Influence of the local-spin-density correlation functional on the stability of bcc ferromagnetic iron

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

Singh, D.; Clougherty, D.P.; MacLaren, J.M.

1991-10-01

The influence of local-spin-dependent correlation effects on the predicted stable ground-state phase of iron is reexamined with use of general-potential linearized augmented-plane-wave calculations. Differences in the form of the Vosko-Wilk-Nusair (VWN) local-spin-density functional used in previous studies are noted, since in previous studies significant additional approximations were made with respect to those of Vosko, Wilk, and Nusan (Can. J. Phys. 58, 1200 (1980)) and of MacLaren, Clougherty, and Albers (Phys. Rev. B 42, 3205 (1990)). While the results of previous linear muffin-tin orbital calculations using the VWN functional predict a bcc ferromagnetic ground state, the present calculations show that themore » VWN spin-correlation effects fail to stabilize a bcc ground state. Considerable sensitivity to the form of the spin interpolation is found.« less

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

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.

Stability analysis of the phytoplankton effect model on changes in nitrogen concentration on integrated multi-trophic aquaculture systems

NASA Astrophysics Data System (ADS)

Widowati; Putro, S. P.; Silfiana

2018-05-01

Integrated Multi-Trophic Aquaculture (IMTA) is a polyculture with several biotas maintained in it to optimize waste recycling as a food source. The interaction between phytoplankton and nitrogen as waste in fish cultivation including ammonia, nitrite, and nitrate studied in the form of mathematical models. The form model is non-linear systems of differential equations with the four variables. The analytical analysis was used to study the dynamic behavior of this model. Local stability analysis is performed at the equilibrium point with the first step linearized model by using Taylor series, then determined the Jacobian matrix. If all eigenvalues have negative real parts, then the equilibrium of the system is locally asymptotic stable. Some numerical simulations were also demonstrated to verify our analytical result.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

Localization in finite vibroimpact chains: Discrete breathers and multibreathers.

PubMed

Grinberg, Itay; Gendelman, Oleg V

2016-09-01

We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.

Multiple origins of linear dunes on Earth and Titan

USGS Publications Warehouse

Rubin, David M.; Hesp, Patrick A.

2009-01-01

Dunes with relatively long and parallel crests are classified as linear dunes. On Earth, they form in at least two environmental settings: where winds of bimodal direction blow across loose sand, and also where single-direction winds blow over sediment that is locally stabilized, be it through vegetation, sediment cohesion or topographic shelter from the winds. Linear dunes have also been identified on Titan, where they are thought to form in loose sand. Here we present evidence that in the Qaidam Basin, China, linear dunes are found downwind of transverse dunes owing to higher cohesiveness in the downwind sediments, which contain larger amounts of salt and mud. We also present a compilation of other settings where sediment stabilization has been reported to produce linear dunes. We suggest that in this dune-forming process, loose sediment accumulates on the dunes and is stabilized; the stable dune then functions as a topographic shelter, which induces the deposition of sediments downwind. We conclude that a model in which Titan's dunes formed similarly in cohesive sediments cannot be ruled out by the existing data.

Experimental and numerical investigation of development of disturbances in the boundary layer on sharp and blunted cone

NASA Astrophysics Data System (ADS)

Borisov, S. P.; Bountin, D. A.; Gromyko, Yu. V.; Khotyanovsky, D. V.; Kudryavtsev, A. N.

2016-10-01

Development of disturbances in the supersonic boundary layer on sharp and blunted cones is studied both experimentally and theoretically. The experiments were conducted at the Transit-M hypersonic wind tunnel of the Institute of Theoretical and Applied Mechanics. Linear stability calculations use the basic flow profiles provided by the numerical simulations performed by solving the Navier-Stokes equations with the ANSYS Fluent and the in-house CFS3D code. Both the global pseudospectral Chebyshev method and the local iteration procedure are employed to solve the eigenvalue problem and determine linear stability characteristics. The calculated amplification factors for disturbances of various frequencies are compared with the experimentally measured pressure fluctuation spectra at different streamwise positions. It is shown that the linear stability calculations predict quite accurately the frequency of the most amplified disturbances and enable us to estimate reasonably well their relative amplitudes.

SALLY LEVEL II- COMPUTE AND INTEGRATE DISTURBANCE AMPLIFICATION RATES ON SWEPT AND TAPERED LAMINAR FLOW CONTROL WINGS WITH SUCTION

NASA Technical Reports Server (NTRS)

Srokowski, A. J.

1994-01-01

The computer program SALLY was developed to compute the incompressible linear stability characteristics and integrate the amplification rates of boundary layer disturbances on swept and tapered wings. For some wing designs, boundary layer disturbance can significantly alter the wing performance characteristics. This is particularly true for swept and tapered laminar flow control wings which incorporate suction to prevent boundary layer separation. SALLY should prove to be a useful tool in the analysis of these wing performance characteristics. The first step in calculating the disturbance amplification rates is to numerically solve the compressible laminar boundary-layer equation with suction for the swept and tapered wing. A two-point finite-difference method is used to solve the governing continuity, momentum, and energy equations. A similarity transformation is used to remove the wall normal velocity as a boundary condition and place it into the governing equations as a parameter. Thus the awkward nonlinear boundary condition is avoided. The resulting compressible boundary layer data is used by SALLY to compute the incompressible linear stability characteristics. The local disturbance growth is obtained from temporal stability theory and converted into a local growth rate for integration. The direction of the local group velocity is taken as the direction of integration. The amplification rate, or logarithmic disturbance amplitude ratio, is obtained by integration of the local disturbance growth over distance. The amplification rate serves as a measure of the growth of linear disturbances within the boundary layer and can serve as a guide in transition prediction. This program is written in FORTRAN IV and ASSEMBLER for batch execution and has been implemented on a CDC CYBER 70 series computer with a central memory requirement of approximately 67K (octal) of 60 bit words. SALLY was developed in 1979.

Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

PubMed Central

2011-01-01

Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T2 p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94). Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design. PMID:21345241

Perturbative stability of SFT-based cosmological models

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

Galli, Federico; Koshelev, Alexey S., E-mail: fgalli@tena4.vub.ac.be, E-mail: alexey.koshelev@vub.ac.be

2011-05-01

We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numericallymore » that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.« less

Instabilities and finger formation in replacement fronts driven by an oversaturated solution

NASA Astrophysics Data System (ADS)

Kondratiuk, Paweł; Tredak, Hanna; Upadhyay, Virat; Ladd, Anthony J. C.; Szymczak, Piotr

2017-08-01

We consider a simple model of infiltration-driven mineral replacement, in which the chemical coupling between precipitation and dissolution leads to the appearance of a reaction front advancing into the system. Such fronts are usually accompanied by a local increase of porosity. We analyze the linear stability of the replacement front to establish whether such a localized porosity increase can lead to global instability and pattern formation in these systems. We find that for a wide range of control parameters such fronts are unstable. However, both short- and long-wavelength perturbations are stabilized, whereas in a purely dissolutional instability only short wavelengths are stable. We analyze the morphologies of the dissolution patterns emerging in the later stages of the evolution of the system, when the dynamics are beyond the linear regime. Implications of these results for the natural systems are discussed, particularly in the context of karst formation in terra rossa-covered carbonate bedrock.

M3D-K Simulations of Beam-Driven Alfven Eigenmodes in ASDEX-U

NASA Astrophysics Data System (ADS)

Wang, Ge; Fu, Guoyong; Lauber, Philipp; Schneller, Mirjam

2013-10-01

Core-localized Alfven eigenmodes are often observed in neutral beam-heated plasma in ASDEX-U tokamak. In this work, hybrid simulations with the global kinetic/MHD hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven Alfven eigenmodes using experimental parameters and profiles of an ASDEX-U discharge. The safety factor q profile is weakly reversed with minimum q value about qmin = 3.0. The simulation results show that the n = 3 mode transits from a reversed shear Alfven eigenmode (RSAE) to a core-localized toroidal Alfven eigenmode (TAE) as qmin drops from 3.0 to 2.79, consistent with results from the stability code NOVA as well as the experimental measurement. The M3D-K results are being compared with those of the linear gyrokinetic stability code LIGKA for benchmark. The simulation results will also be compared with the measured mode frequency and mode structure. This work was funded by the Max-Planck/Princeton Center for Plasma Physics.

Nonlinear waves in repulsive media supported by spatially localized parity-time-symmetric potentials

NASA Astrophysics Data System (ADS)

Devassy, Lini; Jisha, Chandroth P.; Alberucci, Alessandro; Kuriakose, V. C.

2017-06-01

We study the existence, stability and dynamics of solitons in a PT-symmetric potential in the presence of a local defocusing nonlinearity. For the sake of concreteness, we refer to Bose-Einstein condensates, where defocusing nonlinearity stems from a repulsive inter-particle interaction. Two kinds of transverse profiles for the gain-loss mechanism, i.e., the imaginary part of the potential, are considered. Differently from the attractive inter-particle interaction, solitons exist only inside a narrow band of chemical potential and particle number. The existence region shrinks as the magnitude of the gain-loss is increased, with the soliton ceasing to exist above the linear exceptional point, that is, the point at which PT symmetry is broken. Using linear stability analysis together with full numerical simulations of the Gross-Pitaevskii equation, we show that solitons survive on temporal scales much longer than the diffusion time. For magnitude of gain-loss close to the exceptional point, stability depends on the transverse profile of the gain-loss mechanism and the magnitude of the nonlinear excitation.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals.

PubMed

Theocharis, G; Boechler, N; Kevrekidis, P G; Job, S; Porter, Mason A; Daraio, C

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

NASA Astrophysics Data System (ADS)

Theocharis, G.; Boechler, N.; Kevrekidis, P. G.; Job, S.; Porter, Mason A.; Daraio, C.

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Quantifying Stability in Complex Networks: From Linear to Basin Stability

NASA Astrophysics Data System (ADS)

Kurths, Jürgen

The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. Specifically, we employ a component-wise version of basin stability, a nonlinear inspection scheme, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. Various statistics from our ensemble simulations all support one main finding: The widespread and cheapest of all connection schemes, namely dead ends and dead trees, strongly diminish stability. For the Northern European power system we demonstrate that the inverse is also true: `Healing' dead ends by addition of transmission lines substantially enhances stability. This indicates a crucial smart-design principle for tomorrow's sustainable power grids: add just a few more lines to avoid dead ends. Further, we analyse the particular function of certain network motifs to promote the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design. Moreover, it will be shown that basin stability enables uncovering the mechanism for explosive synchronization and understanding of evolving networks. Reference: P. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Physics 9, 89 (2013) P. Menck, J. Heitzig, J. Kurths, and H. Schellnhuber, Nature Communication 5, 3969 (2014) P. Schultz, J. Heitzig, and J. Kurths, New Journal Physics 16, 125001 (2014) V. Kohar, P. Ji, A. Choudhary, S. Sinha, and J. Kurths, Phys. Rev. E 90, 022812 (2014) Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Phys. Rev. Lett. 112, 114102 (2014)

The importance of Thermo-Hydro-Mechanical couplings and microstructure to strain localization in 3D continua with application to seismic faults. Part I: Theory and linear stability analysis

NASA Astrophysics Data System (ADS)

Rattez, Hadrien; Stefanou, Ioannis; Sulem, Jean

2018-06-01

A Thermo-Hydro-Mechanical (THM) model for Cosserat continua is developed to explore the influence of frictional heating and thermal pore fluid pressurization on the strain localization phenomenon. A general framework is presented to conduct a bifurcation analysis for elasto-plastic Cosserat continua with THM couplings and predict the onset of instability. The presence of internal lengths in Cosserat continua enables to estimate the thickness of the localization zone. This is done by performing a linear stability analysis of the system and looking for the selected wavelength corresponding to the instability mode with fastest finite growth coefficient. These concepts are applied to the study of fault zones under fast shearing. For doing so, we consider a model of a sheared saturated infinite granular layer. The influence of THM couplings on the bifurcation state and the shear band width is investigated. Taking representative parameters for a centroidal fault gouge, the evolution of the thickness of the localized zone under continuous shear is studied. Furthermore, the effect of grain crushing inside the shear band is explored by varying the internal length of the constitutive law.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

The importance of Thermo-Hydro-Mechanical couplings and microstructure to strain localization in 3D continua with application to seismic faults. Part II: Numerical implementation and post-bifurcation analysis

NASA Astrophysics Data System (ADS)

Rattez, Hadrien; Stefanou, Ioannis; Sulem, Jean; Veveakis, Manolis; Poulet, Thomas

2018-06-01

In this paper we study the phenomenon of localization of deformation in fault gouges during seismic slip. This process is of key importance to understand frictional heating and energy budget during an earthquake. A infinite layer of fault gouge is modeled as a Cosserat continuum taking into account Thermo-Hydro-Mechanical (THM) couplings. The theoretical aspects of the problem are presented in the companion paper (Rattez et al., 2017a), together with a linear stability analysis to determine the conditions of localization and estimate the shear band thickness. In this Part II of the study, we investigate the post-bifurcation evolution of the system by integrating numerically the full system of non-linear equations using the method of Finite Elements. The problem is formulated in the framework of Cosserat theory. It enables to introduce information about the microstructure of the material in the constitutive equations and to regularize the mathematical problem in the post-localization regime. We emphasize the influence of the size of the microstructure and of the softening law on the material response and the strain localization process. The weakening effect of pore fluid thermal pressurization induced by shear heating is examined and quantified. It enhances the weakening process and contributes to the narrowing of shear band thickness. Moreover, due to THM couplings an apparent rate-dependency is observed, even for rate-independent material behavior. Finally, comparisons show that when the perturbed field of shear deformation dominates, the estimation of the shear band thickness obtained from linear stability analysis differs from the one obtained from the finite element computations, demonstrating the importance of post-localization numerical simulations.

Stability of spanwise-modulated flows behind backward-facing steps

NASA Astrophysics Data System (ADS)

Boiko, A. V.; Dovgal, A. V.; Sorokin, A. M.

2017-10-01

An overview and synthesis of researches on development of local vortical disturbances in laminar separated flows downstream of backward-facing steps, in which the velocity field depends essentially on two variables are given. Peculiarities of transition to turbulence in such spatially inhomogeneous separated zones are discussed. The experimental data are supplemented by the linear stability characteristics of model velocity profiles of the separated flow computed using both the classical local formulation and the nonlocal approach based on the Floquet theory for partial differential equations with periodic coefficients. The results clarify the response of the local separated flows to their modulation with stationary geometrical and temperature inhomogeneities. The results can be useful for the development of new methods of laminar separation control.

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

NASA Astrophysics Data System (ADS)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

Dissipative stability analysis and control of two-dimensional Fornasini-Marchesini local state-space model

NASA Astrophysics Data System (ADS)

Wang, Lanning; Chen, Weimin; Li, Lizhen

2017-06-01

This paper is concerned with the problems of dissipative stability analysis and control of the two-dimensional (2-D) Fornasini-Marchesini local state-space (FM LSS) model. Based on the characteristics of the system model, a novel definition of 2-D FM LSS (Q, S, R)-α-dissipativity is given first, and then a sufficient condition in terms of linear matrix inequality (LMI) is proposed to guarantee the asymptotical stability and 2-D (Q, S, R)-α-dissipativity of the systems. As its special cases, 2-D passivity performance and 2-D H∞ performance are also discussed. Furthermore, by use of this dissipative stability condition and projection lemma technique, 2-D (Q, S, R)-α-dissipative state-feedback control problem is solved as well. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

When linear stability does not exclude nonlinear instability

DOE PAGES

Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.

2015-05-29

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensionalmore » lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.« less

Self-stabilizing byzantine-fault-tolerant clock synchronization system and method

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R. (Inventor)

2012-01-01

Systems and methods for rapid Byzantine-fault-tolerant self-stabilizing clock synchronization are provided. The systems and methods are based on a protocol comprising a state machine and a set of monitors that execute once every local oscillator tick. The protocol is independent of specific application specific requirements. The faults are assumed to be arbitrary and/or malicious. All timing measures of variables are based on the node's local clock and thus no central clock or externally generated pulse is used. Instances of the protocol are shown to tolerate bursts of transient failures and deterministically converge with a linear convergence time with respect to the synchronization period as predicted.

An automated mapping satellite system ( Mapsat).

USGS Publications Warehouse

Colvocoresses, A.P.

1982-01-01

The favorable environment of space permits a satellite to orbit the Earth with very high stability as long as no local perturbing forces are involved. Solid-state linear-array sensors have no moving parts and create no perturbing force on the satellite. Digital data from highly stabilized stereo linear arrays are amenable to simplified processing to produce both planimetric imagery and elevation data. A satellite imaging system, called Mapsat, including this concept has been proposed to produce data from which automated mapping in near real time can be accomplished. Image maps as large as 1:50 000 scale with contours as close as a 20-m interval may be produced from Mapsat data. -from Author

Response of eddy activities to localized diabatic heating in Held-Suarez simulations

NASA Astrophysics Data System (ADS)

Lin, Yanluan; Zhang, Jishi; Li, Xingrui; Deng, Yi

2018-01-01

Widespread air pollutions, such as black carbon over East Asia in recent years, could induce a localized diabatic heating, and thus lead to localized static stability and meridional temperature gradient (MTG) changes. Although effect of static stability and MTG on eddies has been addressed by the linear baroclinic instability theory, impacts of a localized heating on mid-latitude eddy activities have not been well explored and quantified. Via a series of idealized global Held-Suarez simulations with different magnitudes of localized heating at different altitudes and latitudes, responses of mid-latitude eddy activity and circulation to these temperature perturbations are systematically investigated. Climatologically, the localized heating in the lower atmosphere induces a wave-like response of eddy activity near the mid-latitude jet stream. Over the heating region, eddy activity tends to be weakening due to the increased static stability. However, there are cyclonic anomalies over the upstream and downstream of the heating region. The zonal mean eddy activity weakens along the baroclinic zone due to reduced MTG and increased static stability. Furthermore, the response of eddy activity increased as the heating magnitude is increased and moved to higher altitudes. The influence of the heating decreases as the heating is prescribed further away from the climatological mid-latitude jet. This implies that the localized heating is most effective over the region with the maximum baroclinicity. Besides, enhanced storm track downstream of the localized heating area found here suggests that increased aerosols over East Asia might strengthen the North Pacific storm track.

Streamline-curvature effect in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Reed, Helen L.; Lin, Ray-Sing; Petraglia, Media M.

1992-01-01

The effect of including wall and streamline curvature terms in swept-wing boundary-layer stability calculations is studied. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in this formulation and approximated by their local finite-difference values. Convex-wall curvature has a stabilizing effect, while streamline curvature is destabilizing if the curvature exceeds a critical value.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Plasma Density Effects on Toroidal Flow Stabilization of Edge Localized Modes

NASA Astrophysics Data System (ADS)

Cheng, Shikui; Zhu, Ping; Banerjee, Debabrata

2016-10-01

Recent EAST experiments have demonstrated mitigation and suppression of edge localized modes (ELMs) with toroidal rotation flow in higher collisionality regime, suggesting potential roles of plasma density. In this work, the effects of plasma density on the toroidal flow stabilization of the high- n edge localized modes have been extensively studied in linear calculations for a circular-shaped limiter H-mode tokamak, using the initial-value extended MHD code NIMROD. In the single MHD model, toroidal flow has a weak stabilizing effects on the high- n modes. Such a stabilization, however, can be significantly enhanced with the increase in plasma density. Furthermore, our calculations show that the enhanced stabilization of high- n modes from toroidal flow with higher edge plasma density persists in the 2-fluid MHD model. These findings may explain the ELM mitigation and suppression by toroidal rotation in higher collisionality regime due to the enhancement of plasma density obtained in EAST experiment. Supported by the National Magnetic Confinement Fusion Program of China under Grant Nos. 2014GB124002 and 2015GB101004, the 100 Talent Program and the President International Fellowship Initiative of Chinese Academy of Sciences.

Modulation of localized solutions in a system of two coupled nonlinear Schrödinger equations.

PubMed

Cardoso, W B; Avelar, A T; Bazeia, D

2012-08-01

In this work we study localized solutions of a system of two coupled nonlinear Schrödinger equations, with the linear (potential) and nonlinear coefficients engendering spatial and temporal dependencies. Similarity transformations are used to convert the nonautonomous coupled equations into autonomous ones and we use the trial orbit method to help us solving them, presenting solutions in a general way. Numerical experiments are then used to verify the stability of the localized solutions.

Development of Resistive Micromegas for Sampling Calorimetry

NASA Astrophysics Data System (ADS)

Geralis, T.; Fanourakis, G.; Kalamaris, A.; Nikas, D.; Psallidas, A.; Chefdeville, M.; Karyotakis, I.; Koletsou, I.; Titov, M.

2018-02-01

Resistive micromegas is proposed as an active element for sampling calorimetry. Future linear collider experiments or the HL-LHC experiments can profit from those developments for Particle Flow Calorimetry. Micromegas possesses remarkable properties concerning gain stability, reduced ion feedback, response linearity, adaptable sensitive element granularity, fast response and high rate capability. Recent developments on Micromegas with a protective resistive layer present excellent results, resolving the problem of discharges caused by local high charge deposition, thanks to its RC-slowed charge evacuation. Higher resistivity though, may cause loss of the response linearity at high rates. We have scanned a wide range of resistivities and performed laboratory tests with X-rays that demonstrate excellent response linearity up to rates of (a few) times 10MHz/cm2, with simultaneous mitigation of discharges. Beam test studies at SPS/CERN with hadrons have also shown a remarkable stability of the resistive Micromegas and low currents for rates up to 15MHz/cm2. We present results from the aforementioned studies confronted with MC simulation

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

NASA Technical Reports Server (NTRS)

Krishnan, Hariharan

1993-01-01

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.

PubMed

Cao, Jinde; Xiao, Min

2007-03-01

Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.

The influence of geometric imperfections on the stability of three-layer beams with foam core

NASA Astrophysics Data System (ADS)

Wstawska, Iwona

2017-01-01

The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.

Plasma shaping effects on tokamak scrape-off layer turbulence

NASA Astrophysics Data System (ADS)

Riva, Fabio; Lanti, Emmanuel; Jolliet, Sébastien; Ricci, Paolo

2017-03-01

The impact of plasma shaping on tokamak scrape-off layer (SOL) turbulence is investigated. The drift-reduced Braginskii equations are written for arbitrary magnetic geometries, and an analytical equilibrium model is used to introduce the dependence of turbulence equations on tokamak inverse aspect ratio (ε ), Shafranov’s shift (Δ), elongation (κ), and triangularity (δ). A linear study of plasma shaping effects on the growth rate of resistive ballooning modes (RBMs) and resistive drift waves (RDWs) reveals that RBMs are strongly stabilized by elongation and negative triangularity, while RDWs are only slightly stabilized in non-circular magnetic geometries. Assuming that the linear instabilities saturate due to nonlinear local flattening of the plasma gradient, the equilibrium gradient pressure length {L}p=-{p}e/{{\

Concurrent Increases and Decreases in Local Stability and Conformational Heterogeneity in Cu, Zn Superoxide Dismutase Variants Revealed by Temperature-Dependence of Amide Chemical Shifts.

PubMed

Doyle, Colleen M; Rumfeldt, Jessica A; Broom, Helen R; Sekhar, Ashok; Kay, Lewis E; Meiering, Elizabeth M

2016-03-08

The chemical shifts of backbone amide protons in proteins are sensitive reporters of local structural stability and conformational heterogeneity, which can be determined from their readily measured linear and nonlinear temperature-dependences, respectively. Here we report analyses of amide proton temperature-dependences for native dimeric Cu, Zn superoxide dismutase (holo pWT SOD1) and structurally diverse mutant SOD1s associated with amyotrophic lateral sclerosis (ALS). Holo pWT SOD1 loses structure with temperature first at its periphery and, while having extremely high global stability, nevertheless exhibits extensive conformational heterogeneity, with ∼1 in 5 residues showing evidence for population of low energy alternative states. The holo G93A and E100G ALS mutants have moderately decreased global stability, whereas V148I is slightly stabilized. Comparison of the holo mutants as well as the marginally stable immature monomeric unmetalated and disulfide-reduced (apo(2SH)) pWT with holo pWT shows that changes in the local structural stability of individual amides vary greatly, with average changes corresponding to differences in global protein stability measured by differential scanning calorimetry. Mutants also exhibit altered conformational heterogeneity compared to pWT. Strikingly, substantial increases as well as decreases in local stability and conformational heterogeneity occur, in particular upon maturation and for G93A. Thus, the temperature-dependence of amide shifts for SOD1 variants is a rich source of information on the location and extent of perturbation of structure upon covalent changes and ligand binding. The implications for potential mechanisms of toxic misfolding of SOD1 in disease and for general aspects of protein energetics, including entropy-enthalpy compensation, are discussed.

Event detection and localization for small mobile robots using reservoir computing.

PubMed

Antonelo, E A; Schrauwen, B; Stroobandt, D

2008-08-01

Reservoir Computing (RC) techniques use a fixed (usually randomly created) recurrent neural network, or more generally any dynamic system, which operates at the edge of stability, where only a linear static readout output layer is trained by standard linear regression methods. In this work, RC is used for detecting complex events in autonomous robot navigation. This can be extended to robot localization tasks which are solely based on a few low-range, high-noise sensory data. The robot thus builds an implicit map of the environment (after learning) that is used for efficient localization by simply processing the input stream of distance sensors. These techniques are demonstrated in both a simple simulation environment and in the physically realistic Webots simulation of the commercially available e-puck robot, using several complex and even dynamic environments.

Stability analysis of ELMs in long-pulse discharges with ELITE code on EAST tokamak

NASA Astrophysics Data System (ADS)

Wang, Y. F.; Xu, G. S.; Wan, B. N.; Li, G. Q.; Yan, N.; Li, Y. L.; Wang, H. Q.; Peng, Y.-K. Martin; Xia, T. Y.; Ding, S. Y.; Chen, R.; Yang, Q. Q.; Liu, H. Q.; Zang, Q.; Zhang, T.; Lyu, B.; Xu, J. C.; Feng, W.; Wang, L.; Chen, Y. J.; Luo, Z. P.; Hu, G. H.; Zhang, W.; Shao, L. M.; Ye, Y.; Lan, H.; Chen, L.; Li, J.; Zhao, N.; Wang, Q.; Snyder, P. B.; Liang, Y.; Qian, J. P.; Gong, X. Z.; EAST team

2018-05-01

One challenge in long-pulse and high performance tokamak operation is to control the edge localized modes (ELMs) to reduce the transient heat load on plasma facing components. Minute-scale discharges in H-mode have been achieved repeatedly on Experimental Advanced Superconducting Tokamak (EAST) since the 2016 campaign and understanding the characteristics of the ELMs in these discharges can be helpful for effective ELM control in long-pulse discharges. The kinetic profile diagnostics recently developed on EAST make it possible to perform the pedestal stability analysis quantitatively. Pedestal stability calculation of a typical long-pulse discharge with ELITE code is presented. The ideal linear stability results show that the ELM is dominated by toroidal mode number n around 10–15 and the most unstable mode structure is mainly localized in the steep pressure gradient region, which is consistent with experimental results. Compared with a typical type-I ELM discharge with larger total plasma current (I p = 600 kA), pedestal in the long-pulse H-mode discharge (I p = 450 kA) is more stable in peeling-ballooning instability and its critical peak pressure gradient is evaluated to be 65% of the former. Two important features of EAST tokamak in the long-pulse discharge are presented by comparison with other tokamaks, including a wider pedestal correlated with the poloidal pedestal beta and a smaller inverse aspect ratio and their effects on the pedestal stability are discussed. The effects of uncertainties in measurements on the linear stability results are also analyzed, including the edge electron density profile position, the separatrix position and the line-averaged effective ion charge {Z}{{e}{{f}}{{f}}} value.

