leoncini, Xavier; Agullo, Olivier; Benkadda, Sadruddin

2005-08-01

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around {mu}=1.75, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover, the law {gamma}={mu}+1 linking the trapping-time exponent within jets to the transport exponent is confirmed, and an accumulation toward zero ofmore » the spectrum of the finite-time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse-grained picture of the jet, the motion within the jet appears as chaotic, but that chaos is bounded on successive small scales.« less

Chaotic inflation from nonlinear sigma models in supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hellerman, Simeon; Kehayias, John; Yanagida, Tsutomu T.

2015-02-11

We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make theKähler potential of the NLSM invariant in supergravity. This field must have a shift symmetrymore » — making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU(3)/SU(2) × U(1), with the Higgs as the NGB, including breaking the inflaton’s shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E₇/SO(10) × U(1) × U(1) which incorporates the first two generations of (light) quarks as the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten–Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion« less

Exact coherent structures and chaotic dynamics in a model of cardiac tissue

DOE Office of Scientific and Technical Information (OSTI.GOV)

Byrne, Greg; Marcotte, Christopher D.; Grigoriev, Roman O., E-mail: roman.grigoriev@physics.gatech.edu

Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low- and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are referred to as exact coherent structures (ECS) and play an important role in both initiating and sustaining turbulence. The nature of ECS and their role in organizing spatiotemporally chaotic dynamics, however, is reasonably well understood only for systems on relatively small spatial domains lacking continuous Euclidean symmetries. Construction of ECS on large domains and in the presence of continuous translational and/or rotational symmetries remains a challenge. This ismore » especially true for models of excitable media which display spiral turbulence and for which the standard approach to computing ECS completely breaks down. This paper uses the Karma model of cardiac tissue to illustrate a potential approach that could allow computing a new class of ECS on large domains of arbitrary shape by decomposing them into a patchwork of solutions on smaller domains, or tiles, which retain Euclidean symmetries locally.« less

Experimental Demonstration of Coherent Control in Quantum Chaotic Systems

NASA Astrophysics Data System (ADS)

Bitter, M.; Milner, V.

2017-01-01

We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters of the kicking field, as well as its disappearance in the classical regime of excitation.

Persistent stability of a chaotic system

NASA Astrophysics Data System (ADS)

Huber, Greg; Pradas, Marc; Pumir, Alain; Wilkinson, Michael

2018-02-01

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has 'generic' instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems.

Complexity science and leadership in healthcare.

PubMed

Burns, J P

2001-10-01

The emerging field of complexity science offers an alternative leadership strategy for the chaotic, complex healthcare environment. A survey revealed that healthcare leaders intuitively support principles of complexity science. Leadership that uses complexity principles offers opportunities in the chaotic healthcare environment to focus less on prediction and control and more on fostering relationships and creating conditions in which complex adaptive systems can evolve to produce creative outcomes.

Chaotic hybrid inflation with a gauged B -L

NASA Astrophysics Data System (ADS)

Carpenter, Linda M.; Raby, Stuart

2014-11-01

In this paper we present a novel formulation of chaotic hybrid inflation in supergravity. The model includes a waterfall field which spontaneously breaks a gauged U1 (B- L) at a GUT scale. This allows for the possibility of future model building which includes the standard formulation of baryogenesis via leptogenesis with the waterfall field decaying into right-handed neutrinos. We have not considered the following issues in this short paper, i.e. supersymmetry breaking, dark matter or the gravitino or moduli problems. Our focus is on showing the compatibility of the present model with Planck, WMAP and Bicep2 data.

Prize to a Faculty Member for Research in an Undergraduate: Chaotic mixing and front propagation

NASA Astrophysics Data System (ADS)

Solomon, Tom

2014-03-01

We present results from a series of experiments - all done with undergraduate students - on chaotic fluid mixing and the effects of fluid flows on the behavior of reaction systems. Simple, well-ordered laminar fluid flows can give rise to fluid mixing with complexity far beyond that of the underlying flow, with tracers that separate exponentially in time and invariant manifolds that act as barriers to transport. Recently, we have studied how fluid mixing affects the propagation of reaction fronts in a flow. This is an issue with applications to a wide range of systems including microfluidic chemical reactors, blooms of phytoplankton in the oceans, and the spreading of a disease in a moving population. To analyze and predict the behavior of the fronts, we generalize tools developed to describe passive mixing. In particular, the concept of an invariant manifold is expanded to account for reactive burning. ``Burning invariant manifolds'' (BIMs) are predicted and measured experimentally as structures in the flow that act as one-way barriers that block the motion of reaction fronts. We test these ideas experimentally in three fluid flows: (a) and chain of alternating vortices; (b) an extended, spatially-random pattern of vortices; and (c) a time-independent, three-dimensional, nested vortex flow. The reaction fronts are produced chemically with variations of the well-known Belousov-Zhabotinsky reaction. Supported by Research Corporation and the National Science Foundation.

Study of the flow unsteadiness in the human airway using large eddy simulation

NASA Astrophysics Data System (ADS)

Bernate, Jorge A.; Geisler, Taylor S.; Padhy, Sourav; Shaqfeh, Eric S. G.; Iaccarino, Gianluca

2017-08-01

The unsteady flow in a patient-specific geometry of the airways is studied. The geometry comprises the oral cavity, orophrarynx, larynx, trachea, and the bronchial tree extending to generations 5-8. Simulations are carried out for a constant inspiratory flow rate of 60 liters/min, corresponding to a Reynolds number of 4213 for a nominal tracheal diameter of 2 cm. The computed mean flow field is compared extensively with magnetic resonance velocimetry measurements by Banko et al. [Exp. Fluids 56, 117 (2015), 10.1007/s00348-015-1966-y] carried out in the same computed-tomography-based geometry, showing good agreement. In particular, we focus on the dynamics of the flow in the bronchial tree. After becoming unsteady at a constriction in the oropharynx, the flow is found to be chaotic, exhibiting fluctuations with broad-band spectra even at the most distal airways in which the Reynolds numbers are as low as 300. An inertial range signature is present in the trachea but not in the bronchial tree where a narrower range of scales is observed. The unsteadiness is attributed to the convection of turbulent structures produced at the larynx as well as to local kinetic energy production throughout the bronchial tree. Production occurs predominantly at shear layers bounding geometry-induced separation regions.

A new class of asymptotically non-chaotic vacuum singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klinger, Paul, E-mail: paul.klinger@univie.ac.at

2015-12-15

The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some ofmore » them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.« less

Traffic flow theory and chaotic behavior

DOT National Transportation Integrated Search

1989-03-01

Many commonly occurring natural systems are modeled with mathematical experessions and exhibit a certain stability. The inherent stability of these equations allows them to serve as the basis for engineering predictions. More complex models, such as ...

Cooling of a Magmatic System Under Thermal Chaotic Mixing

NASA Astrophysics Data System (ADS)

El Omari, Kamal; Le Guer, Yves; Perugini, Diego; Petrelli, Maurizio

2015-07-01

The cooling of a basaltic melt undergoing chaotic advection is studied numerically for a magma with a temperature-dependent viscosity in a two-dimensional (2D) cavity with moving boundary. Different statistical mixing and energy indicators are used to characterize the efficiency of cooling by thermal chaotic mixing. We show that different cooling rates can be obtained during the thermal mixing of a single basaltic magmatic batch undergoing chaotic advection. This process can induce complex temperature patterns inside the magma chamber. The emergence of chaotic dynamics strongly modulates the temperature fields over time and greatly increases the cooling rates. This mechanism has implications for the thermal lifetime of the magmatic body and may favor the appearance of chemical heterogeneities in the igneous system as a result of different crystallization rates. Results from this study also highlight that even a single magma batch can develop, under chaotic thermal advection, complex thermal and therefore compositional patterns resulting from different cooling rates, which can account for some natural features that, to date, have received unsatisfactory explanations, including the production of magmatic enclaves showing completely different cooling histories compared with the host magma, compositional zoning in mineral phases, and the generation of large-scale compositional zoning observed in many plutons worldwide.

A novel chaotic stream cipher and its application to palmprint template protection

NASA Astrophysics Data System (ADS)

Li, Heng-Jian; Zhang, Jia-Shu

2010-04-01

Based on a coupled nonlinear dynamic filter (NDF), a novel chaotic stream cipher is presented in this paper and employed to protect palmprint templates. The chaotic pseudorandom bit generator (PRBG) based on a coupled NDF, which is constructed in an inverse flow, can generate multiple bits at one iteration and satisfy the security requirement of cipher design. Then, the stream cipher is employed to generate cancelable competitive code palmprint biometrics for template protection. The proposed cancelable palmprint authentication system depends on two factors: the palmprint biometric and the password/token. Therefore, the system provides high-confidence and also protects the user's privacy. The experimental results of verification on the Hong Kong PolyU Palmprint Database show that the proposed approach has a large template re-issuance ability and the equal error rate can achieve 0.02%. The performance of the palmprint template protection scheme proves the good practicability and security of the proposed stream cipher.

Suppression of chaos via control of energy flow

NASA Astrophysics Data System (ADS)

Guo, Shengli; Ma, Jun; Alsaedi, Ahmed

2018-03-01

Continuous energy supply is critical and important to support oscillating behaviour; otherwise, the oscillator will die. For nonlinear and chaotic circuits, enough energy supply is also important to keep electric devices working. In this paper, Hamilton energy is calculated for dimensionless dynamical system (e.g., the chaotic Lorenz system) using Helmholtz's theorem. The Hamilton energy is considered as a new variable and then the dynamical system is controlled by using the scheme of energy feedback. It is found that chaos can be suppressed even when intermittent feedback scheme is applied. This scheme is effective to control chaos and to stabilise other dynamical systems.

Interesting examples of supervised continuous variable systems

NASA Technical Reports Server (NTRS)

Chase, Christopher; Serrano, Joe; Ramadge, Peter

1990-01-01

The authors analyze two simple deterministic flow models for multiple buffer servers which are examples of the supervision of continuous variable systems by a discrete controller. These systems exhibit what may be regarded as the two extremes of complexity of the closed loop behavior: one is eventually periodic, the other is chaotic. The first example exhibits chaotic behavior that could be characterized statistically. The dual system, the switched server system, exhibits very predictable behavior, which is modeled by a finite state automaton. This research has application to multimodal discrete time systems where the controller can choose from a set of transition maps to implement.

Zero Prandtl-number rotating magnetoconvection

NASA Astrophysics Data System (ADS)

Ghosh, Manojit; Pal, Pinaki

2017-12-01

We investigate instabilities and chaos near the onset of Rayleigh-Bénard convection of electrically conducting fluids with free-slip, perfectly electrically and thermally conducting boundary conditions in the presence of uniform rotation about the vertical axis and horizontal external magnetic field by considering zero Prandtl-number limit (Pr → 0). Direct numerical simulations (DNSs) and low-dimensional modeling of the system are done for the investigation. Values of the Chandrasekhar number (Q) and the Taylor number (Ta) are varied in the range 0 < Q, Ta ≤ 50. Depending on the values of the parameters in the chosen range and the choice of initial conditions, the onset of convection is found be either periodic or chaotic. Interestingly, it is found that chaos at the onset can occur through four different routes, namely, homoclinic, intermittent, period doubling, and quasiperiodic routes. Homoclinic and intermittent routes to chaos at the onset occur in the presence of weak magnetic field (Q < 2), while the period doubling route is observed for relatively stronger magnetic field (Q ≥ 2) for one set of initial conditions. On the other hand, the quasiperiodic route to chaos at the onset is observed for another set of initial conditions. However, the rotation rate (value of Ta) also plays an important role in determining the nature of convection at the onset. Analysis of the system simultaneously with DNSs and low-dimensional modeling helps us to clearly identify different flow regimes concentrated near the onset of convection and understand their origins. The periodic or chaotic convection at the onset is found to be connected with rich bifurcation structures involving subcritical pitchfork, imperfect pitchfork, supercritical Hopf, imperfect homoclinic gluing, and Neimark-Sacker bifurcations.

Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lucas, Dan, E-mail: dan.lucas@ucd.ie; Kerswell, Rich R., E-mail: r.r.kerswell@bris.ac.uk

2015-04-15

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2π]{sup 2} torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously [G. J. Chandler and R. R. Kerswell, “Invariant recurrent solutionsmore » embedded in a turbulent two-dimensional Kolmogorov flow,” J. Fluid Mech. 722, 554–595 (2013)] and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Analysis of the recurrent flows shows that the energy is largely trapped in the smallest wavenumbers through a combination of the inverse cascade process and a feature of the advective nonlinearity in 2D. Over the extended torus at low forcing amplitudes, some extracted states mimic the statistics of the spatially localised chaos present surprisingly well recalling the findings of Kawahara and Kida [“Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001)] in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed.« less

Transition to chaos of natural convection between two infinite differentially heated vertical plates

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Sergent, Anne; Podvin, Berengere; Xin, Shihe; Le Quéré, Patrick; Tuckerman, Laurette S.

2013-08-01

Natural convection of air between two infinite vertical differentially heated plates is studied analytically in two dimensions (2D) and numerically in two and three dimensions (3D) for Rayleigh numbers Ra up to 3 times the critical value Rac=5708. The first instability is a supercritical circle pitchfork bifurcation leading to steady 2D corotating rolls. A Ginzburg-Landau equation is derived analytically for the flow around this first bifurcation and compared with results from direct numerical simulation (DNS). In two dimensions, DNS shows that the rolls become unstable via a Hopf bifurcation. As Ra is further increased, the flow becomes quasiperiodic, and then temporally chaotic for a limited range of Rayleigh numbers, beyond which the flow returns to a steady state through a spatial modulation instability. In three dimensions, the rolls instead undergo another pitchfork bifurcation to 3D structures, which consist of transverse rolls connected by counter-rotating vorticity braids. The flow then becomes time dependent through a Hopf bifurcation, as exchanges of energy occur between the rolls and the braids. Chaotic behavior subsequently occurs through two competing mechanisms: a sequence of period-doubling bifurcations leading to intermittency or a spatial pattern modulation reminiscent of the Eckhaus instability.

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

NASA Astrophysics Data System (ADS)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

Illusion optics in chaotic light

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Suheng; Gan Shu; Xiong Jun

2010-08-15

The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoreticalmore » proposal of similar effects in complementary media.« less

Gyroaverage effects on nontwist Hamiltonians: Separatrix reconnection and chaos suppression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Martinell, J.

2012-01-01

A study of finite Larmor radius (FLR) effects on E x B test particle chaotic transport in non-monotonic zonal flows with drift waves in magnetized plasmas is presented. Due to the non-monotonicity of the zonal flow, the Hamiltonian does not satisfy the twist condition. The electrostatic potential is modeled as a linear superposition of a zonal flow and the regular neutral modes of the Hasegawa-Mima equation. FLR effects are incorporated by gyro-averaging the E x B Hamiltonian. It is shown that there is a critical value of the Larmor radius for which the zonal flow transitions from a profile withmore » one maximum to a profile with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor radius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal flow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic separatrix topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections show that, for large enough Larmor radius, chaos can be practically suppressed. In particular, changes of the Larmor radius can restore the shearless curve.« less

Chaotic micromixer utilizing electro-osmosis and induced charge electro-osmosis in eccentric annulus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Huicheng; Wong, Teck Neng, E-mail: mtnwong@ntu.edu.sg; Marcos

Efficient mixing is of significant importance in numerous chemical and biomedical applications but difficult to realize rapidly in microgeometries due to the lack of turbulence. We propose to enhance mixing by introducing Lagrangian chaos through electro-osmosis (EO) or induced charge electro-osmosis (ICEO) in an eccentric annulus. The analysis reveals that the created Lagrangian chaos can achieve a homogeneous mixing much more rapidly than either the pure EO or the pure ICEO. Our systematic investigations on the key parameters, ranging from the eccentricity, the alternating time period, the number of flow patterns in one time period, to the specific flow patternsmore » utilized for the Lagrangian chaos creation, present that the Lagrangian chaos is considerably robust. The system can obtain a good mixing effect with wide ranges of eccentricity, alternating time period, and specific flow patterns utilized for the Lagrangian chaos creation as long as the number of flow patterns in one time period is two. As the electric field increases, the time consumption for homogenous mixing is reduced more remarkably for the Lagrangian chaos of the ICEO than that of the EO.« less

Chaotic time series prediction for prenatal exposure to polychlorinated biphenyls in umbilical cord blood using the least squares SEATR model

NASA Astrophysics Data System (ADS)

Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia

2016-04-01

Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field.

Chaotic time series prediction for prenatal exposure to polychlorinated biphenyls in umbilical cord blood using the least squares SEATR model

PubMed Central

Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia

2016-01-01

Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field. PMID:27118260

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Assessing Chaos in Sickle Cell Anemia Crises

NASA Astrophysics Data System (ADS)

Harris, Wesley; Le Floch, Francois

2006-11-01

Recent developments in sickle cell research and blood flow modeling allow for new interpretations of the sickle cell crises. With an appropriate set of theoretical and empirical equations describing the dynamics of the red cells in their environment, and the response of the capillaries to major changes in the rheology, a complete mathematical system has been derived. This system of equations is believed to be of major importance to provide new and significant insight into the causes of the disease and related crises. With simulations, it has been proven that the system transition from a periodic solution to a chaotic one, which illustrates the onset of crises from a regular blood flow synchronized with the heart beat. Moreover, the analysis of the effects of various physiological parameters exposes the potential to control chaotic solutions, which, in turn, could lead to the creation of new and more effective treatments for sickle cell anemia. .

Spontaneous ordering and vortex states of active fluids in circular confinement

NASA Astrophysics Data System (ADS)

Theillard, Maxime; Ezhilan, Barath; Saintillan, David

2015-11-01

Recent experimental, theoretical and simulation studies have shown that confinement can profoundly affect self-organization in active suspensions leading to striking features such as directed fluid pumping in planar confinement, formation of steady and spontaneous vortices in radial confinement. Motivated by this, we study the dynamics in a suspension of biologically active particles confined in spherical geometries using a mean-field kinetic theory for which we developed a novel numerical solver. In the case of circular confinement, we conduct a systematic exploration of the entire parameter space and distinguish 3 broad states: no-flow, stable vortex and chaotic and several interesting sub-states. Our efficient numerical framework is also employed to study 3D effects and dynamics in more complex geometries.

Gauge theory for finite-dimensional dynamical systems.

PubMed

Gurfil, Pini

2007-06-01

Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently "disordered" flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE PAGES

Finn, John M.

2015-03-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a 'special divergence-free' property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. Wemore » also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Ref. [11], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Ref. [35], appears to work very well.« less

Quantitative Measures of Chaotic Charged Particle Dynamics in the Magnetotail

NASA Astrophysics Data System (ADS)

Holland, D. L.; Martin, R. F., Jr.; Burris, C.

2017-12-01

It has long been noted that the motion of charged particles in magnetotail-like magnetic fields is chaotic, however, efforts to quantify the degree of chaos have had conflicting conclusions. In this paper we re-examine the question by focusing on quantitative measures of chaos. We first examine the percentage of orbits that enter the chaotic region of phase space and the average trapping time of those particles. We then examine the average exponential divergence rate (AEDR) of the chaotic particles between their first and last crossing of the mid-plane. We show that at resonant energies where the underlying phase space has a high degree of symmetry, only a small number of particle enter the chaotic region, but they are trapped for long periods of time and the time asymptotic value of the AEDR is very close to the average value of the AEDR. At the off-resonant energies where the phase space is highly asymmetric, the majority of the particle enter the chaotic region for fairly short periods of time and the time asymptotic value of the AEDR is much smaller than the average value. The root cause is that in the resonant case, the longest-lived orbits tend interact with the current many times and sample the entire chaotic region, whereas in the non-resonant case the longest-lived orbits only interact with the current sheet a small number of times but have very long mirrorings where the motion is nearly regular. Additionally we use an ad-hoc model where we model the current sheet as a Lorentz scattering system with each interaction with the current sheet being considered as a "collision". We find that the average kick per collision is greatest at off-resonant energies. Finally, we propose a chaos parameter as the product of the AEDR times the average chaotic particle trapping time times the percentage of orbits that are chaotic. We find that this takes on peak values at the resonant energies.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

PubMed

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

NASA Astrophysics Data System (ADS)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Sudden Relaminarization and Lifetimes in Forced Isotropic Turbulence.

PubMed

Linkmann, Moritz F; Morozov, Alexander

2015-09-25

We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from a chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase superexponentially with the Reynolds number. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics.

A study in three-dimensional chaotic dynamics: Granular flow and transport in a bi-axial spherical tumbler

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christov, Ivan C.; Lueptow, Richard M.; Ottino, Julio M.

We study three-dimensional (3D) chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial “blinking” tumbler). The flow is essentially quasi-two-dimensional in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (inmore » the absence of stochasticity) particle trajectories are restricted to two-dimensional (2D) surfaces consisting of a portion of a hemispherical shell closed by a “cap''; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov--Arnold--Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.« less

A study in three-dimensional chaotic dynamics: Granular flow and transport in a bi-axial spherical tumbler

DOE PAGES

Christov, Ivan C.; Lueptow, Richard M.; Ottino, Julio M.; ...

2014-05-22

We study three-dimensional (3D) chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial “blinking” tumbler). The flow is essentially quasi-two-dimensional in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (inmore » the absence of stochasticity) particle trajectories are restricted to two-dimensional (2D) surfaces consisting of a portion of a hemispherical shell closed by a “cap''; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov--Arnold--Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.« less

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

Extracting harmonic signal from a chaotic background with local linear model

NASA Astrophysics Data System (ADS)

Li, Chenlong; Su, Liyun

2017-02-01

In this paper, the problems of blind detection and estimation of harmonic signal in strong chaotic background are analyzed, and new methods by using local linear (LL) model are put forward. The LL model has been exhaustively researched and successfully applied for fitting and forecasting chaotic signal in many chaotic fields. We enlarge the modeling capacity substantially. Firstly, we can predict the short-term chaotic signal and obtain the fitting error based on the LL model. Then we detect the frequencies from the fitting error by periodogram, a property on the fitting error is proposed which has not been addressed before, and this property ensures that the detected frequencies are similar to that of harmonic signal. Secondly, we establish a two-layer LL model to estimate the determinate harmonic signal in strong chaotic background. To estimate this simply and effectively, we develop an efficient backfitting algorithm to select and optimize the parameters that are hard to be exhaustively searched for. In the method, based on sensitivity to initial value of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of the parameters of the two-layer LL model. Simulation shows that the two-layer LL model and its estimation technique have appreciable flexibility to model the determinate harmonic signal in different chaotic backgrounds (Lorenz, Henon and Mackey-Glass (M-G) equations). Specifically, the harmonic signal can be extracted well with low SNR and the developed background algorithm satisfies the condition of convergence in repeated 3-5 times.

Chaoticity parameter λ in two-pion interferometry in an expanding boson gas model

DOE PAGES

Liu, Jie; Ru, Peng; Zhang, Wei-Ning; ...

2014-10-15

We investigate the chaoticity parameter λ in two-pion interferometry in an expanding boson gas model. The degree of Bose-Einstein condensation of identical pions, density distributions, and Hanbury-Brown-Twiss (HBT) correlation functions are calculated for the expanding gas within the mean-field description with a harmonic oscillator potential. The results indicate that a sources with thousands of identical pions may exhibit a degree of Bose-Einstein condensation at the temperatures during the hadronic phase in relativistic heavy-ion collisions. This finite condensation may decrease the chaoticity parameter λ in the two-pion interferometry measurements at low pion pair momenta, but influence only slightly the λ valuemore » at high pion pair momentum.« less

Desynchronization in an ensemble of globally coupled chaotic bursting neuronal oscillators by dynamic delayed feedback control

NASA Astrophysics Data System (ADS)

Che, Yanqiu; Yang, Tingting; Li, Ruixue; Li, Huiyan; Han, Chunxiao; Wang, Jiang; Wei, Xile

2015-09-01

In this paper, we propose a dynamic delayed feedback control approach or desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization.

Method of controlling chaos in laser equations

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-01-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

Characterizing the chaotic nature of ocean ventilation

NASA Astrophysics Data System (ADS)

MacGilchrist, Graeme A.; Marshall, David P.; Johnson, Helen L.; Lique, Camille; Thomas, Matthew

2017-09-01

Ventilation of the upper ocean plays an important role in climate variability on interannual to decadal timescales by influencing the exchange of heat and carbon dioxide between the atmosphere and ocean. The turbulent nature of ocean circulation, manifest in a vigorous mesoscale eddy field, means that pathways of ventilation, once thought to be quasi-laminar, are in fact highly chaotic. We characterize the chaotic nature of ventilation pathways according to a nondimensional "filamentation number," which estimates the reduction in filament width of a ventilated fluid parcel due to mesoscale strain. In the subtropical North Atlantic of an eddy-permitting ocean model, the filamentation number is large everywhere across three upper ocean density surfaces—implying highly chaotic ventilation pathways—and increases with depth. By mapping surface ocean properties onto these density surfaces, we directly resolve the highly filamented structure and confirm that the filamentation number captures its spatial variability. These results have implications for the spreading of atmospherically-derived tracers into the ocean interior.

Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier

NASA Astrophysics Data System (ADS)

Geurts, Bernard J.; Wiegel, Frederik W.; Creswick, Richard J.

1990-05-01

The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.

Chaotic one-dimensional domains induced by periodic potentials in normal-dispersion fiber lasers

NASA Astrophysics Data System (ADS)

Urzagasti, Deterlino; Vargas, Bryan A.; Quispe-Flores, Luzmila A.

2017-10-01

We investigate numerically the effects of external time-periodic potentials on time-localized perturbations to the amplitude of electromagnetic waves propagating in normal-dispersion fiber lasers which are described by the complex Ginzburg-Landau equation. Two main effects were found: The formation of domains enclosed by two maxima of the external periodic field and the generation of a chaotic behavior of these domains in the region of relatively high amplitudes and low frequencies of the external fields. Maps and bifurcation diagrams of the largest Lyapunov exponent and moments, such as energy and momentum, are also provided for different values of the amplitude and frequency of such external potentials.

Flow analysis for efficient design of wavy structured microchannel mixing devices

NASA Astrophysics Data System (ADS)

Kanchan, Mithun; Maniyeri, Ranjith

2018-04-01

Microfluidics is a rapidly growing field of applied research which is strongly driven by demands of bio-technology and medical innovation. Lab-on-chip (LOC) is one such application which deals with integrating bio-laboratory on micro-channel based single fluidic chip. Since fluid flow in such devices is restricted to laminar regime, designing an efficient passive modulator to induce chaotic mixing for such diffusion based flow is a major challenge. In the present work two-dimensional numerical simulation of viscous incompressible flow is carried out using immersed boundary method (IBM) to obtain an efficient design for wavy structured micro-channel mixing devices. The continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. IBM uses Eulerian co-ordinates to describe fluid flow and Lagrangian co-ordinates to describe solid boundary. Dirac delta function is used to couple both these co-ordinate variables. A tether forcing term is used to impose the no-slip boundary condition on the wavy structure and fluid interface. Fluid flow analysis by varying Reynolds number is carried out for four wavy structure models and one straight line model. By analyzing fluid accumulation zones and flow velocities, it can be concluded that straight line structure performs better mixing for low Reynolds number and Model 2 for higher Reynolds number. Thus wavy structures can be incorporated in micro-channels to improve mixing efficiency.

