Numerical Simulations of Dynamical Mass Transfer in Binaries

NASA Astrophysics Data System (ADS)

Motl, P. M.; Frank, J.; Tohline, J. E.

1999-05-01

We will present results from our ongoing research project to simulate dynamically unstable mass transfer in near contact binaries with mass ratios different from one. We employ a fully three-dimensional self-consistent field technique to generate synchronously rotating polytropic binaries. With our self-consistent field code we can create equilibrium binaries where one component is, by radius, within about 99 of filling its Roche lobe for example. These initial configurations are evolved using a three-dimensional, Eulerian hydrodynamics code. We make no assumptions about the symmetry of the subsequent flow and the entire binary system is evolved self-consistently under the influence of its own gravitational potential. For a given mass ratio and polytropic index for the binary components, mass transfer via Roche lobe overflow can be predicted to be stable or unstable through simple theoretical arguments. The validity of the approximations made in the stability calculations are tested against our numerical simulations. We acknowledge support from the U.S. National Science Foundation through grants AST-9720771, AST-9528424, and DGE-9355007. This research has been supported, in part, by grants of high-performance computing time on NPACI facilities at the San Diego Supercomputer Center, the Texas Advanced Computing Center and through the PET program of the NAVOCEANO DoD Major Shared Resource Center in Stennis, MS.

A Dynamical Systems Approach to the Design of the Science Orbit Around Europa

NASA Technical Reports Server (NTRS)

Gomez, Gerard; Lara, Martin; Russell, Ryan P.

2006-01-01

The science orbit for a future mission to Europa requires low eccentricity, low altitude, and high inclination. However, high inclination orbits around planetary satellites are unstable due to third-body perturbations. Without control, the orbiter impacts Europa after few weeks. To minimize control, a tour over the stable-unstable, averaged manifolds of unstable frozen orbits has been suggested. We proceed with the unaveraged equations and study the manifolds of unstable orbits that are periodic in a rotating frame attached to Europa. Massive numerical computation helps in understanding the unstable dynamics close to Europa, and, thus, in selecting long lifetime high inclination orbits. A final test of a selected set of initial conditions on a high fidelity, ephemeris model, validate the results.

2D OR NOT 2D: THE EFFECT OF DIMENSIONALITY ON THE DYNAMICS OF FINGERING CONVECTION AT LOW PRANDTL NUMBER

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

Garaud, Pascale; Brummell, Nicholas

2015-12-10

Fingering convection (otherwise known as thermohaline convection) is an instability that occurs in stellar radiative interiors in the presence of unstable compositional gradients. Numerical simulations have been used in order to estimate the efficiency of mixing induced by this instability. However, fully three-dimensional (3D) computations in the parameter regime appropriate for stellar astrophysics (i.e., low Prandtl number) are prohibitively expensive. This raises the question of whether two-dimensional (2D) simulations could be used instead to achieve the same goals. In this work, we address this issue by comparing the outcome of 2D and 3D simulations of fingering convection at low Prandtlmore » number. We find that 2D simulations are never appropriate. However, we also find that the required 3D computational domain does not have to be very wide: the third dimension only needs to contain a minimum of two wavelengths of the fastest-growing linearly unstable mode to capture the essentially 3D dynamics of small-scale fingering. Narrow domains, however, should still be used with caution since they could limit the subsequent development of any large-scale dynamics typically associated with fingering convection.« less

Effects of constant immigration on the dynamics and persistence of stable and unstable Drosophila populations

PubMed Central

Dey, Snigdhadip; Joshi, Amitabh

2013-01-01

Constant immigration can stabilize population size fluctuations but its effects on extinction remain unexplored. We show that constant immigration significantly reduced extinction in fruitfly populations with relatively stable or unstable dynamics. In unstable populations with oscillations of amplitude around 1.5 times the mean population size, persistence and constancy were unrelated. Low immigration enhanced persistence without affecting constancy whereas high immigration increased constancy without enhancing persistence. In relatively stable populations with erratic fluctuations of amplitude close to the mean population size, both low and high immigration enhanced persistence. In these populations, the amplitude of fluctuations relative to mean population size went down due to immigration, and their dynamics were altered to low-period cycles. The effects of immigration on the population size distribution and intrinsic dynamics of stable versus unstable populations differed considerably, suggesting that the mechanisms by which immigration reduced extinction risk depended on underlying dynamics in complex ways. PMID:23470546

Comparison of Laminar and Linear Eddy Model Closures for Combustion Instability Simulations

DTIC Science & Technology

2015-07-01

14. ABSTRACT Unstable liquid rocket engines can produce highly complex dynamic flowfields with features such as rapid changes in temperature and...applicability. In the present study, the linear eddy model (LEM) is applied to an unstable single element liquid rocket engine to assess its performance and to...Sankaran‡ Air Force Research Laboratory, Edwards AFB, CA, 93524 Unstable liquid rocket engines can produce highly complex dynamic flowfields with features

Numerical Investigation of Three-dimensional Instability of Standing Waves

NASA Astrophysics Data System (ADS)

Zhu, Qiang; Liu, Yuming; Yue, Dick K. P.

2002-11-01

We study the three-dimensional instability of finite-amplitude standing waves under the influence of gravity using the transition matrix method. For accurate calculation of the transition matrices, we apply an efficient high-order spectral element method for nonlinear wave dynamics in complex domain. We consider two types of standing waves: (a) plane standing waves; and (b) standing waves in a circular tank. For the former, in addition to the confirmation of the side-band-like instability, we find a new three-dimensional instability for arbitrary base standing waves. The dominant component of the unstable disturbance is an oblique standing wave, with an arbitrary angle relative to the base flow, whose frequency is approximately equal to that of the base standing wave. Based on direct simulations, we confirm such a three-dimensional instability and show the occurrence of the Fermi-Pasta-Ulam recurrence phenomenon during nonlinear evolution. For the latter, we find that beyond a threshold wave steepness, the standing wave with frequency Ω becomes unstable to a small three-dimensional disturbance, which contains two dominant standing-wave components with frequencies ω1 and ω_2, provided that 2Ω ω1 + ω_2. The threshold wave steepness is found to decrease/increase as the radial/azimuthal wavenumber of the base standing wave increases. We show that the instability of standing waves in rectangular and circular tanks is caused by third-order quartet resonances between base flow and disturbance.

Modeling unstable alcohol flooding of DNAPL-contaminated columns

NASA Astrophysics Data System (ADS)

Roeder, Eberhard; Falta, Ronald W.

Alcohol flooding, consisting of injection of a mixture of alcohol and water, is one source removal technology for dense non-aqueous phase liquids (DNAPLs) currently under investigation. An existing compositional multiphase flow simulator (UTCHEM) was adapted to accurately represent the equilibrium phase behavior of ternary and quaternary alcohol/DNAPL systems. Simulator predictions were compared to laboratory column experiments and the results are presented here. It was found that several experiments involved unstable displacements of the NAPL bank by the alcohol flood or of the alcohol flood by the following water flood. Unstable displacement led to additional mixing compared to ideal displacement. This mixing was approximated by a large dispersion in one-dimensional simulations and or by including permeability heterogeneities on a very small scale in three-dimensional simulations. Three-dimensional simulations provided the best match. Simulations of unstable displacements require either high-resolution grids, or need to consider the mixing of fluids in a different manner to capture the resulting effects on NAPL recovery.

Multistability and hidden attractors in a relay system with hysteresis

NASA Astrophysics Data System (ADS)

Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.; Nabokov, Roman A.

2015-06-01

For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.

Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Wang, Ya-Guang

2008-03-01

Compressible vortex sheets are fundamental waves, along with shocks and rarefaction waves, in entropy solutions to multidimensional hyperbolic systems of conservation laws. Understanding the behavior of compressible vortex sheets is an important step towards our full understanding of fluid motions and the behavior of entropy solutions. For the Euler equations in two-dimensional gas dynamics, the classical linearized stability analysis on compressible vortex sheets predicts stability when the Mach number M > sqrt{2} and instability when M < sqrt{2} ; and Artola and Majda’s analysis reveals that the nonlinear instability may occur if planar vortex sheets are perturbed by highly oscillatory waves even when M > sqrt{2} . For the Euler equations in three dimensions, every compressible vortex sheet is violently unstable and this instability is the analogue of the Kelvin Helmholtz instability for incompressible fluids. The purpose of this paper is to understand whether compressible vortex sheets in three dimensions, which are unstable in the regime of pure gas dynamics, become stable under the magnetic effect in three-dimensional magnetohydrodynamics (MHD). One of the main features is that the stability problem is equivalent to a free-boundary problem whose free boundary is a characteristic surface, which is more delicate than noncharacteristic free-boundary problems. Another feature is that the linearized problem for current-vortex sheets in MHD does not meet the uniform Kreiss Lopatinskii condition. These features cause additional analytical difficulties and especially prevent a direct use of the standard Picard iteration to the nonlinear problem. In this paper, we develop a nonlinear approach to deal with these difficulties in three-dimensional MHD. We first carefully formulate the linearized problem for the current-vortex sheets to show rigorously that the magnetic effect makes the problem weakly stable and establish energy estimates, especially high-order energy estimates, in terms of the nonhomogeneous terms and variable coefficients. Then we exploit these results to develop a suitable iteration scheme of the Nash Moser Hörmander type to deal with the loss of the order of derivative in the nonlinear level and establish its convergence, which leads to the existence and stability of compressible current-vortex sheets, locally in time, in three-dimensional MHD.

From Two‐ to Three‐Dimensional Structures of a Supertetrahedral Boran Using Density Functional Calculations

PubMed Central

Getmanskii, Iliya V.; Steglenko, Dmitrii V.; Koval, Vitaliy V.; Zaitsev, Stanislav A.

2017-01-01

Abstract With help of the DFT calculations and imposing of periodic boundary conditions the geometrical and electronic structures were investigated of two‐ and three‐dimensional boron systems designed on the basis of graphane and diamond lattices in which carbons were replaced with boron tetrahedrons. The consequent studies of two‐ and three‐layer systems resulted in the construction of a three‐dimensional supertetrahedral borane crystal structure. The two‐dimensional supertetrahedral borane structures with less than seven layers are dynamically unstable. At the same time the three‐dimensional superborane systems were found to be dynamically stable. Lack of the forbidden electronic zone for the studied boron systems testifies that these structures can behave as good conductors. The low density of the supertetrahedral borane crystal structures (0.9 g cm−3) is close to that of water, which offers the perspective for their application as aerospace and cosmic materials. PMID:28402596

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

DOE PAGES

Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; ...

2011-02-10

Here, this article examines the localization of time harmonic high-frequency modal fields in two-dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This article examines the enhancements for these unstable orbits when the opposing mirrors are convex, constructing the high-frequency field in the scar region using elliptic cylinder coordinates in combination with a random reflection phase from the outer chaotic region. Finally, the enhancements when the cavity is symmetric as well as asymmetric about the orbit are examined.

On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper mesosphere

NASA Astrophysics Data System (ADS)

Fruman, Mark D.; Remmler, Sebastian; Achatz, Ulrich; Hickel, Stefan

2014-10-01

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear "2.5-D" simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.

A note on chaotic unimodal maps and applications.

PubMed

Zhou, C T; He, X T; Yu, M Y; Chew, L Y; Wang, X G

2006-09-01

Based on the word-lift technique of symbolic dynamics of one-dimensional unimodal maps, we investigate the relation between chaotic kneading sequences and linear maximum-length shift-register sequences. Theoretical and numerical evidence that the set of the maximum-length shift-register sequences is a subset of the set of the universal sequence of one-dimensional chaotic unimodal maps is given. By stabilizing unstable periodic orbits on superstable periodic orbits, we also develop techniques to control the generation of long binary sequences.

Structure and Stability of One-Dimensional Detonations in Ethylene-Air Mixtures

NASA Technical Reports Server (NTRS)

Yungster, S.; Radhakrishnan, K.; Perkins, High D. (Technical Monitor)

2003-01-01

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of 0.5 less than phi less than 3 for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures (phi greater than 1.2) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed; that is, a galloping propagation mode is established. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.

Canards and black swans in a model of a 3-D autocatalator

NASA Astrophysics Data System (ADS)

Shchepakina, E.

2005-01-01

The mathematical model of a 3-D autocatalator is studied using the geometric theory of singular perturbations, namely, the black swan and canard techniques. Critical regimes are modeled by canards (one-dimensional stable-unstable slow integral manifolds). The meaning of criticality here is as follows. The critical regime corresponds to a chemical reaction which separates the domain of self-accelerating reactions from the domain of slow reactions. A two-dimensional stable-unstable slow integral manifold (black swan) consisting entirely of canards, which simulate the critical phenomena for different initial data of the dynamical system, is constructed. It is shown that this procedure leads to the phenomenon of auto-oscillations in the chemical system. The geometric approach combined with asymptotic and numerical methods permits us to explain the strong parametric sensitivity and to obtain asymptotic representations of the critical behavior of the chemical system.

From Two- to Three-Dimensional Structures of a Supertetrahedral Boran Using Density Functional Calculations.

PubMed

Getmanskii, Iliya V; Minyaev, Ruslan M; Steglenko, Dmitrii V; Koval, Vitaliy V; Zaitsev, Stanislav A; Minkin, Vladimir I

2017-08-14

With help of the DFT calculations and imposing of periodic boundary conditions the geometrical and electronic structures were investigated of two- and three-dimensional boron systems designed on the basis of graphane and diamond lattices in which carbons were replaced with boron tetrahedrons. The consequent studies of two- and three-layer systems resulted in the construction of a three-dimensional supertetrahedral borane crystal structure. The two-dimensional supertetrahedral borane structures with less than seven layers are dynamically unstable. At the same time the three-dimensional superborane systems were found to be dynamically stable. Lack of the forbidden electronic zone for the studied boron systems testifies that these structures can behave as good conductors. The low density of the supertetrahedral borane crystal structures (0.9 g cm -3 ) is close to that of water, which offers the perspective for their application as aerospace and cosmic materials. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

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.

Act-and-wait time-delayed feedback control of autonomous systems

NASA Astrophysics Data System (ADS)

Pyragas, Viktoras; Pyragas, Kestutis

2018-02-01

Recently an act-and-wait modification of time-delayed feedback control has been proposed for the stabilization of unstable periodic orbits in nonautonomous dynamical systems (Pyragas and Pyragas, 2016 [30]). The modification implies a periodic switching of the feedback gain and makes the closed-loop system finite-dimensional. Here we extend this modification to autonomous systems. In order to keep constant the phase difference between the controlled orbit and the act-and-wait switching function an additional small-amplitude periodic perturbation is introduced. The algorithm can stabilize periodic orbits with an odd number of real unstable Floquet exponents using a simple single-input single-output constraint control.

Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

2017-10-01

Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.

A numerical study of transition control by periodic suction-blowing

NASA Technical Reports Server (NTRS)

Biringen, Sedat

1987-01-01

The applicability of active control of transition by periodic suction-blowing is investigated via direct numerical simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that, for relatively small three dimensional amplitudes, a two dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the flow dynamics during transition.

Perturbation Effects on a Supercritical C7H16/N2 Mixing Layer

NASA Technical Reports Server (NTRS)

Okongo'o, Nora; Bellan, Josette

2008-01-01

A computational-simulation study has been presented of effects of perturbation wavelengths and initial Reynolds numbers on the transition to turbulence of a heptane/nitrogen mixing layer at supercritical pressure. The governing equations for the simulations were the same as those of related prior studies reported in NASA Tech Briefs. Two-dimensional (2D) simulations were performed with initially im posed span wise perturbations whereas three-dimensional (3D) simulations had both streamwise and spanwise initial perturbations. The 2D simulations were undertaken to ascertain whether perturbations having the shortest unstable wavelength obtained from a linear stability analysis for inviscid flow are unstable in viscous nonlinear flows. The goal of the 3D simulations was to ascertain whether perturbing the mixing layer at different wavelengths affects the transition to turbulence. It was found that transitions to turbulence can be obtained at different perturbation wavelengths, provided that they are longer than the shortest unstable wavelength as determined by 2D linear stability analysis for the inviscid case and that the initial Reynolds number is proportionally increased as the wavelength is decreased. The transitional states thus obtained display different dynamic and mixture characteristics, departing strongly from the behaviors of perfect gases and ideal mixtures.

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.

Coarsening and pattern formation during true morphological phase separation in unstable thin films under gravity

NASA Astrophysics Data System (ADS)

Kumar, Avanish; Narayanam, Chaitanya; Khanna, Rajesh; Puri, Sanjay

2017-12-01

We address in detail the problem of true morphological phase separation (MPS) in three-dimensional or (2 +1 )-dimensional unstable thin liquid films (>100 nm) under the influence of gravity. The free-energy functionals of these films are asymmetric and show two points of common tangency, which facilitates the formation of two equilibrium phases. Three distinct patterns formed by relative preponderance of these phases are clearly identified in "true MPS". Asymmetricity induces two different pathways of pattern formation, viz., defect and direct pathway for true MPS. The pattern formation and phase-ordering dynamics have been studied using statistical measures such as structure factor, correlation function, and growth laws. In the late stage of coarsening, the system reaches into a scaling regime for both pathways, and the characteristic domain size follows the Lifshitz-Slyozov growth law [L (t ) ˜t1 /3] . However, for the defect pathway, there is a crossover of domain growth behavior from L (t ) ˜t1 /4→t1 /3 in the dynamical scaling regime. We also underline the analogies and differences behind the mechanisms of MPS and true MPS in thin liquid films and generic spinodal phase separation in binary mixtures.

Longitudinal burnout-collaboration patterns in Japanese medical care workers at special needs schools: a latent class growth analysis

PubMed Central

Kanayama, Mieko; Suzuki, Machiko; Yuma, Yoshikazu

2016-01-01

The present study aimed to identify and characterize potential burnout types and the relationship between burnout and collaboration over time. Latent class growth analysis and the growth mixture model were used to identify and characterize heterogeneous patterns of longitudinal stability and change in burnout, and the relationship between burnout and collaboration. We collected longitudinal data at three time points based on Japanese academic terms. The 396 study participants included academic teachers, yogo teachers, and registered nurses in Japanese special needs schools. The best model included four types of both burnout and collaboration in latent class growth analysis with intercept, slope, and quadratic terms. The four types of burnout were as follows: low stable, moderate unstable, high unstable, and high decreasing. They were identified as involving inverse collaboration function. The results indicated that there could be dynamic burnout types, namely moderate unstable, high unstable, and high decreasing, when focusing on growth trajectories in latent class analyses. The finding that collaboration was dynamic for dynamic burnout types and stable for stable burnout types is of great interest. This was probably related to the inverse relationship between the two constructs. PMID:27366107

Dynamic topology and flux rope evolution during non-linear tearing of 3D null point current sheets

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

Wyper, P. F., E-mail: peterw@maths.dundee.ac.uk; Pontin, D. I., E-mail: dpontin@maths.dundee.ac.uk

2014-10-15

In this work, the dynamic magnetic field within a tearing-unstable three-dimensional current sheet about a magnetic null point is described in detail. We focus on the evolution of the magnetic null points and flux ropes that are formed during the tearing process. Generally, we find that both magnetic structures are created prolifically within the layer and are non-trivially related. We examine how nulls are created and annihilated during bifurcation processes, and describe how they evolve within the current layer. The type of null bifurcation first observed is associated with the formation of pairs of flux ropes within the current layer.more » We also find that new nulls form within these flux ropes, both following internal reconnection and as adjacent flux ropes interact. The flux ropes exhibit a complex evolution, driven by a combination of ideal kinking and their interaction with the outflow jets from the main layer. The finite size of the unstable layer also allows us to consider the wider effects of flux rope generation. We find that the unstable current layer acts as a source of torsional magnetohydrodynamic waves and dynamic braiding of magnetic fields. The implications of these results to several areas of heliophysics are discussed.« less

Plasma crystal dynamics measured with a three-dimensional plenoptic camera

NASA Astrophysics Data System (ADS)

Jambor, M.; Nosenko, V.; Zhdanov, S. K.; Thomas, H. M.

2016-03-01

Three-dimensional (3D) imaging of a single-layer plasma crystal was performed using a commercial plenoptic camera. To enhance the out-of-plane oscillations of particles in the crystal, the mode-coupling instability (MCI) was triggered in it by lowering the discharge power below a threshold. 3D coordinates of all particles in the crystal were extracted from the recorded videos. All three fundamental wave modes of the plasma crystal were calculated from these data. In the out-of-plane spectrum, only the MCI-induced hot spots (corresponding to the unstable hybrid mode) were resolved. The results are in agreement with theory and show that plenoptic cameras can be used to measure the 3D dynamics of plasma crystals.

Plasma crystal dynamics measured with a three-dimensional plenoptic camera.

PubMed

Jambor, M; Nosenko, V; Zhdanov, S K; Thomas, H M

2016-03-01

Three-dimensional (3D) imaging of a single-layer plasma crystal was performed using a commercial plenoptic camera. To enhance the out-of-plane oscillations of particles in the crystal, the mode-coupling instability (MCI) was triggered in it by lowering the discharge power below a threshold. 3D coordinates of all particles in the crystal were extracted from the recorded videos. All three fundamental wave modes of the plasma crystal were calculated from these data. In the out-of-plane spectrum, only the MCI-induced hot spots (corresponding to the unstable hybrid mode) were resolved. The results are in agreement with theory and show that plenoptic cameras can be used to measure the 3D dynamics of plasma crystals.

Preferential flow in the vadose zone and interface dynamics: Impact of microbial exudates

NASA Astrophysics Data System (ADS)

Li, Biting; Pales, Ashley R.; Clifford, Heather M.; Kupis, Shyla; Hennessy, Sarah; Liang, Wei-Zhen; Moysey, Stephen; Powell, Brian; Finneran, Kevin T.; Darnault, Christophe J. G.

2018-03-01

In the hydrological cycle, the infiltration process is a critical component in the distribution of water into the soil and in the groundwater system. The nonlinear dynamics of the soil infiltration process yield preferential flow which affects the water distribution in soil. Preferential flow is influenced by the interactions between water, soil, plants, and microorganisms. Although the relationship among the plant roots, their rhizodeposits and water transport in soil has been the subject of extensive study, the effect of microbial exudates has been studied in only a few cases. Here the authors investigated the influence of two artificial microbial exudates-catechol and riboflavin-on the infiltration process, particularly unstable fingered flow, one form of preferential flow. Flow experiments investigating the effects of types and concentrations of microbial exudates on unstable fingered flow were conducted in a two-dimensional tank that was filled with ASTM

Metastable dynamical patterns and their stabilization in arrays of bidirectionally coupled sigmoidal neurons

NASA Astrophysics Data System (ADS)

Horikawa, Yo

2013-12-01

Transient patterns in a bistable ring of bidirectionally coupled sigmoidal neurons were studied. When the system had a pair of spatially uniform steady solutions, the instability of unstable spatially nonuniform steady solutions decreased exponentially with the number of neurons because of the symmetry of the system. As a result, transient spatially nonuniform patterns showed dynamical metastability: Their duration increased exponentially with the number of neurons and the duration of randomly generated patterns obeyed a power-law distribution. However, these metastable dynamical patterns were easily stabilized in the presence of small variations in coupling strength. Metastable rotating waves and their pinning in the presence of asymmetry in the direction of coupling and the disappearance of metastable dynamical patterns due to asymmetry in the output function of a neuron were also examined. Further, in a two-dimensional array of neurons with nearest-neighbor coupling, intrinsically one-dimensional patterns were dominant in transients, and self-excitation in these neurons affected the metastable dynamical patterns.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

NASA Astrophysics Data System (ADS)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

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

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analysesmore » based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.« less

Evolution and End Point of the Black String Instability: Large D Solution.

PubMed

Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro

2015-08-28

We derive a simple set of nonlinear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.

Assessment of Diagnostic Value of Single View Dynamic Technique in Diagnosis of Developmental Dysplasia of Hip: A Comparison with Static and Dynamic Ultrasond Techniques

PubMed Central

Alamdaran, Seyed Ali; Kazemi, Sahar; Parsa, Ali; Moghadam, Mohammad Hallaj; Feyzi, Ali; Mardani, Reza

2016-01-01

Background: Developmental dysplasia of hip (DDH) is a common childhood disorder, and ultrasonography examination is routinely used for screening purposes. In this study, we aimed to evaluate a modified combined static and dynamic ultrasound technique for the detection of DDH and to compare with the results of static and dynamic ultrasound techniques. Methods: In this cross-sectional study, during 2013- 2015, 300 high-risk infants were evaluated by ultrasound for DDH. Both hips were examined with three techniques: static, dynamic and single view static and dynamic technique. Statistical analysis was performed using SPSS version 11.5. Results: Patients aged 9 days to 83 weeks. 75% of the patients were 1 to 3 months old. Among 600 hip joints, about 5% were immature in static sonography and almost all of them were unstable in dynamic techniques. 0.3% of morphologically normal hips were unstable in dynamic sonography and 9% of unstable hips had normal morphology. The mean β angle differences in coronal view before and after stress maneuver was 14.43±5.47° in unstable hips. Single view static and dynamic technique revealed that all cases with acetabular dysplasia, instability and dislocation, except two dislocations, were detected by dynamic transverse view. For two cases, Ortolani maneuver showed femoral head reversibility in dislocated hips. Using single view static and dynamic technique was indicative and applicable for detection of more than 99% of cases. Conclusion: Single view static and dynamic technique not only is a fast and easy technique, but also it is of high diagnostic value in assessment of DDH. PMID:27847852

Dynamics of Active Separation Control at High Reynolds Numbers

NASA Technical Reports Server (NTRS)

Pack, LaTunia G.; Seifert, Avi

2000-01-01

A series of active flow control experiments were recently conducted at high Reynolds numbers on a generic separated configuration. The model simulates the upper surface of a 20% thick Glauert-Goldschmied type airfoil at zero angle of attack. The flow is fully turbulent since the tunnel sidewall boundary layer flows over the model. The main motivation for the experiments is to generate a comprehensive data base for validation of unsteady numerical simulation as a first step in the development of a CFD design tool, without which it would not be possible to effectively utilize the great potential of unsteady flow control. This paper focuses on the dynamics of several key features of the baseline as well as the controlled flow. It was found that the thickness of the upstream boundary layer has a negligible effect on the flow dynamics. It is speculated that separation is caused mainly by the highly convex surface while viscous effects are less important. The two-dimensional separated flow contains unsteady waves centered on a reduced frequency of 0.9, while in the three dimensional separated flow, frequencies around a reduced frequency of 0.3 and 1 are active. Several scenarios of resonant wave interaction take place at the separated shear-layer and in the pressure recovery region. The unstable reduced frequency bands for periodic excitation are centered on 1.5 and 5, but these reduced frequencies are based on the length of the baseline bubble that shortens due to the excitation. The conventional works well for the coherent wave features. Reproduction of these dynamic effects by a numerical simulation would provide benchmark validation.

Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects

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

Goto, R.; Hatori, T.; Miura, H., E-mail: miura.hideaki@nifs.ac.jp

Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. Themore » formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability.« less

Effective control of complex turbulent dynamical systems through statistical functionals.

PubMed

Majda, Andrew J; Qi, Di

2017-05-30

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.

Counting and classifying attractors in high dimensional dynamical systems.

PubMed

Bagley, R J; Glass, L

1996-12-07

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.

Anosov C-systems and random number generators

NASA Astrophysics Data System (ADS)

Savvidy, G. K.

2016-08-01

We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.

Stability analysis of unsteady ablation fronts

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

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-08-01

The linear stability analysis of unsteady ablation fronts, is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

Stability analysis of unsteady ablation fronts

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

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-11-08

The linear stability analysis of unsteady ablation fronts is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

Mathematical modeling of transformation process of structurally unstable magnetic configurations into structurally stable ones in two-dimensional and three-dimensional geometry

NASA Astrophysics Data System (ADS)

Inovenkov, Igor; Echkina, Eugenia; Ponomarenko, Loubov

Magnetic reconnection is a fundamental process in astrophysical, space and laboratory plasma. In essence, it represents a change of topology of the magnetic field caused by readjustment of the structure of the magnetic field lines. This change leads to release of energy accumulated in the field. We consider transformation process of structurally unstable magnetic configurations into the structurally steady ones from the point of view of the Catastrophe theory. Special attention is paid to modeling of evolution of the structurally unstable three-dimensional magnetic fields.

Cusps enable line attractors for neural computation

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

Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.

Here, line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyzemore » system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.« less

Cusps enable line attractors for neural computation

NASA Astrophysics Data System (ADS)

Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; Tao, Louis

2017-11-01

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

Cusps enable line attractors for neural computation

DOE PAGES

Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; ...

2017-11-07

Here, line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyzemore » system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.« less

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

NASA Astrophysics Data System (ADS)

Scopa, Stefano; Unterberger, Jéremie; Karevski, Dragi

2018-05-01

We study the unitary dynamics of a 1D gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency . Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

Hole growth dynamics in a two dimensional Leidenfrost droplet

NASA Astrophysics Data System (ADS)

Raufaste, Christophe; Celestini, Franck; Barzyk, Alexandre; Frisch, Thomas

2015-03-01

We studied the behaviors of Leidenfrost droplets confined in a Hele-Shaw cell. These droplets are unstable above a critical size and a hole grows at their center. We experimentally investigate two different systems for which the hole growth dynamics exhibits peculiar features that are driven by capillarity and inertia. We report a first regime characterized by the liquid reorganization from a liquid sheet to a liquid torus with similarities to the burst of micron-thick soap films. In the second regime, the liquid torus expands and thins before fragmentation. Finally, we propose models to account for the experimental results.

Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

NASA Astrophysics Data System (ADS)

Mirus, Kevin Andrew

In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

Testing a one-dimensional prescription of dynamical shear mixing with a two-dimensional hydrodynamic simulation

NASA Astrophysics Data System (ADS)

Edelmann, P. V. F.; Röpke, F. K.; Hirschi, R.; Georgy, C.; Jones, S.

2017-07-01

Context. The treatment of mixing processes is still one of the major uncertainties in 1D stellar evolution models. This is mostly due to the need to parametrize and approximate aspects of hydrodynamics in hydrostatic codes. In particular, the effect of hydrodynamic instabilities in rotating stars, for example, dynamical shear instability, evades consistent description. Aims: We intend to study the accuracy of the diffusion approximation to dynamical shear in hydrostatic stellar evolution models by comparing 1D models to a first-principle hydrodynamics simulation starting from the same initial conditions. Methods: We chose an initial model calculated with the stellar evolution code GENEC that is just at the onset of a dynamical shear instability but does not show any other instabilities (e.g., convection). This was mapped to the hydrodynamics code SLH to perform a 2D simulation in the equatorial plane. We compare the resulting profiles in the two codes and compute an effective diffusion coefficient for the hydro simulation. Results: Shear instabilities develop in the 2D simulation in the regions predicted by linear theory to become unstable in the 1D stellar evolution model. Angular velocity and chemical composition is redistributed in the unstable region, thereby creating new unstable regions. After a period of time, the system settles in a symmetric, steady state, which is Richardson stable everywhere in the 2D simulation, whereas the instability remains for longer in the 1D model due to the limitations of the current implementation in the 1D code. A spatially resolved diffusion coefficient is extracted by comparing the initial and final profiles of mean atomic mass. Conclusions: The presented simulation gives a first insight on hydrodynamics of shear instabilities in a real stellar environment and even allows us to directly extract an effective diffusion coefficient. We see evidence for a critical Richardson number of 0.25 as regions above this threshold remain stable for the course of the simulation. The movie of the simulation is available at http://www.aanda.org

Three-dimensional to two-dimensional transition in mode-I fracture microbranching in a perturbed hexagonal close-packed lattice

NASA Astrophysics Data System (ADS)

Heizler, Shay I.; Kessler, David A.

2017-06-01

Mode-I fracture exhibits microbranching in the high velocity regime where the simple straight crack is unstable. For velocities below the instability, classic modeling using linear elasticity is valid. However, showing the existence of the instability and calculating the dynamics postinstability within the linear elastic framework is difficult and controversial. The experimental results give several indications that the microbranching phenomenon is basically a three-dimensional (3D) phenomenon. Nevertheless, the theoretical effort has been focused mostly on two-dimensional (2D) modeling. In this paper we study the microbranching instability using three-dimensional atomistic simulations, exploring the difference between the 2D and the 3D models. We find that the basic 3D fracture pattern shares similar behavior with the 2D case. Nevertheless, we exhibit a clear 3D-2D transition as the crack velocity increases, whereas as long as the microbranches are sufficiently small, the behavior is pure 3D behavior, whereas at large driving, as the size of the microbranches increases, more 2D-like behavior is exhibited. In addition, in 3D simulations, the quantitative features of the microbranches, separating the regimes of steady-state cracks (mirror) and postinstability (mist-hackle) are reproduced clearly, consistent with the experimental findings.

Dynamics of Active Separation Control at High Reynolds Numbers

NASA Technical Reports Server (NTRS)

Pack, LaTunia G.; Seifert, Avi

2000-01-01

A series of active flow control experiments were recently conducted at high Reynolds numbers on a generic separated configuration. The model simulates the upper surface of a 20% thick Glauert-Goldschmied type airfoil at zero angle of attack. The flow is fully turbulent since the tunnel sidewall boundary layer flows over the model. The main motivation for the experiments is to generate a comprehensive data base for validation of unsteady numerical simulation as a first step in the development of a CFD design tool, without which it would not be possible to effectively utilize the great potential of unsteady flow control. This paper focuses on the dynamics of several key features of the baseline as well as the controlled flow. It was found that the thickness of the upstream boundary layer has a negligible effect on the flow dynamics. It is speculated that separation is caused mainly by the highly convex surface while viscous effects are less important. The two-dimensional separated flow contains unsteady waves centered on a reduced frequency of 0.8, while in the three dimensional separated flow, frequencies around a reduced frequency of 0.3 and 1 are active. Several scenarios of resonant wave interaction take place at the separated shear-layer and in the pressure recovery region. The unstable reduced frequency bands for periodic excitation are centered on 1.5 and 5, but these reduced frequencies are based on the length of the baseline bubble that shortens due to the excitation. The conventional swept wing-scaling works well for the coherent wave features. Reproduction of these dynamic effects by a numerical simulation would provide benchmark validation.

The Effect of the Density Ratio on the Nonlinear Dynamics of the Unstable Fluid Interface

NASA Technical Reports Server (NTRS)

Abarzhi, S. I.

2003-01-01

Here we report multiple harmonic theoretical solutions for a complete system of conservation laws, which describe the large-scale coherent dynamics in RTI and RMI for fluids with a finite density ratio in the general three-dimensional case. The analysis yields new properties of the bubble front dynamics. In either RTI or RMI, the obtained dependencies of the bubble velocity and curvature on the density ratio differ qualitatively and quantitatively from those suggested by the models of Sharp (1984), Oron et al. (2001), and Goncharov (2002). We show explicitly that these models violate the conservation laws. For the first time, our theory reveals an important qualitative distinction between the dynamics of the RT and RM bubbles.

Two-dimensional antimonene single crystals grown by van der Waals epitaxy.

PubMed

Ji, Jianping; Song, Xiufeng; Liu, Jizi; Yan, Zhong; Huo, Chengxue; Zhang, Shengli; Su, Meng; Liao, Lei; Wang, Wenhui; Ni, Zhenhua; Hao, Yufeng; Zeng, Haibo

2016-11-15

Unlike the unstable black phosphorous, another two-dimensional group-VA material, antimonene, was recently predicted to exhibit good stability and remarkable physical properties. However, the synthesis of high-quality monolayer or few-layer antimonenes, sparsely reported, has greatly hindered the development of this new field. Here, we report the van der Waals epitaxy growth of few-layer antimonene monocrystalline polygons, their atomical microstructure and stability in ambient condition. The high-quality, few-layer antimonene monocrystalline polygons can be synthesized on various substrates, including flexible ones, via van der Waals epitaxy growth. Raman spectroscopy and transmission electron microscopy reveal that the obtained antimonene polygons have buckled rhombohedral atomic structure, consistent with the theoretically predicted most stable β-phase allotrope. The very high stability of antimonenes was observed after aging in air for 30 days. First-principle and molecular dynamics simulation results confirmed that compared with phosphorene, antimonene is less likely to be oxidized and possesses higher thermodynamic stability in oxygen atmosphere at room temperature. Moreover, antimonene polygons show high electrical conductivity up to 10 4  S m -1 and good optical transparency in the visible light range, promising in transparent conductive electrode applications.

Two-dimensional antimonene single crystals grown by van der Waals epitaxy

PubMed Central

Ji, Jianping; Song, Xiufeng; Liu, Jizi; Yan, Zhong; Huo, Chengxue; Zhang, Shengli; Su, Meng; Liao, Lei; Wang, Wenhui; Ni, Zhenhua; Hao, Yufeng; Zeng, Haibo

2016-01-01

Unlike the unstable black phosphorous, another two-dimensional group-VA material, antimonene, was recently predicted to exhibit good stability and remarkable physical properties. However, the synthesis of high-quality monolayer or few-layer antimonenes, sparsely reported, has greatly hindered the development of this new field. Here, we report the van der Waals epitaxy growth of few-layer antimonene monocrystalline polygons, their atomical microstructure and stability in ambient condition. The high-quality, few-layer antimonene monocrystalline polygons can be synthesized on various substrates, including flexible ones, via van der Waals epitaxy growth. Raman spectroscopy and transmission electron microscopy reveal that the obtained antimonene polygons have buckled rhombohedral atomic structure, consistent with the theoretically predicted most stable β-phase allotrope. The very high stability of antimonenes was observed after aging in air for 30 days. First-principle and molecular dynamics simulation results confirmed that compared with phosphorene, antimonene is less likely to be oxidized and possesses higher thermodynamic stability in oxygen atmosphere at room temperature. Moreover, antimonene polygons show high electrical conductivity up to 104 S m−1 and good optical transparency in the visible light range, promising in transparent conductive electrode applications. PMID:27845327

Detecting unstable periodic orbits in chaotic time series using synchronization

NASA Astrophysics Data System (ADS)

Olyaei, Ali Azimi; Wu, Christine; Kinsner, Witold

2017-07-01

An alternative approach of detecting unstable periodic orbits in chaotic time series is proposed using synchronization techniques. A master-slave synchronization scheme is developed, in which the chaotic system drives a system of harmonic oscillators through a proper coupling condition. The proposed scheme is designed so that the power of the coupling signal exhibits notches that drop to zero once the system approaches an unstable orbit yielding an explicit indication of the presence of a periodic motion. The results shows that the proposed approach is particularly suitable in practical situations, where the time series is short and noisy, or it is obtained from high-dimensional chaotic systems.

A delay differential model of ENSO variability: parametric instability and the distribution of extremes

NASA Astrophysics Data System (ADS)

Ghil, M.; Zaliapin, I.; Thompson, S.

2008-05-01

We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform stability analyses of the model in the three-dimensional space of its physically relevant parameters. Our results illustrate the role of these three parameters: strength of seasonal forcing b, atmosphere-ocean coupling κ, and propagation period τ of oceanic waves across the Tropical Pacific. Two regimes of variability, stable and unstable, are separated by a sharp neutral curve in the (b, τ) plane at constant κ. The detailed structure of the neutral curve becomes very irregular and possibly fractal, while individual trajectories within the unstable region become highly complex and possibly chaotic, as the atmosphere-ocean coupling κ increases. In the unstable regime, spontaneous transitions occur in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values, for purely periodic, seasonal forcing. The model reproduces the Devil's bleachers characterizing other ENSO models, such as nonlinear, coupled systems of partial differential equations; some of the features of this behavior have been documented in general circulation models, as well as in observations. We expect, therefore, similar behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.

Yellow Hypergiants as Dynamically Unstable Post-Red-supergiant Stars

NASA Technical Reports Server (NTRS)

Stothers, Richard B.; Chin, Chao-wen; Hansen, James E. (Technical Monitor)

2001-01-01

According to recent theoretical studies, the majority of single stars more massive than 30 solar mass successfully evolve into red supergiants, but then lose most of their hydrogen envelopes and metamorphose into hot blue remnants. While they are cool, they become dynamically unstable as a result of high radiation pressure and partial ionization of the gases in their outer layers. It is shown here that these unstable red-supergiant models repeatedly shrink and re-expand on a thermal time scale when perturbed by heavy bursts of mass loss. Consequently, they fill up the domain of yellow hypergiants on the Hertzsprung-Russell diagram and display very fast rates of evolution there, as observed.