Low frequency azimuthal stability of the ionization region of the Hall thruster discharge. II. Global analysis

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

Escobar, D.; Ahedo, E., E-mail: eduardo.ahedo@uc3m.es

2015-10-15

The linear stability of the Hall thruster discharge is analysed against axial-azimuthal perturbations in the low frequency range using a time-dependent 2D code of the discharge. This azimuthal stability analysis is spatially global, as opposed to the more common local stability analyses, already afforded previously (D. Escobar and E. Ahedo, Phys. Plasmas 21(4), 043505 (2014)). The study covers both axial and axial-azimuthal oscillations, known as breathing mode and spoke, respectively. The influence on the spoke instability of different operation parameters such as discharge voltage, mass flow, and thruster size is assessed by means of different parametric variations and compared againstmore » experimental results. Additionally, simplified models are used to unveil and characterize the mechanisms driving the spoke. The results indicate that the spoke is linked to azimuthal oscillations of the ionization process and to the Bohm condition in the transition to the anode sheath. Finally, results obtained from local and global stability analyses are compared in order to explain the discrepancies between both methods.« less

A nonlinear optimal control approach for chaotic finance dynamics

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

2017-11-01

A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Lv, Yu; Dolatabadi, Ali; Ihme, Matthias

2014-11-01

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Direct numerical simulations of mack-mode damping on porous coated cones

NASA Astrophysics Data System (ADS)

Lüdeke, H.; Wartemann, V.

2013-06-01

The flow field over a 3 degree blunt cone is investigated with respect to a hypersonic stability analysis of the boundary-layer flow at Mach 6 with porous as well as smooth walls by comparing local direct numerical simulations (DNS) and linear stability theory (LST) data. The original boundary-layer profile is generated by a finite volume solver, using shock capturing techniques to generate an axisymmetric flow field. Local boundary-layer profiles are extracted from this flow field and hypersonic Mack-modes are superimposed for cone-walls with and without a porous surface used as a passive transition-reduction device. Special care is taken of curvature effects of the wall on the mode development over smooth and porous walls.

An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

NASA Astrophysics Data System (ADS)

Van Londersele, Arne; De Zutter, Daniël; Vande Ginste, Dries

2017-08-01

This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications.

Stability and performance tradeoffs in bi-lateral telemanipulation

NASA Technical Reports Server (NTRS)

Hannaford, Blake

1989-01-01

Kinesthetic force feedback provides measurable increase in remote manipulation system performance. Intensive computation time requirements or operation under conditions of time delay can cause serious stability problems in control-system design. Here, a simplified linear analysis of this stability problem is presented for the forward-flow generalized architecture, applying the hybrid two-port representation to express the loop gain of the traditional master-slave architecture, which can be subjected to similar analysis. The hybrid two-port representation is also used to express the effects on the fidelity of manipulation or feel of one design approach used to stabilize the forward-flow architecture. The results suggest that, when local force feedback at the slave side is used to reduce manipulator stability problems, a price is paid in terms of telemanipulation fidelity.

A stability theorem for energy-balance climate models

NASA Technical Reports Server (NTRS)

Cahalan, R. F.; North, G. R.

1979-01-01

The paper treats the stability of steady-state solutions of some simple, latitude-dependent, energy-balance climate models. For north-south symmetric solutions of models with an ice-cap-type albedo feedback, and for the sum of horizontal transport and infrared radiation given by a linear operator, it is possible to prove a 'slope stability' theorem, i.e., if the local slope of the steady-state iceline latitude versus solar constant curve is positive (negative) the steady-state solution is stable (unstable). Certain rather weak restrictions on the albedo function and on the heat transport are required for the proof, and their physical basis is discussed.

Linear calculations of edge current driven kink modes with BOUT++ code

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

Li, G. Q., E-mail: ligq@ipp.ac.cn; Xia, T. Y.; Lawrence Livermore National Laboratory, Livermore, California 94550

This work extends previous BOUT++ work to systematically study the impact of edge current density on edge localized modes, and to benchmark with the GATO and ELITE codes. Using the CORSICA code, a set of equilibria was generated with different edge current densities by keeping total current and pressure profile fixed. Based on these equilibria, the effects of the edge current density on the MHD instabilities were studied with the 3-field BOUT++ code. For the linear calculations, with increasing edge current density, the dominant modes are changed from intermediate-n and high-n ballooning modes to low-n kink modes, and the linearmore » growth rate becomes smaller. The edge current provides stabilizing effects on ballooning modes due to the increase of local shear at the outer mid-plane with the edge current. For edge kink modes, however, the edge current does not always provide a destabilizing effect; with increasing edge current, the linear growth rate first increases, and then decreases. In benchmark calculations for BOUT++ against the linear results with the GATO and ELITE codes, the vacuum model has important effects on the edge kink mode calculations. By setting a realistic density profile and Spitzer resistivity profile in the vacuum region, the resistivity was found to have a destabilizing effect on both the kink mode and on the ballooning mode. With diamagnetic effects included, the intermediate-n and high-n ballooning modes can be totally stabilized for finite edge current density.« less

[Spectral scatter correction of coal samples based on quasi-linear local weighted method].

PubMed

Lei, Meng; Li, Ming; Ma, Xiao-Ping; Miao, Yan-Zi; Wang, Jian-Sheng

2014-07-01

The present paper puts forth a new spectral correction method based on quasi-linear expression and local weighted function. The first stage of the method is to search 3 quasi-linear expressions to replace the original linear expression in MSC method, such as quadratic, cubic and growth curve expression. Then the local weighted function is constructed by introducing 4 kernel functions, such as Gaussian, Epanechnikov, Biweight and Triweight kernel function. After adding the function in the basic estimation equation, the dependency between the original and ideal spectra is described more accurately and meticulously at each wavelength point. Furthermore, two analytical models were established respectively based on PLS and PCA-BP neural network method, which can be used for estimating the accuracy of corrected spectra. At last, the optimal correction mode was determined by the analytical results with different combination of quasi-linear expression and local weighted function. The spectra of the same coal sample have different noise ratios while the coal sample was prepared under different particle sizes. To validate the effectiveness of this method, the experiment analyzed the correction results of 3 spectral data sets with the particle sizes of 0.2, 1 and 3 mm. The results show that the proposed method can eliminate the scattering influence, and also can enhance the information of spectral peaks. This paper proves a more efficient way to enhance the correlation between corrected spectra and coal qualities significantly, and improve the accuracy and stability of the analytical model substantially.

Multidimensional equilibria and their stability in copolymer-solvent mixtures

NASA Astrophysics Data System (ADS)

Glasner, Karl; Orizaga, Saulo

2018-06-01

This paper discusses localized equilibria which arise in copolymer-solvent mixtures. A free boundary problem associated with the sharp-interface limit of a density functional model is used to identify both lamellar and concentric domain patterns composed of a finite number of layers. Stability of these morphologies is studied through explicit linearization of the free boundary evolution. For the multilayered lamellar configuration, transverse instability is observed for sufficiently small dimensionless interfacial energies. Additionally, a crossover between small and large wavelength instabilities is observed depending on whether solvent-polymer or monomer-monomer interfacial energy is dominant. Concentric domain patterns resembling multilayered micelles and vesicles exhibit bifurcations wherein they only exist for sufficiently small dimensionless interfacial energies. The bifurcation of large radii vesicle solutions is studied analytically, and a crossover from a supercritical case with only one solution branch to a subcritical case with two is observed. Linearized stability of these configurations shows that azimuthal perturbation may lead to instabilities as interfacial energy is decreased.

Breathers in a locally resonant granular chain with precompression

DOE PAGES

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

2016-09-01

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computedmore » exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.« less

Modeling lateral geniculate nucleus response with contrast gain control. Part 2: Analysis

PubMed Central

Cope, Davis; Blakeslee, Barbara; McCourt, Mark E.

2014-01-01

Cope, Blakeslee and McCourt (2013) proposed a class of models for LGN ON-cell behavior consisting of a linear response with divisive normalization by local stimulus contrast. Here we analyze a specific model with the linear response defined by a difference-of-Gaussians filter and a circular Gaussian for the gain pool weighting function. For sinusoidal grating stimuli, the parameter region for band-pass behavior of the linear response is determined, the gain control response is shown to act as a switch (changing from “off” to “on” with increasing spatial frequency), and it is shown that large gain pools stabilize the optimal spatial frequency of the total nonlinear response at a fixed value independent of contrast and stimulus magnitude. Under- and super-saturation as well as contrast saturation occur as typical effects of stimulus magnitude. For circular spot stimuli, it is shown that large gain pools stabilize the spot size that yields the maximum response. PMID:24562034

Magnetorotational instability: nonmodal growth and the relationship of global modes to the shearing box

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

Squire, J.; Bhattacharjee, A.

2014-12-10

We study magnetorotational instability (MRI) using nonmodal stability techniques. Despite the spectral instability of many forms of MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very different from the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely different region ofmore » space. These ideas lead—for both axisymmetric and non-axisymmetric modes—to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary differential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using nonmodal analysis techniques, we conclude by analyzing local MRI growth over finite timescales using these methods. The strong growth over a wide range of wave-numbers suggests that nonmodal linear physics could be of fundamental importance in MRI turbulence.« less

An analysis of the effect of defect structures on catalytic surfaces by the boundary element technique

NASA Astrophysics Data System (ADS)

Peirce, Anthony P.; Rabitz, Herschel

1988-08-01

The boundary element (BE) technique is used to analyze the effect of defects on one-dimensional chemically active surfaces. The standard BE algorithm for diffusion is modified to include the effects of bulk desorption by making use of an asymptotic expansion technique to evaluate influences near boundaries and defect sites. An explicit time evolution scheme is proposed to treat the non-linear equations associated with defect sites. The proposed BE algorithm is shown to provide an efficient and convergent algorithm for modelling localized non-linear behavior. Since it exploits the actual Green's function of the linear diffusion-desorption process that takes place on the surface, the BE algorithm is extremely stable. The BE algorithm is applied to a number of interesting physical problems in which non-linear reactions occur at localized defects. The Lotka-Volterra system is considered in which the source, sink and predator-prey interaction terms are distributed at different defect sites in the domain and in which the defects are coupled by diffusion. This example provides a stringent test of the stability of the numerical algorithm. Marginal stability oscillations are analyzed for the Prigogine-Lefever reaction that occurs on a lattice of defects. Dissipative effects are observed for large perturbations to the marginal stability state, and rapid spatial reorganization of uniformly distributed initial perturbations is seen to take place. In another series of examples the effect of defect locations on the balance between desorptive processes on chemically active surfaces is considered. The effect of dynamic pulsing at various time-scales is considered for a one species reactive trapping model. Similar competitive behavior between neighboring defects previously observed for static adsorption levels is shown to persist for dynamic loading of the surface. The analysis of a more complex three species reaction process also provides evidence of competitive behavior between neighboring defect sites. The proposed BE algorithm is shown to provide a useful technique for analyzing the effect of defect sites on chemically active surfaces.

Long-wave instabilities of two interlaced helical vortices

NASA Astrophysics Data System (ADS)

Quaranta, H. U.; Brynjell-Rahkola, M.; Leweke, T.; Henningson, D. S.

2016-09-01

We present a comparison between experimental observations and theoretical predictions concerning long-wave displacement instabilities of the helical vortices in the wake of a two-bladed rotor. Experiments are performed with a small-scale rotor in a water channel, using a set-up that allows the individual triggering of various instability modes at different azimuthal wave numbers, leading to local or global pairing of successive vortex loops. The initial development of the instability and the measured growth rates are in good agreement with the predictions from linear stability theory, based on an approach where the helical vortex system is represented by filaments. At later times, local pairing develops into large-scale distortions of the vortices, whereas for global pairing the non-linear evolution returns the system almost to its initial geometry.

Stability of matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

2010-08-01

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

Tangential acceleration feedback control of friction induced vibration

NASA Astrophysics Data System (ADS)

Nath, Jyayasi; Chatterjee, S.

2016-09-01

Tangential control action is studied on a phenomenological mass-on-belt model exhibiting friction-induced self-excited vibration attributed to the low-velocity drooping characteristics of friction which is also known as Stribeck effect. The friction phenomenon is modelled by the exponential model. Linear stability analysis is carried out near the equilibrium point and local stability boundary is delineated in the plane of control parameters. The system is observed to undergo a Hopf bifurcation as the eigenvalues determined from the linear stability analysis are found to cross the imaginary axis transversally from RHS s-plane to LHS s-plane or vice-versa as one varies the control parameters, namely non-dimensional belt velocity and the control gain. A nonlinear stability analysis by the method of Averaging reveals the subcritical nature of the Hopf bifurcation. Thus, a global stability boundary is constructed so that any choice of control parameters from the globally stable region leads to a stable equilibrium. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO validate these analytically obtained results. Pole crossover design is implemented to optimize the filter parameters with an independent choice of belt velocity and control gain. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.

Variational approach to stability boundary for the Taylor-Goldstein equation

NASA Astrophysics Data System (ADS)

Hirota, Makoto; Morrison, Philip J.

2015-11-01

Linear stability of inviscid stratified shear flow is studied by developing an efficient method for finding neutral (i.e., marginally stable) solutions of the Taylor-Goldstein equation. The classical Miles-Howard criterion states that stratified shear flow is stable if the local Richardson number JR is greater than 1/4 everywhere. In this work, the case of JR > 0 everywhere is considered by assuming strictly monotonic and smooth profiles of the ambient shear flow and density. It is shown that singular neutral modes that are embedded in the continuous spectrum can be found by solving one-parameter families of self-adjoint eigenvalue problems. The unstable ranges of wavenumber are searched for accurately and efficiently by adopting this method in a numerical algorithm. Because the problems are self-adjoint, the variational method can be applied to ascertain the existence of singular neutral modes. For certain shear flow and density profiles, linear stability can be proven by showing the non-existence of a singular neutral mode. New sufficient conditions, extensions of the Rayleigh-Fjortoft stability criterion for unstratified shear flows, are derived in this manner. This work was supported by JSPS Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation # 55053270.

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.; Pop, Ioan

2018-06-01

The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

Singlet fission in linear chains of molecules

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

Ambrosio, Francesco, E-mail: F.Ambrosio@warwick.ac.uk, E-mail: A.Troisi@warwick.ac.uk; Troisi, Alessandro, E-mail: F.Ambrosio@warwick.ac.uk, E-mail: A.Troisi@warwick.ac.uk

2014-11-28

We develop a model configuration interaction Hamiltonian to study the electronic structure of a chain of molecules undergoing singlet fission. We first consider models for dimer and trimer and then we use a matrix partitioning technique to build models of arbitrary size able to describe the relevant electronic structure for singlet fission in linear aggregates. We find that the multi-excitonic state (ME) is stabilized at short inter-monomer distance and the extent of this stabilization depends upon the size of orbital coupling between neighboring monomers. We also find that the coupling between ME states located on different molecules is extremely smallmore » leading to bandwidths in the order of ∼10 meV. This observation suggests that multi-exciton states are extremely localized by electron-phonon coupling and that singlet fission involves the transition between a relatively delocalized Frenkel exciton and a strongly localized multi-exciton state. We adopt the methodology commonly used to study non-radiative transitions to describe the singlet fission dynamics in these aggregates and we discuss the limit of validity of the approach. The results indicate that the phenomenology of singlet fission in molecular crystals is different in many important ways from what is observed in isolated dimers.« less

Local Bifurcations and Optimal Theory in a Delayed Predator-Prey Model with Threshold Prey Harvesting

NASA Astrophysics Data System (ADS)

Tankam, Israel; Tchinda Mouofo, Plaire; Mendy, Abdoulaye; Lam, Mountaga; Tewa, Jean Jules; Bowong, Samuel

2015-06-01

We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator-prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.

On decentralized control of large-scale systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.

1978-01-01

A scheme is presented for decentralized control of large-scale linear systems which are composed of a number of interconnected subsystems. By ignoring the interconnections, local feedback controls are chosen to optimize each decoupled subsystem. Conditions are provided to establish compatibility of the individual local controllers and achieve stability of the overall system. Besides computational simplifications, the scheme is attractive because of its structural features and the fact that it produces a robust decentralized regulator for large dynamic systems, which can tolerate a wide range of nonlinearities and perturbations among the subsystems.

Nonlinear time series analysis of normal and pathological human walking

NASA Astrophysics Data System (ADS)

Dingwell, Jonathan B.; Cusumano, Joseph P.

2000-12-01

Characterizing locomotor dynamics is essential for understanding the neuromuscular control of locomotion. In particular, quantifying dynamic stability during walking is important for assessing people who have a greater risk of falling. However, traditional biomechanical methods of defining stability have not quantified the resistance of the neuromuscular system to perturbations, suggesting that more precise definitions are required. For the present study, average maximum finite-time Lyapunov exponents were estimated to quantify the local dynamic stability of human walking kinematics. Local scaling exponents, defined as the local slopes of the correlation sum curves, were also calculated to quantify the local scaling structure of each embedded time series. Comparisons were made between overground and motorized treadmill walking in young healthy subjects and between diabetic neuropathic (NP) patients and healthy controls (CO) during overground walking. A modification of the method of surrogate data was developed to examine the stochastic nature of the fluctuations overlying the nominally periodic patterns in these data sets. Results demonstrated that having subjects walk on a motorized treadmill artificially stabilized their natural locomotor kinematics by small but statistically significant amounts. Furthermore, a paradox previously present in the biomechanical literature that resulted from mistakenly equating variability with dynamic stability was resolved. By slowing their self-selected walking speeds, NP patients adopted more locally stable gait patterns, even though they simultaneously exhibited greater kinematic variability than CO subjects. Additionally, the loss of peripheral sensation in NP patients was associated with statistically significant differences in the local scaling structure of their walking kinematics at those length scales where it was anticipated that sensory feedback would play the greatest role. Lastly, stride-to-stride fluctuations in the walking patterns of all three subject groups were clearly distinguishable from linearly autocorrelated Gaussian noise. As a collateral benefit of the methodological approach taken in this study, some of the first steps at characterizing the underlying structure of human locomotor dynamics have been taken. Implications for understanding the neuromuscular control of locomotion are discussed.

Stochastic stability properties of jump linear systems

NASA Technical Reports Server (NTRS)

Feng, Xiangbo; Loparo, Kenneth A.; Ji, Yuandong; Chizeck, Howard J.

1992-01-01

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

Dynamic stability of passive dynamic walking on an irregular surface.

PubMed

Su, Jimmy Li-Shin; Dingwell, Jonathan B

2007-12-01

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.

Long-lived oscillons from asymmetric bubbles: Existence and stability

NASA Astrophysics Data System (ADS)

Adib, Artur B.; Gleiser, Marcelo; Almeida, Carlos A.

2002-10-01

The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in (2+1)-dimensional φ4 models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are (a) circularly symmetric and (b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly growing instabilities not seen through the usual ``spectral'' method.

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

Onset of Darrieus-Landau Instability in Expanding Flames

NASA Astrophysics Data System (ADS)

Mohan, Shikhar; Matalon, Moshe

2017-11-01

The effect of small amplitude perturbations on the propagation of circular flames in unconfined domains is investigated, computationally and analytically, within the context of the hydrodynamic theory. The flame, treated as a surface of density discontinuity separating fresh combustible mixture from the burnt gas, propagates at a speed dependent upon local curvature and hydrodynamic strain. For mixtures with Lewis numbers above criticality, thermodiffusive effects have stabilizing influences which largely affect the flame at small radii. The amplitude of these disturbances initially decay and only begin to grow once a critical radius is reached. This instability is hydrodynamic in nature and is a consequence of thermal expansion. Through linear stability analysis, predictions of critical flame radius at the onset of instability are obtained as functions of Markstein length and thermal expansion coefficients. The flame evolution is also examined numerically where the motion of the interface is tracked via a level-set method. Consistent with linear stability results, simulations show the flame initially remaining stable and the existence of a particular mode that will be first to grow and later determine the cellular structure observed experimentally at the onset of instability.

Dependency of Tearing Mode Stability on Current and Pressure Profiles in DIII-D Hybrid Discharges

NASA Astrophysics Data System (ADS)

Kim, K.; Park, J. M.; Murakami, M.; La Haye, R. J.; Na, Y.-S.; SNU/ORAU; ORNL; Atomics, General; SNU; DIII-D Team

2016-10-01

Understanding the physics of the onset and evolution of tearing modes (TMs) in tokamak plasmas is important for high- β steady-state operation. Based on DIII-D steady-state hybrid experiments with accurate equilibrium reconstruction and well-measured plasma profiles, the 2/1 tearing mode can be more stable with increasing local current and pressure gradient at rational surface and with lower pressure peaking and plasma inductance. The tearing stability index Δ', estimated by the Rutherford equation with experimental mode growth rate was validated against Δ' calculated by linear eigenvalue solver (PEST3); preliminary comprehensive MHD modeling by NIMROD reproduced the TM onset reasonably well. We present a novel integrated modeling for the purpose of predicting TM onset in experiment by combining a model equilibrium reconstruction using IPS/FASTRAN, linear stability Δ' calculation using PEST3, and fitting formula for critical Δ' from NIMROD. Work supported in part by the US DoE under DE-AC05-06OR23100, DE-AC05-00OR22725, and DEFC02-04ER54698.

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Krishna, R.; James, P. K.

1980-01-01

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

Linear gyrokinetic simulations of microinstabilities within the pedestal region of H-mode NSTX discharges in a highly shaped geometry

DOE PAGES

Coury, M.; Guttenfelder, W.; Mikkelsen, D. R.; ...

2016-06-30

Linear (local) gyrokinetic predictions of edge microinstabilities in highly shaped, lithiated and non-lithiated NSTX discharges are reported using the gyrokinetic code GS2. Microtearing modes dominate the non-lithiated pedestal top. The stabilization of these modes at the lithiated pedestal top enables the electron temperature pedestal to extend further inwards, as observed experimentally. Kinetic ballooning modes are found to be unstable mainly at the mid-pedestal of both types of discharges, with un- stable trapped electron modes nearer the separatrix region. At electron wavelengths, ETG modes are found to be unstable from mid-pedestal outwards for η e, exp ~2.2 with higher growth ratesmore » for the lithiated discharge. Near the separatrix, the critical temperature gradient for driving ETG modes is reduced in the presence of lithium, re ecting the reduction of the lithiated density gradients observed experimentally. A preliminary linear study in the edge of non-lithiated discharges shows that the equilibrium shaping alters the electrostatic modes stability, found more unstable at high plasma shaping.« less

Output Containment Control of Linear Heterogeneous Multi-Agent Systems Using Internal Model Principle.

PubMed

Zuo, Shan; Song, Yongduan; Lewis, Frank L; Davoudi, Ali

2017-01-04

This paper studies the output containment control of linear heterogeneous multi-agent systems, where the system dynamics and even the state dimensions can generally be different. Since the states can have different dimensions, standard results from state containment control do not apply. Therefore, the control objective is to guarantee the convergence of the output of each follower to the dynamic convex hull spanned by the outputs of leaders. This can be achieved by making certain output containment errors go to zero asymptotically. Based on this formulation, two different control protocols, namely, full-state feedback and static output-feedback, are designed based on internal model principles. Sufficient local conditions for the existence of the proposed control protocols are developed in terms of stabilizing the local followers' dynamics and satisfying a certain H∞ criterion. Unified design procedures to solve the proposed two control protocols are presented by formulation and solution of certain local state-feedback and static output-feedback problems, respectively. Numerical simulations are given to validate the proposed control protocols.

A direct comparison of spine rotational stiffness and dynamic spine stability during repetitive lifting tasks.

PubMed

Graham, Ryan B; Brown, Stephen H M

2012-06-01

Stability of the spinal column is critical to bear loads, allow movement, and at the same time avoid injury and pain. However, there has been a debate in recent years as to how best to define and quantify spine stability, with the outcome being that different methods are used without a clear understanding of how they relate to one another. Therefore, the goal of the present study was to directly compare lumbar spine rotational stiffness, calculated with an EMG-driven biomechanical model, to local dynamic spine stability calculated using Lyapunov analyses of kinematic data, during a series of continuous dynamic lifting challenges. Twelve healthy male subjects performed 30 repetitive lifts under three varying load and three varying rate conditions. With an increase in the load lifted (constant rate) there was a significant increase in mean, maximum, and minimum spine rotational stiffness (p<0.001) and a significant increase in local dynamic stability (p<0.05); both stability measures were moderately to strongly related to one another (r=-0.55 to -0.71). With an increase in lifting rate (constant load), there was also a significant increase in mean and maximum spine rotational stiffness (p<0.01); however, there was a non-significant decrease in the minimum rotational stiffness and a non-significant decrease in local dynamic stability (p>0.05). Weak linear relationships were found for the varying rate conditions (r=-0.02 to -0.27). The results suggest that spine rotational stiffness and local dynamic stability are closely related to one another, as they provided similar information when movement rate was controlled. However, based on the results from the changing lifting rate conditions, it is evident that both models provide unique information and that future research is required to completely understand the relationship between the two models. Using both techniques concurrently may provide the best information regarding the true effects of (in) stability under different loading and movement scenarios, and in comparing healthy and clinical populations. Copyright © 2012 Elsevier Ltd. All rights reserved.

Adjustment of Adaptive Gain with Bounded Linear Stability Analysis to Improve Time-Delay Margin for Metrics-Driven Adaptive Control

NASA Technical Reports Server (NTRS)

Bakhtiari-Nejad, Maryam; Nguyen, Nhan T.; Krishnakumar, Kalmanje Srinvas

2009-01-01

This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a linear damaged twin-engine generic transport model of aircraft. The analysis shows that the system with the adjusted adaptive gain becomes more robust to unmodeled dynamics or time delay.

Chimera regimes in a ring of oscillators with local nonlinear interaction

NASA Astrophysics Data System (ADS)

Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.

2017-03-01

One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.

Stability and dynamic analysis of a slender column with curved longitudinal stiffeners

NASA Technical Reports Server (NTRS)

Lake, Mark S.

1989-01-01

The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

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

Bass, Eric M.; Waltz, R. E.

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEMmore » peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.« less

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

DOE PAGES

Bass, Eric M.; Waltz, R. E.

2017-12-08

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEMmore » peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.« less

Generic pure quantum states as steady states of quasi-local dissipative dynamics

NASA Astrophysics Data System (ADS)

Karuvade, Salini; Johnson, Peter D.; Ticozzi, Francesco; Viola, Lorenza

2018-04-01

We investigate whether a generic pure state on a multipartite quantum system can be the unique asymptotic steady state of locality-constrained purely dissipative Markovian dynamics. In the tripartite setting, we show that the problem is equivalent to characterizing the solution space of a set of linear equations and establish that the set of pure states obeying the above property has either measure zero or measure one, solely depending on the subsystems’ dimension. A complete analytical characterization is given when the central subsystem is a qubit. In the N-partite case, we provide conditions on the subsystems’ size and the nature of the locality constraint, under which random pure states cannot be quasi-locally stabilized generically. Also, allowing for the possibility to approximately stabilize entangled pure states that cannot be exact steady states in settings where stabilizability is generic, our results offer insights into the extent to which random pure states may arise as unique ground states of frustration-free parent Hamiltonians. We further argue that, to a high probability, pure quantum states sampled from a t-design enjoy the same stabilizability properties of Haar-random ones as long as suitable dimension constraints are obeyed and t is sufficiently large. Lastly, we demonstrate a connection between the tasks of quasi-local state stabilization and unique state reconstruction from local tomographic information, and provide a constructive procedure for determining a generic N-partite pure state based only on knowledge of the support of any two of the reduced density matrices of about half the parties, improving over existing results.