Complex magnetohydrodynamic low-Reynolds-number flows.

PubMed

Xiang, Yu; Bau, Haim H

2003-07-01

The interaction between electric currents and a magnetic field is used to produce body (Lorentz) forces in electrolyte solutions. By appropriate patterning of the electrodes, one can conveniently control the direction and magnitude of the electric currents and induce spatially and temporally complicated flow patterns. This capability is useful, not only for fundamental flow studies, but also for inducing fluid flow and stirring in minute devices in which the incorporation of moving components may be difficult. This paper focuses on a theoretical and experimental study of magnetohydrodynamic flows in a conduit with a rectangular cross section. The conduit is equipped with individually controlled electrodes uniformly spaced at a pitch L. The electrodes are aligned transversely to the conduit's axis. The entire device is subjected to a uniform magnetic field. The electrodes are divided into two groups A and C in such a way that there is an electrode of group C between any two electrodes of group A. We denote the various A and C electrodes with subscripts, i.e., A(i) and C(i), where i=0,+/-1,+/-2, .... When positive and negative potentials are, respectively, applied to the even and odd numbered A electrodes, opposing electric currents are induced on the right and left hand sides of each A electrode. These currents generate transverse forces that drive cellular convection in the conduit. We refer to the resulting flow pattern as A. When electrodes of group C are activated, a similar flow pattern results, albeit shifted in space. We refer to this flow pattern as C. By alternating periodically between patterns A and C, one induces Lagrangian chaos. Such chaotic advection may be beneficial for stirring fluids, particularly in microfluidic devices. Since the flow patterns A and C are shifted in space, they also provide a mechanism for Lagrangian drift that allows net migration of passive tracers along the conduit's length.

An Investigation of Chaotic Kolmogorov Flows

DTIC Science & Technology

1990-08-01

plane for the Poincare sections used later. The choice of the constant D controls apparent positioning of the hyperplane in the phase...discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and...examine in some detail the behavior of the flow and its transition states for a range of the bifurcation parameter Re. We use Poincare sections to

Lagrangian analysis of premixed turbulent combustion in hydrogen-air flames

NASA Astrophysics Data System (ADS)

Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter

2016-11-01

Lagrangian analysis has long been a tool used to analyze non-reacting turbulent flows, and has recently gained attention in the reacting flow and combustion communities. The approach itself allows one to separate local molecular effects, such as those due to reactions or diffusion, from turbulent advective effects along fluid pathlines, or trajectories. Accurate calculation of these trajectories can, however, be rather difficult due to the chaotic nature of turbulent flows and the added complexity of reactions. In order to determine resolution requirements and verify the numerical algorithm, extensive tests are described in this talk for prescribed steady, unsteady, and chaotic flows, as well as for direct numerical simulations (DNS) of non-reacting homogeneous isotropic turbulence. The Lagrangian analysis is then applied to DNS of premixed hydrogen-air flames at two different turbulence intensities for both single- and multi-step chemical mechanisms. Non-monotonic temperature and fuel-mass fraction evolutions are found to exist along trajectories passing through the flame brush. Such non-monotonicity is shown to be due to molecular diffusion resulting from large spatial gradients created by turbulent advection. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.

Synchronized chaotic targeting and acceleration of surface chemistry in prebiotic hydrothermal microenvironments

PubMed Central

Priye, Aashish; Yu, Yuncheng; Hassan, Yassin A.; Ugaz, Victor M.

2017-01-01

Porous mineral formations near subsea alkaline hydrothermal vents embed microenvironments that make them potential hot spots for prebiotic biochemistry. But, synthesis of long-chain macromolecules needed to support higher-order functions in living systems (e.g., polypeptides, proteins, and nucleic acids) cannot occur without enrichment of chemical precursors before initiating polymerization, and identifying a suitable mechanism has become a key unanswered question in the origin of life. Here, we apply simulations and in situ experiments to show how 3D chaotic thermal convection—flows that naturally permeate hydrothermal pore networks—supplies a robust mechanism for focused accumulation at discrete targeted surface sites. This interfacial enrichment is synchronized with bulk homogenization of chemical species, yielding two distinct processes that are seemingly opposed yet synergistically combine to accelerate surface reaction kinetics by several orders of magnitude. Our results suggest that chaotic thermal convection may play a previously unappreciated role in mediating surface-catalyzed synthesis in the prebiotic milieu. PMID:28119504

Driving magnetic turbulence using flux ropes in a moderate guide field linear system

NASA Astrophysics Data System (ADS)

Brookhart, Matthew I.; Stemo, Aaron; Waleffe, Roger; Forest, Cary B.

2017-12-01

We present a series of experiments on novel, line-tied plasma geometries as a study of the generation of chaos and turbulence in line-tied systems. Plasma production and the injection scale for magnetic energy is provided by spatially discrete plasma guns that inject both plasma and current. The guns represent a technique for controlling the injection scale of magnetic energy. A two-dimensional (2-D) array of magnetic probes provides spatially resolved time histories of the magnetic fluctuations at a single cross-section of the experimental cylinder, allowing simultaneous spatial measurements of chaotic and turbulent behaviour. The first experiment shows chaotic fluctuations and self-organization in a hollow-current line-tied screw pinch. These dynamics is modulated primarily by the applied magnetic field and weakly by the plasma current and safety factor. The second experiment analyses the interactions of multiple line-tied flux ropes. The flux ropes all exhibit chaotic behaviour, and under certain conditions develop an inverse cascade to larger scales and a turbulent inertial range with magnetic energy ( ) related to perpendicular wave number ( \\bot $ ) as \\bot -2.5\\pm 0.5$ .

Actual Romanian research in post-newtonian dynamics

NASA Astrophysics Data System (ADS)

Mioc, V.; Stavinschi, M.

2007-05-01

We survey the recent Romanian results in the study of the two-body problem in post-Newtonian fields. Such a field is characterized, in general, by a potential of the form U(q)=|q|^{-1}+ something (small, but not compulsorily). We distinguish some classes of post-Newtonian models: relativistic (Schwarzschild, Fock, Einstein PN, Reissner-Nordström, Schwarzschild - de Sitter, etc.) and nonrelativistic (Manev, Mücket-Treder, Seeliger, gravito-elastic, etc.). Generalized models (the zonal-satellite problem, quasihomogeneous fields), as well as special cases (anisotropic Manev-type and Schwarzschild-type models, Popovici or Popovici-Manev photogravitational problem), were also tackled. The methods used in such studies are various: analytical (using mainly the theory of perturbations, but also other theories: functions of complex variable, variational calculus, etc.), geometric (qualitative approach of the theory of dynamical systems), and numerical (especially using the Poincaré-section technique). The areas of interest and the general results obtained focus on: exact or approximate analytical solutions; characteristics of local flows (especially at limit situations: collision and escape); quasiperiodic and periodic orbits; equilibria; symmetries; chaoticity; geometric description of the global flow (and physical interpretation of the phase-space structure). We emphasize some special features, which cannot be met within the Newtonian framework: black-hole effect, oscillatory collisions, radial librations, bounded orbits for nonnegative energy, existence of unstable circular motion (or unstable rest), symmetric periodic orbits within anisotropic models, etc.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field ismore » chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.« less

Seismic responses and controlling factors of Miocene deepwater gravity-flow deposits in Block A, Lower Congo Basin

NASA Astrophysics Data System (ADS)

Wang, Linlin; Wang, Zhenqi; Yu, Shui; Ngia, Ngong Roger

2016-08-01

The Miocene deepwater gravity-flow sedimentary system in Block A of the southwestern part of the Lower Congo Basin was identified and interpreted using high-resolution 3-D seismic, drilling and logging data to reveal development characteristics and main controlling factors. Five types of deepwater gravity-flow sedimentary units have been identified in the Miocene section of Block A, including mass transport, deepwater channel, levee, abandoned channel and sedimentary lobe deposits. Each type of sedimentary unit has distinct external features, internal structures and lateral characteristics in seismic profiles. Mass transport deposits (MTDs) in particular correspond to chaotic low-amplitude reflections in contact with mutants on both sides. The cross section of deepwater channel deposits in the seismic profile is in U- or V-shape. The channel deposits change in ascending order from low-amplitude, poor-continuity, chaotic filling reflections at the bottom, to high-amplitude, moderate to poor continuity, chaotic or sub-parallel reflections in the middle section and to moderate-weak amplitude, good continuity, parallel or sub-parallel reflections in the upper section. The sedimentary lobes are laterally lobate, which corresponds to high-amplitude, good-continuity, moundy reflection signatures in the seismic profile. Due to sediment flux, faults, and inherited terrain, few mass transport deposits occur in the northeastern part of the study area. The front of MTDs is mainly composed of channel-levee complex deposits, while abandoned-channel and lobe-deposits are usually developed in high-curvature channel sections and the channel terminals, respectively. The distribution of deepwater channel, levee, abandoned channel and sedimentary lobe deposits is predominantly controlled by relative sea level fluctuations and to a lesser extent by tectonism and inherited terrain.

Soft inflation

NASA Technical Reports Server (NTRS)

Berkin, Andrew L.; Maeda, Kei-Ichi; Yokoyama, Junichi

1990-01-01

The cosmology resulting from two coupled scalar fields was studied, one which is either a new inflation or chaotic type inflation, and the other which has an exponentially decaying potential. Such a potential may appear in the conformally transformed frame of generalized Einstein theories like the Jordan-Brans-Dicke theory. The constraints necessary for successful inflation are examined. Conventional GUT models such as SU(5) were found to be compatible with new inflation, while restrictions on the self-coupling constant are significantly loosened for chaotic inflation.

Soft inflation. [in cosmology

NASA Technical Reports Server (NTRS)

Berkin, Andrew L.; Maeda, Kei-Ichi; Yokoyama, Jun'ichi

1990-01-01

The cosmology resulting from two coupled scalar fields was studied, one which is either a new inflation or chaotic type inflation, and the other which has an exponentially decaying potential. Such a potential may appear in the conformally transformed frame of generalized Einstein theories like the Jordan-Brans-Dicke theory. The constraints necessary for successful inflation are examined. Conventional GUT models such as SU(5) were found to be compatible with new inflation, while restrictions on the self-coupling constant are significantly loosened for chaotic inflation.

Chaotic Motions in the Real Fuzzy Electronic Circuits (Preprint)

DTIC Science & Technology

2012-12-01

the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good... blending of the linear system models. Consider a continuous-time nonlinear dynamic system as follows: Rule i: IF )(1 tx is ...1iM and )(txn is...Chaos Solitons Fractals, vol. 21, no. 4, pp. 957–965, 2004. 29. L. M. Tam and W. M. SiTou, “Parametric study of the fractional order Chen–Lee

Does Planck really rule out monomial inflation?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Enqvist, Kari; Karčiauskas, Mindaugas, E-mail: kari.enqvist@helsinki.fi, E-mail: mindaugas.karciauskas@helsinki.fi

2014-02-01

We consider the modifications of monomial chaotic inflation models due to radiative corrections induced by inflaton couplings to bosons and/or fermions necessary for reheating. To the lowest order, ignoring gravitational corrections and treating the inflaton as a classical background field, they are of the Coleman-Weinberg type and parametrized by the renormalization scale μ. In cosmology, there are not enough measurements to fix μ so that we end up with a family of models, each having a slightly different slope of the potential. We demonstrate by explicit calculation that within the family of chaotic φ{sup 2} models, some may be ruledmore » out by Planck whereas some remain perfectly viable. In contrast, radiative corrections do not seem to help chaotic φ{sup 4} models to meet the Planck constraints.« less

Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

NASA Astrophysics Data System (ADS)

Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella

2017-03-01

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

Gauge theory for finite-dimensional dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurfil, Pini

2007-06-15

Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differentialmore » equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory.« less

Oscillatory/chaotic thermocapillary flow induced by radiant heating

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung; Thompson, Robert L.; Vanzandt, David; Dewitt, Kenneth; Nash, Jon

1994-01-01

The objective of this paper is to conduct ground-based experiments to measure the onset conditions of oscillatory Marangoni flow in laser-heated silicone oil in a cylindrical container. For a single fluid, experimental data are presented using the aspect ratio and the dynamic Bond number. It is found that for a fixed aspect ratio, there seems to be an asymptotic limit of the dynamic Bond number beyond which no onset of flow oscillation could occur. Experimental results also suggested that there could be a lower limit of the aspect ratio below which there is no onset of oscillatory flow.

Noise, anti-noise and fluid flow control.

PubMed

Williams, J E Ffowcs

2002-05-15

This paper celebrates Thomas Young's discovery that wave interference was responsible for much that is known about light and colour. A substantial programme of work has been aimed at controlling the noise of aerodynamic flows. Much of that field can be explained in terms of interference and it is argued in this paper that the theoretical techniques for analysing noise can also be seen to rest on interference effects. Interference can change the character of wave fields to produce, out of well-ordered fields, wave systems quite different from the interfering wave elements. Lighthill's acoustic analogy is described as an example of this effect, an example in which the exact model of turbulence-generated noise is seen to consist of elementary interfering sound waves; waves that are sometimes heard in advance of their sources. The paper goes on to describe an emerging field of technology where sound is suppressed by superimposing on it a destructively interfering secondary sound; one designed and manufactured specifically for interference. That sound is known as anti-sound, or anti-noise when the sound is chaotic enough. Examples are then referred to where the noisy effect to be controlled is actually a disturbance of a linearly unstable system; a disturbance that is destroyed by destructive interference with a deliberately constructed antidote. The practical benefits of this kind of instability control are much greater and can even change the whole character of flows. It is argued that completely unnatural unstable conditions can be held with active controllers generating destructively interfering elements. Examples are given in which gravitational instability of stratified fluids can be prevented. The Kelvin-Helmholtz instability of shear flows can also be avoided by simple controls. Those are speculative examples of what might be possible in future developments of an interference effect, which has made anti-noise a useful technology.

Chimeralike states in a network of oscillators under attractive and repulsive global coupling.

PubMed

Mishra, Arindam; Hens, Chittaranjan; Bose, Mridul; Roy, Prodyot K; Dana, Syamal K

2015-12-01

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.

The Dynamics of Fibril Magnetic Fields - Part Two - the Mean Field Equations

NASA Astrophysics Data System (ADS)

Parker, E. N.

1982-05-01

A variety of scenarios for the origin and activity of magnetic fields in the convective zone of the Sun have been put forth in recent years. In particular, a number of authors have urged that the magnetic field is in a generally fibril state, much as observed at the surface, with a variety of suggestions as to the consequences. The present paper works out the mean field equations for intense thin fibrils of fixed cross section under the assumption of some significant local ordering. The aim is to establish to what degree new effects may arise as a result of the fibril state. It is shown that the fibril state of a mean field B enhances the tension in the field and the buoyancy of the field by the compression factor m of the field in the individual fibrils. New qualitative effects appear in the slip velocity u of the fibrils through the ambient fluid and in the neutral point reconnection of neighboring fibrils. Some of the novel features are illustrated in later papers in this series. One of the most important consequences is the simplification of the theory of turbulent diffusion by eliminating the looping and tangling that arises when a continuum field is carried in a chaotic turbulent flow. We have been unable to find any effects that would admit of a new concept for the origin of the solar magnetic fields.

Dynamics of Two Point Vortices in an External Compressible Shear Flow

NASA Astrophysics Data System (ADS)

Vetchanin, Evgeny V.; Mamaev, Ivan S.

2017-12-01

This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the "reversible pitch-fork" bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.

Predicting Flow Reversals in a Computational Fluid Dynamics Simulated Thermosyphon Using Data Assimilation.

PubMed

Reagan, Andrew J; Dubief, Yves; Dodds, Peter Sheridan; Danforth, Christopher M

2016-01-01

A thermal convection loop is a annular chamber filled with water, heated on the bottom half and cooled on the top half. With sufficiently large forcing of heat, the direction of fluid flow in the loop oscillates chaotically, dynamics analogous to the Earth's weather. As is the case for state-of-the-art weather models, we only observe the statistics over a small region of state space, making prediction difficult. To overcome this challenge, data assimilation (DA) methods, and specifically ensemble methods, use the computational model itself to estimate the uncertainty of the model to optimally combine these observations into an initial condition for predicting the future state. Here, we build and verify four distinct DA methods, and then, we perform a twin model experiment with the computational fluid dynamics simulation of the loop using the Ensemble Transform Kalman Filter (ETKF) to assimilate observations and predict flow reversals. We show that using adaptively shaped localized covariance outperforms static localized covariance with the ETKF, and allows for the use of less observations in predicting flow reversals. We also show that a Dynamic Mode Decomposition (DMD) of the temperature and velocity fields recovers the low dimensional system underlying reversals, finding specific modes which together are predictive of reversal direction.

Predicting Flow Reversals in a Computational Fluid Dynamics Simulated Thermosyphon Using Data Assimilation

PubMed Central

Reagan, Andrew J.; Dubief, Yves; Dodds, Peter Sheridan; Danforth, Christopher M.

2016-01-01

A thermal convection loop is a annular chamber filled with water, heated on the bottom half and cooled on the top half. With sufficiently large forcing of heat, the direction of fluid flow in the loop oscillates chaotically, dynamics analogous to the Earth’s weather. As is the case for state-of-the-art weather models, we only observe the statistics over a small region of state space, making prediction difficult. To overcome this challenge, data assimilation (DA) methods, and specifically ensemble methods, use the computational model itself to estimate the uncertainty of the model to optimally combine these observations into an initial condition for predicting the future state. Here, we build and verify four distinct DA methods, and then, we perform a twin model experiment with the computational fluid dynamics simulation of the loop using the Ensemble Transform Kalman Filter (ETKF) to assimilate observations and predict flow reversals. We show that using adaptively shaped localized covariance outperforms static localized covariance with the ETKF, and allows for the use of less observations in predicting flow reversals. We also show that a Dynamic Mode Decomposition (DMD) of the temperature and velocity fields recovers the low dimensional system underlying reversals, finding specific modes which together are predictive of reversal direction. PMID:26849061

Inertial particle dynamics in large artery flows - Implications for modeling arterial embolisms.

PubMed

Mukherjee, Debanjan; Shadden, Shawn C

2017-02-08

The complexity of inertial particle dynamics through swirling chaotic flow structures characteristic of pulsatile large-artery hemodynamics renders significant challenges in predictive understanding of transport of such particles. This is specifically crucial for arterial embolisms, where knowledge of embolus transport to major vascular beds helps in disease diagnosis and surgical planning. Using a computational framework built upon image-based CFD and discrete particle dynamics modeling, a multi-parameter sampling-based study was conducted on embolic particle dynamics and transport. The results highlighted the strong influence of material properties, embolus size, release instance, and embolus source on embolus distribution to the cerebral, renal and mesenteric, and ilio-femoral vasculature beds. The study also isolated the importance of shear-gradient lift, and elastohydrodynamic contact, in affecting embolic particle transport. Near-wall particle re-suspension due to lift alters aortogenic embolic particle dynamics significantly as compared to cardiogenic. The observations collectively indicated the complex interplay of particle inertia, fluid-particle density ratio, and wall collisions, with chaotic flow structures, which render the overall motion of the particles to be non-trivially dispersive in nature. Copyright © 2017 Elsevier Ltd. All rights reserved.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

PubMed

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Modeling global vector fields of chaotic systems from noisy time series with the aid of structure-selection techniques.

PubMed

Xu, Daolin; Lu, Fangfang

2006-12-01

We address the problem of reconstructing a set of nonlinear differential equations from chaotic time series. A method that combines the implicit Adams integration and the structure-selection technique of an error reduction ratio is proposed for system identification and corresponding parameter estimation of the model. The structure-selection technique identifies the significant terms from a pool of candidates of functional basis and determines the optimal model through orthogonal characteristics on data. The technique with the Adams integration algorithm makes the reconstruction available to data sampled with large time intervals. Numerical experiment on Lorenz and Rossler systems shows that the proposed strategy is effective in global vector field reconstruction from noisy time series.

Chaotic He-Ne laser

NASA Astrophysics Data System (ADS)

Kuusela, Tom A.

2017-09-01

A He-Ne laser is an example of a class A laser, which can be described by a single nonlinear differential equation of the complex electric field. This laser system has only one degree of freedom and is thus inherently stable. A He-Ne laser can be driven to the chaotic condition when a large fraction of the output beam is injected back to the laser. In practice, this can be done simply by adding an external mirror. In this situation, the laser system has infinite degrees of freedom and therefore it can have a chaotic attractor. We show the fundamental laser equations and perform elementary stability analysis. In experiments, the laser intensity variations are measured by a simple photodiode circuit. The laser output intensity time series is studied using nonlinear analysis tools which can be found freely on the internet. The results show that the laser system with feedback has an attractor of a reasonably high dimension and that the maximal Lyapunov exponent is positive, which is clear evidence of chaotic behaviour. The experimental setup and analysis steps are so simple that the studies can even be implemented in the undergraduate physics laboratory.

Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures

NASA Astrophysics Data System (ADS)

Russell, Francis P.; Düben, Peter D.; Niu, Xinyu; Luk, Wayne; Palmer, T. N.

2017-12-01

Reconfigurable architectures are becoming mainstream: Amazon, Microsoft and IBM are supporting such architectures in their data centres. The computationally intensive nature of atmospheric modelling is an attractive target for hardware acceleration using reconfigurable computing. Performance of hardware designs can be improved through the use of reduced-precision arithmetic, but maintaining appropriate accuracy is essential. We explore reduced-precision optimisation for simulating chaotic systems, targeting atmospheric modelling, in which even minor changes in arithmetic behaviour will cause simulations to diverge quickly. The possibility of equally valid simulations having differing outcomes means that standard techniques for comparing numerical accuracy are inappropriate. We use the Hellinger distance to compare statistical behaviour between reduced-precision CPU implementations to guide reconfigurable designs of a chaotic system, then analyse accuracy, performance and power efficiency of the resulting implementations. Our results show that with only a limited loss in accuracy corresponding to less than 10% uncertainty in input parameters, the throughput and energy efficiency of a single-precision chaotic system implemented on a Xilinx Virtex-6 SX475T Field Programmable Gate Array (FPGA) can be more than doubled.

Banknote authentication using chaotic elements technology

NASA Astrophysics Data System (ADS)

Ambadiyil, Sajan; P. S., Krishnendu; Mahadevan Pillai, V. P.; Prabhu, Radhakrishna

2017-10-01

The counterfeit banknote is a growing threat to the society since the advancements in the field of computers, scanners and photocopiers, as they have made the duplication process for banknote much simpler. The fake note detection systems developed so far have many drawbacks such as high cost, poor accuracy, unavailability, lack of user-friendliness and lower effectiveness. One possible solution to this problem could be the use of a system uniquely linked to the banknote itself. In this paper, we present a unique identification and authentication process for the banknote using chaotic elements embedded in it. A chaotic element means that the physical elements are formed from a random process independent from human intervention. The chaotic elements used in this paper are the random distribution patterns of such security fibres set into the paper pulp. A unique ID is generated from the fibre pattern obtained from UV image of the note, which can be verified by any person who receives the banknote to decide whether the banknote is authentic or not. Performance analysis of the system is also studied in this paper.

Solar and Planetary Dynamos

NASA Astrophysics Data System (ADS)

Proctor, M. R. E.; Matthews, P. C.; Rucklidge, A. M.

2008-02-01

Preface; 1. Magnetic noise and the galactic dynamo; 2. On the oscillation in model Z; 3. Nonlinear dynamos in a spherical shell; 4. The onset of dynamo action in alpha-lambda dynamos; 5. Multifractality, near-singularities and the role of stretching in turbulence; 6. Note on perfect fast dynamo action in a large-amplitude SFS map; 7. A thermally driven disc dynamo; 8. Magnetic instabilities in rapidly rotating systems; 9. Modes of a flux ring lying in the equator of a star; 10. A nonaxisymmetric dynamo in toroidal geometry; 11. Simulating the interaction of convection with magnetic fields in the sun; 12. Experimental aspects of a laboratory scale liquid sodium dynamo model; 13. Influence of the period of an ABC flow on its dynamo action; 14. Numerical calculations of dynamos for ABC and related flows; 15. Incompressible Euler equations; 16. On the quasimagnetostrophic asymptotic approximation related to solar activity; 17. Simple dynamical fast dynamos; 18. A numerical study of dynamos in spherical shells with conducting boundaries; 19. Non-axisymmetric shear layers in a rotating spherical shell; 20. Testing for dynamo action; 21. Alpha-quenching in cylindrical magnetoconvection; 22. On the stretching of line elements in fluids: an approach from different geometry; 23. Instabilities of tidally and precessionally induced flows; 24. Probability distribution of passive scalars with nonlinear mean gradient; 25. Magnetic fluctuations in fast dynamos; 26. A statistical description of MHD turbulence in laboratory plasma; 27. Compressible magnetoconvection in three dimensions; 28. The excitation of nonaxisymmetric magnetic fields in galaxies; 29. Localized magnetic fields in a perfectly conducting fluid; 30. Turbulent dynamo and the geomagnetic secular variation; 31. On-off intermittency: general description and feedback model; 32. Dynamo action in a nearly integrable chaotic flow; 33. The dynamo mechanism in the deep convection zone of the sun; 34. Shearing instabilities in magnetoconvection; 35. On the role of rotation of the internal core relative to the mantle; 36. Evolution of magnetic fields in a swirling jet; 37. Analytic fast dynamo solution for a two-dimensional pulsed flow; 38. On magnetic dynamos in thin accretion disks around compact and young stars; 39. The strong field branch of the Childress-Soward dynamo; 40. Evidence for the suppression of the alpha-effect by weak magnetic fields; 41. Turbulent magnetic transport effects and their relation to magnetic field intermittency; 42. Proving the existence of negative variation of electrical conductivity; 43. Spherical inertial oscillation and convection; 44. Hydrodynamics stability of the ABC flow; 45. Dynamos with ambipolar diffusion; Subject index.

Fast dynamos with finite resistivity in steady flows with stagnation points

NASA Technical Reports Server (NTRS)

Lau, Yun-Tung; Finn, John M.

1993-01-01

Results are presented of a kinematic fast dynamo problem for two classes of steady incompressible flows: the ABC flow and the spatially aperiodic flow of Lau and Finn (1992). The numerical method used to find the solutions is described, together with convergence studies with respect to the time step and the number of points N of the spatial grid. It is shown that the growth rate and frequency can be extrapolated to N = infinity. Results are presented indicating that fast kinematic dynamos can exist in both these flows and that chaotic flow is a necessary condition. It was found that, for the ABC flow with A = B = C, there are two dynamo modes: an oscillating mode and a purely growing mode.