Dynamics of two-dimensional bubbles.

PubMed

Piedra, Saúl; Ramos, Eduardo; Herrera, J Ramón

2015-06-01

The dynamics of two-dimensional bubbles ascending under the influence of buoyant forces is numerically studied with a one-fluid model coupled with the front-tracking technique. The bubble dynamics are described by recording the position, shape, and orientation of the bubbles as functions of time. The qualitative properties of the bubbles and their terminal velocities are described in terms of the Eötvos (ratio of buoyancy to surface tension) and Archimedes numbers (ratio of buoyancy to viscous forces). The terminal Reynolds number result from the balance of buoyancy and drag forces and, consequently, is not an externally fixed parameter. In the cases that yield small Reynolds numbers, the bubbles follow straight paths and the wake is steady. A more interesting behavior is found at high Reynolds numbers where the bubbles follow an approximately periodic zigzag trajectory and an unstable wake with properties similar to the Von Karman vortex street is formed. The dynamical features of the motion of single bubbles are compared to experimental observations of air bubbles ascending in a water-filled Hele-Shaw cell. Although the comparison is not strictly valid in the sense that the effect of the lateral walls is not incorporated in the model, most of the dynamical properties observed are in good qualitative agreement with the numerical calculations. Hele-Shaw cells with different gaps have been used to determine the degree of approximation of the numerical calculation. It is found that for the relation between the terminal Reynolds number and the Archimedes number, the numerical calculations are closer to the observations of bubble dynamics in Hele-Shaw cells of larger gaps.

Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2015-06-01

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

NASA Astrophysics Data System (ADS)

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Noack, Bernd R.

2017-04-01

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Superconductivity in Hydrides Doped with Main Group Elements Under Pressure

NASA Astrophysics Data System (ADS)

Shamp, Andrew; Zurek, Eva

2017-01-01

A priori crystal structure prediction techniques have been used to explore the phase diagrams of hydrides of main group elements under pressure. A number of novel phases with the chemical formulas MHn, n > 1 and M = Li, Na, K, Rb, Cs; MHn, n > 2 and M= Mg, Ca, Sr, Ba; HnI with n > 1 and PH, PH2, PH3 have been predicted to be stable at pressures achievable in diamond anvil cells. The hydrogenic lattices within these phases display a number of structural motifs including H2δ- , H-, H-3 , as well as one-dimensional and three-dimensional extended structures. A wide range of superconducting critical temperatures, Tcs, are predicted for these hydrides. The mechanism of metallization and the propensity for superconductivity are dependent upon the structural motifs present in these phases, and in particular on their hydrogenic sublattices. Phases that are thermodynamically unstable, but dynamically stable, are accessible experimentally. The observed trends provide insight on how to design hydrides that are superconducting at high temperatures.

Transport properties of high quality heterostructures from unstable 2D crystals prepared in inert atmosphere

NASA Astrophysics Data System (ADS)

Yu, Geliang; Yang, Cao; Khestanova, Ekaterina; Mishchenko, Artem; Kretinin, Andy; Gorbachev, Roman; Novoselov, Konstantin; Andre, Geim; Manchester Group Team

Many layered materials can be cleaved down to individual atomic planes, similar to graphene, but only a small minority of them are stable under ambient conditions. The rest reacts and decomposes in air, which has severely hindered their investigation and possible uses. Here we introduce a remedial approach based on cleavage, transfer, alignment and encapsulation of airsensitive crystals, all inside a controlled inert atmosphere. To illustrate the technology, we choose two archetypal two-dimensional crystals unstable in air: black phosphorus and niobium diselenide. Our field-effect devices made from their monolayers are conductive and fully stable under ambient conditions, in contrast to the counterparts processed in air. NbSe2 remains superconducting down to the monolayer thickness. Starting with a trilayer, phosphorene devices reach sufficiently high mobilities to exhibit Landau quantization. The approach offers a venue to significantly expand the range of experimentally accessible two-dimensional crystals and their heterostructures.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Dynamics of a Two-Dimensional System of Quantum Dipoles

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

Mazzanti, F.; Astrakharchik, G. E.; Boronat, J.

2009-03-20

A detailed microscopic analysis of the dynamic structure function S(k,{omega}) of a two-dimensional Bose system of dipoles polarized along the direction perpendicular to the plane is presented and discussed. Starting from ground-state quantities obtained using a quantum diffusion Monte Carlo algorithm, the density-density response is evaluated in the context of the correlated basis functions (CBF) theory. CBF predicts a sharp peak and a multiexcitation component at higher energies produced by the decay of excitations. We discuss the structure of the phonon-roton peak and show that the Feynman and Bogoliubov predictions depart from the CBF result already at low densities. Wemore » finally discuss the emergence of a roton in the spectrum, but find the roton energy not low enough to make the system unstable under density fluctuations up to the highest density considered that is close to the freezing point.« less

Experimental characterization of 3-dimensional gravity-driven fingering in a porous medium

NASA Astrophysics Data System (ADS)

Dalbe, Marie-Julie; Juanes, Ruben

2017-11-01

When water infiltrates a dry porous media, a gravity-driven instability can be observed. Water will penetrate the porous media along preferential paths, called fingers. This gravity-driven unstable multiphase flow has important implications for natural phenomena such as rainwater infiltration in soil and secondary oil migration in reservoir rocks. While several experimental and numerical studies have described the instability in 2-dimensional (2D) settings, fundamental questions remain on the morphodynamics of gravity fingering in 3D. We developed a 3D experimental set-up based on planar laser-induced fluorescence of index-matched fluids that allows us to image this phenomenon dynamically. We study the impact of some crucial parameters such as rainfall rate or grain size on the finger size and velocity. In addition, experiments in stratified media reveal interesting dynamics of finger flow across material interfaces, an essential aspect towards the understanding of water infiltration in soils.

Local stability of a five dimensional food chain model in the ocean

NASA Astrophysics Data System (ADS)

Kusumawinahyu, W. M.; Hidayatulloh, M. R.

2014-02-01

This paper discuss a food chain model on a microbiology ecosystem in the ocean, where predation process occurs. Four population growth rates are discussed, namely bacteria, phytoplankton, zooplankton, and protozoa growth rate. When the growth of nutrient density is also considered, the model is governed by a five dimensional dynamical system. The system considered in this paper is a modification of a model proposed by Hadley and Forbes [1], by taking Holling Type I as the functional response. For sake of simplicity, the model needs to be scaled. Dynamical behavior, such as existence condition of equilibrium points and their local stability are addressed. There are eight equilibrium points, where two of them exist under certain conditions. Three equilibrium points are unstable, while two points stable under certain conditions and the other three points are stable if the Ruth-Hurwitz criteria are satisfied. Numerical simulations are carried out to illustrate analytical findings.

Investigation Into Radiation-Induced Compaction of Zerodur (trademark)

NASA Technical Reports Server (NTRS)

Edwards, D. L.; Herren, K.; Hayden, M.; McDonald, K.; Sims, J. A.; Semmel, C. L.

1996-01-01

Zerodur is a low coefficient of thermal expansion glass-ceramic material. This property makes Zerodur an excellent material for high precision optical substrates. Functioning as a high precision optical substrate, a material must be dimensionally stable in the system operating environment. Published data indicate that Zerodur is dimensionally unstable when exposed to large doses of ionizing radiation. The dimensional instability is discussed as an increase in Zerodur density. This increase in density is described as a compaction. Experimental data showing proton-induced compaction of Zerodur is presented. The dependence of compaction on proton dose was determined to be a power law relationship.

Investigation Into Radiation-Induced Compaction of Zerodur (trademark)

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

Edwards, D.L.; Herren, K.; Hayden, M.

1996-03-01

Zerodur is a low coefficient of thermal expansion glass-ceramic material. This property makes Zerodur an excellent material for high precision optical substrates. Functioning as a high precision optical substrate, a material must be dimensionally stable in the system operating environment. Published data indicate that Zerodur is dimensionally unstable when exposed to large doses of ionizing radiation. The dimensional instability is discussed as an increase in Zerodur density. This increase in density is described as a compaction. Experimental data showing proton-induced compaction of Zerodur is presented. The dependence of compaction on proton dose was determined to be a power law relationship.

Lifecycle of miscible viscous fingering: onset to shutdown

NASA Astrophysics Data System (ADS)

Nijjer, Japinder S.; Hewitt, Duncan R.; Neufeld, Jerome A.

2017-11-01

When a viscous fluid is injected into a porous medium or Hele-Shaw cell that is initially saturated with a more viscous fluid, the flow can be unstable to viscous fingering. We investigate the long-time dynamics of miscible viscous fingering in a homogeneous, planar, two-dimensional porous medium using high-resolution numerical simulations. At late times, we identify a new flow regime which consists of a pair of counter-propagating fingers that diffuse and slow, leaving a linearly well-mixed interior. We derive an analytic solution for this regime, and show that, in contrast to previous suggestions, the flow always evolves to this regime irrespective of the viscosity ratio and Peclet number. As a consequence, we find the instability can only ever generate a finite amount of advective mixing. We also describe the full life-cycle of miscible viscous fingering, which can be partitioned into three regimes: an early-time linearly unstable regime, an intermediate-time non-linear regime, and a late-time exchange-flow regime. We identify, using linear stability theory, a critical Peclet number below which the flow is always stable, and derive a model for the evolution of the transversely averaged concentration in the intermediate-time regime, which extends previous empirical models.

Intermittent gravity-driven flow of grains through narrow pipes

NASA Astrophysics Data System (ADS)

Alvarez, Carlos A.; de Moraes Franklin, Erick

2017-01-01

Grain flows through pipes are frequently found in various settings, such as in pharmaceutical, chemical, petroleum, mining and food industries. In the case of size-constrained gravitational flows, density waves consisting of alternating high- and low-compactness regions may appear. This study investigates experimentally the dynamics of density waves that appear in gravitational flows of fine grains through vertical and slightly inclined pipes. The experimental device consisted of a transparent glass pipe through which different populations of glass spheres flowed driven by gravity. Our experiments were performed under controlled ambient temperature and relative humidity, and the granular flow was filmed with a high-speed camera. Experimental results concerning the length scales and celerities of density waves are presented, together with a one-dimensional model and a linear stability analysis. The analysis exhibits the presence of a long-wavelength instability, with the most unstable mode and a cut-off wavenumber whose values are in agreement with the experimental results.

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems.

PubMed

Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen; Kuna, Tobias

2014-01-01

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

NASA Astrophysics Data System (ADS)

Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen; Kuna, Tobias

2014-02-01

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

Stability of Thin Liquid Sheet Flows

NASA Technical Reports Server (NTRS)

McConley, Marc W.; Chubb, Donald L.; McMaster, Matthew S.; Afjeh, Abdollah A.

1997-01-01

A two-dimensional, linear stability analysis of a thin nonplanar liquid sheet flow in vacuum is carried out. A sheet flow created by a narrow slit of W and tau attains a nonplanar cross section as a consequence of cylinders forming on the sheet edge under the influence of surface tension forces. The region where these edge cylinders join the sheet is one of high curvature, and this is found to be the location where instability is most likely to occur. The sheet flow is found to be unstable, but with low growth rates for symmetric wave disturbances and high growth rates for antisymmetric disturbances. By combining the symmetric and antisymmetric disturbance modes, a wide range of stability characteristics is obtained. The product of unstable growth rate and flow time is proportional to the width-to-thickness ratio of the sift generating the sheet Three-dimensional effects can alter these results, particularly when the sheet length-to-width ratio is not much greater than unity.

Reliability of unstable periodic orbit based control strategies in biological systems.

PubMed

Mishra, Nagender; Hasse, Maria; Biswal, B; Singh, Harinder P

2015-04-01

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

Reliability of unstable periodic orbit based control strategies in biological systems

NASA Astrophysics Data System (ADS)

Mishra, Nagender; Hasse, Maria; Biswal, B.; Singh, Harinder P.

2015-04-01

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

The modeling of the dynamic behavior of an unsymmetrical rotor

NASA Astrophysics Data System (ADS)

Pǎrǎuşanu, Ioan; Gheorghiu, Horia; Petre, Cristian; Jiga, Gabriel; Crişan, Nicoleta

2018-02-01

The purpose of this article is to present the modeling of the dynamic behaviour of unsymmetrical rotors in relatively simple quantitative terms. Numerical simulations show that the shaft orthotropy produces a peak of resonant vibration about half the regular critical speed and, for small damping, a range of possible unstable behavior between the two critical speeds. Rotors having the shaft and/or the disks with unequal diametral moments of inertia (e.g., two-bladed small airplane propellers, wind turbines and fans) are dynamically unstable above a certain speed and some of these may return to a stable condition at a sufficiently high speed, depending on the particular magnitudes of the gyroscopic coupling and the inertia inequality.

Predicting electromagnetic ion cyclotron wave amplitude from unstable ring current plasma conditions

DOE PAGES

Fu, Xiangrong; Cowee, Misa M.; Jordanova, Vania K.; ...

2016-11-01

Electromagnetic ion cyclotron (EMIC) waves in the Earth's inner magnetosphere are enhanced fluctuations driven unstable by ring current ion temperature anisotropy. EMIC waves can resonate with relativistic electrons and play an important role in precipitation of MeV radiation belt electrons. In this study, we investigate the excitation and saturation of EMIC instability in a homogeneous plasma using both linear theory and nonlinear hybrid simulations. We have explored a four-dimensional parameter space, carried out a large number of simulations, and derived a scaling formula that relates the saturation EMIC wave amplitude to initial plasma conditions. Finally, such scaling can be usedmore » in conjunction with ring current models like ring current-atmosphere interactions model with self-consistent magnetic field to provide global dynamic EMIC wave maps that will be more accurate inputs for radiation belt modeling than statistical models.« less

Heating, Cooling, and Gravitational Instabilities in Protostellar and Protoplanetary Disks

NASA Astrophysics Data System (ADS)

Pickett, B. K.; Mejia, A. C.; Durisen, R. H.

2001-12-01

We present three-dimensional hydrodynamic simulations of protostellar disk models, in order to explore how the interplay between heating and cooling regulates significant gravitational instabilities. Artificial viscosity is used to treat irreversible heating, such as would occur in shocks; volumetric cooling at several different rates is also applied throughout a broad radial region of the disk. We study the evolution of a disk that is already unstable (due to the low value of the Toomre Q parameter), and a marginally unstable disk that is cooled towards instability. The evolutions have implications for the transport of mass and angular momentum in protostellar disks, the effects of gravitational instabilities on the vertical structure of the disks, and the formation of stellar and substellar companions on dynamic time scales due to disk instabilties. This work is supported by grants from the NASA Planetary Geology and Geophysics and Origins of Solar Systems Programs.

Exploring Stability of General Relativistic Accretion Disks

NASA Astrophysics Data System (ADS)

Korobkin, Oleg; Abdikamalov, Ernazar; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

2011-04-01

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios, involving core collapse of massive stars and mergers of compact ob jects. I will present results on our recent study of the stability of such disks against runaway and non-axisymmetric instabilities, which we explore using three-dimensional hydrodynamics simulations in full general relativity. All of our models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. We will discuss the types, growth rates and pattern speeds of the unstable modes, as well as the detectability of the gravitational waves from such objects.

High sensitivity of tidewater outlet glacier dynamics to shape

NASA Astrophysics Data System (ADS)

Enderlin, E. M.; Howat, I. M.; Vieli, A.

2013-02-01

Variability in tidewater outlet glacier behavior under similar external forcing has been attributed to differences in outlet shape (i.e. bed elevation and width), but this dependence has not been investigated in detail. Here we use a numerical ice flow model to show that the dynamics of tidewater outlet glaciers under external forcing are highly sensitive to width and bed topography. Our sensitivity tests indicate that for glaciers with similar discharge, the trunks of wider glaciers and those grounded over deeper basal depressions tend to be closer to flotation, so that less dynamically induced thinning results in rapid, unstable retreat following a perturbation. The lag time between the onset of the perturbation and unstable retreat varies with outlet shape, which may help explain intra-regional variability in tidewater outlet glacier behavior. Further, because the perturbation response is dependent on the thickness relative to flotation, varying the bed topography within the range of observational uncertainty can result in either stable or unstable retreat due to the same perturbation. Thus, extreme care must be taken when interpreting the future behavior of actual glacier systems using numerical ice flow models that are not accompanied by comprehensive sensitivity analyses.

High sensitivity of tidewater outlet glacier dynamics to shape

NASA Astrophysics Data System (ADS)

Enderlin, E. M.; Howat, I. M.; Vieli, A.

2013-06-01

Variability in tidewater outlet glacier behavior under similar external forcing has been attributed to differences in outlet shape (i.e., bed elevation and width), but this dependence has not been investigated in detail. Here we use a numerical ice flow model to show that the dynamics of tidewater outlet glaciers under external forcing are highly sensitive to width and bed topography. Our sensitivity tests indicate that for glaciers with similar discharge, the trunks of wider glaciers and those grounded over deeper basal depressions tend to be closer to flotation, so that less dynamically induced thinning results in rapid, unstable retreat following a perturbation. The lag time between the onset of the perturbation and unstable retreat varies with outlet shape, which may help explain intra-regional variability in tidewater outlet glacier behavior. Further, because the perturbation response is dependent on the thickness relative to flotation, varying the bed topography within the range of observational uncertainty can result in either stable or unstable retreat due to the same perturbation. Thus, extreme care must be taken when interpreting the future behavior of actual glacier systems using numerical ice flow models that are not accompanied by comprehensive sensitivity analyses.

Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon

NASA Astrophysics Data System (ADS)

Ornigotti, Luca; Ryabov, Artem; Holubec, Viktor; Filip, Radim

2018-03-01

The trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. A description of the dynamics by moments is therefore not informative. Instead, we propose and analyze local directly measurable characteristics, which overcome this limitation. We discuss the most probable particle position (position of the maximum of the probability density) and the local uncertainty in an unstable cubic potential, V (x ) ˜x3 , both in the transient regime and in the long-time limit. The maximum shifts against the acting force as a function of time and temperature. Simultaneously, the local uncertainty does not increase faster than the observable shift. In the long-time limit, the probability density naturally attains a quasistationary form. We interpret this process as a stabilization via the measurement-feedback mechanism, the Maxwell demon, which works as an entropy pump. The rules for measurement and feedback naturally arise from the basic properties of the unstable dynamics. All reported effects are inherent in any unstable system. Their detailed understanding will stimulate the development of stochastic engines and amplifiers and, later, their quantum counterparts.

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1987-01-01

The research goal was a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. This presents a formidable mathematical problem. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity are defined. Each model is summarized.

Complexity dynamics and Hopf bifurcation analysis based on the first Lyapunov coefficient about 3D IS-LM macroeconomics system

NASA Astrophysics Data System (ADS)

Ma, Junhai; Ren, Wenbo; Zhan, Xueli

2017-04-01

Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.

Kinetic Simulations of the Lowest-order Unstable Mode of Relativistic Magnetostatic Equilibria

NASA Astrophysics Data System (ADS)

Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie; East, William E.; Blandford, Roger D.

2016-08-01

We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold-Beltrami-Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.

KINETIC SIMULATIONS OF THE LOWEST-ORDER UNSTABLE MODE OF RELATIVISTIC MAGNETOSTATIC EQUILIBRIA

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

Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie

2016-08-01

We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold–Beltrami–Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers aremore » disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.« less

Numerical simulation of the three-dimensional river antidunes

NASA Astrophysics Data System (ADS)

Iwasaki, T.; Inoue, T.; Onda, S.; Yabe, H.

2017-12-01

This study presents numerical simulations of the formation and development of the three-dimensional river antidunes. We use a Boussinesq type depth-integrated hydrodynamic model to account for the non-hydrostatic pressure effects on the flow field, dissipative feature of the free surface and the bed shear stress distribution. In addition, a non-equilibrium bedload transport model is incorporated into the model to consider the lag effect of the bedload transport on the bedform dynamics. The model is applied to idealized laboratory-scale conditions, i.e., steady water and sediment supplies, uniform sediment and a straight channel with constant slope and channel width, to understand the model performance and applicability. The results show that the model is able to reproduce an upstream-migrating antidunes and associated free surface dynamics. The model also captures the formation of the two dimensional and the three-dimensional antidunes. The antidunes reproduced by the model are somewhat unstable, i.e., the repeated cycle of dissipation and regeneration of antidunes is observed. In addition, as the calculation progresses, the modelled three-dimensional antidunes generally tend to lose their three-dimensionality, i.e., the reduction of the spanwise wavenumber. In the early stage of the calculation, the antidune mode is dominant, whereas, the free bars also develop when the formative condition of bars is satisfied. The numerical results show the coexisting of free bars and antidunes, which are a common evident in flume experiments and field observations.

Three-dimensional skyrmions in spin-2 Bose–Einstein condensates

NASA Astrophysics Data System (ADS)

Tiurev, Konstantin; Ollikainen, Tuomas; Kuopanportti, Pekko; Nakahara, Mikio; Hall, David S.; Möttönen, Mikko

2018-05-01

We introduce topologically stable three-dimensional skyrmions in the cyclic and biaxial nematic phases of a spin-2 Bose–Einstein condensate. These skyrmions exhibit exceptionally high mapping degrees resulting from the versatile symmetries of the corresponding order parameters. We show how these structures can be created in existing experimental setups and study their temporal evolution and lifetime by numerically solving the three-dimensional Gross–Pitaevskii equations for realistic parameter values. Although the biaxial nematic and cyclic phases are observed to be unstable against transition towards the ferromagnetic phase, their lifetimes are long enough for the skyrmions to be imprinted and detected experimentally.

On the dynamics of exotic matter: Towards creation of Perpetuum Mobile of third kind

NASA Astrophysics Data System (ADS)

Ivanov, Pavel

2009-09-01

The one-dimensional dynamics of a classical ideal ‘exotic’ fluid with equation of state p=p(γ)<0 violating the weak energy condition is discussed. Under certain assumptions it is shown that the well-known Hwa-Bjorken exact solution of one-dimensional relativistic hydrodynamics is confined within the future/past light cone. It is also demonstrated that the total energy of such a solution is equal to zero and that there are regions within the light cone with negative (-) and positive (+) total energies. For certain equations of state there is a continuous energy transfer from the (-)-regions to the (+)-regions resulting in indefinite growth of energy in the (+)-regions with time, which may be interpreted as action of a specific ‘Perpetuum Mobile’ (Perpetuum Motion). It is speculated that if it is possible to construct a three-dimensional non-stationary flow of an exotic fluid having a finite negative value of energy such a situation would also occur. Such a flow may continuously transfer positive energy to gravitational waves, resulting in a runaway. It is conjectured that theories plagued by such solutions should be discarded as inherently unstable.

Development of a two-dimensional skin friction balance nulling circuit using multivariable control theory

NASA Technical Reports Server (NTRS)

Tripp, John S.; Patek, Stephen D.

1988-01-01

Measurement of planar skin friction forces in aerodynamic testing currently requires installation of two perpendicularly mounted, single-axis balances; consequently, force components must be sensed at two distinct locations. A two-axis instrument developed at the Langley Research Center to overcome this disadvantage allows measurement of a two-dimensional force at one location. This paper describes a feedback-controlled nulling circuit developed for the NASA two-axis balance which, without external compensation, is inherently unstable because of its low friction mechanical design. Linear multivariable control theory is applied to an experimentally validated mathematical model of the balance to synthesize a state-variable feedback control law. Pole placement techniques and computer simulation studies are employed to select eigenvalues which provide ideal transient response with decoupled sensing dynamics.

Dynamical analysis of an n‑H‑T cosmological quintessence real gas model with a general equation of state

NASA Astrophysics Data System (ADS)

Ivanov, Rossen I.; Prodanov, Emil M.

2018-01-01

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.

High-frequency electromagnetic scarring in three-dimensional axisymmetric convex cavities

DOE PAGES

Warne, Larry K.; Jorgenson, Roy E.

2016-04-13

Here, this article examines the localization of high-frequency electromagnetic fields in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. When these orbits lead to unstable localized modes, they are known as scars. This article treats the case where the opposing sides, or mirrors, are convex. Particular attention is focused on the normalization through the electromagnetic energy theorem. Both projections of the field along the scarred orbit as well as field point statistics are examined. Statistical comparisons are made with a numerical calculation of the scars run with an axisymmetric simulation.

Three-dimensional Simulations of Jets from Keplerian Disks: Self-regulatory Stability

NASA Astrophysics Data System (ADS)

Ouyed, Rachid; Clarke, David A.; Pudritz, Ralph E.

2003-01-01

We present the extension of previous two-dimensional simulations of the time-dependent evolution of nonrelativistic outflows from the surface of Keplerian accretion disks to three dimensions. As in the previous work, we investigate the outflow that arises from a magnetized accretion disk that is initially in hydrostatic balance with its surrounding cold corona. The accretion disk itself is taken to provide a set of fixed boundary conditions for the problem. We find that the mechanism of jet acceleration is identical to what was established from the previous two-dimensional simulations. The three-dimensional results are consistent with the theory of steady, axisymmetric, centrifugally driven disk winds up to the Alfvén surface of the outflow. Beyond the Alfvén surface, however, the jet in three dimensions becomes unstable to nonaxisymmetric, Kelvin-Helmholtz instabilities. The most important result of our work is that while the jet is unstable at super-Alfvénic speeds, it survives the onset of unstable modes that appear in this physical regime. We show that jets maintain their long-term stability through a self-limiting process wherein the average Alfvénic Mach number within the jet is maintained to the order of unity. This is accomplished in at least two ways. First, the poloidal magnetic field is concentrated along the central axis of the jet forming a ``backbone'' in which the Alfvén speed is sufficiently high to reduce the average jet Alfvénic Mach number to unity. Second, the onset of higher order Kelvin-Helmholtz ``flute'' modes (m>=2) reduces the efficiency with which the jet material is accelerated and transfers kinetic energy of the outflow into the stretched, poloidal field lines of the distorted jet. This too has the effect of increasing the Alfvén speed and thereby reducing the Alfvénic Mach number. The jet is able to survive the onset of the more destructive m=1 mode in this way. Our simulations also show that jets can acquire corkscrew or wobbling types of geometries in this relatively stable end state depending on the nature of the perturbations on them. Finally, we suggest that jets go into alternating periods of low and high activity since the disappearance of unstable modes in the sub-Alfvénic regime enables another cycle of acceleration to super-Alfvénic speeds.

Self-aggregation of clouds in conditionally unstable moist convection

PubMed Central

Pauluis, Olivier; Schumacher, Jörg

2011-01-01

The behavior of moist Rayleigh–Bénard convection is investigated using a Boussinesq model with a simplified thermodynamics for phase transitions. This idealized configuration makes the problem accessible to high-resolution three-dimensional direct numerical simulations without small-scale parameterizations of the turbulence for extended layers with aspect ratios up to 64. Our study is focused on the frequently observed conditionally unstable environment that is stably stratified for unsaturated air, but is unstable for cloudy air. We find that no sharp threshold for the transition to convective turbulence exists, a situation similar to wall-bounded shear flows. Rather, the transition depends on the amplitude of the initial perturbation of the quiescent equilibrium and on the aspect ratio of the convective domain. In contrast to the classical dry Rayleigh–Bénard case, convection is highly asymmetric with respect to the vertical direction. Moist upwelling air inside turbulent cloud aggregates is surrounded by ambient regions of slowly descending unsaturated air. It is also found that conditionally unstable moist convection is inefficient at transporting energy. Our study suggests that there is an upper bound on the Nusselt number in moist convection that is lower than that of the classical dry case. PMID:21768333

Reactive transport in a partially molten system with binary solid solution

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.

2017-12-01

Melt extraction from the Earth's mantle through high-porosity channels is required to explain the composition of the oceanic crust. Feedbacks from reactive melt transport are thought to localize melt into a network of high-porosity channels. Recent studies invoke lithological heterogeneities in the Earth's mantle to seed the localization of partial melts. Therefore, it is necessary to understand the reaction fronts that form as melt flows across the lithological interface of a heterogeneity and the background mantle. Simplified melting models of such systems aide in the interpretation and formulation of larger scale mantle models. Motivated by the aforementioned facts, we present a chromatographic analysis of reactive melt transport across lithological boundaries, using theory for hyperbolic conservation laws. This is an extension of well-known linear trace element chromatography to the coupling of major elements and energy transport. Our analysis allows the prediction of the feedbacks that arise in reactive melt transport due to melting, freezing, dissolution and precipitation for frontal reactions. This study considers the simplified case of a rigid, partially molten porous medium with binary solid solution. As melt traverses a lithological contact-modeled as a Riemann problem-a rich set of features arise, including a reacted zone between an advancing reaction front and partial chemical preservation of the initial contact. Reactive instabilities observed in this study originate at the lithological interface rather than along a chemical gradient as in most studies of mantle dynamics. We present a regime diagram that predicts where reaction fronts become unstable, thereby allowing melt localization into high-porosity channels through reactive instabilities. After constructing the regime diagram, we test the one-dimensional hyperbolic theory against two-dimensional numerical experiments. The one-dimensional hyperbolic theory is sufficient for predicting the qualitative behavior of reactive melt transport simulations conducted in two-dimensions. The theoretical framework presented can be extended to more complex and realistic phase behavior, and is therefore a useful tool for understanding nonlinear feedbacks in reactive melt transport problems relevant to mantle dynamics.

Reliability of unstable periodic orbit based control strategies in biological systems

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

Mishra, Nagender; Singh, Harinder P.; Hasse, Maria

2015-04-15

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry ofmore » the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.« less

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

NASA Astrophysics Data System (ADS)

Sanches, L.; Michon, G.; Berlioz, A.; Alazard, D.

2012-07-01

The present work is aimed at verifying the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters. The periodical equations of motions are analyzed by using Floquet's Theory (FM) and the boundaries of instabilities predicted. The stability chart obtained as a function of asymmetry parameters and rotor speed reveals a complex evolution of critical zones and the existence of bifurcation points at low rotor speed values. Additionally, it is known that when treated as parametric excitations; periodic terms may cause parametric resonances in dynamic systems, some of which can become unstable. Therefore, the helicopter is later considered as a parametrically excited system and the equations are treated analytically by applying the Method of Multiple Scales (MMS). A stability analysis is used to verify the existence of unstable parametric resonances with first and second-order sets of equations. The results are compared and validated with those obtained by Floquet's Theory. Moreover, an explanation is given for the presence of unstable motion at low rotor speeds due to parametric instabilities of the second order.

Three-dimensional hydrodynamic Bondi-Hoyle accretion. 2: Homogeneous medium at Mach 3 with gamma = 5/3

NASA Technical Reports Server (NTRS)

Ruffert, Maximilian; Arnett, David

1994-01-01

We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle accretion. Totally absorbing spheres of varying sizes (from 10 down to 0.01 accretion radii) move at Mach 3 relative to a homogeneous and slightly perturbed medium, which is taken to be an ideal gas (gamma = 5/3). To accommodate the long-range gravitational forces, the extent of the computational volume is 32(exp 3) accretion radii. We examine the influence of numerical procedure on physical behavior. The hydrodynamics is modeled by the 'piecewise parabolic method.' No energy sources (nuclear burning) or sinks (radiation, conduction) are included. The resolution in the vicinity of the accretor is increased by multiply nesting several (5-10) grids around the sphere, each finer grid being a factor of 2 smaller in zone dimension that the next coarser grid. The largest dynamic range (ratio of size of the largest grid to size of the finest zone) is 16,384. This allows us to include a coarse model for the surface of the accretor (vacuum sphere) on the finest grid, while at the same time evolving the gas on the coarser grids. Initially (at time t = 0-10), a shock front is set up, a Mach cone develops, and the accretion column is observable. Eventually the flow becomes unstable, destroying axisymmetry. This happens approximately when the mass accretion rate reaches the values (+/- 10%) predicted by the Bondi-Hoyle accretion formula (factor of 2 included). However, our three-dimensional models do not show the highly dynamic flip-flop flow so prominent in two-dimensional calculations performed by other authors. The flow, and thus the accretion rate of all quantities, shows quasi-periodic (P approximately equals 5) cycles between quiescent and active states. The interpolation formula proposed in an accompanying paper is found to follow the collected numerical data to within approximately 30%. The specific angular momentum accreted is of the same order of magnitude as the values previously found for two-dimensional flows.

Pair aligning improved motility of Quincke rollers.

PubMed

Lu, Shi Qing; Zhang, Bing Yue; Zhang, Zhi Chao; Shi, Yan; Zhang, Tian Hui

2018-06-06

Density-dependent speed is studied in a two-dimensional active colloid in which the colloidal particles are propelled by an external electric field via a Quincke rotation. Above the critcal electric field, dense dynamic clusters form spotaneously, in which the particles are highly aligned in velocity and move much faster than isolated units. Detailed observations on pair collision reveal that the alignment of velocity is induced by the long-ranged hydrodynamic interactions and the improvement of speed in the clusters arises from pair aligning in which two particles are closely paired and rotate synchronically. In the aligning state, the short-range in-plane dipole-dipole attraction enhances the rotation torque and gives rises to a larger rolling speed. The pair aligning becomes difficult and unstable at high electric field where the normal dipole-dipole repulsion becomes dominant. As a consequence, the dependence of speed on density becomes weak increasingly upon the increase of the electric field. This result offers an interpretation for the discrepancy between our and previous observations on Quincke rollers.

Formation and evolution of bubbly screens in confined oscillating bubbly liquids.

PubMed

Shklyaev, Sergey; Straube, Arthur V

2010-01-01

We consider the dynamics of dilute monodisperse bubbly liquid confined by two plane solid walls and subject to small-amplitude high-frequency oscillations normal to the walls. The initial state corresponds to the uniform distribution of bubbles and motionless liquid. The period of external driving is assumed much smaller than typical relaxation times for a single bubble but larger than the period of volume eigenoscillations. The time-averaged description accounting for the two-way coupling between the liquid and the bubbles is applied. We show that the model predicts accumulation of bubbles in thin sheets parallel to the walls. These singular structures, which are formally characterized by infinitely thin width and infinitely high concentration, are referred to as bubbly screens. The formation of a bubbly screen is described analytically in terms of a self-similar solution, which is in agreement with numerical simulations. We study the evolution of bubbly screens and detect a one-dimensional stationary state, which is shown to be unconditionally unstable.

Formation and evolution of bubbly screens in confined oscillating bubbly liquids

NASA Astrophysics Data System (ADS)

Shklyaev, Sergey; Straube, Arthur V.

2010-01-01

We consider the dynamics of dilute monodisperse bubbly liquid confined by two plane solid walls and subject to small-amplitude high-frequency oscillations normal to the walls. The initial state corresponds to the uniform distribution of bubbles and motionless liquid. The period of external driving is assumed much smaller than typical relaxation times for a single bubble but larger than the period of volume eigenoscillations. The time-averaged description accounting for the two-way coupling between the liquid and the bubbles is applied. We show that the model predicts accumulation of bubbles in thin sheets parallel to the walls. These singular structures, which are formally characterized by infinitely thin width and infinitely high concentration, are referred to as bubbly screens. The formation of a bubbly screen is described analytically in terms of a self-similar solution, which is in agreement with numerical simulations. We study the evolution of bubbly screens and detect a one-dimensional stationary state, which is shown to be unconditionally unstable.

A novel three-dimensional smile analysis based on dynamic evaluation of facial curve contour

PubMed Central

Lin, Yi; Lin, Han; Lin, Qiuping; Zhang, Jinxin; Zhu, Ping; Lu, Yao; Zhao, Zhi; Lv, Jiahong; Lee, Mln Kyeong; Xu, Yue

2016-01-01

The influence of three-dimensional facial contour and dynamic evaluation decoding on factors of smile esthetics is essential for facial beauty improvement. However, the kinematic features of the facial smile contour and the contribution from the soft tissue and underlying skeleton are uncharted. Here, the cheekbone-maxilla contour and nasolabial fold were combined into a “smile contour” delineating the overall facial topography emerges prominently in smiling. We screened out the stable and unstable points on the smile contour using facial motion capture and curve fitting, before analyzing the correlation between soft tissue coordinates and hard tissue counterparts of the screened points. Our finding suggests that the mouth corner region was the most mobile area characterizing smile expression, while the other areas remained relatively stable. Therefore, the perioral area should be evaluated dynamically while the static assessment outcome of other parts of the smile contour contribute partially to their dynamic esthetics. Moreover, different from the end piece, morphologies of the zygomatic area and the superior part of the nasolabial crease were determined largely by the skeleton in rest, implying the latter can be altered by orthopedic or orthodontic correction and the former better improved by cosmetic procedures to improve the beauty of smile. PMID:26911450

A novel three-dimensional smile analysis based on dynamic evaluation of facial curve contour

NASA Astrophysics Data System (ADS)

Lin, Yi; Lin, Han; Lin, Qiuping; Zhang, Jinxin; Zhu, Ping; Lu, Yao; Zhao, Zhi; Lv, Jiahong; Lee, Mln Kyeong; Xu, Yue

2016-02-01

The influence of three-dimensional facial contour and dynamic evaluation decoding on factors of smile esthetics is essential for facial beauty improvement. However, the kinematic features of the facial smile contour and the contribution from the soft tissue and underlying skeleton are uncharted. Here, the cheekbone-maxilla contour and nasolabial fold were combined into a “smile contour” delineating the overall facial topography emerges prominently in smiling. We screened out the stable and unstable points on the smile contour using facial motion capture and curve fitting, before analyzing the correlation between soft tissue coordinates and hard tissue counterparts of the screened points. Our finding suggests that the mouth corner region was the most mobile area characterizing smile expression, while the other areas remained relatively stable. Therefore, the perioral area should be evaluated dynamically while the static assessment outcome of other parts of the smile contour contribute partially to their dynamic esthetics. Moreover, different from the end piece, morphologies of the zygomatic area and the superior part of the nasolabial crease were determined largely by the skeleton in rest, implying the latter can be altered by orthopedic or orthodontic correction and the former better improved by cosmetic procedures to improve the beauty of smile.

Generation of dark solitons and their instability dynamics in two-dimensional condensates

NASA Astrophysics Data System (ADS)

Verma, Gunjan; Rapol, Umakant D.; Nath, Rejish

2017-04-01

We analyze numerically the formation and the subsequent dynamics of two-dimensional matter wave dark solitons in a Thomas-Fermi rubidium condensate using various techniques. An initially imprinted sharp phase gradient leads to the dynamical formation of a stationary soliton as well as very shallow gray solitons, whereas a smooth gradient only creates gray solitons. The depth and hence, the velocity of the soliton is provided by the spatial width of the phase gradient, and it also strongly influences the snake-instability dynamics of the two-dimensional solitons. The vortex dipoles stemming from the unstable soliton exhibit rich dynamics. Notably, the annihilation of a vortex dipole via a transient dark lump or a vortexonium state, the exchange of vortices between either a pair of vortex dipoles or a vortex dipole and a single vortex, and so on. For sufficiently large width of the initial phase gradient, the solitons may decay directly into vortexoniums instead of vortex pairs, and also the decay rate is augmented. Later, we discuss alternative techniques to generate dark solitons, which involve a Gaussian potential barrier and time-dependent interactions, both linear and periodic. The properties of the solitons can be controlled by tuning the amplitude or the width of the potential barrier. In the linear case, the number of solitons and their depths are determined by the quench time of the interactions. For the periodic modulation, a transient soliton lattice emerges with its periodicity depending on the modulation frequency, through a wave number selection governed by the local Bogoliubov spectrum. Interestingly, for sufficiently low barrier potential, both Faraday pattern and soliton lattice coexist. The snake instability dynamics of the soliton lattice is characteristically modified if the Faraday pattern is present.

Metastable structure of Li13Si4

NASA Astrophysics Data System (ADS)

Gruber, Thomas; Bahmann, Silvia; Kortus, Jens

2016-04-01

The Li13Si4 phase is one out of several crystalline lithium silicide phases, which is a potential electrode material for lithium ion batteries and contains a high theoretical specific capacity. By means of ab initio methods like density functional theory (DFT) many properties such as heat capacity or heat of formation can be calculated. These properties are based on the calculation of phonon frequencies, which contain information about the thermodynamical stability. The current unit cell of "Li13Si4" given in the ICSD database is unstable with respect to DFT calculations. We propose a modified unit cell that is stable in the calculations. The evolutionary algorithm EVO found a structure very similar to the ICSD one with both of them containing metastable lithium positions. Molecular dynamic simulations show a phase transition between both structures where these metastable lithium atoms move. This phase transition is achieved by a very fast one-dimensional lithium diffusion and stabilizes this phase.