H-mode pedestal stability and ELMs in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Mossessian, Dmitri

2002-11-01

For steady state H-mode operation, a relaxation mechanism is required to limit build-up of the edge gradient and impurity accumulation. The major relaxation mechanism seen on most of the existing tokamaks - large type I ELMs - drive high particle and energy fluxes that present a significant power load on the divertor plates. On Alcator C-Mod, however, type I ELMs are not observed. Instead, more benign mechanisms - EDA and small grassy ELMs - appear to drive enhanced particle transport at the edge of H-mode plasmas. Both have good energy confinement, no impurity accumulation, and are steady state. In EDA the edge relaxation mechanism is provided by a quasicoherent electromagnetic mode localized in the outer part of the pedestal. Non-linear gyrofluid and linear gyrokinetic simulations, as well as real geometry fluctuation modeling based on fluid equations show the presence of a coherent mode. Based on those results the observed mode is tentatively identified as resistive ballooning. At higher edge pressure gradient the mode is replaced by broadband fluctuations and small irregular ELMs are observed. Based on ideal MHD calculations that include effects of bootstrap current, these ELMs are identified as medium n coupled ideal peeling/ballooning modes. The stability threshold and modes structure of these modes are studied with recently developed linear MHD stability code ELITE and the results are compared with the observed dependence of the ELMs' character on pedestal parameters and plasma shape.

An H-infinity approach to optimal control of oxygen and carbon dioxide contents in blood

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Selisteanu, Dan; Precup, Radu

2016-12-01

Nonlinear H-infinity control is proposed for the regulation of the levels of oxygen and carbon dioxide in the blood of patients undergoing heart surgery and extracorporeal blood circulation. The levels of blood gases are administered through a membrane oxygenator and the control inputs are the externally supplied oxygen, the aggregate gas supply (oxygen plus nitrogen), and the blood flow which is regulated by a blood pump. The proposed control method is based on linearization of the oxygenator's dynamical model through Taylor series expansion and the computation of Jacobian matrices. The local linearization points are defined by the present value of the oxygenator's state vector and the last value of the control input that was exerted on this system. The modelling errors due to linearization are considered as disturbances which are compensated by the robustness of the control loop. Next, for the linearized model of the oxygenator an H-infinity control input is computed at each iteration of the control algorithm through the solution of an algebraic Riccati equation. With the use of Lyapunov stability analysis it is demonstrated that the control scheme satisfies the H-infinity tracking performance criterion, which signifies improved robustness against modelling uncertainty and external disturbances. Moreover, under moderate conditions the asymptotic stability of the control loop is also proven.

Integrability and Linear Stability of Nonlinear Waves

NASA Astrophysics Data System (ADS)

Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo

2018-03-01

It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

Revisiting the Stability of Spatially Heterogeneous Predator-Prey Systems Under Eutrophication.

PubMed

Farkas, J Z; Morozov, A Yu; Arashkevich, E G; Nikishina, A

2015-10-01

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than on the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (1) the spatial gradient of the growth rate is due to abiotic factors only, and (2) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism. These results highlight the generality of the stabilization mechanisms we find in spatially structured predator-prey ecological systems in a heterogeneous environment.

Evolution of anisotropy in bcc Fe distorted by interstitial boron

NASA Astrophysics Data System (ADS)

Gölden, Dominik; Zhang, Hongbin; Radulov, Iliya; Dirba, Imants; Komissinskiy, Philipp; Hildebrandt, Erwin; Alff, Lambert

2018-01-01

The evolution of magnetic anisotropy in bcc Fe as a function of interstitial boron atoms was investigated in thin films grown by molecular beam epitaxy. The thermodynamic nonequilibrium conditions during film growth allowed one to stabilize an interstitial boron content of about 14 at .% accompanied by lattice tetragonalization. The c /a ratio scaled linearly with the boron content up to a maximum value of 1.05 at 300 °C substrate growth temperature, with a room-temperature magnetization of. In contrast to nitrogen interstitials, the magnetic easy axis remained in-plane with an anisotropy of approximately -5.1 ×106erg /cm3 . Density functional theory calculations using the measured lattice parameters confirm this value and show that boron local ordering indeed favors in-plane magnetization. Given the increased temperature stability of boron interstitials as compared to nitrogen interstitials, this study will help to find possible ways to manipulate boron interstitials into a more favorable local order.

Weak variations of Lipschitz graphs and stability of phase boundaries

NASA Astrophysics Data System (ADS)

Grabovsky, Yury; Kucher, Vladislav A.; Truskinovsky, Lev

2011-03-01

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.

Dynamic actuation of a novel laser-processed NiTi linear actuator

NASA Astrophysics Data System (ADS)

Pequegnat, A.; Daly, M.; Wang, J.; Zhou, Y.; Khan, M. I.

2012-09-01

A novel laser processing technique, capable of locally modifying the shape memory effect, was applied to enhance the functionality of a NiTi linear actuator. By altering local transformation temperatures, an additional memory was imparted into a monolithic NiTi wire to enable dynamic actuation via controlled resistive heating. Characterizations of the actuator load, displacement and cyclic properties were conducted using a custom-built spring-biased test set-up. Monotonic tensile testing was also implemented to characterize the deformation behaviour of the martensite phase. Observed differences in the deformation behaviour of laser-processed material were found to affect the magnitude of the active strain. Furthermore, residual strain during cyclic actuation testing was found to stabilize after 150 cycles while the recoverable strain remained constant. This laser-processed actuator will allow for the realization of new applications and improved control methods for shape memory alloys.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Standard representation and unified stability analysis for dynamic artificial neural network models.

PubMed

Kim, Kwang-Ki K; Patrón, Ernesto Ríos; Braatz, Richard D

2018-02-01

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. Copyright © 2017. Published by Elsevier Ltd.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117

Non-linear coherent mode interactions and the control of shear layers

NASA Technical Reports Server (NTRS)

Nikitopoulos, D. E.; Liu, J. T. C.

1990-01-01

A nonlinear integral formulation, based on local linear stability considerations, is used to study the collective interactions between discrete wave-modes associated with large-scale structures and the mean flow in a developing shear layer. Aspects of shear layer control are examined in light of the sensitivity of these interactions to the initial frequency parameter, modal energy contents and modal phases. Manipulation of the large-scale structure is argued to be an effective means of controlling the flow, including the small-scale turbulence dominated region far downstream. Cases of fundamental, 1st and 2nd subharmonic forcing are discussed in conjunction with relevant experiments.

An improved linear ion trap physics package

NASA Technical Reports Server (NTRS)

Prestage, J. D.

1993-01-01

This article describes an improvement in the architecture of the physics package used in the Linear Ion Trap (LIT)-based frequency standard recently developed at JPL. This new design is based on the observation that ions can be moved along the axis of an LIT by applied dc voltages. The state selection and interrogation region can be separated from the more critical microwave resonance region where the multiplied local oscillator signal is compared with the stable atomic transition. This separation relaxes many of the design constraints of the present units. Improvements include increased frequency stability and a substantial reduction in size, mass, and cost of the final frequency standard.

Application of Bounded Linear Stability Analysis Method for Metrics-Driven Adaptive Control

NASA Technical Reports Server (NTRS)

Bakhtiari-Nejad, Maryam; Nguyen, Nhan T.; Krishnakumar, Kalmanje

2009-01-01

This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics-driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a second order system that represents a pitch attitude control of a generic transport aircraft. The analysis shows that the system with the metrics-conforming variable adaptive gain becomes more robust to unmodeled dynamics or time delay. The effect of analysis time-window for BLSA is also evaluated in order to meet the stability margin criteria.

Multi-Mode Estimation for Small Fixed Wing Unmanned Aerial Vehicle Localization Based on a Linear Matrix Inequality Approach

PubMed Central

Elzoghby, Mostafa; Li, Fu; Arafa, Ibrahim. I.; Arif, Usman

2017-01-01

Information fusion from multiple sensors ensures the accuracy and robustness of a navigation system, especially in the absence of global positioning system (GPS) data which gets degraded in many cases. A way to deal with multi-mode estimation for a small fixed wing unmanned aerial vehicle (UAV) localization framework is proposed, which depends on utilizing a Luenberger observer-based linear matrix inequality (LMI) approach. The proposed estimation technique relies on the interaction between multiple measurement modes and a continuous observer. The state estimation is performed in a switching environment between multiple active sensors to exploit the available information as much as possible, especially in GPS-denied environments. Luenberger observer-based projection is implemented as a continuous observer to optimize the estimation performance. The observer gain might be chosen by solving a Lyapunov equation by means of a LMI algorithm. Convergence is achieved by utilizing the linear matrix inequality (LMI), based on Lyapunov stability which keeps the dynamic estimation error bounded by selecting the observer gain matrix (L). Simulation results are presented for a small UAV fixed wing localization problem. The results obtained using the proposed approach are compared with a single mode Extended Kalman Filter (EKF). Simulation results are presented to demonstrate the viability of the proposed strategy. PMID:28420214

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations.

PubMed

Feng, Bao-Feng; Malomed, Boris A; Kawahara, Takuji

2002-11-01

We present a two-dimensional (2D) generalization of the stabilized Kuramoto-Sivashinsky system, based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic [Newell-Whitehead-Segel (NWS)] type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear media, combining the weakly 2D dispersion of the KP type with gain and NWS dissipation. Other applications are internal waves in multilayer fluids flowing down an inclined plane, double-front flames in gaseous mixtures, etc. Parallel to this weakly 2D model, we also introduce and study a semiphenomenological one, whose dissipative terms are isotropic, rather than of the NWS type, in order to check if qualitative results are sensitive to the exact form of the lossy terms. The models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, thus opening a way for the existence of stable localized pulses. We focus on the most interesting case, when the dispersive part of the system is of the KP-I type, which corresponds, e.g., to capillary waves, and makes the existence of completely localized 2D pulses possible. Treating the losses and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two steady-state solitons from their continuous family existing in the absence of the dissipative terms (the latter family is found in an exact analytical form, and is numerically demonstrated to be stable). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions, for both the physical and phenomenological models.

Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code

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

Burke, B. J.; Kruger, S. E.; Hegna, C. C.

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition tomore » instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1-20). The results use the compressible MHD model and depend on a precise representation of 'ideal-like' and 'vacuumlike' or 'halo' regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 10{sup 8} and 10{sup 3} for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 10{sup 5}, which is much larger than experimentally measured values using T{sub e} values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.« less

Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Boskovic, Jovan D.

2008-01-01

This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

Stability and sensitivity analysis of hypersonic flow past a blunt cone

NASA Astrophysics Data System (ADS)

Nichols, Joseph W.; Cook, David; Brock, Joseph M.; Candler, Graham V.

2017-11-01

We investigate the effects of nosetip bluntness and low-level distributed roughness on instabilities leading to transition on a 7 degree half-angle blunt cone at Mach 10. To study the sensitivity of boundary layer instabilities to bluntness and roughness, we numerically extract Jacobian matrices directly from the unstructured hypersonic flow solver US3D. These matrices govern the dynamics of small perturbations about otherwise laminar base flows. We consider the frequency response of the resulting linearized dynamical system between different input and output locations along the cone, including close to the nosetip. Using adjoints, our method faithfully captures effects of complex geometry such as strong curvature and roughness that lead to flow acceleration and localized heating in this region. These effects violate the assumption of a slowly-varying base flow that underpins traditional linear stability analyses. We compare our results, which do not rely upon this assumption, to experimental measurements of a Mach 10 blunt cone taken at the AEDC Hypervelocity Ballistic Range G facility. In particular, we assess whether effects of complex geometry can explain discrepancies previously noted between traditional stability analysis and observations. This work is supported by the Office of Naval Research through Grant Number N00014-17-1-2496.

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

NASA Astrophysics Data System (ADS)

Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

2018-06-01

Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics

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

Howell, E. C.; Sovinec, C. R.

The extended magnetohydrodynamic stability of interchange modes is studied in two configurations. In slab geometry, a local dispersion relation for the gravitational interchange mode (g-mode) with three different extensions of the MHD model [P. Zhu, et al., Phys. Rev. Lett. 101, 085005 (2008)] is analyzed. Our results delineate where drifts stablize the g-mode with gyroviscosity alone and with a two-fluid Ohm’s law alone. Including the two-fluid Ohm’s law produces an ion drift wave that interacts with the g-mode. This interaction then gives rise to a second instability at finite k y. A second instability is also observed in numerical extended MHD computations of linear interchange in cylindrical screw-pinch equilibria, the second configuration. Particularly with incomplete models, this mode limits the regions of stability for physically realistic conditions. But, applying a consistent two-temperature extended MHD model that includes the diamagnetic heat flux density (more » $$\\vec{q}$$ *) makes the onset of the second mode occur at larger Hall parameter. For conditions relevant to the SSPX experiment [E.B. Hooper, Plasma Phys. Controlled Fusion 54, 113001 (2012)], significant stabilization is observed for Suydam parameters as large as unity (D s≲1).« less

Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics

DOE PAGES

Howell, E. C.; Sovinec, C. R.

2017-09-11

The extended magnetohydrodynamic stability of interchange modes is studied in two configurations. In slab geometry, a local dispersion relation for the gravitational interchange mode (g-mode) with three different extensions of the MHD model [P. Zhu, et al., Phys. Rev. Lett. 101, 085005 (2008)] is analyzed. Our results delineate where drifts stablize the g-mode with gyroviscosity alone and with a two-fluid Ohm’s law alone. Including the two-fluid Ohm’s law produces an ion drift wave that interacts with the g-mode. This interaction then gives rise to a second instability at finite k y. A second instability is also observed in numerical extended MHD computations of linear interchange in cylindrical screw-pinch equilibria, the second configuration. Particularly with incomplete models, this mode limits the regions of stability for physically realistic conditions. But, applying a consistent two-temperature extended MHD model that includes the diamagnetic heat flux density (more » $$\\vec{q}$$ *) makes the onset of the second mode occur at larger Hall parameter. For conditions relevant to the SSPX experiment [E.B. Hooper, Plasma Phys. Controlled Fusion 54, 113001 (2012)], significant stabilization is observed for Suydam parameters as large as unity (D s≲1).« less

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

Magnetorotational Instability: Nonmodal Growth and the Relationship of Global Modes to the Shearing Box

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

J Squire, A Bhattacharjee

We study the magnetorotational instability (MRI) (Balbus & Hawley 1998) using non-modal stability techniques.Despite the spectral instability of many forms of the MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very diff erent to the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localizedmore » in a completely di fferent region of space. These ideas lead – for both axisymmetric and non-axisymmetric modes – to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary diff erential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using non-modal analysis techniques, we conclude by analyzing local MRI growth over finite time-scales using these methods. The strong growth over a wide range of wave-numbers suggests that non-modal linear physics could be of fundamental importance in MRI turbulence (Squire & Bhattacharjee 2014).« less

Sensor positioning and experimental constraints influence estimates of local dynamic stability during repetitive spine movements.

PubMed

Howarth, Samuel J; Graham, Ryan B

2015-04-13

Application of non-linear dynamics analyses to study human movement has increased recently, which necessitates an understanding of how dependent measures may be influenced by experimental design and setup. Quantifying local dynamic stability for a multi-articulated structure such as the spine presents the possibility for estimates to be influenced by positioning of kinematic sensors used to measure spine angular kinematics. Oftentimes researchers will also choose to constrain the spine's movement by physically restraining the pelvis and/or using targets to control movement endpoints. Ten healthy participants were recruited, and asked to perform separate trials of 35 consecutive cycles of spine flexion under both constrained and unconstrained conditions. Electromagnetic sensors that measure three-dimensional angular orientations were positioned over the pelvis and the spinous processes of L3, L1, and T11. Using the pelvic sensor as a reference, each sensor location on the spine was used to obtain a different representation of the three-dimensional spine angular kinematics. Local dynamic stability of each kinematic time-series was determined by calculating the maximum finite-time Lyapunov exponent (λmax). Estimates for λmax were significantly lower (i.e. dynamically more stable) for spine kinematic data obtained from the L3 sensor than those obtained from kinematic data using either the L1 or T11 sensors. Likewise, λmax was lower when the movement was constrained. These results emphasize the importance of proper placement of instrumentation for quantifying local dynamic stability of spine kinematics and are especially relevant for repeated measures designs where data are obtained from the same individual on multiple days. Copyright © 2015 Elsevier Ltd. All rights reserved.

Transport and Dynamics in Toroidal Fusion Systems

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

Schnack, Dalton D

2006-05-16

This document reports the successful completion of the OFES Theory Milestone for FY2005, namely, Perform parametric studies to better understand the edge physics regimes of laboratory experiments. Simulate at increased resolution (up to 20 toroidal modes), with density evolution, late into the nonlinear phase and compare results from different types of edge modes. Simulate a single case including a study of heat deposition on nearby material walls. The linear stability properties and nonlinear evolution of Edge Localized Modes (ELMs) in tokamak plasmas are investigated through numerical computation. Data from the DIII-D device at General Atomics (http://fusion.gat.com/diii-d/) is used for themore » magnetohydrodynamic (MHD) equilibria, but edge parameters are varied to reveal important physical effects. The equilibrium with very low magnetic shear produces an unstable spectrum that is somewhat insensitive to dissipation coefficient values. Here, linear growth rates from the non-ideal NIMROD code (http://nimrodteam.org) agree reasonably well with ideal, i.e. non-dissipative, results from the GATO global linear stability code at low toroidal mode number (n) and with ideal results from the ELITE edge linear stability code at moderate to high toroidal mode number. Linear studies with a more realistic sequence of MHD equilibria (based on DIII-D discharge 86166) produce more significant discrepancies between the ideal and non-ideal calculations. The maximum growth rate for the ideal computations occurs at toroidal mode index n=10, whereas growth rates in the non-ideal computations continue to increase with n unless strong anisotropic thermal conduction is included. Recent modeling advances allow drift effects associated with the Hall electric field and gyroviscosity to be considered. A stabilizing effect can be observed in the preliminary results, but while the distortion in mode structure is readily apparent at n=40, the growth rate is only 13% less than the non-ideal MHD result. Computations performed with a non-local kinetic closure for parallel electron thermal conduction that is valid over all collisionality regimes identify thermal diffusivity ratios of {chi}{sub ||}/{chi}{sub {perpendicular}} ~ 10{sup 7} - 10{sup 8} as appropriate when using collisional heat flux modeling for these modes. Adding significant parallel viscosity proves to have little effect. Nonlinear ELM computations solve the resistive MHD model with toroidal resolution 0{<=}n{<=}21, including anisotropic thermal conduction, temperature-dependent resistivity, and number density evolution. The computations are based on a realistic equilibrium with high pedestal temperature from the linear study. When the simulated ELM grows to appreciable amplitude, ribbon-like thermal structures extend from the separatrix to the wall as the spectrum broadens about a peak at n=13. Analysis of the results finds the heat flux on the wall to be very nonuniform with greatest intensity occurring in spots on the top and bottom of the chamber. Net thermal energy loss occurs on a time-scale of 100 {micro}s, and the instantaneous loss rate exceeds 1 GW.« less

Non-modal linear stability analysis of thin film spreading by Marangoni stresses

NASA Astrophysics Data System (ADS)

Fischer, Benjamin John

The spontaneous spreading and stability characteristics of a thin Newtonian liquid film partially coated by an insoluble surfactant monolayer are investigated in this thesis. Thin films sheared by Marangoni stresses ire characterized by film thinning in the upstream region near the terminating edge of the initial monolayer and an advancing ridge further downstream. For sufficiently thin films, experiments have shown there develops dendritic fingering patterns upstream of the ridge. To probe the mechanisms responsible for unstable flow, a non-modal linear stability analysis is required because the base-states describing these flows are space and time-dependent. A new measure of disturbance amplification is introduced, based on the relative kinetic energy of the perturbations to the base-states, to analyze surfactant monolayers spreading either from a finite or infinite source. These studies reveal that disturbance amplification is most significant in highly curved regions of the film characterized by a large: change in the shear stress, which can develop at the advancing ridge and at the edge of the initial monolayer. For spreading from both a finite and infinite source, disturbances that convect through the ridge undergo transient amplification but eventually decay to restore film stability. By contrast, disturbances that localize to the thinned region undergo sustained amplification when surfactant is continuously supplied to the liquid film thereby promoting film instability. By focusing on these susceptible regions, the relevant evolution equations are simplified to extract more information about the mechanism leading to instability. The length-scale controlling these "inner" regions represents the balance of viscous, capillary and Marangoni stresses. Simplification of these equations allows identification of steady travelling wave solutions whose linearized stability behavior shows that a flat film subject to a jump increase in shear stress is asymptotically unstable. This thesis concludes by comparing recent experiments in our laboratory of a droplet of low surface tension liquid (oleic acid) spreading on a thin Newtonian film (glycerol) before the onset of instability with numerical simulations. Similar power law behavior for the ridge advance and qualitatively similar film profiles shapes occur when the simulations utilize a non-linear equation of state for the surfactant monolayer.

Mode localization in a class of multidegree-of-freedom nonlinear systems with cyclic symmetry

NASA Astrophysics Data System (ADS)

Vakakis, Alexander F.; Cetinkaya, Cetin

1993-02-01

The free oscillations of n-degree-of-freedom (DOF) nonlinear systems with cyclic symmetry and weak coupling between substructures are examined. An asymptotic methodology is used to detect localized nonsimilar normal modes, i.e., free periodic motions spatially confined to only a limited number of substructures of the cyclic system. It is shown that nonlinear mode localization occurs in the perfectly symmetric, weakly coupled structure, in contrast to linear mode localization, which exists only in the presence of substructure 'mistuning'. In addition to the localized modes, nonlocalized modes are also found in the weakly coupled system. The stability of the identified modes is investigated by means of an approximate two-timing averaging mothodology, and the general theory is applied to the case of a cyclic system with three-DOF. The theoretical results are then verified by direct numerical integrations of the equations of motion.

Discontinuous Galerkin finite element method for the nonlinear hyperbolic problems with entropy-based artificial viscosity stabilization

NASA Astrophysics Data System (ADS)

Zingan, Valentin Nikolaevich

This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.

Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths

NASA Astrophysics Data System (ADS)

Chu, Jixun; Coron, Jean-Michel; Shang, Peipei

2015-10-01

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on the finite interval (0, 2 kπ) where k is a positive integer. The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove that the origin is (locally) asymptotically stable for the nonlinear system if the integer k is such that the kernel of the linear Korteweg-de Vries stationary equation is of dimension 1. This is for example the case if k = 1.

Effects of radial electric fields on linear ITG instabilities in W7-X and LHD

NASA Astrophysics Data System (ADS)

Riemann, J.; Kleiber, R.; Borchardt, M.

2016-07-01

The impact of radial electric fields on the properties of linear ion-temperature-gradient (ITG) modes in stellarators is studied. Numerical simulations have been carried out with the global particle-in-cell (PIC) code EUTERPE, modelling the behaviour of ITG modes in Wendelstein 7-X and an LHD-like configuration. In general, radial electric fields seem to lead to a reduction of ITG instability growth, which can be related to the action of an induced E× B -drift. Focus is set on the modification of mode properties (frequencies, power spectrum, spatial structure and localization) to understand the observed growth rates as the result of competing stabilizing mechanisms.

Linearization of digital derived rate algorithm for use in linear stability analysis

NASA Technical Reports Server (NTRS)

Graham, R. E.; Porada, T. W.

1985-01-01

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is desirable for many applications. A linearization technique for the DDR algorithm is investigated. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for performing classical linear stability analyses, while the DDR itself may be used in time response analysis.

Ideal MHD Stability and Characteristics of Edge Localized Modes on CFETR

NASA Astrophysics Data System (ADS)

Li, Zeyu; Chan, Vincent; Xu, Xueqiao; Wang, Xiaogang; Cfetr Physics Team

2017-10-01

Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario derived from multi-code integrated modeling, with key parameters varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for engineering design. The linear stabilities of low-n and intermediate-n peeling-ballooning modes for CFETR baseline scenario are analyzed. Multi-code benchmarking, including GATO, ELITE, BOUT + + and NIMROD, demonstrated good agreement in predicting instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT + + . Instabilities are found both at the pedestal top and inside the pedestal region, which lead to a mix of grassy and type I ELMs. Pedestal structures extending inward beyond the pedestal top are also varied to study the influence on ELM characteristic. Preliminary results on the dependence of the Type-I ELM divertor heat load scaling on machine size and pedestal pressure will also be presented. Prepared by LLNL under Contract DE-AC52-07NA27344 and National Magnetic Confinement Fusion Research Program of China (Grant No. 2014GB110003 and 2014GB107004).

Stability analysis and stabilization strategies for linear supply chains

NASA Astrophysics Data System (ADS)

Nagatani, Takashi; Helbing, Dirk

2004-04-01

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.

Uncontrolled Stability in Freely Flying Insects

NASA Astrophysics Data System (ADS)

Melfi, James, Jr.; Wang, Z. Jane

2015-11-01

One of the key flight modes of a flying insect is longitudinal flight, traveling along a localized two-dimensional plane from one location to another. Past work on this topic has shown that flying insects, unless stabilized by some external stimulus, are typically unstable to a well studied pitching instability. In our work, we examine this instability in a computational study to understand whether it is possible for either evolution or an aero-vehicle designer to stabilize longitudinal flight through changes to insect morphology, kinematics, or aerodynamic quantities. A quasi-steady wingbeat averaged flapping flight model is used to describe the insect. From this model, a number of non-dimensional parameters are identified. The effect of these parameters was then quantified using linear stability analysis, applied to various translational states of the insect. Based on our understanding of these parameters, we demonstrate how to find an intrinsically stable flapping flight sequence for a dragonfly-like flapping flier in an instantaneous flapping flight model.

Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems

NASA Astrophysics Data System (ADS)

Lenka, Bichitra Kumar; Banerjee, Soumitro

2018-03-01

We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems. Then by using the obtained results and linearization technique, a stability theorem is presented for autonomous nonlinear fractional order system. Finally, we design a control strategy for stabilization of autonomous nonlinear fractional order systems, and apply the results to the chaotic fractional order Lorenz system in order to verify its effectiveness.

Local Voltage Control in Distribution Networks: A Game-Theoretic Perspective

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

Zhou, Xinyang; Tian, Jie; Chen, Lijun

Inverter-based voltage regulation is gaining importance to alleviate emerging reliability and power-quality concerns related to distribution systems with high penetration of photovoltaic (PV) systems. This paper seeks contribution in the domain of reactive power compensation by establishing stability of local Volt/VAr controllers. In lieu of the approximate linear surrogate used in the existing work, the paper establishes existence and uniqueness of an equilibrium point using nonlinear AC power flow model. Key to this end is to consider a nonlinear dynamical system with non-incremental local Volt/VAr control, cast the Volt/VAr dynamics as a game, and leverage the fixed-point theorem as wellmore » as pertinent contraction mapping argument. Numerical examples are provided to complement the analytical results.« less

Local Voltage Control in Distribution Networks: A Game-Theoretic Perspective: Preprint

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

Zhou, Xinyang; Tian, Jie; Chen, Lijun

Inverter-based voltage regulation is gaining importance to alleviate emerging reliability and power-quality concerns related to distribution systems with high penetration of photovoltaic (PV) systems. This paper seeks contribution in the domain of reactive power compensation by establishing stability of local Volt/VAr controllers. In lieu of the approximate linear surrogate used in the existing work, the paper establishes existence and uniqueness of an equilibrium point using nonlinear AC power flow model. Key to this end is to consider a nonlinear dynamical system with non-incremental local Volt/VAr control, cast the Volt/VAr dynamics as a game, and leverage the fixed-point theorem as wellmore » as pertinent contraction mapping argument. Numerical examples are provided to complement the analytical results.« less

Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph

NASA Astrophysics Data System (ADS)

Noja, Diego; Pelinovsky, Dmitry; Shaikhova, Gaukhar

2015-07-01

We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear Schrödinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the junction). It is shown in the recent work [7] by using explicit Jacobi elliptic functions that the cubic NLS equation on a tadpole graph admits a rich structure of standing waves. Among these, there are different branches of localized waves bifurcating from the edge of the essential spectrum of an associated Schrödinger operator. We show by using a modified Lyapunov-Schmidt reduction method that the bifurcation of localized standing waves occurs for every positive power nonlinearity. We distinguish a primary branch of never vanishing standing waves bifurcating from the trivial solution and an infinite sequence of higher branches with oscillating behavior in the ring. The higher branches bifurcate from the branches of degenerate standing waves with vanishing tail outside the ring. Moreover, we analyze stability of bifurcating standing waves. Namely, we show that the primary branch is composed by orbitally stable standing waves for subcritical power nonlinearities, while all nontrivial higher branches are linearly unstable near the bifurcation point. The stability character of the degenerate branches remains inconclusive at the analytical level, whereas heuristic arguments based on analysis of embedded eigenvalues of negative Krein signatures support the conjecture of their linear instability at least near the bifurcation point. Numerical results for the cubic NLS equation show that this conjecture is valid and that the degenerate branches become spectrally stable far away from the bifurcation point.