Temporal chaos in Boussinesq magnetoconvection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bekki, Naoaki; Moriguchi, Hirofumi; Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495

2007-01-15

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famousmore » Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.« less

Flame dynamics in a micro-channeled combustor

NASA Astrophysics Data System (ADS)

Hussain, Taaha; Markides, Christos N.; Balachandran, Ramanarayanan

2015-01-01

The increasing use of Micro-Electro-Mechanical Systems (MEMS) has generated a significant interest in combustion-based power generation technologies, as a replacement of traditional electrochemical batteries which are plagued by low energy densities, short operational lives and low power-to-size and power-to-weight ratios. Moreover, the versatility of integrated combustion-based systems provides added scope for combined heat and power generation. This paper describes a study into the dynamics of premixed flames in a micro-channeled combustor. The details of the design and the geometry of the combustor are presented in the work by Kariuki and Balachandran [1]. This work showed that there were different modes of operation (periodic, a-periodic and stable), and that in the periodic mode the flame accelerated towards the injection manifold after entering the channels. The current study investigates these flames further. We will show that the flame enters the channel and propagates towards the injection manifold as a planar flame for a short distance, after which the flame shape and propagation is found to be chaotic in the middle section of the channel. Finally, the flame quenches when it reaches the injector slots. The glow plug position in the exhaust side ignites another flame, and the process repeats. It is found that an increase in air flow rate results in a considerable increase in the length (and associated time) over which the planar flame travels once it has entered a micro-channel, and a significant decrease in the time between its conversion into a chaotic flame and its extinction. It is well known from the literature that inside small channels the flame propagation is strongly influenced by the flow conditions and thermal management. An increase of the combustor block temperature at high flow rates has little effect on the flame lengths and times, whereas at low flow rates the time over which the planar flame front can be observed decreases and the time of existence of the chaotic flame increases. The frequency of re-ignition of successive flames decreases at higher flow rates and increases at higher temperatures. The data and results from this study will not only help the development of new micro-power generation devices, but they will also serve as a validation case for combustion models capable of predicting flame behavior in the presence of strong thermal and flow boundary layers, a situation common to many industrial applications.

ALMA Observations of Molecular Clouds in Three Group-centered Elliptical Galaxies: NGC 5846, NGC 4636, and NGC 5044

NASA Astrophysics Data System (ADS)

Temi, Pasquale; Amblard, Alexandre; Gitti, Myriam; Brighenti, Fabrizio; Gaspari, Massimo; Mathews, William G.; David, Laurence

2018-05-01

We present new ALMA CO(2–1) observations of two well-studied group-centered elliptical galaxies: NGC 4636 and NGC 5846. In addition, we include a revised analysis of Cycle 0 ALMA observations of the central galaxy in the NGC 5044 group. We find evidence that molecular gas is a common presence in bright group-centered galaxies (BGG). CO line widths are broader than Galactic molecular clouds, and using the reference Milky Way X CO, the total molecular mass ranges from 2.6 × 105 M ⊙ in NGC 4636 to 6.1 × 107 M ⊙ in NGC 5044. Complementary observations using the ALMA Compact Array do not exhibit any detection of a CO diffuse component at the sensitivity level achieved by current exposures. The origin of the detected molecular features is still uncertain, but these ALMA observations suggest that they are the end product of the hot gas cooling process and not the result of merger events. Some of the molecular clouds are associated with dust features as revealed by HST dust extinction maps, suggesting that these clouds formed from dust-enhanced cooling. The global nonlinear condensation may be triggered via the chaotic turbulent field or buoyant uplift. The large virial parameter of the molecular structures and correlation with the warm ({10}3{--}{10}5 {{K}})/hot (≥106) phase velocity dispersion provide evidence that they are unbound giant molecular associations drifting in the turbulent field, consistent with numerical predictions of the chaotic cold accretion process. Alternatively, the observed large CO line widths may be generated by molecular gas flowing out from cloud surfaces due to heating by the local hot gas atmosphere.

Body-force-driven multiplicity and stability of combined free and forced convection in rotating curved ducts: Coriolis force

NASA Astrophysics Data System (ADS)

Yang, T.; Wang, L.

A numerical study is made on the fully developed bifurcation structure and stability of forced convection in a rotating curved duct of square cross-section. Solution structure is determined as variation of a parameter that indicates the effect of rotation (Coriolis-force-driven multiplicity). Three solutions for the flows in a stationary curved duct obtained in the work of Yang and Wang [1] are used as initial solutions of continuation calculations to unfold the solution branches. Twenty-one solution branches are found comparing with five obtained by Selmi and Nandakumar [2]. Dynamic responses of the multiple solutions to finite random disturbances are examined by the direct transient computation. Results show that characteristics of physically realizable fully developed flows changes significantly with variation of effect of rotation. Fourteen sub-ranges are identified according to characteristics of physically realizable solutions. As rotation effect changes, possible physically realizable fully-developed flows can be stable steady 2-cell state, stable multi-cell state, temporal periodic oscillation between symmetric/asymmetric 2-cell/4-cell flows, temporal oscillation with intermittency, temporal chaotic oscillation and temporal oscillation with pseudo intermittency. Among these possible physically realizable fully developed flows, stable multi-cell state and stable steady 2-cell state exist as dual stable. And oscillation with pseudo intermittency is a new phenomenon. In addition to the temporal oscillation with intermittency, sudden shift from stationary stable solution to temporal chaotic oscillation is identified to be another way of onset of chaos.

Discrete dynamical laser equation for the critical onset of bistability, entanglement and disappearance

NASA Astrophysics Data System (ADS)

Abdul, M.; Farooq, U.; Akbar, Jehan; Saif, F.

2018-06-01

We transform the semi-classical laser equation for single mode homogeneously broadened lasers to a one-dimensional nonlinear map by using the discrete dynamical approach. The obtained mapping, referred to as laser logistic mapping (LLM), characteristically exhibits convergent, cyclic and chaotic behavior depending on the control parameter. Thus, the so obtained LLM explains stable, bistable, multi-stable, and chaotic solutions for output field intensity. The onset of bistability takes place at a critical value of the effective gain coefficient. The obtained analytical results are confirmed through numerical calculations.

Exact Recovery of Chaotic Systems from Highly Corrupted Data

DTIC Science & Technology

2016-08-01

dimension to reconstruct a state space which preserves the topological properties of the original system. In [CM87, RS92], the authors use the singular...in high dimensional nonlinear functional spaces [Spr94, SL00, LCC04]. In this work, we bring together connections between compressed sensing, splitting... compact , connected attractor Λ and the flow admits a unique so-called “physical" measure µ with supp(µ) = Λ. An invariant probability measure µ for a flow

Chaos in an Eulerian Based Model of Sickle Cell Blood Flow

NASA Astrophysics Data System (ADS)

Apori, Akwasi; Harris, Wesley

2001-11-01

A novel Eulerian model describing the manifestation of sickle cell blood flow in the capillaries has been formulated to study the apparently chaotic onset of sickle cell crises. This Eulerian model was based on extending previous models of sickle cell blood flow which were limited due to their Lagrangian formulation. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.

Nonequilibrium electrokinetic effects in beds of ion-permselective particles.

PubMed

Leinweber, Felix C; Tallarek, Ulrich

2004-12-21

Electrokinetic transport of fluorescent tracer molecules in a bed of porous glass beads was investigated by confocal laser scanning microscopy. Refractive index matching between beads and the saturating fluid enabled a quantitative analysis of intraparticle and extraparticle fluid-side concentration profiles. Kinetic data were acquired for the uptake and release of electroneutral and counterionic tracer under devised conditions with respect to constant pressure-driven flow through the device and the effect of superimposed electrical fields. Transport of neutral tracer is controlled by intraparticle mass transfer resistance which can be strongly reduced by electroosmotic flow, while steady-state distributions and bead-averaged concentrations are unaffected by the externally applied fields. Electrolytes of low ionic strength caused the transport through the charged (mesoporous) beads to become highly ion-permselective, and concentration polarization is induced in the bulk solution due to the superimposed fields. The depleted concentration polarization zone comprises extraparticle fluid-side mass transfer resistance. Ionic concentrations in this diffusion boundary layer decrease at increasing field strength, and the flux densities approach an upper limit. Meanwhile, intraparticle transport of counterions by electromigration and electroosmosis continues to increase and finally exceeds the transport from bulk solution into the beads. A nonequilibrium electrical double layer is induced which consists of mobile and immobile space charge regions in the extraparticle bulk solution and inside a bead, respectively. These electrical field-induced space charges form the basis for nonequilibrium electrokinetic phenomena. Caused by the underlying transport discrimination (intraparticle electrokinetic vs extraparticle boundary-layer mass transfer), the dynamic adsorption capacity for counterions can be drastically reduced. Further, the extraparticle mobile space charge region leads to nonlinear electroosmosis. Flow patterns can become highly chaotic, and electrokinetic instability mixing is shown to increase lateral dispersion. Under these conditions, the overall axial dispersion of counterionic tracer can be reduced by more than 2 orders of magnitude, as demonstrated by pulse injections.

Reaction patterns in a blinking vortex flow

NASA Astrophysics Data System (ADS)

Nugent, Carolyn

2005-11-01

We study the patterns formed by the excitable Belousov-Zhabotinsky reaction in a blinking vortex flow produced by magnetohydrodynamic forcing. Mixing in this flow is chaotic, as has been documented extensively in previous studies. The reaction is triggered by a silver wire, and the result is a pulse (``trigger wave'') that propagates through the system. We investigate the patterns formed by the propagating pulse and compare them with theoriesootnotetextT. Tel, A. de Moura, C. Grebogi and G. Karolyi, Phys. Rep. 413, 91 (2005). that predict fractal patterns determined by the unstable manifolds of the flow. We also consider ``burn-like'' reaction fronts, and compare the results with previous experiments for patterns of oscillatory reactions in this flow.

Chaotic Dynamics of Linguistic-Like Processes at the Syntactical and Semantic Levels: in the Pursuit of a Multifractal Attractor

NASA Astrophysics Data System (ADS)

Nicolis, John S.; Katsikas, Anastassis A.

Collective parameters such as the Zipf's law-like statistics, the Transinformation, the Block Entropy and the Markovian character are compared for natural, genetic, musical and artificially generated long texts from generating partitions (alphabets) on homogeneous as well as on multifractal chaotic maps. It appears that minimal requirements for a language at the syntactical level such as memory, selectivity of few keywords and broken symmetry in one dimension (polarity) are more or less met by dynamically iterating simple maps or flows e.g. very simple chaotic hardware. The same selectivity is observed at the semantic level where the aim refers to partitioning a set of enviromental impinging stimuli onto coexisting attractors-categories. Under the regime of pattern recognition and classification, few key features of a pattern or few categories claim the lion's share of the information stored in this pattern and practically, only these key features are persistently scanned by the cognitive processor. A multifractal attractor model can in principle explain this high selectivity, both at the syntactical and the semantic levels.

Noise-driven switching and chaotic itinerancy among dynamic states in a three-mode intracavity second-harmonic generation laser operating on a Λ transition

NASA Astrophysics Data System (ADS)

Otsuka, Kenju; Ohtomo, Takayuki; Maniwa, Tsuyoshi; Kawasaki, Hazumi; Ko, Jing-Yuan

2003-09-01

We studied the antiphase self-pulsation in a globally coupled three-mode laser operating in different optical spectrum configurations. We observed locking of modal pulsation frequencies, quasiperiodicity, clustering behaviors, and chaos, resulting from the nonlinear interaction among modes. The robustness of [p:q:r] three-frequency locking states and quasiperiodic oscillations against residual noise has been examined by using joint time-frequency analysis of long-term experimental time series. Two sharply antithetical types of switching behaviors among different dynamic states were observed during temporal evolutions; noise-driven switching and self-induced switching, which manifests itself in chaotic itinerancy. The modal interplay behind observed behaviors was studied by using the statistical dynamic quantity of the information circulation. Well-organized information flows among modes, which correspond to the number of degeneracies of modal pulsation frequencies, were found to be established in accordance with the inherent antiphase dynamics. Observed locking behaviors, quasiperiodic motions, and chaotic itinerancy were reproduced by numerical simulation of the model equations.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Finn, John M., E-mail: finn@lanl.gov

2015-03-15

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint.more » We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012)], appears to work very well.« less

Application of laser chaos control methods to controlling thyroid-catatonic oscillations and burst firing of dopamine neurons

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-11-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang and Bau. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the lasers equations are isomorphic to the Lorenz equations, we use this new method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential lasers controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills and Hunt. This method of control chaos is now extended to various medical and biological systems.

Plasticity performance of Al 0.5 CoCrCuFeNi high-entropy alloys under nanoindentation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Li-ping; Chen, Shu-ying; Ren, Jing-li

2017-04-01

The statistical and dynamic behaviors of the displacement-load curves of a high-entropy alloy, Al0.5 CoCrCuFeNi, were analyzed for the nanoindentation performed at two temperatures. Critical behavior of serrations at room temperature and chaotic flows at 200 °C were detected. These results are attributed to the interaction among a large number of slip bands. For the nanoindentation at room temperature, recurrent partial events between slip bands introduce a hierarchy of length scales, leading to a critical state. For the nanoindentation at 200 °C, there is no spatial interference between two slip bands, which is corresponding to the evolution of separated trajectorymore » of chaotic behavior« less

Tori and chaos in a simple C1-system

NASA Astrophysics Data System (ADS)

Roessler, O. E.; Kahiert, C.; Ughleke, B.

A piecewise-linear autonomous 3-variable ordinary differential equation is presented which permits analytical modeling of chaotic attractors. A once-differentiable system of equations is defined which consists of two linear half-systems which meet along a threshold plane. The trajectories described by each equation is thereby continuous along the divide, forming a one-parameter family of invariant tori. The addition of a damping term produces a system of equations for various chaotic attractors. Extension of the system by means of a 4-variable generalization yields hypertori and hyperchaos. It is noted that the hierarchy established is amenable to analysis by the use of Poincare half-maps. Applications of the systems of ordinary differential equations to modeling turbulent flows are discussed.

Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

NASA Astrophysics Data System (ADS)

Figueroa, Aldo; Meunier, Patrice; Cuevas, Sergio; Villermaux, Emmanuel; Ramos, Eduardo

2014-01-01

We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, "The diffusive strip method for scalar mixing in two-dimensions," J. Fluid Mech. 662, 134-172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement with quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors.

Mass transport-related stratal disruption and sedimentary products

NASA Astrophysics Data System (ADS)

Ogata, Kei; Mutti, Emiliano; Tinterri, Roberto

2010-05-01

From an outcrop perspective, mass transport deposit are commonly represented by "chaotic" units, characterized by dismembered and internally deformed slide blocks of different sizes and shapes, embedded in a more or less abundant fine-grained matrix. The large amount of data derived from geophysical investigations of modern continental margins have permitted the characterization of the overall geometry of many of these deposits, which, however, remain still relatively poorly described from outcrop studies of collisional basins. Results of this work show that in mass-transport deposits an unsorted, strongly mixed, relatively fine-grained clastic matrix almost invariably occurs in irregularly interconnected patches and pseudo-veins, infilling space between large clasts and blocks. We interpreted the aspect of this matrix as typical of a liquefied mixture of water and sediment, characterized by an extremely high mobility due to overpressured conditions, as evidenced by both lateral and vertical injections. On a much larger scale this kind of matrix is probably represented by the seismically "transparent" facies separating slide blocks of many mass-transport deposits observed in seismic-reflection profiles. The inferred mechanism of matrix production suggests a progressive soft-sediment deformation, linked to different phases of submarine landslide evolution (i.e. triggering, translation, accumulation and post-depositional stages), leading to an almost complete stratal disruption within the chaotic units. From our data we suggest that most submarine landslides move because of the development of ductile shear zones marked by the presence of "overpressured" matrix, both internally and along the basal surface. The matrix acts as a lubricating medium, accommodating friction forces and deformation, thus permitting the differential movement of discrete internal portions and enhancing the submarine slide mobility. Based on our experience, we suggest that this kind of deposit is quite common in the sedimentary record though still poorly reported and understood. Mutti and Carminatti (oral presentation from Mutti et al., 2006) have suggested to call these deposits "blocky-flow deposits", i.e. the deposit of a complex flow that is similar to a debris flow, or hyper-concentrated flow, except that it carries also out-size coherent and internally deformed blocks (meters to hundreds of meters across) usually arranged in isolated slump folds. The origin of blocky flows is difficult to understand on presently available data, particularly because it involves the contemporary origin of coherent slide blocks and a plastic flow that carries them as floating elements over considerable run-out distances. The recognition of the above-mentioned characteristics should be a powerful tool to discriminate sedimentary and tectonic "chaotic" units within accretionary systems, and to distinguish submarine landslide deposits transported as catastrophic blocky flows (and therefore part of the broad family of sediment gravity flows) from those in which transport took place primarily along shear planes (i.e. slumps, coherent slides), also highlighting a possible continuum from slides to turbidity currents. The discussed examples fall into a broad category of submarine slide deposits ranging from laterally extensive carbonate megabreccias (lower-middle Eocene "megaturbidites" of the south-central Pyrenees), to mass transport deposits with a very complex internal geometry developed in a highly tectonically mobile basin (upper Eocene - lower Oligocene Ranzano Sandstone, northern Apennines). References: Mutti, E., Carminatti, M., Moreira, J.L.P. & Grassi, A.A. (2006) - Chaotic Deposits: examples from the Brazilian offshore and from outcrop studies in the Spanish Pyrenees and Northern Apennines, Italy. - A.A.P.G. Annual Meeting, April 9-12, Houston, Texas.

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fakhari, Abbas, E-mail: afakhari@nd.edu; Geier, Martin; Lee, Taehun

2016-06-15

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude fastermore » than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a typical chaotic structure in the flow field is observed at a Reynolds number of 10000, which indicates that the proposed model is a promising tool for direct numerical simulation of two-phase flows.« less

Chaotic vortex induced vibrations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, J.; Sheridan, J.; Leontini, J. S.

2014-12-15

This study investigates the nature of the dynamic response of an elastically mounted cylinder immersed in a free stream. A novel method is utilized, where the motion of the body during a free vibration experiment is accurately recorded, and then a second experiment is conducted where the cylinder is externally forced to follow this recorded trajectory. Generally, the flow response during both experiments is identical. However, particular regimes exist where the flow response is significantly different. This is taken as evidence of chaos in these regimes.

Application of cross recurrence plot for identification of temperature fluctuations synchronization in parallel minichannels

NASA Astrophysics Data System (ADS)

Grzybowski, H.; Mosdorf, R.

2016-09-01

The temperature fluctuations occurring in flow boiling in parallel minichannels with diameter of 1 mm have been experimentally investigated and analysed. The wall temperature was recorded at each minichannel outlet by thermocouple with 0.08 mm diameter probe. The time series where recorded during dynamic two-phase flow instabilities which are accompanied by chaotic temperature fluctuations. Time series were denoised using wavelet decomposition and were analysed using cross recurrence plots (CRP) which enables the study of two time series synchronization.

Method of chaotic mixing and improved stirred tank reactors

DOEpatents

Muzzio, F.J.; Lamberto, D.J.

1999-07-13

The invention provides a method and apparatus for efficiently achieving a homogeneous mixture of fluid components by introducing said components having a Reynolds number of between about [le]1 to about 500 into a vessel and continuously perturbing the mixing flow by altering the flow speed and mixing time until homogeneity is reached. This method prevents the components from aggregating into non-homogeneous segregated regions within said vessel during mixing and substantially reduces the time the admixed components reach homogeneity. 19 figs.

Method of chaotic mixing and improved stirred tank reactors

DOEpatents

Muzzio, Fernando J.; Lamberto, David J.

1999-01-01

The invention provides a method and apparatus for efficiently achieving a homogeneous mixture of fluid components by introducing said components having a Reynolds number of between about .ltoreq.1 to about 500 into a vessel and continuously perturbing the mixing flow by altering the flow speed and mixing time until homogeniety is reached. This method prevents the components from aggregating into non-homogeneous segregated regions within said vessel during mixing and substantially reduces the time the admixed components reach homogeneity.

Orientational dynamics of a triaxial ellipsoid in simple shear flow: Influence of inertia.

PubMed

Rosén, Tomas; Kotsubo, Yusuke; Aidun, Cyrus K; Do-Quang, Minh; Lundell, Fredrik

2017-07-01

The motion of a single ellipsoidal particle in simple shear flow can provide valuable insights toward understanding suspension flows with nonspherical particles. Previously, extensive studies have been performed on the ellipsoidal particle with rotational symmetry, a so-called spheroid. The nearly prolate ellipsoid (one major and two minor axes of almost equal size) is known to perform quasiperiodic or even chaotic orbits in the absence of inertia. With small particle inertia, the particle is also known to drift toward this irregular motion. However, it is not previously understood what effects from fluid inertia could be, which is of highest importance for particles close to neutral buoyancy. Here, we find that fluid inertia is acting strongly to suppress the chaotic motion and only very weak fluid inertia is sufficient to stabilize a rotation around the middle axis. The mechanism responsible for this transition is believed to be centrifugal forces acting on fluid, which is dragged along with the rotational motion of the particle. With moderate fluid inertia, it is found that nearly prolate triaxial particles behave similarly to the perfectly spheroidal particles. Finally, we also are able to provide predictions about the stable rotational states for the general triaxial ellipsoid in simple shear with weak inertia.

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

DOE PAGES

del-Castillo-Negrete, Diego; Blazevski, Daniel

2016-04-01

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in 3-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands and remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. The key parameter ismore » $$\\gamma=\\sqrt{\\omega/2 \\chi_\\parallel}$$ that determines the length scale, $$1/\\gamma$$, of the heat wave penetration along the magnetic field line. For large perturbation frequencies, $$\\omega \\gg 1$$, or small parallel thermal conductivities, $$\\chi_\\parallel \\ll 1$$, parallel heat transport is strongly damped and the magnetic field partial barriers act as robust barriers where the heat wave amplitude vanishes and its phase speed slows down to a halt. On the other hand, in the limit of small $$\\gamma$$, parallel heat transport is largely unimpeded, global transport is observed and the radial amplitude and phase speed of the heat wave remain finite. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in LHD and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude and the time delay of modulated heat pulses.« less

Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

NASA Astrophysics Data System (ADS)

Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal

2017-12-01

Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

NASA Astrophysics Data System (ADS)

Sayed, Gehad Ismail; Darwish, Ashraf; Hassanien, Aboul Ella

2018-03-01

Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO's performance.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

Shukla, P. K.; Mirza, Arshad M.; Faria, R. T.

1998-03-01

By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

Global chaotization of fluid particle trajectories in a sheared two-layer two-vortex flow.

PubMed

Ryzhov, Evgeny A; Koshel, Konstantin V

2015-10-01

In a two-layer quasi-geostrophic approximation, we study the irregular dynamics of fluid particles arising due to two interacting point vortices embedded in a deformation flow consisting of shear and rotational components. The two vortices are arranged within the bottom layer, but an emphasis is on the upper-layer fluid particle motion. Vortices moving in one layer induce stirring of passive scalars in the other layer. This is of interest since point vortices induce singular velocity fields in the layer they belong to; however, in the other layer, they induce regular velocity fields that generally result in a change in passive particle stirring. If the vortices are located at stagnation points, there are three different types of the fluid flow. We examine how properties of each flow configuration are modified if the vortices are displaced from the stagnation points and thus circulate in the immediate vicinity of these points. To that end, an analysis of the steady-state configurations is presented with an emphasis on the frequencies of fluid particle oscillations about the elliptic stagnation points. Asymptotic relations for the vortex and fluid particle zero-oscillation frequencies are derived in the vicinity of the corresponding elliptic points. By comparing the frequencies of fluid particles with the ones of the vortices, relations between the parameters that lead to enhanced stirring of fluid particles are established. It is also demonstrated that, if the central critical point is elliptic, then the fluid particle trajectories in its immediate vicinity are mostly stable making it harder for the vortex perturbation to induce stirring. Change in the type of the central point to a hyperbolic one enhances drastically the size of the chaotic dynamics region. Conditions on the type of the central critical point also ensue from the derived asymptotic relations.

Role of Orbital Dynamics in Spin Relaxation and Weak Antilocalization in Quantum Dots

NASA Astrophysics Data System (ADS)

Zaitsev, Oleg; Frustaglia, Diego; Richter, Klaus

2005-01-01

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.

Mixing and segregation of microspheres in microchannel flows of mono- and bidispersed suspensions

NASA Astrophysics Data System (ADS)

Gao, C.; Xu, B.; Gilchrist, J. F.

2009-03-01

We investigate the mixing and segregation of mono- and bidispersed microsphere suspensions in microchannel flows. These flows are common in biological microelectromechanical systems (BioMEMS) applications handling blood or suspensions of DNA. Suspension transport in pressure driven flows is significantly hindered by shear-induced migration, where particles migrate away from the walls and are focused in the center due to multibody hydrodynamic interactions. The microchannels used in this study have geometries that induce chaotic advection in Newtonian fluids. Our results show that mixing in straight, herringbone and staggered herringbone channels depends strongly on volume fraction. Due to this complex interplay of advection and shear-induced migration, a staggered herringbone channel that typically results in chaotic mixing is not always effective for dispersing particles. The maximum degree of segregation is observed in a straight channel once the maximum packing fraction is reached at channel center. We modify a one-dimensional suspension balance model [R. Miller and J. Morris, J. Non-Newtonian Fluid Mech. 135, 149 (2006)] to describe the behavior at the center of the straight channel. The degree of mixing is then calculated as a function of bulk volume fraction, predicting the volume fraction that results in the maximum degree of segregation. In bidispersed suspension flow, it is shown that mixing of the larger species is enhanced in straight and staggered herringbone channels while segregation is enhanced at moderate volume fractions in herringbone channels. This suggests mixing and separations can be tailored by adjusting both the suspension properties and the channel geometry.

A New Mixing Diagnostic and Gulf Oil Spill Movement

NASA Astrophysics Data System (ADS)

Mezić, Igor; Loire, S.; Fonoberov, Vladimir A.; Hogan, P.

2010-10-01

Chaotic advection has served as the paradigm for mixing in fluid flows with simple time dependence. Its skeletal structure is based on analysis of invariant attracting and repelling manifolds in fluid flows. Here we develop a finite-time theory for two-dimensional incompressible fluid flows with arbitrary time dependence and introduce a new mixing diagnostic based on it. Besides stretching events around attracting and repelling manifolds, this allows us to detect hyperbolic mixing zones. We used the new diagnostic to forecast the spatial location and timing of oil washing ashore in Plaquemines Parish and Grand Isle, Louisiana, and Pensacola, Florida, in May 2010 and the flow of oil toward Panama City Beach, Florida, in June 2010.