Evolving Gravitationally Unstable Disks over Cosmic Time: Implications for Thick Disk Formation

NASA Astrophysics Data System (ADS)

Forbes, John; Krumholz, Mark; Burkert, Andreas

2012-07-01

Observations of disk galaxies at z ~ 2 have demonstrated that turbulence driven by gravitational instability can dominate the energetics of the disk. We present a one-dimensional simulation code, which we have made publicly available, that economically evolves these galaxies from z ~ 2 to z ~ 0 on a single CPU in a matter of minutes, tracking column density, metallicity, and velocity dispersions of gaseous and multiple stellar components. We include an H2-regulated star formation law and the effects of stellar heating by transient spiral structure. We use this code to demonstrate a possible explanation for the existence of a thin and thick disk stellar population and the age-velocity-dispersion correlation of stars in the solar neighborhood: the high velocity dispersion of gas in disks at z ~ 2 decreases along with the cosmological accretion rate, while at lower redshift the dynamically colder gas forms the low velocity dispersion stars of the thin disk.

Motion and dural sac compression in the upper cervical spine during the application of a cervical collar in case of unstable craniocervical junction—A study in two new cadaveric trauma models

PubMed Central

Hüttlin, Petra; Grützner, Paul A.; Weilbacher, Frank; Matschke, Stefan; Popp, Erik

2018-01-01

Background Unstable conditions of the craniocervical junction such as atlanto-occipital dislocation (AOD) or atlanto-axial instability (AAI) are severe injuries with a high risk of tetraplegia or death. Immobilization by a cervical collar to protect the patient from secondary damage is a standard procedure in trauma patients. If the application of a cervical collar to a patient with an unstable craniocervical condition may cause segmental motion and secondary injury to the spinal cord is unknown. The aim of the current study is (i) to analyze compression on the dural sac and (ii) to determine relative motion of the cervical spine during the procedure of applying a cervical collar in case of ligamentous unstable craniocervical junction. Methods and findings Ligamentous AOD as well as AOD combined with ligamentous AAI was simulated in two newly developed cadaveric trauma models. Compression of the dural sac and segmental angulation in the upper cervical spine were measured on video fluoroscopy after myelography during the application of a cervical collar. Furthermore, overall three-dimensional motion of the cervical spine was measured by a motion tracking system. In six cadavers each, the two new trauma models on AOD and AOD combined with AAI could be implemented. Mean dural sac compression was significantly increased to -1.1 mm (-1.3 to -0.7 mm) in case of AOD and -1.2 mm (-1.6 to -0.6 mm) in the combined model of AOD and AAI. Furthermore, there is a significant increased angulation at the C0/C1 level in the AOD model. Immense three-dimensional movement up to 22.9° of cervical spine flexion was documented during the procedure. Conclusion The current study pointed out that applying a cervical collar in general will cause immense three-dimensional movement. In case of unstable craniocervical junction, this leads to a dural sac compression and thus to possible damage to the spinal cord. PMID:29624623

A mathematical model of the structure and evolution of small-scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, Charles E.

1990-01-01

A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.

Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

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

Rajpathak, Bhooshan, E-mail: bhooshan@ee.iitb.ac.in; Pillai, Harish K., E-mail: hp@ee.iitb.ac.in; Bandyopadhyay, Santanu, E-mail: santanu@me.iitb.ac.in

2015-10-15

In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.

Energy harvesting by dynamic unstability and internal resonance for piezoelectric beam

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

Lan, Chunbo; Qin, Weiyang, E-mail: 353481781@qq.com; Deng, Wangzheng

We investigated the energy harvesting of a vertical beam with tip mass under vertical excitations. We applied dynamic unstability and internal resonance to improve the efficiency of harvesting. The experiments of harmonic excitation were carried out. Results show that for the beam there exist internal resonances in the dynamically unstable and the buckling bistable cases. The dynamic unstability is a determinant for strong internal resonance or mode coupling, which can be used to create a large output from piezoelectric patches. Then, the experiments of stochastic excitation were carried out. Results prove that the internal resonance or mode coupling can transfermore » the excitation energy to the low order modes, mainly the first and the second one. This can bring about a large output voltage. For a stochastic excitation, it is proved that there is an optimal weight of tip mass for realizing internal resonance and producing large outputs.« less

Reduced dimensionality (3,2)D NMR experiments and their automated analysis: implications to high-throughput structural studies on proteins.

PubMed

Reddy, Jithender G; Kumar, Dinesh; Hosur, Ramakrishna V

2015-02-01

Protein NMR spectroscopy has expanded dramatically over the last decade into a powerful tool for the study of their structure, dynamics, and interactions. The primary requirement for all such investigations is sequence-specific resonance assignment. The demand now is to obtain this information as rapidly as possible and in all types of protein systems, stable/unstable, soluble/insoluble, small/big, structured/unstructured, and so on. In this context, we introduce here two reduced dimensionality experiments – (3,2)D-hNCOcanH and (3,2)D-hNcoCAnH – which enhance the previously described 2D NMR-based assignment methods quite significantly. Both the experiments can be recorded in just about 2-3 h each and hence would be of immense value for high-throughput structural proteomics and drug discovery research. The applicability of the method has been demonstrated using alpha-helical bovine apo calbindin-D9k P43M mutant (75 aa) protein. Automated assignment of this data using AUTOBA has been presented, which enhances the utility of these experiments. The backbone resonance assignments so derived are utilized to estimate secondary structures and the backbone fold using Web-based algorithms. Taken together, we believe that the method and the protocol proposed here can be used for routine high-throughput structural studies of proteins. Copyright © 2014 John Wiley & Sons, Ltd.

The Effect of Weak Resistivity and Weak Thermal Diffusion on Short-wavelength Magnetic Buoyancy Instability

NASA Astrophysics Data System (ADS)

Gradzki, Marek J.; Mizerski, Krzysztof A.

2018-03-01

Magnetic buoyancy instability in weakly resistive and thermally conductive plasma is an important mechanism of magnetic field expulsion in astrophysical systems. It is often invoked, e.g., in the context of the solar interior. Here, we revisit a problem introduc`ed by Gilman: the short-wavelength linear stability of a plane layer of compressible isothermal and weakly diffusive fluid permeated by a horizontal magnetic field of strength decreasing with height. In this physical setting, we investigate the effect of weak resistivity and weak thermal conductivity on the short-wavelength perturbations, localized in the vertical direction, and show that the presence of diffusion allows to establish the wavelength of the most unstable mode, undetermined in an ideal fluid. When diffusive effects are neglected, the perturbations are amplified at a rate that monotonically increases as the wavelength tends to zero. We demonstrate that, when the resistivity and thermal conduction are introduced, the wavelength of the most unstable perturbation is established and its scaling law with the diffusion parameters depends on gradients of the mean magnetic field, temperature, and density. Three main dynamical regimes are identified, with the wavelength of the most unstable mode scaling as either λ /d∼ {{ \\mathcal U }}κ 3/5 or λ /d∼ {{ \\mathcal U }}κ 3/4 or λ /d∼ {{ \\mathcal U }}κ 1/3, where d is the layer thickness and {{ \\mathcal U }}κ is the ratio of the characteristic thermal diffusion velocity scale to the free-fall velocity. Our analytic results are backed up by a series of numerical solutions. The two-dimensional interchange modes are shown to dominate over three-dimensional ones when the magnetic field and/or temperature gradients are strong enough.

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

(1173) Anchises - thermophysical and dynamical studies of a dynamically unstable Jovian Trojan

NASA Astrophysics Data System (ADS)

Horner, J.; Müller, T. G.; Lykawka, P. S.

2012-07-01

We have performed detailed thermophysical and dynamical modelling of the Jovian Trojan (1173) Anchises. Our results show that this is the most unusual object. By examining observational data of Anchises taken by IRAS, Akari and WISE at wavelengths between 11.5 and 60 μm, together with the variations in its optical light curve, we find that Anchises is most likely an elongated body, with an axis ratio, a/b, of around 1.4. This results in calculated best-fitting dimensions for Anchises of 170 × 121 × 121 km (or an equivalent diameter of 136 +18/-11 km). We find that the observations of Anchises are best fitted by the object having a retrograde sense of rotation, and an unusually high thermal inertia in the range 25-100 J m-2 s-0.5 K-1 (3σ confidence level). The geometric albedo of Anchises is found to be 0.027 (+0.006/-0.007). Anchises therefore has one of the highest published thermal inertias of any object larger than 100 km in diameter, at such large heliocentric distances, as well as being one of the lowest albedo objects ever observed. More observations (visual and thermal) are needed to see whether there is a link between the very shallow phase curve, with almost no opposition effect, and the derived thermal properties for this large Trojan asteroid. Our dynamical investigation of Anchises' orbit has revealed it to be dynamically unstable on time-scales of hundreds of millions of years, similar to the unstable Neptunian Trojans 2001 QR322 and 2008 LC18. Unlike those objects, however, we find that the dynamical stability of Anchises is not a function of its initial orbital elements, the result of the exceptional precision with which its orbit is known. Our results are the first to show that a Jovian Trojan is dynamically unstable, and add further weight to the idea that the planetary Trojans likely represent a significant ongoing contribution to the dynamically unstable Centaur population, the parents of the short-period comets. The observed instability (fully half of all clones of Anchises escape the Solar system within 350 Myr) does not rule out a primordial origin for Anchises, but, when taken in concert with the result of our thermophysical analysis, suggest that it would be a fascinating target for a future study.

Complexity of the laminar-turbulent boundary in pipe flow

NASA Astrophysics Data System (ADS)

Budanur, Nazmi Burak; Hof, Björn

2018-05-01

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry reduction, which we formulate here for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling-wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.

Evaluation of three-dimensional printing for internal fixation of unstable pelvic fracture from minimal invasive para-rectus abdominis approach: a preliminary report.

PubMed

Zeng, Canjun; Xiao, Jidong; Wu, Zhanglin; Huang, Wenhua

2015-01-01

The aim of this study is to evaluate the efficacy and feasibility of three-dimensional printing (3D printing) assisted internal fixation of unstable pelvic fracture from minimal invasive para-rectus abdominis approach. A total of 38 patients with unstable pelvic fractures were analyzed retrospectively from August 2012 to February 2014. All cases were treated operatively with internal fixation assisted by three-dimensional printing from minimal invasive para-rectus abdominis approach. Both preoperative CT and three-dimensional reconstruction were performed. Pelvic model was created by 3D printing. Data including the best entry points, plate position and direction and length of screw were obtained from simulated operation based on 3D printing pelvic model. The diaplasis and internal fixation were performed by minimal invasive para-rectus abdominis approach according to the optimized dada in real surgical procedure. Matta and Majeed score were used to evaluate currative effects after operation. According to the Matta standard, the outcome of the diaplasis achieved 97.37% with excellent and good. Majeed assessment showed 94.4% with excellent and good. The imageological examination showed consistency of internal fixation and simulated operation. The mean operation time was 110 minutes, mean intraoperative blood loss 320 ml, and mean incision length 6.5 cm. All patients have achieved clinical healing, with mean healing time of 8 weeks. Three-dimensional printing assisted internal fixation of unstable pelvic fracture from minimal invasive para-rectus abdominis approach is feasible and effective. This method has the advantages of trauma minimally, bleeding less, healing rapidly and satisfactory reduction, and worthwhile for spreading in clinical practice.

Metastable states and energy flow pathway in square graphene resonators

NASA Astrophysics Data System (ADS)

Wang, Yisen; Zhu, Zhigang; Zhang, Yong; Huang, Liang

2018-01-01

Nonlinear interaction between flexural modes is critical to heat conductivity and mechanical vibration of two-dimensional materials such as graphene. Much effort has been devoted to understand the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during thermalization process. The key is the development of a universal scheme that numerically characterizes the strength of nonlinear interactions between normal modes. In particular, for our square graphene system, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes. As a result, the equations for the normal modes in the same class as the initially excited one can be approximated by driven harmonic oscillators, therefore, they get energy almost instantaneously. Because of the hierarchical organization of the mode coupling, the energy distribution among the modes will arrive at a stable profile, where most of the energy is localized on a few modes, leading to the formation of "natural package" and metastable states. The dynamics for modes in other symmetry classes follows a Mathieu type of equation, thus, interclass energy flow, when the initial excitation energy is small, starts typically when there is a mode that lies in the unstable region in the parameter space of Mathieu equation. Due to strong coupling of the modes inside the class, the whole class will get energy and be lifted up by the unstable mode. This characterizes the energy flow pathway of the system. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two-dimensional systems with complex potentials, and reveal clearly the physical picture of dynamical interactions between the flexural modes, which will be crucial to the understanding of their abnormal contribution to heat conduction and nonlinear mechanical vibrations.

Jets and Water Clouds on Jupiter

NASA Astrophysics Data System (ADS)

Lian, Yuan; Showman, A. P.

2012-10-01

Ground-based and spacecraft observations show that Jupiter exhibits multiple banded zonal jet structures. These banded jets correlate with dark and bright clouds, often called "belts" and "zones". The mechanisms that produce these banded zonal jets and clouds are poorly understood. Our previous studies showed that the latent heat released by condensation of water vapor could produce equatorial superrotation along with multiple zonal jets in the mid-to-high latitudes. However, that previous work assumed complete and instant removal of condensate and therefore could not predict the cloud formation. Here we present an improved 3D Jupiter model to investigate some effects of cloud microphysics on large-scale dynamics using a closed water cycle that includes condensation, three-dimensional advection of cloud material by the large-scale circulation, evaporation and sedimentation. We use a dry convective adjustment scheme to adjust the temperature towards a dry adiabat when atmospheric columns become convectively unstable, and the tracers are mixed within the unstable layers accordingly. Other physics parameterizations included in our model are the bottom drag and internal heat flux as well as the choices of either Newtonian heating scheme or gray radiative transfer. Given the poorly understood cloud microphysics, we perform case studies by treating the particle size and condensation/evaporation time scale as free parameters. We find that, in some cases, the active water cycle can produce multiple banded jets and clouds. However, the equatorial jet is generally very weak in all the cases because of insufficient supply of eastward eddy momentum fluxes. These differences may result from differences in the overall vertical stratification, baroclinicity, and moisture distribution in our new models relative to the older ones; we expect to elucidate the dynamical mechanisms in continuing work.

Dynamics of a class of vortex rings. Ph.D. Thesis - Stanford Univ.

NASA Technical Reports Server (NTRS)

Shariff, Karim; Leonard, Anthony; Ferziger, Joel H.

1989-01-01

The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows.

Can common measures of core stability distinguish performance in a shoulder pressing task under stable and unstable conditions?

PubMed

Keogh, Justin W L; Aickin, Sam E; Oldham, Anthony R H

2010-02-01

The primary purpose of this study was to determine whether a range of static core stability (CS) measures could distinguish shoulder press performance in unstable vs. stable conditions. Thirty resistance-trained men gave informed consent to participate in this study. One-repetition maximum strength (from < 6 repetitions) was predicted in the seated shoulder dumbbell press performed in unstable (Swiss ball[SB]) and stable (back-support bench) environments. Three CS muscle endurance tests were performed, with 4 CS ratios also calculated. The degree of strength decrement, referred to as the instability strength level (ISL), was calculated by dividing the predicted 1RM Unstable score by the 1RM Stable score. All subjects were categorized as high (ISL > 0.90), moderate (0.85 < or = ISL < or = 0.90), or low (ISL < 0.85). Between-group differences for the high- and low-ISL groups were assessed using analysis of variance and effect sizes. Pearson product moment correlations were then performed to examine the relationships between the CS measures and the ISL for the entire group. No significant between-group differences (p = 0.132-0.999) or large effect sizes were observed for any of the CS measures. Trunk flexion endurance was the only CS measure significantly correlated to the ISL (r = 0.477). In line with muscular strength research, these results suggest that CS exhibits relatively high levels of task specificity and that CS performance in static single-joint exercises may not be highly related to that in more dynamic multijoint activities. Core stability training (with or without a SB) may therefore only lead to significant improvements in functional dynamic performance if the postures, mode and velocity of contraction performed in training, are similar to the competitive tasks.

A delay differential model of ENSO variability: Extreme values and stability analysis

NASA Astrophysics Data System (ADS)

Zaliapin, I.; Ghil, M.

2009-04-01

We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) variability [Ghil et al. (2008), Nonlin. Proc. Geophys., 15, 417-433.] The model combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. Toy models of this type were shown to capture major features of the ENSO phenomenon [Jin et al., Science (1994); Tziperman et al., Science (1994)]; they provide a convenient paradigm for explaining interannual ENSO variability and shed new light on its dynamical properties. So far, though, DDE model studies of ENSO have been limited to linear stability analysis of steady-state solutions, which are not typical in forced systems, case studies of particular trajectories, or one-dimensional scenarios of transition to chaos, varying a single parameter while the others are kept fixed. In this work we take several steps toward a comprehensive analysis of DDE models relevant for ENSO phenomenology and illustrate the complexity of phase-parameter space structure for even such a simple model of climate dynamics. We formulate an initial value problem for our model and prove the existence, uniqueness, and continuous dependence theorem. We then use this theoretical result to perform detailed numerical stability analyses of the model in the three-dimensional space of its physically relevant parameters: strength of seasonal forcing b, atmosphere-ocean coupling ΰ, and propagation period ? of oceanic waves across the Tropical Pacific. Two regimes of variability, stable and unstable, are reported; they are separated by a sharp neutral curve in the (b,?) plane at constant ΰ. The detailed structure of the neutral curve becomes very irregular and possibly fractal, while individual trajectories within the unstable region become highly complex and possibly chaotic, as the atmosphere-ocean coupling ΰ increases. In the unstable regime, spontaneous transitions occur in the mean temperature (i.e., thermocline depth), period, and extreme annual values, for purely periodic, seasonal forcing. The model reproduces the Devils bleachers characterizing other ENSO models, such as nonlinear, coupled systems of partial differential equations; some of the features of this behavior have been documented in general circulation models, as well as in observations. We analyze the values of annual extremes and their location within an annual cycle and report the phase-locking phenomenon, which is connected to the occurrence of El-Niño events during the boreal (Northern Hemisphere) winter. We report existence of multiple solutions and study their basins of attraction in a space of initial conditions. We also present a model-based justification for the observed quasi-biennial oscillation in Tropical Pacific SSTs. We expect similar behavior in much more detailed and realistic models, where it is harder to describe its causes as completely. The basic mechanisms used in our model (delayed feedback and forcing) may be relevant to other natural systems in which internal instabilities interact with external forcing and give rise to extreme events.

A new general circulation model of Jupiter's atmosphere based on the UKMO Unified Model: Three-dimensional evolution of isolated vortices and zonal jets in mid-latitudes

NASA Astrophysics Data System (ADS)

Yamazaki, Y. H.; Skeet, D. R.; Read, P. L.

2004-04-01

We have been developing a new three-dimensional general circulation model for the stratosphere and troposphere of Jupiter based on the dynamical core of a portable version of the Unified Model of the UK Meteorological Office. Being one of the leading terrestrial GCMs, employed for operational weather forecasting and climate research, the Unified Model has been thoroughly tested and performance tuned for both vector and parallel computers. It is formulated as a generalized form of the standard primitive equations to handle a thick atmosphere, using a scaled pressure as the vertical coordinate. It is able to accurately simulate the dynamics of a three-dimensional fully compressible atmosphere on the whole or a part of a spherical shell at high spatial resolution in all three directions. Using the current version of the GCM, we examine the characteristics of the Jovian winds in idealized configurations based on the observed vertical structure of temperature. Our initial focus is on the evolution of isolated eddies in the mid-latitudes. Following a brief theoretical investigation of the vertical structure of the atmosphere, limited-area cyclic channel domains are used to numerically investigate the nonlinear evolution of the mid-latitude winds. First, the evolution of deep and shallow cyclones and anticyclones are tested in the atmosphere at rest to identify a preferred horizontal and vertical structure of the vortices. Then, the dependency of the migration characteristics of the vortices are investigated against modelling parameters to find that it is most sensitive to the horizontal diffusion. We also examine the hydrodynamical stability of observed subtropical jets in both northern and southern hemispheres in the three-dimensional nonlinear model as initial value problems. In both cases, it was found that the prominent jets are unstable at various scales and that vorteces of various sizes are generated including those comparable to the White Ovals and the Great Red Spot.

Multi-Baker Map as a Model of Digital PD Control

NASA Astrophysics Data System (ADS)

Csernák, Gábor; Gyebrószki, Gergely; Stépán, Gábor

Digital stabilization of unstable equilibria of linear systems may lead to small amplitude stochastic-like oscillations. We show that these vibrations can be related to a deterministic chaotic dynamics induced by sampling and quantization. A detailed analytical proof of chaos is presented for the case of a PD controlled oscillator: it is shown that there exists a finite attracting domain in the phase-space, the largest Lyapunov exponent is positive and the existence of a Smale horseshoe is also pointed out. The corresponding two-dimensional micro-chaos map is a multi-baker map, i.e. it consists of a finite series of baker’s maps.

Hypothesis testing for band size detection of high-dimensional banded precision matrices.

PubMed

An, Baiguo; Guo, Jianhua; Liu, Yufeng

2014-06-01

Many statistical analysis procedures require a good estimator for a high-dimensional covariance matrix or its inverse, the precision matrix. When the precision matrix is banded, the Cholesky-based method often yields a good estimator of the precision matrix. One important aspect of this method is determination of the band size of the precision matrix. In practice, crossvalidation is commonly used; however, we show that crossvalidation not only is computationally intensive but can be very unstable. In this paper, we propose a new hypothesis testing procedure to determine the band size in high dimensions. Our proposed test statistic is shown to be asymptotically normal under the null hypothesis, and its theoretical power is studied. Numerical examples demonstrate the effectiveness of our testing procedure.

Invariant polygons in systems with grazing-sliding.

PubMed

Szalai, R; Osinga, H M

2008-06-01

The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system has an attractor that consists of forward sliding orbits. We analyze this attractor in a suitably chosen Poincare section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.

Quasi-periodic Oscillations in Flares and Coronal Mass Ejections Associated with Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Takahashi, Takuya; Qiu, Jiong; Shibata, Kazunari

2017-10-01

We propose a mechanism for quasi-periodic oscillations of both coronal mass ejections (CMEs) and flare loops as related to magnetic reconnection in eruptive solar flares. We perform two-dimensional numerical MHD simulations of magnetic flux rope eruption, with three different values of the global Lundquist number. In the low Lundquist number run, no oscillatory behavior is found. In the moderate Lundquist number run, on the other hand, quasi-periodic oscillations are excited both at the bottom of the flux rope and at the flare loop top. In the high Lundquist number run, quasi-periodic oscillations are also excited; in the meanwhile, the dynamics become turbulent owing to the formation of multiple plasmoids in the reconnection current sheet. In high and moderate Lundquist number runs, thin reconnection jets collide with the flux rope bottom or flare loop top and dig them deeply. Steep oblique shocks are formed as termination shocks where reconnection jets are bent (rather than decelerated) in the horizontal direction, resulting in supersonic backflows. The structure becomes unstable, and quasi-periodic oscillations of supersonic backflows appear at locally confined high-beta regions at both the flux rope bottom and flare loop top. We compare the observational characteristics of quasi-periodic oscillations in erupting flux ropes, post-CME current sheets, flare ribbons, and light curves with corresponding dynamical structures found in our simulation.

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

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

Smith, L. D., E-mail: lachlan.smith@monash.edu; CSIRO Mineral Resources, Clayton, Victoria 3800; Rudman, M.

2016-05-15

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversalmore » in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.« less

Boundary between stable and unstable regimes of accretion. Ordered and chaotic unstable regimes

NASA Astrophysics Data System (ADS)

Blinova, A. A.; Romanova, M. M.; Lovelace, R. V. E.

2016-07-01

We present a new study of the Rayleigh-Taylor unstable regime of accretion on to rotating magnetized stars in a set of high grid resolution three-dimensional magnetohydrodynamic simulations performed in low-viscosity discs. We find that the boundary between the stable and unstable regimes is determined almost entirely by the fastness parameter ωs = Ω⋆/ΩK(rm), where Ω⋆ is the angular velocity of the star and ΩK(rm) is the angular velocity of the Keplerian disc at the disc-magnetosphere boundary r = rm. We found that accretion is unstable if ωs ≲ 0.6. Accretion through instabilities is present in stars with different magnetospheric sizes. However, only in stars with relatively small magnetospheres, rm/R⋆ ≲ 7, do the unstable tongues produce chaotic hotspots on the stellar surface and irregular light curves. At even smaller values of the fastness parameter, ωs ≲ 0.45, multiple irregular tongues merge, forming one or two ordered unstable tongues that rotate with the angular frequency of the inner disc. This transition occurs in stars with even smaller magnetospheres, rm/R⋆ ≲ 4.2. Most of our simulations were performed at a small tilt of the dipole magnetosphere, Θ = 5°, and a small viscosity parameter α = 0.02. Test simulations at higher α values show that many more cases become unstable, and the light curves become even more irregular. Test simulations at larger tilts of the dipole Θ show that instability is present, however, accretion in two funnel streams dominates if Θ ≳ 15°. The results of these simulations can be applied to accreting magnetized stars with relatively small magnetospheres: Classical T Tauri stars, accreting millisecond X-ray pulsars, and cataclysmic variables.

Quantization improves stabilization of dynamical systems with delayed feedback

NASA Astrophysics Data System (ADS)

Stepan, Gabor; Milton, John G.; Insperger, Tamas

2017-11-01

We show that an unstable scalar dynamical system with time-delayed feedback can be stabilized by quantizing the feedback. The discrete time model corresponds to a previously unrecognized case of the microchaotic map in which the fixed point is both locally and globally repelling. In the continuous-time model, stabilization by quantization is possible when the fixed point in the absence of feedback is an unstable node, and in the presence of feedback, it is an unstable focus (spiral). The results are illustrated with numerical simulation of the unstable Hayes equation. The solutions of the quantized Hayes equation take the form of oscillations in which the amplitude is a function of the size of the quantization step. If the quantization step is sufficiently small, the amplitude of the oscillations can be small enough to practically approximate the dynamics around a stable fixed point.

Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo

NASA Astrophysics Data System (ADS)

Wei, Zhouchao; Moroz, Irene; Sprott, J. C.; Akgul, Akif; Zhang, Wei

2017-03-01

We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two stable equilibrium states in certain regions of parameter space. The new 5D hyperchaotic self-exciting homopolar disc dynamo has multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, hidden chaos or hyperchaos, as well as coexisting attractors. We use numerical integrations to create the phase plane trajectories, produce bifurcation diagram, and compute Lyapunov exponents to verify the hidden attractors. Because no unstable equilibria exist in two parameter regions, the system has a multistability and six kinds of complex dynamic behaviors. To the best of our knowledge, this feature has not been previously reported in any other high-dimensional system. Moreover, the 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations. Both Matlab and the oscilloscope outputs produce similar phase portraits. Such implementations in real time represent a new type of hidden attractor with important consequences for engineering applications.

Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo.

PubMed

Wei, Zhouchao; Moroz, Irene; Sprott, J C; Akgul, Akif; Zhang, Wei

2017-03-01

We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two stable equilibrium states in certain regions of parameter space. The new 5D hyperchaotic self-exciting homopolar disc dynamo has multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, hidden chaos or hyperchaos, as well as coexisting attractors. We use numerical integrations to create the phase plane trajectories, produce bifurcation diagram, and compute Lyapunov exponents to verify the hidden attractors. Because no unstable equilibria exist in two parameter regions, the system has a multistability and six kinds of complex dynamic behaviors. To the best of our knowledge, this feature has not been previously reported in any other high-dimensional system. Moreover, the 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations. Both Matlab and the oscilloscope outputs produce similar phase portraits. Such implementations in real time represent a new type of hidden attractor with important consequences for engineering applications.

DYNAMICAL INSTABILITIES IN HIGH-OBLIQUITY SYSTEMS

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

Tamayo, D.; Nicholson, P. D.; Burns, J. A.

2013-03-01

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations-large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. found that, for planets with obliquities >68. Degree-Sign 875, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we findmore » that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68. Degree-Sign 875. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. For low-eccentricity orbits in the equilibrium Laplace plane, we find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this occurs because radiation pressure modifies the equilibrium Laplace plane.« less

Muscular outputs during dynamic bench press under stable versus unstable conditions.

PubMed

Koshida, Sentaro; Urabe, Yukio; Miyashita, Koji; Iwai, Kanzunori; Kagimori, Aya

2008-09-01

Previous studies have suggested that resistance training exercise under unstable conditions decreases the isometric force output, yet little is known about its influence on muscular outputs during dynamic movement. The objective of this study was to investigate the effect of an unstable condition on power, force, and velocity outputs during the bench press. Twenty male collegiate athletes (mean age, 21.3 +/- 1.5 years; mean height, 167.7 +/- 7.7 cm; mean weight, 75.9 +/- 17.5 kg) participated in this study. Each subject attempted 3 sets of single bench presses with 50% of 1 repetition maximum (1RM) under a stable condition with a flat bench and an unstable condition with a Swiss ball. Acceleration data were obtained with an accelerometer attached to the center of a barbell shaft, and peak outputs of power, force, and velocity were computed. Although significant loss of the peak outputs was found under the unstable condition (p < 0.017), their reduction rates remained relatively low, approximately 6% for force and 10% for power and velocity outputs, compared with previous findings. Such small reduction rates of muscular outputs may not compromise the training effect. Prospective studies are necessary to confirm whether the resistance training under an unstable condition permits the improvement of dynamic performance and trunk stability.

On the Transition from Two-Dimensional to Three-Dimensional MHD Turbulence

NASA Technical Reports Server (NTRS)

Thess, A.; Zikanov, Oleg

2004-01-01

We report a theoretical investigation of the robustness of two-dimensional inviscid MHD flows at low magnetic Reynolds numbers with respect to three-dimensional perturbations. We analyze three model problems, namely flow in the interior of a triaxial ellipsoid, an unbounded vortex with elliptical streamlines, and a vortex sheet parallel to the magnetic field. We demonstrate that motion perpendicular to the magnetic field with elliptical streamlines becomes unstable with respect to the elliptical instability once the velocity has reached a critical magnitude whose value tends to zero as the eccentricity of the streamlines becomes large. Furthermore, vortex sheets parallel to the magnetic field, which are unstable for any velocity and any magnetic field, are found to emit eddies with vorticity perpendicular to the magnetic field and with an aspect ratio proportional to N(sup 1/2). The results suggest that purely two-dimensional motion without Joule energy dissipation is a singular type of flow which does not represent the asymptotic behaviour of three-dimensional MHD turbulence in the limit of infinitely strong magnetic fields.

Singularity perturbed zero dynamics of nonlinear systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

1992-01-01

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

On the secondary instability of the most dangerous Goertler vortex

NASA Technical Reports Server (NTRS)

Otto, S. R.; Denier, James P.

1993-01-01

Recent studies have demonstrated the most unstable Goertler vortex mode is found in flows, both two and three-dimensional, with regions of (moderately) large body curvature and these modes reside within a thin layer situated at the base of the conventional boundary layer. Further work concerning the nonlinear development of the most dangerous mode demonstrates that the flow results in a self induced flow reversal. However, prior to the point at which flow reversal is encountered, the total streamwise velocity profile is found to be highly inflectional in nature. Previous work then suggests that the nonlinear vortex state will become unstable to secondary, inviscid, Rayleigh wave instabilities prior to the point of flow reversal. Our concern is with the secondary instability of the nonlinear vortex states, which result from the streamwise evolution of the most unstable Goertler vortex mode, with the aim of determining whether such modes can induce a transition to a fully turbulent state before separation is encountered.

The Goertler vortex instability mechanism in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.

1984-01-01

The two dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

Inertial and stick-slip regimes of unstable adhesive tape peeling.

PubMed

Dalbe, Marie-Julie; Villey, Richard; Ciccotti, Matteo; Santucci, Stéphane; Cortet, Pierre-Philippe; Vanel, Loïc

2016-05-18

We present an experimental characterization of the detachment front unstable dynamics observed during the peeling of pressure sensitive adhesives. We use an experimental set-up specifically designed to control the peeling angle θ and the peeled tape length L, while peeling an adhesive tape from a flat substrate at a constant driving velocity V. High-speed imaging allows us to report the evolution of the period and amplitude of the front oscillations, as well as the relative durations of their fast and slow phases, as a function of the control parameters V, L and θ. Our study shows that, as the driving velocity or the peeling angle increases, the oscillations of the peeling front progressively evolve from genuine "stick-slip" oscillations, made of alternating long stick phases and very brief slip phases, to sinusoidal oscillations of amplitude twice the peeling velocity. We propose a model which, taking into account the peeling angle-dependent kinetic energy cost to accelerate and decelerate the peeled tape, explains the transition from the "stick-slip" to the "inertial" regime of the dynamical instability. Using independent direct measurements of the effective fracture energy of the adhesive-substrate joint, we show that our model quantitatively accounts for the two regimes of the unstable dynamics.

Cellular Spacing Selection During the Directional Solidification of Binary Alloys. A Numerical Approach

NASA Technical Reports Server (NTRS)

Catalina, Adrian V.; Sen, S.; Rose, M. Franklin (Technical Monitor)

2001-01-01

The evolution of cellular solid/liquid interfaces from an initially unstable planar front was studied by means of a two-dimensional computer simulation. The developed numerical model makes use of an interface tracking procedure and has the capability to describe the dynamics of the interface morphology based on local changes of the thermodynamic conditions. The fundamental physics of this formulation was validated against experimental microgravity results and the predictions of the analytical linear stability theory. The performed simulations revealed that in certain conditions, based on a competitive growth mechanism, an interface could become unstable to random perturbations of infinitesimal amplitude even at wavelengths smaller than the neutral wavelength, lambda(sub c), predicted by the linear stability theory. Furthermore, two main stages of spacing selection have been identified. In the first stage, at low perturbations amplitude, the selection mechanism is driven by the maximum growth rate of instabilities while in the second stage the selection is influenced by nonlinear phenomena caused by the interactions between the neighboring cells. Comparison of these predictions with other existing theories of pattern formation and experimental results will be discussed.

Assimilation of Sea Color Data Into A Three Dimensional Biogeochemical Model: Sensitivity Experiments

NASA Astrophysics Data System (ADS)

Echevin, V.; Levy, M.; Memery, L.

The assimilation of two dimensional sea color data fields into a 3 dimensional coupled dynamical-biogeochemical model is performed using a 4DVAR algorithm. The biogeochemical model includes description of nitrates, ammonium, phytoplancton, zooplancton, detritus and dissolved organic matter. A subset of the biogeochemical model poorly known parameters (for example,phytoplancton growth, mortality,grazing) are optimized by minimizing a cost function measuring misfit between the observations and the model trajectory. Twin experiments are performed with an eddy resolving model of 5 km resolution in an academic configuration. Starting from oligotrophic conditions, an initially unstable baroclinic anticyclone splits into several eddies. Strong vertical velocities advect nitrates into the euphotic zone and generate a phytoplancton bloom. Biogeochemical parameters are perturbed to generate surface pseudo-observations of chlorophyll,which are assimilated in the model in order to retrieve the correct parameter perturbations. The impact of the type of measurement (quasi-instantaneous, daily mean, weekly mean) onto the retrieved set of parameters is analysed. Impacts of additional subsurface measurements and of errors in the circulation are also presented.

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

On the global dynamics of a chronic myelogenous leukemia model

NASA Astrophysics Data System (ADS)

Krishchenko, Alexander P.; Starkov, Konstantin E.

2016-04-01

In this paper we analyze some features of global dynamics of a three-dimensional chronic myelogenous leukemia (CML) model with the help of the stability analysis and the localization method of compact invariant sets. The behavior of CML model is defined by concentrations of three cellpopulations circulating in the blood: naive T cells, effector T cells specific to CML and CML cancer cells. We prove that the dynamics of the CML system around the tumor-free equilibrium point is unstable. Further, we compute ultimate upper bounds for all three cell populations and provide the existence conditions of the positively invariant polytope. One ultimate lower bound is obtained as well. Moreover, we describe the iterative localization procedure for refining localization bounds; this procedure is based on cyclic using of localizing functions. Applying this procedure we obtain conditions under which the internal tumor equilibrium point is globally asymptotically stable. Our theoretical analyses are supplied by results of the numerical simulation.

Manual control of unstable systems

NASA Technical Reports Server (NTRS)

Allen, R. W.; Hogue, J. R.; Parseghian, Z.

1986-01-01

Under certain operational regimes and failure modes, air and ground vehicles can present the human operator with a dynamically unstable or divergent control task. Research conducted over the last two decades has explored the ability of the human operator to control unstable systems under a variety of circumstances. Past research is reviewed and human operator control capabilities are summarized. A current example of automobile directional control under rear brake lockup conditions is also reviewed. A control system model analysis of the driver's steering control task is summarized, based on a generic driver/vehicle model presented at last year's Annual Manual. Results from closed course braking tests are presented that confirm the difficulty the average driver has in controlling the unstable directional dynamics arising from rear wheel lockup.

Toward understanding the roaming mechanism in H + MgH → Mg + HH reaction

DOE PAGES

Mauguiere, Frederic A. L.; Collins, Peter; Stamatiadis, Stamatis; ...

2016-02-26

The roaming mechanism in the reaction H + MgH →Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio threedimensional ground electronic state potential energy surface. The reaction dynamics are explored by running trajectories initialized on a four-dimensional dividing surface anchored on three-dimensional normally hyperbolic invariant manifold associated with a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase spacemore » where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. As a result, the complex forming trajectories in the HMgH well can either return to the radical channel or “roam” to the MgHH minimum from where the molecule may react.« less

Two-component dark-bright solitons in three-dimensional atomic Bose-Einstein condensates.

PubMed

Wang, Wenlong; Kevrekidis, P G

2017-03-01

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.

Multi-dimensional dynamics of stimulated Brillouin scattering in a laser speckle: Ion acoustic wave bowing, breakup, and laser-seeded two-ion-wave decay

DOE PAGES

Albright, B. J.; Yin, L.; Bowers, K. J.; ...

2016-03-04

Two- and three-dimensional particle-in-cell simulations of stimulated Brillouin scattering(SBS) in laser speckle geometry have been analyzed to evaluate the relative importance of competing nonlinear processes in the evolution and saturation of SBS. It is found that ion-trapping-induced wavefront bowing and breakup of ion acoustic waves(IAW) and the associated side-loss of trapped ions dominate electron-trapping-induced IAW wavefront bowing and breakup, as well as the two-ion-wave decay instability over a range of ZT e/T i conditions and incident laser intensities. In the simulations, the latter instability does not govern the nonlinear saturation of SBS; however, evidence of two-ion-wave decay is seen, appearingmore » as a modulation of the ion acoustic wavefronts. This modulation is periodic in the laser polarization plane, anti-symmetric across the speckle axis, and of a wavenumber matching that of the incident laser pulse. Furthermore, a simple analytic model is provided for how spatial “imprinting” from a high frequency inhomogeneity (in this case, the density modulation from the laser) in an unstable system with continuum eigenmodes can selectively amplify modes with wavenumbers that match that of the inhomogeneity.« less

Quasinormal modes of scale dependent black holes in (1 +2 )-dimensional Einstein-power-Maxwell theory

NASA Astrophysics Data System (ADS)

Rincón, Ángel; Panotopoulos, Grigoris

2018-01-01

We study for the first time the stability against scalar perturbations, and we compute the spectrum of quasinormal modes of three-dimensional charged black holes in Einstein-power-Maxwell nonlinear electrodynamics assuming running couplings. Adopting the sixth order Wentzel-Kramers-Brillouin (WKB) approximation we investigate how the running of the couplings change the spectrum of the classical theory. Our results show that all modes corresponding to nonvanishing angular momentum are unstable both in the classical theory and with the running of the couplings, while the fundamental mode can be stable or unstable depending on the running parameter and the electric charge.