A linear quadratic regulator approach to the stabilization of uncertain linear systems

NASA Technical Reports Server (NTRS)

Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

1990-01-01

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

NASA Technical Reports Server (NTRS)

Ottander, John A.; Hall, Robert A.; Powers, J. F.

2018-01-01

A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.

Unsupervised Gaussian Mixture-Model With Expectation Maximization for Detecting Glaucomatous Progression in Standard Automated Perimetry Visual Fields.

PubMed

Yousefi, Siamak; Balasubramanian, Madhusudhanan; Goldbaum, Michael H; Medeiros, Felipe A; Zangwill, Linda M; Weinreb, Robert N; Liebmann, Jeffrey M; Girkin, Christopher A; Bowd, Christopher

2016-05-01

To validate Gaussian mixture-model with expectation maximization (GEM) and variational Bayesian independent component analysis mixture-models (VIM) for detecting glaucomatous progression along visual field (VF) defect patterns (GEM-progression of patterns (POP) and VIM-POP). To compare GEM-POP and VIM-POP with other methods. GEM and VIM models separated cross-sectional abnormal VFs from 859 eyes and normal VFs from 1117 eyes into abnormal and normal clusters. Clusters were decomposed into independent axes. The confidence limit (CL) of stability was established for each axis with a set of 84 stable eyes. Sensitivity for detecting progression was assessed in a sample of 83 eyes with known progressive glaucomatous optic neuropathy (PGON). Eyes were classified as progressed if any defect pattern progressed beyond the CL of stability. Performance of GEM-POP and VIM-POP was compared to point-wise linear regression (PLR), permutation analysis of PLR (PoPLR), and linear regression (LR) of mean deviation (MD), and visual field index (VFI). Sensitivity and specificity for detecting glaucomatous VFs were 89.9% and 93.8%, respectively, for GEM and 93.0% and 97.0%, respectively, for VIM. Receiver operating characteristic (ROC) curve areas for classifying progressed eyes were 0.82 for VIM-POP, 0.86 for GEM-POP, 0.81 for PoPLR, 0.69 for LR of MD, and 0.76 for LR of VFI. GEM-POP was significantly more sensitive to PGON than PoPLR and linear regression of MD and VFI in our sample, while providing localized progression information. Detection of glaucomatous progression can be improved by assessing longitudinal changes in localized patterns of glaucomatous defect identified by unsupervised machine learning.

Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Perturbation and Stability Analysis of the Multi-Anticipative Intelligent Driver Model

NASA Astrophysics Data System (ADS)

Chen, Xi-Qun; Xie, Wei-Jun; Shi, Jing; Shi, Qi-Xin

This paper discusses three kinds of IDM car-following models that consider both the multi-anticipative behaviors and the reaction delays of drivers. Here, the multi-anticipation comes from two ways: (1) the driver is capable of evaluating the dynamics of several preceding vehicles, and (2) the autonomous vehicles can obtain the velocity and distance information of several preceding vehicles via inter-vehicle communications. In this paper, we study the stability of homogeneous traffic flow. The linear stability analysis indicates that the stable region will generally be enlarged by the multi-anticipative behaviors and reduced by the reaction delays. The temporal amplification and the spatial divergence of velocities for local perturbation are also studied, where the results further prove this conclusion. Simulation results also show that the multi-anticipative behaviors near the bottleneck will lead to a quicker backwards propagation of oscillations.

Waves on radial film flows

NASA Astrophysics Data System (ADS)

Cholemari, Murali R.; Arakeri, Jaywant H.

2005-08-01

We study the stability of surface waves on the radial film flow created by a vertical cylindrical water jet striking a horizontal plate. In such flows, surface waves have been found to be unstable and can cause transition to turbulence. This surface-wave-induced transition is different from the well-known Tollmien-Schlichting wave-induced transition. The present study aims at understanding the instability and the transition process. We do a temporal stability analysis by assuming the flow to be locally two-dimensional but including spatial variations to first order in the basic flow. The waves are found to be dispersive, mostly unstable, and faster than the mean flow. Spatial variation is the major destabilizing factor. Experiments are done to test the results of the linear stability analysis and to document the wave breakup and transition. Comparison between theory and experiments is fairly good and indicates the adequacy of the model.

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

Computerized dynamic posturography: the influence of platform stability on postural control.

PubMed

Palm, Hans-Georg; Lang, Patricia; Strobel, Johannes; Riesner, Hans-Joachim; Friemert, Benedikt

2014-01-01

Postural stability can be quantified using posturography systems, which allow different foot platform stability settings to be selected. It is unclear, however, how platform stability and postural control are mathematically correlated. Twenty subjects performed tests on the Biodex Stability System at all 13 stability levels. Overall stability index, medial-lateral stability index, and anterior-posterior stability index scores were calculated, and data were analyzed using analysis of variance and linear regression analysis. A decrease in platform stability from the static level to the second least stable level was associated with a linear decrease in postural control. The overall stability index scores were 1.5 ± 0.8 degrees (static), 2.2 ± 0.9 degrees (level 8), and 3.6 ± 1.7 degrees (level 2). The slope of the regression lines was 0.17 for the men and 0.10 for the women. A linear correlation was demonstrated between platform stability and postural control. The influence of stability levels seems to be almost twice as high in men as in women.

A nonlinear approach to transition in subcritical plasmas with sheared flow

NASA Astrophysics Data System (ADS)

Pringle, Chris C. T.; McMillan, Ben F.; Teaca, Bogdan

2017-12-01

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growth rates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs, with a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provide confidence in the derivation of a semi-analytic approximation for the minimal seed.

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Collapse for the higher-order nonlinear Schrödinger equation

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

Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data,more » are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.« less

Collapse for the higher-order nonlinear Schrödinger equation

DOE PAGES

Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; ...

2016-02-01

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data,more » are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.« less

Pattern dynamics of the reaction-diffusion immune system.

PubMed

Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

2018-01-01

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

Mathematical model of unmanned aerial vehicle used for endurance autonomous monitoring

NASA Astrophysics Data System (ADS)

Chelaru, Teodor-Viorel; Chelaru, Adrian

2014-12-01

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system, based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.

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

Chelaru, Teodor-Viorel, E-mail: teodor.chelaru@upb.ro; Chelaru, Adrian, E-mail: achelaru@incas.ro

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system,more » based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.« less

Electron Localization in Molecular Fragmentation of H{sub 2} by Carrier-Envelope Phase Stabilized Laser Pulses

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

Kremer, Manuel; Fischer, Bettina; Feuerstein, Bernold

2009-11-20

Fully differential data for H{sub 2} dissociation in ultrashort (6 fs, 760 nm), linearly polarized, intense (0.44 PW/cm{sup 2}) laser pulses with a stabilized carrier-envelope phase (CEP) were recorded with a reaction microscope. Depending on the CEP, the molecular orientation, and the kinetic energy release (KER), we find asymmetric proton emission at low KERs (0-3 eV), basically predicted by Roudnev and Esry, and much stronger than reported by Kling et al. Wave packet propagation calculations reproduce the salient features and discard, together with the observed KER-independent electron asymmetry, the first ionization step to be the reason for the asymmetric protonmore » emission.« less

Mineral Nutritional Yield and Nutrient Density of Locally Adapted Wheat Genotypes under Organic Production

PubMed Central

Moreira-Ascarrunz, Sergio Daniel; Larsson, Hans; Prieto-Linde, Maria Luisa; Johansson, Eva

2016-01-01

The aim of the present investigation was to investigate the nutritional yield, nutrient density, stability, and adaptability of organically produced wheat for sustainable and nutritional high value food production. This study evaluated the nutritional yield of four minerals (Fe, Zn, Cu, and Mg) in 19 wheat genotypes, selected as being locally adapted under organic agriculture conditions. The new metric of nutritional yield was calculated for each genotype and they were evaluated for stability using the Additive Main effects and Multiplicative Interaction (AMMI) stability analysis and for genotypic value, stability, and adaptability using the Best Linear Unbiased Prediction (BLUP procedure). The results indicated that there were genotypes suitable for production under organic agriculture conditions with satisfactory yields (>4000 kg·ha−1). Furthermore, these genotypes showed high nutritional yield and nutrient density for the four minerals studied. Additionally, since these genotypes were stable and adaptable over three environmentally different years, they were designated “balanced genotypes” for the four minerals and for the aforementioned characteristics. Selection and breeding of such “balanced genotypes” may offer an alternative to producing nutritious food under low-input agriculture conditions. Furthermore, the type of evaluation presented here may also be of interest for implementation in research conducted in developing countries, following the objectives of producing enough nutrients for a growing population. PMID:28231184

Toroidal Geometry Stabilizing a Latitudinal Ring of Point Vortices on a Torus

NASA Astrophysics Data System (ADS)

Sakajo, Takashi; Shimizu, Yuuki

2018-06-01

We carry out the linear stability analysis of a polygonal ring configuration of N point vortices, called an N-ring, along the line of latitude θ _0 on a torus with the aspect ratio α . Deriving a criterion for the stability depending on the parameters N, θ _0 and α , we reveal how the aspect ratio α contributes to the stability of the N-ring. While the N-ring necessarily becomes unstable when N is sufficiently large for fixed α , the stability is closely associated with the geometric property of the torus for variable α ; for low aspect ratio α ˜ 1, N=7 is a critical number determining the stability of the N-ring when it is located along a certain range of latitudes, which is an analogous result to those in a plane and on a sphere. On the other hand, the stability is determined by the sign of curvature for high aspect ratio α ≫ 1. That is to say, the N-ring is neutrally stable if it is located on the inner side of the toroidal surface with a negative curvature, while the N-ring on its outer side with a positive curvature is unstable. Furthermore, based on the linear stability analysis, we describe nonlinear evolution of the N-ring when it becomes unstable. It is difficult to deal with this problem, since the evolution equation of the N point vortices is formulated as a Hamiltonian system with N degrees of freedom, which is in general non-integrable. Thus, we reduce the Hamiltonian system to a simple integrable system by introducing a cyclic symmetry. Owing to this reduction, we successfully find some periodic orbits in the reduced system, whose local bifurcations and global transitions for variable α are characterized in terms of the fundamental group of the torus.

Local coexistence of VO 2 phases revealed by deep data analysis

DOE PAGES

Strelcov, Evgheni; Ievlev, Anton; Tselev, Alexander; ...

2016-07-07

We report a synergistic approach of micro-Raman spectroscopic mapping and deep data analysis to study the distribution of crystallographic phases and ferroelastic domains in a defected Al-doped VO 2 microcrystal. Bayesian linear unmixing revealed an uneven distribution of the T phase, which is stabilized by the surface defects and uneven local doping that went undetectable by other classical analysis techniques such as PCA and SIMPLISMA. This work demonstrates the impact of information recovery via statistical analysis and full mapping in spectroscopic studies of vanadium dioxide systems, which is commonly substituted by averaging or single point-probing approaches, both of which suffermore » from information misinterpretation due to low resolving power.« less

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

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.

Stability of multiloop LQ regulators with nonlinearities. I - Regions of attraction. II - Regions of ultimate boundedness

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1986-01-01

An investigation is conducted for the closed loop stability of linear time-invariant systems controlled by linear quadratic (LQ) regulators, in cases where nonlinearities exist in the control channels lying outside the stability sector in regions away from the origin. The estimate of the region of attraction thus obtained furnishes methods for the selection of performance function weights for more robust LQ designs. Attention is then given to the closed loop stability of linear time-invariant systems controlled by the LQ regulators when the nonlinearities in the loops escape the stability sector in a bounded region containing the origin.

Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems

NASA Technical Reports Server (NTRS)

Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.

Microsegregation during directional solidification

NASA Technical Reports Server (NTRS)

Coriell, S. R.; Mcfadden, G. B.

1984-01-01

During the directional solidification of alloys, solute inhomogeneities transverse to the growth direction arise due to morphological instabilities (leading to cellular or dendritic growth) and/or due to convection in the melt. In the absence of convection, the conditions for the onset of morphological instability are given by the linear stability analysis of Mullins and Sekerka. For ordinary solidification rates, the predictions of linear stability analysis are similar to the constitutional supercooling criterion. However, at very rapid solidification rates, linear stability analysis predicts a vast increase in stabilization in comparison to constitutional supercooling.

Robust stability of bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Park, Ju H.

2006-01-01

Based on the Lyapunov Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

NASA Astrophysics Data System (ADS)

Chang, Xia; Xie, Jiayu; Wu, Tianle; Tang, Bing

2018-07-01

A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.

ULF waves and plasma stability in different regions of the magnetosheath

NASA Astrophysics Data System (ADS)

Soucek, Jan; Escoubet, C. Philippe; Grison, Benjamin

2016-04-01

We present a statistical study of the occurrence and properties of ultra low frequency waves in the magnetosheath and interpret the results in terms of the competition of mirror and Alfvén-ion-cyclotron (AIC) instabilities. Both mirror and AIC waves are generated in high beta plasma of the magnetosheath when ion temperature anisotropy exceeds the threshold of the respective instabilities. These waves are frequently observed in the terrestrial and planetary magnetosheaths, but their distribution within the magnetosheath is inhomogeneous and their character varies as a function of location, local and upstream plasma parameters. We studied the spatial distribution of the two wave modes in the magnetosheath together with the local plasma parameters important for the stability of ULF waves. This analysis was performed on a dataset of all magnetosheath crossings observed by Cluster spacecraft over two years. For each observation we used bow shock, magnetopause and magnetosheath flow models to identify the relative position of the spacecraft with respect to magnetosheath boundaries and local properties of the upstream shock crossing. A strong dependence of parameters characterizing plasma stability and mirror/AIC wave occurrence on upstream ΘBn and MA is identified. The occurrence of mirror and AIC modes was compared against the respective instability thresholds and it was observed that AIC waves occurred nearly exclusively under mirror stable conditions. This is interpreted in terms of the different character of non-linear saturation of the two modes.

Analysis of quality control data of eight modern radiotherapy linear accelerators: the short- and long-term behaviours of the outputs and the reproducibility of quality control measurements

NASA Astrophysics Data System (ADS)

Kapanen, Mika; Tenhunen, Mikko; Hämäläinen, Tuomo; Sipilä, Petri; Parkkinen, Ritva; Järvinen, Hannu

2006-07-01

Quality control (QC) data of radiotherapy linear accelerators, collected by Helsinki University Central Hospital between the years 2000 and 2004, were analysed. The goal was to provide information for the evaluation and elaboration of QC of accelerator outputs and to propose a method for QC data analysis. Short- and long-term drifts in outputs were quantified by fitting empirical mathematical models to the QC measurements. Normally, long-term drifts were well (<=1%) modelled by either a straight line or a single-exponential function. A drift of 2% occurred in 18 ± 12 months. The shortest drift times of only 2-3 months were observed for some new accelerators just after the commissioning but they stabilized during the first 2-3 years. The short-term reproducibility and the long-term stability of local constancy checks, carried out with a sealed plane parallel ion chamber, were also estimated by fitting empirical models to the QC measurements. The reproducibility was 0.2-0.5% depending on the positioning practice of a device. Long-term instabilities of about 0.3%/month were observed for some checking devices. The reproducibility of local absorbed dose measurements was estimated to be about 0.5%. The proposed empirical model fitting of QC data facilitates the recognition of erroneous QC measurements and abnormal output behaviour, caused by malfunctions, offering a tool to improve dose control.

Improved Power System Stability Using Backtracking Search Algorithm for Coordination Design of PSS and TCSC Damping Controller.

PubMed

Niamul Islam, Naz; Hannan, M A; Mohamed, Azah; Shareef, Hussain

2016-01-01

Power system oscillation is a serious threat to the stability of multimachine power systems. The coordinated control of power system stabilizers (PSS) and thyristor-controlled series compensation (TCSC) damping controllers is a commonly used technique to provide the required damping over different modes of growing oscillations. However, their coordinated design is a complex multimodal optimization problem that is very hard to solve using traditional tuning techniques. In addition, several limitations of traditionally used techniques prevent the optimum design of coordinated controllers. In this paper, an alternate technique for robust damping over oscillation is presented using backtracking search algorithm (BSA). A 5-area 16-machine benchmark power system is considered to evaluate the design efficiency. The complete design process is conducted in a linear time-invariant (LTI) model of a power system. It includes the design formulation into a multi-objective function from the system eigenvalues. Later on, nonlinear time-domain simulations are used to compare the damping performances for different local and inter-area modes of power system oscillations. The performance of the BSA technique is compared against that of the popular particle swarm optimization (PSO) for coordinated design efficiency. Damping performances using different design techniques are compared in term of settling time and overshoot of oscillations. The results obtained verify that the BSA-based design improves the system stability significantly. The stability of the multimachine power system is improved by up to 74.47% and 79.93% for an inter-area mode and a local mode of oscillation, respectively. Thus, the proposed technique for coordinated design has great potential to improve power system stability and to maintain its secure operation.

Stability analysis of the onset of vortex shedding for wakes behind flat plates

NASA Astrophysics Data System (ADS)

Wang, Shuai; Liu, Li; Zhang, Shi-Bo; Wen, Feng-Bo; Zhou, Xun

2018-04-01

Above a critical Reynolds number, wake flows behind flat plates become globally unstable, the leading modal instability in this case is known as Kelvin-Helmholtz mechanism. In this article, both local and BiGlobal linear instability analyses are performed numerically to study the onset of the shedding process. Flat plates with different base shapes are considered to assess geometry effects, and the relation between the critical shedding Reynolds number, Re_cr , and the boundary layer thickness is studied. Three types of base shapes are used: square, triangular and elliptic. It is found that the base shape has a great impact on the growth rate of least stable disturbance mode, thus would influence Re_cr greatly, but it has little effect on the vortex shedding frequency. The shedding frequency is determined mainly by boundary layer thickness and has little dependence on the Reynolds number and base shape. We find that for a fixed Reynolds number, increasing boundary layer thickness acted in two ways to modify the global stability characteristics: It increases the length of the absolute unstable region and it makes the flow less locally absolutely unstable in the near-wake region, and these two effects work against each other to destabilize or stabilize the flow.

Local dynamic stability and gait variability during attentional tasks in young adults.

PubMed

Magnani, Rina Márcia; Lehnen, Georgia Cristina; Rodrigues, Fábio Barbosa; de Sá E Souza, Gustavo Souto; de Oliveira Andrade, Adriano; Vieira, Marcus Fraga

2017-06-01

Cell phone use while walking may be a cognitive distraction and reduce visual and motor attention. Thus, the aim of this study was to verify the effects of attentional dual-tasks while using a cell phone in different conditions. Stability, regularity, and linear variability of trunk kinematics, and gait spatiotemporal parameters in young adults were measured. Twenty young subjects of both genders were asked to walk on a treadmill for 4min under the following conditions: (a) looking forward at a fixed target 2.5m away (walking); (b) talking on a cell phone with unilateral handling (talking); (c) texting messages on a cell phone with unilateral handling (texting); and (d) looking forward at the aforementioned target while listening to music without handling the phone (listening). Local dynamic stability measured in terms of the largest Lyapunov exponent decreased while handling a cell phone (talking and texting). Gait variability and regularity increased when talking on a cell phone, but no variable changed in the listening condition. Under all dual-task conditions, there were significant increases in stride width and its variability. We conclude that young adults who use a cell phone when walking adapt their gait pattern conservatively, which can be because of increased attentional demand during cell phone use. Copyright © 2017 Elsevier B.V. All rights reserved.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

The stability cycle—A universal pathway for the stability of films over topography

NASA Astrophysics Data System (ADS)

Schörner, Mario; Aksel, Nuri

2018-01-01

In the present study on the linear stability of gravity-driven Newtonian films flowing over inclined topographies, we consider a fundamental question: Is there a universal principle, being valid to describe the parametric evolution of the flow's stability chart for variations of different system parameters? For this sake, we first screened all experimental and numerical stability charts available in the literature. In a second step, we performed experiments to fill the gaps which remained. Variations of the fluid's viscosity and the topography's specific shape, amplitude, wavelength, tip width, and inclination were considered. That way, we identified a set of six characteristic patterns of stability charts to be sufficient to describe and unify all results on the linear stability of Newtonian films flowing over undulated inclines. We unveiled a universal pathway—the stability cycle—along which the linear stability charts of all considered Newtonian films flowing down periodically corrugated inclines evolved when the system parameters were changed.

Review of LFTs, LMIs, and mu. [Linear Fractional Transformations, Linear Matrix Inequalities

NASA Technical Reports Server (NTRS)

Doyle, John; Packard, Andy; Zhou, Kemin

1991-01-01

The authors present a tutorial overview of linear fractional transformations (LFTs) and the role of the structured singular value, mu, and linear matrix inequalities (LMIs) in solving LFT problems. The authors first introduce the notation for LFTs and briefly discuss some of their properties. They then describe mu and its connections with LFTs. They focus on two standard notions of robust stability and performance, mu stability and performance and Q stability and performance, and their relationship is discussed. Comparisons with the L1 theory of robust performance with structured uncertainty are considered.

Photoinduced intramolecular charge transfer (ICT) reaction in trans-methyl p-(dimethylamino) cinnamate: A combined fluorescence measurement and quantum chemical calculations

NASA Astrophysics Data System (ADS)

Chakraborty, Amrita; Kar, Samiran; Guchhait, Nikhil

2006-01-01

The photophysical behaviour of trans-methyl p-(dimethylamino) cinnamate ( t-MDMAC) donor-acceptor system has been investigated by steady-state absorption and emission spectroscopy and quantum chemical calculations. The molecule t-MDMAC shows an emission from the locally excited state in non-polar solvents. In addition to weak local emission, a strong solvent dependent red shifted fluorescence in polar aprotic solvents is attributed to highly polar intramolecular charge transfer state. However, the formation of hydrogen-bonded clusters with polar protic solvents has been suggested from a linear correlation between the observed red shifted fluorescence band maxima with hydrogen bonding parameters ( α). Calculations by ab initio and density functional theory show that the lone pair electron at nitrogen center is out of plane of the benzene ring in the global minimum ground state structure. In the gas phase, a potential energy surface along the twist coordinate at the donor (-NMe 2) and acceptor (-CH = CHCOOMe) sites shows stabilization of S 1 state and destabilization S 2 and S 0 states. A similar potential energy calculation along the twist coordinate in acetonitrile solvent using non-equilibrium polarized continuum model also shows more stabilization of S 1 state relative to other states and supports solvent dependent red shifted emission properties. In all types of calculations it is found that the nitrogen lone pair is delocalized over the benzene ring in the global minimum ground state and is localized on the nitrogen centre at the 90° twisted configuration. The S 1 energy state stabilization along the twist coordinate at the donor site and localized nitrogen lone pair at the perpendicular configuration support well the observed dual fluorescence in terms of proposed twisted intramolecular charge transfer (TICT) model.

PROGRESS IN THE PEELING-BALLOONING MODEL OF ELMS: TOROIDAL ROTATION AND 3D NONLINEAR DYNAMICS

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

SNYDER,P.B; WILSON,H.R; XU,X.Q

2004-06-01

Understanding the physics of the H-Mode pedestal and edge localized modes (ELMs) is very important to next-step fusion devices for two primary reasons: (1) The pressure at the top of the edge barrier (''pedestal height'') strongly impacts global confinement and fusion performance, and (2) large ELMs lead to localized transient heat loads on material surfaces that may constrain component lifetimes. The development of the peeling-ballooning model has shed light on these issues by positing a mechanism for ELM onset and constraints on the pedestal height. The mechanism involves instability of ideal coupled ''peeling-ballooning'' modes driven by the sharp pressure gradientmore » and consequent large bootstrap current in the H-mode edge. It was first investigated in the local, high-n limit [1], and later quantified for non-local, finite-n modes in general toroidal geometry [2,3]. Important aspects are that a range of wavelengths may potentially be unstable, with intermediate n's (n {approx} 3-30) generally limiting in high performance regimes, and that stability bounds are strongly sensitive to shape [Fig l(a)], and to collisionality (i.e. temperature and density) [4] through the bootstrap current. The development of efficient MHD stability codes such as ELITE [3,2] and MISHKA [5] has allowed detailed quantification of peeling-ballooning stability bounds (e.g. [6]) and extensive and largely successful comparisons with observation (e.g. [2,6-9]). These previous calculations are ideal, static, and linear. Here we extend this work to incorporate the impact of sheared toroidal rotation, and the non-ideal, nonlinear dynamics which must be studied to quantify ELM size and heat deposition on material surfaces.« less

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1995-01-01

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Effect of turbulent eddy viscosity on the unstable surface mode above an acoustic liner

NASA Astrophysics Data System (ADS)

Marx, David; Aurégan, Yves

2013-07-01

Lined ducts are used to reduce noise radiation from ducts in turbofan engines. In certain conditions they may sustain hydrodynamic instabilities. A local linear stability analysis of the flow in a 2D lined channel is performed using a numerical integration of the governing equations. Several model equations are used, one of them taking into account turbulent eddy viscosity, and a realistic turbulent mean flow profile is used that vanishes at the wall. The stability analysis results are compared to published experimental results. Both the model and the experiments show the existence of an unstable mode, and the importance of taking into account eddy viscosity in the model is shown. When this is done, quantities such as the growth rate and the velocity eigenfunctions are shown to agree correctly.

Crossflow Stability and Transition Experiments in Swept-Wing Flow

NASA Technical Reports Server (NTRS)

Dagenhart, J. Ray; Saric, William S.

1999-01-01

An experimental examination of crossflow instability and transition on a 45deg swept wing was conducted in the Arizona State University Unsteady Wind Tunnel. The stationary-vortex pattern and transition location are visualized by using both sublimating chemical and liquid-crystal coatings. Extensive hot-wire measurements were obtained at several measurement stations across a single vortex track. The mean and travelling wave disturbances were measured simultaneously. Stationary crossflow disturbance profiles were determined by subtracting either a reference or a span-averaged velocity profile from the mean velocity data. Mean, stationary crossflow, and traveling wave velocity data were presented as local boundary layer profiles and contour plots across a single stationary crossflow vortex track. Disturbance mode profiles and growth rates were determined. The experimental data are compared with predictions from linear stability theory.

Kinematic measures for assessing gait stability in elderly individuals: a systematic review

PubMed Central

Hamacher, D.; Singh, N.B.; Van Dieën, J.H.; Heller, M.O.; Taylor, W.R.