Analysis of chaotic saddles in a nonlinear vibro-impact system

NASA Astrophysics Data System (ADS)

Feng, Jinqian

2017-07-01

In this paper, a computational investigation of chaotic saddles in a nonlinear vibro-impact system is presented. For a classical Duffing vibro-impact oscillator, we employ the bisection procedure and an improved stagger-and-step method to present evidence of visual chaotic saddles on the fractal basin boundary and in the internal basin, respectively. The results show that the period saddles play an important role in the evolution of chaotic saddle. The dynamics mechanics of three types of bifurcation such as saddle-node bifurcation, chaotic saddle crisis bifurcation and interior chaotic crisis bifurcation are discussed. The results reveal that the period saddle created at saddle-node bifurcation is responsible for the switch of the internal chaotic saddle to the boundary chaotic saddle. At chaotic saddle crisis bifurcation, a large chaotic saddle can divide into two different chaotic saddle connected by a period saddle. The intersection points between stable and unstable manifolds of this period saddle supply access for chaotic orbits from one chaotic saddle to another and eventually induce the coupling of these two chaotic saddle. Interior chaotic crisis bifurcation is associated with the intersection of stable and unstable manifolds of the period saddle connecting two chaotic invariant sets. In addition, the gaps in chaotic saddle is responsible for the fractal structure.

Heteroclinic tangle phenomena in nanomagnets subject to time-harmonic excitations

NASA Astrophysics Data System (ADS)

Serpico, C.; Quercia, A.; Bertotti, G.; d'Aquino, M.; Mayergoyz, I.; Perna, S.; Ansalone, P.

2015-05-01

Magnetization dynamics in uniformly magnetized nanomagnets excited by time-harmonic (AC) external fields or spin-polarized injected currents is considered. The analysis is focused on the behaviour of the AC-excited dynamics near saddle equilibria. It turns out that this dynamics has a chaotic character at moderately low power level. This chaotic and fractal nature is due to the phenomenon of heteroclinic tangle which is produced by the combined effect of AC-excitations and saddle type dynamics. By using the perturbation technique based on Melnikov function, analytical formulas for the threshold AC excitation amplitudes necessary to create the heteroclinic tangle are derived. Both the cases of AC applied fields and AC spin-polarized injected currents are treated. Then, by means of numerical simulations, we show how heteroclinic tangle is accompanied by the erosion of the safe basin around the stable regimes.

A novel high-resolution chaotic lidar with optical injection to chaotic laser diode

NASA Astrophysics Data System (ADS)

Wang, Yun-cai; Wang, An-bang

2008-03-01

A novel chaotic lidar with high resolution is proposed and studied theoretically. In chaotic lidar system, the chaotic laser emitted from chaotic laser diode is split into two beams: the probe and the reference light. The ranging is achieved by correlating the reference waveform with the delayed probe waveform backscattered from the target. In chaotic lidar systems presented previously, the chaotic signal source is laser diode with optical feedback or with optical injection by another one. The ranging resolution is limited by the bandwidth of chaotic laser which determined by the configuration of chaotic signal source. We proposed a novel chaotic lidar which ranging resolution is enhanced significantly by external optical injected chaotic laser diode. With the bandwidth-enhanced chaotic laser, the range resolution of the chaotic lidar system with optical injection is roughly two times compared with that of without optical injection. The resolution increases with injection strength increasing in a certain frequency detuning range.

Recurrence Quantification of Fractal Structures

PubMed Central

Webber, Charles L.

2012-01-01

By definition, fractal structures possess recurrent patterns. At different levels repeating patterns can be visualized at higher magnifications. The purpose of this chapter is threefold. First, general characteristics of dynamical systems are addressed from a theoretical mathematical perspective. Second, qualitative and quantitative recurrence analyses are reviewed in brief, but the reader is directed to other sources for explicit details. Third, example mathematical systems that generate strange attractors are explicitly defined, giving the reader the ability to reproduce the rich dynamics of continuous chaotic flows or discrete chaotic iterations. The challenge is then posited for the reader to study for themselves the recurrent structuring of these different dynamics. With a firm appreciation of the power of recurrence analysis, the reader will be prepared to turn their sights on real-world systems (physiological, psychological, mechanical, etc.). PMID:23060808

Hamiltonian flows with random-walk behaviour originating from zero-sum games and fictitious play

NASA Astrophysics Data System (ADS)

van Strien, Sebastian

2011-06-01

In this paper we introduce Hamiltonian dynamics, inspired by zero-sum games (best response and fictitious play dynamics). The Hamiltonian functions we consider are continuous and piecewise affine (and of a very simple form). It follows that the corresponding Hamiltonian vector fields are discontinuous and multi-valued. Differential equations with discontinuities along a hyperplane are often called 'Filippov systems', and there is a large literature on such systems, see for example (di Bernardo et al 2008 Theory and applications Piecewise-Smooth Dynamical Systems (Applied Mathematical Sciences vol 163) (London: Springer); Kunze 2000 Non-Smooth Dynamical Systems (Lecture Notes in Mathematics vol 1744) (Berlin: Springer); Leine and Nijmeijer 2004 Dynamics and Bifurcations of Non-smooth Mechanical Systems (Lecture Notes in Applied and Computational Mechanics vol 18) (Berlin: Springer)). The special feature of the systems we consider here is that they have discontinuities along a large number of intersecting hyperplanes. Nevertheless, somewhat surprisingly, the flow corresponding to such a vector field exists, is unique and continuous. We believe that these vector fields deserve attention, because it turns out that the resulting dynamics are rather different from those found in more classically defined Hamiltonian dynamics. The vector field is extremely simple: outside codimension-one hyperplanes it is piecewise constant and so the flow phit piecewise a translation (without stationary points). Even so, the dynamics can be rather rich and complicated as a detailed study of specific examples show (see for example theorems 7.1 and 7.2 and also (Ostrovski and van Strien 2011 Regular Chaotic Dynf. 16 129-54)). In the last two sections of the paper we give some applications to game theory, and finish with posing a version of the Palis conjecture in the context of the class of non-smooth systems studied in this paper. To Jacob Palis on his 70th birthday.

Stochastic dynamics and combinatorial optimization

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Wang, Kang L.

2017-11-01

Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, etc., that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs) exhibiting this type of dynamics belong to the finite-width phase (N-phase for brevity) that precedes ordinary chaotic behavior and that is known under such names as noise-induced chaos, self-organized criticality, dynamical complexity, etc. Within the recently proposed supersymmetric theory of stochastic dynamics, the N-phase can be roughly interpreted as the noise-induced “overlap” between integrable and chaotic deterministic dynamics. As a result, the N-phase dynamics inherits the properties of the both. Here, we analyze this unique set of properties and conclude that the N-phase DSs must naturally be the most efficient optimizers: on one hand, N-phase DSs have integrable flows with well-defined attractors that can be associated with candidate solutions and, on the other hand, the noise-induced attractor-to-attractor dynamics in the N-phase is effectively chaotic or aperiodic so that a DS must avoid revisiting solutions/attractors thus accelerating the search for the best solution. Based on this understanding, we propose a method for stochastic dynamical optimization using the N-phase DSs. This method can be viewed as a hybrid of the simulated and chaotic annealing methods. Our proposition can result in a new generation of hardware devices for efficient solution of various search and/or combinatorial optimization problems.

Chaotic mixing in a planar, curved channel using periodic slip

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garg, P.; Picardo, J. R.; Pushpavanam, S., E-mail: spush@iitm.ac.in

2015-03-15

We propose a novel strategy for designing chaotic micromixers using curved channels confined between two flat planes. The location of the separatrix between the Dean vortices, induced by centrifugal forces, is dependent on the location of the maxima of axial velocity. An asymmetry in the axial velocity profile can change the location of the separatrix. This is achieved physically by introducing slip alternatingly at the top and bottom walls. This leads to streamline crossing and Lagrangian chaos. An approximate analytical solution of the velocity field is obtained using perturbation theory. This is used to find the Lagrangian trajectories of fluidmore » particles. Poincare sections taken at periodic locations in the axial direction are used to study the extent of chaos. We study two microchannel designs, called circlet and serpentine, in which the Dean vortices in adjacent half cells are co-rotating and counter-rotating, respectively. The extent of mixing, at low Re and low slip length, is shown to be greater in the serpentine case. Wide channels are observed to have much better mixing than tall channels; an important observation not made for separatrix flows till now. Eulerian indicators are used to gauge the extent of mixing, with varying slip length, and it is shown that an optimum slip length exists which maximizes the mixing in a particular geometry. Once the parameter space of relatively high mixing is identified, detailed variance computations are carried out to identify the detailed features.« less

Chaotic mixing in a planar, curved channel using periodic slip

NASA Astrophysics Data System (ADS)

Garg, P.; Picardo, J. R.; Pushpavanam, S.

2015-03-01

We propose a novel strategy for designing chaotic micromixers using curved channels confined between two flat planes. The location of the separatrix between the Dean vortices, induced by centrifugal forces, is dependent on the location of the maxima of axial velocity. An asymmetry in the axial velocity profile can change the location of the separatrix. This is achieved physically by introducing slip alternatingly at the top and bottom walls. This leads to streamline crossing and Lagrangian chaos. An approximate analytical solution of the velocity field is obtained using perturbation theory. This is used to find the Lagrangian trajectories of fluid particles. Poincare sections taken at periodic locations in the axial direction are used to study the extent of chaos. We study two microchannel designs, called circlet and serpentine, in which the Dean vortices in adjacent half cells are co-rotating and counter-rotating, respectively. The extent of mixing, at low Re and low slip length, is shown to be greater in the serpentine case. Wide channels are observed to have much better mixing than tall channels; an important observation not made for separatrix flows till now. Eulerian indicators are used to gauge the extent of mixing, with varying slip length, and it is shown that an optimum slip length exists which maximizes the mixing in a particular geometry. Once the parameter space of relatively high mixing is identified, detailed variance computations are carried out to identify the detailed features.

Flame dynamics in a micro-channeled combustor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hussain, Taaha; Balachandran, Ramanarayanan, E-mail: r.balachandran@ucl.ac.uk; Markides, Christos N.

2015-01-22

The increasing use of Micro-Electro-Mechanical Systems (MEMS) has generated a significant interest in combustion-based power generation technologies, as a replacement of traditional electrochemical batteries which are plagued by low energy densities, short operational lives and low power-to-size and power-to-weight ratios. Moreover, the versatility of integrated combustion-based systems provides added scope for combined heat and power generation. This paper describes a study into the dynamics of premixed flames in a micro-channeled combustor. The details of the design and the geometry of the combustor are presented in the work by Kariuki and Balachandran [1]. This work showed that there were different modesmore » of operation (periodic, a-periodic and stable), and that in the periodic mode the flame accelerated towards the injection manifold after entering the channels. The current study investigates these flames further. We will show that the flame enters the channel and propagates towards the injection manifold as a planar flame for a short distance, after which the flame shape and propagation is found to be chaotic in the middle section of the channel. Finally, the flame quenches when it reaches the injector slots. The glow plug position in the exhaust side ignites another flame, and the process repeats. It is found that an increase in air flow rate results in a considerable increase in the length (and associated time) over which the planar flame travels once it has entered a micro-channel, and a significant decrease in the time between its conversion into a chaotic flame and its extinction. It is well known from the literature that inside small channels the flame propagation is strongly influenced by the flow conditions and thermal management. An increase of the combustor block temperature at high flow rates has little effect on the flame lengths and times, whereas at low flow rates the time over which the planar flame front can be observed decreases and the time of existence of the chaotic flame increases. The frequency of re-ignition of successive flames decreases at higher flow rates and increases at higher temperatures. The data and results from this study will not only help the development of new micro-power generation devices, but they will also serve as a validation case for combustion models capable of predicting flame behavior in the presence of strong thermal and flow boundary layers, a situation common to many industrial applications.« less

Impacts of Non-Divergence-Free Flows on the Coalescence of Initially Distant Buoyant Scalars on a Turbulent Free Surface

NASA Astrophysics Data System (ADS)

Pratt, K.; Crimaldi, J. P.

2016-02-01

Lagrangian Coherent Structures (LCS) have been shown to play a predictive role in the coalescence of initially distant scalars in incompressible flows. Buoyant scalars on the free surface of a 3D incompressible turbulent fluid, however, are advected by a 2D compressible velocity field, resulting in scalar distributions that differ from those seen in a 2D incompressible flow. Our research uses both numerical and experimental approaches to investigate the coalescence of two initially distant reactive scalars to infer the impact of non-divergence-free behavior on buoyant scalar coalescence. Preliminary numerical results, utilizing incompressible and compressible chaotic 2D models, indicate that non-divergence-free behavior increases the likelihood of scalar coalescence and therefore enhances any interactions or reactions between the scalars. In addition, the shape and distribution of LCS is altered in compressible flows, which may explain the increased likelihood of scalar coalescence. Experimentally, we have constructed a 60 X 60 X 60 cm tank that generates three-dimensional turbulence via random pulsing of 36 jets on the tank bottom. Buoyant fluorescent red and green particles are used to quantify coalescence. Through the addition of a thin surfactant film on the free surface, results for incompressible flow cases are also obtained and directly compared to the compressible results. From these results, we hope to elucidate the role of free-surface flow on the coalescence of initially distant buoyant scalars, and extend these results to oceanic mixing problems, such as the transport of phytoplankton blooms and oil spills.

Classifying and quantifying basins of attraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprott, J. C.; Xiong, Anda

2015-08-15

A scheme is proposed to classify the basins for attractors of dynamical systems in arbitrary dimensions. There are four basic classes depending on their size and extent, and each class can be further quantified to facilitate comparisons. The calculation uses a Monte Carlo method and is applied to numerous common dissipative chaotic maps and flows in various dimensions.

A novel model for the chaotic dynamics of superdiffusion

NASA Astrophysics Data System (ADS)

Cushman, J. H.; Park, M.; O'Malley, D.

2009-04-01

Previously we've shown that by modeling the convective velocity in a turbulent flow field as Brownian, one obtains Richardson super diffusion where the expected distance between pairs of particles scales with time cubed. By proving generalized central limit type theorems it's possible to show that modeling the velocity or the acceleration as α-stable Levy gives rise to more general scaling laws that can easily explain other super diffusive regimes. The problem with this latter approach is that the mean square displacement of a particle is infinite. Here we provide an alternate approach that gives a power law mean square displacement of any desired order. We do so by constructing compressed and stretched extensions to Brownian motion. The finite size Lyapunov exponent, the underlying stochastic differential equation and its corresponding Fokker-Planck equations are derived. The fractal dimension of these processes turns out to be the same as that of classical Brownian motion.

Effect Of Molecular Rotations On High Intensity Absorption In CO2

NASA Astrophysics Data System (ADS)

Bandrauk, Andre D.; Claveau, Lorraine

1986-10-01

In intense fields, the Rabi frequency ωR = pE/h can easily be of the order of rotational and vibrational energies of molecules. This means that rotations as well as vibrations become strongly perturbed so that perturbative methods no longer apply. We will show that nonperturbative methods can be derived from the concept of the dressed molecule. This leads to coupled equations which are used ko simulate numerically the multiphoton processes which will occur at intensities > 108 W/cm2. Furthermore, for multiphoton rotational tran-sitions, one can derive analytical models which help one understand the temporal behaviour of energy flow in a molecule in terms of its dressed spectrum, such as chaotic or regular (nonchaotic) behaviour. These results are of relevance to the manifestation of multiphoton coherences in a CO2 spectrum at very high intensities (I % 1012 W/cm2).

Observation of optical solitons in PT-symmetric lattices

PubMed Central

Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf

2015-01-01

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated. PMID:26215165

Observation of optical solitons in PT-symmetric lattices

NASA Astrophysics Data System (ADS)

Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf

2015-07-01

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

Nonlinear dynamics and rheology of active fluids: simulations in two dimensions.

PubMed

Fielding, S M; Marenduzzo, D; Cates, M E

2011-04-01

We report simulations of a continuum model for (apolar, flow aligning) active fluids in two dimensions. Both free and anchored boundary conditions are considered, at parallel confining walls that are either static or moving at fixed relative velocity. We focus on extensile materials and find that steady shear bands, previously shown to arise ubiquitously in one dimension for the active nematic phase at small (or indeed zero) shear rate, are generally replaced in two dimensions by more complex flow patterns that can be stationary, oscillatory, or apparently chaotic. The consequences of these flow patterns for time-averaged steady-state rheology are examined. ©2011 American Physical Society

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

NASA Technical Reports Server (NTRS)

Helleman, R. H. G.

1980-01-01

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

Role of groundwater in formation of Martian channels

NASA Technical Reports Server (NTRS)

Howard, Alan D.

1991-01-01

A global 3-D model of groundwater flow has been used to study possible behavior of groundwater on Mars and its role in creating fluvial features. Conclusions drawn from an earlier 2-D groundwater model are supplemented and expanded. Topical headings are discussed as follows: timescales of groundwater flow; wet areas on Mars and location of outflow channels; implications for valley networks; the enigma of Hellas; absence of fluvial or periglacial features on Syrtis Major; development of chaotic terrain and associated outflow channels; and structurally controlled valley networks.

Periodicity and chaos from switched flow systems - Contrasting examples of discretely controlled continuous systems

NASA Technical Reports Server (NTRS)

Chase, Christopher; Serrano, Joseph; Ramadge, Peter J.

1993-01-01

We analyze two examples of the discrete control of a continuous variable system. These examples exhibit what may be regarded as the two extremes of complexity of the closed-loop behavior: one is eventually periodic, the other is chaotic. Our examples are derived from sampled deterministic flow models. These are of interest in their own right but have also been used as models for certain aspects of manufacturing systems. In each case, we give a precise characterization of the closed-loop behavior.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

NASA Astrophysics Data System (ADS)

Gros, J.-B.; Kuhl, U.; Legrand, O.; Mortessagne, F.

2016-03-01

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

Polariton Chimeras: Bose-Einstein Condensates with Intrinsic Chaoticity and Spontaneous Long-Range Ordering

NASA Astrophysics Data System (ADS)

Gavrilov, S. S.

2018-01-01

The system of cavity polaritons driven by a plane electromagnetic wave is found to undergo the spontaneous breaking of spatial symmetry, which results in a lifted phase locking with respect to the driving field and, consequently, in the possibility of internal ordering. In particular, periodic spin and intensity patterns arise in polariton wires; they exhibit strong long-range order and can serve as media for signal transmission. Such patterns have the properties of dynamical chimeras: they are formed spontaneously in perfectly homogeneous media and can be partially chaotic. The reported new mechanism of chimera formation requires neither time-delayed feedback loops nor nonlocal interactions.

Study of some chaotic inflationary models in f(R) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nawazish, Iqra

2018-04-01

In this paper, we discuss an inflationary scenario via scalar field and fluid cosmology for an anisotropic homogeneous universe model in f(R) gravity. We consider an equation of state which corresponds to a quasi-de Sitter expansion and investigate the effect of the anisotropy parameter for different values of the deviation parameter. We evaluate potential models like linear, quadratic and quartic models which correspond to chaotic inflation. We construct the observational parameters for a power-law model of f(R) gravity and construct the graphical analysis of tensor-scalar ratio and spectral index which indicates the consistency of these parameters with Planck 2015 data.

Epileptic Seizure Prediction Using a New Similarity Index for Chaotic Signals

NASA Astrophysics Data System (ADS)

Niknazar, Hamid; Nasrabadi, Ali Motie

Epileptic seizures are generated by abnormal activity of neurons. The prediction of epileptic seizures is an important issue in the field of neurology, since it may improve the quality of life of patients suffering from drug resistant epilepsy. In this study a new similarity index based on symbolic dynamic techniques which can be used for extracting behavior of chaotic time series is presented. Using Freiburg EEG dataset, it is found that the method is able to detect the behavioral changes of the neural activity prior to epileptic seizures, so it can be used for prediction of epileptic seizure. A sensitivity of 63.75% with 0.33 false positive rate (FPR) in all 21 patients and sensitivity of 96.66% with 0.33 FPR in eight patients were achieved using the proposed method. Moreover, the method was evaluated by applying on Logistic and Tent map with different parameters to demonstrate its robustness and ability in determining similarity between two time series with the same chaotic characterization.

Retrogressive failures recorded in mass transport deposits in the Ursa Basin, Northern Gulf of Mexico

NASA Astrophysics Data System (ADS)

Sawyer, Derek E.; Flemings, Peter B.; Dugan, Brandon; Germaine, John T.

2009-10-01

Clay-rich mass transport deposits (MTDs) in the Ursa Basin, Gulf of Mexico, record failures that mobilized along extensional failure planes and transformed into long runout flows. Failure proceeded retrogressively: scarp formation unloaded adjacent sediment causing extensional failure that drove successive scarp formation updip. This model is developed from three-dimensional seismic reflection data, core and log data from Integrated Ocean Drilling Project (IODP) Expedition 308, and triaxial shear experiments. MTDs are imaged seismically as low-amplitude zones above continuous, grooved, high-amplitude basal reflections and are characterized by two seismic facies. A Chaotic facies typifies the downdip interior, and a Discontinuous Stratified facies typifies the headwalls/sidewalls. The Chaotic facies contains discontinuous, high-amplitude reflections that correspond to flow-like features in amplitude maps: it has higher bulk density, resistivity, and shear strength, than bounding sediment. In contrast, the Discontinuous Stratified facies contains relatively dim reflections that abut against intact pinnacles of parallel-stratified reflections: it has only slightly higher bulk density, resistivity, and shear strength than bounding sediment, and deformation is limited. In both facies, densification is greatest at the base, resulting in a strong basal reflection. Undrained shear tests document strain weakening (sensitivity = 3). We estimate that failure at 30 meters below seafloor will occur when overpressure = 70% of the hydrostatic effective stress: under these conditions soil will liquefy and result in long runout flows.

Finite Larmor radius effects on weak turbulence transport

NASA Astrophysics Data System (ADS)

Kryukov, N.; Martinell, J. J.

2018-06-01

Transport of test particles in two-dimensional weak turbulence with waves propagating along the poloidal direction is studied using a reduced model. Finite Larmor radius (FLR) effects are included by gyroaveraging over one particle orbit. For low wave amplitudes the motion is mostly regular with particles trapped in the potential wells. As the amplitude increases the trajectories become chaotic and the Larmor radius modifies the orbits. For a thermal distribution of Finite Larmor radii the particle distribution function (PDF) is Gaussian for small th$ (thermal gyroradius) but becomes non-Gaussian for large th$ . However, the time scaling of transport is diffusive, as characterized by a linear dependence of the variance of the PDF with time. An explanation for this behaviour is presented that provides an expression for an effective diffusion coefficient and reproduces the numerical results for large wave amplitudes which implies generalized chaos. When a shear flow is added in the direction of wave propagation, a modified model is obtained that produces free-streaming particle trajectories in addition to trapped ones; these contribute to ballistic transport for low wave amplitude but produce super-ballistic transport in the chaotic regime. As in the previous case, the PDF is Gaussian for low th$ becoming non-Gaussian as it increases. The perpendicular transport presents the same behaviour as in the case with no flow but the diffusion is faster in the presence of the flow.

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

Virtual Libraries: Interactive Support Software and an Application in Chaotic Models.

ERIC Educational Resources Information Center

Katsirikou, Anthi; Skiadas, Christos; Apostolou, Apostolos; Rompogiannakis, Giannis

This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and…

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Using heteroclinic orbits to quantify topological entropy in fluid flows

NASA Astrophysics Data System (ADS)

Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.

2016-03-01

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or "ghost," rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Mathematical problems arising in interfacial electrohydrodynamics

NASA Astrophysics Data System (ADS)

Tseluiko, Dmitri

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order terms are need to be retained to regularize the problem in the sense that the long wave approximation remains valid for long times. For the case of a horizontal plane the fully nonlinear evolution equation which is derived at the leading order, is asymptotically correct and no regularization procedure is required. In both physical situations, the effect of the electric field is to introduce a non-local term which arises from the potential region above the liquid film, and enters through the electric Maxwell stresses at the interface. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cut-off, that is, all sufficiently short waves are linearly stable. For the case of film flow down an inclined plane, the fully nonlinear equation can produce singular solutions (for certain parameter values) after a finite time, even in the absence of an electric field. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations for a generalized class of modified KS equations. The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this, and a general conjecture is made based on extensive computations. We also carry out a complete study of the nonlinear behavior of competing physical mechanisms: long wave instability above a critical Reynolds number, short wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we elucidate parameter regimes that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow, which is known to be stable for this class of problems (an analogous statement holds for horizontally supported films also). Our theoretical results indicate that such highly stable flows can be rendered unstable by using electric fields. This opens the way for possible heat and mass transfer applications which can benefit significantly from interfacial oscillations and interfacial turbulence. For the case of a horizontal plane, a weakly nonlinear theory is not possible due to the absence of the shear flow generated by the gravitational force along the plate when the latter is inclined. We study the fully nonlinear equation, which in this case is asymptotically correct and is obtained at the leading order. The model equation describes both overlying and hanging films - in the former case gravity is stabilizing while in the latter it is destabilizing. The numerical and theoretical analysis of the fully nonlinear evolution is complicated by the fact that the coefficients of the highest order terms (surface tension in this instance) are nonlinear. We implement a fully implicit two level numerical scheme and perform numerical experiments. We also prove global boundedness of positive periodic smooth solutions, using an appropriate energy functional. This global boundedness result is seen in all our numerical results. Through a combination of analysis and extensive numerical experiments we present evidence for global existence of positive smooth solutions. This means, in turn, that the film does not touch the wall in finite time but asymptotically at infinite time. Numerical solutions are presented to support such phenomena.

Nonlinear stability of traffic models and the use of Lyapunov vectors for estimating the traffic state

NASA Astrophysics Data System (ADS)

Palatella, Luigi; Trevisan, Anna; Rambaldi, Sandro

2013-08-01

Valuable information for estimating the traffic flow is obtained with current GPS technology by monitoring position and velocity of vehicles. In this paper, we present a proof of concept study that shows how the traffic state can be estimated using only partial and noisy data by assimilating them in a dynamical model. Our approach is based on a data assimilation algorithm, developed by the authors for chaotic geophysical models, designed to be equivalent but computationally much less demanding than the traditional extended Kalman filter. Here we show that the algorithm is even more efficient if the system is not chaotic and demonstrate by numerical experiments that an accurate reconstruction of the complete traffic state can be obtained at a very low computational cost by monitoring only a small percentage of vehicles.

Emergent thermodynamics in a system of macroscopic, chaotic surface waves

NASA Astrophysics Data System (ADS)

Welch, Kyle J.