Is a Higgs vacuum instability fatal for high-scale inflation?

DOE PAGES

Kearney, John; Yoo, Hojin; Zurek, Kathryn M.

2015-06-25

We study the inflationary evolution of a scalar field h with an unstable potential for the case where the Hubble parameter H during inflation is larger than the instability scale Λ I of the potential. Quantum fluctuations in the field of size δh ~ H/2π imply that the unstable part of the potential is sampled during inflation. We investigate the evolution of these fluctuations to the unstable regime and in particular whether they generate cosmological defects or even terminate inflation. We apply the results of a toy scalar model to the case of the Standard Model (SM) Higgs boson, themore » quartic of which evolves to negative values at high scales, and extend previous analyses of Higgs dynamics during inflation utilizing statistical methods to a perturbative and fully gauge-invariant formulation. We show that the dynamics are controlled by the renormalization group-improved quartic coupling λ(μ) evaluated at a scale μ = H, such that Higgs fluctuations are enhanced by the instability if H > Λ I. Even if H > Λ I, the instability in the Standard Model Higgs potential does not end inflation; instead the universe slowly sloughs off crunching patches of space that never come to dominate the evolution. As inflation proceeds past 50 e-folds, a significant proportion of patches exits inflation in the unstable vacuum, and as much as 1% of the spacetime can rapidly evolve to a defect. Depending on the nature of these defects, however, the resulting universe could still be compatible with ours.« less

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Small, Des; Wiggins, Stephen

2006-12-01

In the past 15 years the framework and ideas from dynamical systems theory have been applied to a variety of transport and mixing problems in oceanic flows. The motivation for this approach comes directly from advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.) which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. In this tutorial, we motivate this approach by showing the relationship between fluid transport in two-dimensional time-periodic incompressible flows and the geometrical structures that exist for two-dimensional area-preserving maps, such as hyperbolic periodic orbits, their stable and unstable manifolds and KAM (Kolmogorov-Arnold-Moser) tori. This serves to set the stage for the attempt to “transfer” this approach to more realistic flows modelling the ocean. However, in order to accomplish this several difficulties must be overcome. The first difficulty that confronts us that any attempt to carry out a dynamical systems approach to transport requires us to obtain the appropriate “dynamical system”, which is the velocity field describing the fluid flow. In general, adequate model velocity fields are obtained by numerical solution of appropriate partial differential equations describing the dynamical evolution of the velocity field. Numerical solution of the partial differential equations can only be done for a finite time interval, and since the ocean is generally not time-periodic, this leads to a new type of dynamical system: a finite-time, aperiodically time-dependent velocity field defined as a data set on a space-time grid. The global, geometrical analysis of transport in such dynamical systems requires both new concepts and new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. The purpose of this tutorial is to describe these new concepts and analytical tools first using simple dynamical systems where quantities can be computed exactly. We then discuss their computational implications and implementation in the context of a model geophysical flow: a turbulent wind-driven double-gyre in the quasigeostrophic approximation.

Imaging a multidimensional multichannel potential energy surface: Photodetachment of H(-)(NH3) and NH4 (.).

PubMed

Hu, Qichi; Song, Hongwei; Johnson, Christopher J; Li, Jun; Guo, Hua; Continetti, Robert E

2016-06-28

Probes of the Born-Oppenheimer potential energy surfaces governing polyatomic molecules often rely on spectroscopy for the bound regions or collision experiments in the continuum. A combined spectroscopic and half-collision approach to image nuclear dynamics in a multidimensional and multichannel system is reported here. The Rydberg radical NH4 and the double Rydberg anion NH4 (-) represent a polyatomic system for benchmarking electronic structure and nine-dimensional quantum dynamics calculations. Photodetachment of the H(-)(NH3) ion-dipole complex and the NH4 (-) DRA probes different regions on the neutral NH4 PES. Photoelectron energy and angular distributions at photon energies of 1.17, 1.60, and 2.33 eV compare well with quantum dynamics. Photoelectron-photofragment coincidence experiments indicate dissociation of the nascent NH4 Rydberg radical occurs to H + NH3 with a peak kinetic energy of 0.13 eV, showing the ground state of NH4 to be unstable, decaying by tunneling-induced dissociation on a time scale beyond the present scope of multidimensional quantum dynamics.

Data center thermal management

DOEpatents

Hamann, Hendrik F.; Li, Hongfei

2016-02-09

Historical high-spatial-resolution temperature data and dynamic temperature sensor measurement data may be used to predict temperature. A first formulation may be derived based on the historical high-spatial-resolution temperature data for determining a temperature at any point in 3-dimensional space. The dynamic temperature sensor measurement data may be calibrated based on the historical high-spatial-resolution temperature data at a corresponding historical time. Sensor temperature data at a plurality of sensor locations may be predicted for a future time based on the calibrated dynamic temperature sensor measurement data. A three-dimensional temperature spatial distribution associated with the future time may be generated based on the forecasted sensor temperature data and the first formulation. The three-dimensional temperature spatial distribution associated with the future time may be projected to a two-dimensional temperature distribution, and temperature in the future time for a selected space location may be forecasted dynamically based on said two-dimensional temperature distribution.

An Analysis of the Oil-Whirl Instability

NASA Astrophysics Data System (ADS)

Schultz, William W.; Han, Heng-Chu; Boyd, John P.; Schumack, Mark

1997-11-01

We investigate the hydrodynamic stability of a rotating journal translating inside a stationary bearing. A long (two-dimensional) journal bearing separated by a Newtonian non-cavitating lubricant is studied for shaft stability. Spectral element methods, perturbation methods, and linear stability analyses are used. The influences of fluid inertia, eccentricity, ellipticity, shaft mass, and finite gap on hydrodynamic stability are explored. Lubrication theory using Reynolds equation ignoring fluid inertia leads to erroneous conclusions. Without fluid inertia, the shaft is always unstable. However, the journal is conditionally stable even in the limit Rearrow 0 if fluid inertia is included. Increasing eccentricity helps stabilize a whirling shaft. Non-circular shaft bearings, for example elliptical bearings, are observed to have better dynamic stability.

Complexity analysis of dual-channel game model with different managers' business objectives

NASA Astrophysics Data System (ADS)

Li, Ting; Ma, Junhai

2015-01-01

This paper considers dual-channel game model with bounded rationality, using the theory of bifurcations of dynamical system. The business objectives of retailers are assumed to be different, which is closer to reality than previous studies. We study the local stable region of Nash equilibrium point and find that business objectives can expand the stable region and play an important role in price strategy. One interesting finding is that a fiercer competition tends to stabilize the Nash equilibrium. Simulation shows the complex behavior of two dimensional dynamic system, we find period doubling bifurcation and chaos phenomenon. We measure performances of the model in different period by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of adaptive adjustment mechanism when the model exhibits chaotic behavior and then allows the retailers to eliminate the negative effects.

A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

RECURRENT EXPLOSIVE ERUPTIONS AND THE ''SIGMOID-TO-ARCADE'' TRANSFORMATION IN THE SUN DRIVEN BY DYNAMICAL MAGNETIC FLUX EMERGENCE

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

Archontis, V.; Hood, A. W.; Tsinganos, K., E-mail: va11@st-andrews.ac.uk

2014-05-10

We report on three-dimensional MHD simulations of recurrent mini coronal mass ejection (CME)-like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions develop as a result of the repeated formation and expulsion of new flux ropes due to continuous emergence and reconnection of sheared field lines along the polarity inversion line of the AR. The acceleration of the eruptions is triggered by tether-cutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed bymore » reformation of a sigmoidal structure and a subsequent ''sigmoid-to-flare arcade'' transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies.« less

Quantum demolition filtering and optimal control of unstable systems.

PubMed

Belavkin, V P

2012-11-28

A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

Plasma Instabilities in the Context of Current Helium Sedimentation Models: Dynamical Implications for the ICM in Galaxy Clusters

NASA Astrophysics Data System (ADS)

Berlok, Thomas; Pessah, Martin E.

2015-11-01

Understanding whether Helium can sediment to the core of galaxy clusters is important for a number of problems in cosmology and astrophysics. All current models addressing this question are one-dimensional and do not account for the fact that magnetic fields can effectively channel ions and electrons, leading to anisotropic transport of momentum, heat, and particle diffusion in the weakly collisional intracluster medium (ICM). This anisotropy can lead to a wide variety of instabilities, which could be relevant for understanding the dynamics of heterogeneous media. In this paper, we consider the radial temperature and composition profiles as obtained from a state-of-the-art Helium sedimentation model and analyze its stability properties. We find that the associated radial profiles are unstable to different kinds of instabilities depending on the magnetic field orientation at all radii. The fastest growing modes are usually related to generalizations of the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability which operate in heterogeneous media. We find that the effect of sedimentation is to increase (decrease) the predicted growth rates in the inner (outer) cluster region. The unstable modes grow quickly compared to the sedimentation timescale. This suggests that the composition gradients as inferred from sedimentation models, which do not fully account for the anisotropic character of the weakly collisional environment, might not be very robust. Our results emphasize the subtleties involved in understanding the gas dynamics of the ICM and argue for the need of a comprehensive approach to address the issue of Helium sedimentation beyond current models.

PLASMA INSTABILITIES IN THE CONTEXT OF CURRENT HELIUM SEDIMENTATION MODELS: DYNAMICAL IMPLICATIONS FOR THE ICM IN GALAXY CLUSTERS

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

Berlok, Thomas; Pessah, Martin E., E-mail: berlok@nbi.dk, E-mail: mpessah@nbi.dk

2015-11-01

Understanding whether Helium can sediment to the core of galaxy clusters is important for a number of problems in cosmology and astrophysics. All current models addressing this question are one-dimensional and do not account for the fact that magnetic fields can effectively channel ions and electrons, leading to anisotropic transport of momentum, heat, and particle diffusion in the weakly collisional intracluster medium (ICM). This anisotropy can lead to a wide variety of instabilities, which could be relevant for understanding the dynamics of heterogeneous media. In this paper, we consider the radial temperature and composition profiles as obtained from a state-of-the-artmore » Helium sedimentation model and analyze its stability properties. We find that the associated radial profiles are unstable to different kinds of instabilities depending on the magnetic field orientation at all radii. The fastest growing modes are usually related to generalizations of the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability which operate in heterogeneous media. We find that the effect of sedimentation is to increase (decrease) the predicted growth rates in the inner (outer) cluster region. The unstable modes grow quickly compared to the sedimentation timescale. This suggests that the composition gradients as inferred from sedimentation models, which do not fully account for the anisotropic character of the weakly collisional environment, might not be very robust. Our results emphasize the subtleties involved in understanding the gas dynamics of the ICM and argue for the need of a comprehensive approach to address the issue of Helium sedimentation beyond current models.« less

Passive control of a falling sphere by elliptic-shaped appendages

NASA Astrophysics Data System (ADS)

Lācis, Uǧis; Olivieri, Stefano; Mazzino, Andrea; Bagheri, Shervin

2017-03-01

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies—either surface imperfections or appendages that serve a function—are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, similar to how an inverted pendulum is unstable under gravity. Due to this instability, nontrivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.

Universally Unstable Nature of Velocity Ring Distributions

NASA Astrophysics Data System (ADS)

Mithaiwala, Manish

2010-11-01

Although it is typically believed that an ion ring velocity distribution has a stability threshold, we find that they are universally unstable. This can substantially impact the understanding of dynamics in both laboratory and space plasmas. A high ring density neutralizes the stabilizing effect of ion Landau damping in a warm plasma and the ring is unstable to the generation of waves below the lower hybrid frequency- even for a very high temperature plasma. For ring densities lower than the background plasma density there is a slow instability with growth rate less than the background ion cyclotron frequency and consequently the background ion response is magnetized. This is in addition to the widely discussed fast instability where the wave growth rate exceeds the background ion cyclotron frequency and hence the background ions are effectively unmagnetized. Thus, even a low density ring is unstable to waves around the lower hybrid frequency range for any ring speed. This implies that effectively there is no velocity threshold for a sufficiently cold ring. The importance of these conclusions on the nonlinear evolution of space plasmas, in particular to solar wind-comet interaction, post-magnetospheric storm conditions, and chemical release experiments in the ionosphere will be discussed.

Dynamics of three-tori in a periodically forced navier-stokes flow

PubMed

Lopez; Marques

2000-07-31

Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homoclinic and heteroclinic connections to unstable solutions (two-tori). These unstable two-tori act as organizing centers for the three-tori dynamics. A discrete space-time symmetry influences the dynamics.

Metastability in plyometric training on unstable surfaces: a pilot study

PubMed Central

2014-01-01

Background In the past, plyometric training (PT) has been predominantly performed on stable surfaces. The purpose of this pilot study was to examine effects of a 7-week lower body PT on stable vs. unstable surfaces. This type of exercise condition may be denoted as metastable equilibrium. Methods Thirty-three physically active male sport science students (age: 24.1 ± 3.8 years) were randomly assigned to a PT group (n = 13) exercising on stable (STAB) and a PT group (n = 20) on unstable surfaces (INST). Both groups trained countermovement jumps, drop jumps, and practiced a hurdle jump course. In addition, high bar squats were performed. Physical fitness tests on stable surfaces (hexagonal obstacle test, countermovement jump, hurdle drop jump, left-right hop, dynamic and static balance tests, and leg extension strength) were used to examine the training effects. Results Significant main effects of time (ANOVA) were found for the countermovement jump, hurdle drop jump, hexagonal test, dynamic balance, and leg extension strength. A significant interaction of time and training mode was detected for the countermovement jump in favor of the INST group. No significant improvements were evident for either group in the left-right hop and in the static balance test. Conclusions These results show that lower body PT on unstable surfaces is a safe and efficient way to improve physical performance on stable surfaces. PMID:25089202

The effects of wing flexibility on the flight performance and stability of flapping wing micro air vehicles

NASA Astrophysics Data System (ADS)

Bluman, James Edward

Insect wings are flexible. However, the influence of wing flexibility on the flight dynamics of insects and flapping wing micro air vehicles is unknown. Most studies in the literature consider rigid wings and conclude that the hover equilibrium is unstable. This dissertation shows that a flapping wing flyer with flexible wings exhibits stable natural modes of the open loop system in hover, never reported before. The free-flight insect flight dynamics is modeled for both flexible and rigid wings. Wing mass and inertia are included in the nonlinear equations of motion. The flapping wing aerodynamics are modeled using a quasi-steady model, a well-validated two dimensional Navier Stokes model, and a coupled, two dimensional Navier Stokes - Euler Bernoulli beam model that accurately models the fluid-structure interaction of flexible wings. Hover equilibrium is systematically and efficiently determined with a coupled quasi-steady and Navier-Stokes equation trimmer. The power and stability are reported at hover while parametrically varying the pitch axis location for rigid wings and the structural stiffness for flexible wings. The results indicate that the rigid wings possess an unstable oscillatory mode mainly due to their pitch sensitivity to horizontal velocity perturbations. The flexible wings stabilize this mode primarily by adjusting their wing shape in the presence of perturbations. The wing's response to perturbations generates significantly more horizontal velocity damping and pitch rate damping than in rigid wings. Furthermore, the flexible wings experience substantially less wing wake interaction, which, for rigid wings, is destabilizing. The power required to hover a fruit fly with actively rotating rigid wings varies between 16.9 and 34.2 W/kg. The optimal power occurs when the pitch axis is located at 30% chord, similar to some biological observations. Flexible wings require 23.1 to 38.5 W/kg. However, flexible wings exhibit more stable system dynamics and allow for simpler and lighter designs since they do not require pitch actuation mechanisms. This study is the first to evaluate the impact of wing flexibility on the hovering stability of flapping flyers, which can explain the ranges of flexibility seen in insects and can inform designs of synthetic flapping wing robots.

From globally coupled maps to complex-systems biology

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

Kaneko, Kunihiko, E-mail: kaneko@complex.c.u-tokyo.ac.jp

Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.

Drift Wave Simulation in Toroidal Geometry.

NASA Astrophysics Data System (ADS)

Lebrun, Maurice Joseph, III

1988-12-01

The drift wave, a general category of plasma behavior arising from a plasma inhomogeneity, is studied using the particle simulation method. In slab geometry, the drift wave (or universal mode) is stabilized by any finite amount of magnetic shear. In toroidal geometry, however, the coupling of the poloidal harmonics gives rise to a new branch of drift wave eigenmodes called the toroidicity -induced mode, which is predicted to be unstable in some regimes. The drift wave in a toroidal system is intrinsically three-dimensional, and is sensitive to the handling of the parallel electron dynamics, the (nearly) perpendicular wave dynamics, and the radial variation of magnetic field vector (shear). A simulation study must therefore be kinetic in nature, motivating the extension of particle simulation techniques to complex geometries. From this effort a three dimensional particle code in a toroidal coordinate system has been developed and applied to the toroidal drift wave problem. The code uses an (r,theta,phi) -type coordinate system, and a nonuniform radial grid that increases resolution near the mode-rational surfaces. Full ion dynamics and electron guiding center dynamics are employed. Further, the algorithm incorporates a straightforward limiting process to cylindrical geometry and slab geometry, enabling comparison to the theoretical results in these regimes. Simulations of the density-driven modes in toroidal geometry retain a single toroidal mode number (n = 9). In this regime, the poloidal harmonics are expected to be strongly coupled, giving rise to the marginally unstable toroidicity-induced drift mode. Analysis of the simulation data reveals a strong, low-frequency response that peaks near each mode rational surface. Further, the characteristic oscillation frequencies persist from one mode rational surface to the next, which identifies them as multiple harmonics of the toroidicity-induced mode. The lowest harmonic occurs at a frequency of omega/ omega^{*} ~ 0.26, which is reasonably close to the prediction of linear theory. Interferogram analysis of these modes indicates a "ballooning" structure toward the outside of the torus. The amplitude of the potential is observed to grow exponentially for the m = 8 through m = 10 poloidal mode numbers, with a growth rate of approximately gamma/omega ^{*} ~ 0.075. Saturation occurs at time t ~ 1000 Omega_sp{i}{-1}, and may be caused by quasilinear flattening of the density profile.

The Multi-dimensional Character of Core-collapse Supernovae

DOE PAGES

Hix, W. R.; Lentz, E. J.; Bruenn, S. W.; ...

2016-03-01

Core-collapse supernovae, the culmination of massive stellar evolution, are spectacular astronomical events and the principle actors in the story of our elemental origins. Our understanding of these events, while still incomplete, centers around a neutrino-driven central engine that is highly hydrodynamically unstable. Increasingly sophisticated simulations reveal a shock that stalls for hundreds of milliseconds before reviving. Though brought back to life by neutrino heating, the development of the supernova explosion is inextricably linked to multi-dimensional fluid flows. In this paper, the outcomes of three-dimensional simulations that include sophisticated nuclear physics and spectral neutrino transport are juxtaposed to learn about themore » nature of the three-dimensional fluid flow that shapes the explosion. Comparison is also made between the results of simulations in spherical symmetry from several groups, to give ourselves confidence in the understanding derived from this juxtaposition.« less

Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae

NASA Astrophysics Data System (ADS)

Zingale, M.; Woosley, S. E.; Rendleman, C. A.; Day, M. S.; Bell, J. B.

2005-10-01

Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low-Mach number hydrodynamics method is used, freeing us from the harsh time step restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, 1.5×107 g cm-3, and half-carbon, half-oxygen fuel: conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation and show that while fire polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning regime occurs at higher densities in three dimensions. Detailed turbulence diagnostics are provided. We show that the turbulence follows a Kolmogorov spectrum and is highly anisotropic on the large scales, with a much larger integral scale in the direction of gravity. Furthermore, we demonstrate that it becomes more isotropic as it cascades down to small scales. On the basis of the turbulent statistics and the flame properties of our simulation, we compute the Gibson scale. We show the progress of the turbulent flame through a classic combustion regime diagram, indicating that the flame just enters the distributed burning regime near the end of our simulation.

'Trophic whales' as biotic buffers: weak interactions stabilize ecosystems against nutrient enrichment.

PubMed

Schwarzmüller, Florian; Eisenhauer, Nico; Brose, Ulrich

2015-05-01

Human activities may compromise biodiversity if external stressors such as nutrient enrichment endanger overall network stability by inducing unstable dynamics. However, some ecosystems maintain relatively high diversity levels despite experiencing continuing disturbances. This indicates that some intrinsic properties prevent unstable dynamics and resulting extinctions. Identifying these 'ecosystem buffers' is crucial for our understanding of the stability of ecosystems and an important tool for environmental and conservation biologists. In this vein, weak interactions have been suggested as stabilizing elements of complex systems, but their relevance has rarely been tested experimentally. Here, using network and allometric theory, we present a novel concept for a priori identification of species that buffer against externally induced instability of increased population oscillations via weak interactions. We tested our model in a microcosm experiment using a soil food-web motif. Our results show that large-bodied species feeding at the food web's base, so called 'trophic whales', can buffer ecosystems against unstable dynamics induced by nutrient enrichment. Similar to the functionality of chemical or mechanical buffers, they serve as 'biotic buffers' that take up stressor effects and thus protect fragile systems from instability. We discuss trophic whales as common functional building blocks across ecosystems. Considering increasing stressor effects under anthropogenic global change, conservation of these network-intrinsic biotic buffers may help maintain the stability and diversity of natural ecosystems. © 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society.

Unstable 3D phenomena: Dynamic interactions of a cavitation bubble and Richtmyer-Meshkov unstable divot

NASA Astrophysics Data System (ADS)

Buttler, William; Renner, Dru; Morris, Chris; Manzanares, Ruben; Heidemann, Joel; Kalas, Ryan; Llobet, Anna; Martinez, John; Payton, Jeremy; Saunders, Andy; Schmidt, Derek; Tainter, Amy; Vincent, Samuel; Vogan-McNeil, Wendy

2017-06-01

We radiographically explore a shock-induced Sn cavitation bubble as it interacts with a transverse cavitation wave caused by a Richtmyer-Meshkov unstable spike from a divot. The cavitation bubble forms as two shockwaves collide under the divot, as the shockwaves release to ambient pressure at the surface. The divot inverts and unstably grows, as expected and predicted, but the release waves that form the cavitation bubble reflect from and constrain the cavitation wave growth. As the cavitation wave grows it pierces the cavitation bubble, deflating it onto the unstable transverse cavitation wave.

Numerical analysis of rotating stall instabilities of a pump- turbine in pump mode

NASA Astrophysics Data System (ADS)

Xia, L. S.; Cheng, Y. G.; Zhang, X. X.; Yang, J. D.

2014-03-01

Rotating stall may occur at part load flow of a pump-turbine in pump mode. Unstable flow structures developing under stall condition can lead to a sudden drop of efficiency, high dynamic load and even cavitation. CFD simulations on a pump-turbine model in pump mode were carried out to reveal the onset and developed mechanisms of these unstable flow phenomena at part load. The simulation results of energy-discharge and efficiency characteristics are in good agreement with those obtained by experiments. The more deviate from design conditions with decreasing flow rate, the more flow separations within the vanes. Under specific conditions, four stationary separation zones begin to progress on the circumference, rotating at a fraction of the impeller rotation rate. Rotating stalls lead to the flow in the vane diffuser channels alternating between outward jet flow and blockage. Strong jets impact the spiral casing wall causing high pressure pulsations. Severe separations of the stall cells disturb the flow inducing periodical large amplitude pressure fluctuations, of which the intensity at different span wise of the guide vanes is different. The enforced rotating nonuniform pressure distributions on the circumference lead to dynamic uniform forces on the impeller and guide vanes. The results show that the CFD simulations are capable to gain the complicated flow structure information for analysing the unstable characteristics of the pump mode at part load.

On nodes and modes in resting state fMRI

PubMed Central

Friston, Karl J.; Kahan, Joshua; Razi, Adeel; Stephan, Klaas Enno; Sporns, Olaf

2014-01-01

This paper examines intrinsic brain networks in light of recent developments in the characterisation of resting state fMRI timeseries — and simulations of neuronal fluctuations based upon the connectome. Its particular focus is on patterns or modes of distributed activity that underlie functional connectivity. We first demonstrate that the eigenmodes of functional connectivity – or covariance among regions or nodes – are the same as the eigenmodes of the underlying effective connectivity, provided we limit ourselves to symmetrical connections. This symmetry constraint is motivated by appealing to proximity graphs based upon multidimensional scaling. Crucially, the principal modes of functional connectivity correspond to the dynamically unstable modes of effective connectivity that decay slowly and show long term memory. Technically, these modes have small negative Lyapunov exponents that approach zero from below. Interestingly, the superposition of modes – whose exponents are sampled from a power law distribution – produces classical 1/f (scale free) spectra. We conjecture that the emergence of dynamical instability – that underlies intrinsic brain networks – is inevitable in any system that is separated from external states by a Markov blanket. This conjecture appeals to a free energy formulation of nonequilibrium steady-state dynamics. The common theme that emerges from these theoretical considerations is that endogenous fluctuations are dominated by a small number of dynamically unstable modes. We use this as the basis of a dynamic causal model (DCM) of resting state fluctuations — as measured in terms of their complex cross spectra. In this model, effective connectivity is parameterised in terms of eigenmodes and their Lyapunov exponents — that can also be interpreted as locations in a multidimensional scaling space. Model inversion provides not only estimates of edges or connectivity but also the topography and dimensionality of the underlying scaling space. Here, we focus on conceptual issues with simulated fMRI data and provide an illustrative application using an empirical multi-region timeseries. PMID:24862075

Deterministic annealing for density estimation by multivariate normal mixtures

NASA Astrophysics Data System (ADS)

Kloppenburg, Martin; Tavan, Paul

1997-03-01

An approach to maximum-likelihood density estimation by mixtures of multivariate normal distributions for large high-dimensional data sets is presented. Conventionally that problem is tackled by notoriously unstable expectation-maximization (EM) algorithms. We remove these instabilities by the introduction of soft constraints, enabling deterministic annealing. Our developments are motivated by the proof that algorithmically stable fuzzy clustering methods that are derived from statistical physics analogs are special cases of EM procedures.

Fully nonlinear development of the most unstable goertler vortex in a three dimensional boundary layer

NASA Technical Reports Server (NTRS)

Otto, S. R.; Bassom, Andrew P.

1992-01-01

The nonlinear development is studied of the most unstable Gortler mode within a general 3-D boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui (1991) who demonstrated that the growth rate of this instability is O(G sup 3/5) where G is the Gortler number (taken to be large here), which is effectively a measure of the curvature of the surface. Previous researchers have described the fate of the most unstable mode within a 2-D boundary layer. Denier and Hall (1992) discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall (1991). They demonstrated that crossflow tends to stabilize the most unstable Gortler mode, and for certain crossflow/frequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis; work which is described in a previous article by the present author. Here we extend the ideas of Denier and Hall (1992) to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilized by Denier and Hall (1992). The influence of crossflow and unsteadiness upon the breakdown of the flow is described.

Comparison and analysis of reoperations in two different treatment protocols for trochanteric hip fractures - postoperative technical complications with dynamic hip screw, intramedullary nail and Medoff sliding plate.

PubMed

Paulsson, Johnny; Stig, Josefine Corin; Olsson, Ola

2017-08-24

In treatment of unstable trochanteric fractures dynamic hip screw and Medoff sliding plate devices are designed to allow secondary fracture impaction, whereas intramedullary nails aim to maintain fracture alignment. Different treatment protocols are used by two similar Swedish regional emergency care hospitals. Dynamic hip screw is used for fractures considered as stable within the respective treatment protocol, whereas one treatment protocol (Medoff sliding plate/dynamic hip screw) uses biaxial Medoff sliding plate for unstable pertrochanteric fractures and uniaxial Medoff sliding plate for subtrochanteric fractures, the second (intramedullary nail/dynamic hip screw) uses intramedullary nail for subtrochanteric fractures and for pertrochanteric fractures with intertrochanteric comminution or subtrochanteric extension. All orthopedic surgeries are registered in a regional database. All consecutive trochanteric fracture operations during 2011-2012 (n = 856) and subsequent technical reoperations (n = 40) were derived from the database. Reoperations were analysed and classified into the categories adjustment (percutaneous removal of the locking screw of the Medoff sliding plate or the intramedullary nail, followed by fracture healing) or minor, intermediate (reosteosynthesis) or major (hip joint replacement, Girdlestone or persistent nonunion) technical complications. The relative risk of intermediate or major technical complications was 4.2 (1.2-14) times higher in unstable pertrochanteric fractures and 4.6 (1.1-19) times higher in subtrochanteric fractures with treatment protocol: intramedullary nail/dynamic hip screw, compared to treatment protocol: Medoff sliding plate/dynamic hip screw. Overall rates of intermediate and major technical complications in unstable pertrochanteric and subtrochanteric fractures were with biaxial Medoff sliding plate 0.68%, with uniaxial Medoff sliding plate 1.4%, with dynamic hip screw 3.4% and with intramedullary nail 7.2%. The treatment protocol based on use of biaxial Medoff sliding plate for unstable pertrochanteric and uniaxial Medoff sliding plate for subtrochanteric fractures reduced the risk of severe technical complications compared to using the treatment protocol based on dynamic hip screw and intramedullary nail.

Dynamic stability and handling qualities tests on a highly augmented, statically unstable airplane

NASA Technical Reports Server (NTRS)

Gera, Joseph; Bosworth, John T.

1987-01-01

Novel flight test and analysis techniques in the flight dynamics and handling qualities area are described. These techniques were utilized at NASA Ames-Dryden during the initial flight envelope clearance of the X-29A aircraft. It is shown that the open-loop frequency response of an aircraft with highly relaxed static stability can be successfully computed on the ground from telemetry data. Postflight closed-loop frequency response data were obtained from pilot-generated frequency sweeps and it is found that the current handling quality requirements for high-maneuverability aircraft are generally applicable to the X-29A.

Lattice dynamics and elasticity for ε-plutonium [First-principles lattice dynamics for ε-plutonium

DOE PAGES

Söderlind, Per

2017-04-25

Here, lattice dynamics and elasticity for the high-temperature ε phase (body-centered cubic; bcc) of plutonium is predicted utilizing first-principles electronic structure coupled with a self-consistent phonon method that takes phonon-phonon interaction and strong anharmonicity into account. These predictions establish the first sensible lattice-dynamics and elasticity data on ε-Pu. The atomic forces required for the phonon scheme are highly accurate and derived from the total energies obtained from relativistic and parameter-free density-functional theory. The results appear reasonable but no data exist to compare with except those from dynamical mean-field theory that suggest ε-plutonium is mechanically unstable. Fundamental knowledge and understanding ofmore » the high-temperature bcc phase, that is generally present in all actinide metals before melting, is critically important for a proper interpretation of the phase diagram as well as practical modeling of high-temperature properties.« less

Three-dimensional relativistic jet simulations and the morphological classification of radio-loud AGN

NASA Astrophysics Data System (ADS)

Schuh, Terance; Li, Yutong; Elghossain, Geena; Wiita, Paul J.

2018-06-01

We have computed a suite of simulations of propagating three-dimensional relativistic jets, involving substantial ranges of initial jet Lorentz factors and ratios of jet density to external medium density. These allow us to categorize the respective AGN into Fanaroff-Riley class I (jet dominated) and FR class II (lobe-dominated) based upon the stability and morphology of the simulations. We used the Athena code to produce a substantial collection of large 3D variations of jets, many of which propagate stably and quickly for over 100 jet radii, but others of which eventually go unstable and fill up slowing advancing lobes. Most of these simulations have jet-to-ambient medium densities between 0.005 and 0.5 and velocities between 0.90c and 0.995c. Comparing the times when some jets go unstable to these initial parameters allow us to find a threshold where radio-loud AGNs transition from class II to class I. With these high resolution fully 3D relativistic simulations we can represent the jets more accurately and thus improve upon and refine earlier results that were based on 2D simulations.

Stability of imploding shocks generated by underwater electrical explosion of cylindrical wire array

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

Kozlov, M.; Gurovich, V. Tz.; Krasik, Ya. E.

2013-11-15

The results of two-dimensional hydrodynamic simulations of the dynamics and stability of azimuthal non-uniformities in converging shock waves generated by an underwater explosion of a cylindrical wire array and their effect on the cumulation of energy in the vicinity of the converging axis are presented. It has been shown that in spite of the fact that such non-uniformities are always weakly unstable, for a broad range of experimentally relevant regimes these non-uniformities remain small and do not significantly affect the cumulation of energy. Only the non-uniformities with wavelengths comparable to the distance from the axis of convergence exhibit substantial growthmore » that considerably attenuates the energy cumulation.« less

Gravitational-wave emission from rotating gravitational collapse in three dimensions.

PubMed

Baiotti, L; Hawke, I; Rezzolla, L; Schnetter, E

2005-04-08

We present the first three-dimensional (3D) calculations of the gravitational-wave emission in the collapse of uniformly rotating stars to black holes. The initial models are polytropes which are dynamically unstable and near the mass-shedding limit. The waveforms have been extracted using a gauge-invariant approach and reflect the properties of both the initial stellar models and of newly produced black holes, being in good qualitative agreement with those computed in previous 2D simulations. The wave amplitudes, however, are about 1 order of magnitude smaller, giving, for a source at 10 kpc, a signal-to-noise ratio S/N approximately 0.25 for LIGO-VIRGO and S/N less than or approximately equal 4 for LIGO II.

The Stability of Radiatively Cooling Jets I. Linear Analysis

NASA Technical Reports Server (NTRS)

Hardee, Philip E.; Stone, James M.

1997-01-01

The results of a spatial stability analysis of a two-dimensional slab jet, in which optically thin radiative cooling is dynamically important, are presented. We study both magnetized and unmagnetized jets at external Mach numbers of 5 and 20. We model the cooling rate by using two different cooling curves: one appropriate to interstellar gas, and the other to photoionized gas of reduced metallicity. Thus, our results will be applicable to both protostellar (Herbig-Haro) jets and optical jets from active galactic nuclei. We present analytical solutions to the dispersion relations in useful limits and solve the dispersion relations numerically over a broad range of perturbation frequencies. We find that the growth rates and wavelengths of the unstable Kelvin-Helmholtz (K-H) modes are significantly different from the adiabatic limit, and that the form of the cooling function strongly affects the results. In particular, if the cooling curve is a steep function of temperature in the neighborhood of the equilibrium state, then the growth of K-H modes is reduced relative to the adiabatic jet. On the other hand, if the cooling curve is a shallow function of temperature, then the growth of K-H modes can be enhanced relative to the adiabatic jet by the increase in cooling relative to heating in overdense regions. Inclusion of a dynamically important magnetic field does not strongly modify the important differences between an adiabatic jet and a cooling jet, provided the jet is highly supermagnetosonic and not magnetic pressure-dominated. In the latter case, the unstable modes behave more like the transmagnetosonic magnetic pressure-dominated adiabatic limit. We also plot fluid displacement surfaces associated with the various waves in a cooling jet in order to predict the structures that might arise in the nonlinear regime. This analysis predicts that low-frequency surface waves and the lowest order body modes will be the most effective at producing observable features in the jet.

A delay differential model of ENSO variability: parametric instability and the distribution of extremes

NASA Astrophysics Data System (ADS)

Zaliapin, I.; Ghil, M.; Thompson, S.

2007-12-01

We consider a Delay Differential Equation (DDE) model for El-Nino Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in the ENSO dynamics: delayed negative feedback and seasonal forcing. Descriptive and metric stability analyses of the model are performed in a complete 3D space of its physically relevant parameters. Existence of two regimes --- stable and unstable --- is reported. The domains of the regimes are separated by a sharp neutral curve in the parameter space. The detailed structure of the neutral curve become very complicated (possibly fractal), and individual trajectories within the unstable region become highly complex (possibly chaotic) as the atmosphere-ocean coupling increases. In the unstable regime, spontaneous transitions in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values occur, for purely periodic, seasonal forcing. This indicates (via the continuous dependence theorem) the existence of numerous unstable solutions responsible for the complex dynamics of the system. In the stable regime, only periodic solutions are found. Our results illustrate the role of the distinct parameters of ENSO variability, such as strength of seasonal forcing vs. atmosphere ocean coupling and propagation period of oceanic waves across the Tropical Pacific. The model reproduces, among other phenomena, the Devil's bleachers (caused by period locking) documented in other ENSO models, such as nonlinear PDEs and GCMs, as well as in certain observations. We expect such behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.

From Large-scale to Protostellar Disk Fragmentation into Close Binary Stars

NASA Astrophysics Data System (ADS)

Sigalotti, Leonardo Di G.; Cruz, Fidel; Gabbasov, Ruslan; Klapp, Jaime; Ramírez-Velasquez, José

2018-04-01

Recent observations of young stellar systems with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array are helping to cement the idea that close companion stars form via fragmentation of a gravitationally unstable disk around a protostar early in the star formation process. As the disk grows in mass, it eventually becomes gravitationally unstable and fragments, forming one or more new protostars in orbit with the first at mean separations of 100 au or even less. Here, we report direct numerical calculations down to scales as small as ∼0.1 au, using a consistent Smoothed Particle Hydrodynamics code, that show the large-scale fragmentation of a cloud core into two protostars accompanied by small-scale fragmentation of their circumstellar disks. Our results demonstrate the two dominant mechanisms of star formation, where the disk forming around a protostar (which in turn results from the large-scale fragmentation of the cloud core) undergoes eccentric (m = 1) fragmentation to produce a close binary. We generate two-dimensional emission maps and simulated ALMA 1.3 mm continuum images of the structure and fragmentation of the disks that can help explain the dynamical processes occurring within collapsing cloud cores.

Excito-oscillatory dynamics as a mechanism of ventricular fibrillation.

PubMed

Gray, Richard A; Huelsing, Delilah J

2008-04-01

The instabilities associated with reentrant spiral waves are of paramount importance to the initiation and maintenance of tachyarrhythmias, especially ventricular fibrillation (VF). In addition to tissue heterogeneities, there are only a few basic purported mechanisms of spiral wave breakup, most notably restitution. We test the hypothesis that oscillatory membrane properties act to destabilize spiral waves. We recorded transmembrane potential (V(m)) from isolated rabbit myocytes using a constant current stimulation protocol. We developed a mathematical model that included both the stable excitable equilibrium point at resting V(m) (-80 mV) and the unstable oscillatory equilibrium point at elevated V(m) (-10 mV). Spiral wave dynamics were studied in 2-dimensional grids using variants of the model. All models showed restitution and reproduced the experimental values of transmembrane resistance at rest and during the action potential plateau. Stable spiral waves were observed when the model showed only 1 equilibrium point. However, spatio-temporal complexity was observed if the model showed both excitable and oscillatory equilibrium points (i.e., excito-oscillatory models). The initial wave breaks resulted from oscillatory waves expanding in all directions; after a few beats, the patterns were characterized by a combination of unstable spiral waves and target patterns consistent with the patterns observed on the heart surface during VF. In our model, this VF-like activity only occurred when the single cell period of V(m) oscillations was within a specific range. The VF-like patterns observed in our excito-oscillatory models could not be explained by the existing proposed instability mechanisms. Our results introduce the important suggestion that membrane dynamics responsible for V(m) oscillations at elevated V(m) levels can destabilize spiral waves and thus may be a novel therapeutic target for preventing VF.

One- and two-dimensional gap solitons and dynamics in the PT-symmetric lattice potential and spatially-periodic momentum modulation

NASA Astrophysics Data System (ADS)

Chen, Yong; Yan, Zhenya; Li, Xin

2018-02-01

The influence of spatially-periodic momentum modulation on beam dynamics in parity-time (PT) symmetric optical lattice is systematically investigated in the one- and two-dimensional nonlinear Schrödinger equations. In the linear regime, we demonstrate that the momentum modulation can alter the first and second PT thresholds of the classical lattice, periodically or regularly change the shapes of the band structure, rotate and split the diffraction patterns of beams leading to multiple refraction and emissions. In the Kerr-nonlinear regime for one-dimension (1D) case, a large family of fundamental solitons within the semi-infinite gap can be found to be stable, even beyond the second PT threshold; it is shown that the momentum modulation can shrink the existing range of fundamental solitons and not change their stability. For two-dimension (2D) case, most solitons with higher intensities are relatively unstable in their existing regions which are narrower than those in 1D case, but we also find stable fundamental solitons corroborated by linear stability analysis and direct beam propagation. More importantly, the momentum modulation can also utterly change the direction of the transverse power flow and control the energy exchange among gain or loss regions.