2011-01-01

Falls not only present a considerable health threat, but the resulting treatment and loss of working days also place a heavy economic burden on society. Gait instability is a major fall risk factor, particularly in geriatric patients, and walking is one of the most frequent dynamic activities of daily living. To allow preventive strategies to become effective, it is therefore imperative to identify individuals with an unstable gait. Assessment of dynamic stability and gait variability via biomechanical measures of foot kinematics provides a viable option for quantitative evaluation of gait stability, but the ability of these methods to predict falls has generally not been assessed. Although various methods for assessing gait stability exist, their sensitivity and applicability in a clinical setting, as well as their cost-effectiveness, need verification. The objective of this systematic review was therefore to evaluate the sensitivity of biomechanical measures that quantify gait stability among elderly individuals and to evaluate the cost of measurement instrumentation required for application in a clinical setting. To assess gait stability, a comparative effect size (Cohen's d) analysis of variability and dynamic stability of foot trajectories during level walking was performed on 29 of an initial yield of 9889 articles from four electronic databases. The results of this survey demonstrate that linear variability of temporal measures of swing and stance was most capable of distinguishing between fallers and non-fallers, whereas step width and stride velocity prove more capable of discriminating between old versus young (OY) adults. In addition, while orbital stability measures (Floquet multipliers) applied to gait have been shown to distinguish between both elderly fallers and non-fallers as well as between young and old adults, local stability measures (λs) have been able to distinguish between young and old adults. Both linear and nonlinear measures of foot time series during gait seem to hold predictive ability in distinguishing healthy from fall-prone elderly adults. In conclusion, biomechanical measurements offer promise for identifying individuals at risk of falling and can be obtained with relatively low-cost tools. Incorporation of the most promising measures in combined retrospective and prospective studies for understanding fall risk and designing preventive strategies is warranted. PMID:21880615

Kinematic measures for assessing gait stability in elderly individuals: a systematic review.

PubMed

Hamacher, D; Singh, N B; Van Dieën, J H; Heller, M O; Taylor, W R

2011-12-07

Falls not only present a considerable health threat, but the resulting treatment and loss of working days also place a heavy economic burden on society. Gait instability is a major fall risk factor, particularly in geriatric patients, and walking is one of the most frequent dynamic activities of daily living. To allow preventive strategies to become effective, it is therefore imperative to identify individuals with an unstable gait. Assessment of dynamic stability and gait variability via biomechanical measures of foot kinematics provides a viable option for quantitative evaluation of gait stability, but the ability of these methods to predict falls has generally not been assessed. Although various methods for assessing gait stability exist, their sensitivity and applicability in a clinical setting, as well as their cost-effectiveness, need verification. The objective of this systematic review was therefore to evaluate the sensitivity of biomechanical measures that quantify gait stability among elderly individuals and to evaluate the cost of measurement instrumentation required for application in a clinical setting. To assess gait stability, a comparative effect size (Cohen's d) analysis of variability and dynamic stability of foot trajectories during level walking was performed on 29 of an initial yield of 9889 articles from four electronic databases. The results of this survey demonstrate that linear variability of temporal measures of swing and stance was most capable of distinguishing between fallers and non-fallers, whereas step width and stride velocity prove more capable of discriminating between old versus young (OY) adults. In addition, while orbital stability measures (Floquet multipliers) applied to gait have been shown to distinguish between both elderly fallers and non-fallers as well as between young and old adults, local stability measures (λs) have been able to distinguish between young and old adults. Both linear and nonlinear measures of foot time series during gait seem to hold predictive ability in distinguishing healthy from fall-prone elderly adults. In conclusion, biomechanical measurements offer promise for identifying individuals at risk of falling and can be obtained with relatively low-cost tools. Incorporation of the most promising measures in combined retrospective and prospective studies for understanding fall risk and designing preventive strategies is warranted.

Numerical simulations and linear stability analysis of a boundary layer developed on wavy surfaces

NASA Astrophysics Data System (ADS)

Siconolfi, Lorenzo; Camarri, Simone; Fransson, Jens H. M.

2015-11-01

The development of passive methods leading to a laminar to turbulent transition delay in a boundary layer (BL) is a topic of great interest both for applications and academic research. In literature it has been shown that a proper and stable spanwise velocity modulation can reduce the growth rate of Tollmien-Schlichting (TS) waves and delay transition. In this study, we investigate numerically the possibility of obtaining a stabilizing effect of the TS waves through the use of a spanwise sinusoidal modulation of a flat plate. This type of control has been already successfully investigated experimentally. An extensive set of direct numerical simulations is carried out to study the evolution of a BL flow developed on wavy surfaces with different geometric characteristics, and the results will be presented here. Moreover, since this configuration is characterized by a slowly-varying flow field in streamwise direction, a local stability analysis is applied to define the neutral stability curves for the BL flow controlled by this type of wall modifications. These results give the possibility of investigating this control strategy and understanding the effect of the free parameters on the stabilization mechanism.

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.

Stability of Local Quantum Dissipative Systems

NASA Astrophysics Data System (ADS)

Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David

2015-08-01

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.

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.

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

A nonlinear H-infinity approach to optimal control of the depth of anaesthesia

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Rigatou, Efthymia; Zervos, Nikolaos

2016-12-01

Controlling the level of anaesthesia is important for improving the success rate of surgeries and for reducing the risks to which operated patients are exposed. This paper proposes a nonlinear H-infinity approach to optimal control of the level of anaesthesia. The dynamic model of the anaesthesia, which describes the concentration of the anaesthetic drug in different parts of the body, is subjected to linearization at local operating points. These are defined at each iteration of the control algorithm and consist of the present value of the system's state vector and of the last control input that was exerted on it. For this linearization Taylor series expansion is performed and the system's Jacobian matrices are computed. For the linearized model an H-infinity controller is designed. The feedback control gains are found by solving at each iteration of the control algorithm an algebraic Riccati equation. The modelling errors due to this approximate linearization are considered as disturbances which are compensated by the robustness of the control loop. The stability of the control loop is confirmed through Lyapunov analysis.

Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

PubMed

Li, Hongwei; Guo, Yue

2017-12-01

The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Homoepitaxial graphene tunnel barriers for spin transport

NASA Astrophysics Data System (ADS)

Friedman, Adam L.; van't Erve, Olaf M. J.; Robinson, Jeremy T.; Whitener, Keith E.; Jonker, Berend T.

2016-05-01

Tunnel barriers are key elements for both charge-and spin-based electronics, offering devices with reduced power consumption and new paradigms for information processing. Such devices require mating dissimilar materials, raising issues of heteroepitaxy, interface stability, and electronic states that severely complicate fabrication and compromise performance. Graphene is the perfect tunnel barrier. It is an insulator out-of-plane, possesses a defect-free, linear habit, and is impervious to interdiffusion. Nonetheless, true tunneling between two stacked graphene layers is not possible in environmental conditions usable for electronics applications. However, two stacked graphene layers can be decoupled using chemical functionalization. Here, we demonstrate that hydrogenation or fluorination of graphene can be used to create a tunnel barrier. We demonstrate successful tunneling by measuring non-linear IV curves and a weakly temperature dependent zero-bias resistance. We demonstrate lateral transport of spin currents in non-local spin-valve structures, and determine spin lifetimes with the non-local Hanle effect. We compare the results for hydrogenated and fluorinated tunnel and we discuss the possibility that ferromagnetic moments in the hydrogenated graphene tunnel barrier affect the spin transport of our devices.

Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers

NASA Astrophysics Data System (ADS)

Schulze, Morgan W.; Lewis, Ronald M.; Lettow, James H.; Hickey, Robert J.; Gillard, Timothy M.; Hillmyer, Marc A.; Bates, Frank S.

2017-05-01

Small angle x-ray scattering experiments on three model low molar mass diblock copolymer systems containing minority polylactide and majority hydrocarbon blocks demonstrate that conformational asymmetry stabilizes the Frank-Kasper σ phase. Differences in block flexibility compete with space filling at constant density inducing the formation of polyhedral shaped particles that assemble into this low symmetry ordered state with local tetrahedral coordination. These results confirm predictions from self-consistent field theory that establish the origins of symmetry breaking in the ordering of block polymer melts subjected to compositional and conformational asymmetry.

Byzantine-fault tolerant self-stabilizing protocol for distributed clock synchronization systems

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R. (Inventor)

2010-01-01

A rapid Byzantine self-stabilizing clock synchronization protocol that self-stabilizes from any state, tolerates bursts of transient failures, and deterministically converges within a linear convergence time with respect to the self-stabilization period. Upon self-stabilization, all good clocks proceed synchronously. The Byzantine self-stabilizing clock synchronization protocol does not rely on any assumptions about the initial state of the clocks. Furthermore, there is neither a central clock nor an externally generated pulse system. The protocol converges deterministically, is scalable, and self-stabilizes in a short amount of time. The convergence time is linear with respect to the self-stabilization period.

Stability analysis of piecewise non-linear systems and its application to chaotic synchronisation with intermittent control

NASA Astrophysics Data System (ADS)

Wang, Qingzhi; Tan, Guanzheng; He, Yong; Wu, Min

2017-10-01

This paper considers a stability analysis issue of piecewise non-linear systems and applies it to intermittent synchronisation of chaotic systems. First, based on piecewise Lyapunov function methods, more general and less conservative stability criteria of piecewise non-linear systems in periodic and aperiodic cases are presented, respectively. Next, intermittent synchronisation conditions of chaotic systems are derived which extend existing results. Finally, Chua's circuit is taken as an example to verify the validity of our methods.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Nearly metastable rhombohedral phases of bcc metals

NASA Astrophysics Data System (ADS)

Mehl, Michael J.; Finkenstadt, Daniel

2008-02-01

The energy E(c/a) for a bcc element stretched along its [001] axis (the Bain path) has a minimum at c/a=1 , a maximum at c/a=2 , and an elastically unstable local minimum at c/a>2 . An alternative path connecting the bcc and fcc structures is the rhombohedral lattice. The primitive lattice has R3¯m symmetry, with the angle α changing from 109.4° (bcc), to 90° (simple cubic), to 60 ° (fcc). We study this path for the non-magnetic bcc transition metals (V, Nb, Mo, Ta, and W) using both all-electron linearized augmented plane wave and projector augmented wave VASP codes. Except for Ta, the energy E(α) has a local maximum at α=60° , with local minima near 55° and 70° , the latter having lower energy, suggesting the possibility of a metastable rhombohedral state for these materials. We first examine the elastic stability of the 70° minimum structure, and determine that only W is elastically stable in this structure, with the smallest eigenvalue of the elastic tensor at 4GPa . We then consider the possibility that tungsten is actually metastable in this structure by looking at its vibrational and third-order elastic stability.

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers. M.S. Thesis

NASA Technical Reports Server (NTRS)

Berry, S. A.

1986-01-01

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

Network-Cognizant Voltage Droop Control for Distribution Grids

DOE PAGES

Baker, Kyri; Bernstein, Andrey; Dall'Anese, Emiliano; ...

2017-08-07

Our paper examines distribution systems with a high integration of distributed energy resources (DERs) and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies where the active and reactive output-powers of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximation of the AC power-flow equations and is network-cognizant; that is, the coefficients of the controllers embed information on the location of the DERs and forecasted non-controllable loads/injections and, consequently, on themore » effect of DER power adjustments on the overall voltage profile. We pursued a robust approach to cope with uncertainty in the forecasted non-controllable loads/power injections. Stability of the proposed local controllers is analytically assessed and numerically corroborated.« less

Network-Cognizant Voltage Droop Control for Distribution Grids

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

Baker, Kyri; Bernstein, Andrey; Dall'Anese, Emiliano

Our paper examines distribution systems with a high integration of distributed energy resources (DERs) and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies where the active and reactive output-powers of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximation of the AC power-flow equations and is network-cognizant; that is, the coefficients of the controllers embed information on the location of the DERs and forecasted non-controllable loads/injections and, consequently, on themore » effect of DER power adjustments on the overall voltage profile. We pursued a robust approach to cope with uncertainty in the forecasted non-controllable loads/power injections. Stability of the proposed local controllers is analytically assessed and numerically corroborated.« less

Mathematical modelling and linear stability analysis of laser fusion cutting

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

Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg

A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.

Stabilization of nucleic acids by unusual polyamines produced by an extreme thermophile, Thermus thermophilus

PubMed Central

2005-01-01

Extreme thermophiles produce two types of unusual polyamine: long linear polyamines such as caldopentamine and caldohexamine, and branched polyamines such as quaternary ammonium compounds [e.g. tetrakis(3-aminopropyl)ammonium]. To clarify the physiological roles of long linear and branched polyamines in thermophiles, we synthesized them chemically and tested their effects on the stability of ds (double-stranded) and ss (single-stranded) DNAs and tRNA in response to thermal denaturation, as measured by differential scanning calorimetry. Linear polyamines stabilized dsDNA in proportion to the number of amino nitrogen atoms within their molecular structure. We used the empirical results to derive formulae that estimate the melting temperature of dsDNA in the presence of polyamines of a particular molecular composition. ssDNA and tRNA were stabilized more effectively by tetrakis(3-aminopropyl)ammonium than any of the other polyamines tested. We propose that long linear polyamines are effective to stabilize DNA, and tetrakis(3-aminopropyl)ammonium plays important roles in stabilizing RNAs in thermophile cells. PMID:15673283

Control method for physical systems and devices

DOEpatents

Guckenheimer, John

1997-01-01

A control method for stabilizing systems or devices that are outside the control domain of a linear controller is provided. When applied to nonlinear systems, the effectiveness of this method depends upon the size of the domain of stability that is produced for the stabilized equilibrium. If this domain is small compared to the accuracy of measurements or the size of disturbances within the system, then the linear controller is likely to fail within a short period. Failure of the system or device can be catastrophic: the system or device can wander far from the desired equilibrium. The method of the invention presents a general procedure to recapture the stability of a linear controller, when the trajectory of a system or device leaves its region of stability. By using a hybrid strategy based upon discrete switching events within the state space of the system or device, the system or device will return from a much larger domain to the region of stability utilized by the linear controller. The control procedure is robust and remains effective under large classes of perturbations of a given underlying system or device.

The algebraic criteria for the stability of control systems

NASA Technical Reports Server (NTRS)

Cremer, H.; Effertz, F. H.

1986-01-01

This paper critically examines the standard algebraic criteria for the stability of linear control systems and their proofs, reveals important previously unnoticed connections, and presents new representations. Algebraic stability criteria have also acquired significance for stability studies of non-linear differential equation systems by the Krylov-Bogoljubov-Magnus Method, and allow realization conditions to be determined for classes of broken rational functions as frequency characteristics of electrical network.

Failure analysis of thick composite cylinders under external pressure

NASA Technical Reports Server (NTRS)

Caiazzo, A.; Rosen, B. W.

1992-01-01

Failure of thick section composites due to local compression strength and overall structural instability is treated. Effects of material nonlinearity, imperfect fiber architecture, and structural imperfections upon anticipated failure stresses are determined. Comparisons with experimental data for a series of test cylinders are described. Predicting the failure strength of composite structures requires consideration of stability and material strength modes of failure using linear and nonlinear analysis techniques. Material strength prediction requires the accurate definition of the local multiaxial stress state in the material. An elasticity solution for the linear static analysis of thick anisotropic cylinders and rings is used herein to predict the axisymmetric stress state in the cylinders. Asymmetric nonlinear behavior due to initial cylinder out of roundness and the effects of end closure structure are treated using finite element methods. It is assumed that local fiber or ply waviness is an important factor in the initiation of material failure. An analytical model for the prediction of compression failure of fiber composites, which includes the effects of fiber misalignments, matrix inelasticity, and multiaxial applied stresses is used for material strength calculations. Analytical results are compared to experimental data for a series of glass and carbon fiber reinforced epoxy cylinders subjected to external pressure. Recommendations for pretest characterization and other experimental issues are presented. Implications for material and structural design are discussed.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Slope stabilization guide for Minnesota local government engineers.

DOT National Transportation Integrated Search

2017-06-01

This user guide provides simple, costeffective methods for stabilizing locally maintained slopes along roadways in Minnesota. Eight slope stabilization techniques are presented that local government engineers can undertake using locally available ...

Acoustic wave propagation in a temporal evolving shear-layer for low-Mach number perturbations

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Müller, Björn

2018-01-01

We study wave packets with the small perturbation/gradient Mach number interacting with a smooth shear-layer in the linear regime of small amplitude perturbations. In particular, we investigate the temporal evolution of wave packets in shear-layers with locally curved regions of variable size using non-modal linear analysis and direct numerical simulations of the two-dimensional gas-dynamical equations. Depending on the wavenumber of the initially imposed wave packet, three different types of behavior are observed: (i) The wave packet passes through the shear-layer and constantly transfers energy back to the mean flow. (ii) It is turned around (or reflected) within the sheared region and extracts energy from the base flow. (iii) It is split into two oppositely propagating packages when reaching the upper boundary of the linearly sheared region. The conducted direct numerical simulations confirm that non-modal linear stability analysis is able to predict the wave packet dynamics, even in the presence of non-linearly sheared regions. In the light of existing studies in this area, we conclude that the sheared regions are responsible for the highly directed propagation of linearly generated acoustic waves when there is a dominating source, as it is the case for jet flows.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Ab initio calculations of the elastic and thermodynamic properties of gold under pressure

NASA Astrophysics Data System (ADS)

Smirnov, N. A.

2017-03-01

The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: fcc\\to hcp\\to bcc . The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.

Graphene oxide bonded fused-silica fiber for solid-phase microextraction-gas chromatography of polycyclic aromatic hydrocarbons in water.

PubMed

Xu, Lili; Feng, Juanjuan; Li, Jubai; Liu, Xia; Jiang, Shengxiang

2012-01-01

A novel chemically bonded graphene oxide/fused-silica fiber was prepared and applied in solid-phase microextraction of six polycyclic aromatic hydrocarbons from water samples coupled with gas chromatography. It exhibited high extraction efficiency and excellent stability. Effects of extraction time, extraction temperature, ionic strength, stirring rate and desorption conditions were investigated and optimized in our work. Detection limits to the six polycyclic aromatic hydrocarbons were less than 0.08 μg/L, and their calibration curves were all linear (R(2)≥0.9954) in the range from 0.05 to 200 μg/L. Single fiber repeatability and fiber-to-fiber reproducibility were less than 6.13 and 15.87%, respectively. This novel fiber was then utilized to analyze two real water samples from the Yellow River and local waterworks, and the recoveries of samples spiked at 1 and 10 μg/L ranged from 84.48 to 118.24%. Compared with other coating materials, this graphene oxide-coated fiber showed many advantages: wide linear range, low detection limit, and good stability in acid, alkali, organic solutions and at high temperature. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Ab initio calculations of the elastic and thermodynamic properties of gold under pressure.

PubMed

Smirnov, N A

2017-03-15

The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: [Formula: see text]. The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.

Comprehensive evaluation of the linear stability of Alfvén eigenmodes driven by alpha particles in an ITER baseline scenario

NASA Astrophysics Data System (ADS)

Figueiredo, A. C. A.; Rodrigues, P.; Borba, D.; Coelho, R.; Fazendeiro, L.; Ferreira, J.; Loureiro, N. F.; Nabais, F.; Pinches, S. D.; Polevoi, A. R.; Sharapov, S. E.

2016-07-01

The linear stability of Alfvén eigenmodes in the presence of fusion-born alpha particles is thoroughly assessed for two variants of an ITER baseline scenario, which differ significantly in their core and pedestal temperatures. A systematic approach based on CASTOR-K (Borba and Kerner 1999 J. Comput. Phys. 153 101; Nabais et al 2015 Plasma Sci. Technol. 17 89) is used that considers all possible eigenmodes for a given magnetic equilibrium and determines their growth rates due to alpha-particle drive and Landau damping on fuel ions, helium ashes and electrons. It is found that the fastest growing instabilities in the aforementioned ITER scenario are core-localized, low-shear toroidal Alfvén eigenmodes. The largest growth-rates occur in the scenario variant with higher core temperatures, which has the highest alpha-particle density and density gradient, for eigenmodes with toroidal mode numbers n≈ 30 . Although these eigenmodes suffer significant radiative damping, which is also evaluated, their growth rates remain larger than those of the most unstable eigenmodes found in the variant of the ITER baseline scenario with lower core temperatures, which have n≈ 15 and are not affected by radiative damping.

Three-dimensional modelling of slope stability using the Local Factor of Safety concept

NASA Astrophysics Data System (ADS)

Moradi, Shirin; Huisman, Sander; Beck, Martin; Vereecken, Harry; Class, Holger

2017-04-01

Slope stability is governed by coupled hydrological and mechanical processes. The slope stability depends on the effective stress, which in turn depends on the weight of the soil and the matrix potential. Therefore, changes in water content and matrix potential associated with infiltration will affect slope stability. Most available models describing these coupled hydro-mechanical processes either rely on a one- or two-dimensional representation of hydrological and mechanical properties and processes, which obviously is a strong simplification in many applications. Therefore, the aim of this work is to develop a three-dimensional hydro-mechanical model that is able to capture the effect of spatial and temporal variability of both mechanical and hydrological parameters on slope stability. For this, we rely on DuMux, which is a free and open-source simulator for flow and transport processes in porous media that facilitates coupling of different model approaches and offers flexibility for model development. We use the Richards equation to model unsaturated water flow. The simulated water content and matrix potential distribution is used to calculate the effective stress. We only consider linear elasticity and solve for statically admissible fields of stress and displacement without invoking failure or the redistribution of post-failure stress or displacement. The Local Factor of Safety concept is used to evaluate slope stability in order to overcome some of the main limitations of commonly used methods based on limit equilibrium considerations. In a first step, we compared our model implementation with a 2D benchmark model that was implemented in COMSOL Multiphysics. In a second step, we present in-silico experiments with the newly developed 3D model to show the effect of slope morphology, spatial variability in hydraulic and mechanical material properties, and spatially variable soil depth on simulated slope stability. It is expected that this improved physically-based three-dimensional hydro-mechanical model is able to provide more reliable slope instability predictions in more complex situations.

Stability of local anesthetics in the dental cartridge.

PubMed

Hondrum, S O; Seng, G F; Rebert, N W

1993-01-01

Recent manufacturer recalls of local anesthetics have emphasized the problems with storage stability. This article reviews the principles of drug stability, mechanisms of degradation of commonly used vasoconstrictors, research on the stability of commercially produced local anesthetic preparations, and possible effects of the container-closure system. The review concludes with a list of practical and clinical suggestions on how to minimize storage stability problems with dental local anesthetics.

Combined influence of inertia, gravity, and surface tension on the linear stability of Newtonian fiber spinning

NASA Astrophysics Data System (ADS)

Bechert, M.; Scheid, B.

2017-11-01

The draw resonance effect appears in fiber spinning processes if the ratio of take-up to inlet velocity, the so-called draw ratio, exceeds a critical value and manifests itself in steady oscillations of flow velocity and fiber diameter. We study the effect of surface tension on the draw resonance behavior of Newtonian fiber spinning in the presence of inertia and gravity. Utilizing an alternative scaling makes it possible to visualize the results in stability maps of highly practical relevance. The interplay of the destabilizing effect of surface tension and the stabilizing effects of inertia and gravity lead to nonmonotonic stability behavior and local stability maxima with respect to the dimensionless fluidity and the dimensionless inlet velocity. A region of unconditional instability caused by the influence of surface tension is found in addition to the region of unconditional stability caused by inertia, which was described in previous works [M. Bechert, D. W. Schubert, and B. Scheid, Eur. J. Mech B 52, 68 (2015), 10.1016/j.euromechflu.2015.02.005; Phys. Fluids 28, 024109 (2016), 10.1063/1.4941762]. Due to its importance for a particular group of fiber spinning applications, a viscous-gravity-surface-tension regime, i.e., negligible effect of inertia, is analyzed separately. The mechanism underlying the destabilizing effect of surface tension is discussed and established stability criteria are tested for validity in the presence of surface tension.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Switched periodic systems in discrete time: stability and input-output norms

NASA Astrophysics Data System (ADS)

Bolzern, Paolo; Colaneri, Patrizio

2013-07-01

This paper deals with the analysis of stability and the characterisation of input-output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H2 and H∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.

Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

NASA Technical Reports Server (NTRS)

Gao, Zhiqiang; Antsaklis, Panos J.

1993-01-01

The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

Linear and nonlinear stability characteristics of whistlers

NASA Technical Reports Server (NTRS)

Brinca, A. L.

1972-01-01

Linear and nonlinear propagating characteristics of right-hand polarized, slow electromagnetic, magnetoplasma waves (whistlers) are discussed in terms of stability and dispersion. An analysis of the stability of whistlers propagating at an angle to the static magnetic field is presented. A new mechanism is derived for the onset of stimulated emissions, and modulational instability for nonlinear whistlers are discussed.

A Crank–Nicolson Leapfrog stabilization: Unconditional stability and two applications

DOE PAGES

Jiang, Nan; Kubacki, Michaela; Layton, William; ...

2014-12-09

We propose and analyze a linear stabilization of the Crank-Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. As a result, we illustrate two applications of the method: uncoupling groundwater-surface water flows and Stokes flow plus a Coriolis term.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

NASA Astrophysics Data System (ADS)

Goh, Shu Ting

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due to the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft's range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method's error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability.

PubMed

Terrier, Philippe; Dériaz, Olivier

2013-01-01

It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

NASA Technical Reports Server (NTRS)

Gupta, Sandeep

1996-01-01

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Relevance of Linear Stability Results to Enhanced Oil Recovery

NASA Astrophysics Data System (ADS)

Ding, Xueru; Daripa, Prabir

2012-11-01

How relevant can the results based on linear stability theory for any problem for that matter be to full scale simulation results? Put it differently, is the optimal design of a system based on linear stability results is optimal or even near optimal for the complex nonlinear system with certain objectives of interest in mind? We will address these issues in the context of enhanced oil recovery by chemical flooding. This will be based on an ongoing work. Supported by Qatar National Research Fund (a member of the Qatar Foundation).

Crossflow Stability and Transition Experiments in a Swept-Wing Flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dagenhart, John Ray

1992-01-01

An experimental examination of crossflow instability and transition on a 45 degree swept wing is conducted in the Arizona State University Unsteady Wind Tunnel. The stationary-vortex pattern and transition location are visualized using both sublimating-chemical and liquid-crystal coatings. Extensive hot-wire measurements are conducted at several measurement stations across a single vortex track. The mean and travelling-wave disturbances are measured simultaneously. Stationary-crossflow disturbance profiles are determined by subtracting either a reference or a span-averaged velocity profile from the mean-velocity data. Mean, stationary-crossflow, and travelling-wave velocity data are presented as local boundary-layer profiles and as contour plots across a single stationary-crossflow vortex track. Disturbance-mode profiles and growth rates are determined. The experimental data are compared to predictions from linear stability theory.

Influence of driven current on resistive tearing mode in Tokamaks

NASA Astrophysics Data System (ADS)

Ma, Zhiwei; Wang, Sheng; Zhang, Wei

2016-10-01

Influence of driven current on the m / n = 2 / 1 resistive tearing mode is studied systematically using a three-dimensional toroidal MHD code (CLT). A uniform driven current with Gaussian distribution in the radial direction is imposed around the unperturbed rational surface. It is found that the driven current can locally modify the profiles of the current and safety factor, such that the tearing mode becomes linearly stable. The stabilizing effect increases with increase of the driven current Icd or decrease of its width δcd, unless an excessively large driven current reverses the magnetic shear near the rational surface and drives other instabilities such as double or triple tearing modes. The stabilizing effect can be negligible or becomes reversed if the maximum driven current density is not at the unperturbed rational surface. ITER-CN Program.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Many-body localization proximity effects in platforms of coupled spins and bosons

NASA Astrophysics Data System (ADS)

Marino, J.; Nandkishore, R. M.

