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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Chaotic dynamics of flexible Euler-Bernoulli beams

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

A new type of instability—electrokinetic instability—and an unusual transition to chaotic motion near a charge-selective surface (semiselective electric membrane, electrode, or system of micro-/nanochannels) was studied by the numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. A special finite-difference method was used for the space discretization along with a semi-implicit 31/3 -step Runge-Kutta scheme for the integration in time. Two kinds of initial conditions were considered: (a) white-noise initial conditions to mimic “room disturbances” and subsequent natural evolution of the solution, and (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. Our weakly nonlinear analysis and numerical integration of the entire system predict possibility of both kinds of bifurcations at the critical point, supercritical and subcritical, depending on the system parameters. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution, two-dimensional steady electroconvective vortices (stationary point in a proper phase space), unsteady vortices aperiodically changing their parameters (homoclinic contour), periodic motion (limit cycle), and chaotic motion. The transition to chaotic motion does not include Hopf bifurcation. The numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt–current characteristics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise

We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Multi-scale coarse-graining of non-conservative interactions in molecular liquids

A new bottom-up procedure for constructing non-conservative (dissipative and stochastic) interactions for dissipative particle dynamics (DPD) models is described and applied to perform hierarchical coarse-graining of a polar molecular liquid (nitromethane). The distant-dependent radial and shear frictions in functional-free form are derived consistently with a chosen form for conservative interactions by matching two-body force-velocity and three-body velocity-velocity correlations along the microscopic trajectories of the centroids of Voronoi cells (clusters), which represent the dissipative particles within the DPD description. The Voronoi tessellation is achieved by application of the K-means clustering algorithm at regular time intervals. Consistently with a notion of many-body DPD, the conservative interactions are determined through the multi-scale coarse-graining (MS-CG) method, which naturally implements a pairwise decomposition of the microscopic free energy. A hierarchy of MS-CG/DPD models starting with one molecule per Voronoi cell and up to 64 molecules per cell is derived. The radial contribution to the friction appears to be dominant for all models. As the Voronoi cell sizes increase, the dissipative forces rapidly become confined to the first coordination shell. For Voronoi cells of two and more molecules the time dependence of the velocity autocorrelation function becomes monotonic and well reproduced by the respective MS-CG/DPD models. A comparative analysis of force and velocity correlations in the atomistic and CG ensembles indicates Markovian behavior with as low as two molecules per dissipative particle. The models with one and two molecules per Voronoi cell yield transport properties (diffusion and shear viscosity) that are in good agreement with the atomistic data. The coarser models produce slower dynamics that can be appreciably attributed to unaccounted dissipation introduced by regular Voronoi re-partitioning as well as by larger numerical errors in mapping out the dissipative forces. The framework presented herein can be used to develop computational models of real liquids which are capable of bridging the atomistic and mesoscopic scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

A test for a conjecture on the nature of attractors for smooth dynamical systems

Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter include many classical examples such as Lorenz and Hénon-like attractors and enjoy strong statistical properties. It is natural to conjecture (or at least hope) that most dynamical systems fall into these two extreme situations. We describe a numerical test for such a conjecture/hope and apply this to the logistic map where the conjecture holds by a theorem of Lyubich, and to the 40-dimensional Lorenz-96 system where there is no rigorous theory. The numerical outcome is almost identical for both (except for the amount of data required) and provides evidence for the validity of the conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Novel insight into the hydrogen absorption mechanism at the Pd(110) surface