A minimization principle for the description of modes associated with finite-time instabilities

PubMed Central

Babaee, H.

2016-01-01

We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have finite lifetime, they can play a crucial role either by altering the system dynamics through the activation of other instabilities or by creating sudden nonlinear energy transfers that lead to extreme responses. However, their essentially transient character makes their description a particularly challenging task. We develop a minimization framework that focuses on the optimal approximation of the system dynamics in the neighbourhood of the system state. This minimization formulation results in differential equations that evolve a time-dependent basis so that it optimally approximates the most unstable directions. We demonstrate the capability of the method for two families of problems: (i) linear systems, including the advection–diffusion operator in a strongly non-normal regime as well as the Orr–Sommerfeld/Squire operator, and (ii) nonlinear problems, including a low-dimensional system with transient instabilities and the vertical jet in cross-flow. We demonstrate that the time-dependent subspace captures the strongly transient non-normal energy growth (in the short-time regime), while for longer times the modes capture the expected asymptotic behaviour. PMID:27118900

Harnessing the relativistic Buneman instability for laser-ion acceleration in the transparency regime

NASA Astrophysics Data System (ADS)

Stark, D. J.; Yin, L.; Albright, B. J.

2018-06-01

We examine the relativistic Buneman instability in systems relevant to high-intensity laser-plasma interactions under conditions of relativistically-induced transparency, as this instability can generate large-amplitude electrostatic waves at low frequencies that are pertinent to ion dynamics in these systems. Ion flows are shown to significantly alter the range of unstable wave numbers and to increase the phase velocities of the unstable modes; we particularly highlight the relativistic effects from both the ion and electron (with transverse motion) populations. These findings are related to the mode structure seen in particle-in-cell simulation results of a short-pulse laser breaking through an initially opaque target with the onset of relativistic transparency. Additionally, driving mechanisms from free energy present in density and velocity gradients are shown to be capable of significantly enhancing the growth rates, and these instabilities furthermore extend the breadth of the unstable wave number range. Lastly, we discuss how the transverse self-generated magnetic fields characteristic of short-pulse interactions can potentially constrain the unstable wave numbers in a non-trivial manner.

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

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

Choi, Youngsoo; Carlberg, Kevin Thomas

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over allmore » space and time in a weighted ℓ 2-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.« less

Dynamical Cognitive Models of Social Issues in Russia

NASA Astrophysics Data System (ADS)

Mitina, Olga; Abraham, Fred; Petrenko, Victor

We examine and model dynamics in three areas of social cognition: (1) political transformations within Russia, (2) evaluation of political trends in other countries by Russians, and (3) evaluation of Russian stereotypes concerning women. We try to represent consciousness as vectorfields and trajectories in a cognitive state space. We use psychosemantic techniques that allow definition of the state space and the systematic construction of these vectorfields and trajectories and their portrait from research data. Then we construct models to fit them, using multiple regression methods to obtain linear differential equations. These dynamical models of social cognition fit the data quite well. (1) The political transformations were modeled by a spiral repellor in a two-dimensional space of a democratic-totalitarian factor and social depression-optimism factor. (2) The evaluation of alien political trends included a flow away from a saddle toward more stable and moderate political regimes in a 2D space, of democratic-totalitarian and unstable-stable cognitive dimensions. (3) The gender study showed expectations (attractors) for more liberated, emancipated roles for women in the future.

The Modelling of Axially Translating Flexible Beams

NASA Astrophysics Data System (ADS)

Theodore, R. J.; Arakeri, J. H.; Ghosal, A.

1996-04-01

The axially translating flexible beam with a prismatic joint can be modelled by using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, a non-dimensional form of the Euler Bernoulli beam equation is presented, obtained by using the concept of group velocity, and also the conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions leads to a time-dependent frequency equation for the translating flexible beam. A novel method is presented for solving this time dependent frequency equation by using a differential form of the frequency equation. The assume mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. It is shown by using Lyapunov's first method that the dynamic responses of flexural modal variables become unstable during retraction of the flexible beam, which the dynamic response during extension of the beam is stable. Numerical simulation results are presented for the uniform axial motion induced transverse vibration for a typical flexible beam.

On the influence of the local maxima of total pressure on the current sheet stability to the kink-like (flapping) mode

NASA Astrophysics Data System (ADS)

Korovinskiy, D. B.; Erkaev, N. V.; Semenov, V. S.; Ivanov, I. B.; Kiehas, S. A.; Ryzhkov, I. I.

2018-02-01

The stability of the Fadeev-like current sheet with respect to transversally propagating kink-like perturbations (flapping mode) is considered in terms of two-dimensional linear magnetohydrodynamic numerical simulations. It is found that the current sheet is stable when the total pressure minimum is located in the sheet center and unstable when the maximum value is reached there. It is shown that an unstable spot of any size enforces the whole sheet to be unstable, though the increment of instability decreases with the reduction of the unstable domain. In unstable sheets, the dispersion curve of instability shows a good match with the double-gradient (DG) model prediction. Here, the typical growth rate (short-wavelength limit) is close to the DG estimate averaged over the unstable region. In stable configurations, the typical frequency matches the maximum DG estimate. The dispersion curve of oscillations demonstrates a local maximum at wavelength ˜0.7 sheet half-width, which is a new feature that is absent in simplified analytical solutions.

Indirect Identification of Linear Stochastic Systems with Known Feedback Dynamics

NASA Technical Reports Server (NTRS)

Huang, Jen-Kuang; Hsiao, Min-Hung; Cox, David E.

1996-01-01

An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.

Control of unstable interfaces through ballistic induced alloying: Monte Carlo and molecular dynamics calculations

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

Gomez, Liliana; Slutzky, Claudia; Ferron, Julio

2005-06-15

The explosive features of highly cohesive materials growing over soft metal substrates can be suppressed, and layer by layer growth achieved, by controlling a slight alloying at the interface. By means of Monte Carlo and molecular dynamic simulations, applied to the Co/Cu(111) system, we have proved the stability reached by Co growing over an alloyed CoCu surface, and the factibility of using hyperthermal ions to tailor this alloying.

Analysis of high-rise constructions with the using of three-dimensional models of rods in the finite element program PRINS

NASA Astrophysics Data System (ADS)

Agapov, Vladimir

2018-03-01

The necessity of new approaches to the modeling of rods in the analysis of high-rise constructions is justified. The possibility of the application of the three-dimensional superelements of rods with rectangular cross section for the static and dynamic calculation of the bar and combined structures is considered. The results of the eighteen-story spatial frame free vibrations analysis using both one-dimensional and three-dimensional models of rods are presented. A comparative analysis of the obtained results is carried out and the conclusions on the possibility of three-dimensional superelements application in static and dynamic analysis of high-rise constructions are given on its basis.

Stability of Bose-Einstein condensates in a Kronig-Penney potential

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

Danshita, Ippei; Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555; Tsuchiya, Shunji

2007-03-15

We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused bymore » the excitations with small q and the dynamical instability is caused by the excitations with q={pi}/a at their onsets, where q is the quasimomentum of excitation and a is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.« less

Turbulence and the Stabilization Principle

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Imaging a multidimensional multichannel potential energy surface: Photodetachment of H{sup −}(NH{sub 3}) and NH{sub 4}{sup −}

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

Hu, Qichi; Johnson, Christopher J.; Continetti, Robert E., E-mail: hguo@umn.edu, E-mail: rcontinetti@ucsd.edu

2016-06-28

Probes of the Born-Oppenheimer potential energy surfaces governing polyatomic molecules often rely on spectroscopy for the bound regions or collision experiments in the continuum. A combined spectroscopic and half-collision approach to image nuclear dynamics in a multidimensional and multichannel system is reported here. The Rydberg radical NH{sub 4} and the double Rydberg anion NH{sub 4}{sup −} represent a polyatomic system for benchmarking electronic structure and nine-dimensional quantum dynamics calculations. Photodetachment of the H{sup −}(NH{sub 3}) ion-dipole complex and the NH{sub 4}{sup −} DRA probes different regions on the neutral NH{sub 4} PES. Photoelectron energy and angular distributions at photon energiesmore » of 1.17, 1.60, and 2.33 eV compare well with quantum dynamics. Photoelectron-photofragment coincidence experiments indicate dissociation of the nascent NH{sub 4} Rydberg radical occurs to H + NH{sub 3} with a peak kinetic energy of 0.13 eV, showing the ground state of NH{sub 4} to be unstable, decaying by tunneling-induced dissociation on a time scale beyond the present scope of multidimensional quantum dynamics.« less

Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses

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

Mortazavi, M.; Urzay, J., E-mail: jurzay@stanford.edu; Mani, A.

2015-06-15

This study addresses the optical performance of a plasma adaptive lens for aero-optical applications by using both axisymmetric and three-dimensional numerical simulations. Plasma adaptive lenses are based on the effects of free electrons on the phase velocity of incident light, which, in theory, can be used as a phase-conjugation mechanism. A closed cylindrical chamber filled with Argon plasma is used as a model lens into which a beam of light is launched. The plasma is sustained by applying a radio-frequency electric current through a coil that envelops the chamber. Four different operating conditions, ranging from low to high powers andmore » induction frequencies, are employed in the simulations. The numerical simulations reveal complex hydrodynamic phenomena related to buoyant and electromagnetic laminar transport, which generate, respectively, large recirculating cells and wall-normal compression stresses in the form of local stagnation-point flows. In the axisymmetric simulations, the plasma motion is coupled with near-wall axial striations in the electron-density field, some of which propagate in the form of low-frequency traveling disturbances adjacent to vortical quadrupoles that are reminiscent of Taylor-Görtler flow structures in centrifugally unstable flows. Although the refractive-index fields obtained from axisymmetric simulations lead to smooth beam wavefronts, they are found to be unstable to azimuthal disturbances in three of the four three-dimensional cases considered. The azimuthal striations are optically detrimental, since they produce high-order angular aberrations that account for most of the beam wavefront error. A fourth case is computed at high input power and high induction frequency, which displays the best optical properties among all the three-dimensional simulations considered. In particular, the increase in induction frequency prevents local thermalization and leads to an axisymmetric distribution of electrons even after introduction of spatial disturbances. The results highlight the importance of accounting for spatial effects in the numerical computations when optical analyses of plasma lenses are pursued in this range of operating conditions.« less

Hysteresis in the trade cycle

NASA Astrophysics Data System (ADS)

Mc Namara, Hugh A.; Pokrovskii, Alexei V.

2006-02-01

The Kaldor model-one of the first nonlinear models of macroeconomics-is modified to incorporate a Preisach nonlinearity. The new dynamical system thus created shows highly complicated behaviour. This paper presents a rigorous (computer aided) proof of chaos in this new model, and of the existence of unstable periodic orbits of all minimal periods p>57.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

NASA Astrophysics Data System (ADS)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

Safety assurance of non-deterministic flight controllers in aircraft applications

NASA Astrophysics Data System (ADS)

Noriega, Alfonso

Loss of control is a serious problem in aviation that primarily affects General Aviation. Technological advancements can help mitigate the problem, but the FAA certification process makes certain solutions economically unfeasible. This investigation presents the design of a generic adaptive autopilot that could potentially lead to a single certification for use in several makes and models of aircraft. The autopilot consists of a conventional controller connected in series with a robust direct adaptive model reference controller. In this architecture, the conventional controller is tuned once to provide outer-loop guidance and navigation to a reference model. The adaptive controller makes unknown aircraft behave like the reference model, allowing the conventional controller to successfully provide navigation without the need for retuning. A strong theoretical foundation is presented as an argument for the safety and stability of the controller. The stability proof of direct adaptive controllers require that the plant being controlled has no unstable transmission zeros and has a nonzero high frequency gain. Because most conventional aircraft do not readily meet these requirements, a process known as sensor blending was used. Sensor blending consists of using a linear combination of the plant's outputs that has no unstable transmission zeros and has a nonzero high frequency gain to drive the adaptive controller. Although this method does not present a problem for regulators, it can lead to a steady state error in tracking applications. The sensor blending theory was expanded to take advantage of the system's dynamics to allow for zero steady state error tracking. This method does not need knowledge of the specific system's dynamics, but instead uses the structure of the A and B matrices to perform the blending for the general case. The generic adaptive autopilot was tested in two high-fidelity nonlinear simulators of two typical General Aviation aircraft. The results show that the autopilot was able to adapt appropriately to the different aircraft and was able to perform three-dimensional navigation and an ILS approach, without any modification to the controller. The autopilot was tested in moderate atmospheric turbulence, using consumer-grade sensors and actuators currently available in General Aviation aircraft. The generic adaptive autopilot was shown to be robust to atmospheric turbulence and sensor and actuator random noise. In both aircraft simulators, the autopilot adapted successfully to changes in airspeed, altitude, and configuration. This investigation proves the feasibility of a generic autopilot using direct adaptive controller. The autopilot does not need a priori information of the specific aircraft's dynamics to maintain its safety and stability arguments. Real-time parameter estimation of the aircraft dynamics are not needed. Recommendations for future work are provided.

Entrenched time delays versus accelerating opinion dynamics: are advanced democracies inherently unstable?

NASA Astrophysics Data System (ADS)

Gros, Claudius

2017-11-01

Modern societies face the challenge that the time scale of opinion formation is continuously accelerating in contrast to the time scale of political decision making. With the latter remaining of the order of the election cycle we examine here the case that the political state of a society is determined by the continuously evolving values of the electorate. Given this assumption we show that the time lags inherent in the election cycle will inevitable lead to political instabilities for advanced democracies characterized both by an accelerating pace of opinion dynamics and by high sensibilities (political correctness) to deviations from mainstream values. Our result is based on the observation that dynamical systems become generically unstable whenever time delays become comparable to the time it takes to adapt to the steady state. The time needed to recover from external shocks grows in addition dramatically close to the transition. Our estimates for the order of magnitude of the involved time scales indicate that socio-political instabilities may develop once the aggregate time scale for the evolution of the political values of the electorate falls below 7-15 months.

Origin of Slope Failure in the Ursa Region, Northern Gulf of Mexico

NASA Astrophysics Data System (ADS)

Stigall, J.; Dugan, B.

2008-12-01

We use one-dimensional fluid flow and stability models to predict the evolution of overpressure and stability conditions of IODP Expedition Sites U1322 and U1324 in the Ursa region, northern Gulf of Mexico. Simulations of homogenous mud deposited at 3 and 12 mm/yr for Sites U1322 and U1324, with permeability (k) on the order of 10-17m2 and bulk compressibility of .4 /MPa, predict overpressures up to .45MPa and 1MPa in shallow sediments (<200m below sea floor). With limit equilibrium calculations for an infinite slope, these overpressures equate to a factor of safety (FS) greater than 10 and 4.5 for a internal friction angle of 26° and a seafloor slope of 2°. This implies stability throughout the last 50,000 years. Seismic and core observations, however, document major slope failures that span the entire Ursa region. Permeability in this region is well constrained by laboratory experiments, so we investigate how pulsed (high-to-low) sedimentation rates could have created unstable conditions, FS <1. Models with periods of high sedimentation generate overpressure that create unstable conditions while maintaining the time-averaged sedimentation rates. Other factors which are not possible to simulate in one dimension, such as a complex basin geometry, also influence the conditions that caused the past failures. A two-dimensional model linking lateral flow between the sites with the interpreted geometry from seismic stratigraphy gives a better picture of the flow field and instability within the basin. Asymmetrical loading of permeable sediments could have created a lateral difference in pore pressures which would have driven lateral flow from Site U1324 to Site U1322 where overpressures are higher than our one-dimensional models suggest. We anticipate that two-dimensional models with transient sedimentation patterns will enhance our understanding of flow in marginally stable environments and triggers of slope failures in passive margin systems.

Control of viscous fingering by nanoparticles

NASA Astrophysics Data System (ADS)

Sabet, Nasser; Hassanzadeh, Hassan; Abedi, Jalal

2017-12-01

A substantial viscosity increase by the addition of a low dose of nanoparticles to the base fluids can well influence the dynamics of viscous fingering. There is a lack of detailed theoretical studies that address the effect of the presence of nanoparticles on unstable miscible displacements. In this study, the impact of nonreactive nanoparticle presence on the stability and subsequent mixing of an originally unstable binary system is examined using linear stability analysis (LSA) and pseudospectral-based direct numerical simulations (DNS). We have parametrized the role of both nondepositing and depositing nanoparticles on the stability of miscible displacements using the developed static and dynamic parametric analyses. Our results show that nanoparticles have the potential to weaken the instabilities of an originally unstable system. Our LSA and DNS results also reveal that nondepositing nanoparticles can be used to fully stabilize an originally unstable front while depositing particles may act as temporary stabilizers whose influence diminishes in the course of time. In addition, we explain the existing inconsistencies concerning the effect of the nanoparticle diffusion coefficient on the dynamics of the system. This study provides a basis for further research on the application of nanoparticles for control of viscosity-driven instabilities.

Configurational entropy as a tool to select a physical thick brane model

NASA Astrophysics Data System (ADS)

Chinaglia, M.; Cruz, W. T.; Correa, R. A. C.; de Paula, W.; Moraes, P. H. R. S.

2018-04-01

We analize braneworld scenarios via a configurational entropy (CE) formalism. Braneworld scenarios have drawn attention mainly due to the fact that they can explain the hierarchy problem and unify the fundamental forces through a symmetry breaking procedure. Those scenarios localize matter in a (3 + 1) hypersurface, the brane, which is inserted in a higher dimensional space, the bulk. Novel analytical braneworld models, in which the warp factor depends on a free parameter n, were recently released in the literature. In this article we will provide a way to constrain this parameter through the relation between information and dynamics of a system described by the CE. We demonstrate that in some cases the CE is an important tool in order to provide the most probable physical system among all the possibilities. In addition, we show that the highest CE is correlated to a tachyonic sector of the configuration, where the solutions for the corresponding model are dynamically unstable.

Periodicity and Chaos Amidst Twisting and Folding in Two-Dimensional Maps

NASA Astrophysics Data System (ADS)

Garst, Swier; Sterk, Alef E.

We study the dynamics of three planar, noninvertible maps which rotate and fold the plane. Two maps are inspired by real-world applications whereas the third map is constructed to serve as a toy model for the other two maps. The dynamics of the three maps are remarkably similar. A stable fixed point bifurcates through a Hopf-Neĭmark-Sacker which leads to a countably infinite set of resonance tongues in the parameter plane of the map. Within a resonance tongue a periodic point can bifurcate through a period-doubling cascade. At the end of the cascade we detect Hénon-like attractors which are conjectured to be the closure of the unstable manifold of a saddle periodic point. These attractors have a folded structure which can be explained by means of the concept of critical lines. We also detect snap-back repellers which can either coexist with Hénon-like attractors or which can be formed when the saddle-point of a Hénon-like attractor becomes a source.

Three-dimensional benchmark for variable-density flow and transport simulation: matching semi-analytic stability modes for steady unstable convection in an inclined porous box

USGS Publications Warehouse

Voss, Clifford I.; Simmons, Craig T.; Robinson, Neville I.

2010-01-01

This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.

Dynamic stability and handling qualities tests on a highly augmented, statically unstable airplane

NASA Technical Reports Server (NTRS)

Gera, Joseph; Bosworth, John T.

1987-01-01

This paper describes some novel flight tests and analysis techniques in the flight dynamics and handling qualities area. These techniques were utilized during the initial flight envelope clearance of the X-29A aircraft and were largely responsible for the completion of the flight controls clearance program without any incidents or significant delays. The resulting open-loop and closed-loop frequency responses and the time history comparison using flight and linear simulation data are discussed.

Flutter, Postflutter, and Control of a Supersonic Wing Section

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2002-01-01

A number of issues related to the flutter and postflutter of two-dimensional supersonic lifting surfaces are addressed. Among them there are the 1) investigation of the implications of the nonlinear unsteady aerodynamics and structural nonlinearities on the stable/unstable character of the limit cycle and 2) study of the implications of the incorporation of a control capability on both the flutter boundary and the postflutter behavior. To this end, a powerful methodology based on the Lyapunov first quantity is implemented. Such a treatment of the problem enables one to get a better understanding of the various factors involved in the nonlinear aeroelastic problem, including the stable and unstable limit cycle. In addition, it constitutes a first step toward a more general investigation of nonlinear aeroelastic phenomena of three-dimensional lifting surfaces.

High spatial resolution three-dimensional mapping of vegetation spectral dynamics using computer vision

Treesearch

Jonathan P. Dandois; Erle C. Ellis

2013-01-01

High spatial resolution three-dimensional (3D) measurements of vegetation by remote sensing are advancing ecological research and environmental management. However, substantial economic and logistical costs limit this application, especially for observing phenological dynamics in ecosystem structure and spectral traits. Here we demonstrate a new aerial remote sensing...

The engine of microtubule dynamics comes into focus.

PubMed

Mitchison, T J

2014-05-22

In this issue, Alushin et al. report high-resolution structures of three states of the microtubule lattice: GTP-bound, which is stable to depolymerization; unstable GDP-bound; and stable Taxol and GDP-bound. By comparing these structures at near-atomic resolution, they are able to propose a detailed model for how GTP hydrolysis destabilizes the microtubule and thus powers dynamic instability and chromosome movement. Destabilization of cytoskeleton filaments by nucleotide hydrolysis is an important general principle in cell dynamics, and this work represents a major step forward on a problem with a long history. Copyright © 2014 Elsevier Inc. All rights reserved.

Appearance of Unstable Monopoly State Caused by Selective and Concentrative Mergers in Business Networks.

PubMed

Goto, Hayato; Viegas, Eduardo; Jensen, Henrik Jeldtoft; Takayasu, Hideki; Takayasu, Misako

2017-07-11

Recently, growth mechanism of firms in complex business networks became new targets of scientific study owing to increasing availability of high quality business firms' data. Here, we paid attention to comprehensive data of M&A events for 40 years and derived empirical laws by applying methods and concepts of aggregation dynamics of aerosol physics. It is found that the probability of merger between bigger firms is bigger than that between smaller ones, and such tendency is enhancing year by year. We introduced a numerical model simulating the whole ecosystem of firms and showed that the system is already in an unstable monopoly state in which growth of middle sized firms are suppressed.

Hawking radiation and propagation of massive charged scalar field on a three-dimensional Gödel black hole

NASA Astrophysics Data System (ADS)

González, P. A.; Övgün, Ali; Saavedra, Joel; Vásquez, Yerko

2018-06-01

In this paper we consider the three-dimensional Gödel black hole as a background and we study the vector particle tunneling from this background in order to obtain the Hawking temperature. Then, we study the propagation of a massive charged scalar field and we find the quasinormal modes analytically, which turns out be unstable as a consequence of the existence of closed time-like curves. Also, we consider the flux at the horizon and at infinity, and we compute the reflection and transmission coefficients as well as the absorption cross section. Mainly, we show that massive charged scalar waves can be superradiantly amplified by the three-dimensional Gödel black hole and that the coefficients have an oscillatory behavior. Moreover, the absorption cross section is null at the high frequency limit and for certain values of the frequency.

Conjugated organic framework with three-dimensionally ordered stable structure and delocalized π clouds

NASA Astrophysics Data System (ADS)

Guo, Jia; Xu, Yanhong; Jin, Shangbin; Chen, Long; Kaji, Toshihiko; Honsho, Yoshihito; Addicoat, Matthew A.; Kim, Jangbae; Saeki, Akinori; Ihee, Hyotcherl; Seki, Shu; Irle, Stephan; Hiramoto, Masahiro; Gao, Jia; Jiang, Donglin

2013-11-01

Covalent organic frameworks are a class of crystalline organic porous materials that can utilize π-π-stacking interactions as a driving force for the crystallization of polygonal sheets to form layered frameworks and ordered pores. However, typical examples are chemically unstable and lack intrasheet π-conjugation, thereby significantly limiting their applications. Here we report a chemically stable, electronically conjugated organic framework with topologically designed wire frameworks and open nanochannels, in which the π conjugation-spans the two-dimensional sheets. Our framework permits inborn periodic ordering of conjugated chains in all three dimensions and exhibits a striking combination of properties: chemical stability, extended π-delocalization, ability to host guest molecules and hole mobility. We show that the π-conjugated organic framework is useful for high on-off ratio photoswitches and photovoltaic cells. Therefore, this strategy may constitute a step towards realizing ordered semiconducting porous materials for innovations based on two-dimensionally extended π systems.

Flare particle acceleration in the interaction of twisted coronal flux ropes

NASA Astrophysics Data System (ADS)

Threlfall, J.; Hood, A. W.; Browning, P. K.

2018-03-01

Aim. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods: We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results: The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.

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.

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1988-01-01

The goal of the research is a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity were defined. The research performed during the second year fall into four areas: sensitivity studies involving Model 1; evaluation of Model 2; reformation of Model 1 for greater compatibility with Model 2; development of Model 3 (radiative transfer equation); and making the model more responsive to the observations.

Studies of human dynamic space orientation using techniques of control theory

NASA Technical Reports Server (NTRS)

Young, L. R.

1974-01-01

Studies of human orientation and manual control in high order systems are summarized. Data cover techniques for measuring and altering orientation perception, role of non-visual motion sensors, particularly the vestibular and tactile sensors, use of motion cues in closed loop control of simple stable and unstable systems, and advanced computer controlled display systems.

Coevolutionary dynamics of rice blast resistance gene Pi-ta and Magnaporthe oryzae avirulence gene AVR-Pita 1

USDA-ARS?s Scientific Manuscript database

The Pi-ta gene in rice is effective in preventing infections by Magnaporthe oryzae strains that contain the corresponding avirulence gene, AVR-Pita1. Genome sequencing and mapping studies demonstrated that AVR-Pita1 is highly unstable, and diverse haplotypes of AVR-Pita1 have been identified from is...

Survival, Growth, and Ecosystem Dynamics of Displaced Bromeliads in a Montane Tropical Forest.

Treesearch

Jennifer Pett-Ridge; Whendee L. Silver

2002-01-01

Epiphytes generally occupy arboreal perches, which are inherently unstable environments due to periodic windstorms, branch falls, and treefalls. During high wind events, arboreal bromeliads are often knocked from the canopy and deposited on the forest floor. In this study, we used a common epiphytic tank bromeliad, Guzmania berteroniana (R. & S.) Mez, to determine...

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

Approximating high-dimensional dynamics by barycentric coordinates with linear programming

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

Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics ofmore » the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.« less

Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

PubMed

Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

2015-01-01

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

Weighted Distance Functions Improve Analysis of High-Dimensional Data: Application to Molecular Dynamics Simulations.

PubMed

Blöchliger, Nicolas; Caflisch, Amedeo; Vitalis, Andreas

2015-11-10

Data mining techniques depend strongly on how the data are represented and how distance between samples is measured. High-dimensional data often contain a large number of irrelevant dimensions (features) for a given query. These features act as noise and obfuscate relevant information. Unsupervised approaches to mine such data require distance measures that can account for feature relevance. Molecular dynamics simulations produce high-dimensional data sets describing molecules observed in time. Here, we propose to globally or locally weight simulation features based on effective rates. This emphasizes, in a data-driven manner, slow degrees of freedom that often report on the metastable states sampled by the molecular system. We couple this idea to several unsupervised learning protocols. Our approach unmasks slow side chain dynamics within the native state of a miniprotein and reveals additional metastable conformations of a protein. The approach can be combined with most algorithms for clustering or dimensionality reduction.

Supporting Dynamic Quantization for High-Dimensional Data Analytics.

PubMed

Guzun, Gheorghi; Canahuate, Guadalupe

2017-05-01

Similarity searches are at the heart of exploratory data analysis tasks. Distance metrics are typically used to characterize the similarity between data objects represented as feature vectors. However, when the dimensionality of the data increases and the number of features is large, traditional distance metrics fail to distinguish between the closest and furthest data points. Localized distance functions have been proposed as an alternative to traditional distance metrics. These functions only consider dimensions close to query to compute the distance/similarity. Furthermore, in order to enable interactive explorations of high-dimensional data, indexing support for ad-hoc queries is needed. In this work we set up to investigate whether bit-sliced indices can be used for exploratory analytics such as similarity searches and data clustering for high-dimensional big-data. We also propose a novel dynamic quantization called Query dependent Equi-Depth (QED) quantization and show its effectiveness on characterizing high-dimensional similarity. When applying QED we observe improvements in kNN classification accuracy over traditional distance functions. Gheorghi Guzun and Guadalupe Canahuate. 2017. Supporting Dynamic Quantization for High-Dimensional Data Analytics. In Proceedings of Ex-ploreDB'17, Chicago, IL, USA, May 14-19, 2017, 6 pages. https://doi.org/http://dx.doi.org/10.1145/3077331.3077336.

Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

DOE PAGES

Carretero-González, R.; Kevrekidis, P. G.; Kolokolnikov, T.

2016-03-01

In this work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μ of the system, increasing proportionally to μ 2/3. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We showmore » how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetry-breaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. We conclude that these results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.« less

Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

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

Warne, Larry Kevin; Jorgenson, Roy Eberhardt

This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through themore » electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank« less

Compound Poisson Law for Hitting Times to Periodic Orbits in Two-Dimensional Hyperbolic Systems

NASA Astrophysics Data System (ADS)

Carney, Meagan; Nicol, Matthew; Zhang, Hong-Kun

2017-11-01

We show that a compound Poisson distribution holds for scaled exceedances of observables φ uniquely maximized at a periodic point ζ in a variety of two-dimensional hyperbolic dynamical systems with singularities (M,T,μ ), including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form φ (z)=-ln d(z,ζ ) where d is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a Pólya-Aeppli distibution of index θ . We calculate θ in terms of the derivative of the map T. Furthermore if we define M_n=\\max {φ ,\\ldots ,φ circ T^n} and u_n (τ ) by \\lim _{n→ ∞} nμ (φ >u_n (τ ) )=τ the maximal process satisfies an extreme value law of form μ (M_n ≤ u_n)=e^{-θ τ }. These results generalize to a broader class of functions maximized at ζ , though the formulas regarding the parameters in the distribution need to be modified.

Sliding-Mode Control Applied for Robust Control of a Highly Unstable Aircraft

NASA Technical Reports Server (NTRS)

Vetter, Travis Kenneth

2002-01-01

An investigation into the application of an observer based sliding mode controller for robust control of a highly unstable aircraft and methods of compensating for actuator dynamics is performed. After a brief overview of some reconfigurable controllers, sliding mode control (SMC) is selected because of its invariance properties and lack of need for parameter identification. SMC is reviewed and issues with parasitic dynamics, which cause system instability, are addressed. Utilizing sliding manifold boundary layers, the nonlinear control is converted to a linear control and sliding manifold design is performed in the frequency domain. An additional feedback form of model reference hedging is employed which is similar to a prefilter and has large benefits to system performance. The effects of inclusion of actuator dynamics into the designed plant is heavily investigated. Multiple Simulink models of the full longitudinal dynamics and wing deflection modes of the forward swept aero elastic vehicle (FSAV) are constructed. Additionally a linear state space models to analyze effects from various system parameters. The FSAV has a pole at +7 rad/sec and is non-minimum phase. The use of 'model actuators' in the feedback path, and varying there design, is heavily investigated for the resulting effects on plant robustness and tolerance to actuator failure. The use of redundant actuators is also explored and improved robustness is shown. All models are simulated with severe failure and excellent tracking, and task dependent handling qualities, and low pilot induced oscillation tendency is shown.

Closed-loop control of a fragile network: application to seizure-like dynamics of an epilepsy model

PubMed Central

Ehrens, Daniel; Sritharan, Duluxan; Sarma, Sridevi V.

2015-01-01

It has recently been proposed that the epileptic cortex is fragile in the sense that seizures manifest through small perturbations in the synaptic connections that render the entire cortical network unstable. Closed-loop therapy could therefore entail detecting when the network goes unstable, and then stimulating with an exogenous current to stabilize the network. In this study, a non-linear stochastic model of a neuronal network was used to simulate both seizure and non-seizure activity. In particular, synaptic weights between neurons were chosen such that the network's fixed point is stable during non-seizure periods, and a subset of these connections (the most fragile) were perturbed to make the same fixed point unstable to model seizure events; and, the model randomly transitions between these two modes. The goal of this study was to measure spike train observations from this epileptic network and then apply a feedback controller that (i) detects when the network goes unstable, and then (ii) applies a state-feedback gain control input to the network to stabilize it. The stability detector is based on a 2-state (stable, unstable) hidden Markov model (HMM) of the network, and detects the transition from the stable mode to the unstable mode from using the firing rate of the most fragile node in the network (which is the output of the HMM). When the unstable mode is detected, a state-feedback gain is applied to generate a control input to the fragile node bringing the network back to the stable mode. Finally, when the network is detected as stable again, the feedback control input is switched off. High performance was achieved for the stability detector, and feedback control suppressed seizures within 2 s after onset. PMID:25784851

Large N phase transitions and the fate of small Schwarzschild-AdS black holes

NASA Astrophysics Data System (ADS)

Yaffe, Laurence G.

2018-01-01

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS5×S5 spacetime are known to become dynamically unstable toward deformation of the internal S5 geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-N Yang-Mills theory on R ×S3. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large-N limit in the dual field theory and typical large volume thermodynamic limits.

Numerical modeling of consolidation processes in hydraulically deposited soils

NASA Astrophysics Data System (ADS)

Brink, Nicholas Robert

Hydraulically deposited soils are encountered in many common engineering applications including mine tailing and geotextile tube fills, though the consolidation process for such soils is highly nonlinear and requires the use of advanced numerical techniques to provide accurate predictions. Several commercially available finite element codes poses the ability to model soil consolidation, and it was the goal of this research to assess the ability of two of these codes, ABAQUS and PLAXIS, to model the large-strain, two-dimensional consolidation processes which occur in hydraulically deposited soils. A series of one- and two-dimensionally drained rectangular models were first created to assess the limitations of ABAQUS and PLAXIS when modeling consolidation of highly compressible soils. Then, geotextile tube and TSF models were created to represent actual scenarios which might be encountered in engineering practice. Several limitations were discovered, including the existence of a minimum preconsolidation stress below which numerical solutions become unstable.

Investigating Long-Range Dependence in American Treasury Bills Variations and Volatilities during Stable and Unstable Periods

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2016-05-01

Detrended fluctuation analysis (DFA) is used to examine long-range dependence in variations and volatilities of American treasury bills (TB) during periods of low and high movements in TB rates. Volatility series are estimated by generalized autoregressive conditional heteroskedasticity (GARCH) model under Gaussian, Student, and the generalized error distribution (GED) assumptions. The DFA-based Hurst exponents from 3-month, 6-month, and 1-year TB data indicates that in general the dynamics of the TB variations process is characterized by persistence during stable time period (before 2008 international financial crisis) and anti-persistence during unstable time period (post-2008 international financial crisis). For volatility series, it is found that; for stable period; 3-month volatility process is more likely random, 6-month volatility process is anti-persistent, and 1-year volatility process is persistent. For unstable period, estimation results show that the generating process is persistent for all maturities and for all distributional assumptions.

Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux

NASA Astrophysics Data System (ADS)

Balasuriya, Sanjeeva

2016-12-01

State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses destroy the smooth invariant manifolds, necessitating new definitions for stable and unstable pseudo-manifolds. Their time-evolution is characterised by solving a Volterra integral equation of the second kind with discontinuous inhomogeniety. A criteria for heteroclinic trajectory persistence in this impulsive context is developed, as is a quantification of an instantaneous flux across broken heteroclinic manifolds. Several examples, including a kicked Duffing oscillator and an underwater explosion in the vicinity of an eddy, are used to illustrate the theory.

Modeling and simulation of combustion chamber and propellant dynamics and issues in active control of combustion instabilities

NASA Astrophysics Data System (ADS)

Isella, Giorgio Carlo

A method for a comprehensive approach to analysis of the dynamics of an actively controlled combustion chamber, with detailed analysis of the combustion models for the case of a solid rocket propellant, is presented here. The objective is to model the system as interconnected blocks describing the dynamics of the chamber, combustion and control. The analytical framework for the analysis of the dynamics of a combustion chamber is based on spatial averaging, as introduced by Culick. Combustion dynamics are analyzed for the case of a solid propellant. Quasi-steady theory is extended to include the dynamics of the gas-phase and also of a surface layer. The models are constructed so that they produce a combustion response function for the solid propellant that can be immediately introduced in the our analytical framework. The principal objective mechanisms responsible for the large sensitivity, observed experimentally, of propellant response to small variations. We show that velocity coupling, and not pressure coupling, has the potential to be the mechanism responsible for that high sensitivity. We also discuss the effect of particulate modeling on the global dynamics of the chamber and revisit the interpretation of the intrinsic stability limit for burning of solid propellants. Active control is also considered. Particular attention is devoted to the effect of time delay (between sensing and actuation); several methods to compensate for it are discussed, with numerical examples based on the approximate analysis produced by our framework. Experimental results are presented for the case of a Dump Combustor. The combustor exhibits an unstable burning mode, defined through the measurement of the pressure trace and shadowgraph imaging. The transition between stable and unstable modes of operation is characterized by the presence of hysteresis, also observed in other experimental works, and hence not a special characteristic of this combustor. Control is introduced in the form of pulsed secondary fuel. We show the capability of forcing the transition from unstable to stable burning, hence extending the stable operating regime of the combustor. The transition, characterized by the use of a shadowgraph movie sequence, is attributed to a combined fluid-mechanic and combustion mechanism.

Superradiant instability of near extremal and extremal four-dimensional charged hairy black holes in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

González, P. A.; Papantonopoulos, Eleftherios; Saavedra, Joel; Vásquez, Yerko

2017-03-01

We study the instability of near extremal and extremal four-dimensional anti-de Sitter charged hairy black holes to radial neutral massive and charged massless scalar field perturbations. We solve the scalar field equation by using the improved asymptotic iteration method and the time domain analysis, and we find the quasinormal frequencies. For the charged scalar perturbations, we find the superradiance condition by computing the reflection coefficient in the low-frequency limit, and we show that in the superradiance regime, which depends on the scalar hair charge, all modes of radial charged massless perturbations are unstable, indicating that the charged hairy black hole is superradiantly unstable. On the other hand, calculating the quasinormal frequencies of radial neutral scalar perturbations in this background, we find stability of the charged hairy black hole.

Small aspect ratio Taylor-Couette flow: onset of a very-low-frequency three-torus state.

PubMed

Lopez, Juan M; Marques, Francisco

2003-09-01

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is SO(2)xZ2. In this paper, we systematically investigate primary and subsequent bifurcations of the basic state, concentrating on a parameter regime where the basic state becomes unstable via Hopf bifurcations. We derive the four distinct cases for the symmetries of the bifurcated orbit, and numerically find two of these. In the parameter regime considered, we also locate the codimension-two double Hopf bifurcation where these two Hopf bifurcations coincide. Secondary Hopf bifurcations (Neimark-Sacker bifurcations), leading to modulated rotating waves, are subsequently found and a saddle-node-infinite-period bifurcation between a stable (node) and an unstable (saddle) modulated rotating wave is located, which gives rise to a very-low-frequency three-torus. This paper provides the computed example of such a state, along with a comprehensive bifurcation sequence leading to its onset.

Kinetic study of radiation-reaction-limited particle acceleration during the relaxation of unstable force-free equilibria

DOE PAGES

Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; ...

2016-09-07

Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focusmore » on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The "flares" are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. As a result, higher magnetization studies are promising and will be carried out in the future.« less

KINETIC STUDY OF RADIATION-REACTION-LIMITED PARTICLE ACCELERATION DURING THE RELAXATION OF UNSTABLE FORCE-FREE EQUILIBRIA

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

Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan

2016-09-10

Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focusmore » on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The “flares” are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. Higher magnetization studies are promising and will be carried out in the future.« less

Study of the X-Ray Diagnosis of Unstable Pelvic Fracture Displacements in Three-Dimensional Space and its Application in Closed Reduction.