2018-02-01

We discuss the onset of many-body localization in a one-dimensional system composed of a XXZ quantum spin chain and a Bose-Hubbard model linearly coupled together. We consider two complementary setups, depending whether spatial disorder is initially imprinted on spins or on bosons; in both cases, we explore the conditions for the disordered portion of the system to localize by proximity of the other clean half. Assuming that the dynamics of one of the two parts develops on shorter time scales than the other, we can adiabatically eliminate the fast degrees of freedom, and derive an effective Hamiltonian for the system's remainder using projection operator techniques. Performing a locator expansion on the strength of the many-body interaction term or on the hopping amplitude of the effective Hamiltonian thus derived, we present results on the stability of the many-body localized phases induced by proximity effect. We also briefly comment on the feasibility of the proposed model through modern quantum optics architectures, with the long-term perspective to realize experimentally, in composite open systems, Anderson or many-body localization proximity effects.

Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.

PubMed

Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent

2015-11-02

Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions.

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

NASA Technical Reports Server (NTRS)

Lin, Ray-Sing; Reed, Helen L.

1993-01-01

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Synchronization control in multiplex networks of nonlinear multi-agent systems

NASA Astrophysics Data System (ADS)

He, Wangli; Xu, Zhiwei; Du, Wenli; Chen, Guanrong; Kubota, Naoyuki; Qian, Feng

2017-12-01

This paper is concerned with synchronization control of a multiplex network, in which two different kinds of relationships among agents coexist. Hybrid coupling, including continuous linear coupling and impulsive coupling, is proposed to model the coexisting distinguishable interactions. First, by adding impulsive controllers on a small portion of agents, local synchronization is analyzed by linearizing the error system at the desired trajectory. Then, global synchronization is studied based on the Lyapunov stability theory, where a time-varying coupling strength is involved. To further deal with the time-varying coupling strength, an adaptive updating law is introduced and a corresponding sufficient condition is obtained to ensure synchronization of the multiplex network towards the desired trajectory. Networks of Chua's circuits and other chaotic systems with double layers of interactions are simulated to verify the proposed method.

Boundary-layer stability and airfoil design

NASA Technical Reports Server (NTRS)

Viken, Jeffrey K.

1986-01-01

Several different natural laminar flow (NLF) airfoils have been analyzed for stability of the laminar boundary layer using linear stability codes. The NLF airfoils analyzed come from three different design conditions: incompressible; compressible with no sweep; and compressible with sweep. Some of the design problems are discussed, concentrating on those problems associated with keeping the boundary layer laminar. Also, there is a discussion on how a linear stability analysis was effectively used to improve the design for some of the airfoils.

A diffuse interface model of grain boundary faceting

NASA Astrophysics Data System (ADS)

Abdeljawad, F.; Medlin, D. L.; Zimmerman, J. A.; Hattar, K.; Foiles, S. M.

2016-06-01

Interfaces, free or internal, greatly influence the physical properties and stability of materials microstructures. Of particular interest are the processes that occur due to anisotropic interfacial properties. In the case of grain boundaries (GBs) in metals, several experimental observations revealed that an initially flat GB may facet into hill-and-valley structures with well defined planes and corners/edges connecting them. Herein, we present a diffuse interface model that is capable of accounting for strongly anisotropic GB properties and capturing the formation of hill-and-valley morphologies. The hallmark of our approach is the ability to independently examine the various factors affecting GB faceting and subsequent facet coarsening. More specifically, our formulation incorporates higher order expansions to account for the excess energy due to facet junctions and their non-local interactions. As a demonstration of the modeling capability, we consider the Σ5 <001 > tilt GB in body-centered-cubic iron, where faceting along the {210} and {310} planes was experimentally observed. Atomistic calculations were utilized to determine the inclination-dependent GB energy, which was then used as an input in our model. Linear stability analysis and simulation results highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. Broadly speaking, our modeling approach provides a general framework to examine the microstructural stability of polycrystalline systems with highly anisotropic GBs.

Feasibility study of basic characterization of MAGAT polymer gel using CBCT attached in linear accelerator: Preliminary study

NASA Astrophysics Data System (ADS)

Sathiyaraj, P.; Samuel, E. James jebaseelan

2018-01-01

The aim of this study is to evaluate the methacrylic acid, gelatin and tetrakis (hydroxymethyl) phosphonium chloride gel (MAGAT) by cone beam computed tomography (CBCT) attached with modern linear accelerator. To compare the results of standard diagnostic computed tomography (CT) with CBCT, different parameters such as linearity, sensitivity and temporal stability were checked. MAGAT gel showed good linearity for both diagnostic CT and CBCT measurements. Sensitivity and temporal stability were also comparable with diagnostic CT measurements. In both the modalities, the sensitivity of the MAGAT increased to 4 days and decreased till the 10th day of post irradiation. Since all measurements (linearity, sensitivity and temporal stability) from diagnostic CT and CBCT were comparable, CBCT could be a potential tool for dose analysis study for polymer gel dosimeter.

Stability analysis and future singularity of the m{sup 2} R □{sup -2} R model of non-local gravity

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

Dirian, Yves; Mitsou, Ermis, E-mail: yves.dirian@unige.ch, E-mail: ermis.mitsou@unige.ch

2014-10-01

We analyse the classical stability of the model proposed by Maggiore and Mancarella, where gravity is modified by a term ∼ m{sup 2} R □{sup -2} R to produce the late-time acceleration of the expansion of the universe. Our study takes into account all excitations of the metric that can potentially drive an instability. There are some subtleties in identifying these modes, as a non-local field theory contains dynamical fields which yet do not correspond to degrees of freedom. Since some of them are ghost-like, we clarify the impact of such modes on the stability of the solutions of interest that are the flatmore » space-time and cosmological solutions. We then find that flat space-time is unstable under scalar perturbations, but the instability manifests itself only at cosmological scales, i.e. out of the region of validity of this solution. It is therefore the stability of the FLRW solution which is relevant there, in which case the scalar perturbations are known to be well-behaved by numerical studies. By finding the analytic solution for the late-time behaviour of the scale factor, which leads to a big rip singularity, we argue that the linear perturbations are bounded in the future because of the domination of Hubble friction. In particular, this effect damps the scalar ghost perturbations which were responsible for destabilizing Minkowski space-time. Thus, the model remains phenomenologically viable.« less

Hg(+) Frequency Standards

NASA Technical Reports Server (NTRS)

Prestage, John D.; Tjoelker, Robert L.; Maleki, Lute

2000-01-01

In this paper we review the development of Hg(+) microwave frequency standards for use in high reliability and continuous operation applications. In recent work we have demonstrated short-term frequency stability of 3 x 10(exp -14)/nu(sub tau) when a cryogenic oscillator of stability 2-3 x 10(exp 15) was used a the local oscillator. The trapped ion frequency standard employs a Hg-202 discharge lamp to optically pump the trapped Hg(+)-199 clock ions and a helium buffer gas to cool the ions to near room temperature. We describe a small Hg(+) ion trap based frequency standard with an extended linear ion trap (LITE) architecture which separates the optical state selection region from the clock resonance region. This separation allows the use of novel trap configurations in the resonance region since no optical pumping is carried out there. A method for measuring the size of an ion cloud inside a linear trap with a 12-rod trap is currently being investigated. At approx. 10(exp -12), the 2nd order Doppler shift for trapped mercury ion frequency standards is one of the largest frequency offsets and its measurement to the 1% level would represent an advance in insuring the very long-term stability of these standards to the 10(exp -14) or better level. Finally, we describe atomic clock comparison experiments that can probe for a time variation of the fine structure constant, alpha = e(exp 2)/2(pi)hc, at the level of 10(exp -20)/year as predicted in some Grand Unified String Theories.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Bifurcations and Chaos of AN Immersed Cantilever Beam in a Fluid and Carrying AN Intermediate Mass

NASA Astrophysics Data System (ADS)

AL-QAISIA, A. A.; HAMDAN, M. N.

2002-06-01

The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.

Investigation of ODE integrators using interactive graphics. [Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Brown, R. L.

1978-01-01

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry I.; Kasimov, Aslan R.

2018-03-01

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Stability of Electrons in the Virtual Cathode Region of an IEC

NASA Astrophysics Data System (ADS)

Kim, Hyng-Jin; Miley, George; Momota, Hiromu

2003-04-01

In the Inertial Electrostatic Confinement (IEC) device, electrons are confined inside a virtual anode that in turn confines ions. Prior stability studies [1, 2] have considered systems in which one species is electrostatically confined by the other, and either or both species are out of local thermal equilibrium. In the present research, electron stability in the virtual cathode region of an ion injected IEC is being studied. The ion density in an IEC is non-uniform due to the radial electrostatic potential, and increases toward the center region. The potential near the virtual cathode is assumed to have a parabolic shape and is determined assuming that the net space charge density is constant in that region. The corresponding ion distribution function is assumed to have the form f = C [sigma] (H W) /L^0.5 and the electron response is taken to be diabatic. Then using a variational principle after linearizing the hydrodynamic equations, stability properties of the electron layer are determined. Results will be presented as a function of injected ion/electron current ratios. 1. L. Chacon and D. C. Barnes, Phys. Plasma 7, 4774 (2000). 2. D. C. Barnes, L. Chacon, and J. M. Finn, Phys. Plasmas 9, 4448 (2002).

Convective and global stability analysis of a Mach 5.8 boundary layer grazing a compliant surface

NASA Astrophysics Data System (ADS)

Dettenrieder, Fabian; Bodony, Daniel

2016-11-01

Boundary layer transition on high-speed vehicles is expected to be affected by unsteady surface compliance. The stability properties of a Mach 5.8 zero-pressure-gradient laminar boundary layer grazing a nominally-flat thermo-mechanically compliant panel is considered. The linearized compressible Navier-Stokes equations describe small amplitude disturbances in the fluid while the panel deformations are described by the Kirchhoff-Love plate equation and its thermal state by the transient heat equation. Compatibility conditions that couple disturbances in the fluid to those in the solid yield simple algebraic and robin boundary conditions for the velocity and thermal states, respectively. A local convective stability analysis shows that the panel can modify both the first and second Mack modes when, for metallic-like panels, the panel thickness exceeds the lengthscale δ99 Rex- 0 . 5 . A global stability analysis, which permits finite panel lengths with clamped-clamped boundary conditions, shows a rich eigenvalue spectrum with several branches. Unstable modes are found with streamwise-growing panel deformations leading to Mach wave-type radiation. Stable global modes are also found and have distinctly different panel modes but similar radiation patterns. Air Force Office of Scientific Research.

On The Stability Of Model Flows For Chemical Vapour Deposition

NASA Astrophysics Data System (ADS)

Miller, Robert

2016-11-01

The flow in a chemical vapour deposition (CVD) reactor is assessed. The reactor is modelled as a flow over an infinite-radius rotating disk, where the mean flow and convective instability of the disk boundary layer are measured. Temperature-dependent viscosity and enforced axial flow are used to model the steep temperature gradients present in CVD reactors and the pumping of the gas towards the disk, respectively. Increasing the temperature-dependence parameter of the fluid viscosity (ɛ) results in an overall narrowing of the fluid boundary layer. Increasing the axial flow strength parameter (Ts) accelerates the fluid both radially and axially, while also narrowing the thermal boundary layer. It is seen that when both effects are imposed, the effects of axial flow generally dominate those of the viscosity temperature dependence. A local stability analysis is performed and the linearized stability equations are solved using a Galerkin projection in terms of Chebyshev polynomials. The neutral stability curves are then plotted for a range of ɛ and Ts values. Preliminary results suggest that increasing Ts has a stabilising effect on both type I and type II stationary instabilities, while small increases in ɛ results in a significant reduction to the critical Reynolds number.

Prediction of trivalent actinide amino(poly)carboxylate complex stability constants using linear free energy relationships with the lanthanide series

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

Uhnak, Nic E.

Prediction of Trivalent Actinide Amino(poly)carboxylate Complex Stability Constants Using Linear Free Energy Relationships with the Lanthanide Series Alternative title: LFER Based Prediction of An(III) APC Stability Constants There is a gap in the literature regarding the complexation of amino(poly)carboxylate (APC) ligands with trivalent actinides (An(III))). The chemistry of the An(III) is nearly identical to that of the trivalent lanthanides Lns, but the An(III) express a slight enhancement when binding APC ligands. Presented in this report is a simple method of predicting the stability constants of the An(III), Pu, Am, Cm, Bk and Cf by using linear free energy relationships (LFER)more » of the An and the lanthanide (Ln) series for 91 APCs. This method produced An stability constants within uncertainty to available literature values for most ligands.« less

Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

Flow-induced conformational changes in gelatin structure and colloidal stabilization.

PubMed

Akbulut, Mustafa; Reddy, Naveen K; Bechtloff, Bernd; Koltzenburg, Sebastian; Vermant, Jan; Prud'homme, Robert K

2008-09-02

Flow can change the rate at which solutes adsorb on surfaces by changing mass transfer to the surface, but moreover, flow can induce changes in the conformation of macromolecules in solution by providing sufficient stresses to perturb the segmental distribution function. However, there are few studies where the effect of flow on macromolecules has been shown to alter the structure of macromolecules adsorbed on surfaces. We have studied how the local energy dissipation alters the adsorption of gelatin onto polystyrene nanoparticles ( r = 85 nm). The change in the nature of the adsorbed layer is manifest in the change in the ability of the nanoparticles to resist aggregation. Circular dichroism spectroscopy was used to assess conformational changes in gelatin, and dynamic light scattering was used to assess the colloid stability. Experiments were conducted in a vortex jet mixer where energy density and mixing times have been quantified; mixing of the gelatin and unstable nanoparticles occurs on the order of milliseconds. The adsorption of the gelatin provides steric stabilization to the nanoparticles. We found that the stability of the gelatin-adsorbed nanoparticles increased with increasing mixing velocities: when the mixing velocities were changed from 0.9 to 550 m/s, the radius of the nanoclusters (aggregates) formed 12 h after the mixing decreased from 2620 to 600 nm. Increasing temperature also gave rise to similar trends in the stability behavior with increasing temperature, leading to increasing colloid stability. Linear flow birefringence studies also suggested that the velocity fields in the mixer are sufficiently strong to produce conformational changes in the gelatin. These results suggest that the energy dissipation produced by mixing can activate conformational changes in gelatin to alter its adsorption on the surfaces of nanoparticles. Understanding how such conformational changes in gelatin can be driven by local fluid mechanics and how these changes are related to the adsorption behavior of gelatin is very important both industrially and scientifically.

Control design for robust stability in linear regulators: Application to aerospace flight control

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1986-01-01

Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Linearized mathematical models for De Havilland Canada "Buffalo & Twin Otter" STOL transports.

DOT National Transportation Integrated Search

1971-06-01

Linearized six degree of freedom rigid body aircraft equations of motion are presented in a stability axes system. Values of stability derivatives are estimated for two representative STOL aircraft - the DeHavilland of Canada 'Buffalo' and 'Twin Otte...

Drifts and Environmental Disturbances in Atomic Clock Subsystems: Quantifying Local Oscillator, Control Loop, and Ion Resonance Interactions.

PubMed

Enzer, Daphna G; Diener, William A; Murphy, David W; Rao, Shanti R; Tjoelker, Robert L

2017-03-01

Linear ion trap frequency standards are among the most stable continuously operating frequency references and clocks. Depending on the application, they have been operated with a variety of local oscillators (LOs), including quartz ultrastable oscillators, hydrogen-masers, and cryogenic sapphire oscillators. The short-, intermediate-, and long-term stability of the frequency output is a complicated function of the fundamental performances, the time dependence of environmental disturbances, the atomic interrogation algorithm, the implemented control loop, and the environmental sensitivity of the LO and the atomic system components. For applications that require moving these references out of controlled lab spaces and into less stable environments, such as fieldwork or spaceflight, a deeper understanding is needed of how disturbances at different timescales impact the various subsystems of the clock and ultimately the output stability. In this paper, we analyze which perturbations have an impact and to what degree. We also report on a computational model of a control loop, which keeps the microwave source locked to the ion resonance. This model is shown to agree with laboratory measurements of how well the feedback removes various disturbances and also with a useful analytic approach we developed for predicting these impacts.

The Absolute Stability Analysis in Fuzzy Control Systems with Parametric Uncertainties and Reference Inputs

NASA Astrophysics Data System (ADS)

Wu, Bing-Fei; Ma, Li-Shan; Perng, Jau-Woei

This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed in the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur'e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Finally, the comparisons are also given to show the effectiveness of the analysis method.

An adaptive PID like controller using mix locally recurrent neural network for robotic manipulator with variable payload.

PubMed

Sharma, Richa; Kumar, Vikas; Gaur, Prerna; Mittal, A P

2016-05-01

Being complex, non-linear and coupled system, the robotic manipulator cannot be effectively controlled using classical proportional-integral-derivative (PID) controller. To enhance the effectiveness of the conventional PID controller for the nonlinear and uncertain systems, gains of the PID controller should be conservatively tuned and should adapt to the process parameter variations. In this work, a mix locally recurrent neural network (MLRNN) architecture is investigated to mimic a conventional PID controller which consists of at most three hidden nodes which act as proportional, integral and derivative node. The gains of the mix locally recurrent neural network based PID (MLRNNPID) controller scheme are initialized with a newly developed cuckoo search algorithm (CSA) based optimization method rather than assuming randomly. A sequential learning based least square algorithm is then investigated for the on-line adaptation of the gains of MLRNNPID controller. The performance of the proposed controller scheme is tested against the plant parameters uncertainties and external disturbances for both links of the two link robotic manipulator with variable payload (TL-RMWVP). The stability of the proposed controller is analyzed using Lyapunov stability criteria. A performance comparison is carried out among MLRNNPID controller, CSA optimized NNPID (OPTNNPID) controller and CSA optimized conventional PID (OPTPID) controller in order to establish the effectiveness of the MLRNNPID controller. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Local Dynamic Stability Associated with Load Carrying

PubMed Central

Lockhart, Thurmon E

2013-01-01

Objectives Load carrying tasks are recognized as one of the primary occupational factors leading to slip and fall injuries. Nevertheless, the mechanisms associated with load carrying and walking stability remain illusive. The objective of the current study was to apply local dynamic stability measure in walking while carrying a load, and to investigate the possible adaptive gait stability changes. Methods Current study involved 25 young adults in a biomechanics research laboratory. One tri-axial accelerometer was used to measure three-dimensional low back acceleration during continuous treadmill walking. Local dynamic stability was quantified by the maximum Lyapunov exponent (maxLE) from a nonlinear dynamics approach. Results Long term maxLE was found to be significant higher under load condition than no-load condition in all three reference axes, indicating the declined local dynamic stability associated with load carrying. Conclusion Current study confirmed the sensitivity of local dynamic stability measure in load carrying situation. It was concluded that load carrying tasks were associated with declined local dynamic stability, which may result in increased risk of fall accident. This finding has implications in preventing fall accidents associated with occupational load carrying. PMID:23515183

Nonlinear defect localized modes and composite gray and anti-gray solitons in one-dimensional waveguide arrays with dual-flip defects

NASA Astrophysics Data System (ADS)

Liu, Yan; Guan, Yefeng; Li, Hai; Luo, Zhihuan; Mai, Zhijie

2017-08-01

We study families of stationary nonlinear localized modes and composite gray and anti-gray solitons in a one-dimensional linear waveguide array with dual phase-flip nonlinear point defects. Unstaggered fundamental and dipole bright modes are studied when the defect nonlinearity is self-focusing. For the fundamental modes, symmetric and asymmetric nonlinear modes are found. Their stable areas are studied using different defect coefficients and their total power. For the nonlinear dipole modes, the stability conditions of this type of mode are also identified by different defect coefficients and the total power. When the defect nonlinearity is replaced by the self-defocusing one, staggered fundamental and dipole bright modes are created. Finally, if we replace the linear waveguide with a full nonlinear waveguide, a new type of gray and anti-gray solitons, which are constructed by a kink and anti-kink pair, can be supported by such dual phase-flip defects. In contrast to the usual gray and anti-gray solitons formed by a single kink, their backgrounds on either side of the gray hole or bright hump have the same phase.

Attitude stability of spinning satellites

NASA Technical Reports Server (NTRS)

Caughey, T. K.

1980-01-01

Some problems of attitude stability of spinning satellites are treated in a rigorous manner. With certain restrictions, linearized stability analysis correctly predicts the attitude stability of spinning satellites, even in the critical cases of the Liapunov-Poincare stability theory.

A Study on a Centralized Under-Voltage Load Shedding Scheme Considering the Load Characteristics

NASA Astrophysics Data System (ADS)

Deng, Jiyu; Liu, Junyong

Under-voltage load shedding is an important measure for maintaining voltage stability.Aiming at the optimal load shedding problem considering the load characteristics,firstly,the traditional under-voltage load shedding scheme based on a static load model may cause the analysis inaccurate is pointed out on the equivalent Thevenin circuit.Then,the dynamic voltage stability margin indicator is derived through local measurement.The derived indicator can reflect the voltage change of the key area in a myopia linear way.Dimensions of the optimal problem will be greatly simplified using this indicator.In the end,mathematical model of the centralized load shedding scheme is built with the indicator considering load characteristics.HSPPSO is introduced to slove the optimal problem.Simulation results on IEEE-39 system show that the proposed scheme display a good adaptability in solving the under-voltage load shedding considering dynamic load characteristics.

Reynolds stress closure in jet flows using wave models

NASA Technical Reports Server (NTRS)

Morris, Philip J.

1990-01-01

A collection of papers is presented. The outline of this report is as follows. Chapter three contains a description of a weakly nonlinear turbulence model that was developed. An essential part of the application of such a closure scheme to general geometry jets is the solution of the local hydrodynamic stability equation for a given jet cross-section. Chapter four describes the conformal mapping schemes used to map such geometries onto a simple computational domain. Chapter five describes a solution of a stability problem for circular, elliptic, and rectangular geometries. In chapter six linear models for the shock shell structure in non-circular jets is given. The appendices contain reprints of papers also published during this study including the following topics: (1) instability of elliptic jets; (2) a technique for predicting the shock cell structure in non-circular jets using a vortex sheet model; and (3) the resonant interaction between twin supersonic jets.

A priori Estimates for 3D Incompressible Current-Vortex Sheets

NASA Astrophysics Data System (ADS)

Coulombel, J.-F.; Morando, A.; Secchi, P.; Trebeschi, P.

2012-04-01

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics.

Lyapunov function-based control laws for revolute robot arms - Tracking control, robustness, and adaptive control

NASA Technical Reports Server (NTRS)

Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.

1992-01-01

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).

A new class of energy based control laws for revolute robot arms - Tracking control, robustness enhancement and adaptive control

NASA Technical Reports Server (NTRS)

Wen, John T.; Kreutz, Kenneth; Bayard, David S.

1988-01-01

A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

NASA Technical Reports Server (NTRS)

Majda, G.

1985-01-01

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor

NASA Technical Reports Server (NTRS)

Tesch, W. A.; Moszee, R. H.; Steenken, W. G.

1976-01-01

NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.

General methods for determining the linear stability of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.

1988-01-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

General methods for determining the linear stability of coronal magnetic fields

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

Craig, I.J.D.; Sneyd, A.D.; McClymont, A.N.

1988-12-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak. 19 references.

Asymptotic Stability of Interconnected Passive Non-Linear Systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Joshi, S. M.; Kelkar, A. G.

1999-01-01

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Qualitative analysis of certain generalized classes of quadratic oscillator systems

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

Bagchi, Bijan, E-mail: bbagchi123@gmail.com; Ghosh, Samiran, E-mail: sran-g@yahoo.com; Pal, Barnali, E-mail: barrna.roo@gmail.com

2016-02-15

We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis.more » We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.« less

Multi-water-bag models of ion temperature gradient instability in cylindrical geometry

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

Coulette, David; Besse, Nicolas

2013-05-15

Ion temperature gradient instabilities play a major role in the understanding of anomalous transport in core fusion plasmas. In the considered cylindrical geometry, ion dynamics is described using a drift-kinetic multi-water-bag model for the parallel velocity dependency of the ion distribution function. In a first stage, global linear stability analysis is performed. From the obtained normal modes, parametric dependencies of the main spectral characteristics of the instability are then examined. Comparison of the multi-water-bag results with a reference continuous Maxwellian case allows us to evaluate the effects of discrete parallel velocity sampling induced by the Multi-Water-Bag model. Differences between themore » global model and local models considered in previous works are discussed. Using results from linear, quasilinear, and nonlinear numerical simulations, an analysis of the first stage saturation dynamics of the instability is proposed, where the divergence between the three models is examined.« less

Pediatric morphea (localized scleroderma): review of 136 patients.

PubMed

Christen-Zaech, Stéphanie; Hakim, Miriam D; Afsar, F Sule; Paller, Amy S

2008-09-01

Morphea is an autoimmune inflammatory sclerosing disorder that may cause permanent functional disability and disfigurement. We sought to determine the clinical features of morphea in a large pediatric cohort. We conducted a retrospective chart review of 136 pediatric patients with morphea from one center, 1989 to 2006. Most children showed linear morphea, with a disproportionately high number of Caucasian and female patients. Two patients with rapidly progressing generalized or extensive linear morphea and arthralgias developed restrictive pulmonary disease. Initial oral corticosteroid treatment and long-term methotrexate administration stabilized and/or led to disease improvement in most patients with aggressive disease. Retrospective analysis, relatively small sample size, and risk of a selected referral population to the single site are limitations. These data suggest an increased prevalence of morphea in Caucasian girls, and support methotrexate as treatment for problematic forms. Visceral manifestations rarely occur; the presence of progressive problematic cutaneous disease and arthralgias should trigger closer patient monitoring.

Electromagnetic drift waves dispersion for arbitrarily collisional plasmas

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

Lee, Wonjae, E-mail: wol023@ucsd.edu; Krasheninnikov, Sergei I., E-mail: skrash@mae.ucsd.edu; Angus, J. R.

2015-07-15

The impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic drift-kinetic equation with Bhatnagar-Gross-Krook-like collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The wave-particle interactions drive collisionless drift-Alfvén wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionlessmore » and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the drift-Alfvén wave instability with synergistic effects of high beta stabilization and Landau resonance.« less

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Dynamics of thin-shell wormholes with different cosmological models

NASA Astrophysics Data System (ADS)

Sharif, Muhammad; Mumtaz, Saadia

This work is devoted to investigate the stability of thin-shell wormholes in Einstein-Hoffmann-Born-Infeld electrodynamics. We also study the attractive and repulsive characteristics of these configurations. A general equation-of-state is considered in the form of linear perturbation which explores the stability of the respective wormhole solutions. We assume Chaplygin, linear and logarithmic gas models to study exotic matter at thin-shell and evaluate stability regions for different values of the involved parameters. It is concluded that the Hoffmann-Born-Infeld parameter and electric charge enhance the stability regions.

Statespace geometry of puff formation in pipe flow

NASA Astrophysics Data System (ADS)

Budanur, Nazmi Burak; Hof, Bjoern

2017-11-01

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

Surface code quantum communication.

PubMed

Fowler, Austin G; Wang, David S; Hill, Charles D; Ladd, Thaddeus D; Van Meter, Rodney; Hollenberg, Lloyd C L

2010-05-07

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate of existing protocols is low as two-way classical communication is used. By using a surface code across the repeater chain and generating Bell pairs between neighboring stations with probability of heralded success greater than 0.65 and fidelity greater than 0.96, we show that two-way communication can be avoided and quantum information can be sent over arbitrary distances with arbitrarily low error at a rate limited only by the local gate speed. This is achieved by using the unreliable Bell pairs to measure nonlocal stabilizers and feeding heralded failure information into post-transmission error correction. Our scheme also applies when the probability of heralded success is arbitrarily low.