The microscopic mechanism of low-temperature (80 K < T < 160 K) hydrogen (H) ingress into the H{sub 2} (<2.66 × 10{sup −3} Pa) exposed Pd(110) surface is explored by H depth profiling with {sup 15}N nuclear reaction analysis (NRA) and thermal desorption spectroscopy (TDS) with isotope (H, D) labeled surface hydrogen. NRA and TDS reveal two types of absorbed hydrogen states of distinctly different depth distributions. Between 80 K and ∼145 K a near-surface hydride phase evolving as the TDS α{sub 1} feature at 160 K forms, which initially extends only several nanometers into depth. On the other hand, a bulk-absorbed hydrogen state develops between 80 K and ∼160 K which gives rise to a characteristic α{sub 3} TDS feature above 190 K. These two absorbed states are populated at spatially separated surface entrance channels. The near-surface hydride is populated through rapid penetration at minority sites (presumably defects) while the bulk-absorbed state forms at regular terraces with much lower probability per site. In both cases, absorption of gas phase hydrogen transfers pre-adsorbed hydrogen atoms below the surface and replaces them at the chemisorption sites by post-dosed hydrogen in a process that requires much less activation energy (<100 meV) than monatomic diffusion of chemisorbed H atoms into subsurface sites. This small energy barrier suggests that the rate-determining step of the absorption process is either H{sub 2} dissociation on the H-saturated Pd surface or a concerted penetration mechanism, where excess H atoms weakly bound to energetically less favorable adsorption sites stabilize themselves in the chemisorption wells while pre-chemisorbed H atoms simultaneously transit into the subsurface. The peculiarity of absorption at regular Pd(110) terraces in comparison to Pd(111) and Pd(100) is discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Non-invasive material discrimination using spectral x-ray radiography

Current radiographic methods are limited in their ability to determine the presence of nuclear materials in containers or composite objects. A central problem is the inability to distinguish the attenuation pattern of high-density metals from those with a greater thickness of a less dense material. Here, we show that spectrally sensitive detectors can be used to discriminate plutonium from multiple layers of other materials using a single-view radiograph. An inverse algorithm with adaptive regularization is used. The algorithm can determine the presence of plutonium in simulated radiographs with a mass resolution per unit area of at least 0.07 g cm{sup −2}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays

In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A novel electron density reconstruction method for asymmetrical toroidal plasmas

A novel reconstruction method is developed for acquiring the electron density profile from multi-channel interferometric measurements of strongly asymmetrical toroidal plasmas. It is based on a regularization technique, and a generalized cross-validation function is used to optimize the regularization parameter with the aid of singular value decomposition. The feasibility of method could be testified by simulated measurements based on a magnetic configuration of the flexible helical-axis heliotron device, Heliotron J, which has an asymmetrical poloidal cross section. And the successful reconstruction makes possible to construct a multi-channel Far-infrared laser interferometry on this device. The advantages of this method are demonstrated by comparison with a conventional method. The factors which may affect the accuracy of the results are investigated, and an error analysis is carried out. Based on the obtained results, the proposed method is highly promising for accurately reconstructing the electron density in the asymmetrical toroidal plasma.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle

The present article is concerned with the charge conserving Poisson-Boltzmann (CCPB) equation in high-dimensional bounded smooth domains. The CCPB equation is a Poisson-Boltzmann type of equation with nonlocal coefficients. First, under the Robin boundary condition, we get the existence of weak solutions to this equation. The main approach is variational, based on minimization of a logarithm-type energy functional. To deal with the regularity of weak solutions, we establish a maximum modulus estimate for the standard Poisson-Boltzmann (PB) equation to show that weak solutions of the CCPB equation are essentially bounded. Then the classical solutions follow from the elliptic regularity theorem. Second, a maximum principle for the CCPB equation is established. In particular, we show that in the case of global electroneutrality, the solution achieves both its maximum and minimum values at the boundary. However, in the case of global non-electroneutrality, the solution may attain its maximum value at an interior point. In addition, under certain conditions on the boundary, we show that the global non-electroneutrality implies pointwise non-electroneutrality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Plasma wakefields driven by an incoherent combination of laser pulses: A path towards high-average power laser-plasma accelerators

The wakefield generated in a plasma by incoherently combining a large number of low energy laser pulses (i.e., without constraining the pulse phases) is studied analytically and by means of fully self-consistent particle-in-cell simulations. The structure of the wakefield has been characterized and its amplitude compared with the amplitude of the wake generated by a single (coherent) laser pulse. We show that, in spite of the incoherent nature of the wakefield within the volume occupied by the laser pulses, behind this region, the structure of the wakefield can be regular with an amplitude comparable or equal to that obtained from a single pulse with the same energy. Wake generation requires that the incoherent structures in the laser energy density produced by the combined pulses exist on a time scale short compared to the plasma period. Incoherent combination of multiple laser pulses may enable a technologically simpler path to high-repetition rate, high-average power laser-plasma accelerators, and associated applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Origins of interlayer formation and misfit dislocation displacement in the vicinity of InAs/GaAs quantum dots