PubMed

Shi, Chengdi; Cai, Leyi; Hu, Wei; Sun, Junying

2017-09-19

ABSTRACTS Objective: To study the method of X-ray diagnosis of unstable pelvic fractures displaced in three-dimensional (3D) space and its clinical application in closed reduction. Five models of hemipelvic displacement were made in an adult pelvic specimen. Anteroposterior radiographs of the pelvis were analyzed in PACS. The method of X-ray diagnosis was applied in closed reductions. From February 2012 to June 2016, 23 patients (15 men, 8 women; mean age, 43.4 years) with unstable pelvic fractures were included. All patients were treated by closed reduction and percutaneous cannulate screw fixation of the pelvic ring. According to Tile's classification, the patients were classified into type B1 in 7 cases, B2 in 3, B3 in 3, C1 in 5, C2 in 3, and C3 in 2. The operation time and intraoperative blood loss were recorded. Postoperative images were evaluated by Matta radiographic standards. Five models of displacement were made successfully. The X-ray features of the models were analyzed. For clinical patients, the average operation time was 44.8 min (range, 20-90 min) and the average intraoperative blood loss was 35.7 (range, 20-100) mL. According to the Matta standards, 7 cases were excellent, 12 cases were good, and 4 were fair. The displacements in 3D space of unstable pelvic fractures can be diagnosed rapidly by X-ray analysis to guide closed reduction, with a satisfactory clinical outcome.

Non-linear Evolution of Velocity Ring Distributions: Generation of Whistler Waves

NASA Astrophysics Data System (ADS)

Mithaiwala, M.; Rudakov, L.; Ganguli, G.

2010-12-01

Although it is typically believed that an ion ring velocity distribution has a stability threshold, we find that they are universally unstable. This can substantially impact the understanding of dynamics in both laboratory and space plasmas. A high ring density neutralizes the stabilizing effect of ion Landau damping in a warm plasma and the ring is unstable to the generation of waves below the lower hybrid frequency- even for a very high temperature plasma. For ring densities lower than the background plasma density there is a slow instability with growth rate less than the background ion cyclotron frequency and consequently the background ion response is magnetized. This is in addition to the widely discussed fast instability where the wave growth rate exceeds the background ion cyclotron frequency and hence the background ions are effectively unmagnetized. Thus, even a low density ring is unstable to waves around the lower hybrid frequency range for any ring speed. This implies that effectively there is no velocity threshold for a sufficiently cold ring. The importance of these conclusions on the nonlinear evolution of space plasmas, in particular to solar wind-comet interaction, post-magnetospheric storm conditions, and chemical release experiments in the ionosphere will be discussed.

Landscape sensitivity in a dynamic environment

NASA Astrophysics Data System (ADS)

Lin, Jiun-Chuan; Jen, Chia-Horn

2010-05-01

Landscape sensitivity at different scales and topics is presented in this study. Methodological approach composed most of this paper. According to the environmental records in the south eastern Asia, the environment change is highly related with five factors, such as scale of influence area, background of environment characters, magnitude and frequency of events, thresholds of occurring hazards and influence by time factor. This paper tries to demonstrate above five points from historical and present data. It is found that landscape sensitivity is highly related to the degree of vulnerability of the land and the processes which put on the ground including human activities. The scale of sensitivity and evaluation of sensitivities is demonstrated in this paper by the data around east Asia. The methods of classification are mainly from the analysis of environmental data and the records of hazards. From the trend of rainfall records, rainfall intensity and change of temperature, the magnitude and frequency of earthquake, dust storm, days of draught, number of hazards, there are many coincidence on these factors with landscape sensitivities. In conclusion, the landscape sensitivities could be classified as four groups: physical stable, physical unstable, unstable, extremely unstable. This paper explain the difference.

Nature of the octahedral tilting phase transitions in perovskites: A case study of CaMnO3

NASA Astrophysics Data System (ADS)

Klarbring, Johan; Simak, Sergei I.

2018-01-01

The temperature-induced antiferrodistortive (AFD) structural phase transitions in CaMnO3, a typical perovskite oxide, are studied using first-principles density functional theory calculations. These transitions are caused by tilting of the MnO6 octahedra that are related to unstable phonon modes in the high-symmetry cubic perovskite phase. Transitions due to octahedral tilting in perovskites normally are believed to fit into the standard soft-mode picture of displacive phase transitions. We calculate phonon-dispersion relations and potential-energy landscapes as functions of the unstable phonon modes and argue based on the results that the phase transitions are better described as being of order-disorder type. This means that the cubic phase emerges as a dynamical average when the system hops between local minima on the potential-energy surface. We then perform ab initio molecular dynamics simulations and find explicit evidence of the order-disorder dynamics in the system. Our conclusions are expected to be valid for other perovskite oxides, and we finally suggest how to predict the nature (displacive or order-disorder) of the AFD phase transitions in any perovskite system.

Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.

PubMed

Xue, Hongqi; Wu, Shuang; Wu, Yichao; Ramirez Idarraga, Juan C; Wu, Hulin

2018-05-02

Mechanism-driven low-dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low-dimensional mechanism-based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large-scale nonlinear networks from time-course gene expression data remains an unresolved issue. Here, we use high-dimensional nonlinear additive ODEs to model GRNs and propose a 4-step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2-stage smoothing-based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non-polynomial dimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae. Copyright © 2018 John Wiley & Sons, Ltd.

A Burst Mode, Ultrahigh Temperature UF4 Vapor Core Reactor Rankine Cycle Space Power System Concept

NASA Technical Reports Server (NTRS)

Dugan, E. T.; Kahook, S. D.; Diaz, N. J.

1996-01-01

Static and dynamic neutronic analyses have been performed on an innovative burst mode (100's of MW output for a few thousand seconds) Ulvahigh Temperature Vapor Core Reactor (UTVR) space nuclear power system. The NVTR employs multiple, neutronically-coupled fissioning cores and operates on a direct, closed Rankine cycle using a disk Magnetohydrodynamic (MHD) generater for energy conversion. The UTVR includes two types of fissioning core regions: (1) the central Ultrahigh Temperature Vapor Core (UTVC) which contains a vapor mixture of highly enriched UF4 fuel and a metal fluoride working fluid and (2) the UF4 boiler column cores located in the BeO moderator/reflector region. The gaseous nature of the fuel the fact that the fuel is circulating, the multiple coupled fissioning cores, and the use of a two phase fissioning fuel lead to unique static and dynamic neutronic characteristics. Static neutronic analysis was conducted using two-dimensional S sub n, transport theory calculations and three-dimensional Monte Carlo transport theory calculations. Circulating-fuel, coupled-core point reactor kinetics equations were used for analyzing the dynamic behavior of the UTVR. In addition to including reactivity feedback phenomena associated with the individual fissioning cores, the effects of core-to-core neutronic and mass flow coupling between the UTVC and the surrounding boiler cores were also included in the dynamic model The dynamic analysis of the UTVR reveals the existence of some very effectlve inherent reactivity feedback effects that are capable of quickly stabilizing this system, within a few seconds, even when large positive reactivity insertions are imposed. If the UTVC vapor fuel density feedback is suppressed, the UTVR is still inherently stable because of the boiler core liquid-fuel volume feedback; in contrast, suppression of the vapor fuel density feedback in 'conventional" gas core cavity reactors causes them to become inherently unstable. Due to the strength of the negative reactivity feedback in the UTVR, it is found that external reactivity insertions alone are inadequate for bringing about significant power level changes during normal reactor operations. Additional methods of reactivity control such as variations in the gaseous fuel mass flow rate, are needed to achieve the desired power level oontrol.

Dynamical model of binary asteroid systems through patched three-body problems

NASA Astrophysics Data System (ADS)

Ferrari, Fabio; Lavagna, Michèle; Howell, Kathleen C.

2016-08-01

The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.

Dynamic stability of stacked disk type flywheels

NASA Astrophysics Data System (ADS)

Younger, F. C.

1981-04-01

A flywheel assembly formed from adhesively bonded stacked fiber composite disks was analyzed. The stiffness and rigidity of the assembly required to prevent uncontrolled growth in the deformations due to centrifugal force was determined. It is shown that stacked disk type flywheels become unstable when the speed exceeds a critical value. This critical value of speed depends upon the stiffness of the bonded attachments between the disks. It is found that elastomeric bonds do not provide adequate stiffness to insure dynamic stability for high speed stacked disk type flywheels.

Robust adaptive cruise control of high speed trains.

PubMed

Faieghi, Mohammadreza; Jalali, Aliakbar; Mashhadi, Seyed Kamal-e-ddin Mousavi

2014-03-01

The cruise control problem of high speed trains in the presence of unknown parameters and external disturbances is considered. In particular a Lyapunov-based robust adaptive controller is presented to achieve asymptotic tracking and disturbance rejection. The system under consideration is nonlinear, MIMO and non-minimum phase. To deal with the limitations arising from the unstable zero-dynamics we do an output redefinition such that the zero-dynamics with respect to new outputs becomes stable. Rigorous stability analyses are presented which establish the boundedness of all the internal states and simultaneously asymptotic stability of the tracking error dynamics. The results are presented for two common configurations of high speed trains, i.e. the DD and PPD designs, based on the multi-body model and are verified by several numerical simulations. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Designing for Damage: Robust Flight Control Design using Sliding Mode Techniques

NASA Technical Reports Server (NTRS)

Vetter, T. K.; Wells, S. R.; Hess, Ronald A.; Bacon, Barton (Technical Monitor); Davidson, John (Technical Monitor)

2002-01-01

A brief review of sliding model control is undertaken, with particular emphasis upon the effects of neglected parasitic dynamics. Sliding model control design is interpreted in the frequency domain. The inclusion of asymptotic observers and control 'hedging' is shown to reduce the effects of neglected parasitic dynamics. An investigation into the application of observer-based sliding mode control to the robust longitudinal control of a highly unstable is described. The sliding mode controller is shown to exhibit stability and performance robustness superior to that of a classical loop-shaped design when significant changes in vehicle and actuator dynamics are employed to model airframe damage.

Investigations of quantum pendulum dynamics in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We investigate the quantum spin dynamics of a spin-1 BEC initialized to an unstable critical point of the dynamical phase space. The subsequent evolution of the collective states of the system is analogous to an inverted simple pendulum in the quantum limit and yields non-classical states with quantum correlations. For short evolution times in the low depletion limit, we observe squeezed states and for longer times beyond the low depletion limit we observe highly non-Gaussian distributions. C.D. Hamley, C.S. Gerving, T.M. Hoang, E.M. Bookjans, and M.S. Chapman, ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Linking Dynamics of the Near-surface Flow to Deeper Boundary Layer Forcing in the Nocturnal Boundary Layer

DTIC Science & Technology

2012-06-01

Kaimal and Finnigan (1994), modified) Figure 2.2 illustrates the evolution from unstable CBL to a nocturnal Stable Bound- ary Layer ( SBL ) in the absence...mixed layer acts as a cap for the SBL . The SBL persists through the night until sunrise when surface heating resumes and a new unstable layer begins...to form at the surface, gradually returning to a CBL. 7 2.2.1 Dynamics of the stable boundary layer Because the SBL is stably stratified, buoyancy

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

NASA Astrophysics Data System (ADS)

Molokov, Sergei; El, Gennady; Lukyanov, Alexander

2011-10-01

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele's modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele's modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

Malaria control under unstable dynamics: reactive vs. climate-based strategies.

PubMed

Baeza, Andres; Bouma, Menno J; Dhiman, Ramesh; Pascual, Mercedes

2014-01-01

In areas of the world where malaria prevails under unstable conditions, attacking the adult vector population through insecticide-based Indoor Residual Spraying (IRS) is the most common method for controlling epidemics. Defined in policy guidance, the use of Annual Parasitic Incidence (API) is an important tool for assessing the effectiveness of control and for planning new interventions. To investigate the consequences that a policy based on API in previous seasons might have on the population dynamics of the disease and on control itself in regions of low and seasonal transmission, we formulate a mathematical malaria model that couples epidemiologic and vector dynamics with IRS intervention. This model is parameterized for a low transmission and semi-arid region in northwest India, where epidemics are driven by high rainfall variability. We show that this type of feedback mechanism in control strategies can generate transient cycles in malaria even in the absence of environmental variability, and that this tendency to cycle can in turn limit the effectiveness of control in the presence of such variability. Specifically, for realistic rainfall conditions and over a range of control intensities, the effectiveness of such 'reactive' intervention is compared to that of an alternative strategy based on rainfall and therefore vector variability. Results show that the efficacy of intervention is strongly influenced by rainfall variability and the type of policy implemented. In particular, under an API 'reactive' policy, high vector populations can coincide more frequently with low control coverage, and in so doing generate large unexpected epidemics and decrease the likelihood of elimination. These results highlight the importance of incorporating information on climate variability, rather than previous incidence, in planning IRS interventions in regions of unstable malaria. These findings are discussed in the more general context of elimination and other low transmission regions such as highlands. Copyright © 2013. Published by Elsevier B.V.

Development of Turbulent Magnetic Reconnection in a Magnetic Island

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

Huang, Can; Lu, Quanming; Wang, Rongsheng

In this paper, with two-dimensional particle-in-cell simulations, we report that the electron Kelvin–Helmholtz instability is unstable in the current layer associated with a large-scale magnetic island, which is formed in multiple X-line guide field reconnections. The current sheet is fragmented into many small current sheets with widths down to the order of the electron inertial length. Secondary magnetic reconnection then occurs in these fragmented current sheets, which leads to a turbulent state. The electrons are highly energized in such a process.

Effects of ankle strengthening exercise program on an unstable supporting surface on proprioception and balance in adults with functional ankle instability.

PubMed

Ha, Sun-Young; Han, Jun-Ho; Sung, Yun-Hee

2018-04-01

The present study was conducted to investigate the effect of ankle strengthening exercise applied on unstable supporting surfaces on the proprioceptive sense and balance in adults with functional ankle instability. As for the study method, 30 adults with functional ankle instability were randomly assigned to an ankle strengthening exercise group and a stretching group on unstable supporting surfaces, and the interventions were implemented for 40 min. Before and after the interventions, a digital dual inclinometer was used to measure the proprioceptive sense of the ankle, the Balancia program was used to measure static balance ability, and the functional reach test was used to measure dynamic balance ability. In the results, both proprioceptive sense and static dynamic balance ability were significantly different between before and after the intervention in the experimental group ( P <0.05). When such results are put together, it can be seen that ankle strengthening exercise applied on unstable supporting surfaces may be presented as an effective treatment method for enhancing the proprioceptive sense and balance ability in adults with functional ankle instability.

High-frame-rate full-vocal-tract 3D dynamic speech imaging.

PubMed

Fu, Maojing; Barlaz, Marissa S; Holtrop, Joseph L; Perry, Jamie L; Kuehn, David P; Shosted, Ryan K; Liang, Zhi-Pei; Sutton, Bradley P

2017-04-01

To achieve high temporal frame rate, high spatial resolution and full-vocal-tract coverage for three-dimensional dynamic speech MRI by using low-rank modeling and sparse sampling. Three-dimensional dynamic speech MRI is enabled by integrating a novel data acquisition strategy and an image reconstruction method with the partial separability model: (a) a self-navigated sparse sampling strategy that accelerates data acquisition by collecting high-nominal-frame-rate cone navigator sand imaging data within a single repetition time, and (b) are construction method that recovers high-quality speech dynamics from sparse (k,t)-space data by enforcing joint low-rank and spatiotemporal total variation constraints. The proposed method has been evaluated through in vivo experiments. A nominal temporal frame rate of 166 frames per second (defined based on a repetition time of 5.99 ms) was achieved for an imaging volume covering the entire vocal tract with a spatial resolution of 2.2 × 2.2 × 5.0 mm 3 . Practical utility of the proposed method was demonstrated via both validation experiments and a phonetics investigation. Three-dimensional dynamic speech imaging is possible with full-vocal-tract coverage, high spatial resolution and high nominal frame rate to provide dynamic speech data useful for phonetic studies. Magn Reson Med 77:1619-1629, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Characterization of quantum vortex dynamics in superfluid helium

NASA Astrophysics Data System (ADS)

Meichle, David P.

Liquid helium obtains superfluid properties when cooled below the Lambda transition temperature of 2.17 K. A superfluid, which is a partial Bose Einstein condensate, has many exotic properties including free flow without friction, and ballistic instead of diffusive heat transport. A superfluid is also uniquely characterized by the presence of quantized vortices, dynamical line-like topological phase defects around which all circulation in the flow is constrained. Two vortices can undergo a violent process called reconnection when they approach, cross, and retract having exchanged tails. With a numerical examination of a local, linearized solution near reconnection we discovered a dynamically unstable stationary solution to the Gross-Pitaevskii equation, which was relaxed to a fully non-linear solution using imaginary time propagation. This investigation explored vortex reconnection in the context of the changing topology of the order parameter, a complex field governing the superfluid dynamics at zero temperature. The dynamics of the vortices can be studied experimentally by dispersing tracer particles into a superfluid flow and recording their motions with movie cameras. The pioneering work of Bewley et al. provided the first visualization technique using frozen gases to create tracer particles. Using this technique, we experimentally observed for the first time the excitation of helical traveling waves on a vortex core called Kelvin waves. Kelvin waves are thought to be a central mechanism for dissipation in this inviscid fluid, as they provide an efficient cascade mechanism for transferring energy from large to microscopic length scales. We examined the Kelvin waves in detail, and compared their dynamics in fully self-similar non-dimensional coordinates to theoretical predictions. Additionally, two experimental advances are presented. A newly invented technique for reliably dispersing robust, nanometer-scale fluorescent tracer particles directly into the superfluid is described. A detailed numerical investigation of the particle-vortex interactions provides novel calculations of the force trapping particles on vortices, and a scaling was found suggesting that smaller particles may remain bound to the vortices at much higher speeds than larger particles. Lastly, a new stereographic imaging system has been developed, allowing for the world-first three-dimensional reconstruction of individual particles and vortex filament trajectories. Preliminary data, including the first three-dimensional observation of a vortex reconnection are presented.

Capital, population and urban patterns.

PubMed

Zhang, W

1994-04-01

The author develops an approach to urban dynamics with endogenous capital and population growth, synthesizing the Alonso location model, the two-sector neoclassical growth model, and endogenous population theory. A dynamic model for an isolated island economy with endogenous capital, population, and residential structure is developed on the basis of Alonso's residential model and the two-sector neoclassical growth model. The model describes the interdependence between residential structure, economic growth, population growth, and economic structure over time and space. It has a unique long-run equilibrium, which may be either stable or unstable, depending upon the population dynamics. Applying the Hopf theorem, the author also shows that when the system is unstable, the economic geography exhibits permanent endogenous oscillations.

Kinetic simulations and reduced modeling of longitudinal sideband instabilities in non-linear electron plasma waves

DOE PAGES

Brunner, S.; Berger, R. L.; Cohen, B. I.; ...

2014-10-01

Kinetic Vlasov simulations of one-dimensional finite amplitude Electron Plasma Waves are performed in a multi-wavelength long system. A systematic study of the most unstable linear sideband mode, in particular its growth rate γ and quasi- wavenumber δk, is carried out by scanning the amplitude and wavenumber of the initial wave. Simulation results are successfully compared against numerical and analytical solutions to the reduced model by Kruer et al. [Phys. Rev. Lett. 23, 838 (1969)] for the Trapped Particle Instability (TPI). A model recently suggested by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)], which in addition to the TPImore » accounts for the so-called Negative Mass Instability because of a more detailed representation of the trapped particle dynamics, is also studied and compared with simulations.« less

Visual exploration of high-dimensional data through subspace analysis and dynamic projections

DOE PAGES

Liu, S.; Wang, B.; Thiagarajan, J. J.; ...

2015-06-01

Here, we introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that createmore » smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Visual Exploration of High-Dimensional Data through Subspace Analysis and Dynamic Projections

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

Liu, S.; Wang, B.; Thiagarajan, Jayaraman J.

2015-06-01

We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smoothmore » animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Design and Implementation of High-Performance GIS Dynamic Objects Rendering Engine

NASA Astrophysics Data System (ADS)

Zhong, Y.; Wang, S.; Li, R.; Yun, W.; Song, G.

2017-12-01

Spatio-temporal dynamic visualization is more vivid than static visualization. It important to use dynamic visualization techniques to reveal the variation process and trend vividly and comprehensively for the geographical phenomenon. To deal with challenges caused by dynamic visualization of both 2D and 3D spatial dynamic targets, especially for different spatial data types require high-performance GIS dynamic objects rendering engine. The main approach for improving the rendering engine with vast dynamic targets relies on key technologies of high-performance GIS, including memory computing, parallel computing, GPU computing and high-performance algorisms. In this study, high-performance GIS dynamic objects rendering engine is designed and implemented for solving the problem based on hybrid accelerative techniques. The high-performance GIS rendering engine contains GPU computing, OpenGL technology, and high-performance algorism with the advantage of 64-bit memory computing. It processes 2D, 3D dynamic target data efficiently and runs smoothly with vast dynamic target data. The prototype system of high-performance GIS dynamic objects rendering engine is developed based SuperMap GIS iObjects. The experiments are designed for large-scale spatial data visualization, the results showed that the high-performance GIS dynamic objects rendering engine have the advantage of high performance. Rendering two-dimensional and three-dimensional dynamic objects achieve 20 times faster on GPU than on CPU.

Quasi-periodic Oscillations in Flares and Coronal Mass Ejections Associated with Magnetic Reconnection

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

Takahashi, Takuya; Shibata, Kazunari; Qiu, Jiong, E-mail: takahasi@kusastro.kyoto-u.ac.jp

We propose a mechanism for quasi-periodic oscillations of both coronal mass ejections (CMEs) and flare loops as related to magnetic reconnection in eruptive solar flares. We perform two-dimensional numerical MHD simulations of magnetic flux rope eruption, with three different values of the global Lundquist number. In the low Lundquist number run, no oscillatory behavior is found. In the moderate Lundquist number run, on the other hand, quasi-periodic oscillations are excited both at the bottom of the flux rope and at the flare loop top. In the high Lundquist number run, quasi-periodic oscillations are also excited; in the meanwhile, the dynamicsmore » become turbulent owing to the formation of multiple plasmoids in the reconnection current sheet. In high and moderate Lundquist number runs, thin reconnection jets collide with the flux rope bottom or flare loop top and dig them deeply. Steep oblique shocks are formed as termination shocks where reconnection jets are bent (rather than decelerated) in the horizontal direction, resulting in supersonic backflows. The structure becomes unstable, and quasi-periodic oscillations of supersonic backflows appear at locally confined high-beta regions at both the flux rope bottom and flare loop top. We compare the observational characteristics of quasi-periodic oscillations in erupting flux ropes, post-CME current sheets, flare ribbons, and light curves with corresponding dynamical structures found in our simulation.« less

Trapping virtual pores by crystal retro-engineering

NASA Astrophysics Data System (ADS)

Little, Marc A.; Briggs, Michael E.; Jones, James T. A.; Schmidtmann, Marc; Hasell, Tom; Chong, Samantha Y.; Jelfs, Kim E.; Chen, Linjiang; Cooper, Andrew I.

2015-02-01

Stable guest-free porous molecular crystals are uncommon. By contrast, organic molecular crystals with guest-occupied cavities are frequently observed, but these cavities tend to be unstable and collapse on removal of the guests—this feature has been referred to as ‘virtual porosity’. Here, we show how we have trapped the virtual porosity in an unstable low-density organic molecular crystal by introducing a second molecule that matches the size and shape of the unstable voids. We call this strategy ‘retro-engineering’ because it parallels organic retrosynthetic analysis, and it allows the metastable two-dimensional hexagonal pore structure in an organic solvate to be trapped in a binary cocrystal. Unlike the crystal with virtual porosity, the cocrystal material remains single crystalline and porous after removal of guests by heating.

Stable Versus Unstable Grade II High Ankle Sprains: A Prospective Study Predicting the Need for Surgical Stabilization and Time to Return to Sports.

PubMed

Calder, James D; Bamford, Richard; Petrie, Aviva; McCollum, Graham A

2016-04-01

To investigate grade II syndesmosis injuries in athletes and identify factors important in differentiating stable from dynamically unstable ankle sprains and those associated with a longer time to return to sports. Sixty-four athletes with an isolated syndesmosis injury (without fracture) were prospectively assessed, with a mean follow-up period of 37 months (range, 24 to 66 months). Those with an associated deltoid ligament injury or osteochondral lesion were included. Those whose injuries were considered stable (grade IIa) were treated conservatively with a boot and rehabilitation. Those whose injuries were clinically unstable underwent arthroscopy, and if instability was confirmed (grade IIb), the syndesmosis was stabilized. Clinical and magnetic resonance imaging assessments of injury to individual ligaments were recorded, along with time to return to play. A power analysis estimated that each group would need 28 patients. All athletes returned to the same level of professional sport. The 28 patients with grade IIa injuries returned at a mean of 45 days (range, 23 to 63 days) compared with 64 days (range, 27 to 104 days) for those with grade IIb injuries (P < .0001). There was a highly significant relationship between clinical and magnetic resonance imaging assessments of ligament injury (anterior tibiofibular ligament [ATFL], anterior-inferior tibiofibular ligament [AITFL], and deltoid ligament, P < .0001). Instability was 9.5 times as likely with a positive squeeze test and 11 times as likely with a deltoid injury. Combined injury to the anterior-inferior tibiofibular ligament and deltoid ligament was associated with a delay in return to sports. Concomitant injury to the ATFL indicated a different mechanism of injury-the syndesmosis is less likely to be unstable and is associated with an earlier return to sports. A positive squeeze test and injury to the ATFL and deltoid ligament are important factors in differentiating stable from dynamically unstable grade II injuries and may be used to identify which athletes may benefit from early arthroscopic assessment and stabilization. They may also be important in predicting the time frame for athletes' expected return to play. Level II, prospective comparative study. Copyright © 2016 Arthroscopy Association of North America. Published by Elsevier Inc. All rights reserved.

Characteristics of Turbulent Transfer during Episodes of Heavy Haze Pollution in Beijing in Winter 2016/17

NASA Astrophysics Data System (ADS)

Ren, Yan; Zheng, Shuwen; Wei, Wei; Wu, Bingui; Zhang, Hongsheng; Cai, Xuhui; Song, Yu

2018-02-01

We analyzed the structure and evolution of turbulent transfer and the wind profile in the atmospheric boundary layer in relation to aerosol concentrations during an episode of heavy haze pollution from 6 December 2016 to 9 January 2017. The turbulence data were recorded at Peking University's atmospheric science and environment observation station. The results showed a negative correlation between the wind speed and the PM2.5 concentration. The turbulence kinetic energy was large and showed obvious diurnal variations during unpolluted (clean) weather, but was small during episodes of heavy haze pollution. Under both clean and heavy haze conditions, the relation between the non-dimensional wind components and the stability parameter z/ L followed a 1/3 power law, but the normalized standard deviations of the wind speed were smaller during heavy pollution events than during clean periods under near-neutral conditions. Under unstable conditions, the normalized standard deviation of the potential temperature σ θ /| θ *| was related to z/ L, roughly following a -1/3 power law, and the ratio during pollution days was greater than that during clean days. The three-dimensional turbulence energy spectra satisfied a -2/3 power exponent rate in the high-frequency band. In the low-frequency band, the wind velocity spectrum curve was related to the stability parameters under clear conditions, but was not related to atmospheric stratification under polluted conditions. In the dissipation stage of the heavy pollution episode, the horizontal wind speed first started to increase at high altitudes and then gradually decreased at lower altitudes. The strong upward motion during this stage was an important dynamic factor in the dissipation of the heavy haze.

Development of adaptive control applied to chaotic systems

NASA Astrophysics Data System (ADS)

Rhode, Martin Andreas

1997-12-01

Continuous-time derivative control and adaptive map-based recursive feedback control techniques are used to control chaos in a variety of systems and in situations that are of practical interest. The theoretical part of the research includes the review of fundamental concept of control theory in the context of its applications to deterministic chaotic systems, the development of a new adaptive algorithm to identify the linear system properties necessary for control, and the extension of the recursive proportional feedback control technique, RPF, to high dimensional systems. Chaos control was applied to models of a thermal pulsed combustor, electro-chemical dissolution and the hyperchaotic Rossler system. Important implications for combustion engineering were suggested by successful control of the model of the thermal pulsed combustor. The system was automatically tracked while maintaining control into regions of parameter and state space where no stable attractors exist. In a simulation of the electrochemical dissolution system, application of derivative control to stabilize a steady state, and adaptive RPF to stabilize a period one orbit, was demonstrated. The high dimensional adaptive control algorithm was applied in a simulation using the Rossler hyperchaotic system, where a period-two orbit with two unstable directions was stabilized and tracked over a wide range of a system parameter. In the experimental part, the electrochemical system was studied in parameter space, by scanning the applied potential and the frequency of the rotating copper disk. The automated control algorithm is demonstrated to be effective when applied to stabilize a period-one orbit in the experiment. We show the necessity of small random perturbations applied to the system in order to both learn the dynamics and control the system at the same time. The simultaneous learning and control capability is shown to be an important part of the active feedback control.

Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons

NASA Astrophysics Data System (ADS)

Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Font, José A.; Herdeiro, Carlos; Radu, Eugen

2017-08-01

Recent numerical relativity simulations within the Einstein-Maxwell-(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordström black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these unstable solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordström BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

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

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE PAGES

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

2016-02-15

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

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

Antonini, Fabio; Lithwick, Yoram; Hamers, Adrian S.

Gas giants orbiting their host star within the ice line are thought to have migrated to their current locations from farther out. Here we consider the origin and dynamical evolution of observed Jupiters, focusing on hot and warm Jupiters with outer friends. We show that the majority of the observed Jupiter pairs (20 out of 24) are dynamically unstable if the inner planet is placed at ≳1 au distance from the stellar host. This finding is at odds with formation theories that invoke the migration of such planets from semimajor axes ≳1 au due to secular dynamical processes (e.g., secularmore » chaos, Lidov–Kozai [LK] oscillations) coupled with tidal dissipation. In fact, the results of N -body integrations show that the evolution of dynamically unstable systems does not lead to tidal migration but rather to planet ejections and collisions with the host star. This and other arguments lead us to suggest that most of the observed planets with a companion could not have been transported from farther out through secular migration processes. More generally, by using a combination of numerical and analytic techniques, we show that the high- e LK migration scenario can only account for less than 10% of all gas giants observed between 0.1 and 1 au. Simulations of multiplanet systems support this result. Our study indicates that rather than starting on highly eccentric orbits with orbital periods above 1 yr, these “warm” Jupiters are more likely to have reached the region where they are observed today without having experienced significant tidal dissipation.« less

Formation of rogue waves from a locally perturbed condensate.

PubMed

Gelash, A A

2018-02-01

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

Formation of rogue waves from a locally perturbed condensate

NASA Astrophysics Data System (ADS)

Gelash, A. Â. A.

2018-02-01

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

Dynamical criterion for a marginally unstable, quasi-linear behavior in a two-layer model

NASA Technical Reports Server (NTRS)

Ebisuzaki, W.

1988-01-01

A two-layer quasi-geostrophic flow forced by meridional variations in heating can be in regimes ranging from radiative equilibrium to forced geostrophic turbulence. Between these extremes is a regime where the time-mean (zonal) flow is marginally unstable. Using scaling arguments, it is concluded that such a marginally unstable state should occur when a certain parameter, measuring the strength of wave-wave interactions relative to the beta effect and advection by the thermal wind, is small. Numerical simulations support this proposal. A transition from the marginally unstable regime to a more nonlinear regime is then examined through numerical simulations with different radiative forcings. It is found that transition is not caused by secondary instability of waves in the marginally unstable regime. Instead, the time-mean flow can support a number of marginally unstable normal modes. These normal modes interact with each other, and if they are of sufficient amplitude, the flow enters a more nonlinear regime.

Detection of one-dimensional migration of single self-interstitial atoms in tungsten using high-voltage electron microscopy

PubMed Central

Amino, T.; Arakawa, K.; Mori, H.

2016-01-01

The dynamic behaviour of atomic-size disarrangements of atoms—point defects (self-interstitial atoms (SIAs) and vacancies)—often governs the macroscopic properties of crystalline materials. However, the dynamics of SIAs have not been fully uncovered because of their rapid migration. Using a combination of high-voltage transmission electron microscopy and exhaustive kinetic Monte Carlo simulations, we determine the dynamics of the rapidly migrating SIAs from the formation process of the nanoscale SIA clusters in tungsten as a typical body-centred cubic (BCC) structure metal under the constant-rate production of both types of point defects with high-energy electron irradiation, which must reflect the dynamics of individual SIAs. We reveal that the migration dimension of SIAs is not three-dimensional (3D) but one-dimensional (1D). This result overturns the long-standing and well-accepted view of SIAs in BCC metals and supports recent results obtained by ab-initio simulations. The SIA dynamics clarified here will be one of the key factors to accurately predict the lifetimes of nuclear fission and fusion materials. PMID:27185352

Implications of the Corotation Theorem on the MRI in Axial Symmetry

NASA Astrophysics Data System (ADS)

Montani, G.; Cianfrani, F.; Pugliese, D.

2016-08-01

We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the corotation theorem on the linear mode structure. Using some specific assumptions (e.g., plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvénic nature of the magnetorotational instability, and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the corotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, in both the axisymmetric and three-dimensional cases). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin-disk profile, and the z-dependence has a simple parametric role.

The investigation of tethered satellite system dynamics

NASA Technical Reports Server (NTRS)

Lorenzini, E.

1985-01-01

A progress report is presented that deals with three major topics related to Tethered Satellite System Dynamics. The SAO rotational dynamics computer code was updated. The program is now suitable to deal with inclined orbits. The output has been also modified in order to show the satellite Euler angles referred to the rotating orbital frame. The three-dimensional high resolution computer program SLACK3 was developed. The code simulates the three-dimensional dynamics of a tether going slack taking into account the effect produced by boom rotations. Preliminary simulations on the three-dimensional dynamics of a recoiling slack tether are shown in this report. A program to evaluate the electric potential around a severed tether is immersed in a plasma. The potential is computed on a three-dimensional grid axially symmetric with respect to the tether longitudinal axis. The electric potential variations due to the plasma are presently under investigation.

Low-temperature, ultrahigh-vacuum tip-enhanced Raman spectroscopy combined with molecular beam epitaxy for in situ two-dimensional materials' studies

NASA Astrophysics Data System (ADS)

Sheng, Shaoxiang; Li, Wenbin; Gou, Jian; Cheng, Peng; Chen, Lan; Wu, Kehui

2018-05-01

Tip-enhanced Raman spectroscopy (TERS), which combines scanning probe microscopy with the Raman spectroscopy, is capable to access the local structure and chemical information simultaneously. However, the application of ambient TERS is limited by the unstable and poorly controllable experimental conditions. Here, we designed a high performance TERS system based on a low-temperature ultrahigh-vacuum scanning tunneling microscope (LT-UHV-STM) and combined with a molecular beam epitaxy (MBE) system. It can be used for growing two-dimensional (2D) materials and for in situ STM and TERS characterization. Using a 2D silicene sheet on the Ag(111) surface as a model system, we achieved an unprecedented 109 Raman single enhancement factor in combination with a TERS spatial resolution down to 0.5 nm. The results show that TERS combined with a MBE system can be a powerful tool to study low dimensional materials and surface science.

Conjugated organic framework with three-dimensionally ordered stable structure and delocalized π clouds

PubMed Central

Guo, Jia; Xu, Yanhong; Jin, Shangbin; Chen, Long; Kaji, Toshihiko; Honsho, Yoshihito; Addicoat, Matthew A.; Kim, Jangbae; Saeki, Akinori; Ihee, Hyotcherl; Seki, Shu; Irle, Stephan; Hiramoto, Masahiro; Gao, Jia; Jiang, Donglin

2013-01-01

Covalent organic frameworks are a class of crystalline organic porous materials that can utilize π–π-stacking interactions as a driving force for the crystallization of polygonal sheets to form layered frameworks and ordered pores. However, typical examples are chemically unstable and lack intrasheet π-conjugation, thereby significantly limiting their applications. Here we report a chemically stable, electronically conjugated organic framework with topologically designed wire frameworks and open nanochannels, in which the π conjugation-spans the two-dimensional sheets. Our framework permits inborn periodic ordering of conjugated chains in all three dimensions and exhibits a striking combination of properties: chemical stability, extended π-delocalization, ability to host guest molecules and hole mobility. We show that the π-conjugated organic framework is useful for high on-off ratio photoswitches and photovoltaic cells. Therefore, this strategy may constitute a step towards realizing ordered semiconducting porous materials for innovations based on two-dimensionally extended π systems. PMID:24220603

Constraint counting for frictional jamming

NASA Astrophysics Data System (ADS)

Quint, D. A.; Henkes, S.; Schwarz, J. M.

2012-02-01

While the frictionless jamming transition has been intensely studied in recent years, more realistic frictional packings are less well understood. In frictionless sphere packings, the transition is predicted by a simple mean-field constraint counting argument, the isostaticity argument. For frictional packings, a modified constraint counting argument, which includes slipping contacts at the Coulomb threshold, has had limited success in accounting for the transition. We propose that the frictional jamming transition is not mean field and is triggered by the nucleation of unstable regions, which are themselves dynamical objects due to the Coulomb criterion. We create frictional packings using MD simulations and test for the presence and shape of rigid clusters with the pebble game to identify the partition of the packing into stable and unstable regions. To understand the dynamics of these unstable regions we follow perturbations at contacts crucial to the stability of the ``frictional house of cards.''

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Predator prey oscillations in a simple cascade model of drift wave turbulence

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

Berionni, V.; Guercan, Oe. D.

2011-11-15

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separationmore » for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.« less

Spontaneous decay of periodic magnetostatic equilibria

DOE PAGES

East, William E.; Zrake, Jonathan; Yuan, Yajie; ...

2015-08-28

In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field satisfies ∇ x B = αB , where \\alpha is spatially uniform, on a periodic domain. Using numerical solutions we show that generic examples of such equilibria are unstable to ideal modes (including incompressible ones) which are marked by exponential growth in the linear phase. We characterize the unstable mode, showing how it can be understood in terms of merging magnetic and current structures,more » and explicitly demonstrate its instability using the energy principle. Following the nonlinear evolution of these solutions, we find that they rapidly develop regions with relativistic velocities and electric fields of comparable magnitude to the magnetic field, liberating magnetic energy on dynamical timescales and eventually settling into a configuration with the largest allowable wavelength. Furthermore, these properties make such solutions a promising setting for exploring the mechanisms behind extreme cosmic sources of gamma rays.« less

Bounded tracking for nonminimum phase nonlinear systems with fast zero dynamics

DOT National Transportation Integrated Search

1996-12-01

A PostScript file. In this paper, tracking control laws for nonminimum phase nonlinear systems with both fast and slow, possibly unstable, zero dynamics are derived. The fast zero dynamics arise from a perturbation of a nominal system. These fast zer...

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

Superfluidity, Bose-Einstein condensation, and structure in one-dimensional Luttinger liquids

NASA Astrophysics Data System (ADS)

Vranješ Markić, L.; Vrcan, H.; Zuhrianda, Z.; Glyde, H. R.

2018-01-01

We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ρS/ρ0 , the one-body density matrix n (x ) , the pair distribution function g (x ) , and the static structure factor S (q ) are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter K . The 1D Bose fluid examined is a single chain of 4He atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid 4He. In this range, K varies from K >2 at low density, where a robust superfluid is predicted, to K <0.5 , where fragile 1D superflow and solidlike peaks in S (q ) are predicted. For uniform pore walls, the ρS/ρ0 scales as predicted by LL theory. The n (x ) and g (x ) show long range oscillations and decay with x as predicted by LL theory. The amplitude of the oscillations is large at high density (small K ) and small at low density (large K ). The K values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ρS/ρ0 does not scale as predicted by LL theory. A single vJ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The "dynamical" superfluid fraction, ρSD/ρ0 , is determined. The physics of the deviation from LL theory in disorder and the "dynamical" ρSD/ρ0 are discussed.

One-dimensional analysis of unsteady flows due to supercritical heat addition in high speed condensing steam

NASA Astrophysics Data System (ADS)

Malek, N. A.; Hasini, H.; Yusoff, M. Z.