Local Laplacian Coding From Theoretical Analysis of Local Coding Schemes for Locally Linear Classification.

PubMed

Pang, Junbiao; Qin, Lei; Zhang, Chunjie; Zhang, Weigang; Huang, Qingming; Yin, Baocai

2015-12-01

Local coordinate coding (LCC) is a framework to approximate a Lipschitz smooth function by combining linear functions into a nonlinear one. For locally linear classification, LCC requires a coding scheme that heavily determines the nonlinear approximation ability, posing two main challenges: 1) the locality making faraway anchors have smaller influences on current data and 2) the flexibility balancing well between the reconstruction of current data and the locality. In this paper, we address the problem from the theoretical analysis of the simplest local coding schemes, i.e., local Gaussian coding and local student coding, and propose local Laplacian coding (LPC) to achieve the locality and the flexibility. We apply LPC into locally linear classifiers to solve diverse classification tasks. The comparable or exceeded performances of state-of-the-art methods demonstrate the effectiveness of the proposed method.

Nonlinear Diamagnetic Stabilization of Double Tearing Modes in Cylindrical MHD Simulations

NASA Astrophysics Data System (ADS)

Abbott, Stephen; Germaschewski, Kai

2014-10-01

Double tearing modes (DTMs) may occur in reversed-shear tokamak configurations if two nearby rational surfaces couple and begin reconnecting. During the DTM's nonlinear evolution it can enter an ``explosive'' growth phase leading to complete reconnection, making it a possible driver for off-axis sawtooth crashes. Motivated by similarities between this behavior and that of the m = 1 kink-tearing mode in conventional tokamaks we investigate diamagnetic drifts as a possible DTM stabilization mechanism. We extend our previous linear studies of an m = 2 , n = 1 DTM in cylindrical geometry to the fully nonlinear regime using the MHD code MRC-3D. A pressure gradient similar to observed ITB profiles is used, together with Hall physics, to introduce ω* effects. We find the diamagnetic drifts can have a stabilizing effect on the nonlinear DTM through a combination of large scale differential rotation and mechanisms local to the reconnection layer. MRC-3D is an extended MHD code based on the libMRC computational framework. It supports nonuniform grids in curvilinear coordinates with parallel implicit and explicit time integration.

A Self-Stabilizing Byzantine-Fault-Tolerant Clock Synchronization Protocol

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2009-01-01

This report presents a rapid Byzantine-fault-tolerant self-stabilizing clock synchronization protocol that is independent of application-specific requirements. It is focused on clock synchronization of a system in the presence of Byzantine faults after the cause of any transient faults has dissipated. A model of this protocol is mechanically verified using the Symbolic Model Verifier (SMV) [SMV] where the entire state space is examined and proven to self-stabilize in the presence of one arbitrary faulty node. Instances of the protocol are proven to tolerate bursts of transient failures and deterministically converge with a linear convergence time with respect to the synchronization period. This protocol does not rely on assumptions about the initial state of the system other than the presence of sufficient number of good nodes. All timing measures of variables are based on the node s local clock, and no central clock or externally generated pulse is used. The Byzantine faulty behavior modeled here is a node with arbitrarily malicious behavior that is allowed to influence other nodes at every clock tick. The only constraint is that the interactions are restricted to defined interfaces.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

The Hagen-Poiseuille, Plane Couette and Poiseuille Flows Linear Instability and Rogue Waves Excitation Mechanism

NASA Astrophysics Data System (ADS)

Chefranov, Sergey; Chefranov, Alexander

2016-04-01

Linear hydrodynamic stability theory for the Hagen-Poiseuille (HP) flow yields a conclusion of infinitely large threshold Reynolds number, Re, value. This contradiction to the observation data is bypassed using assumption of the HP flow instability having hard type and possible for sufficiently high-amplitude disturbances. HP flow disturbance evolution is considered by nonlinear hydrodynamic stability theory. Similar is the case of the plane Couette (PC) flow. For the plane Poiseuille (PP) flow, linear theory just quantitatively does not agree with experimental data defining the threshold Reynolds number Re= 5772 ( S. A. Orszag, 1971), more than five-fold exceeding however the value observed, Re=1080 (S. J. Davies, C. M. White, 1928). In the present work, we show that the linear stability theory conclusions for the HP and PC on stability for any Reynolds number and evidently too high threshold Reynolds number estimate for the PP flow are related with the traditional use of the disturbance representation assuming the possibility of separation of the longitudinal (along the flow direction) variable from the other spatial variables. We show that if to refuse from this traditional form, conclusions on the linear instability for the HP and PC flows may be obtained for finite Reynolds numbers (for the HP flow, for Re>704, and for the PC flow, for Re>139). Also, we fit the linear stability theory conclusion on the PP flow to the experimental data by getting an estimate of the minimal threshold Reynolds number as Re=1040. We also get agreement of the minimal threshold Reynolds number estimate for PC with the experimental data of S. Bottin, et.al., 1997, where the laminar PC flow stability threshold is Re = 150. Rogue waves excitation mechanism in oppositely directed currents due to the PC flow linear instability is discussed. Results of the new linear hydrodynamic stability theory for the HP, PP, and PC flows are published in the following papers: 1. S.G. Chefranov, A.G. Chefranov, JETP, v.119, No.2, 331, 2014 2. S.G. Chefranov, A.G. Chefranov, Doklady Physics, vol.60, No.7, 327-332, 2015 3. S.G. Chefranov, A. G. Chefranov, arXiv: 1509.08910v1 [physics.flu-dyn] 29 Sep 2015 (accepted to JETP)

Wavelength selection beyond turing

NASA Astrophysics Data System (ADS)

Zelnik, Yuval R.; Tzuk, Omer

2017-06-01

Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from periodic patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the context of a Turing instability, where patterns emerge due to two locally interacting components that diffuse with different speeds in the medium. Turing patterns are multistable, meaning that many different patterns with different wavelengths are possible for the same set of parameters. Nevertheless, in a given region typically only one such wavelength is dominant. In the Turing instability region, random initial conditions will mostly lead to a wavelength that is similar to that of the leading eigenvector that arises from the linear stability analysis, but when venturing beyond, little is known about the pattern that will emerge. Using dryland vegetation as a case study, we use different models of drylands ecosystems to study the wavelength pattern that is selected in various scenarios beyond the Turing instability region, focusing on the phenomena of localized states and repeated local disturbances.

A biomechanical testing system to determine micromotion between hip implant and femur accounting for deformation of the hip implant: Assessment of the influence of rigid body assumptions on micromotions measurements.

PubMed

Leuridan, Steven; Goossens, Quentin; Roosen, Jorg; Pastrav, Leonard; Denis, Kathleen; Mulier, Michiel; Desmet, Wim; Vander Sloten, Jos

2017-02-01

Accurate pre-clinical evaluation of the initial stability of new cementless hip stems using in vitro micromotion measurements is an important step in the design process to assess the new stem's potential. Several measuring systems, linear variable displacement transducer-based and other, require assuming bone or implant to be rigid to obtain micromotion values or to calculate derived quantities such as relative implant tilting. An alternative linear variable displacement transducer-based measuring system not requiring a rigid body assumption was developed in this study. The system combined advantages of local unidirectional and frame-and-bracket micromotion measuring concepts. The influence and possible errors that would be made by adopting a rigid body assumption were quantified. Furthermore, as the system allowed emulating local unidirectional and frame-and-bracket systems, the influence of adopting rigid body assumptions were also analyzed for both concepts. Synthetic and embalmed bone models were tested in combination with primary and revision implants. Single-legged stance phase loading was applied to the implant - bone constructs. Adopting a rigid body assumption resulted in an overestimation of mediolateral micromotion of up to 49.7μm at more distal measuring locations. Maximal average relative rotational motion was overestimated by 0.12° around the anteroposterior axis. Frontal and sagittal tilting calculations based on a unidirectional measuring concept underestimated the true tilting by an order of magnitude. Non-rigid behavior is a factor that should not be dismissed in micromotion stability evaluations of primary and revision femoral implants. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

NASA Technical Reports Server (NTRS)

Majda, George

1986-01-01

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

A study of fluid-structure problems

NASA Astrophysics Data System (ADS)

Lam, Dennis Kang-Por

The stability of structures with and without fluid load is investigated. A method is developed for determining the fluid load in terms of added structural mass. Finite element methods are employed to study the buckling of a cylindrical shell under axial compression and liquid storage tanks under hydrodynamic load. Both linear and nonlinear analyses are performed. Diamond modes are found to be the possible postbuckling shapes of the cylindrical shell. Local buckling including elephant-foot buckle and diamond buckle are found for the liquid storage tank models. Comparison between the linear and nonlinear results indicates a substantial difference in buckling mode shapes, though the buckling loads are close to each other. The method for determining the hydrodynamic mass is applied to the impeller stage of a centrifugal pump. The method is based on a linear perturbation technique which assumes that the disturbance in the flow boundaries and velocities caused by the motion of the structure is small. A potential method is used to estimate the velocity flow field. The hydrodynamic mass is then obtained by calculating the total force which results from the pressure induced by a perturbation of the structure.

Conditions for Stabilizability of Linear Switched Systems

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu

2011-06-01

This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

A small-scale hyperacute compound eye featuring active eye tremor: application to visual stabilization, target tracking, and short-range odometry.

PubMed

Colonnier, Fabien; Manecy, Augustin; Juston, Raphaël; Mallot, Hanspeter; Leitel, Robert; Floreano, Dario; Viollet, Stéphane

2015-02-25

In this study, a miniature artificial compound eye (15 mm in diameter) called the curved artificial compound eye (CurvACE) was endowed for the first time with hyperacuity, using similar micro-movements to those occurring in the fly's compound eye. A periodic micro-scanning movement of only a few degrees enables the vibrating compound eye to locate contrasting objects with a 40-fold greater resolution than that imposed by the interommatidial angle. In this study, we developed a new algorithm merging the output of 35 local processing units consisting of adjacent pairs of artificial ommatidia. The local measurements performed by each pair are processed in parallel with very few computational resources, which makes it possible to reach a high refresh rate of 500 Hz. An aerial robotic platform with two degrees of freedom equipped with the active CurvACE placed over naturally textured panels was able to assess its linear position accurately with respect to the environment thanks to its efficient gaze stabilization system. The algorithm was found to perform robustly at different light conditions as well as distance variations relative to the ground and featured small closed-loop positioning errors of the robot in the range of 45 mm. In addition, three tasks of interest were performed without having to change the algorithm: short-range odometry, visual stabilization, and tracking contrasting objects (hands) moving over a textured background.

Effects of alcohols on the stability and low-frequency local motions that control the slow changes in structural dynamics of ferrocytochrome c.

PubMed

Jain, Rishu; Sharma, Deepak; Kumar, Rajesh

2013-10-01

To determine the effects of alcohols on the low-frequency local motions that control slow changes in structural dynamics of native-like compact states of proteins, we have studied the effects of alcohols on structural fluctuation of M80-containing Ω-loop by measuring the rate of thermally driven CO dissociation from a natively folded carbonmonoxycytochrome c under varying concentrations of alcohols (methanol, ethanol, 1-propanol, 2-propanol, 3°-butanol, 2,2,2-trifluoroethanol). As alcohol is increased, the rate coefficient of CO dissociation (k(diss)) first decreases in subdenaturing region and then increases on going from subdenaturing to denaturing milieu. This decrease in k(diss) is more for 2,2,2-trifluroethanol and 1-propanol and least for methanol, indicating that the first phase of motional constraint is due to the hydrophobicity of alcohols and intramolecular protein cross-linking effect of alcohols, which results in conformational entropy loss of protein. The thermal denaturation midpoint for ferrocytochrome c decreases with increase in alcohol, indicating that alcohol decrease the global stability of protein. The stabilization free energy (ΔΔG) in alcohols' solution was calculated from the slope of the Wyman-Tanford plot and water activity. The m-values obtained from the slope of ΔΔG versus alcohols plot were found to be more negative for longer and linear chain alcohols, indicating destabilization of proteins by alcohols through disturbance of hydrophobic interactions and hydrogen bonding.

An extended car-following model to describe connected traffic dynamics under cyberattacks

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Yu, Guizhen; Wu, Xinkai; Qin, Hongmao; Wang, Yunpeng

2018-04-01

In this paper, the impacts of the potential cyberattacks on vehicles are modeled through an extended car-following model. To better understand the mechanism of traffic disturbance under cyberattacks, the linear and nonlinear stability analysis are conducted respectively. Particularly, linear stability analysis is performed to obtain different neutral stability conditions with various parameters; and nonlinear stability analysis is carried out by using reductive perturbation method to derive the soliton solution of the modified Korteweg de Vries equation (mKdV) near the critical point, which is used to draw coexisting stability lines. Furthermore, by applying linear and nonlinear stability analysis, traffic flow state can be divided into three states, i.e., stable, metastable and unstable states which are useful to describe shockwave dynamics and driving behaviors under cyberattacks. The theoretical results show that the proposed car-following model is capable of successfully describing the car-following behavior of connected vehicles with cyberattacks. Finally, numerical simulation using real values has confirmed the validity of theoretical analysis. The results further demonstrate our model can be used to help avoid collisions and relieve traffic congestion with cybersecurity threats.

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Local study of helical magnetorotational instability in viscous Keplerian disks

NASA Astrophysics Data System (ADS)

MahdaviGharavi, M.; Hajisharifi, K.; Mehidan, H.

2018-03-01

In this paper, regarding the recent detection of significant azimuthal magnetic field in some accretion disks such as protostellar (Donati et al. in Nature 438:466, 2005), the multi-fluid model has been employed to analysis the stability of Keplerian rotational viscous dusty plasma system in a current-free helical magnetic field structure. Using the fluid-Maxwell equations, the general dispersion relation of the excited modes in the system has been obtained by applying the local approximation method in the linear perturbation theory. The typical numerical analysis of the obtained dispersion relation in the high-frequency regime shows that the presence of azimuthal magnetic field component in Keplerian flow has a considerable role in the stability conditions of the system. It also shows that the magnetic field helicity has a stabilization role against the magnetorotational instability (MRI) in the system due to contraction of the unstable wavelength region and decreasing the maximum growth rate of the instability. In this sense, the stabilization role of the viscosity term is more considerable for HMRI (instability in the presence of azimuthal magnetic field component) than the corresponding MRI (instability in the absence of azimuthal magnetic field component). Moreover, considering the discovered azimuthal magnetic field in these systems, the MRI can be arisen in the over-all range of dust grains construction values in contract with traditional MRI. This investigation can greatly contribute to better understanding the physics of some astrophysical phenomena, such as the main source of turbulence and angular momentum transport in protostellar and the other sufficiently ionized astrophysical disks, where the azimuthal magnetic field component in these systems can play a significant role.

Asynchrony among local communities stabilises ecosystem function of metacommunities.

PubMed

Wilcox, Kevin R; Tredennick, Andrew T; Koerner, Sally E; Grman, Emily; Hallett, Lauren M; Avolio, Meghan L; La Pierre, Kimberly J; Houseman, Gregory R; Isbell, Forest; Johnson, David Samuel; Alatalo, Juha M; Baldwin, Andrew H; Bork, Edward W; Boughton, Elizabeth H; Bowman, William D; Britton, Andrea J; Cahill, James F; Collins, Scott L; Du, Guozhen; Eskelinen, Anu; Gough, Laura; Jentsch, Anke; Kern, Christel; Klanderud, Kari; Knapp, Alan K; Kreyling, Juergen; Luo, Yiqi; McLaren, Jennie R; Megonigal, Patrick; Onipchenko, Vladimir; Prevéy, Janet; Price, Jodi N; Robinson, Clare H; Sala, Osvaldo E; Smith, Melinda D; Soudzilovskaia, Nadejda A; Souza, Lara; Tilman, David; White, Shannon R; Xu, Zhuwen; Yahdjian, Laura; Yu, Qiang; Zhang, Pengfei; Zhang, Yunhai

2017-12-01

Temporal stability of ecosystem functioning increases the predictability and reliability of ecosystem services, and understanding the drivers of stability across spatial scales is important for land management and policy decisions. We used species-level abundance data from 62 plant communities across five continents to assess mechanisms of temporal stability across spatial scales. We assessed how asynchrony (i.e. different units responding dissimilarly through time) of species and local communities stabilised metacommunity ecosystem function. Asynchrony of species increased stability of local communities, and asynchrony among local communities enhanced metacommunity stability by a wide range of magnitudes (1-315%); this range was positively correlated with the size of the metacommunity. Additionally, asynchronous responses among local communities were linked with species' populations fluctuating asynchronously across space, perhaps stemming from physical and/or competitive differences among local communities. Accordingly, we suggest spatial heterogeneity should be a major focus for maintaining the stability of ecosystem services at larger spatial scales. © 2017 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.

Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials

NASA Astrophysics Data System (ADS)

Yang, Jianke; Nixon, Sean

2016-11-01

Stability of soliton families in one-dimensional nonlinear Schrödinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets (λ , - λ ,λ* , -λ*), similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non- PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.

Langley Stability and Transition Analysis Code (LASTRAC) Version 1.2 User Manual

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2004-01-01

LASTRAC is a general-purposed, physics-based transition prediction code released by NASA for Laminar Flow Control studies and transition research. The design and development of the LASTRAC code is aimed at providing an engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. It was written from scratch based on the state-of-the-art numerical methods for stability analysis and modern software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory or linear parabolized stability equations method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. This document describes the governing equations, numerical methods, code development, detailed description of input/output parameters, and case studies for the current release of LASTRAC.

Theoretical considerations of some nonlinear aspects of hypersonic panel flutter

NASA Technical Reports Server (NTRS)

Mcintosh, S. C., Jr.

1974-01-01

A research project to analyze the effects of hypersonic nonlinear aerodynamic loading on panel flutter is reported. The test equipment and procedures for conducting the tests are explained. The effects of aerodynamic linearities on stability were evaluated by determining constant-initial-energy amplitude-sensitive stability boundaries and comparing them with the corresponding linear stability boundaries. An attempt to develop an alternative method of analysis for systems where amplitude-sensitive instability is possible is presented.

Role of stereotactic radiosurgery with a linear accelerator in treatment of intracranial arteriovenous malformations and tumors in children.

PubMed

Loeffler, J S; Rossitch, E; Siddon, R; Moore, M R; Rockoff, M A; Alexander, E

1990-05-01

Between 1986 and 1988, 16 children were treated for 10 arteriovenous malformations and 6 recurrent intracranial tumors with stereotactic radiation therapy using a modified Clinac 6/100 linear accelerator. The median age of our patients was 10.5 years. For the group with arteriovenous malformation, follow-up ranged from 6 months to 37 months (median was 20 months). No patient bled during the follow-up period. Five of eight patients with follow-up longer than 12 months have achieved complete obliteration of their arteriovenous malformation by angiogram. The four remaining patients who have not achieved a complete obliteration are awaiting their 2-year posttreatment angiogram. The other patient has been treated within the year and have not yet been studied. Five of the six recurrent tumor patients are alive with a median follow-up of 8 months. The remaining patient was controlled locally, but he died of recurrent disease outside the area treated with radiosurgery. The radiographic responses of these patients have included three complete responses, two substantial reductions in tumor volume (greater than 50%) and one stabilization. Despite previous radiotherapy, there have been no significant complications in these patients. We conclude that stereotactic radiation therapy using a standard linear accelerator is an effective and safe technique in the treatment of selected intracranial arteriovenous malformations and tumors in children. In addition, stereotactic radiosurgery may have unique applications in the treatment of localized primary and recurrent pediatric brain tumors.

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. I - Velocity selection. II - Stability

NASA Technical Reports Server (NTRS)

Tanveer, S.

1989-01-01

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. First the bubble velocity relative to the fluid velocity at infinity is determined for small surface tension by means of a transcendentally small correction to the asymptotic series solution. In addition, a linear stability analysis shows that only the solution branch corresponding to the largest possible bubble velocity for given surface tension is stable, while all the others are unstable.

Orbital stability of periodic traveling-wave solutions for the log-KdV equation

NASA Astrophysics Data System (ADS)

Natali, Fábio; Pastor, Ademir; Cristófani, Fabrício

2017-09-01

In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work [3], in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in [20] to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in [13] and [25] to deduce the orbital stability of the periodic traveling waves in the energy space.

R-parametrization and its role in classification of linear multivariable feedback systems

NASA Technical Reports Server (NTRS)

Chen, Robert T. N.

1988-01-01

A classification of all the compensators that stabilize a given general plant in a linear, time-invariant multi-input, multi-output feedback system is developed. This classification, along with the associated necessary and sufficient conditions for stability of the feedback system, is achieved through the introduction of a new parameterization, referred to as R-Parameterization, which is a dual of the familiar Q-Parameterization. The classification is made to the stability conditions of the compensators and the plant by themselves; and necessary and sufficient conditions are based on the stability of Q and R themselves.

Stability of linear systems in second-order form based on structure preserving similarity transformations

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

Stoustrup, Jakob; Pommer, Christian; Kliem, Wolfhard

2015-10-31

This paper deals with two stability aspects of linear systems of the form I ¨ x +B˙ x +Cx = 0 given by the triple (I;B;C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I;B1;C1) with a symmetrizable matrix C1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

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

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

Metal pad instabilities in liquid metal batteries.

PubMed

Zikanov, Oleg

2015-12-01

A mechanical analogy is used to analyze the interaction between the magnetic field, electric current, and deformation of interfaces in liquid metal batteries. In the framework of a low-mode, nondissipative, linear stability model, it is found that, during charging or discharging, a sufficiently large battery is prone to instabilities of two types. One is similar to the metal pad instability known to exist in the aluminum reduction cells. Another type is new. It is related to the destabilizing effect of the Lorentz force formed by the azimuthal magnetic field induced by the base current, and the current perturbations caused by the local variations of the thickness of the electrolyte layer.

Stability of Nonlinear Principal Components Analysis: An Empirical Study Using the Balanced Bootstrap

ERIC Educational Resources Information Center

Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Kooij, Anita J.

2007-01-01

Principal components analysis (PCA) is used to explore the structure of data sets containing linearly related numeric variables. Alternatively, nonlinear PCA can handle possibly nonlinearly related numeric as well as nonnumeric variables. For linear PCA, the stability of its solution can be established under the assumption of multivariate…

Development and validation of a stability-indicating high performance liquid chromatographic assay for benoxinate.

PubMed

Chorny, Michael; Levy, Daniel; Schumacher, Ilana; Lichaa, Chaim; Gruzman, Boris; Livshits, Oleg; Lomnicky, Yossi

2003-04-24

Benoxinate is a local anaesthetic used for ophthalmic applications. The aim of this study was to develop a rapid and simple stability-indicating method for the determination of benoxinate formulated for ophthalmic use, evaluate its long-term stability and identify its major degradation product. Benoxinate was eluted on a 10 microm Spherisorb phenyl column, 250 x 3.2 mm, with a mobile phase consisting of acetonitrile-buffer (pH 3.5) (35:65, v/v), pumped at 0.8 ml min(-1) flow rate. The buffer was composed of sodium dihydrogen phosphate (50 mM), sodium hydrogen sulfate (2.5 mM) and 1-heptanesulfonic acid sodium salt (5 mM). The analyte was quantified spectrophotometrically at 308 nm. The chromatograms of benoxinate formulations obtained by this method showed benoxinate (t = 4.5 min) well resolved from its degradation product (t = 2.3 min), which was separately identified by means of HPLC-MS as 4-amino-3-butoxybenzoic acid. The assay was demonstrated to have high accuracy, precision and linearity. The method was implemented in investigating the long-term stability of benoxinate 0.4% ophthalmic solutions. The method was found to be simple, quick and selective in determining benoxinate concentrations in fresh and aged preparations.

Geometry of thin liquid sheet flows

NASA Technical Reports Server (NTRS)

Chubb, Donald L.; Calfo, Frederick D.; Mcconley, Marc W.; Mcmaster, Matthew S.; Afjeh, Abdollah A.

1994-01-01

Incompresible, thin sheet flows have been of research interest for many years. Those studies were mainly concerned with the stability of the flow in a surrounding gas. Squire was the first to carry out a linear, invicid stability analysis of sheet flow in air and compare the results with experiment. Dombrowski and Fraser did an experimental study of the disintegration of sheet flows using several viscous liquids. They also detected the formulation of holes in their sheet flows. Hagerty and Shea carried out an inviscid stability analysis and calculated growth rates with experimental values. They compared their calculated growth rates with experimental values. Taylor studied extensively the stability of thin liquid sheets both theoretically and experimentally. He showed that thin sheets in a vacuum are stable. Brown experimentally investigated thin liquid sheet flows as a method of application of thin films. Clark and Dumbrowski carried out second-order stability analysis for invicid sheet flows. Lin introduced viscosity into the linear stability analysis of thin sheet flows in a vacuum. Mansour and Chigier conducted an experimental study of the breakup of a sheet flow surrounded by high-speed air. Lin et al. did a linear stability analysis that included viscosity and a surrounding gas. Rangel and Sirignano carried out both a linear and nonlinear invisid stability analysis that applies for any density ratio between the sheet liquid and the surrounding gas. Now there is renewed interest in sheet flows because of their possible application as low mass radiating surfaces. The objective of this study is to investigate the fluid dynamics of sheet flows that are of interest for a space radiator system. Analytical expressions that govern the sheet geometry are compared with experimental results. Since a space radiator will operate in a vacuum, the analysis does not include any drag force on the sheet flow.

Local structure preserving sparse coding for infrared target recognition

PubMed Central

Han, Jing; Yue, Jiang; Zhang, Yi; Bai, Lianfa

2017-01-01

Sparse coding performs well in image classification. However, robust target recognition requires a lot of comprehensive template images and the sparse learning process is complex. We incorporate sparsity into a template matching concept to construct a local sparse structure matching (LSSM) model for general infrared target recognition. A local structure preserving sparse coding (LSPSc) formulation is proposed to simultaneously preserve the local sparse and structural information of objects. By adding a spatial local structure constraint into the classical sparse coding algorithm, LSPSc can improve the stability of sparse representation for targets and inhibit background interference in infrared images. Furthermore, a kernel LSPSc (K-LSPSc) formulation is proposed, which extends LSPSc to the kernel space to weaken the influence of the linear structure constraint in nonlinear natural data. Because of the anti-interference and fault-tolerant capabilities, both LSPSc- and K-LSPSc-based LSSM can implement target identification based on a simple template set, which just needs several images containing enough local sparse structures to learn a sufficient sparse structure dictionary of a target class. Specifically, this LSSM approach has stable performance in the target detection with scene, shape and occlusions variations. High performance is demonstrated on several datasets, indicating robust infrared target recognition in diverse environments and imaging conditions. PMID:28323824

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

On the linear stability of blood flow through model capillary networks.

PubMed

Davis, Jeffrey M

2014-12-01

Under the approximation that blood behaves as a continuum, a numerical implementation is presented to analyze the linear stability of capillary blood flow through model tree and honeycomb networks that are based on the microvascular structures of biological tissues. The tree network is comprised of a cascade of diverging bifurcations, in which a parent vessel bifurcates into two descendent vessels, while the honeycomb network also contains converging bifurcations, in which two parent vessels merge into one descendent vessel. At diverging bifurcations, a cell partitioning law is required to account for the nonuniform distribution of red blood cells as a function of the flow rate of blood into each descendent vessel. A linearization of the governing equations produces a system of delay differential equations involving the discharge hematocrit entering each network vessel and leads to a nonlinear eigenvalue problem. All eigenvalues in a specified region of the complex plane are captured using a transformation based on contour integrals to construct a linear eigenvalue problem with identical eigenvalues, which are then determined using a standard QR algorithm. The predicted value of the dimensionless exponent in the cell partitioning law at the instability threshold corresponds to a supercritical Hopf bifurcation in numerical simulations of the equations governing unsteady blood flow. Excellent agreement is found between the predictions of the linear stability analysis and nonlinear simulations. The relaxation of the assumption of plug flow made in previous stability analyses typically has a small, quantitative effect on the stability results that depends on the specific network structure. This implementation of the stability analysis can be applied to large networks with arbitrary structure provided only that the connectivity among the network segments is known.