The properties of conventional materials are inextricably linked with their molecular composition; to make water flow like wine would require changing its molecular identity. To circumvent this restriction, I have constructed and characterized a two-dimensional metafluid, so-called because its constitutive dynamics are derived not from atoms and molecules but from macroscopic, chaotic surface waves excited on a vertically agitated fluid. Unlike in conventional fluids, the viscosity and temperature of this metafluid are independently tunable. Despite this unconventional property, our system is surprisingly consistent with equilibrium thermodynamics, despite being constructed from macroscopic, non-equilibrium elements. As a programmable material, our metafluid represents a new platform on which to study complex phenomena such as self-assembly and pattern formation. We demonstrate one such application in our study of short-chain polymer analogs embedded in our system.

Jet Engine Noise Reduction

DTIC Science & Technology

2009-04-01

greatest attention. 4 Excessive noise can cause temporary or permanent hearing loss or tinnitus , a constant ringing in the ear. In addition...industry effort focused on a ten-fold improvement in turbine engine affordable capability by the year 2017. This is following the model of the...exhibit a mix of chaotic and deterministic behavior . Although the governing equations describing fluid flows, the Navier Stokes equations, are based

How to test for partially predictable chaos.

PubMed

Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius

2017-04-24

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

Interfacial instability of wormlike micellar solutions sheared in a Taylor-Couette cell

NASA Astrophysics Data System (ADS)

Mohammadigoushki, Hadi; Muller, Susan J.

2014-11-01

We report experiments on wormlike micellar solutions sheared in a custom-made Taylor-Couette (TC) cell. The computer controlled TC cell allows us to rotate both cylinders independently. Wormlike micellar solutions containing water, CTAB, and NaNo3 with different compositions are highly elastic and exhibit shear banding. We visualized the flow field in the θ-z as well as r-z planes, using multiple cameras. When subject to low shear rates, the flow is stable and azimuthal, but becomes unstable above a certain threshold shear rate. This shear rate coincides with the onset of shear banding. Visualizing the θ-z plane shows that this instability is characterized by stationary bands equally spaced in the z direction. Increasing the shear rate results to larger wave lengths. Above a critical shear rate, experiments reveal a chaotic behavior reminiscent of elastic turbulence. We also studied the effect of ramp speed on the onset of instability and report an acceleration below which the critical Weissenberg number for onset of instability is unaffected. Moreover, visualizations in the r-z direction reveals that the interface between the two bands undulates with shear bands evolving towards the outer cylinder regardless of which cylinder is rotating.

Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Figueroa, Aldo; Meunier, Patrice; Villermaux, Emmanuel

2014-01-15

We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, “The diffusive strip method for scalar mixing in two-dimensions,” J. Fluid Mech. 662, 134–172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement withmore » quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors.« less

Improving degradation of emerging organic compounds by applying chaotic advection in Managed Aquifer Recharge in randomly heterogeneous porous media

NASA Astrophysics Data System (ADS)

Rodríguez-Escales, P.; Fernà ndez-Garcia, D.; Drechsel, J.; Folch, A.; Sanchez-Vila, X.

2017-05-01

Improving degradation rates of emerging organic compounds (EOCs) in groundwater is still a challenge. Although their degradation is not fully understood, it has been observed that some substances are preferably degraded under specific redox conditions. The coupling of Managed Aquifer Recharge with soil aquifer remediation treatment, by placing a reactive layer containing organic matter at the bottom of the infiltration pond, is a promising technology to improve the rate of degradation of EOCs. Its success is based on assuming that recharged water and groundwater get well mixed, which is not always true. It has been demonstrated that mixing can be enhanced by inducing chaotic advection through extraction-injection-engineering. In this work, we analyze how chaotic advection might enhance the spreading of redox conditions with the final aim of improving degradation of a mix of benzotriazoles: benzotriazole, 5-methyl-benzotriazole, and 5-chloro-benzotriazole. The degradation of the first two compounds was fastest under aerobic conditions whereas the third compound was best degraded under denitrification conditions. We developed a reactive transport model that describes how a recharged water rich in organic matter mixes with groundwater, how this organic matter is oxidized by different electron acceptors, and how the benzotriazoles are degraded attending for the redox state. The model was tested in different scenarios of recharge, both in homogenous and in heterogenous media. It was found that chaotic flow increases the spreading of the plume of recharged water. Consequently, different redox conditions coexist at a given time, facilitating the degradation of EOCs.

Investigations at berkeley on fracture flow in rocks: From the parallel plate model to chaotic systems

NASA Astrophysics Data System (ADS)

Witherspoon, Paul A.

This is a review of research at Berkeley over the past 35 years on characterization of fractured rocks and their hydrologic behavior when subjected to perturbations of various kinds. The parallel plate concept was useful as a first approach, but researchers have found that it has limitations when used to examine rough fractures and understand effects of aperture distributions on heterogeneous flow paths, especially when the fracture is deformed under stress. Results of investigations have been applied to fractured and faulted geothermal systems, where the inherent, nonisothermal conditions produce a different kind of perturbation. In 1977, the Stripa project in Sweden provided an unusual underground laboratory excavated in granite where new methods of investigating fractured rock were developed. New theoretical studies have been carried out on the fundamental role of heterogeneous flow paths in controlling fluid migration in fractured rocks. A major field study is now underway at the Yucca Mountain Project in Nevada, where a site for a radioactive waste repository may be constructed. The main effort has been to characterize the rock mass (fractured tuff) in sufficient detail so that a site scale model can be constructed and used to simulate operation of the repository. A new and entirely different problem has been identified through infiltration tests in the fractured basalt layers of the Eastern Snake River Plane in Idaho. Water flow through the unusual heterogeneities of these layers is so erratic that a model based on a hierarchy of scales is being investigated.

River flow prediction using hybrid models of support vector regression with the wavelet transform, singular spectrum analysis and chaotic approach

NASA Astrophysics Data System (ADS)

Baydaroğlu, Özlem; Koçak, Kasım; Duran, Kemal

2018-06-01

Prediction of water amount that will enter the reservoirs in the following month is of vital importance especially for semi-arid countries like Turkey. Climate projections emphasize that water scarcity will be one of the serious problems in the future. This study presents a methodology for predicting river flow for the subsequent month based on the time series of observed monthly river flow with hybrid models of support vector regression (SVR). Monthly river flow over the period 1940-2012 observed for the Kızılırmak River in Turkey has been used for training the method, which then has been applied for predictions over a period of 3 years. SVR is a specific implementation of support vector machines (SVMs), which transforms the observed input data time series into a high-dimensional feature space (input matrix) by way of a kernel function and performs a linear regression in this space. SVR requires a special input matrix. The input matrix was produced by wavelet transforms (WT), singular spectrum analysis (SSA), and a chaotic approach (CA) applied to the input time series. WT convolutes the original time series into a series of wavelets, and SSA decomposes the time series into a trend, an oscillatory and a noise component by singular value decomposition. CA uses a phase space formed by trajectories, which represent the dynamics producing the time series. These three methods for producing the input matrix for the SVR proved successful, while the SVR-WT combination resulted in the highest coefficient of determination and the lowest mean absolute error.

Proceedings of the Antenna Applications Symposium (1993). Volume 2,

DTIC Science & Technology

1994-02-01

Fig. 2). Even though Pwill can be computed accurately (Pial = PBWG - Pm), its field distribution and its chaotic behavior inside the lossy BWG is...34s""I+(n-1)M1)] (4) where M1 = K / N1. Since eq. (4) can be used to obtain the actual field, the time comsuming computation of matix [Y] need only be

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaojun; School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001; Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn

Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuousmore » change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.« less

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, L. H.; Xiang, Y. Y.; Dun, G. T.

The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaoticmore » attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.« less

Case study: Mapping tsunami hazards associated with debris flow into a reservoir

USGS Publications Warehouse

Walder, J.S.; Watts, P.; Waythomas, C.F.

2006-01-01

Debris-flow generated impulse waves (tsunamis) pose hazards in lakes, especially those used for hydropower or recreation. We describe a method for assessing tsunami-related hazards for the case in which inundation by coherent water waves, rather than chaotic splashing, is of primary concern. The method involves an experimentally based initial condition (tsunami source) and a Boussinesq model for tsunami propagation and inundation. Model results are used to create hazard maps that offer guidance for emergency planners and responders. An example application explores tsunami hazards associated with potential debris flows entering Baker Lake, a reservoir on the flanks of the Mount Baker volcano in the northwestern United States. ?? 2006 ASCE.

Disintegration of liquid sheets

NASA Technical Reports Server (NTRS)

Mansour, Adel; Chigier, Norman

1990-01-01

The development, stability, and disintegration of liquid sheets issuing from a two-dimensional air-assisted nozzle is studied. Detailed measurements of mean drop size and velocity are made using a phase Doppler particle analyzer. Without air flow the liquid sheet converges toward the axis as a result of surface tension forces. With airflow a quasi-two-dimensional expanding spray is formed. The air flow causes small variations in sheet thickness to develop into major disturbances with the result that disruption starts before the formation of the main break-up region. In the two-dimensional variable geometry air-blast atomizer, it is shown that the air flow is responsible for the formation of large, ordered, and small chaotic 'cell' structures.

A numerical simulation of finite-length Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Streett, C. L.; Hussaini, M. Y.

1987-01-01

The processes leading to laminar-turbulent transition in finite-channel-length Taylor-Couette flow are investigated analytically, solving the unsteady incompressible Navier-Stokes equations by spectral-collocation methods. A time-split algorithm, implementable in both axisymmetric and fully three-dimensional time-accurate versions, and an algorithm based on the staggered-mesh discretization of Bernardi and Maday (1986) are described in detail, and results obtained by applying the axisymmetric version of the first algorithm and a steady-state version of the second are presented graphically and compared with published experimental data. The feasibility of full three-dimensional simulations of the progression through chaotic states to turbulence under the constraints of Taylor-Couette flow is demonstrated.

Design of an Efficient Turbulent Micro-Mixer for Protein Folding Experiments

NASA Astrophysics Data System (ADS)

Inguva, Venkatesh; Perot, Blair

2015-11-01

Protein folding studies require the development of micro-mixers that require less sample, mix at faster rates, and still provide a high signal to noise ratio. Chaotic to marginally turbulent micro-mixers are promising candidates for this application. In this study, various turbulence and unsteadiness generation concepts are explored that avoid cavitation. The mixing enhancements include flow turning regions, flow splitters, and vortex shedding. The relative effectiveness of these different approaches for rapid micro-mixing is discussed. Simulations found that flow turning regions provided the best mixing profile. Experimental validation of the optimal design is verified through laser confocal microscopy experiments. This work is support by the National Science Foundation.

Rogue wave spectra of the Kundu-Eckhaus equation.

PubMed

Bayındır, Cihan

2016-06-01

In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.

Diffusion of chaotic field lines in tokamaks

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh

2006-10-01

An important instability for the destruction of magnetic surfaces in tokamaks due to island overlapping is the tearing modes. Magnetic fields perturbed by tearing modes are given by the sinusoidal form Br=-1rR∑m,nbm^n ( mθ-n ) . The sinusoidal nature of perturbation creates islands structure near resonant surfaces. In this work, we consider two modes, ( m1,n1 )and ( m2,n2 )that interact with each other, leading to two chains of islands, called primary islands. We use a previously derived Hamiltonian map, the ψ-θ map, with and without higher order control terms to study the diffusion of chaotic field lines. We will present and discuss the results of this work, and discuss its implications with regard to magnetic transport barriers for a fixed q-profile and increasing strength of magnetic perturbations. This work is done under the DOE grant number DE-FG02-01ER54624. 1.A. Punjabi et al, Phys. Rev. lett., 69, 3322 (1992). 2. H. Ali, A. Punjabi, and A. Boozer, Int. J. Comp. Num. Ana. Applications 6, 17 (2005).

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Breaking chaotic secure communication using a spectrogram

NASA Astrophysics Data System (ADS)

Yang, Tao; Yang, Lin-Bao; Yang, Chun-Mei

1998-10-01

We present the results of breaking a kind of chaotic secure communication system called chaotic switching scheme, also known as chaotic shift keying, in which a binary message signal is scrambled by two chaotic attractors. The spectrogram which can reveal the energy evolving process in the spectral-temporal space is used to distinguish the two different chaotic attractors, which are qualitatively and statistically similar in phase space. Then mathematical morphological filters are used to decode the binary message signal without the knowledge of the binary message signal and the transmitter. The computer experimental results are provided to show how our method works when both the chaotic and hyper-chaotic transmitter are used.

Nonlinear response of the immune system to power-frequency magnetic fields.

PubMed

Marino, A A; Wolcott, R M; Chervenak, R; Jourd'Heuil, F; Nilsen, E; Frilot, C

2000-09-01

Studies of the effects of power-frequency electromagnetic fields (EMFs) on the immune and other body systems produced positive and negative results, and this pattern was usually interpreted to indicate the absence of real effects. However, if the biological effects of EMFs were governed by nonlinear laws, deterministic responses to fields could occur that were both real and inconsistent, thereby leading to both types of results. The hypothesis of real inconsistent effects due to EMFs was tested by exposing mice to 1 G, 60 Hz for 1-105 days and observing the effect on 20 immune parameters, using flow cytometry and functional assays. The data were evaluated by means of a novel statistical procedure that avoided averaging away oppositely directed changes in different animals, which we perceived to be the problem in some of the earlier EMF studies. The reliability of the procedure was shown using appropriate controls. In three independent experiments involving exposure for 21 or more days, the field altered lymphoid phenotype even though the changes in individual immune parameters were inconsistent. When the data were evaluated using traditional linear statistical methods, no significant difference in any immune parameter was found. We were able to mimic the results by sampling from known chaotic systems, suggesting that deterministic chaos could explain the effect of fields on the immune system. We conclude that exposure to power-frequency fields produced changes in the immune system that were both real and inconsistent.

Classification of Arnold-Beltrami flows and their hidden symmetries

NASA Astrophysics Data System (ADS)

Fré, P.; Sorin, A. S.

2015-07-01

In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds ℳ3, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★ g d, which can be solved by using time-honored harmonic analysis. Taking for ℳ3, a torus T 3 constructed as ℝ3/Λ, where Λ is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B A of three-vectors in the momentum lattice *Λ. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group which contains all space groups as proper subgroups. We show that the ★ g d eigenfunctions are naturally arranged into irreducible representations of and by means of a systematic use of the branching rules with respect to various possible subgroups we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O24 and the Universal Classifying Group is a finite group G1536 of order |G1536| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G1536. In this way we obtain an exhaustive classification of all generalized ABC- flows and of their hidden symmetries. We make several conceptual comments about the need of a field-theory yielding Beltrami equation as a field equation and/or an instanton equation and on the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that are different from the non-linear one proposed by Arnold and possibly make contact with M-theory and the geometry of flux-compactifications.

Sedimentological and geochimical features of chaotic deposits in the Ventimiglia Flysch (Roya-Argentina valley- NW Italy)

NASA Astrophysics Data System (ADS)

Perotti, Elena; Bertok, Carlo; D'Atri, Anna; Martire, Luca; Musso, Alessia; Piana, Fabrizio; Varrone, Dario

2010-05-01

The Ventimiglia Flysch is a Upper Eocene turbidite succession deposited in the SE part of the Eocene Alpine foreland basin, truncated at the top by the basal thrust of the Helminthoides Flysch, a Ligurian tectonic unit that presently covers part of the Dauphinois and Briançonnais successions of Western Ligurian Alps. The Ventimiglia Flysch is made of alternations of sandstones and shales. The upper part is characterized by chaotic deposits. The chaotic deposits are constituted by: - km to hm-sized intrabasinal blocks (Ventimiglia Flysch) and extrabasinal blocks (Cretaceous sediments of Dauphinois Domain, Nummulite Limestone of the Alpine foreland basin and Helminthoides Flysch ); - conglomerates with block-in-matrix fabric interpreted as debris flow deposits. They occur as m-thick beds interbedded with the normal turbidite succession or locally as matrix of the larger blocks. Debris flow clasts show: - different sizes, ranging from metre to centimetre; - different shapes, from rounded to subangular; - different lithologies, such as fine-grained quartz-arenites, marls, dark shales and fine-grained calcisiltites. They may be referred to both coeval, intrabasinal lithologies (Ventimiglia Flysch), and extrabasinal formations (Nummulite Limestone, Globigerina Marl and Helminthoides Flysch). The clasts are disposed randomly into a chaotic matrix that consists of a dark mudstone in which submillimetre- to millimetre-sized lithic grains, with the same compositions of larger clasts, are present. Locally matrix consists of sandstones with quartz and feldspar grains and fragments of nummulitids that suggest reworking of unlithified Eocene sediments. Cathodoluminescence observations allow the distinction of two kinds of clasts: dull clasts that underwent a cementation before the formation of conglomerates, and clasts with the same orange luminescence as the matrix that may be interpreted as soft mud clasts that were cemented together with the matrix. Debris flow deposits are cross-cut by a network of crumpled and broken veins, 10's mm to cm-large, filled with orange luminescing calcite and locally with quartz. Their complex cross-cutting relationships with clasts and matrix show that several systems of veins are present, that may be referred to different fracturing events. Some clasts are crossed or bordered by veins that end at the edge of the clasts. These veins show the same features as those that crosscut the whole rock. This indicates reworking of plastic sediments crossed by calcite-filled veins by mass gravity flows. Polyphase debris flow processes, proceeding along with fluid expulsion and veining, are thus documented. Ellipsoidal, dm-large concretions of cemented pelites also occur. They represent a previous phase of concretionary growth within homogenous pelites subsequently involved in the mass gravity flow. Stable O and C isotope analyses, performed on matrix, clasts, concretions and veins, show: - δ13C close to normal marine values (-3 to 0 δ13C ‰ PDB) - δ18O markedly negative (-9 to -7 δ18O ‰ PDB) that could be related to precipitation from relatively hot waters (60-70 ° C). The block-in-matrix fabric and the variable composition and size of blocks show that these sediments are a sedimentary mélange related to mass wasting processes involving both extrabasinal and intrabasinal sediments. These gravitational movements took place along slopes of submarine tectonic ridges created by transpressional faults (Piana et al., 2009) that juxtaposed tectonic slices of different paleogeographic domains (Dauphinois, Briançonnais, Ligurian Units) in Late Eocene times, and involved both rock fall processes of huge blocks of lithified, older formations, and debris flows of unlithified intrabasinal sediment. Faults also acted as conduits for an upward flow of hot fluids supersaturated in calcium carbonate. These fluids crossed unlithified sediments close to the sea floor resulting in localized concretionary cementation and formation of vein swarms within unlithified sediments prone to subsequent mass wasting.

Statespace geometry of puff formation in pipe flow

NASA Astrophysics Data System (ADS)

Budanur, Nazmi Burak; Hof, Bjoern

2017-11-01

Localized patches of chaotically moving fluid known as puffs play a central role in the transition to turbulence in pipe flow. Puffs coexist with the laminar flow and their large-scale dynamics sets the critical Reynolds number: When the rate of puff splitting exceeds that of decaying, turbulence in a long pipe becomes sustained in a statistical sense. Since puffs appear despite the linear stability of the Hagen-Poiseuille flow, one expects them to emerge from the bifurcations of finite-amplitude solutions of Navier-Stokes equations. In numerical simulations of pipe flow, Avila et al., discovered a pair of streamwise localized relative periodic orbits, which are time-periodic solutions with spatial drifts. We combine symmetry reduction and Poincaré section methods to compute the unstable manifolds of these orbits, revealing statespace structures associated with different stages of puff formation.

Microelectrokinetic turbulence in microfluidics at low Reynolds number.

PubMed

Wang, Guiren; Yang, Fang; Zhao, Wei

2016-01-01

There is commonly no turbulence in microfluidics, and the flows are believed to be either laminar or chaotic, since Reynolds number (Re) in microflows is usually on the order of unity or lower. However, we recently demonstrated that it is possible to achieve turbulence with low Re (based on the measured flow velocity and the width of the channel entrance) when a pressure-driven flow is electrokinetically forced in a quasi T-microchannel. To be able to measure high frequency velocity fluctuations in microchannels, a velocimeter with submicrometer spatial resolution and microsecond temporal resolution, called a laser-induced fluorescence photobleaching anemometer, is developed. Here we characterize the microelectrokinetic turbulence and observe some typical and important features of high Re flows, such as Kolmogorov -5/3 spectrum of velocity fluctuation, which usually can be realized only at very high Re in macroturbulent flows.

Novel design and fabrication of a geometrical obstacle-embedded micromixer with notched wall

NASA Astrophysics Data System (ADS)

Wu, Shih-Jeh; Hsu, Hsiang-Chen; Feng, Wen-Jui

2014-09-01

A microfluidic embedded MEMS mixer with a Y-junction type channel and cylindrical obstructions was designed and fabricated for improving the fluid mixing mechanism under low Reynolds number (\\mathit{Re}) condition. The flow field was simulated numerically by software (COMSOL multiphysics®) first. The design was then realized through casting the device in PDMS by lithographed SU-8 photo-resistive mold on silicon wafer. Parametric experimental studies were conducted for optimal design. Two different fluids were pumped into the two legs of the Y-junction channel, and the fluids were broken-up by an embedded cylindrical obstacle in the middle of the tapered micro-channel. The chaotic convection took place in the mixing channel behind the embedded cylindrical obstacles. The flow motion was observed under CCD camera and analyzed by grey level. The developed micromixer in this study can enhance the fluid mixing by the interaction of diffusion and convection for wide range of Reynolds numbers (0.01 < \\mathit{Re} < 100). Experimental results showed that the mixing index reached the required value at 0.1 within 0.024 seconds when the inlet fluid velocity is 0.499 m/s (i.e., at 1200 µl/min flow rate) for merely four cylindrical obstacles. A shorter mixing distance can be accomplished compared to the current devices reported due to faster mixing and shorter mixing time.

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices

PubMed Central

Wang, Shau-Chun; Chen, Hsiao-Ping; Lai, Yi-Wen; Chau, Lai-Kwan; Chuang, Yu-Chun; Chen, Yi-Jie

2007-01-01

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate Nα-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cm∕s, are generated around a small (∼1.2 mm) conductive ion exchange granule when ac electric fields (133 V∕cm) are applied across a miniature chamber smaller than 10 μl. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of ∼30 and ∼8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate. PMID:19693360

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices.

PubMed

Wang, Shau-Chun; Chen, Hsiao-Ping; Lai, Yi-Wen; Chau, Lai-Kwan; Chuang, Yu-Chun; Chen, Yi-Jie

2007-09-04

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate N(alpha)-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cms, are generated around a small ( approximately 1.2 mm) conductive ion exchange granule when ac electric fields (133 Vcm) are applied across a miniature chamber smaller than 10 mul. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of approximately 30 and approximately 8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate.

Slump dominated upper slope reservoir facies, Intra Qua Iboe (Pliocene), Edop Field, offshore Nigeria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shanmugam, G.; Hermance, W.E.; Olaifa, J.O.

An integration of sedimentologic and 3D seismic data provides a basis for unraveling complex depositional processes and sand distribution of the Intra Qua Iboe (IQI) reservoir (Pliocene), Edop Field, offshore Nigeria. Nearly 3,000 feet of conventional core was examined in interpreting slump/slide/debris flow, bottom current, turbidity current, pelagic/hemipelagic, wave and tide dominated facies. The IQI was deposited on an upper slope in close proximity to the shelf edge. Through time, as the shelf edge migrated seaward, deposition began with a turbidite channel dominated slope system (IQI 1 and 2) and progressed through a slump/debris flow dominated slope system (IQI 3,more » the principal reservoir) to a tide and wave dominated, collapsed shelf-edge deltaic system (IQI 4). Using seismic time slices and corresponding depositional facies in the core, a sandy {open_quotes}fairway{open_quotes} has been delineated in the IQI 3. Because of differences in stacking patterns of sandy and muddy slump intervals, seismic facies show: (1) both sheet-like and mounded external forms (geometries), and (2) parallel/continuous as well as chaotic/hummocky internal reflections. In wireline logs, slump facies exhibits blocky, coarsening-up, fining-up, and serrated motifs. In the absence of conventional core, slump facies may be misinterpreted and even miscorrelated because seismic facies and log motifs of slumps and debris flows tend to mimic properties of turbidite fan deposits. The slump dominated reservoir facies is composed of unconsolidated fine-grained sand. Thickness of individual units varies from 1 to 34 feet, but amalgamated intervals reach a thickness of up to 70 feet and apparently form connected sand bodies. Porosity commonly ranges from 20 to 35%. Horizontal permeability commonly ranges from 1,000 to 3,000 md.« less

Internally driven inertial waves in geodynamo simulations

NASA Astrophysics Data System (ADS)

Ranjan, A.; Davidson, P. A.; Christensen, U. R.; Wicht, J.

2018-05-01

Inertial waves are oscillations in a rotating fluid, such as the Earth's outer core, which result from the restoring action of the Coriolis force. In an earlier work, it was argued by Davidson that inertial waves launched near the equatorial regions could be important for the α2 dynamo mechanism, as they can maintain a helicity distribution which is negative (positive) in the north (south). Here, we identify such internally driven inertial waves, triggered by buoyant anomalies in the equatorial regions in a strongly forced geodynamo simulation. Using the time derivative of vertical velocity, ∂uz/∂t, as a diagnostic for traveling wave fronts, we find that the horizontal movement in the buoyancy field near the equator is well correlated with a corresponding movement of the fluid far from the equator. Moreover, the azimuthally averaged spectrum of ∂uz/∂t lies in the inertial wave frequency range. We also test the dispersion properties of the waves by computing the spectral energy as a function of frequency, ϖ, and the dispersion angle, θ. Our results suggest that the columnar flow in the rotation-dominated core, which is an important ingredient for the maintenance of a dipolar magnetic field, is maintained despite the chaotic evolution of the buoyancy field on a fast timescale by internally driven inertial waves.

Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Linde, Andrei

2015-02-23

I describe the first model of chaotic inflation in supergravity, which was proposed by Goncharov and the present author in 1983. The inflaton potential of this model has a plateau-type behavior V{sub 0}(1−(8/3) e{sup −√6|ϕ|}) at large values of the inflaton field. This model predicts n{sub s}=1−(2/N)≈0.967 and r=(4/(3N{sup 2}))≈4×10{sup −4}, in good agreement with the Planck data. I propose a slight generalization of this model, which allows to describe not only inflation but also dark energy and supersymmetry breaking.

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior

PubMed Central

da Cunha, C. R.; Mineharu, M.; Matsunaga, M.; Matsumoto, N.; Chuang, C.; Ochiai, Y.; Kim, G.-H.; Watanabe, K.; Taniguchi, T.; Ferry, D. K.; Aoki, N.

2016-01-01

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene. PMID:27609184

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior.

PubMed

da Cunha, C R; Mineharu, M; Matsunaga, M; Matsumoto, N; Chuang, C; Ochiai, Y; Kim, G-H; Watanabe, K; Taniguchi, T; Ferry, D K; Aoki, N

2016-09-09

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

Hybrid electronic/optical synchronized chaos communication system.

