Search NASA⌕ Search

SEARCH · Search NASA

Results for “chaotic motion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

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

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.

Abedian, B.↗
DOE OSTI2021

How Hall electric fields intrinsically chaotize and heat ions during collisionless magnetic reconnection

The origin of extreme and anomalous ion heating during magnetic reconnection has been a longstanding mystery. It is shown in this paper that, at the core of the process, the stochastic heating mechanism is responsible for this energization. The in-plane Hall electric fields that intrinsically develop during collisionless reconnection not only accelerate ions, but also thermalize them by inducing chaotic motion. The mechanism explains various observed features of ion heating, e.g., its relation to the guide field strength and the ion mass-to-charge ratio.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Guiding center and gyrokinetic orbit theory for large electric field gradients and strong shear flows

The guiding center and gyrokinetic theory of magnetized particle motion is extended to the regime of large electric field gradients perpendicular to the magnetic field. A gradient in the electric field directly modifies the oscillation frequency and causes the Larmor orbits to deform from circular to elliptical trajectories. In order to retain a good adiabatic invariant, there can only be strong dependence on a single coordinate at lowest order, so that resonances do not generate chaotic motion that destroys the invariant. When the gradient across magnetic flux surfaces is dominant, the guiding center drift velocity becomes anisotropic in response to external forces and additional curvature drifts must be included. The electric polarization density remains gyrotropic, but both the polarization and magnetization are modified by the change in gyrofrequency. The theory can be applied to shear flows that are even stronger than those observed in the edge transport barrier of a high-performance tokamak (H-mode) pedestal, even if the toroidal field is as small as or even smaller than the poloidal field. Yet, the theory retains a mathematical form that is similar to the standard case and can readily be implemented within existing simulation tools.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1985

A model of flow in a closed-loop thermosyphon including the Soret effect

This theoretical study addresses the nature of convective motions in a toroidal loop of binary fluid oriented in the vertical plane and heated from below. The boundaries of the loop are impermeable, but gradients of the solute can be set up by Soret diffusion in the direction around the loop. The existence and stability of steady solutions are discussed over the Rayleigh number-Soret coefficient parameter plane. When the Soret coefficient is negative, periodic and chaotic oscillations analogous to those of thermohaline convection are predicted. When the Soret coefficient is positive, relaxation oscillations and low Rayleigh number chaotic motions are found. Both sets of phenomena are predicted to occur for realistic thermosyphon parameters.

Hart, J. E.↗
NASA NTRS2002

Laminar-Turbulent Transition in an Electromagnetically-Levitated Droplet

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 can be inferred from motion of impurity particulates on the surface. In the experiments, subsequent to melting, Joule heating produces a continuous reduction of viscosity of the fluid resulting in an acceleration of the flow with time. These observations indicate formation of a pair of corotating toroidal flow structures inside the spheroidal drop that undergo flow instabilities. As the fluid temperature rises, the amplitude of the secondary flow increases; and beyond a point, the tracers exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. Assuming that the observed laminar-turbulent transition is shear-layer type, the internal structure of the toroidal loops is used to develop a semi-empirical correlation for the onset of turbulence. Our calculations indicate that the suggested correlation is in modest agreement with the experimental data, with the transition occurring at a Reynolds number of 600.

Hyers, Robert W.↗
NASA NTRS2002

Laminar-Turbulent Transition in an Electromagnetically-Levitated Droplet

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 can be inferred from motion of impurity particulates on the surface. In the experiments, subsequent to melting, Joule heating produces a continuous reduction of viscosity of the fluid resulting in an acceleration of the flow with time. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal drop that undergo flow instabilities. As the fluid temperature rises, the amplitude of the secondary flow increases; and beyond a point, the tracers exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. Assuming that the observed laminar-turbulent transition is shear-layer type, the internal structure of the toroidal loops is used to develop a semi- empirical correlation for the onset of turbulence. Our calculations indicate that the suggested correlation is in modest agreement with the experimental data, with the transition occurring at a Reynolds number of 600.

Hyers, R. W.↗
DOE OSTI2021

Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases

Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions.Today, tools such as transfer matrix and finite elements enable the calculation of the rotordynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems.In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered.The purpose of this chapter is to show examples of how the linear vs. nonlinear formulations differ. This chapter also shows how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.

Laos, Hector↗
DOE OSTI2021

Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases

Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotor dynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this paper is to show examples of how the linear vs. nonlinear formulations differ. This paper will also show how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.