2013-06-01

Unsteadiness in supersonic flow in nozzles can be generated by the release of heat due to spontaneous condensation. The heat released is termed "supercritical" and may be responsible for turbine blades failure in turbine cascade as it causes a supersonic flow to decelerate. When the Mach number is reduced to unity, the flow can no longer sustain the additional heat and becomes unstable. This paper aims to numerically investigate the unsteadiness caused by supercritical heat addition in one-dimensional condensing flows. The governing equations for mass, momentum and energy, coupled with the equations describing the wetness fraction and droplet growth are integrated and solved iteratively to reveal the final solution. Comparison is made with well-established experimental and numerical solution done by previous researchers that shows similar phenomena.

Unifying dynamical and structural stability of equilibria

NASA Astrophysics Data System (ADS)

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

Unifying dynamical and structural stability of equilibria.

PubMed

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

NASA Technical Reports Server (NTRS)

Duck, P. W.; Hall, P.

1988-01-01

Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

NASA Technical Reports Server (NTRS)

Duck, P. W.; Hall, P.

1989-01-01

Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub O. At values of the radius above a sub O all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

Vibration-Resistant Support for Halide Lamps

NASA Technical Reports Server (NTRS)

Kiss, J.

1987-01-01

Lamp envelope protected against breakage. Old and new mounts for halide arc lamp sealed in housing with parabolic refector and quartz window. New version supports lamp with compliant garters instead of rigid brazed joint at top and dimensionally unstable finger stock at bottom.

Establishing resolution-improved NMR spectroscopy in high magnetic fields with unknown spatiotemporal variations

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

Zhang, Zhiyong; Cai, Shuhui; Zheng, Zhenyao

A half-century quest for higher magnetic fields has been an integral part of the progress undergone in the Nuclear Magnetic Resonance (NMR) study of materials’ structure and dynamics. Because 2D NMR relies on systematic changes in coherences’ phases as a function of an encoding time varied over a series of independent experiments, it generally cannot be applied in temporally unstable fields. This precludes most NMR methods from being used to characterize samples situated in hybrid or resistive magnets that are capable of achieving extremely high magnetic field strength. Recently, “ultrafast” NMR has been developed into an effective and widely applicablemore » methodology enabling the acquisition of a multidimensional NMR spectrum in a single scan; it can therefore be used to partially mitigate the effects of temporally varying magnetic fields. Nevertheless, the strong interference of fluctuating fields with the spatial encoding of ultrafast NMR still severely restricts measurement sensitivity and resolution. Here, we introduce a strategy for obtaining high resolution NMR spectra that exploits the immunity of intermolecular zero-quantum coherences (iZQCs) to field instabilities and inhomogeneities. The spatial encoding of iZQCs is combined with a J-modulated detection scheme that removes the influence of arbitrary field inhomogeneities during acquisition. This new method can acquire high-resolution one-dimensional NMR spectra in large inhomogeneous and fluctuating fields, and it is tested with fields experimentally modeled to mimic those of resistive and resistive-superconducting hybrid magnets.« less

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.

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

NASA Technical Reports Server (NTRS)

Rohrs, C. E.; Valavani, L.; Athans, M.; Stein, G.

1985-01-01

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implications of the existence of such infinite-gain operators is that: (1) sinusoidal reference inputs at specific frequencies and/or (2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

A new paradigm for human stick balancing: a suspended not an inverted pendulum.

PubMed

Lee, Kwee-Yum; O'Dwyer, Nicholas; Halaki, Mark; Smith, Richard

2012-09-01

We studied 14 skilled subjects balancing a stick (a television antenna, 52 cm, 34 g) on their middle fingertip. Comprehensive three-dimensional analyses revealed that the movement of the finger was 1.75 times that of the stick tip, such that the balanced stick behaved more like a normal noninverted pendulum than the inverted pendulum common to engineering models for stick balancing using motors. The average relation between the torque applied to the stick and its angle of deviation from the vertical was highly linear, consistent with simple harmonic motion. We observed clearly greater rotational movement of the stick in the anteroposterior plane than the mediolateral plane. Despite this magnitude difference, the duration of stick oscillatory cycles was very similar in both planes, again consistent with simple harmonic motion. The control parameter in balancing was the ratio of active torque applied to the stick relative to gravitational torque. It determined both the pivot point and oscillatory cycle period of the pendulum. The pivot point was located at the radius of gyration (about the centre of mass) of the stick from its centre of mass, showing that the subjects attuned to the gravitational dynamics and mass distribution of the stick. Hence, the key to controlling instability here was mastery of the physics of the unstable object. The radius of gyration may--similar to centre of mass--contribute to the kinesthesis of rotating limb segments and control of their gravitational dynamics.

A complex noise reduction method for improving visualization of SD-OCT skin biomedical images

NASA Astrophysics Data System (ADS)

Myakinin, Oleg O.; Zakharov, Valery P.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Khramov, Alexander G.

2014-05-01

In this paper we consider the original method of solving noise reduction problem for visualization's quality improvement of SD-OCT skin and tumors biomedical images. The principal advantages of OCT are high resolution and possibility of in vivo analysis. We propose a two-stage algorithm: 1) process of raw one-dimensional A-scans of SD-OCT and 2) remove a noise from the resulting B(C)-scans. The general mathematical methods of SD-OCT are unstable: if the noise of the CCD is 1.6% of the dynamic range then result distortions are already 25-40% of the dynamic range. We use at the first stage a resampling of A-scans and simple linear filters to reduce the amount of data and remove the noise of the CCD camera. The efficiency, improving productivity and conservation of the axial resolution when using this approach are showed. At the second stage we use an effective algorithms based on Hilbert-Huang Transform for more accurately noise peaks removal. The effectiveness of the proposed approach for visualization of malignant and benign skin tumors (melanoma, BCC etc.) and a significant improvement of SNR level for different methods of noise reduction are showed. Also in this study we consider a modification of this method depending of a specific hardware and software features of used OCT setup. The basic version does not require any hardware modifications of existing equipment. The effectiveness of proposed method for 3D visualization of tissues can simplify medical diagnosis in oncology.

Molecular-dynamics study of propane-hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis.

PubMed

Ghaani, Mohammad Reza; English, Niall J

2018-03-21

Equilibrium and non-equilibrium molecular-dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar propane-hydrate interfaces in contact with liquid water over the 260-320 K range. Two types of hydrate-surface water-lattice molecular termination were adopted, at the hydrate edge with water, for comparison: a 001-direct surface cleavage and one with completed cages. Statistically significant differences in melting temperatures and initial break-up rates were observed between both interface types. Dissociation rates were observed to be strongly dependent on temperature, with higher rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model, developed previously, was applied to fit the observed dissociation profiles, and this helps us to identify clearly two distinct hydrate-decomposition régimes; following a highly temperature-dependent break-up phase, a second well-defined stage is essentially independent of temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. Further equilibrium MD-analysis of the two-phase systems at their melting point, with consideration of the relaxation times gleaned from the auto-correlation functions of fluctuations in a number of enclathrated guest molecules, led to statistically significant differences between the two surface-termination cases; a consistent correlation emerged in both cases between the underlying, non-equilibrium, thermal-driven dissociation rates sampled directly from melting with that from an equilibrium-MD fluctuation-dissipation approach.

Molecular-dynamics study of propane-hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis

NASA Astrophysics Data System (ADS)

Ghaani, Mohammad Reza; English, Niall J.

2018-03-01

Equilibrium and non-equilibrium molecular-dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar propane-hydrate interfaces in contact with liquid water over the 260-320 K range. Two types of hydrate-surface water-lattice molecular termination were adopted, at the hydrate edge with water, for comparison: a 001-direct surface cleavage and one with completed cages. Statistically significant differences in melting temperatures and initial break-up rates were observed between both interface types. Dissociation rates were observed to be strongly dependent on temperature, with higher rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model, developed previously, was applied to fit the observed dissociation profiles, and this helps us to identify clearly two distinct hydrate-decomposition régimes; following a highly temperature-dependent break-up phase, a second well-defined stage is essentially independent of temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. Further equilibrium MD-analysis of the two-phase systems at their melting point, with consideration of the relaxation times gleaned from the auto-correlation functions of fluctuations in a number of enclathrated guest molecules, led to statistically significant differences between the two surface-termination cases; a consistent correlation emerged in both cases between the underlying, non-equilibrium, thermal-driven dissociation rates sampled directly from melting with that from an equilibrium-MD fluctuation-dissipation approach.

Thunderstorm-environment interactions determined with three-dimensional trajectories

NASA Technical Reports Server (NTRS)

Wilson, G. S.

1980-01-01

Diagnostically determined three dimensional trajectories were used to reveal some of the scale interaction processes that occur between convective storms and their environment. Data from NASA's fourth Atmospheric Variability Experiment are analyzed. Two intense squall lines and numerous reports of severe weather occurred during the period. Convective storm systems with good temporal and spatial continuity are shown to be related to the development and movement of short wave circulation systems aloft that propagate eastward within a zonal mid tropospheric wind pattern. These short wave systems are found to produce the potential instability and dynamic triggering needed for thunderstorm formation. The environmental flow patterns, relative to convective storm systems, are shown to produce large upward air parcel movements in excess of 50 mb/3h in the immediate vicinity of the storms. The air undergoing strong lifting originates as potentially unstable low level air traveling into the storm environment from southern and southwestern directions. The thermo and hydrodynamical processes that lead to changes in atmospheric structure before, during, and after convective storm formation are described using total time derivatives of pressure or net vertical displacement, potential temperature, and vector wind calculated by following air parcels.

Exploring the Molecular Design of Protein Interaction Sites with Molecular Dynamics Simulations and Free Energy Calculations†

PubMed Central

Liang, Shide; Li, Liwei; Hsu, Wei-Lun; Pilcher, Meaghan N.; Uversky, Vladimir; Zhou, Yaoqi; Dunker, A. Keith; Meroueh, Samy O.

2009-01-01

The significant work that has been invested toward understanding protein–protein interaction has not translated into significant advances in structure-based predictions. In particular redesigning protein surfaces to bind to unrelated receptors remains a challenge, partly due to receptor flexibility, which is often neglected in these efforts. In this work, we computationally graft the binding epitope of various small proteins obtained from the RCSB database to bind to barnase, lysozyme, and trypsin using a previously derived and validated algorithm. In an effort to probe the protein complexes in a realistic environment, all native and designer complexes were subjected to a total of nearly 400 ns of explicit-solvent molecular dynamics (MD) simulation. The MD data led to an unexpected observation: some of the designer complexes were highly unstable and decomposed during the trajectories. In contrast, the native and a number of designer complexes remained consistently stable. The unstable conformers provided us with a unique opportunity to define the structural and energetic factors that lead to unproductive protein–protein complexes. To that end we used free energy calculations following the MM-PBSA approach to determine the role of nonpolar effects, electrostatics and entropy in binding. Remarkably, we found that a majority of unstable complexes exhibited more favorable electrostatics than native or stable designer complexes, suggesting that favorable electrostatic interactions are not prerequisite for complex formation between proteins. However, nonpolar effects remained consistently more favorable in native and stable designer complexes reinforcing the importance of hydrophobic effects in protein–protein binding. While entropy systematically opposed binding in all cases, there was no observed trend in the entropy difference between native and designer complexes. A series of alanine scanning mutations of hot-spot residues at the interface of native and designer complexes showed less than optimal contacts of hot-spot residues with their surroundings in the unstable conformers, resulting in more favorable entropy for these complexes. Finally, disorder predictions revealed that secondary structures at the interface of unstable complexes exhibited greater disorder than the stable complexes. PMID:19113835

Molecular Dynamics Simulation of the Three-Dimensional Ordered State in Laser-Cooled Heavy-Ion Beams

NASA Astrophysics Data System (ADS)

Yuri, Yosuke

A molecular dynamics simulation is performed to study the formation of three-dimensional ordered beams by laser cooling in a cooler storage ring. Ultralow-temperature heavy-ion beams are generated by transverse cooling with displaced Gaussian lasers and resonant coupling. A three-dimensional ordered state of the ion beam is attained at a high line density. The ordered beam exhibits several unique characteristics different from those of an ideal crystalline beam.

Effects of dynamic information in recognising facial expressions on dimensional and categorical judgments.

PubMed

Fujimura, Tomomi; Suzuki, Naoto

2010-01-01

We investigated the effects of dynamic information on decoding facial expressions. A dynamic face entailed a change from a neutral to a full-blown expression, whereas a static face included only the full-blown expression. Sixty-eight participants were divided into two groups, the dynamic condition and the static condition. The facial stimuli expressed eight kinds of emotions (excited, happy, calm, sleepy, sad, angry, fearful, and surprised) according to a dimensional perspective. Participants evaluated each facial stimulus using two methods, the Affect Grid (Russell et al, 1989 Personality and Social Psychology 29 497-510) and the forced-choice task, allowing for dimensional and categorical judgment interpretations. For activation ratings in dimensional judgments, the results indicated that dynamic calm faces, low-activation expressions were rated as less activated than static faces. For categorical judgments, dynamic excited, happy, and fearful faces, which are high- and middle-activation expressions, had higher ratings than did those under the static condition. These results suggest that the beneficial effect of dynamic information depends on the emotional properties of facial expressions.

Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2015-07-01

The dynamic stability of dynamical systems with time-periodic stiffness is addressed here. Cracked rotor systems with time-periodic stiffness are well-known examples of such systems. Time-varying area moments of inertia at the cracked element cross-section of a cracked rotor have been used to formulate the time-periodic finite element stiffness matrix. The semi-infinite coefficient matrix obtained by applying the harmonic balance (HB) solution to the finite element (FE) equations of motion is employed here to study the dynamic stability of the system. Consequently, the sign of the determinant of a scaled version of a sub-matrix of this semi-infinite coefficient matrix at a finite number of harmonics in the HB solution is found to be sufficient for identifying the major unstable zones of the system in the parameter plane. Specifically, it is found that the negative determinant always corresponds to unstable zones in all of the systems considered. This approach is applied to a parametrically excited Mathieu's equation, a two degree-of-freedom linear time-periodic dynamical system, a cracked Jeffcott rotor and a finite element model of the cracked rotor system. Compared to the corresponding results obtained by Floquet's theory, the sign of the determinant of the scaled sub-matrix is found to be an efficient tool for identifying the major unstable zones of the linear time-periodic parametrically excited systems, especially large-scale FE systems. Moreover, it is found that the unstable zones for a FE cracked rotor with an open transverse crack model only appear at the backward whirl. The theoretical and experimental results have been found to agree well for verifying that the open crack model excites the backward whirl amplitudes at the critical backward whirling rotational speeds.

Facile synthesis of tin dioxide-based high performance anodes for lithium ion batteries assisted by graphene gel

NASA Astrophysics Data System (ADS)

Wan, Yuanxin; Sha, Ye; Luo, Shaochuan; Deng, Weijia; Wang, Xiaoliang; Xue, Gi; Zhou, Dongshan

2015-11-01

Tin dioxide (SnO2) is an attractive material for anodes in energy storage devices, because it has four times the theoretical capacity of the prevalent anode material (graphite). The main obstacle hampers SnO2 from practical application is the pulverization problem caused by drastic volume change (∼300%) during lithium-ion insertion or extraction, which would lead to the loss of electrical conductivity, unstable solid-electrolyte interphase (SEI) formation and consequently severe capacity fading in the cycling. Here, we anchored the SnO2 nanocrystals into three dimensional graphene gel network to tackle this problem. As a result of the three dimensional (3-D) architecture, the huge volume change during cycling was tolerated by the large free space in this 3-D construction, resulting in a high capacity of 1090 mAh g-1 even after 200 cycles. What's more, at a higher current density 5 A g-1, a reversible capacity of about 491 mAh g-1 was achieved with this electrode.

Error behavior of multistep methods applied to unstable differential systems

NASA Technical Reports Server (NTRS)

Brown, R. L.

1977-01-01

The problem of modeling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulas. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulas and two different stepsizes to illustrate the appropriateness of the criteria.

Stability of general-relativistic accretion disks

NASA Astrophysics Data System (ADS)

Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

2011-02-01

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a Γ-law equation of state with Γ=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.

Stable monolayer honeycomb-like structures of RuX2 (X =S,Se)

NASA Astrophysics Data System (ADS)

Ersan, Fatih; Cahangirov, Seymur; Gökoǧlu, Gökhan; Rubio, Angel; Aktürk, Ethem

2016-10-01

Recent studies show that several metal oxides and dichalcogenides (M X2) , which exist in nature, can be stable in two-dimensional (2D) form and each year several new M X2 structures are explored. The unstable structures in H (hexagonal) or T (octahedral) forms can be stabilized through Peierls distortion. In this paper, we propose new 2D forms of RuS2 and RuSe2 materials. We investigate in detail the stability, electronic, magnetic, optical, and thermodynamic properties of 2D Ru X2 (X =S,Se) structures from first principles. While their H and T structures are unstable, the distorted T structures (T'-Ru X2) are stable and have a nonmagnetic semiconducting ground state. The molecular dynamic simulations also confirm that T'-Ru X2 systems are stable even at 500 K without any structural deformation. T'-RuS2 and T'-RuSe2 have indirect band gaps with 0.745 eV (1.694 eV with HSE) and 0.798 eV (1.675 eV with HSE) gap values, respectively. We also examine their bilayer and trilayer forms and find direct and smaller band gaps. We find that AA stacking is more favorable than the AB configuration. The new 2D materials obtained can be good candidates with striking properties for applications in semiconductor electronic, optoelectronic devices, and sensor technology.

Full evaporation dynamic headspace in combination with selectable one-dimensional/two-dimensional gas chromatography-mass spectrometry for the determination of suspected fragrance allergens in cosmetic products.

PubMed

Devos, Christophe; Ochiai, Nobuo; Sasamoto, Kikuo; Sandra, Pat; David, Frank

2012-09-14

Suspected fragrance allergens were determined in cosmetic products using a combination of full evaporation-dynamic headspace (FEDHS) with selectable one-dimensional/two-dimensional GC-MS. The full evaporation dynamic headspace approach allows the non-discriminating extraction and injection of both apolar and polar fragrance compounds, without contamination of the analytical system by high molecular weight non-volatile matrix compounds. The method can be applied to all classes of cosmetic samples, including water containing matrices such as shower gels or body creams. In combination with selectable (1)D/(2)D GC-MS, consisting of a dedicated heart-cutting GC-MS configuration using capillary flow technology (CFT) and low thermal mass GC (LTM-GC), a highly flexible and easy-to-use analytical solution is offered. Depending on the complexity of the perfume fraction, analyses can be performed in one-dimensional GC-MS mode or in heart-cutting two-dimensional GC-MS mode, without the need of hardware reconfiguration. The two-dimensional mode with independent temperature control of the first and second dimension column is especially useful to confirm the presence of detected allergen compounds when mass spectral deconvolution is not possible. Copyright © 2012 Elsevier B.V. All rights reserved.

A transition in the viscous fingering instability in miscible fluids

NASA Astrophysics Data System (ADS)

Videbaek, Thomas; Nagel, Sidney R.

2017-11-01

The viscous fingering instability in a quasi-two dimensional Hele-Shaw cell is an example of complex structure formation from benign initial conditions. When the invading fluid has the lesser viscosity, the interface between the two fluids is unstable to finger formation. Here, we study the instability between pairs of miscible fluids in a circular cell with fluid injected at its center. As the injection rate is decreased, diffusion will smooth out the discontinuity in the gap-averaged viscosity at the interface between the fluids. At high injection rates (i.e., high Péclet number, Pe), fingering is associated with three-dimensional structure within the gap between the confining plates. On lowering Pe, we find a sharp transition in the finger morphology at a critical value, Pec (ηi /ηo) 1 / 2 , with ηi (ηo) being the viscosity of the inner (outer) fluid; at this point, the width of the fingers jumps, the length of the fingers shrinks towards zero and the three-dimensional structure goes from half filling to fully filling the gap. Thus, by controlling the viscosity contrast at the interface, one can alter and even completely suppress the instability.

Three-dimensional structure of the curved mixing layer using image reconstruction and volume rendering

NASA Astrophysics Data System (ADS)

Karasso, P. S.; Mungal, M. G.

1991-05-01

This study investigates the structure and mixing of the two-dimensional turbulent mixing layer when subjected to longitudinal streamwise curvature. The straight layer is now well known to be dominated by the primary Kelvin-Helmholtz (KH) instability as well as the secondary Taylor-Goertler (TG) instability. For equal density fluids, placing the high-speed fluid on the inside of a streamwise bend causes the TG instability to be enhanced (unstable case), while placing the low-speed fluid on the inside of the same bend leads to the suppression of the TG instability (stable case). The location of the mixing transition is correspondingly altered. Our goal is to study the changes to the mixing field and growth rate resulting from the competition between instabilities. Our studies are performed in a newly constructed blow-down water facility capable of high Reynolds numbers and excellent optical access. Maximum flow speeds are 2 and 0.25 m/sec for the high- and low-speed sides, respectively, leading to maximum Reynolds numbers of 80 000 based on velocity difference and the width of the layer. We are able to dye one stream with a fluorescent dye, thus providing several planar views of the flow under laser sheet illumination. These views are superior to conventional approaches as they are free of wall effects and are not spatially integrating. However, our most useful diagnostic of the structure of the flow is the ability to record high-speed images of the end view of the flow that are then reconstructed by computer using the volume rendering technique of Jiménez et al.1 This approach is especially useful as it allows us to compare the structural changes to the flow resulting from the competition between the KH and TG instabilities. Another advantage is the fact that several hundred frames, covering many characteristic times, are incorporated into the rendered image and thus capture considerably more flow physics than do still images. We currently have our rendering techniques fully operational,2 and are presently acquiring high quality high-speed movies of the various flow cases. Our findings to date, based on planar time-averaged and instantaneous views, show the following: (1) a 50% increase in growth rate from the stable to the unstable case resulting from mild curvature; (2) an enhancement of the TG vortices in the unstable case, but without major disruption of the KH instability which remains relatively intact; and (3) the occurrence of the KH instability at angles tilted with respect to the splitter plate tip, in agreement with the predictions of linear stability theory. This final observation has not been reported to date, primarily because sheet techniques have not been used at Reynolds numbers as high as the present study. The presentation will provide detailed views of the changes between the stable, straight, and unstable cases using our volume rendering approach, and will provide statistical measures such as changes to vortex spacing and size, to quantify such changes.

Unsteady Full Annulus Simulations of a Transonic Axial Compressor Stage

NASA Technical Reports Server (NTRS)

Herrick, Gregory P.; Hathaway, Michael D.; Chen, Jen-Ping

2009-01-01

Two recent research endeavors in turbomachinery at NASA Glenn Research Center have focused on compression system stall inception and compression system aerothermodynamic performance. Physical experiment and computational research are ongoing in support of these research objectives. TURBO, an unsteady, three-dimensional, Navier-Stokes computational fluid dynamics code commissioned and developed by NASA, has been utilized, enhanced, and validated in support of these endeavors. In the research which follows, TURBO is shown to accurately capture compression system flow range-from choke to stall inception-and also to accurately calculate fundamental aerothermodynamic performance parameters. Rigorous full-annulus calculations are performed to validate TURBO s ability to simulate the unstable, unsteady, chaotic stall inception process; as part of these efforts, full-annulus calculations are also performed at a condition approaching choke to further document TURBO s capabilities to compute aerothermodynamic performance data and support a NASA code assessment effort.

Isotope effect in normal-to-local transition of acetylene bending modes

DOE PAGES

Ma, Jianyi; Xu, Dingguo; Guo, Hua; ...

2012-01-01

The normal-to-local transition for the bending modes of acetylene is considered a prelude to its isomerization to vinylidene. Here, such a transition in fully deuterated acetylene is investigated using a full-dimensional quantum model. It is found that the local benders emerge at much lower energies and bending quantum numbers than in the hydrogen isotopomer HCCH. This is accompanied by a transition to a second kind of bending mode called counter-rotator, again at lower energies and quantum numbers than in HCCH. These transitions are also investigated using bifurcation analysis of two empirical spectroscopic fitting Hamiltonians for pure bending modes, which helpsmore » to understand the origin of the transitions semiclassically as branchings or bifurcations out of the trans and normal bend modes when the latter become dynamically unstable. The results of the quantum model and the empirical bifurcation analysis are in very good agreement.« less

Development of a computational testbed for numerical simulation of combustion instability

NASA Technical Reports Server (NTRS)

Grenda, Jeffrey; Venkateswaran, Sankaran; Merkle, Charles L.

1993-01-01

A synergistic hierarchy of analytical and computational fluid dynamic techniques is used to analyze three-dimensional combustion instabilities in liquid rocket engines. A mixed finite difference/spectral procedure is employed to study the effects of a distributed vaporization zone on standing and spinning instability modes within the chamber. Droplet atomization and vaporization are treated by a variety of classical models found in the literature. A multi-zone, linearized analytical solution is used to validate the accuracy of the numerical simulations at small amplitudes for a distributed vaporization region. This comparison indicates excellent amplitude and phase agreement under both stable and unstable operating conditions when amplitudes are small and proper grid resolution is used. As amplitudes get larger, expected nonlinearities are observed. The effect of liquid droplet temperature fluctuations was found to be of critical importance in driving the instabilities of the combustion chamber.

Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yuan, Qigang

2017-08-01

A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.

Stability of surface plastic flow in large strain deformation of metals

NASA Astrophysics Data System (ADS)

Viswanathan, Koushik; Udapa, Anirduh; Sagapuram, Dinakar; Mann, James; Chandrasekar, Srinivasan

We examine large-strain unconstrained simple shear deformation in metals using a model two-dimensional cutting system and high-speed in situ imaging. The nature of the deformation mode is shown to be a function of the initial microstructure state of the metal and the deformation geometry. For annealed metals, which exhibit large ductility and strain hardening capacity, the commonly assumed laminar flow mode is inherently unstable. Instead, the imposed shear is accommodated by a highly rotational flow-sinuous flow-with vortex-like components and large-amplitude folding on the mesoscale. Sinuous flow is triggered by a plastic instability on the material surface ahead of the primary region of shear. On the other hand, when the material is extensively strain-hardened prior to shear, laminar flow again becomes unstable giving way to shear banding. The existence of these flow modes is established by stability analysis of laminar flow. The role of the initial microstructure state in determining the change in stability from laminar to sinuous / shear-banded flows in metals is elucidated. The implications for cutting, forming and wear processes for metals, and to surface plasticity phenomena such as mechanochemical Rehbinder effects are discussed.

Detection of bifurcations in noisy coupled systems from multiple time series

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

Williamson, Mark S., E-mail: m.s.williamson@exeter.ac.uk; Lenton, Timothy M.

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, themore » possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.« less

Detection of bifurcations in noisy coupled systems from multiple time series

NASA Astrophysics Data System (ADS)

Williamson, Mark S.; Lenton, Timothy M.

2015-03-01

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.

Geometry Modeling and Adaptive Control of Air-Breathing Hypersonic Vehicles

NASA Astrophysics Data System (ADS)

Vick, Tyler Joseph

Air-breathing hypersonic vehicles have the potential to provide global reach and affordable access to space. Recent technological advancements have made scramjet-powered flight achievable, as evidenced by the successes of the X-43A and X-51A flight test programs over the last decade. Air-breathing hypersonic vehicles present unique modeling and control challenges in large part due to the fact that scramjet propulsion systems are highly integrated into the airframe, resulting in strongly coupled and often unstable dynamics. Additionally, the extreme flight conditions and inability to test fully integrated vehicle systems larger than X-51 before flight leads to inherent uncertainty in hypersonic flight. This thesis presents a means to design vehicle geometries, simulate vehicle dynamics, and develop and analyze control systems for hypersonic vehicles. First, a software tool for generating three-dimensional watertight vehicle surface meshes from simple design parameters is developed. These surface meshes are compatible with existing vehicle analysis tools, with which databases of aerodynamic and propulsive forces and moments can be constructed. A six-degree-of-freedom nonlinear dynamics simulation model which incorporates this data is presented. Inner-loop longitudinal and lateral control systems are designed and analyzed utilizing the simulation model. The first is an output feedback proportional-integral linear controller designed using linear quadratic regulator techniques. The second is a model reference adaptive controller (MRAC) which augments this baseline linear controller with an adaptive element. The performance and robustness of each controller are analyzed through simulated time responses to angle-of-attack and bank angle commands, while various uncertainties are introduced. The MRAC architecture enables the controller to adapt in a nonlinear fashion to deviations from the desired response, allowing for improved tracking performance, stability, and robustness.

Adam Smith's invisible hand is unstable: physics and dynamics reasoning applied to economic theorizing

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2002-11-01

Neo-classical economic theory is based on the postulated, nonempiric notion of utility. Neo-classical economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics, however, a utility function generally does not exist mathematically due to nonintegrability. Price as a function of demand does not exist and all equilibria are unstable. Qualitatively, and empirically, the neo-classical prediction of price as a function of demand describes neither consumer nor trader demand. We also discuss five inconsistent definitions of equilibrium used in economics and finance, only one of which is correct, and then explain the fallacy in the economists’ notion of ‘temporary price equilibria’.

Instabilities in large economies: aggregate volatility without idiosyncratic shocks

NASA Astrophysics Data System (ADS)

Bonart, Julius; Bouchaud, Jean-Philippe; Landier, Augustin; Thesmar, David

2014-10-01

We study a dynamical model of interconnected firms which allows for certain market imperfections and frictions, restricted here to be myopic price forecasts and slow adjustment of production. Whereas the standard rational equilibrium is still formally a stationary solution of the dynamics, we show that this equilibrium becomes linearly unstable in a whole region of parameter space. When agents attempt to reach the optimal production target too quickly, coordination breaks down and the dynamics becomes chaotic. In the unstable, ‘turbulent’ phase, the aggregate volatility of the total output remains substantial even when the amplitude of idiosyncratic shocks goes to zero or when the size of the economy becomes large. In other words, crises become endogenous. This suggests an interesting resolution of the ‘small shocks, large business cycles’ puzzle.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

NASA Astrophysics Data System (ADS)

Pier, Benoît; Govindarajan, Rama

2018-03-01

The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.

Dynamic stability and handling qualities tests on a highly augmented, statically unstable airplane

NASA Technical Reports Server (NTRS)

Gera, Joseph; Bosworth, John T.

1987-01-01

Initial envelope clearance and subsequent flight testing of a new, fully augmented airplane with an extremely high degree of static instability can place unusual demands on the flight test approach. Previous flight test experience with these kinds of airplanes is very limited or nonexistent. The safe and efficient flight testing may be further complicated by a multiplicity of control effectors that may be present on this class of airplanes. This paper describes some novel flight test and analysis techniques in the flight dynamics and handling qualities area. These techniques were utilized during the initial flight envelope clearance of the X-29A aircraft and were largely responsible for the completion of the flight controls clearance program without any incidents or significant delays.

Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions

NASA Astrophysics Data System (ADS)

Chen, Nan; Majda, Andrew J.

2018-02-01

Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed highly intermittent probability density functions (PDFs) of complex systems in turbulence, neuroscience and excitable media. In this article, efficient statistically accurate algorithms are developed for solving both the transient and the equilibrium solutions of Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. The algorithms involve a hybrid strategy that requires only a small number of ensembles. Here, a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious non-parametric Gaussian kernel density estimation in the remaining low-dimensional subspace. Particularly, the parametric method provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace and is therefore computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from traditional particle methods, each conditional Gaussian distribution here covers a significant portion of the high-dimensional PDF. Therefore a small number of ensembles is sufficient to recover the full PDF, which overcomes the curse of dimensionality. Notably, the mixture distribution has significant skill in capturing the transient behavior with fat tails of the high-dimensional non-Gaussian PDFs, and this facilitates the algorithms in accurately describing the intermittency and extreme events in complex turbulent systems. It is shown in a stringent set of test problems that the method only requires an order of O (100) ensembles to successfully recover the highly non-Gaussian transient PDFs in up to 6 dimensions with only small errors.

Neural network modelling and dynamical system theory: are they relevant to study the governing dynamics of association football players?

PubMed

Dutt-Mazumder, Aviroop; Button, Chris; Robins, Anthony; Bartlett, Roger

2011-12-01

Recent studies have explored the organization of player movements in team sports using a range of statistical tools. However, the factors that best explain the performance of association football teams remain elusive. Arguably, this is due to the high-dimensional behavioural outputs that illustrate the complex, evolving configurations typical of team games. According to dynamical system analysts, movement patterns in team sports exhibit nonlinear self-organizing features. Nonlinear processing tools (i.e. Artificial Neural Networks; ANNs) are becoming increasingly popular to investigate the coordination of participants in sports competitions. ANNs are well suited to describing high-dimensional data sets with nonlinear attributes, however, limited information concerning the processes required to apply ANNs exists. This review investigates the relative value of various ANN learning approaches used in sports performance analysis of team sports focusing on potential applications for association football. Sixty-two research sources were summarized and reviewed from electronic literature search engines such as SPORTDiscus, Google Scholar, IEEE Xplore, Scirus, ScienceDirect and Elsevier. Typical ANN learning algorithms can be adapted to perform pattern recognition and pattern classification. Particularly, dimensionality reduction by a Kohonen feature map (KFM) can compress chaotic high-dimensional datasets into low-dimensional relevant information. Such information would be useful for developing effective training drills that should enhance self-organizing coordination among players. We conclude that ANN-based qualitative analysis is a promising approach to understand the dynamical attributes of association football players.

Far-from-Equilibrium Field Theory of Many-Body Quantum Spin Systems: Prethermalization and Relaxation of Spin Spiral States in Three Dimensions

NASA Astrophysics Data System (ADS)

Babadi, Mehrtash; Demler, Eugene; Knap, Michael

2015-10-01

We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-1 /2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1 /N expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild et al., Phys. Rev. Lett. 113, 147205 (2014), 10.1103/PhysRevLett.113.147205].

The decay process of rotating unstable systems through the passage time distribution

NASA Astrophysics Data System (ADS)

Jiménez-Aquino, J. I.; Cortés, Emilio; Aquino, N.

2001-05-01

In this work we propose a general scheme to characterize, through the passage time distribution, the decay process of rotational unstable systems in the presence of external forces of large amplitude. The formalism starts with a matricial Langevin type equation formulated in the context of two dynamical representations given, respectively, by the vectors x and y, both related by a time dependent rotation matrix. The transformation preserves the norm of the vector and decouples the set of dynamical equations in the transformed space y. We study the dynamical characterization of the systems of two variables and show that the statistical properties of the passage time distribution are essentially equivalent in both dynamics. The theory is applied to the laser system studied in Dellunde et al. (Opt. Commun. 102 (1993) 277), where the effect of large injected signals on the transient dynamics of the laser has been studied in terms of complex electric field. The analytical results are compared with numerical simulation.

Dynamic Stability Testing of the Genesis Sample Return Capsule

NASA Technical Reports Server (NTRS)

Cheatwood, F. McNeil; Winchenbach, Gerald L.; Hathaway, Wayne; Chapman, Gary

2000-01-01

This paper documents a series of free flight tests of a scale model of the Genesis Sample Return Capsule. These tests were conducted in the Aeroballistic Research Facility (ARF), located at Eglin AFB, FL, during April 1999 and were sponsored by NASA Langley Research Center. Because these blunt atmospheric entry shapes tend to experience small angle of attack dynamic instabilities (frequently leading to limit cycle motions), the primary purpose of the present tests was to determine the dynamic stability characteristics of the Genesis configuration. The tests were conducted over a Mach number range of 1.0 to 4.5. The results for this configuration indicate that the models were dynamically unstable at low angles of attack for all Mach numbers tested. At Mach numbers below 2.5, the models were also unstable at the higher angles of attack (above 15 deg), and motion amplitudes of up to 40 deg were experienced. Above Mach 2.5, the models were dynamically stable at the higher angles of attack.

Dynamic Fracture Simulations of Explosively Loaded Cylinders

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

Arthur, Carly W.; Goto, D. M.

2015-11-30

This report documents the modeling results of high explosive experiments investigating dynamic fracture of steel (AerMet® 100 alloy) cylinders. The experiments were conducted at Lawrence Livermore National Laboratory (LLNL) during 2007 to 2008 [10]. A principal objective of this study was to gain an understanding of dynamic material failure through the analysis of hydrodynamic computer code simulations. Two-dimensional and three-dimensional computational cylinder models were analyzed using the ALE3D multi-physics computer code.

Instabilities in Englert-type supergravity solutions

NASA Astrophysics Data System (ADS)

Page, Don N.; Pope, C. N.

1984-09-01

We show that all eleven-dimensional Englert-type supergravity solutions (in which the four-index field has internal components) constructed from internal spaces M7 having two or more Killing spinors, are unstable. Permanent address: Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom.

Elliptical Instability of Rotating Von Karman Street

NASA Astrophysics Data System (ADS)

Stegner, A.; Pichon, T.; Beunier, M.

Clouds often reveal a meso-scale vortex shedding in the wake of mountainous islands. Unlike the classical bi-dimensional Von-Karman street, these observed vortex street are affected by the earth rot ation and vertical stratification. Theses effects could induce a selective destabilization of anticyclonic vortices. It is well known that inertial instability (also called centrifugal instability) induce a three- dimensional destabilization of anticyclonic structures when the absolute vorticity is larger than the local Coriolis parameter. However, we have shown, by the mean of laboratory experiments, that it is a different type of instability which is mainly responsible for asymmetric rotating Von-Karman street. A serie of experiments were performed to study the wake of a cylinder in a rotating fluid, at medium Reynolds number and order one Rossby number. We have shown that the vertical structure of unstable anticyclonic vortices is characteristic of an elliptical instability. Besides, unlike the inertial instability, the vertical unstable wavelength depends on the Rossby number.

Oxidation behavior of TD-NiCr in a dynamic high temperature environment

NASA Technical Reports Server (NTRS)

Tenney, D. R.; Young, C. T.; Herring, H. W.

1974-01-01

The oxidation behavior of TD-NiCr has been studied in static and high-speed flowing air environments at 1100 and 1200 C. It has been found that the stable oxide morphologies formed on the specimens exposed to the static and dynamic environments were markedly different. The faceted crystal morphology characteristic of static oxidation was found to be unstable under high-temperature, high-speed flow conditions and was quickly replaced by a porous NiO 'mushroom' type structure. Also, it was found that the rate of formation of CrO3 from Cr2O3 was greatly enhanced by high gas velocity conditions. The stability of Cr2-O3 was found to be greatly improved by the presence of an outer NiO layer, even though the NiO layer was very porous. An oxidation model is proposed to explain the observed microstructures and overall oxidation behavior of TD-NiCr alloys.

Three-dimensional envelope instability in periodic focusing channels

NASA Astrophysics Data System (ADS)

Qiang, Ji

2018-03-01

The space-charge driven envelope instability can be of great danger in high intensity accelerators and was studied using a two-dimensional (2D) envelope model and three-dimensional (3D) macroparticle simulations before. In this paper, we study the instability for a bunched beam using a three-dimensional envelope model in a periodic solenoid and radio-frequency (rf) focusing channel and a periodic quadrupole and rf focusing channel. This study shows that when the transverse zero current phase advance is below 90 ° , the beam envelope can still become unstable if the longitudinal zero current phase advance is beyond 90 ° . For the transverse zero current phase advance beyond 90 ° , the instability stopband width becomes larger with the increase of the longitudinal focusing strength and even shows different structure from the 2D case when the longitudinal zero current phase advance is beyond 90 ° . Breaking the symmetry of two longitudinal focusing rf cavities and the symmetry between the horizontal focusing and the vertical focusing in the transverse plane in the periodic quadrupole and rf channel makes the instability stopband broader. This suggests that a more symmetric accelerator lattice design might help reduce the range of the envelope instability in parameter space.

An explanation of unstable wetting fronts in soils

NASA Astrophysics Data System (ADS)

Steenhuis, Tammo; Parlange, Jean-Yves; Kung, Samuel; Stoof, Cathelijne; Baver, Christine

2016-04-01

Despite the findings of Raats on unstable wetting front almost a half a century ago, simulating wetting fronts in soils is still an area of active research. One of the critical questions currently is whether Darcy law is valid at the wetting front. In this talk, we pose that in many cases for dry soils, Darcy's law does not apply because the pressure field across the front is not continuous. Consequently, the wetting front pressure is not dependent on the pressure ahead of the front but is determined by the radius of water meniscuses and the dynamic contact angle of the water. If we further assume since the front is discontinuous, that water flows at one pore at the time, then by using the modified Hoffman relationship - relating the dynamic contact angle to the pore water velocity - we find the elevated pressures at the wetting front typical for unstable flows that are similar to those observed experimentally in small diameter columns. The theory helps also explain the funnel flow phenomena observed in layered soils.