PubMed

Toomey, J P; Kane, D M; Davidović, A; Huntington, E H

2009-04-27

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows.

PubMed

Manneville, Paul

2009-02-01

By use of a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-->laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number Rlow, whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond Rlow.

Terminal Model Of Newtonian Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

Investigating transport pathways in the ocean

NASA Astrophysics Data System (ADS)

Griffa, Annalisa; Haza, Angelique; Özgökmen, Tamay M.; Molcard, Anne; Taillandier, Vincent; Schroeder, Katrin; Chang, Yeon; Poulain, P.-M.

2013-01-01

The ocean is a very complex medium with scales of motion that range from thousands of kilometers to the dissipation scales. Transport by ocean currents plays an important role in many practical applications ranging from climatic problems to coastal management and accident mitigation at sea. Understanding transport is challenging because of the chaotic nature of particle motion. In the last decade, new methods have been put forth to improve our understanding of transport. Powerful tools are provided by dynamical system theory, that allow the identification of the barriers to transport and their time variability for a given flow. A shortcoming of this approach, though, is that it is based on the assumption that the velocity field is known with good accuracy, which is not always the case in practical applications. Improving model performance in terms of transport can be addressed using another important methodology that has been recently developed, namely the assimilation of Lagrangian data provided by floating buoys. The two methodologies are technically different but in many ways complementary. In this paper, we review examples of applications of both methodologies performed by the authors in the last few years, considering flows at different scales and in various ocean basins. The results are among the very first examples of applications of the methodologies to the real ocean including testing with Lagrangian in-situ data. The results are discussed in the general framework of the extended fields related to these methodologies, pointing out to open questions and potential for improvements, with an outlook toward future strategies.

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Plastic dynamics of the Al0.5CoCrCuFeNi high entropy alloy at cryogenic temperatures: Jerky flow, stair-like fluctuation, scaling behavior, and non-chaotic state

NASA Astrophysics Data System (ADS)

Guo, Xiaoxiang; Xie, Xie; Ren, Jingli; Laktionova, Marina; Tabachnikova, Elena; Yu, Liping; Cheung, Wing-Sum; Dahmen, Karin A.; Liaw, Peter K.

2017-12-01

This study investigates the plastic behavior of the Al0.5CoCrCuFeNi high-entropy alloy at cryogenic temperatures. The samples are uniaxially compressed at 4.2 K, 7.5 K, and 9 K. A jerky evolution of stress and stair-like fluctuation of strain are observed during plastic deformation. A scaling relationship is detected between the released elastic energy and strain-jump sizes. Furthermore, the dynamical evolution of serrations is characterized by the largest Lyapunov exponent. The largest Lyapunov exponents of the serrations at the three temperatures are all negative, which indicates that the dynamical regime is non-chaotic. This trend reflects an ordered slip process, and this ordered slip process exhibits a more disordered slip process, as the temperature decreases from 9 K to 4.2 K or 7.5 K.

A model for seasonal phytoplankton blooms.

PubMed

Huppert, Amit; Blasius, Bernd; Olinky, Ronen; Stone, Lewi

2005-10-07

We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time-series. Instead the model has a tendency to 'skip' with outbreaks often being suppressed from 1 year to the next. This behaviour is studied in detail and we develop analytical expressions to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics.

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp; Yamada, Michio; Chian, Abraham C.-L.

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originatemore » from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.« less

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

PubMed

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

2015-10-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-06-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-03-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Pulsatile flow in a compliant stenosed asymmetric model

NASA Astrophysics Data System (ADS)

Usmani, Abdullah Y.; Muralidhar, K.

2016-12-01

Time-varying velocity field in an asymmetric constricted tube is experimentally studied using a two-dimensional particle image velocimetry system. The geometry resembles a vascular disease which is characterized by arterial narrowing due to plaque deposition. The present study compares the nature of flow patterns in rigid and compliant asymmetric constricted tubes for a range of dimensionless parameters appearing in a human artery. A blood analogue fluid is employed along with a pump that mimics cardioflow conditions. The peak Reynolds number range is Re 300-800, while the Womersley number range considered in experiments is Wo 6-8. These values are based on the peak velocity in a straight rigid tube connected to the model, over a pulsation frequency range of 1.2-2.4 Hz. The medial-plane velocity distribution is used to investigate the nature of flow patterns. Temporal distribution of stream traces and hemodynamic factors including WSS, TAWSS and OSI at important phases of the pulsation cycle are discussed. The flow patterns obtained from PIV are compared to a limited extent against numerical simulation. Results show that the region downstream of the constriction is characterized by a high-velocity jet at the throat, while a recirculation zone, attached to the wall, evolves in time. Compliant models reveal large flow disturbances upstream during the retrograde flow. Wall shear stress values are lower in a compliant model as compared to the rigid. Cross-plane flow structures normal to the main flow direction are visible at select phases of the cycle. Positive values of largest Lyapunov exponent are realized for wall movement and are indicative of chaotic motion transferred from the flow to the wall. These exponents increase with Reynolds number as well as compliance. Period doubling is observed in wall displacement of highly compliant models, indicating possible triggering of hemodynamic events in a real artery that may cause fissure in the plaque deposits.

Perception-action map learning in controlled multiscroll systems applied to robot navigation.

PubMed

Arena, Paolo; De Fiore, Sebastiano; Fortuna, Luigi; Patané, Luca

2008-12-01

In this paper a new technique for action-oriented perception in robots is presented. The paper starts from exploiting the successful implementation of the basic idea that perceptual states can be embedded into chaotic attractors whose dynamical evolution can be associated with sensorial stimuli. In this way, it can be possible to encode, into the chaotic dynamics, environment-dependent patterns. These have to be suitably linked to an action, executed by the robot, to fulfill an assigned mission. This task is addressed here: the action-oriented perception loop is closed by introducing a simple unsupervised learning stage, implemented via a bio-inspired structure based on the motor map paradigm. In this way, perceptual meanings, useful for solving a given task, can be autonomously learned, based on the environment-dependent patterns embedded into the controlled chaotic dynamics. The presented framework has been tested on a simulated robot and the performance have been successfully compared with other traditional navigation control paradigms. Moreover an implementation of the proposed architecture on a Field Programmable Gate Array is briefly outlined and preliminary experimental results on a roving robot are also reported.

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Santana, W. M.; Rempel, E. L.; Borotto, F. A.; Hada, T.; Kamide, Y.

2007-01-01

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

Influence of Landscape Morphology and Vegetation Cover on the Sampling of Mixed Igneous Bodies

NASA Astrophysics Data System (ADS)

Perugini, Diego; Petrelli, Maurizio; Poli, Giampiero

2010-05-01

A plethora of evidence indicates that magma mixing processes can take place at any evolutionary stage of magmatic systems and that they are extremely common in both plutonic and volcanic environments (e.g. Bateman, 1995). Furthermore, recent studies have shown that the magma mixing process is governed by chaotic dynamics whose evolution in space and time generates complex compositional patterns that can span several length scales producing fractal domains (e.g. Perugini et al., 2003). The fact that magma mixing processes can produce igneous bodies exhibiting a large compositional complexity brings up the key question about the potential pitfalls that may be associated with the sampling of these systems for petrological studies. In particular, since commonly only exiguous portions of the whole magmatic system are available as outcrops for sampling, it is important to address the point whether the sampling may be considered representative of the complexity of the magmatic system. We attempt to address this crucial point by performing numerical simulations of chaotic magma mixing processes in 3D. The numerical system used in the simulations is the so-called ABC (Arnold-Beltrami-Childress) flow (e.g. Galluccio and Vulpiani, 1994), which is able to generate the contemporaneous occurrence of chaotic and regular streamlines in which the mixing efficiency is differently modulated. This numerical system has already been successfully utilized as a kinematic template to reproduce magma mixing structures observed on natural outcrops (Perugini et al., 2007). The best conditions for sampling are evaluated considering different landscape morphologies and percentages of vegetation cover. In particular, synthetic landscapes with different degree of roughness are numerically reproduced using the Random Mid-point Displacement Method (RMDM; e.g. Fournier et al., 1982) in two dimensions and superimposed to the compositional fields generated by the magma mixing simulation. Vegetation cover is generated using a random Brownian motion process in 2D. Such an approach allows us to produce vegetation patches that closely match the general topology of natural vegetation (e.g., Mandelbrot, 1982). Results show that the goodness of sampling is strongly dependant on the roughness of the landscape, with highly irregular morphologies being the best candidates to give the most complete information on the whole magma body. Conversely, sampling on flat or nearly flat surfaces should be avoided because they may contain misleading information about the magmatic system. Contrary to common sense, vegetation cover does not appear to significantly influence the representativeness of sampling if sample collection occurs on topographically irregular outcrops. Application of the proposed method for sampling area selection is straightforward. The irregularity of natural landscapes and the percentage of vegetation can be estimated by using natural landscapes extracted from digital elevation models (DEM) of the Earth's surface and satellite images by employing a variety of methods (e.g., Develi and Babadagli, 1998), thus giving one the opportunity to select a priori the best outcrops for sampling. References Bateman R (1995) The interplay between crystallization, replenishment and hybridization in large felsic magma chambers. Earth Sci Rev 39: 91-106 Develi K, Babadagli T (1998) Quantfication of natural fracture surfaces using fractal geometry. Math Geol 30: 971-998 Fournier A, Fussel D, Carpenter L (1982) Computer rendering of stochastic models. Comm ACM 25: 371-384 Galluccio S, Vulpiani A (1994) Stretching of material lines and surfaces in systems with Lagrangian chaos. Physica A 212: 75-98 Mandelbrot BB (1982) The fractal geometry of nature. W. H. Freeman, San Francisco Perugini D, Petrelli M, Poli G (2007) A Virtual Voyage through 3D Structures Generated by Chaotic Mixing of Magmas and Numerical Simulations: a New Approach for Understanding Spatial and Temporal Complexity of Magma Dynamics, Visual Geosciences, 10.1007/s10069-006-0004-x Perugini D, Poli G, Mazzuoli R (2003) Chaotic advection, fractals and diffusion during mixing of magmas: evidences from lava flows. J Volcanol Geotherm Res 124: 255-279

Chaotic gas turbine subject to augmented Lorenz equations.

PubMed

Cho, Kenichiro; Miyano, Takaya; Toriyama, Toshiyuki

2012-09-01

Inspired by the chaotic waterwheel invented by Malkus and Howard about 40 years ago, we have developed a gas turbine that randomly switches the sense of rotation between clockwise and counterclockwise. The nondimensionalized expressions for the equations of motion of our turbine are represented as a starlike network of many Lorenz subsystems sharing the angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We show qualitative similarities between the statistical properties of the angular velocity of the turbine rotor and the velocity field of large-scale wind in turbulent Rayleigh-Bénard convection reported by Sreenivasan et al. [Phys. Rev. E 65, 056306 (2002)]. Our equations of motion achieve the random reversal of the turbine rotor through the stochastic resonance of the angular velocity in a double-well potential and the force applied by rapidly oscillating fields. These results suggest that the augmented Lorenz model is applicable as a dynamical model for the random reversal of turbulent large-scale wind through cessation.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

Nonguiding Center Motion and Substorm Effects in the Magnetotail

NASA Technical Reports Server (NTRS)

Kaufmann, Richard L.; Kontodinas, Ioannis D.; Ball, Bryan M.; Larson, Douglas J.

1997-01-01

Thick and thin models of the middle magnetotail were developed using a consistent orbit tracing technique. It was found that currents carried near the equator by groups of ions with anisotropic distribution functions are not well approximated by the guiding center expressions. The guiding center equations fail primarily because the calculated pressure tensor is not magnetic field aligned. The pressure tensor becomes field aligned as one moves away from the equator, but here there is a small region in which the guiding center equations remain inadequate because the two perpendicular components of the pressure tensor are unequal. The significance of nonguiding center motion to substorm processes then was examined. One mechanism that may disrupt a thin cross-tail current sheet involves field changes that cause ions to begin following chaotic orbits. The lowest-altitude chaotic region, characterized by an adiabaticity parameter kappa approx. equal to 0.8, is especially important. The average cross-tail particle drift is slow, and we were unable to generate a thin current sheet using such ions. Therefore, any process that tends to create a thin current sheet in a region with kappa approaching 0.8 may cause the cross-tail current to get so low that it becomes insufficient to support the lobes. A different limit may be important in resonant orbit regions of a thin current sheet because particles reach a maximum cross-tail drift velocity. If the number of ions per unit length decreases as the tail is stretched, this part of the plasma sheet also may become unable to carry the cross-tail current needed to support the lobes. Thin sheets are needed for both resonant and chaotic orbit mechanisms because the distribution function must be highly structured. A description of current continuity is included to show how field aligned currents can evolve during the transition from a two-dimensional (2-D) to a 3-D configuration.

Comparisons of the hydraulics of water flows in Martian outflow channels with flows of similar scale on earth

NASA Technical Reports Server (NTRS)

Komar, P. D.

1979-01-01

The hydraulics of channelized water flows on Mars and the resulting sediment transport rates are calculated, and similar computations are performed for such terrestrial analogs as the Mississippi River and the catastrophic Lake Missoula floods that formed the Channeled Scabland in eastern Washington State. The morphologies of deep-sea channels formed by catastrophic turbidity currents are compared with the Martian channels, many similarities are pointed out, and the hydraulics of the various flows are compared. The results indicate that the velocities, discharges, bottom shear stresses, and sediment-transport capacity of water flows along the Martian channels would be comparable to those of the oceanic turbidity currents and the Lake Missoula floods. It is suggested that the submarine canyons from which turbidity currents originate are the terrestrial counterparts to the chaotic-terrain areas or craters that serve as sources for many of the Martian channels.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sattari, Sulimon, E-mail: ssattari2@ucmerced.edu; Chen, Qianting, E-mail: qchen2@ucmerced.edu; Mitchell, Kevin A., E-mail: kmitchell@ucmerced.edu

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding ofmore » ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.« less

Modeling microflow and stirring around a microrotor in creeping flow using a quasi-steady-state analysis.

PubMed

Vuppu, Anil K; Garcia, Antonio A; Saha, Sanjoy K; Phelan, Patrick E; Hayes, Mark A; Calhoun, Ronald

2004-06-01

The microflow and stirring around paramagnetic particle microchains, referred to as microrotors, are modeled as a circular cylinder rotating about its radial axis at very low Reynolds number. Time scales for momentum transfer under these conditions are determined to be much smaller than those for boundary movement, hence a quasi-steady approximation can be used. The flow is derived at every instant from the case of a steady motion of a horizontally translating cylinder, with the rotation approximated to a series of differential incremental translations. A numerical simulation is used to determine the pathlines and material lines of virtual point fluid elements, which were analyzed to understand the behavior of the flow around the microrotor. The results indicate the flow to be unsteady, with chaotic advection observed in the system. The fluid motion is primarily two-dimensional, parallel to the rotational plane, with mixing limited to the immediate area around the rotating cylinder. Fluid layers, up to many cylinder diameters, in the axial direction experience the disturbance. Elliptic and star shaped pathlines, including periodic orbits, are observed depending on the fluid element's initial location. The trajectories and phase angles compare well with the experimental results, as well as with data from particle dynamics simulations. Material lines and streaklines display stretching and folding, which are indicative of the chaotic behavior and stirring characteristics of the system. The material lines have similar lengths for the same amount of rotation at different speeds, and the effect of rotational speeds appears to be primarily to change the time of mixing. The results are expected to help in the design of a particle microrotor based sensing technique.

Understanding the Chaotic Behavior of Field Lines using the Simple Map

NASA Astrophysics Data System (ADS)

Saralkar, R.; White, C.; Ali, H.; Punjabi, A.

1998-11-01

The Simple Map is given by x_n+1=x_n-ky_n(1-y_n), y_n+1=y_n+kx_n+1. Different initial values of x and y create different surfaces. We can see at what point the order begins to fade, at what point the surface breaks up and islands form, and at what point chaos occurs. The outer surfaces are chaotic as expected because the plasma is nearing the X-point in the tokamak, where the order begins to break up. We are specifically investigating two areas of the Simple Map. First we want to see what ther surfaces look like if they are magnified near the X-point. We are looking for self-similar structures in which order can be found in chaos, and chaos can be found in order. Our second investigation deals with how neighboring field lines separate in the chaotic region. We are expecting to see the distance between two close points drastically increase as we near the X-point. Reshama Saralkar and Cedric White are HU CFRT 1998 Summer Fusion High School Workshop Participants from the NASA SHARP PLUS Program. RS attends Watkins Mill High School in Gaithersburg, MD. CW attends Gwynn Park High School in Brandywine,MD. They are mentored by Dr. Ali and Dr. Punjabi of HU CFRT. 1. Punjabi et al, Phys Rev Lett 69 3322 (1992) 2. Punjabi et al, J Plasma Phys 52 91 (1994)

New Optical Field Generated by Partial Tracing Over Two-Mode Squeezing-Rotating Entangled Vacuum State ^{{*}}

NASA Astrophysics Data System (ADS)

Ren, Gang; Du, Jian-ming; Zhang, Wen-Hai

2018-05-01

Based on the two-mode squeezing-rotating entangled vacuum state (Fan and Fan in Commun Theor Phys 33:701-704, 2000), we obtained a new quantum state by using partial tracing method. This new state can be considered as a real chaotic field. We also studied its squeezing properties and quantum statistical properties by giving the analytic results and exact numerical results. It was established that the rotation angle's parameter plays an important role in this new optical field.

Application of Chaos Theory to 1/f Noise

DTIC Science & Technology

1988-02-12

recently, we lacked the mathematical sophistication to analyze chaotic behavior. However, that situation is changing rapidly. We are now beginning to...along with nonlinear coupling between dependent variables. Linked with the notion of chaos is a mathematical construct known as a "strange attractor". 11...flow 12 S as the Reynolds number, Re, is increased above some critical value. We can observe this transition in the mathematics by watching the

Vesicle dynamics in a confined Poiseuille flow: from steady state to chaos.

PubMed

Aouane, Othmane; Thiébaud, Marine; Benyoussef, Abdelilah; Wagner, Christian; Misbah, Chaouqi

2014-09-01

Red blood cells (RBCs) are the major component of blood, and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: (i) the degree of confinement of vesicles within the channel and (ii) the flow strength. Rich and complex dynamics for vesicles are revealed, ranging from steady-state shapes (in the form of parachute and slipper shapes) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple periodic oscillations of the vesicle shape. We summarize our results in a phase diagram in the parameter plane (degree of confinement and flow strength). This finding highlights the level of complexity of a flowing vesicle in the small Reynolds number where the flow is laminar in the absence of vesicles and can be rendered turbulent due to elasticity of vesicles.

Periodic orbit analysis of a system with continuous symmetry--A tutorial.

PubMed

Budanur, Nazmi Burak; Borrero-Echeverry, Daniel; Cvitanović, Predrag

2015-07-01

Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid in terms of a Fourier series truncated to a finite number of modes. Here, we study a 4-dimensional model with chaotic dynamics and SO(2) symmetry similar to those that appear in fluid dynamics problems. A crucial step in the analysis of such a system is symmetry reduction. We use the model to illustrate different symmetry-reduction techniques. The system's relative equilibria are conveniently determined by rewriting the dynamics in terms of a symmetry-invariant polynomial basis. However, for the analysis of its chaotic dynamics, the "method of slices," which is applicable to very high-dimensional problems, is preferable. We show that a Poincaré section taken on the "slice" can be used to further reduce this flow to what is for all practical purposes a unimodal map. This enables us to systematically determine all relative periodic orbits and their symbolic dynamics up to any desired period. We then present cycle averaging formulas adequate for systems with continuous symmetry and use them to compute dynamical averages using relative periodic orbits. The convergence of such computations is discussed.

Laboratory Layered Latte

NASA Astrophysics Data System (ADS)

Xue, Nan; Khodaparast, Sepideh; Zhu, Lailai; Nunes, Janine; Kim, Hyoungsoo; Stone, Howard

2017-11-01

Layered composite fluids are sometimes observed in confined systems of rather chaotic initial states, for example, layered lattes formed by pouring espresso into a glass of warm milk. In such configurations, pouring forces a lower density liquid (espresso) into a higher density ambient, which is similar to the fountain effects that characterize a wide range of flows driven by injecting a fluid into a second miscible phase. Although the initial state of the mixture is complex and chaotic, there are conditions where the mixture cools at room temperature and exhibits an organized layered pattern. Here we report controlled experiments injecting a fluid into a miscible phase and show that, above a critical injection velocity, layering naturally emerges over the time scale of minutes. We perform experimental and numerical analyses of the time-dependent flows to observe and understand the convective circulation in the layers. We identify critical conditions to produce the layering and relate the results quantitatively to the critical Rayleigh number in double-diffusive convection, which indicates the competition between the horizontal thermal gradient and the vertical density gradient generated by the fluid injection. Based on this understanding, we show how to employ this single-step process to produce layered structures in soft materials, where the local elastic properties as well as the local material concentration vary step-wise along the length of the material.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

Computation of entropy and Lyapunov exponent by a shift transform.

PubMed

Matsuoka, Chihiro; Hiraide, Koichi

2015-10-01

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown that the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.

Computation of entropy and Lyapunov exponent by a shift transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsuoka, Chihiro, E-mail: matsuoka.chihiro.mm@ehime-u.ac.jp; Hiraide, Koichi

2015-10-15

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown thatmore » the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.« less

Active control and synchronization chaotic satellite via the geomagnetic Lorentz force

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Yehia

2016-07-01

The use of geomagnetic Lorentz force is considered in this paper for the purpose of satellite attitude control. A satellite with an electrostatic charge will interact with the Earth's magnetic field and experience the Lorentz force. An analytical attitude control and synchronization two identical chaotic satellite systems with different initial condition Master/ Slave are proposed to allows a charged satellite remains near the desired attitude. Asymptotic stability for the closed-loop system are investigated by means of Lyapunov stability theorem. The control feasibility depend on the charge requirement. Given a significantly and sufficiently accurate insertion, a charged satellite could maintains the desired attitude orientation without propellant. Simulations is performed to prove the efficacy of the proposed method.

Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ellis, George F.R.; Platts, Emma; Weltman, Amanda

2016-04-01

We use the phase plane analysis technique of Madsen and Ellis [1] to consider a universe with a true cosmological constant as well as a cosmological 'constant' that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological constant. We present only a proof ofmore » principle, with no definite claim on the physical mechanism required for the present dark energy to decay.« less

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-03-15

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performedmore » simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-{mu}m single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with {+-}2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.« less

Partially chaotic orbits in a perturbed cubic force model

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2017-11-01

Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincaré maps to show that partially chaotic orbits are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit.

Extreme concentration fluctuations due to local reversibility of mixing in turbulent flows

NASA Astrophysics Data System (ADS)

Xia, Hua; Francois, Nicolas; Punzmann, Horst; Szewc, Kamil; Shats, Michael

2018-05-01

Mixing of a passive scalar in a fluid (e.g. a radioactive spill in the ocean) is the irreversible process towards homogeneous distribution of a substance. In a moving fluid, due to the chaotic advection [H. Aref, J. Fluid Mech. 143 (1984) 1; J. M. Ottino, The Kinematics of Mixing: Stretching,Chaos and Transport (Cambridge University Press, Cambridge, 1989)] mixing is much faster than if driven by molecular diffusion only. Turbulence is known as the most efficient mixing flow [B. I. Shraiman and E. D. Siggia, Nature 405 (2000) 639]. We show that in contrast to spatially periodic flows, two-dimensional turbulence exhibits local reversibility in mixing, which leads to the generation of unpredictable strong fluctuations in the scalar concentration. These fluctuations can also be detected from the analysis of the fluid particle trajectories of the underlying flow.

Study on Controls of Fluids in Nanochannel via Hybrid Surface

NASA Astrophysics Data System (ADS)

Ye, Ziran

This thesis contributes to the investigation of controls of nanofluidic fluids by utilizing hybrid surface patterns in nanochannel. Nanofluidics is a core and interdisciplinary research field which manipulates, controls and analyzes fluids in nanoscale and develop potential bio/chemical applications. This thesis studies the surface-induced phenomena in nanofluidics, we use surface decoration on nanochannel walls to investigate the influences on fluid motion and further explore the fundamental physical principle of this behavior. To begin with, we designed and fabricated the nanofluidic mixer for the first time, which comprised hybrid surface patterns with different wettabilities on both top and bottom walls of nanochannel. Although microfluidic mixers have been intensively investigated, nanofluidic mixer has never been reported. Without any inside geometric structure of nanochannel, the mixing phenomenon can be achieved by the surface patterns and the mixing length can be significantly shortened comparing with micromixer. We attribute this achievement to the chaotic flows of two fluids induced by the patterned surface. The surface-related phenomena may not be so prominent on large scale, however, it is pronounced when the scale shrinks down to nanometer due to the large surface-to-volume ratio in nanochannel. In the second part of this work, based on the technology of nanofabrication and similar principle, we built up another novel method to control the speed of capillary flow in nanochannel in a quantitative manner. Surface patterns were fabricated on the nanochannel walls to slow down the capillary flow. The flow speed can be precisely controlled by modifying hydrophobicity ratio. Under the extreme surface-to-volume ratio in nanochannel, the significant surface effect on the fluid effectively reduced the speed of capillary flow without any external energy source and equipment. Such approach may be adopted for a wide variety of nanofluidicsbased biochemical analysis systems.