42 ENGINEERING↗
NASA NTRS1994

Electron collection by a highly positive satellite in the ionosphere: Test aprticle simulation

Collection of electrons by a satellite at a relatively high potential in low Earth orbit, including the effects of the satellite's orbital motion, remains a poorly understood phenomenon. Using a test particle simulation in which charged particle motion is tracked in prescribed electric fields, we calculate here the current collection and the nature of the energy distribution function of the electrons collected by the satellite, including the effects of the satellite orbital motion. Calculations of the collected current without the orbital motion show an excellent agreement with the current from the Parker-Murphy model, but with the orbital motion of the satellite the current collection is enhanced, the degree of enhancement depending on the size of the satellite sheath extending along the magnetic field line. In the latter case, the flow of electrons around the satellite shows some interesting behaviors including azimuthal E x B drift around the satellite, axial trapping along the magnetic field, and formation of field-aligned flow of electrons in the wake region. The total energy of the collected electrons is approximately equal e phi(sub 0), where phi(sub 0) is the satellite potential, but the partition of the energy into components parallel (W(sub parallel)) and perpendicular (W(sub perpendicular)) to the magnetic field shows interesting features. For the magnetic field along the polar axis Z, the energy distributions near the poles are perfectly field aligned, that is, the parallel energy (W(sub parallel) = e phi(sub 0). The perpendicular component (W(sub perpendicular)) progressively increases toward the 'equator' of the spherical satellite. For a sufficiently large bias potential phi(sub 0), the equatorial energy distributions f(W(sub parallel)) and f(W(sub perpendicular)) show fine structures having multiple peaks. These features of the distribution functions result from the chaotic motion of electrons and the associated coupling between the electron motions parallel and perpendicular to the magnetic field in strongly nonuniform electric fields near the satellite.

Singh, Nagendra↗
DOE OSTI2020

Fast dynamic aperture optimization with forward-reversal integration

A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. “backward integrations.” The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. Finally, the DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Shaker-structure interaction modeling and analysis for nonlinear force appropriation testing

Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. Finally, the results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system’s dynamics.

42 ENGINEERING↗
DOE OSTI2021

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. Finally, the patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Dynamics of Magnus-dominated particle clusters, collisions, pinning, and ratchets

Motivated by the recent work in skyrmions and active chiral matter systems, we examine pairs and small clusters of repulsively interacting point particles in the limit where the dynamics is dominated by the Magnus force. We find that particles with the same Magnus force can form stable pairs, triples, and higher ordered clusters or exhibit chaotic motion. For mixtures of particles with opposite Magnus force, particle pairs can combine to form translating dipoles. Under an applied drive, particles with the same Magnus force translate; however, particles with different or opposite Magnus force exhibit a drive-dependent decoupling transition. When the particles interact with a repulsive obstacle, they can form localized orbits with depinning or unwinding transitions under an applied drive. We examine the interaction of these particles with clusters or lines of obstacles and find that the particles can become trapped in orbits that encircle multiple obstacles. Under an ac drive, we observe a series of ratchet effects, including ratchet reversals, for particles interacting with a line of obstacles due to the formation of commensurate orbits. Lastly, in assemblies of particles with mixed Magnus forces of the same sign, we find that the particles with the largest Magnus force become localized in the center of the cluster, while for mixtures with opposite Magnus forces, the motion is dominated by transient local pairs or clusters, where the translating pairs can be regarded as a form of active matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Fast Dynamic Aperture Optimization with Reversal Integration

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.

36 MATERIALS SCIENCE↗
NASA NTRS1972

Parameters of small scale ionization inhomogeneities in the F region of the ionosphere

The results of the parameters of small-scale ionization inhomogeneities study of the ionosphere's F-region for October-November 1965 and January-February 1966 are presented. It is shown that the most probable values of the inhomogeneity parameters are as follows: degree of anisotropy 1.4-2; vertical dimension 200-400 m; horizontal dimensions along major and minor axes 400-1000 and 200-600 m, respectively; rate of chaotic motions 30-60 m/sec; lifetime 6-9 sec.

Drobzhev, V. I.↗
NASA NTRS1987

Deterministic representation of chaos with application to turbulence

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

Zak, M.↗
NASA NTRS1988

Dynamics of the Uranian and Saturnian satellite systems - A chaotic route to melting Miranda?

Miranda's anomalously large inclination, in conjunction with the postaccretional resurfacing of both Miranda and Ariel and anomalously large eccentricities characterizing the inner Uranian satellites, are presently held to suggest the disruption of resonant configurations that once existed in this satellite system. Classical analytical methods for the dynamics of resonance are here used to demonstrate how temporary capture into a second- or higher-order resonance can generate large increases in eccentricity and inclination on comparatively short time-scales. Such capture into resonance may result in chaotic motion.

Dermott, Stanley F.↗
NASA NTRS1989

Evanescent radiation, quantum mechanics and the Casimir effect

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

Schatten, Kenneth H.↗