Enhanced Air Stability in REPb3 (RE = Rare Earths) by Dimensional Reduction Mediated Valence Transition.

PubMed

Subbarao, Udumula; Sarkar, Sumanta; Jana, Rajkumar; Bera, Sourav S; Peter, Sebastian C

2016-06-06

We conceptually selected the compounds REPb3 (RE = Eu, Yb), which are unstable in air, and converted them to the stable materials in ambient conditions by the chemical processes of "nanoparticle formation" and "dimensional reduction". The nanoparticles and the bulk counterparts were synthesized by the solvothermal and high-frequency induction furnace heating methods, respectively. The reduction of the particle size led to the valence transition of the rare earth atom, which was monitored through magnetic susceptibility and X-ray absorption near edge spectroscopy (XANES) measurements. The stability was checked by X-ray diffraction and thermogravimetric analysis over a period of seven months in oxygen and argon atmospheres and confirmed by XANES. The nanoparticles showed outstanding stability toward aerial oxidation over a period of seven months compared to the bulk counterpart, as the latter one is more prone to the oxidation within a few days.

Overview of Orion Crew Module and Launch Abort Vehicle Dynamic Stability

NASA Technical Reports Server (NTRS)

Owens, Donald B.; Aibicjpm. Vamessa V.

2011-01-01

With the retirement of the Space Shuttle, NASA is designing a new spacecraft, called Orion, to fly astronauts to low earth orbit and beyond. Characterization of the dynamic stability of the Orion spacecraft is important for the design of the spacecraft and trajectory construction. Dynamic stability affects the stability and control of the Orion Crew Module during re-entry, especially below Mach = 2.0 and including flight under the drogues. The Launch Abort Vehicle is affected by dynamic stability as well, especially during the re-orientation and heatshield forward segments of the flight. The dynamic stability was assessed using the forced oscillation technique, free-to-oscillate, ballistic range, and sub-scale free-flight tests. All of the test techniques demonstrated that in heatshield-forward flight the Crew Module and Launch Abort Vehicle are dynamically unstable in a significant portion of their flight trajectory. This paper will provide a brief overview of the Orion dynamic aero program and a high-level summary of the dynamic stability characteristics of the Orion spacecraft.

Three Dimensional Simulations of Multiphase Flows Using a Lattice Boltzmann Method Suitable for High Density Ratios - 12126

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

Gokaltun, Seckin; McDaniel, Dwayne; Roelant, David

2012-07-01

Multiphase flows involving gas and liquid phases can be observed in engineering operations at various Department of Energy sites, such as mixing of slurries using pulsed-air mixers and hydrogen gas generation in liquid waste tanks etc. The dynamics of the gas phase in the liquid domain play an important role in the mixing effectiveness of the pulsed-air mixers or in the level of gas pressure build-up in waste tanks. To understand such effects, computational fluid dynamics methods (CFD) can be utilized by developing a three-dimensional computerized multiphase flow model that can predict accurately the behavior of gas motion inside liquid-filledmore » tanks by solving the governing mathematical equations that represent the physics of the phenomena. In this paper, such a CFD method, lattice Boltzmann method (LBM), is presented that can model multiphase flows accurately and efficiently. LBM is favored over traditional Navier-Stokes based computational models since interfacial forces are handled more effectively in LBM. The LBM is easier to program, more efficient to solve on parallel computers, and has the ability to capture the interface between different fluid phases intrinsically. The LBM used in this paper can solve for the incompressible and viscous flow field in three dimensions, while at the same time, solve the Cahn-Hillard equation to track the position of the gas-liquid interface specifically when the density and viscosity ratios between the two fluids are high. This feature is of primary importance since the previous LBM models proposed for multiphase flows become unstable when the density ratio is larger than 10. The ability to provide stable and accurate simulations at large density ratios becomes important when the simulation case involves fluids such as air and water with a density ratio around 1000 that are common to many engineering problems. In order to demonstrate the capability of the 3D LBM method at high density ratios, a static bubble simulation is conducted to solve for the pressure difference between the inside and outside of a gas bubble in a liquid domain. Once the results show that the method is in agreement with the Laplace law, buoyant bubble simulations are conducted. The initial results obtained for bubble shape during the rising process was found to be in agreement with the theoretical expectations. (authors)« less

Dynamic correlations in the highly dilute 2D electron liquid: Loss function, critical wave vector and analytic plasmon dispersion

NASA Astrophysics Data System (ADS)

Drachta, Jürgen T.; Kreil, Dominik; Hobbiger, Raphael; Böhm, Helga M.

2018-03-01

Correlations, highly important in low-dimensional systems, are known to decrease the plasmon dispersion of two-dimensional electron liquids. Here we calculate the plasmon properties, applying the 'Dynamic Many-Body Theory', accounting for correlated two-particle-two-hole fluctuations. These dynamic correlations are found to significantly lower the plasmon's energy. For the data obtained numerically, we provide an analytic expression that is valid across a wide range both of densities and of wave vectors. Finally, we demonstrate how this can be invoked in determining the actual electron densities from measurements on an AlGaAs quantum well.

Zeno effect in spontaneous decay induced by coupling to an unstable level

NASA Astrophysics Data System (ADS)

Luis, Alfredo

2001-09-01

A metastable atomic level can be rendered unstable in a controllable way by coupling it to a decaying state. In this work we carry out a full dynamical analysis of the Zeno effect in this kind of unstable systems, comparing it to the inhibition of purely coherent Rabi oscillations. Simple and experimentally feasible measuring strategies involving three atomic levels are considered. It is shown that this induced decay is actually an example of a partial Zeno effect so that the observed evolution results from the competition of two Zeno effects. We also show that a three-level scheme can display both coherent, incoherent, and anti-Zeno effects.

Universality classes for unstable crystal growth

NASA Astrophysics Data System (ADS)

Biagi, Sofia; Misbah, Chaouqi; Politi, Paolo

2014-06-01

Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with nonequilibrium problems, however, the distinction in universality classes is not as clear and few are the examples, such as phase separation and kinetic roughening, for which universality has allowed to classify results in a general spirit. Here we focus on an out-of-equilibrium case, unstable crystal growth, lying in between phase ordering and pattern formation. We consider a well-established 2+1-dimensional family of continuum nonlinear equations for the local height h(x,t) of a crystal surface having the general form ∂th(x,t)=-∇.[j(∇h)+∇(∇2h)]: j (∇h) is an arbitrary function, which is linear for small ∇h, and whose structure expresses instabilities which lead to the formation of pyramidlike structures of planar size L and height H. Our task is the choice and calculation of the quantities that can operate as critical exponents, together with the discussion of what is relevant or not to the definition of our universality class. These aims are achieved by means of a perturbative, multiscale analysis of our model, leading to phase diffusion equations whose diffusion coefficients encapsulate all relevant information on dynamics. We identify two critical exponents: (i) the coarsening exponent, n, controlling the increase in time of the typical size of the pattern, L ˜tn; (ii) the exponent β, controlling the increase in time of the typical slope of the pattern, M ˜tβ, where M ≈H/L. Our study reveals that there are only two different universality classes, according to the presence (n =1/3, β =0) or the absence (n =1/4, β >0) of faceting. The symmetry of the pattern, as well as the symmetry of the surface mass current j (∇h) and its precise functional form, is irrelevant. Our analysis seems to support the idea that also space dimensionality is irrelevant.

Cross Flow Effects on Glaze Ice Roughness Formation

NASA Technical Reports Server (NTRS)

Tsao, Jen-Ching

2004-01-01

The present study examines the impact of large-scale cross flow on the creation of ice roughness elements on the leading edge of a swept wing under glaze icing conditions. A three-dimensional triple-deck structure is developed to describe the local interaction of a 3 D air boundary layer with ice sheets and liquid films. A linear stability analysis is presented here. It is found that, as the sweep angle increases, the local icing instabilities enhance and the most linearly unstable modes are strictly three dimensional.

High speed, precision motion strategies for lightweight structures

NASA Technical Reports Server (NTRS)

Book, Wayne J.

1989-01-01

Research on space telerobotics is summarized. Adaptive control experiments on the Robotic Arm, Large and Flexible (RALF) were preformed and are documented, along with a joint controller design for the Small Articulated Manipulator (SAM), which is mounted on the RALF. A control algorithm is described as a robust decentralized adaptive control based on a bounded uncertainty approach. Dynamic interactions between SAM and RALF are examined. Unstability of the manipulator is studied from the perspective that the inertial forces generated could actually be used to more rapidly damp out the flexible manipulator's vibration. Currently being studied is the modeling of the constrained dynamics of flexible arms.

Learning an intrinsic-variable preserving manifold for dynamic visual tracking.

PubMed

Qiao, Hong; Zhang, Peng; Zhang, Bo; Zheng, Suiwu

2010-06-01

Manifold learning is a hot topic in the field of computer science, particularly since nonlinear dimensionality reduction based on manifold learning was proposed in Science in 2000. The work has achieved great success. The main purpose of current manifold-learning approaches is to search for independent intrinsic variables underlying high dimensional inputs which lie on a low dimensional manifold. In this paper, a new manifold is built up in the training step of the process, on which the input training samples are set to be close to each other if the values of their intrinsic variables are close to each other. Then, the process of dimensionality reduction is transformed into a procedure of preserving the continuity of the intrinsic variables. By utilizing the new manifold, the dynamic tracking of a human who can move and rotate freely is achieved. From the theoretical point of view, it is the first approach to transfer the manifold-learning framework to dynamic tracking. From the application point of view, a new and low dimensional feature for visual tracking is obtained and successfully applied to the real-time tracking of a free-moving object from a dynamic vision system. Experimental results from a dynamic tracking system which is mounted on a dynamic robot validate the effectiveness of the new algorithm.

The effects of bridge exercise on an unstable base of support on lumbar stability and the thickness of the transversus abdominis.

PubMed

Cho, Misuk; Jeon, Hyewon

2013-06-01

[Purpose] We examined the effects of an abdominal drawing-in bridge exercise using a pressure biofeedback unit on different bases on the thickness of trunk and abdominal muscles, and lumbar stability. [Subjects] Thirty healthy young adults (2 males, 28 females) took part in this study. The subjects were randomly and equally assigned to a stable bridge exercise group and an unstable bridge exercise group. [Methods] The subjects performed bridge exercises using an abdominal drawing-in method on a stable base and on an unstable base, and changes in their abdominal muscle thickness and on the stable and on unstable bases lumbar stability were evaluated. [Results] After the intervention, the stable bridge exercise group showed a statistically significantly increased muscle thickness in the transversus abdominis, and the unstable bridge exercise group showed significantly increased muscle thicknesses of the transversus abdominis and internal obliques in static and dynamic lumbar stability. The unstable bridge exercise group showed significant increase after performing the exercise. [Conclusion] Lumbar stability exercise, with the compensation of the lumbar spine minimized, using an abdominal drawing-in method on an unstable support of base is effective and efforts to prevent the compensation may induce a greater exercise effect.

The evolution of chromosomal instability in Chinese hamster cells: a changing picture?

NASA Technical Reports Server (NTRS)

Ponnaiya, B.; Limoli, C. L.; Corcoran, J.; Kaplan, M. I.; Hartmann, A.; Morgan, W. F.

1998-01-01

PURPOSE: To investigate the kinetics of chromosomal instability induced in clones of Chinese hamster cells following X-irradiation. MATERIALS AND METHODS: X-irradiated clones of GM10115, human-hamster hybrid cells containing a single human chromosome 4 (HC4), have been previously established. These clones were defined as unstable if they contained > or = three subpopulations of cells with unique rearrangements of HC4 as detected by FISH. Stable and unstable clones were analysed by FISH and Giemsa staining at various times post-irradiation. RESULTS: While most of the stable clones continued to show chromosomal stability of HC4 over time, one became marginally unstable at approximately 45 population doublings post-irradiation. Clones exhibiting chromosomal instability had one of several fates. Many of the unstable clones were showed similar levels of instability over time. However, one unstable clone became stable with time in culture, while another became even more unstable over time. Cytogenetic analyses of all clones after Giemsa staining indicated that in some clones the hamster chromosomes were rearranged independent of HC4, demonstrating increased frequencies of chromatid breaks and dicentric chromosomes. The majority of the unstable clones also had higher yields of chromatid gaps. CONCLUSIONS: These data demonstrate the dynamic nature of chromosomal instability as measured by two different cytogenetic assays.

A new illusion of projected three-dimensional space

NASA Technical Reports Server (NTRS)

Ellis, Stephen R.; Grunwald, Arthur

1987-01-01

When perspective projections of orbital trajectories plotted in local-vertical local-horizontal coordinates are viewed with certain viewing angles, their appearance becomes perceptually unstable. They often lose their trochoidal appearance and reorganize as helices. This reorganization may be due to the viewer's familiarity with coiled springs.

Dimensionality and entropy of spontaneous and evoked rate activity

NASA Astrophysics Data System (ADS)

Engelken, Rainer; Wolf, Fred

Cortical circuits exhibit complex activity patterns both spontaneously and evoked by external stimuli. Finding low-dimensional structure in population activity is a challenge. What is the diversity of the collective neural activity and how is it affected by an external stimulus? Using concepts from ergodic theory, we calculate the attractor dimensionality and dynamical entropy production of these networks. We obtain these two canonical measures of the collective network dynamics from the full set of Lyapunov exponents. We consider a randomly-wired firing-rate network that exhibits chaotic rate fluctuations for sufficiently strong synaptic weights. We show that dynamical entropy scales logarithmically with synaptic coupling strength, while the attractor dimensionality saturates. Thus, despite the increasing uncertainty, the diversity of collective activity saturates for strong coupling. We find that a time-varying external stimulus drastically reduces both entropy and dimensionality. Finally, we analytically approximate the full Lyapunov spectrum in several limiting cases by random matrix theory. Our study opens a novel avenue to characterize the complex dynamics of rate networks and the geometric structure of the corresponding high-dimensional chaotic attractor. received funding from Evangelisches Studienwerk Villigst, DFG through CRC 889 and Volkswagen Foundation.

Prediction of B1 to B10 phase transition in LuN under pressure: An ab-initio investigation

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

Sahoo, B. D., E-mail: bdsahoo@barc.gov.in; Mukherjee, D.; Joshi, K. D.

2016-05-23

Ab-initio total energy calculations have been performed in lutetium nitride (LuN) as a function of hydrostatic compression to understand the high pressure behavior of this compound. Our calculations predict a phase transition from ambient rocksalt type structure (B1 phase) to a tetragonal structure (B10 phase) at ~ 240 GPa. The phase transition has been identified as first order in nature with volume discontinuity of ~ 6%. The predicted high pressure phase has been found to be stable up to at least 400 GPa, the maximum pressure up to which calculations have been performed.Further, to substantiate the results of static lattice calculations analysismore » of lattice dynamic stability of B1 and B10 phase has been carried out at different pressures. Apart from this, we have analyzed the lattice dynamic stability CsCl type (B2) phase around the 240 GPa, the pressure reported for B1 to B2 transition in previous all-electron calculations by Gupta et al. 2013. We find that the B2 structure is lattice dynamically unstable at this pressure and remains unstable up to ~ 400 GPa, ruling out the possibility of B1 to B2 phase transition at least up to ~ 400 GPa. Further, the theoretically determined equation of state has been utilized to derive various physical quantities such as zero pressure equilibrium volume, bulk modulus, and pressure derivative of bulk modulus of B1 phase at ambient conditions.« less

One Dimensional(1D)-to-2D Crossover of Spin Correlations in the 3D Magnet ZnMn 2O 4

DOE PAGES

Disseler, S. M.; Chen, Y.; Yeo, S.; ...

2015-12-08

In this paper we report on the intriguing evolution of the dynamical spin correlations of the frustrated spinel ZnMn 2O 4. Inelastic neutron scattering and magnetization studies reveal that the dynamical correlations at high temperatures are 1D. At lower temperature, these dynamical correlations become 2D. Surprisingly, the dynamical correlations condense into a quasi 2D Ising-like ordered state, making this a rare observation of two dimensional order on the spinel lattice. Remarkably, 3D ordering is not observed down to temperatures as low as 300 mK. This unprecedented dimensional crossover stems from frustrated exchange couplings due to the huge Jahn-Teller distortions aroundmore » Mn 3+ ions on the spinel lattice.« less

On mass transport in magmatic porosity waves

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.; Rudge, J. F.

2017-12-01

Geochemical analyses of oceanic basalts indicate the mantle is lithologically heterogenous and subject to partial melting. Here we show that porosity waves-which arise naturally in models of buoyancy driven melt migration-transport mass and preserve geochemical signatures, at least partially. Prior studies of tracer transport in one dimensional porosity waves conclude that porosity waves do not transfer mass. However, it is well known that one-dimensional porosity waves are unstable in two and three dimensions and break up into sets of cylindrical or spherical porosity waves. We show that tracer transport in higher dimensional porosity waves is dramatically different than in one dimension. Lateral melt focusing into these high porosity regions leads to melt recirculating in the center of the wave. Melt focusing and recirculation are not resolvable in one dimension where no sustained transport is observed in numerical experiments of solitary porosity waves. In two and three dimensions, the recirculating melt is separated from the background melt-flow field by a circular or spherical dividing streamline and transported with the phase velocity of the porosity wave. The amount of melt focusing that occurs within any given porosity wave, and thus, the extent of the dividing streamline, and resultant volume of transported melt is extremely sensitive to the selection of porosity-permeability and porosity-rheology relationships. Therefore, we present a regime diagram spanning common parameterizations that illustrates the minimum amplitude and phase velocity required for a solitary porosity wave to transport mass as a function of material properties and common parameters used in magma dynamics and mid-ocean ridge models. The realization that solitary waves are capable of sustaining melt transport may require the reinterpretation of previous studies. For example, transport in porosity waves may allow melts that originated from the partial melting of fertile heterogeneities to retain their incompatible trace element signatures as they rise through the mantle. Porosity waves may also provide a mechanism for mixing melts derived from heterogeneities with ambient melts derived from different depths in the mantle.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Exciton Dynamics, Transport, and Annihilation in Atomically Thin Two-Dimensional Semiconductors.

PubMed

Yuan, Long; Wang, Ti; Zhu, Tong; Zhou, Mingwei; Huang, Libai

2017-07-20

Large binding energy and unique exciton fine structure make the transition metal dichalcogenides (TMDCs) an ideal platform to study exciton behaviors in two-dimensional (2D) systems. While excitons in these systems have been extensively researched, there currently lacks a consensus on mechanisms that control dynamics. In this Perspective, we discuss extrinsic and intrinsic factors in exciton dynamics, transport, and annihilation in 2D TMDCs. Intrinsically, dark and bright exciton energy splitting is likely to play a key role in modulating the dynamics. Extrinsically, defect scattering is prevalent in single-layer TMDCs, which leads to rapid picosecond decay and limits exciton transport. The exciton-exciton annihilation process in single-layer TMDCs is highly efficient, playing an important role in the nonradiative recombination rate in the high exciton density regime. Future challenges and opportunities to control exciton dynamics are discussed.

Taylor-Goertler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

NASA Technical Reports Server (NTRS)

Hall, Philip; Bennett, James

1986-01-01

The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.

Penalized gaussian process regression and classification for high-dimensional nonlinear data.

PubMed

Yi, G; Shi, J Q; Choi, T

2011-12-01

The model based on Gaussian process (GP) prior and a kernel covariance function can be used to fit nonlinear data with multidimensional covariates. It has been used as a flexible nonparametric approach for curve fitting, classification, clustering, and other statistical problems, and has been widely applied to deal with complex nonlinear systems in many different areas particularly in machine learning. However, it is a challenging problem when the model is used for the large-scale data sets and high-dimensional data, for example, for the meat data discussed in this article that have 100 highly correlated covariates. For such data, it suffers from large variance of parameter estimation and high predictive errors, and numerically, it suffers from unstable computation. In this article, penalized likelihood framework will be applied to the model based on GPs. Different penalties will be investigated, and their ability in application given to suit the characteristics of GP models will be discussed. The asymptotic properties will also be discussed with the relevant proofs. Several applications to real biomechanical and bioinformatics data sets will be reported. © 2011, The International Biometric Society No claim to original US government works.

Time-Dependent CO[subscript 2] Sorption Hysteresis in a One-Dimensional Microporous Octahedral Molecular Sieve

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

Espinal, Laura; Wong-Ng, Winnie; Kaduk, James A.

2014-09-24

The development of sorbents for next-generation CO{sub 2} mitigation technologies will require better understanding of CO{sub 2}/sorbent interactions. Among the sorbents under consideration are shape-selective microporous molecular sieves with hierarchical pore morphologies of reduced dimensionality. We have characterized the non-equilibrium CO{sub 2} sorption of OMS-2, a well-known one-dimensional microporous octahedral molecular sieve with manganese oxide framework. Remarkably, we find that the degree of CO{sub 2} sorption hysteresis increases when the gas/sorbent system is allowed to equilibrate for longer times at each pressure step. Density functional theory calculations indicate a 'gate-keeping' role of the cation in the tunnel, only allowing CO{submore » 2} molecules to enter fully into the tunnel via a highly unstable transient state when CO{sub 2} loadings exceed 0.75 mmol/g. The energy barrier associated with the gate-keeping effect suggests an adsorption mechanism in which kinetic trapping of CO{sub 2} is responsible for the observed hysteretic behavior.« less

A mechanism for hot-spot generation in a reactive two-dimensional sheared viscous layer

NASA Astrophysics Data System (ADS)

Timms, Robert; Purvis, Richard; Curtis, John P.

2018-05-01

A two-dimensional model for the non-uniform melting of a thin sheared viscous layer is developed. An asymptotic solution is presented for both a non-reactive and a reactive material. It is shown that the melt front is linearly stable to small perturbations in the non-reactive case, but becomes linearly unstable upon introduction of an Arrhenius source term to model the chemical reaction. Results demonstrate that non-uniform melting acts as a mechanism to generate hot spots that are found to be sufficient to reduce the time to ignition when compared with the corresponding one-dimensional model of melting.

A SIMPLE CELLULAR AUTOMATON MODEL FOR HIGH-LEVEL VEGETATION DYNAMICS

EPA Science Inventory

We have produced a simple two-dimensional (ground-plan) cellular automata model of vegetation dynamics specifically to investigate high-level community processes. The model is probabilistic, with individual plant behavior determined by physiologically-based rules derived from a w...

Dynamic Morphologies and Stability of Droplet Interface Bilayers

NASA Astrophysics Data System (ADS)

Guiselin, Benjamin; Law, Jack O.; Chakrabarti, Buddhapriya; Kusumaatmaja, Halim

2018-06-01

We develop a theoretical framework for understanding dynamic morphologies and stability of droplet interface bilayers (DIBs), accounting for lipid kinetics in the monolayers and bilayer, and droplet evaporation due to imbalance between osmotic and Laplace pressures. Our theory quantitatively describes distinct pathways observed in experiments when DIBs become unstable. We find that when the timescale for lipid desorption is slow compared to droplet evaporation, the lipid bilayer will grow and the droplets approach a hemispherical shape. In contrast, when lipid desorption is fast, the bilayer area will shrink and the droplets eventually detach. Our model also suggests there is a critical size below which DIBs can become unstable, which may explain experimental difficulties in miniaturizing the DIB platform.

Monitoring Unstable Glaciers with Seismic Noise Interferometry

NASA Astrophysics Data System (ADS)

Preiswerk, L. E.; Walter, F.

2016-12-01

Gravity-driven glacier instabilities are a threat to human infrastructure in alpine terrain, and this hazard is likely to increase with future changes in climate. Seismometers have been used previously on hazardous glaciers to monitor the natural englacial seismicity. In some situations, an increase in "icequake" activity may indicate fracture growth and thus an imminent major break-off. However, without independent constraints on unstable volumes, such mere event counting is of little use. A promising new approach to monitor unstable masses in Alpine terrain is coda wave interferometry of ambient noise. While already established in the solid earth, application to glaciers is not straightforward, because the lack of inhomogeneities typically suppresses seismic coda waves in glacier ice. Only glaciers with pervasive crevasses provide enough scattering to generate long codas. This is requirement is likely met for highly dynamic unstable glaciers. Here, we report preliminary results from a temporary 5-station on-ice array of seismometers (corner frequencies: 1 Hz, array aperture: 500m) on Bisgletscher (Switzerland). The seismometers were deployed in shallow boreholes, directly above the unstable tongue of the glacier. In the frequency band 4-12 Hz, we find stable noise cross-correlations, which in principle allows monitoring on a subdaily scale. The origin and the source processes of the ambient noise in these frequencies are however uncertain. As a first step, we evaluate the stability of the sources in order to separate effects of changing source parameters from changes of englacial properties. Since icequakes occurring every few seconds may dominate the noise field, we compare their temporal and spatial occurrences with the cross-correlation functions (stability over time, the asymmetry between causal and acausal parts of the cross-correlation functions) as well as with results from beamforming to assess the influence of these transient events on the noise field.

Observations of supra-arcade fans: instabilities at the head of reconnection jets

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

Innes, D. E.; Guo, L.-J.; Schmit, D.

2014-11-20

Supra-arcade fans are bright, irregular regions of emission that develop during eruptive flares above flare arcades. The underlying flare arcades are thought to be a consequence of magnetic reconnection along a current sheet in the corona. At the same time, theory predicts plasma jets from the reconnection sites which are extremely difficult to observe directly because of their low densities. It has been suggested that the dark supra-arcade downflows (SADs) seen falling through supra-arcade fans may be low-density jet plasma. The head of a low-density jet directed toward higher-density plasma would be Rayleigh-Taylor unstable, and lead to the development ofmore » rapidly growing low- and high-density fingers along the interface. Using Solar Dynamics Observatory/Atmospheric Imaging Assembly 131 Å images, we show details of SADs seen from three different orientations with respect to the flare arcade and current sheet, and highlight features that have been previously unexplained, such as the splitting of SADs at their heads, but are a natural consequence of instabilities above the arcade. Comparison with three-dimensional magnetohydrodynamic simulations suggests that SADs are the result of secondary instabilities of the Rayleigh-Taylor type in the exhaust of reconnection jets.« less

One-dimensional Turbulence Models of Type I X-ray Bursts

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

Hou, Chen

Type I X-ray bursts are caused by thermonuclear explosions occurring on the surface of an accreting neutron star in a binary star system. Observations and simulations of these phenomena are of great importance for understanding the fundamental properties of neutron stars and dense matter because the equation of state for cold dense matter can be constrained by the mass-radius relationship of neutron stars. During the bursts, turbulence plays a key role in mixing the fuels and driving the unstable nuclear burning process. This dissertation presents one-dimensional models of photospheric radius expansion bursts with a new approach to simulate turbulent advection.more » Compared with the traditional mixing length theory, the one-dimensional turbulence (ODT) model represents turbulent motions by a sequence of maps that are generated according to a stochastic process. The light curves I obtained with the ODT models are in good agreement with those of the KEPLER model in which the mixing length theory and various diffusive processes are applied. The abundance comparison, however, indicates that the differences in turbulent regions and turbulent diffusivities result in more 12C survival during the bursts in the ODT models, which can make a difference in the superbursts phenomena triggered by unstable carbon burning.« less

Electrostatic wave modulation in collisional pair-ion plasmas

NASA Astrophysics Data System (ADS)

Sikdar, Arnab; Adak, Ashish; Ghosh, Samiran; Khan, Manoranjan

2018-05-01

The effects of ion-neutral collision on the electrostatic wave packets in the absence of the magnetic field in a pair-ion plasma have been investigated. Considering a two-fluid plasma model with the help of the standard perturbation technique, two distinct electrostatic modes have been observed, namely, a low-frequency ion acoustic mode and a high-frequency ion plasma mode. The dynamics of the modulated wave is governed by a damped nonlinear Schrödinger equation. Damping of the soliton occurs due to the ion-neutral collision. The analytical and numerical investigation reveals that the ion acoustic mode is both stable and unstable, which propagates in the form of dark solitons and bright solitons, respectively, whereas the ion plasma mode is unstable, propagating in the form of a bright soliton. Results are discussed in the context of the fullerene pair-ion plasma experiments.

Numerical simulations of thermoacoustic waves in transcritical fluids employing the spectral difference approach

NASA Astrophysics Data System (ADS)

Scalo, Carlo; Migliorino, Mario Tindaro; Chapelier, Jean-Baptiste

2017-11-01

We investigate the stability properties of thermoacoustically unstable planar waves in transcritical fluids via high-fidelity Navier-Stokes simulations based on a Spectral Difference (SD) discretization coupled with the Peng-Robinson equation of state and Chung's method for the fluid transport properties. A canonical thermoacoustically unstable standing-wave resonator filled with supercritical CO2 kept in pseudoboiling conditions in the stack is considered. Real fluid effects near the critical point are shown to boost thermoacoustic energy production, as also confirmed by companion eigenvalue analysis supporting the closure of the acoustic energy budgets. A kink in the eigenmode shape is observed at the location of pseudo phase change, consistent with the abrupt change in base impedance. The current study demonstrates a transformative approach to thermoacoustic energy generation, exploiting otherwise unwanted fluid dynamics instabilities commonly observed in aeronautical applications employing transcritical fluids.

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

PubMed Central

Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.

2016-01-01

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics. PMID:27991513

Motion stability of the magnetic levitation and suspension with YBa2Cu3O7-x high-Tc superconducting bulks and NdFeB magnets

NASA Astrophysics Data System (ADS)

Li, Jipeng; Zheng, Jun; Huang, Huan; Li, Yanxing; Li, Haitao; Deng, Zigang

2017-10-01

The flux pinning effect of YBa2Cu3O7-x high temperature superconducting (HTS) bulk can achieve self-stable levitation over a permanent magnet or magnet array. Devices based on this phenomenon have been widely developed. However, the self-stable flux pinning effect is not unconditional, under disturbances, for example. To disclose the roots of this amazing self-stable levitation phenomenon in theory, mathematical and mechanical calculations using Lyapunov's stability theorem and the Hurwitz criterion were performed under the conditions of magnetic levitation and suspension of HTS bulk near permanent magnets in Halbach array. It is found that the whole dynamical system, in the case of levitation, has only one equilibrium solution, and the singular point is a stable focus. In the general case of suspension, the system has two singular points: one is a stable focus, and the other is an unstable saddle. With the variation of suspension force, the two first-order singular points mentioned earlier will get closer and closer, and finally degenerate to a high-order singular point, which means the stable region gets smaller and smaller, and finally vanishes. According to the center manifold theorem, the high-order singular point is unstable. With the interaction force varying, the HTS suspension dynamical system undergoes a saddle-node bifurcation. Moreover, a deficient damping can also decrease the stable region. These findings, together with existing experiments, could enlighten the improvement of HTS devices with strong anti-interference ability.

Auditory sensitivity may require dynamically unstable spike generators: evidence from a model of electrical stimulation.

PubMed

O'Gorman, David E; Colburn, H Steven; Shera, Christopher A

2010-11-01

The response of the auditory nerve to electrical stimulation is highly sensitive to small modulations (<0.5%). This report demonstrates that dynamical instability (i.e., a positive Lyapunov exponent) can account for this sensitivity in a modified FitzHugh-Nagumo model of spike generation, so long as the input noise is not too large. This finding suggests both that spike generator instability is necessary to account for auditory nerve sensitivity and that the amplitude of physiological noise, such as that produced by the random behavior of voltage-gated sodium channels, is small. Based on these results with direct electrical stimulation, it is hypothesized that spike generator instability may be the mechanism that reconciles high sensitivity with the cross-fiber independence observed under acoustic stimulation.

Ab initio description of the first stages of laser-induced ultra-fast nonthermal melting of InSb

NASA Astrophysics Data System (ADS)

Zijlstra, E. S.; Walkenhorst, J.; Gilfert, C.; Sippel, C.; Töws, W.; Garcia, M. E.

2008-12-01

Using first principles, all-electron calculations and dynamical simulations we study the behavior of solid InSb immediately after intense femtosecond excitation. First, we determine the laser-excited potential energy surfaces with high accuracy for different electronic temperatures (corresponding to different laser fluences). Then, we demonstrate that, although most phonon modes become only slightly softened even for high electron temperatures, the transverse acoustic modes at the boundary of the Brillouin zone undergo dramatic changes and become unstable. This is the origin of nonthermal melting. Based on these results, the dynamics during the first hundreds of femtoseconds after laser excitation can be unambiguously elucidated. Our results are in agreement with recent experiments and support the predictions made by Stampfli and Bennemann for silicon.

Four dimensional material movies: High speed phase-contrast tomography by backprojection along dynamically curved paths.

PubMed

Ruhlandt, A; Töpperwien, M; Krenkel, M; Mokso, R; Salditt, T

2017-07-26

We present an approach towards four dimensional (4d) movies of materials, showing dynamic processes within the entire 3d structure. The method is based on tomographic reconstruction on dynamically curved paths using a motion model estimated by optical flow techniques, considerably reducing the typical motion artefacts of dynamic tomography. At the same time we exploit x-ray phase contrast based on free propagation to enhance the signal from micron scale structure recorded with illumination times down to a millisecond (ms). The concept is demonstrated by observing the burning process of a match stick in 4d, using high speed synchrotron phase contrast x-ray tomography recordings. The resulting movies reveal the structural changes of the wood cells during the combustion.

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

Coastal wetlands, sea level, and the dimensions of geomorphic resilience

NASA Astrophysics Data System (ADS)

Phillips, Jonathan D.

2018-03-01

Geomorphic system resilience is often perceived as an intrinsic property of system structure and interactions but is also related to idiosyncratic place and history factors. The importance of geographical and historical circumstances makes it difficult to generate categorical statements about geomorphic resilience. However, network-based analyses of system structure can be used to determine the dynamical stability (= resilience) based on generally applicable relationships and to determine scenarios of stability or instability. These provide guidelines for assessing place and history factors to assess resilience. A model of coastal wetlands is analyzed, based on interactions among relative sea level, wetland surface elevation, hydroperiod, vegetation, and sedimentation. The system is generally (but not always) dynamically unstable and non-resilient. Because of gradients of environmental factors and patchy distributions of microtopography and vegetation, a coastal wetland landscape may have extensive local variations in stability/resilience and in the key relationships that trigger instabilities. This is illustrated by a case study where dynamically unstable fragmentation is found in two nearby coastal wetlands in North Carolina's Neuse River estuary-Otter Creek Mouth and Anderson Creek. Neither is keeping pace with relative sea level rise, and both show unstable state transitions within the wetland system; but locally stable relationships exist within the wetland systems.

Use of dynamic 3-dimensional transvaginal and transrectal ultrasonography to assess posterior pelvic floor dysfunction related to obstructed defecation.

PubMed

Murad-Regadas, Sthela M; Regadas Filho, Francisco Sergio Pinheiro; Regadas, Francisco Sergio Pinheiro; Rodrigues, Lusmar Veras; de J R Pereira, Jacyara; da S Fernandes, Graziela Olivia; Dealcanfreitas, Iris Daiana; Mendonca Filho, Jose Jader

2014-02-01

New ultrasound techniques may complement current diagnostic tools, and combined techniques may help to overcome the limitations of individual techniques for the diagnosis of anorectal dysfunction. A high degree of agreement has been demonstrated between echodefecography (dynamic 3-dimensional anorectal ultrasonography) and conventional defecography. Our aim was to evaluate the ability of a combined approach consisting of dynamic 3-dimensional transvaginal and transrectal ultrasonography by using a 3-dimensional biplane endoprobe to assess posterior pelvic floor dysfunctions related to obstructed defecation syndrome in comparison with echodefecography. This was a prospective, observational cohort study conducted at a tertiary-care hospital. Consecutive female patients with symptoms of obstructed defecation were eligible. Each patient underwent assessment of posterior pelvic floor dysfunctions with a combination of dynamic 3-dimensional transvaginal and transrectal ultrasonography by using a biplane transducer and with echodefecography. Kappa (κ) was calculated as an index of agreement between the techniques. Diagnostic accuracy (sensitivity, specificity, and positive and negative predictive values) of the combined technique in detection of posterior dysfunctions was assessed with echodefecography as the standard for comparison. A total of 33 women were evaluated. Substantial agreement was observed regarding normal relaxation and anismus. In detecting the absence or presence of rectocele, the 2 methods agreed in all cases. Near-perfect agreement was found for rectocele grade I, grade II, and grade III. Perfect agreement was found for entero/sigmoidocele, with near-perfect agreement for rectal intussusception. Using echodefecography as the standard for comparison, we found high diagnostic accuracy of transvaginal and transrectal ultrasonography in the detection of posterior dysfunctions. This combined technique should be compared with other dynamic techniques and validated with conventional defecography. Dynamic 3-dimensional transvaginal and transrectal ultrasonography is a simple and fast ultrasound technique that shows strong agreement with echodefecography and may be used as an alternative method to assess patients with obstructed defecation syndrome.

Gas clump formation via thermal instability in high-redshift dwarf galaxy mergers

NASA Astrophysics Data System (ADS)

Arata, Shohei; Yajima, Hidenobu; Nagamine, Kentaro

2018-04-01

Star formation in high-redshift dwarf galaxies is a key to understand early galaxy evolution in the early Universe. Using the three-dimensional hydrodynamics code GIZMO, we study the formation mechanism of cold, high-density gas clouds in interacting dwarf galaxies with halo masses of ˜3 × 107 M⊙, which are likely to be the formation sites of early star clusters. Our simulations can resolve both the structure of interstellar medium on small scales of ≲ 0.1 pc and the galactic disc simultaneously. We find that the cold gas clouds form in the post-shock region via thermal instability due to metal-line cooling, when the cooling time is shorter than the galactic dynamical time. The mass function of cold clouds shows almost a power-law initially with an upper limit of thermally unstable scale. We find that some clouds merge into more massive ones with ≳104 M⊙ within ˜ 2 Myr. Only the massive cold clouds with ≳ 103 M⊙ can keep collapsing due to gravitational instability, resulting in the formation of star clusters. We find that the clump formation is more efficient in the prograde-prograde merger than the prograde-retrograde case due to the difference in the degree of shear flow. In addition, we investigate the dependence of cloud mass function on metallicity and H2 abundance, and show that the cases with low metallicities (≲10-2 Z⊙) or high H2 abundance (≳10-3) cannot form massive cold clouds with ≳103 M⊙.

Electromechanical vortex filaments during cardiac fibrillation

NASA Astrophysics Data System (ADS)

Christoph, J.; Chebbok, M.; Richter, C.; Schröder-Schetelig, J.; Bittihn, P.; Stein, S.; Uzelac, I.; Fenton, F. H.; Hasenfuß, G.; Gilmour, R. F., Jr.; Luther, S.

2018-03-01

The self-organized dynamics of vortex-like rotating waves, which are also known as scroll waves, are the basis of the formation of complex spatiotemporal patterns in many excitable chemical and biological systems. In the heart, filament-like phase singularities that are associated with three-dimensional scroll waves are considered to be the organizing centres of life-threatening cardiac arrhythmias. The mechanisms that underlie the onset, maintenance and control of electromechanical turbulence in the heart are inherently three-dimensional phenomena. However, it has not previously been possible to visualize the three-dimensional spatiotemporal dynamics of scroll waves inside cardiac tissues. Here we show that three-dimensional mechanical scroll waves and filament-like phase singularities can be observed deep inside the contracting heart wall using high-resolution four-dimensional ultrasound-based strain imaging. We found that mechanical phase singularities co-exist with electrical phase singularities during cardiac fibrillation. We investigated the dynamics of electrical and mechanical phase singularities by simultaneously measuring the membrane potential, intracellular calcium concentration and mechanical contractions of the heart. We show that cardiac fibrillation can be characterized using the three-dimensional spatiotemporal dynamics of mechanical phase singularities, which arise inside the fibrillating contracting ventricular wall. We demonstrate that electrical and mechanical phase singularities show complex interactions and we characterize their dynamics in terms of trajectories, topological charge and lifetime. We anticipate that our findings will provide novel perspectives for non-invasive diagnostic imaging and therapeutic applications.

Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Calini, A.; Schober, C. M.

2013-09-01

In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.