MRI-Based Computational Model of Heterogeneous Tracer Transport following Local Infusion into a Mouse Hind Limb Tumor

PubMed Central

Magdoom, Kulam Najmudeen; Pishko, Gregory L.; Rice, Lori; Pampo, Chris; Siemann, Dietmar W.; Sarntinoranont, Malisa

2014-01-01

Systemic drug delivery to solid tumors involving macromolecular therapeutic agents is challenging for many reasons. Amongst them is their chaotic microvasculature which often leads to inadequate and uneven uptake of the drug. Localized drug delivery can circumvent such obstacles and convection-enhanced delivery (CED) - controlled infusion of the drug directly into the tissue - has emerged as a promising delivery method for distributing macromolecules over larger tissue volumes. In this study, a three-dimensional MR image-based computational porous media transport model accounting for realistic anatomical geometry and tumor leakiness was developed for predicting the interstitial flow field and distribution of albumin tracer following CED into the hind-limb tumor (KHT sarcoma) in a mouse. Sensitivity of the model to changes in infusion flow rate, catheter placement and tissue hydraulic conductivity were investigated. The model predictions suggest that 1) tracer distribution is asymmetric due to heterogeneous porosity; 2) tracer distribution volume varies linearly with infusion volume within the whole leg, and exponentially within the tumor reaching a maximum steady-state value; 3) infusion at the center of the tumor with high flow rates leads to maximum tracer coverage in the tumor with minimal leakage outside; and 4) increasing the tissue hydraulic conductivity lowers the tumor interstitial fluid pressure and decreases the tracer distribution volume within the whole leg and tumor. The model thus predicts that the interstitial fluid flow and drug transport is sensitive to porosity and changes in extracellular space. This image-based model thus serves as a potential tool for exploring the effects of transport heterogeneity in tumors. PMID:24619021

Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging

PubMed Central

Redding, Brandon; Cerjan, Alexander; Huang, Xue; Lee, Minjoo Larry; Stone, A. Douglas; Choma, Michael A.; Cao, Hui

2015-01-01

The spatial coherence of laser sources has limited their application to parallel imaging and projection due to coherent artifacts, such as speckle. In contrast, traditional incoherent light sources, such as thermal sources or light emitting diodes (LEDs), provide relatively low power per independent spatial mode. Here, we present a chip-scale, electrically pumped semiconductor laser based on a novel design, demonstrating high power per mode with much lower spatial coherence than conventional laser sources. The laser resonator was fabricated with a chaotic, D-shaped cavity optimized to achieve highly multimode lasing. Lasing occurs simultaneously and independently in ∼1,000 modes, and hence the total emission exhibits very low spatial coherence. Speckle-free full-field imaging is demonstrated using the chaotic cavity laser as the illumination source. The power per mode of the sample illumination is several orders of magnitude higher than that of a LED or thermal light source. Such a compact, low-cost source, which combines the low spatial coherence of a LED with the high spectral radiance of a laser, could enable a wide range of high-speed, full-field imaging and projection applications. PMID:25605946

Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging.

PubMed

Redding, Brandon; Cerjan, Alexander; Huang, Xue; Lee, Minjoo Larry; Stone, A Douglas; Choma, Michael A; Cao, Hui

2015-02-03

The spatial coherence of laser sources has limited their application to parallel imaging and projection due to coherent artifacts, such as speckle. In contrast, traditional incoherent light sources, such as thermal sources or light emitting diodes (LEDs), provide relatively low power per independent spatial mode. Here, we present a chip-scale, electrically pumped semiconductor laser based on a novel design, demonstrating high power per mode with much lower spatial coherence than conventional laser sources. The laser resonator was fabricated with a chaotic, D-shaped cavity optimized to achieve highly multimode lasing. Lasing occurs simultaneously and independently in ∼1,000 modes, and hence the total emission exhibits very low spatial coherence. Speckle-free full-field imaging is demonstrated using the chaotic cavity laser as the illumination source. The power per mode of the sample illumination is several orders of magnitude higher than that of a LED or thermal light source. Such a compact, low-cost source, which combines the low spatial coherence of a LED with the high spectral radiance of a laser, could enable a wide range of high-speed, full-field imaging and projection applications.

Crisis of the chaotic attractor of a climate model: a transfer operator approach

NASA Astrophysics Data System (ADS)

Tantet, Alexis; Lucarini, Valerio; Lunkeit, Frank; Dijkstra, Henk A.

2018-05-01

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are known to be characterised by a single or a pair of characteristic exponents crossing the imaginary axis. As a result, the approach of such bifurcations in the presence of noise can be inferred from the slowing down of the decay of correlations (Held and Kleinen 2004 Geophys. Res. Lett. 31 1–4). On the other hand, little is known about global bifurcations involving high-dimensional attractors with several positive Lyapunov exponents. It is known that the global stability of chaotic attractors may be characterised by the spectral properties of the Koopman (Mauroy and Mezić 2016 IEEE Trans. Autom. Control 61 3356–69) or the transfer operators governing the evolution of statistical ensembles. Accordingly, it has recently been shown (Tantet 2017 J. Stat. Phys. 1–33) that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second class of resonances, the unstable resonances, are responsible for the decay of correlations and mixing on the attractor. In the deterministic case, these cannot be expected to be affected by general boundary crises. Here, however, we give an example of a chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice-albedo feedback, is also active on the attractor. Finally, we discuss implications regarding response theory and the design of early-warning signals.

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

NASA Astrophysics Data System (ADS)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

NASA Astrophysics Data System (ADS)

Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

Mobility of pyroclastic density currents

NASA Astrophysics Data System (ADS)

Giordano, G.; Porreca, M.; Lesti, C.; Cas, R. A. F.

2012-04-01

Mobility of pyroclastic density currents is a hot topic largely still poorly understood. Here we review three case studies of low aspect ratio (10-4) ignimbrites that encompass the spectrum from small to large volume, from basic to felsic in composition and from hot magmatic to cold phreatomagmatic endmembers. The 0.87 km3, phreatomagmatic, K-foiditic, Peperino Albano ignimbrite (Colli Albani, Italy), was erupted from the Albano maar at < 23 ka. The ignimbrite displays both thick valley pond and veneer facies. The juvenile component is 30-40% of the total volume and is highly fragmented to ash, with only a very minor proportion of small, vesicular lapilli. The unit reaches 10 km from vent, where it is confined in major valleys. Emplacement temperatures retrieved from paleomagnetic data and field data are at 350°-100°C. The 69 km3, tephritic, Pozzolane Rosse ignimbrite was erupted from the caldera of Colli Albani at 460 ka. The succession starts with subplinian fallout of poorly vesicular scoria lapilli. The overlying ignimbrite cover more than 2000 km2 and relate to pyroclastic flows with significant mobility, able to surmount hills at more than 20 km from vent. The facies is almost ubiquitously massive and chaotic. Juvenile pyroclasts are made of variably porphyritic, poorly to moderately vesicular scoria and spatter lapilli, and coarse ash. The texture of juvenile clasts indicates that the presence of little fine ash is not due to elutriation but to weak fragmentation of poorly vesicular and poorly viscous magma. The > 500 km3, rhyodacitic Galan ignimbrite (Altiplano Puna, Argentina) was erupted at 2.1 Ma. There is no basal fallout deposit. The ignimbrite is lithic poor, very crystal rich, massive and chaotic throughout, emplaced above Curie temperature, and develops valley confined facies, but no veneer facies, from proximal to distal (> 80 km) locations. The three cases show that: - the mobility of pyroclastic flows does not necessarily relate to the conversion of potential energy into kinetic energy during the collapse of an initially buoyant column; - extreme fragmentation and entrapment of fine ash does not seem to be a pre-requisite for mobility; - temperature also seems not to be a pre-requisite.

Instability of 2D Flows to Hydrostatic 3D Perturbations.

NASA Astrophysics Data System (ADS)

Straub, David N.

2003-01-01

Considered here is the evolution of three-dimensional perturbations to the hydrostatic equations linearized about a two-dimensional base state U. Motivated by an argument by T. Warn, this study begins with the nonrotating, unstratified case, and draws analogies between the perturbation equations and equations describing evolution of material line elements and scalar gradients embedded in the same 2D flow. When U is chaotic, both scalar gradients and line elements are characterized by rapid growth, and this leads one to suspect that the perturbations behave similarly. A generalized Okubo-Weiss parameter is proposed, and it is argued that this gives a reasonable litmus test for identifying regions where growth is most probable. Rotation modifies the generalized Okubo-Weiss parameter and tends to curb growth of the perturbation fields, as expected. It is also pointed out that, in realistic geophysical settings, the stability parameter can be suggestive of growth locally, even when a globally defined Rossby number is small.Also considered is the effect of a constant stratification. The perturbation equations can then be separated into vertical modes that have simple sinusoidal structures. The equations describing the evolution of a given mode take a form analogous to the shallow water equations, linearized about U. Numerical simulations of these, assuming a simple but chaotic prescription of U, are carried out. For sufficiently strong stratification, a balance dynamics similar to that suggested by Riley, Metcalfe, and Weissman is recovered. For a given value of the buoyancy frequency N, however, this balance breaks down at high vertical wavenumbers. For high vertical wavenumbers, the modified Okubo-Weiss parameter once again appears to give a potentially useful indication of when growth should be expected. When the Rossby number is small, this criterion predicts stability, and growth occurs only when stratification effects are comparable to or larger than rotational effects. More specifically, growth is seen when the relevant Rossby radius is comparable to or larger than the characteristic length scale of U. It is also found in this limit that approximate geostrophic adjustment occurs prior to growth.

The formation of rings and gaps in magnetically coupled disc-wind systems: ambipolar diffusion and reconnection

NASA Astrophysics Data System (ADS)

Suriano, Scott S.; Li, Zhi-Yun; Krasnopolsky, Ruben; Shang, Hsien

2018-06-01

Radial substructures in circumstellar discs are now routinely observed by Atacama Large Millimeter/submillimeter Array. There is also growing evidence that disc winds drive accretion in such discs. We show through 2D (axisymmetric) simulations that rings and gaps develop naturally in magnetically coupled disc-wind systems on the scale of tens of au, where ambipolar diffusion (AD) is the dominant non-ideal magnetohydrodynamic effect. In simulations where the magnetic field and matter are moderately coupled, the disc remains relatively laminar with the radial electric current steepened by AD into a thin layer near the mid-plane. The toroidal magnetic field sharply reverses polarity in this layer, generating a large magnetic torque that drives fast accretion, which drags the poloidal field into a highly pinched radial configuration. The reconnection of this pinched field creates magnetic loops where the net poloidal magnetic flux (and thus the accretion rate) is reduced, yielding dense rings. Neighbouring regions with stronger poloidal magnetic fields accrete faster, forming gaps. In better magnetically coupled simulations, the so-called avalanche accretion streams develop continuously near the disc surface, rendering the disc-wind system more chaotic. Nevertheless, prominent rings and gaps are still produced, at least in part, by reconnection, which again enables the segregation of the poloidal field and the disc material similar to the more diffusive discs. However, the reconnection is now driven by the non-linear growth of magnetorotational instability channel flows. The formation of rings and gaps in rapidly accreting yet laminar discs has interesting implications for dust settling and trapping, grain growth, and planet formation.

Interfacial instability of wormlike micellar solutions sheared in a Taylor-Couette cell

NASA Astrophysics Data System (ADS)

Mohammadigoushki, Hadi; Muller, Susan J.

2014-10-01

We report experiments on wormlike micellar solutions sheared in a custom-made Taylor-Couette (TC) cell. The computer controlled TC cell allows us to rotate both cylinders independently. Wormlike micellar solutions containing water, CTAB, and NaNo3 with different compositions are highly elastic and exhibit shear banding within a range of shear rate. We visualized the flow field in the θ-z as well as r-z planes, using multiple cameras. When subject to low shear rates, the flow is stable and azimuthal, but becomes unstable above a certain threshold shear rate. This shear rate coincides with the onset of shear banding. Visualizing the θ-z plane shows that this instability is characterized by stationary bands equally spaced in the z direction. Increasing the shear rate results to larger wave lengths. Above a critical shear rate, experiments reveal a chaotic behavior reminiscent of elastic turbulence. We also studied the effect of ramp speed on the onset of instability and report an acceleration below which the critical Weissenberg number for onset of instability is unaffected. Moreover, visualizations in the r-z direction reveals that the interface between the two bands undulates. The shear band evolves towards the outer cylinder upon increasing the shear rate, regardless of which cylinder is rotating.

Ultrafast synchrotron X-ray imaging studies of microstructure fragmentation in solidification under ultrasound

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Bing; Tan, Dongyue; Lee, Tung Lik

Ultrasound processing of metal alloys is an environmental friendly and promising green technology for liquid metal degassing and microstructural refinement. However many fundamental issues in this field are still not fully understood, because of the difficulties in direct observation of the dynamic behaviours caused by ultrasound inside liquid metal and semisolid metals during the solidification processes. In this paper, we report a systematic study using the ultrafast synchrotron X-ray imaging (up to 271,554 frame per second) technique available at the Advanced Photon Source, USA and Diamond Light Source, UK to investigate the dynamic interactions between the ultrasonic bubbles/acoustic flow andmore » the solidifying phases in a Bi-8%Zn alloy. The experimental results were complimented by numerical modelling. The chaotic bubble implosion and dynamic bubble oscillations were revealed in-situ for the first time in liquid metal and semisolid metal. The fragmentation of the solidifying Zn phases and breaking up of the liquid-solid interface by ultrasonic bubbles and enhanced acoustic flow were clearly demonstrated and agreed very well with the theoretical calculations. The research provides unambiguous experimental evidence and robust theoretical interpretation in elucidating the dominant mechanisms of microstructure fragmentation and refinement in solidification under ultrasound.« less

Ultrafast synchrotron X-ray imaging studies of microstructure fragmentation in solidification under ultrasound

DOE PAGES

Wang, Bing; Tan, Dongyue; Lee, Tung Lik; ...

2017-11-03

Ultrasound processing of metal alloys is an environmental friendly and promising green technology for liquid metal degassing and microstructural refinement. However many fundamental issues in this field are still not fully understood, because of the difficulties in direct observation of the dynamic behaviours caused by ultrasound inside liquid metal and semisolid metals during the solidification processes. In this paper, we report a systematic study using the ultrafast synchrotron X-ray imaging (up to 271,554 frame per second) technique available at the Advanced Photon Source, USA and Diamond Light Source, UK to investigate the dynamic interactions between the ultrasonic bubbles/acoustic flow andmore » the solidifying phases in a Bi-8%Zn alloy. The experimental results were complimented by numerical modelling. The chaotic bubble implosion and dynamic bubble oscillations were revealed in-situ for the first time in liquid metal and semisolid metal. The fragmentation of the solidifying Zn phases and breaking up of the liquid-solid interface by ultrasonic bubbles and enhanced acoustic flow were clearly demonstrated and agreed very well with the theoretical calculations. The research provides unambiguous experimental evidence and robust theoretical interpretation in elucidating the dominant mechanisms of microstructure fragmentation and refinement in solidification under ultrasound.« less

A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

PubMed

Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki

2005-01-01

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kandidov, V P; Kosareva, O G; Nyakk, A V

A method for spatial regularisation of chaotically located filaments, which appear in a high-power femtosecond laser pulse, is proposed, numerically substantiated, and experimentally tested. This method is based on the introduction of regular light-field perturbations into the femtosecond-pulse cross section. (letters)

Adjoint Sensitivity Analysis for Scale-Resolving Turbulent Flow Solvers

NASA Astrophysics Data System (ADS)

Blonigan, Patrick; Garai, Anirban; Diosady, Laslo; Murman, Scott

2017-11-01

Adjoint-based sensitivity analysis methods are powerful design tools for engineers who use computational fluid dynamics. In recent years, these engineers have started to use scale-resolving simulations like large-eddy simulations (LES) and direct numerical simulations (DNS), which resolve more scales in complex flows with unsteady separation and jets than the widely-used Reynolds-averaged Navier-Stokes (RANS) methods. However, the conventional adjoint method computes large, unusable sensitivities for scale-resolving simulations, which unlike RANS simulations exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional adjoint methods, but has a high computational cost even for relatively small simulations. The following talk discusses a more computationally efficient formulation of LSS, ``non-intrusive'' LSS, and its application to turbulent flows simulated with a discontinuous-Galkerin spectral-element-method LES/DNS solver. Results are presented for the minimal flow unit, a turbulent channel flow with a limited streamwise and spanwise domain.

Suppressing Taylor vortices in a Taylor-Couette flow system with free surface

NASA Astrophysics Data System (ADS)

Bouabdallah, A.; Oualli, H.; Mekadem, M.; Gad-El-Hak, M.

2016-11-01

Taylor-Couette flows have been extensively investigated due to their many industrial applications, such as catalytic reactors, electrochemistry, photochemistry, biochemistry, and polymerization. Mass transfer applications include extraction, tangential filtration, crystallization, and dialysis. A 3D study is carried out to simulate a Taylor-Couette flow with a rotating and pulsating inner cylinder. We utilize FLUENT to simulate the incompressible flow with a free surface. The study reveals that flow structuring is initiated with the development of an Ekman vortex at low Taylor number, Ta = 0 . 01 . For all encountered flow regimes, the Taylor vortices are systematically inhibited by the pulsatile motion of the inner cylinder. A spectral analysis shows that this pulsatile motion causes a rapid decay of the free surface oscillations, from a periodic wavy movement to a chaotic one, then to a fully turbulent motion. This degenerative free surface behavior is interpreted as the underlying mechanism responsible for the inhibition of the Taylor vortices.

Video encryption using chaotic masks in joint transform correlator

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2015-03-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.

Mechanisms of chaos in billiards: dispersing, defocusing and nothing else

NASA Astrophysics Data System (ADS)

Bunimovich, Leonid A.

2018-02-01

We explain and justify that the only mechanisms of chaotic dynamics for billiards are dispersing and defocusing. We also introduce boomerang billiards which dynamics demonstrate that two rather broadly accepted views about some features of nonlinear dynamics are actually wrong. Namely correlations in billiards having focusing components of the boundary can decay exponentially, and continuous time correlations for a billiard flow may decay faster than discrete time correlations for a billiard map.

Chronology, Eruption Duration, and Atmospheric Contribution of the Martian Volcano Apollinaris Patera

USGS Publications Warehouse

Robinson, M.S.; Mouginis-Mark, P. J.; Zimbelman, J.R.; Wu, S.S.C.; Ablin, K.K.; Howington-Kraus, A. E.

1993-01-01

Geologic mapping, thermal inertia measurements, and an analysis of the color (visual wavelengths) of the martian volcano Apollinaris Patera indicate the existence of two different surface materials, comprising an early, easily eroded edifice, and a more recent, competent fan on the southern flank. A chronology of six major events that is consistent with the present morphology of the volcano has been identified. We propose that large scale explosive activity occurred during the formation of the main edifice and that the distinctive fan on the southern flank appears to have been formed by lavas of low eruptive rate similar to those that form compound pahoehoe flow fields on Earth. A basal escarpment typically 500 m in relief and morphologically similar to the one surrounding Olympus Mons was produced between the formation of the main edifice and the fan, indicating multistage eruptions over a protracted period of time. Contact relations between the volcanic units and the adjacent chaotic material indicate that formation of the chaotic material occurred over an extended period of time and may be related to the volcanic activity that formed Apollinaris Patera. Stereophotogrammetric measurements permit the volume of the volcano to be estimated at 105 km3. From this volume measurement and an inferred eruption rate (1.5 ?? 10-2 km3 yr-1) we estimate the total eruption duration for the main edifice to be ???107 yrs. Plausible estimates of the exsolved volatile content of the parent magma imply that greater than 1015 kg of water vapor was released into the atmosphere as a consequence of this activity. This large amount of water vapor as well as other exsolved gases must have had a significant impact on local, and possibly global, climatic conditions. ?? 1993 Academic Press. All rights reserved.

Visibility graphlet approach to chaotic time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mutua, Stephen; Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega; Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems.more » Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.« less

Vortex flow structures and interactions for the optimum thrust efficiency of a heaving airfoil at different mean angles of attack

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martín-Alcántara, A.; Fernandez-Feria, R.; Sanmiguel-Rojas, E.

The thrust efficiency of a two-dimensional heaving airfoil is studied computationally for a low Reynolds number using a vortex force decomposition. The auxiliary potentials that separate the total vortex force into lift and drag (or thrust) are obtained analytically by using an elliptic airfoil. With these auxiliary potentials, the added-mass components of the lift and drag (or thrust) coefficients are also obtained analytically for any heaving motion of the airfoil and for any value of the mean angle of attack α. The contributions of the leading- and trailing-edge vortices to the thrust during their down- and up-stroke evolutions are computedmore » quantitatively with this formulation for different dimensionless frequencies and heave amplitudes (St{sub c} and St{sub a}) and for several values of α. Very different types of flows, periodic, quasi-periodic, and chaotic described as St{sub c}, St{sub a}, and α, are varied. The optimum values of these parameters for maximum thrust efficiency are obtained and explained in terms of the interactions between the vortices and the forces exerted by them on the airfoil. As in previous numerical and experimental studies on flapping flight at low Reynolds numbers, the optimum thrust efficiency is reached for intermediate frequencies (St{sub c} slightly smaller than one) and a heave amplitude corresponding to an advance ratio close to unity. The optimal mean angle of attack found is zero. The corresponding flow is periodic, but it becomes chaotic and with smaller average thrust efficiency as |α| becomes slightly different from zero.« less

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

NASA Astrophysics Data System (ADS)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1985-01-01

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction.

PubMed

Rostami, Zahra; Jafari, Sajad

2018-04-01

Complex anatomical and physiological structure of an excitable tissue (e.g., cardiac tissue) in the body can represent different electrical activities through normal or abnormal behavior. Abnormalities of the excitable tissue coming from different biological reasons can lead to formation of some defects. Such defects can cause some successive waves that may end up to some additional reorganizing beating behaviors like spiral waves or target waves. In this study, formation of defects and the resulting emitted waves in an excitable tissue are investigated. We have considered a square array network of neurons with nearest-neighbor connections to describe the excitable tissue. Fundamentally, electrophysiological properties of ion currents in the body are responsible for exhibition of electrical spatiotemporal patterns. More precisely, fluctuation of accumulated ions inside and outside of cell causes variable electrical and magnetic field. Considering undeniable mutual effects of electrical field and magnetic field, we have proposed the new Hindmarsh-Rose (HR) neuronal model for the local dynamics of each individual neuron in the network. In this new neuronal model, the influence of magnetic flow on membrane potential is defined. This improved model holds more bifurcation parameters. Moreover, the dynamical behavior of the tissue is investigated in different states of quiescent, spiking, bursting and even chaotic state. The resulting spatiotemporal patterns are represented and the time series of some sampled neurons are displayed, as well.

Real-time prediction of atmospheric Lagrangian coherent structures based on forecast data: An application and error analysis

NASA Astrophysics Data System (ADS)

BozorgMagham, Amir E.; Ross, Shane D.; Schmale, David G.

2013-09-01

The language of Lagrangian coherent structures (LCSs) provides a new means for studying transport and mixing of passive particles advected by an atmospheric flow field. Recent observations suggest that LCSs govern the large-scale atmospheric motion of airborne microorganisms, paving the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans. In addition, having reliable predictions of the timing of hyperbolic LCSs may contribute to improved aerobiological sampling of microorganisms with unmanned aerial vehicles and LCS-based early warning systems. Chaotic atmospheric dynamics lead to unavoidable forecasting errors in the wind velocity field, which compounds errors in LCS forecasting. In this study, we reveal the cumulative effects of errors of (short-term) wind field forecasts on the finite-time Lyapunov exponent (FTLE) fields and the associated LCSs when realistic forecast plans impose certain limits on the forecasting parameters. Objectives of this paper are to (a) quantify the accuracy of prediction of FTLE-LCS features and (b) determine the sensitivity of such predictions to forecasting parameters. Results indicate that forecasts of attracting LCSs exhibit less divergence from the archive-based LCSs than the repelling features. This result is important since attracting LCSs are the backbone of long-lived features in moving fluids. We also show under what circumstances one can trust the forecast results if one merely wants to know if an LCS passed over a region and does not need to precisely know the passage time.

Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer.

PubMed

Naruse, Makoto; Kim, Song-Ju; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi

2014-08-12

By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs.

Global relativistic effects in chaotic scattering.

PubMed

Bernal, Juan D; Seoane, Jesús M; Sanjuán, Miguel A F

2017-03-01

The phenomenon of chaotic scattering is very relevant in different fields of science and engineering. It has been mainly studied in the context of Newtonian mechanics, where the velocities of the particles are low in comparison with the speed of light. Here, we analyze global properties such as the escape time distribution and the decay law of the Hénon-Heiles system in the context of special relativity. Our results show that the average escape time decreases with increasing values of the relativistic factor β. As a matter of fact, we have found a crossover point for which the KAM islands in the phase space are destroyed when β≃0.4. On the other hand, the study of the survival probability of particles in the scattering region shows an algebraic decay for values of β≤0.4, and this law becomes exponential for β>0.4. Surprisingly, a scaling law between the exponent of the decay law and the β factor is uncovered where a quadratic fitting between them is found. The results of our numerical simulations agree faithfully with our qualitative arguments. We expect this work to be useful for a better understanding of both chaotic and relativistic systems.

Innovative hyperchaotic encryption algorithm for compressed video

NASA Astrophysics Data System (ADS)

Yuan, Chun; Zhong, Yuzhuo; Yang, Shiqiang

2002-12-01

It is accepted that stream cryptosystem can achieve good real-time performance and flexibility which implements encryption by selecting few parts of the block data and header information of the compressed video stream. Chaotic random number generator, for example Logistics Map, is a comparatively promising substitute, but it is easily attacked by nonlinear dynamic forecasting and geometric information extracting. In this paper, we present a hyperchaotic cryptography scheme to encrypt the compressed video, which integrates Logistics Map with Z(232 - 1) field linear congruential algorithm to strengthen the security of the mono-chaotic cryptography, meanwhile, the real-time performance and flexibility of the chaotic sequence cryptography are maintained. It also integrates with the dissymmetrical public-key cryptography and implements encryption and identity authentification on control parameters at initialization phase. In accord with the importance of data in compressed video stream, encryption is performed in layered scheme. In the innovative hyperchaotic cryptography, the value and the updating frequency of control parameters can be changed online to satisfy the requirement of the network quality, processor capability and security requirement. The innovative hyperchaotic cryprography proves robust security by cryptoanalysis, shows good real-time performance and flexible implement capability through the arithmetic evaluating and test.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Experimental Induction of Genome Chaos.

PubMed

Ye, Christine J; Liu, Guo; Heng, Henry H

2018-01-01

Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.

Palatini side of inflationary attractors

NASA Astrophysics Data System (ADS)

Järv, Laur; Racioppi, Antonio; Tenkanen, Tommi

2018-04-01

We perform an analysis of models of chaotic inflation where the inflaton field ϕ is coupled nonminimally to gravity via ξ ϕngμ νRμ ν(Γ ),n >0 . We focus on the Palatini theory of gravity, i.e., the case where the assumptions of general relativity are relaxed (that of the connection being the Levi-Civita one) and the gravitational degrees of freedom are encoded in not only the metric but also the connection Γ , which is treated as an independent variable. We show that in this case the famous attractor behavior of simple nonminimally coupled models of inflation is lost. Therefore the attractors are not universal, but their existence depends on the underlying theory of gravity in a subtle way. We discuss what this means for chaotic models and their observational consequences.

An adaptive front tracking technique for three-dimensional transient flows

NASA Astrophysics Data System (ADS)

Galaktionov, O. S.; Anderson, P. D.; Peters, G. W. M.; van de Vosse, F. N.

2000-01-01

An adaptive technique, based on both surface stretching and surface curvature analysis for tracking strongly deforming fluid volumes in three-dimensional flows is presented. The efficiency and accuracy of the technique are demonstrated for two- and three-dimensional flow simulations. For the two-dimensional test example, the results are compared with results obtained using a different tracking approach based on the advection of a passive scalar. Although for both techniques roughly the same structures are found, the resolution for the front tracking technique is much higher. In the three-dimensional test example, a spherical blob is tracked in a chaotic mixing flow. For this problem, the accuracy of the adaptive tracking is demonstrated by the volume conservation for the advected blob. Adaptive front tracking is suitable for simulation of the initial stages of fluid mixing, where the interfacial area can grow exponentially with time. The efficiency of the algorithm significantly benefits from parallelization of the code. Copyright

Characteristics of level-spacing statistics in chaotic graphene billiards.