We have examined the origins of interlayer formation and misfit dislocation (MD) displacement in the vicinity of InAs/GaAs quantum dots (QDs). For QDs formed by the Stranski-Krastanov mode, regularly spaced MDs nucleate at the interface between the QD and the GaAs buffer layer. In the droplet epitaxy case, both In island formation and In-induced “nano-drilling” of the GaAs buffer layer are observed during In deposition. Upon annealing under As flux, the In islands are converted to InAs QDs, with an InGaAs interlayer at the QD/buffer interface. Meanwhile, MDs nucleate at the QD/interlayer interface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaks

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at the Large Helical Device. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICS can provide profile measurements of the local emissivity, temperature, and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modified Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example, geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Photo-ionization and residual electron effects in guided streamers

Complementary experiments and numerical modeling reveal the important role of photo-ionization in the guided streamer propagation in helium-air gas mixtures. It is shown that the minimum electron concentration ∼10{sup 8 }cm{sup −3} is required for the regular, repeated propagation of the plasma bullets, while the streamers propagate in the stochastic mode below this threshold. The stochastic-to-regular mode transition is related to the higher background electron density in front of the propagating streamers. These findings help improving control of guided streamer propagation in applications from health care to nanotechnology and improve understanding of generic pre-breakdown phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

High-speed atomic force microscope based on an astigmatic detection system

High-speed atomic force microscopy (HS-AFM) enables visualizing dynamic behaviors of biological molecules under physiological conditions at a temporal resolution of 1s or shorter. A small cantilever with a high resonance frequency is crucial in increasing the scan speed. However, detecting mechanical resonances of small cantilevers is technically challenging. In this study, we constructed an atomic force microscope using a digital versatile disc (DVD) pickup head to detect cantilever deflections. In addition, a flexure-guided scanner and a sinusoidal scan method were implemented. In this work, we imaged a grating sample in air by using a regular cantilever and a small cantilever with a resonance frequency of 5.5 MHz. Poor tracking was seen at the scan rate of 50 line/s when a cantilever for regular AFM imaging was used. Using a small cantilever at the scan rate of 100 line/s revealed no significant degradation in the topographic images. The results indicate that a smaller cantilever can achieve a higher scan rate and superior force sensitivity. This work shows the potential for using a DVD pickup head in future HS-AFM technology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Zonal wavefront estimation using an array of hexagonal grating patterns

Accuracy of Shack-Hartmann type wavefront sensors depends on the shape and layout of the lenslet array that samples the incoming wavefront. It has been shown that an array of gratings followed by a focusing lens provide a substitution for the lensslet array. Taking advantage of the computer generated holography technique, any arbitrary diffraction grating aperture shape, size or pattern can be designed with little penalty for complexity. In the present work, such a holographic technique is implemented to design regular hexagonal grating array to have zero dead space between grating patterns, eliminating the possibility of leakage of wavefront during the estimation of the wavefront. Tessellation of regular hexagonal shape, unlike other commonly used shapes, also reduces the estimation error by incorporating more number of neighboring slope values at an equal separation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Efficient field-theoretic simulation of polymer solutions

We present several developments that facilitate the efficient field-theoretic simulation of polymers by complex Langevin sampling. A regularization scheme using finite Gaussian excluded volume interactions is used to derive a polymer solution model that appears free of ultraviolet divergences and hence is well-suited for lattice-discretized field theoretic simulation. We show that such models can exhibit ultraviolet sensitivity, a numerical pathology that dramatically increases sampling error in the continuum lattice limit, and further show that this pathology can be eliminated by appropriate model reformulation by variable transformation. We present an exponential time differencing algorithm for integrating complex Langevin equations for field theoretic simulation, and show that the algorithm exhibits excellent accuracy and stability properties for our regularized polymer model. These developments collectively enable substantially more efficient field-theoretic simulation of polymers, and illustrate the importance of simultaneously addressing analytical and numerical pathologies when implementing such computations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