PubMed

Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2011-03-01

A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.

Fluids by design using chaotic surface waves to create a metafluid that is Newtonian, thermal, and entirely tunable

PubMed Central

Welch, Kyle J.; Liebman-Peláez, Alexander; Corwin, Eric I.

2016-01-01

In conventional fluids, viscosity depends on temperature according to a strict relationship. To change this relationship, one must change the molecular nature of the fluid. Here, we create a metafluid whose properties are derived not from the properties of molecules but rather from chaotic waves excited on the surface of vertically agitated water. By making direct rheological measurements of the flow properties of our metafluid, we show that it has independently tunable viscosity and temperature, a quality that no conventional fluid possesses. We go on to show that the metafluid obeys the Einstein relation, which relates many-body response (viscosity) to single-particle dynamics (diffusion) and is a fundamental result in equilibrium thermal systems. Thus, our metafluid is wholly consistent with equilibrium thermal physics, despite being markedly nonequilibrium. Taken together, our results demonstrate a type of material that retains equilibrium physics while simultaneously allowing for direct programmatic control over material properties. PMID:27621467

Flutter Analysis of the Thermal Protection Layer on the NASA HIAD

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2013-01-01

A combination of classical plate theory and a supersonic aerodynamic model is used to study the aeroelastic flutter behavior of a proposed thermal protection system (TPS) for the NASA HIAD. The analysis pertains to the rectangular configurations currently being tested in a NASA wind-tunnel facility, and may explain why oscillations of the articles could be observed. An analysis using a linear flat plate model indicated that flutter was possible well within the supersonic flow regime of the wind tunnel tests. A more complex nonlinear analysis of the TPS, taking into account any material curvature present due to the restraint system or substructure, indicated that significantly greater aerodynamic forcing is required for the onset of flutter. Chaotic and periodic limit cycle oscillations (LCOs) of the TPS are possible depending on how the curvature is imposed. When the pressure from the base substructure on the bottom of the TPS is used as the source of curvature, the flutter boundary increases rapidly and chaotic behavior is eliminated.

Chryse Basin channels: low-gradients and ponded flows.

USGS Publications Warehouse

Lucchitta, B.K.; Ferguson, H.M.

1983-01-01

Gradients on the floors of the Martian outflow channels that are derived from radar-elevation profiles across Lunae Planum and Chryse Basin have much lower values than those obtained from the U.S. Geological Survey's topographic map. Whereas the gradients of Maja and Ares Valles are similar to those of the catastrophic flood channels in the Scablands of Washington State, the gradients of Simud and Tiu Valles are essentially level, and the movement of fluids to the N poses problems. It is proposed that ponding may have formed lakes in depressions associated with the Valles Marineris grabens, ancient craters in the chaotic terrain area, and possibly even the regional low where most chaotic terrains occur. It is envisaged that lakes eventually overflowed, forming the present channels. When dams broke, floods were released catastrophically, with a final gigantic flood from the Valles Marineris system of troughs, which would have had sufficient head to move fluids across nearly level gradients through the Simud and Tiu channels. -P.Br.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Yanmei; Li, Xinli; Bai, Yan

The measurement of multiphase flow parameters is of great importance in a wide range of industries. In the measurement of multiphase, the signals from the sensors are extremely weak and often buried in strong background noise. It is thus desirable to develop effective signal processing techniques that can detect the weak signal from the sensor outputs. In this paper, two methods, i.e., lock-in-amplifier (LIA) and improved Duffing chaotic oscillator are compared to detect and process the weak signal. For sinusoidal signal buried in noise, the correlation detection with sinusoidal reference signal is simulated by using LIA. The improved Duffing chaoticmore » oscillator method, which based on the Wigner transformation, can restore the signal waveform and detect the frequency. Two methods are combined to detect and extract the weak signal. Simulation results show the effectiveness and accuracy of the proposed improved method. The comparative analysis shows that the improved Duffing chaotic oscillator method can restrain noise strongly since it is sensitive to initial conditions.« less

Stages of chaotic synchronization.

PubMed

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1990-01-01

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

NASA Astrophysics Data System (ADS)

Sun, Changchun; Chen, Zhongtang; Xu, Qicheng

2017-12-01

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

Chaotic Signal Denoising Based on Hierarchical Threshold Synchrosqueezed Wavelet Transform

NASA Astrophysics Data System (ADS)

Wang, Wen-Bo; Jing, Yun-yu; Zhao, Yan-chao; Zhang, Lian-Hua; Wang, Xiang-Li

2017-12-01

In order to overcoming the shortcoming of single threshold synchrosqueezed wavelet transform(SWT) denoising method, an adaptive hierarchical threshold SWT chaotic signal denoising method is proposed. Firstly, a new SWT threshold function is constructed based on Stein unbiased risk estimation, which is two order continuous derivable. Then, by using of the new threshold function, a threshold process based on the minimum mean square error was implemented, and the optimal estimation value of each layer threshold in SWT chaotic denoising is obtained. The experimental results of the simulating chaotic signal and measured sunspot signals show that, the proposed method can filter the noise of chaotic signal well, and the intrinsic chaotic characteristic of the original signal can be recovered very well. Compared with the EEMD denoising method and the single threshold SWT denoising method, the proposed method can obtain better denoising result for the chaotic signal.

Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor

NASA Astrophysics Data System (ADS)

Dong, En-Zeng; Wang, Zhen; Yu, Xiao; Chen, Zeng-Qiang; Wang, Zeng-Hui

2018-01-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 61502340 and 61374169), the Application Base and Frontier Technology Research Project of Tianjin, China (Grant No. 15JCYBJC51800), and the South African National Research Foundation Incentive Grants (Grant No. 81705).

Dynamics, Analysis and Implementation of a Multiscroll Memristor-Based Chaotic Circuit

NASA Astrophysics Data System (ADS)

Alombah, N. Henry; Fotsin, Hilaire; Ngouonkadi, E. B. Megam; Nguazon, Tekou

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element — another inductor — is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication.

Electromagnetic banana kinetic equation and its applications in tokamaks

NASA Astrophysics Data System (ADS)

Shaing, K. C.; Chu, M. S.; Sabbagh, S. A.; Seol, J.

2018-03-01

A banana kinetic equation in tokamaks that includes effects of the finite banana width is derived for the electromagnetic waves with frequencies lower than the gyro-frequency and the bounce frequency of the trapped particles. The radial wavelengths are assumed to be either comparable to or shorter than the banana width, but much wider than the gyro-radius. One of the consequences of the banana kinetics is that the parallel component of the vector potential is not annihilated by the orbit averaging process and appears in the banana kinetic equation. The equation is solved to calculate the neoclassical quasilinear transport fluxes in the superbanana plateau regime caused by electromagnetic waves. The transport fluxes can be used to model electromagnetic wave and the chaotic magnetic field induced thermal particle or energetic alpha particle losses in tokamaks. It is shown that the parallel component of the vector potential enhances losses when it is the sole transport mechanism. In particular, the fact that the drift resonance can cause significant transport losses in the chaotic magnetic field in the hitherto unknown low collisionality regimes is emphasized.

Force Analysis and Energy Operation of Chaotic System of Permanent-Magnet Synchronous Motor

NASA Astrophysics Data System (ADS)

Qi, Guoyuan; Hu, Jianbing

2017-12-01

The disadvantage of a nondimensionalized model of a permanent-magnet synchronous Motor (PMSM) is identified. The original PMSM model is transformed into a Kolmogorov system to aid dynamic force analysis. The vector field of the PMSM is analogous to the force field including four types of torque — inertial, internal, dissipative, and generalized external. Using the feedback thought, the error torque between external torque and dissipative torque is identified. The pitchfork bifurcation of the PMSM is performed. Four forms of energy are identified for the system — kinetic, potential, dissipative, and supplied. The physical interpretations of the decomposition of force and energy exchange are given. Casimir energy is stored energy, and its rate of change is the error power between the dissipative energy and the energy supplied to the motor. Error torque and error power influence the different types of dynamic modes. The Hamiltonian energy and Casimir energy are compared to find the function of each in producing the dynamic modes. A supremum bound for the chaotic attractor is proposed using the error power and Lagrange multiplier.

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators

PubMed Central

2016-01-01

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors. PMID:27997930

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators.

PubMed

Tlelo-Cuautle, Esteban; Quintas-Valles, Antonio de Jesus; de la Fraga, Luis Gerardo; Rangel-Magdaleno, Jose de Jesus

2016-01-01

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.

Computing Rydberg Electron Transport Rates Using Periodic Orbits

NASA Astrophysics Data System (ADS)

Sattari, Sulimon; Mitchel, Kevin

2017-04-01

Electron transport rates in chaotic atomic systems are computable from classical periodic orbits. This technique allows for replacing a Monte Carlo simulation launching millions of orbits with a sum over tens or hundreds of properly chosen periodic orbits using a formula called the spectral determiant. A firm grasp of the structure of the periodic orbits is required to obtain accurate transport rates. We apply a technique called homotopic lobe dynamics (HLD) to understand the structure of periodic orbits to compute the ionization rate in a classically chaotic atomic system, namely the hydrogen atom in strong parallel electric and magnetic fields. HLD uses information encoded in the intersections of stable and unstable manifolds of a few orbits to compute relevant periodic orbits in the system. All unstable periodic orbits are computed up to a given period, and the ionization rate computed from periodic orbits converges exponentially to the true value as a function of the period used. Using periodic orbit continuation, the ionization rate is computed over a range of electron energy and magnetic field values. The future goal of this work is to semiclassically compute quantum resonances using periodic orbits.

Velocity Field of the McMurdo Shear Zone from Annual Three-Dimensional Ground Penetrating Radar Imaging and Crevasse Matching

NASA Astrophysics Data System (ADS)

Ray, L.; Jordan, M.; Arcone, S. A.; Kaluzienski, L. M.; Koons, P. O.; Lever, J.; Walker, B.; Hamilton, G. S.

2017-12-01

The McMurdo Shear Zone (MSZ) is a narrow, intensely crevassed strip tens of km long separating the Ross and McMurdo ice shelves (RIS and MIS) and an important pinning feature for the RIS. We derive local velocity fields within the MSZ from two consecutive annual ground penetrating radar (GPR) datasets that reveal complex firn and marine ice crevassing; no englacial features are evident. The datasets were acquired in 2014 and 2015 using robot-towed 400 MHz and 200 MHz GPR over a 5 km x 5.7 km grid. 100 west-to-east transects at 50 m spacing provide three-dimensional maps that reveal the length of many firn crevasses, and their year-to-year structural evolution. Hand labeling of crevasse cross sections near the MSZ western and eastern boundaries reveal matching firn and marine ice crevasses, and more complex and chaotic features between these boundaries. By matching crevasse features from year to year both on the eastern and western boundaries and within the chaotic region, marine ice crevasses along the western and eastern boundaries are shown to align directly with firn crevasses, and the local velocity field is estimated and compared with data from strain rate surveys and remote sensing. While remote sensing provides global velocity fields, crevasse matching indicates greater local complexity attributed to faulting, folding, and rotation.

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

PubMed Central

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

PubMed

Pei, Yan

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

Hybrid information privacy system: integration of chaotic neural network and RSA coding

NASA Astrophysics Data System (ADS)

Hsu, Ming-Kai; Willey, Jeff; Lee, Ting N.; Szu, Harold H.

2005-03-01

Electronic mails are adopted worldwide; most are easily hacked by hackers. In this paper, we purposed a free, fast and convenient hybrid privacy system to protect email communication. The privacy system is implemented by combining private security RSA algorithm with specific chaos neural network encryption process. The receiver can decrypt received email as long as it can reproduce the specified chaos neural network series, so called spatial-temporal keys. The chaotic typing and initial seed value of chaos neural network series, encrypted by the RSA algorithm, can reproduce spatial-temporal keys. The encrypted chaotic typing and initial seed value are hidden in watermark mixed nonlinearly with message media, wrapped with convolution error correction codes for wireless 3rd generation cellular phones. The message media can be an arbitrary image. The pattern noise has to be considered during transmission and it could affect/change the spatial-temporal keys. Since any change/modification on chaotic typing or initial seed value of chaos neural network series is not acceptable, the RSA codec system must be robust and fault-tolerant via wireless channel. The robust and fault-tolerant properties of chaos neural networks (CNN) were proved by a field theory of Associative Memory by Szu in 1997. The 1-D chaos generating nodes from the logistic map having arbitrarily negative slope a = p/q generating the N-shaped sigmoid was given first by Szu in 1992. In this paper, we simulated the robust and fault-tolerance properties of CNN under additive noise and pattern noise. We also implement a private version of RSA coding and chaos encryption process on messages.

Branched Hamiltonians and supersymmetry

DOE PAGES

Curtright, Thomas L.; Zachos, Cosmas K.

2014-03-21

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.

Applicability of Complexity Theory to Martian Fluvial Systems: A Preliminary Analysis

NASA Technical Reports Server (NTRS)

Rosenshein, E. B.

2003-01-01

In the last 15 years, terrestrial geomorphology has been revolutionized by the theories of chaotic systems, fractals, self-organization, and selforganized criticality. Except for the application of fractal theory to the analysis of lava flows and rampart craters on Mars, these theories have not yet been applied to problems of Martian landscape evolution. These complexity theories are elucidated below, along with the methods used to relate these theories to the realities of Martian fluvial systems.

Periodic orbit analysis of a system with continuous symmetry—A tutorial

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budanur, Nazmi Burak, E-mail: budanur3@gatech.edu; Cvitanović, Predrag; Borrero-Echeverry, Daniel

2015-07-15

Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid in terms of a Fourier series truncated to a finite number of modes. Here, we study a 4-dimensional model with chaotic dynamics and SO(2) symmetry similar to those that appear in fluid dynamics problems. A crucial step in the analysis of such a system is symmetry reduction. We use the model to illustrate different symmetry-reduction techniques. The system's relative equilibria are conveniently determined bymore » rewriting the dynamics in terms of a symmetry-invariant polynomial basis. However, for the analysis of its chaotic dynamics, the “method of slices,” which is applicable to very high-dimensional problems, is preferable. We show that a Poincaré section taken on the 'slice' can be used to further reduce this flow to what is for all practical purposes a unimodal map. This enables us to systematically determine all relative periodic orbits and their symbolic dynamics up to any desired period. We then present cycle averaging formulas adequate for systems with continuous symmetry and use them to compute dynamical averages using relative periodic orbits. The convergence of such computations is discussed.« less

A "twisted" microfluidic mixer suitable for a wide range of flow rate applications.

PubMed

Sivashankar, Shilpa; Agambayev, Sumeyra; Mashraei, Yousof; Li, Er Qiang; Thoroddsen, Sigurdur T; Salama, Khaled Nabil

2016-05-01

This paper proposes a new "twisted" 3D microfluidic mixer fabricated by a laser writing/microfabrication technique. Effective and efficient mixing using the twisted micromixers can be obtained by combining two general chaotic mixing mechanisms: splitting/recombining and chaotic advection. The lamination of mixer units provides the splitting and recombination mechanism when the quadrant of circles is arranged in a two-layered serial arrangement of mixing units. The overall 3D path of the microchannel introduces the advection. An experimental investigation using chemical solutions revealed that these novel 3D passive microfluidic mixers were stable and could be operated at a wide range of flow rates. This micromixer finds application in the manipulation of tiny volumes of liquids that are crucial in diagnostics. The mixing performance was evaluated by dye visualization, and using a pH test that determined the chemical reaction of the solutions. A comparison of the tornado-mixer with this twisted micromixer was made to evaluate the efficiency of mixing. The efficiency of mixing was calculated within the channel by acquiring intensities using ImageJ software. Results suggested that efficient mixing can be obtained when more than 3 units were consecutively placed. The geometry of the device, which has a length of 30 mm, enables the device to be integrated with micro total analysis systems and other lab-on-chip devices.

A “twisted” microfluidic mixer suitable for a wide range of flow rate applications

PubMed Central

Sivashankar, Shilpa; Agambayev, Sumeyra; Mashraei, Yousof; Li, Er Qiang; Thoroddsen, Sigurdur T.; Salama, Khaled Nabil

2016-01-01

This paper proposes a new “twisted” 3D microfluidic mixer fabricated by a laser writing/microfabrication technique. Effective and efficient mixing using the twisted micromixers can be obtained by combining two general chaotic mixing mechanisms: splitting/recombining and chaotic advection. The lamination of mixer units provides the splitting and recombination mechanism when the quadrant of circles is arranged in a two-layered serial arrangement of mixing units. The overall 3D path of the microchannel introduces the advection. An experimental investigation using chemical solutions revealed that these novel 3D passive microfluidic mixers were stable and could be operated at a wide range of flow rates. This micromixer finds application in the manipulation of tiny volumes of liquids that are crucial in diagnostics. The mixing performance was evaluated by dye visualization, and using a pH test that determined the chemical reaction of the solutions. A comparison of the tornado-mixer with this twisted micromixer was made to evaluate the efficiency of mixing. The efficiency of mixing was calculated within the channel by acquiring intensities using ImageJ software. Results suggested that efficient mixing can be obtained when more than 3 units were consecutively placed. The geometry of the device, which has a length of 30 mm, enables the device to be integrated with micro total analysis systems and other lab-on-chip devices. PMID:27453767

Spatial Models of Prebiotic Evolution: Soup Before Pizza?

NASA Astrophysics Data System (ADS)

Scheuring, István; Czárán, Tamás; Szabó, Péter; Károlyi, György; Toroczkai, Zoltán

2003-10-01

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance of any feasible replicator system. Based on a detailed critical survey of spatial models on prebiotic information integration, we suggest a possible scenario for replicator system evolution leading to the emergence of the first protocells capable of independent life. We show that even the spatial versions of the hypercycle model are vulnerable to selfish parasites in heterogeneous habitats. Contrary, the metabolic system remains persistent and coexistent with its parasites both on heterogeneous surfaces and in chaotically mixing flowing media. Persistent metabolic parasites can be converted to metabolic cooperators, or they can gradually obtain replicase activity. Our simulations show that, once replicase activity emerged, a gradual and simultaneous evolutionary improvement of replicase functionality (speed and fidelity) and template efficiency is possible only on a surface that constrains the mobility of macromolecule replicators. Based on the results of the models reviewed, we suggest that open chaotic flows (`soup') and surface dynamics (`pizza') both played key roles in the sequence of evolutionary events ultimately concluding in the appearance of the first living cell on Earth.

Lagrangian chaos in three- dimensional steady buoyancy-driven flows

NASA Astrophysics Data System (ADS)

Contreras, Sebastian; Speetjens, Michel; Clercx, Herman

2016-11-01

Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr<1 and Pr>1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).

A pilot study of river flow prediction in urban area based on phase space reconstruction

NASA Astrophysics Data System (ADS)

Adenan, Nur Hamiza; Hamid, Nor Zila Abd; Mohamed, Zulkifley; Noorani, Mohd Salmi Md

2017-08-01

River flow prediction is significantly related to urban hydrology impact which can provide information to solve any problems such as flood in urban area. The daily river flow of Klang River, Malaysia was chosen to be forecasted in this pilot study which based on phase space reconstruction. The reconstruction of phase space involves a single variable of river flow data to m-dimensional phase space in which the dimension (m) is based on the optimal values of Cao method. The results from the reconstruction of phase space have been used in the forecasting process using local linear approximation method. From our investigation, river flow at Klang River is chaotic based on the analysis from Cao method. The overall results provide good value of correlation coefficient. The value of correlation coefficient is acceptable since the area of the case study is influence by a lot of factors. Therefore, this pilot study may be proposed to forecast daily river flow data with the purpose of providing information about the flow of the river system in urban area.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, Samuel Lee; Miller, William Michael; McWhorter, Paul Jackson

1997-01-01

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, S.L.; Miller, W.M.; McWhorter, P.J.

1997-10-21

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals. 32 figs.

Using Chaotic System in Encryption

NASA Astrophysics Data System (ADS)

Findik, Oğuz; Kahramanli, Şirzat

In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.

Design and Hardware Implementation of a New Chaotic Secure Communication Technique

PubMed Central

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness. PMID:27548385

Design and Hardware Implementation of a New Chaotic Secure Communication Technique.

PubMed

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness.

Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Liu, Bocheng; Hu, Hanping; Miao, Suoxia

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime

NASA Astrophysics Data System (ADS)

Druzgalski, Clara; Mani, Ali

2016-11-01

We investigate electroconvection and its impact on ion transport in a model system comprised of an ion-selective membrane, an aqueous electrolyte, and an external electric field applied normal to the membrane. We develop a direct numerical simulation code to solve the governing Poisson-Nernst-Planck and Navier-Stokes equations in three dimensions using a specialized parallel numerical algorithm and sufficient resolution to capture the high frequency and high wavenumber physics. We show a comprehensive statistical analysis of the transport phenomena in the highly chaotic regime. Qualitative and quantitative comparisons of two-dimensional (2D) and 3D simulations include prediction of the mean concentration fields as well as the spectra of concentration, charge density, and velocity signals. Our analyses reveal a significant quantitative difference between 2D and 3D electroconvection. Furthermore, we show that high-intensity yet short-lived current density hot spots appear randomly on the membrane surface, contributing significantly to the mean current density. By examining cross correlations between current density on the membrane and other field quantities we explore the physical mechanisms leading to current hot spots. We also present analysis of transport fluxes in the context of ensemble-averaged equations. Our analysis reveals that in the highly chaotic regime the mixing layer (ML), which spans the majority of the domain extent, is governed by advective fluctuations. Furthermore, we show that in the ML the mean electromigration fluxes cancel out for positive and negative ions, indicating that the mean transport of total salt content within the ML can be represented via the electroneutral approximation. Finally, we present an assessment of the importance of different length scales in enhancing transport by computing the cross covariance of concentration and velocity fluctuations in the wavenumber space. Our analysis indicates that in the majority of the domain the large scales contribute most significantly to transport, while the effects of small scales become more appreciable in regions very near the membrane.

A model for complex flows of soft glassy materials with application to flows through fixed fiber beds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarkar, Arijit; Koch, Donald L., E-mail: dlk15@cornell.edu

2015-11-15

The soft glassy rheology (SGR) model has successfully described the time dependent simple shear rheology of a broad class of complex fluids including foams, concentrated emulsions, colloidal glasses, and solvent-free nanoparticle-organic hybrid materials (NOHMs). The model considers a distribution of mesoscopic fluid elements that hop from trap to trap at a rate which is enhanced by the work done to strain the fluid element. While an SGR fluid has a broad exponential distribution of trap energies, the rheology of NOHMs is better described by a narrower energy distribution and we consider both types of trap energy distributions in this study.more » We introduce a tensorial version of these models with a hopping rate that depends on the orientation of the element relative to the mean stress field, allowing a range of relative strengths of the extensional and simple shear responses of the fluid. As an application of these models we consider the flow of a soft glassy material through a dilute fixed bed of fibers. The dilute fixed bed exhibits a range of local linear flows which alternate in a chaotic manner with time in a Lagrangian reference frame. It is amenable to an analytical treatment and has been used to characterize the strong flow response of many complex fluids including fiber suspensions, dilute polymer solutions and emulsions. We show that the accumulated strain in the fluid elements has an abrupt nonlinear growth at a Deborah number of order one in a manner similar to that observed for polymer solutions. The exponential dependence of the hopping rate on strain leads to a fluid element deformation that grows logarithmically with Deborah number at high Deborah numbers. SGR fluids having a broad range of trap energies flowing through fixed beds can exhibit a range of rheological behaviors at small Deborah numbers ranging from a yield stress, to a power law response and finally to Newtonian behavior.« less

Quantum-chaotic cryptography

NASA Astrophysics Data System (ADS)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Chimera states in coupled Kuramoto oscillators with inertia.

PubMed

Olmi, Simona

2015-12-01

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.

A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator

NASA Astrophysics Data System (ADS)

Tong, Xiaojun; Cui, Minggen; Wang, Zhu

2009-07-01

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.

Passive micromixers with dual helical channels

NASA Astrophysics Data System (ADS)

Liu, Keyin; Yang, Qing; Chen, Feng; Zhao, Yulong; Meng, Xiangwei; Shan, Chao; Li, Yanyang

2015-02-01

In this study, a three-dimensional (3D) micromixer with cross-linked double helical microchannels is studied to achieve rapid mixing of fluids at low Reynolds numbers (Re). The 3D micromixer takes full advantages of the chaotic advection model with helical microchannels; meanwhile, the proposed crossing structure of double helical microchannels enables two flow patterns of repelling flow and straight flow in the fluids to promote the agitation effect. The complex 3D micromixer is realized by an improved femtosecond laser wet etching (FLWE) technology embedded in fused silica. The mixing results show that cross-linked double helical microchannels can achieve excellent mixing within 3 cycles (300 μm) over a wide range of low Re (1.5×10-3~600), which compare well with the conventional passive micromixers. This highly-effective micromixer is hoped to contribute to the integration of microfluidic systems.

Ion dynamics in the Venus ionosphere

NASA Astrophysics Data System (ADS)

Miller, K. L.; Whitten, R. C.

1991-02-01

Measurement data on the ion velocity in the Venus ionosphere (mainly from the Pioneer Venus Orbiter Retarding Potential Analyzer) are summarized, and theoretical models developed to explain them are reviewed. Data and theoretical predictions are compared in extensive graphs and diagrams and discussed in detail. It is shown that the predominant flow is away from the subsolar point, at up to 3 km/sec in the terminator region. A model of axisymmetric flow based on momentum, energy, and mass conservation laws is found to reproduce the observed ion velocities at solar zenith angles less than about 140 deg, but not the high velocities and chaotic behavior seen near the antisolar point. Also discussed are significant differences between the flow above and below about 400 km and the effects of changes in the dynamic pressure of the solar wind.

A New Method for Suppressing Periodic Narrowband Interference Based on the Chaotic van der Pol Oscillator

NASA Astrophysics Data System (ADS)

Lu, Jia; Zhang, Xiaoxing; Xiong, Hao

The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.

Robust synchronization of spin-torque oscillators with an LCR load.

PubMed

Pikovsky, Arkady

2013-09-01

We study dynamics of a serial array of spin-torque oscillators with a parallel inductor-capacitor-resistor (LCR) load. In a large range of parameters the fully synchronous regime, where all the oscillators have the same state and the output field is maximal, is shown to be stable. However, not always such a robust complete synchronization develops from a random initial state; in many cases nontrivial clustering is observed, with a partial synchronization resulting in a quasiperiodic or chaotic mean-field dynamics.