Topological entanglement entropy of fracton stabilizer codes

NASA Astrophysics Data System (ADS)

Ma, Han; Schmitz, A. T.; Parameswaran, S. A.; Hermele, Michael; Nandkishore, Rahul M.

2018-03-01

Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are three-dimensional gapped topologically ordered states of matter that lack a TQFT description. We show that three-dimensional fracton phases are nevertheless characterized, at least partially, by universal structure in the entanglement entropy of their ground-state wave functions. We explicitly compute the entanglement entropy for two archetypal fracton models, the "X-cube model" and "Haah's code," and demonstrate the existence of a nonlocal contribution that scales linearly in subsystem size. We show via Schrieffer-Wolff transformations that this piece of the entanglement entropy of fracton models is robust against arbitrary local perturbations of the Hamiltonian. Finally, we argue that these results may be extended to characterize localization-protected fracton topological order in excited states of disordered fracton models.

Itinerancy enhanced quantum fluctuation of magnetic moments in iron-based superconductors

DOE PAGES

Tam, Yu -T.; Ku, W.; Yao, D. -X.

2015-09-10

We investigate the influence of itinerant carriers on dynamics and fluctuation of local moments in Fe-based superconductors, via linear spin-wave analysis of a spin-fermion model containing both itinerant and local degrees of freedom. Surprisingly against the common lore, instead of enhancing the (π,0) order, itinerant carriers with well nested Fermi surfaces is found to induce significant amount of spatial and temporal quantum fluctuation that leads to the observed small ordered moment. Interestingly, the underlying mechanism is shown to be intra-pocket nesting-associated long-range coupling, rather than the previously believed ferromagnetic double-exchange effect. This challenges the validity of ferromagnetically compensated first-neighbor couplingmore » reported from short-range fitting to the experimental dispersion, which turns out to result instead from the ferro-orbital order that is also found instrumental in stabilizing the magnetic order.« less

Simulation of magnetic holes formation in the magnetosheath

NASA Astrophysics Data System (ADS)

Ahmadi, Narges; Germaschewski, Kai; Raeder, Joachim

2017-12-01

Magnetic holes have been frequently observed in the Earth's magnetosheath and are believed to be the consequence of the nonlinear evolution of the mirror instability. Mirror mode perturbations mainly form as magnetic holes in regions where the plasma is marginally mirror stable with respect to the linear instability criterion. We present an expanding box particle-in-cell simulation to mimic the changing conditions in the magnetosheath as the plasma is convected through it that produces mirror mode magnetic holes. We show that in the initial nonlinear evolution, where the plasma conditions are mirror unstable, the magnetic peaks are dominant, while later, as the plasma relaxes toward marginal stability, the fluctuations evolve into deep magnetic holes. While the averaged plasma parameters in the simulation remain close to the mirror instability threshold, the local plasma in the magnetic holes is highly unstable to mirror instability and locally mirror stable in the magnetic peaks.

Absolute instability of the Gaussian wake profile

NASA Technical Reports Server (NTRS)

Hultgren, Lennart S.; Aggarwal, Arun K.

1987-01-01

Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

Absence of metastable states in strained monoatomic cubic crystals.

NASA Astrophysics Data System (ADS)

Aguayo, Aarón; Mehl, Michael L.; de Coss, Romeo

2005-03-01

The Bain path distortion of a metal with an fcc (bcc) ground state toward the bcc (fcc) structure initially requires an increase in energy, but at some point along the Bain path the energy will again decrease until a local minimum is reached. We have studied the tetragonal distortion (Bain path) of monoatomic cubic crystals, using a combination of parametrized tight-binding and first-principles linearized augmented plane wave calculations. We show that this local minimum is unstable with respect to an elastic distortion, except in the rare case that the minimum is at the bcc (fcc) point on the Bain path. This shows that body-centered-tetragonal phases of these materials, which have been seen in epitaxially grown thin films, must be stabilized by the substrate and cannot be freestanding films. This work was partially supported by Consejo Nacional de Ciencia y Tecnolog'ia (CONACYT, M'exico) under Grant No. 43830-F.

Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile.

PubMed

Martínez, P J; Meister, M; Floría, L M; Falo, F

2003-06-01

The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations. (c) 2003 American Institute of Physics.

Assessment of Walking Stability of Elderly by Means of Nonlinear Time-Series Analysis and Simple Accelerometry

NASA Astrophysics Data System (ADS)

Ohtaki, Yasuaki; Arif, Muhammad; Suzuki, Akihiro; Fujita, Kazuki; Inooka, Hikaru; Nagatomi, Ryoichi; Tsuji, Ichiro

This study presents an assessment of walking stability in elderly people, focusing on local dynamic stability of walking. Its main objectives were to propose a technique to quantify local dynamic stability using nonlinear time-series analyses and a portable instrument, and to investigate their reliability in revealing the efficacy of an exercise training intervention for elderly people for improvement of walking stability. The method measured three-dimensional acceleration of the upper body, and computation of Lyapunov exponents, thereby directly quantifying the local stability of the dynamic system. Straight level walking of young and elderly subjects was investigated in the experimental study. We compared Lyapunov exponents of young and the elderly subjects, and of groups before and after the exercise intervention. Experimental results demonstrated that the exercise intervention improved local dynamic stability of walking. The proposed method was useful in revealing effects and efficacies of the exercise intervention for elderly people.

dAdd1 and dXNP prevent genome instability by maintaining HP1a localization at Drosophila telomeres.

PubMed

Chavez, Joselyn; Murillo-Maldonado, Juan Manuel; Bahena, Vanessa; Cruz, Ana Karina; Castañeda-Sortibrán, América; Rodriguez-Arnaiz, Rosario; Zurita, Mario; Valadez-Graham, Viviana

2017-12-01

Telomeres are important contributors to genome stability, as they prevent linear chromosome end degradation and contribute to the avoidance of telomeric fusions. An important component of the telomeres is the heterochromatin protein 1a (HP1a). Mutations in Su(var)205, the gene encoding HP1a in Drosophila, result in telomeric fusions, retrotransposon regulation loss and larger telomeres, leading to chromosome instability. Previously, it was found that several proteins physically interact with HP1a, including dXNP and dAdd1 (orthologues to the mammalian ATRX gene). In this study, we found that mutations in the genes encoding the dXNP and dAdd1 proteins affect chromosome stability, causing chromosomal aberrations, including telomeric defects, similar to those observed in Su(var)205 mutants. In somatic cells, we observed that dXNP and dAdd1 participate in the silencing of the telomeric HTT array of retrotransposons, preventing anomalous retrotransposon transcription and integration. Furthermore, the lack of dAdd1 results in the loss of HP1a from the telomeric regions without affecting other chromosomal HP1a binding sites; mutations in dxnp also affected HP1a localization but not at all telomeres, suggesting a specialized role for dAdd1 and dXNP proteins in locating HP1a at the tips of the chromosomes. These results place dAdd1 as an essential regulator of HP1a localization and function in the telomere heterochromatic domain.

Does competition improve financial stability of the banking sector in ASEAN countries? An empirical analysis.

PubMed

Noman, Abu Hanifa Md; Gee, Chan Sok; Isa, Che Ruhana

2017-01-01

This study examines the influence of competition on the financial stability of the commercial banks of Association of Southeast Asian Nation (ASEAN) over the 1990 to 2014 period. Panzar-Rosse H-statistic, Lerner index and Herfindahl-Hirschman Index (HHI) are used as measures of competition, while Z-score, non-performing loan (NPL) ratio and equity ratio are used as measures of financial stability. Two-step system Generalized Method of Moments (GMM) estimates demonstrate that competition measured by H-statistic is positively related to Z-score and equity ratio, and negatively related to non-performing loan ratio. Conversely, market power measured by Lerner index is negatively related to Z-score and equity ratio and positively related to NPL ratio. These results strongly support the competition-stability view for ASEAN banks. We also capture the non-linear relationship between competition and financial stability by incorporating a quadratic term of competition in our models. The results show that the coefficient of the quadratic term of H-statistic is negative for the Z-score model given a positive coefficient of the linear term in the same model. These results support the non-linear relationship between competition and financial stability of the banking sector. The study contains significant policy implications for improving the financial stability of the commercial banks.

Does competition improve financial stability of the banking sector in ASEAN countries? An empirical analysis

PubMed Central

Gee, Chan Sok; Isa, Che Ruhana

2017-01-01

This study examines the influence of competition on the financial stability of the commercial banks of Association of Southeast Asian Nation (ASEAN) over the 1990 to 2014 period. Panzar-Rosse H-statistic, Lerner index and Herfindahl-Hirschman Index (HHI) are used as measures of competition, while Z-score, non-performing loan (NPL) ratio and equity ratio are used as measures of financial stability. Two-step system Generalized Method of Moments (GMM) estimates demonstrate that competition measured by H-statistic is positively related to Z-score and equity ratio, and negatively related to non-performing loan ratio. Conversely, market power measured by Lerner index is negatively related to Z-score and equity ratio and positively related to NPL ratio. These results strongly support the competition-stability view for ASEAN banks. We also capture the non-linear relationship between competition and financial stability by incorporating a quadratic term of competition in our models. The results show that the coefficient of the quadratic term of H-statistic is negative for the Z-score model given a positive coefficient of the linear term in the same model. These results support the non-linear relationship between competition and financial stability of the banking sector. The study contains significant policy implications for improving the financial stability of the commercial banks. PMID:28486548

Evans function computation for the stability of travelling waves

NASA Astrophysics Data System (ADS)

Barker, B.; Humpherys, J.; Lyng, G.; Lytle, J.

2018-04-01

In recent years, the Evans function has become an important tool for the determination of stability of travelling waves. This function, a Wronskian of decaying solutions of the eigenvalue equation, is useful both analytically and computationally for the spectral analysis of the linearized operator about the wave. In particular, Evans-function computation allows one to locate any unstable eigenvalues of the linear operator (if they exist); this allows one to establish spectral stability of a given wave and identify bifurcation points (loss of stability) as model parameters vary. In this paper, we review computational aspects of the Evans function and apply it to multidimensional detonation waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Localized tearing modes in the magnetotail driven by curvature effects

NASA Technical Reports Server (NTRS)

Sundaram, A. K.; Fairfield, D. H.

1995-01-01

The stability of collisionless tearing modes is examined in the presence of curvature drift resonances and the trapped particle effects. A kinetic description for both electrons and ions is employed to investigate the stability of a two-dimensional equilibrium model. The main features of the study are to treat the ion dynamics properly by incorporating effects associated with particle trajectories in the tail fields and to include the linear coupling of trapped particle modes. Generalized dispersion relations are derived in several parameter regimes by considering two important sublayers of the reconnecting region. For a typical choice of parameters appropriate to the current sheet region, we demonstrate that localized tearing modes driven by ion curvature drift resonance effects are excited in the current sheet region with growth time of the order of a few seconds. Also, we examine nonlocal characteristics of tearing modes driven by curvature effects and show that modes growing in a fraction of a second arise when mode widths are larger than the current sheet width. Further, we show that trapped particle effects, in an interesting frequency regime, significantly enhance the growth rate of the tearing mode. The relevance of this theory for substorm onset phase and other features of the substorms is briefly discussed.

Aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics

NASA Technical Reports Server (NTRS)

Horne, W. Clifton; Smith, Charles A.; Karamcheti, Krishnamurty

1991-01-01

Recent developments in the field of nonequilibrium thermodynamics associated with viscous flows are examined and related to developments to the understanding of specific phenomena in aerodynamics and aeroacoustics. A key element of the nonequilibrium theory is the principle of minimum entropy production rate for steady dissipative processes near equilibrium, and variational calculus is used to apply this principle to several examples of viscous flow. A review of nonequilibrium thermodynamics and its role in fluid motion are presented. Several formulations are presented of the local entropy production rate and the local energy dissipation rate, two quantities that are of central importance to the theory. These expressions and the principle of minimum entropy production rate for steady viscous flows are used to identify parallel-wall channel flow and irrotational flow as having minimally dissipative velocity distributions. Features of irrotational, steady, viscous flow near an airfoil, such as the effect of trailing-edge radius on circulation, are also found to be compatible with the minimum principle. Finally, the minimum principle is used to interpret the stability of infinitesimal and finite amplitude disturbances in an initially laminar, parallel shear flow, with results that are consistent with experiment and linearized hydrodynamic stability theory. These results suggest that a thermodynamic approach may be useful in unifying the understanding of many diverse phenomena in aerodynamics and aeroacoustics.

The local stability of the magnetized advection-dominated discs with the radial viscous force

NASA Astrophysics Data System (ADS)

Ghoreyshi, S. M.; Shadmehri, M.

2018-06-01

We study local stability of the advection-dominated optically thick (slim) and optically thin discs with purely toroidal magnetic field and the radial viscous force using a linear perturbation analysis. Our dispersion relation indicates that the presence of magnetic fields and radial viscous force cannot give rise to any new mode of the instability. We find, however, that growth rate of the thermal mode in the slim discs and that of the acoustic modes in the slim and optically thin discs are dramatically affected by the radial viscous force. This force tends to strongly decrease the growth rate of the outward-propagating acoustic mode (O-mode) in the short-wavelength limit, but it causes a slim disc to become thermally more unstable. This means that growth rate of the thermal mode increases in the presence of radial viscous force. This enhancement is more significant when the viscosity parameter is large. The growth rates of the thermal and acoustic modes depend on the magnetic field. Although the instability of O-mode for a stronger magnetic field case has a higher growth rate, the thermal mode of the slim discs can be suppressed when the magnetic field is strong. The inertial-acoustic instability of a magnetized disc may explain the quasi-periodic oscillations (QPOs) from the black holes.

Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems

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

Zocco, A.; Plunk, G. G.; Xanthopoulos, P.

The effects of a non-axisymmetric (3D) equilibrium magnetic field on the linear ion-temperature-gradient (ITG) driven mode are investigated. We consider the strongly driven, toroidal branch of the instability in a global (on the magnetic surface) setting. Previous studies have focused on particular features of non-axisymmetric systems, such as strong local shear or magnetic ripple, that introduce inhomogeneity in the coordinate along the magnetic field. In contrast, here we include non-axisymmetry explicitly via the dependence of the magnetic drift on the field line label α, i.e., across the magnetic field, but within the magnetic flux surface. We consider the limit wheremore » this variation occurs on a scale much larger than that of the ITG mode, and also the case where these scales are similar. Close to axisymmetry, we find that an averaging effect of the magnetic drift on the flux surface causes global (on the surface) stabilization, as compared to the most unstable local mode. In the absence of scale separation, we find destabilization is also possible, but only if a particular resonance occurs between the magnetic drift and the mode, and finite Larmor radius effects are neglected. We discuss the relative importance of surface global effects and known radially global effects.« less

Competitions between Rayleigh-Taylor instability and Kelvin-Helmholtz instability with continuous density and velocity profiles

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

Ye, W. H.; He, X. T.; CAPT, Peking University, Beijing 100871

2011-02-15

In this research, competitions between Rayleigh-Taylor instability (RTI) and Kelvin-Helmholtz instability (KHI) in two-dimensional incompressible fluids within a linear growth regime are investigated analytically. Normalized linear growth rate formulas for both the RTI, suitable for arbitrary density ratio with continuous density profile, and the KHI, suitable for arbitrary density ratio with continuous density and velocity profiles, are obtained. The linear growth rates of pure RTI ({gamma}{sub RT}), pure KHI ({gamma}{sub KH}), and combined RTI and KHI ({gamma}{sub total}) are investigated, respectively. In the pure RTI, it is found that the effect of the finite thickness of the density transition layermore » (L{sub {rho}}) reduces the linear growth of the RTI (stabilizes the RTI). In the pure KHI, it is found that conversely, the effect of the finite thickness of the density transition layer increases the linear growth of the KHI (destabilizes the KHI). It is found that the effect of the finite thickness of the density transition layer decreases the ''effective'' or ''local'' Atwood number (A) for both the RTI and the KHI. However, based on the properties of {gamma}{sub RT}{proportional_to}{radical}(A) and {gamma}{sub KH}{proportional_to}{radical}(1-A{sup 2}), the effect of the finite thickness of the density transition layer therefore has a completely opposite role on the RTI and the KHI noted above. In addition, it is found that the effect of the finite thickness of the velocity shear layer (L{sub u}) stabilizes the KHI, and for the most cases, the combined effects of the finite thickness of the density transition layer and the velocity shear layer (L{sub {rho}=}L{sub u}) also stabilize the KHI. Regarding the combined RTI and KHI, it is found that there is a competition between the RTI and the KHI because of the completely opposite effect of the finite thickness of the density transition layer on these two kinds of instability. It is found that the competitions between the RTI and the KHI depend, respectively, on the Froude number, the density ratio of the light fluid to the heavy one, and the finite thicknesses of the density transition layer and the velocity shear layer. Furthermore, for the fixed Froude number, the linear growth rate ratio of the RTI to the KHI decreases with both the density ratio and the finite thickness of the density transition layer, but increases with the finite thickness of the velocity shear layer and the combined finite thicknesses of the density transition layer and the velocity shear layer (L{sub {rho}=}L{sub u}). In summary, our analytical results show that the effect of the finite thickness of the density transition layer stabilizes the RTI and the overall combined effects of the finite thickness of the density transition layer and the velocity shear layer (L{sub {rho}=}L{sub u}) also stabilize the KHI. Thus, it should be included in applications where the transition layer effect plays an important role, such as the formation of large-scale structures (jets) in high energy density physics and astrophysics and turbulent mixing.« less

Synchronization of cyclic power grids: Equilibria and stability of the synchronous state

NASA Astrophysics Data System (ADS)

Xi, Kaihua; Dubbeldam, Johan L. A.; Lin, Hai Xiang

2017-01-01

Synchronization is essential for the proper functioning of power grids; we investigate the synchronous states and their stability for cyclic power grids. We calculate the number of stable equilibria and investigate both the linear and nonlinear stabilities of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. We use the energy barrier to measure the nonlinear stability and calculate it by comparing the potential energy of the type-1 saddles with that of the stable synchronous state. We find that the energy barrier depends on the network size (N) in a more complicated fashion compared to the linear stability. In particular, when the generators and consumers are evenly distributed in an alternating way, the energy barrier decreases to a constant when N approaches infinity. For a heterogeneous distribution of generators and consumers, the energy barrier decreases with N. The more heterogeneous the distribution is, the stronger the energy barrier depends on N. Finally, we find that by comparing situations with equal line loads in cyclic and tree networks, tree networks exhibit reduced stability. This difference disappears in the limit of N →∞ . This finding corroborates previous results reported in the literature and suggests that cyclic (sub)networks may be applied to enhance power transfer while maintaining stable synchronous operation.

Linear instability in the wake of an elliptic wing

NASA Astrophysics Data System (ADS)

He, Wei; Tendero, Juan Ángel; Paredes, Pedro; Theofilis, Vassilis

2017-12-01

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of Rec=1750 and two angles of attack, {AoA}=0° and 5°. Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.

Evaluation of design flood estimates with respect to sample size

NASA Astrophysics Data System (ADS)

Kobierska, Florian; Engeland, Kolbjorn

2016-04-01

Estimation of design floods forms the basis for hazard management related to flood risk and is a legal obligation when building infrastructure such as dams, bridges and roads close to water bodies. Flood inundation maps used for land use planning are also produced based on design flood estimates. In Norway, the current guidelines for design flood estimates give recommendations on which data, probability distribution, and method to use dependent on length of the local record. If less than 30 years of local data is available, an index flood approach is recommended where the local observations are used for estimating the index flood and regional data are used for estimating the growth curve. For 30-50 years of data, a 2 parameter distribution is recommended, and for more than 50 years of data, a 3 parameter distribution should be used. Many countries have national guidelines for flood frequency estimation, and recommended distributions include the log Pearson II, generalized logistic and generalized extreme value distributions. For estimating distribution parameters, ordinary and linear moments, maximum likelihood and Bayesian methods are used. The aim of this study is to r-evaluate the guidelines for local flood frequency estimation. In particular, we wanted to answer the following questions: (i) Which distribution gives the best fit to the data? (ii) Which estimation method provides the best fit to the data? (iii) Does the answer to (i) and (ii) depend on local data availability? To answer these questions we set up a test bench for local flood frequency analysis using data based cross-validation methods. The criteria were based on indices describing stability and reliability of design flood estimates. Stability is used as a criterion since design flood estimates should not excessively depend on the data sample. The reliability indices describe to which degree design flood predictions can be trusted.

Stability Analysis for Rotating Stall Dynamics in Axial Flow Compressors

DTIC Science & Technology

1999-01-01

modes determines collectively local stability of the compressor model. Explicit conditions are obtained for local stability of rotating stall which...critical modes determines the stability for rotating stall collectively . We point out that although in a special case our stability condition for...strict crossing assumption implies that the zero solution changes its stability as ~, crosses ~’c. For instance, odk (yc ) > 0 implies that the zero

Investigating homology between proteins using energetic profiles.

PubMed

Wrabl, James O; Hilser, Vincent J

2010-03-26

Accumulated experimental observations demonstrate that protein stability is often preserved upon conservative point mutation. In contrast, less is known about the effects of large sequence or structure changes on the stability of a particular fold. Almost completely unknown is the degree to which stability of different regions of a protein is generally preserved throughout evolution. In this work, these questions are addressed through thermodynamic analysis of a large representative sample of protein fold space based on remote, yet accepted, homology. More than 3,000 proteins were computationally analyzed using the structural-thermodynamic algorithm COREX/BEST. Estimated position-specific stability (i.e., local Gibbs free energy of folding) and its component enthalpy and entropy were quantitatively compared between all proteins in the sample according to all-vs.-all pairwise structural alignment. It was discovered that the local stabilities of homologous pairs were significantly more correlated than those of non-homologous pairs, indicating that local stability was indeed generally conserved throughout evolution. However, the position-specific enthalpy and entropy underlying stability were less correlated, suggesting that the overall regional stability of a protein was more important than the thermodynamic mechanism utilized to achieve that stability. Finally, two different types of statistically exceptional evolutionary structure-thermodynamic relationships were noted. First, many homologous proteins contained regions of similar thermodynamics despite localized structure change, suggesting a thermodynamic mechanism enabling evolutionary fold change. Second, some homologous proteins with extremely similar structures nonetheless exhibited different local stabilities, a phenomenon previously observed experimentally in this laboratory. These two observations, in conjunction with the principal conclusion that homologous proteins generally conserved local stability, may provide guidance for a future thermodynamically informed classification of protein homology.

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.

Species dispersal rates alter diversity and ecosystem stability in pond metacommunities.

PubMed

Howeth, Jennifer G; Leibold, Mathew A

2010-09-01

Metacommunity theory suggests that relationships between diversity and ecosystem stability can be determined by the rate of species dispersal among local communities. The predicted relationships, however, may depend upon the relative strength of local environmental processes and disturbance. Here we evaluate the role of dispersal frequency and local predation perturbations in affecting patterns of diversity and stability in pond plankton metacommunities. Pond metacommunities were composed of three mesocosm communities: one of the three communities maintained constant "press" predation from a selective predator, bluegill sunfish (Lepomis macrochirus); the second community maintained "press" conditions without predation; and the third community experienced recurrent "pulsed" predation from bluegill sunfish. The triads of pond communities were connected at either no, low (0.7%/d), or high (20%/d) planktonic dispersal. Richness and composition of zooplankton and stability of plankton biomass and ecosystem productivity were measured at local and regional spatial scales. Dispersal significantly affected diversity such that local and regional biotas at the low dispersal rate maintained the greatest number of species. The unimodal local dispersal-diversity relationship was predator-dependent, however, as selective press predation excluded species regardless of dispersal. Further, there was no effect of dispersal on beta diversity because predation generated local conditions that selected for distinct community assemblages. Spatial and temporal ecosystem stability responded to dispersal frequency but not predation. Low dispersal destabilized the spatial stability of producer biomass but stabilized temporal ecosystem productivity. The results indicate that selective predation can prevent species augmentation from mass effects but has no apparent influence on stability. Dispersal rates, in contrast, can have significant effects on both species diversity and ecosystem stability at multiple spatial scales in metacommunities.

Effects of Density and Impurity on Edge Localized Modes in Tokamaks

NASA Astrophysics Data System (ADS)

Zhu, Ping

2017-10-01

Plasma density and impurity concentration are believed to be two of the key elements governing the edge tokamak plasma conditions. Optimal levels of plasma density and impurity concentration in the edge region have been searched for in order to achieve the desired fusion gain and divertor heat/particle load mitigation. However, how plasma density or impurity would affect the edge pedestal stability may have not been well known. Our recent MHD theory modeling and simulations using the NIMROD code have found novel effects of density and impurity on the dynamics of edge-localized modes (ELMs) in tokamaks. First, previous MHD analyses often predict merely a weak stabilizing effect of toroidal flow on ELMs in experimentally relevant regimes. We find that the stabilizing effects on the high- n ELMs from toroidal flow can be significantly enhanced with the increased edge plasma density. Here n denotes the toroidal mode number. Second, the stabilizing effects of the enhanced edge resistivity due to lithium-conditioning on the low- n ELMs in the high confinement (H-mode) discharges in NSTX have been identified. Linear stability analysis of the experimentally constrained equilibrium suggests that the change in the equilibrium plasma density and pressure profiles alone due to lithium-conditioning may not be sufficient for a complete suppression of the low- n ELMs. The enhanced resistivity due to the increased effective electric charge number Zeff after lithium-conditioning provides additional stabilization of the low- n ELMs. These new effects revealed in our theory analyses may help further understand recent ELM experiments and suggest new control schemes for ELM suppression and mitigation in future experiments. They may also pose additional constraints on the optimal levels of plasma density and impurity concentration in the edge region for H-mode tokamak operation. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks*

NASA Astrophysics Data System (ADS)

Ham, C. J.; Cowley, S. C.; Brochard, G.; Wilson, H. R.

2016-06-01

The theory of tokamak stability to nonlinear "ballooning" displacements of elliptical magnetic flux tubes is presented. Above a critical pressure profile the energy stored in the plasma may be lowered by finite (but not infinitesimal) displacements of such tubes (metastability). Above a higher pressure profile, the linear stability boundary, such tubes are linearly and nonlinearly unstable. The predicted saturated flux tube displacement can be of the order of the pressure gradient scale length. Plasma transport from these displaced flux tubes may explain the rapid loss of confinement in some experiments.

Stability analysis of gyroscopic systems with delay via decomposition

NASA Astrophysics Data System (ADS)

Aleksandrov, A. Yu.; Zhabko, A. P.; Chen, Y.

2018-05-01

A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

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

Jeffries, H. P.

Distributions of organic constituents in marine communities should yield a worldwide classification scheme within which any localized phenomena would be immediately apparent. This idea was tested on the zooplankton along an environmental gradient extending from Rhode Island Sound, through Narragansett Bay and into its polluted tributary, the Providence River. On the basis of fatty acid composition, both the macro- and microzooplankton could be precisely classified to the habitat of origin. Biochemically the microzooplankton changed uniformly with respect to linear distance though the riverine, estuarine and offshore habitats. In macrozooplankton, the relation between biochemical change and linear distance from the rivermore » seaward was a power curve: sharply changing at first, becoming more nearly constant offshore. Particulate pollution in the river merely reinforced natural fatty acid sources in the zooplankton's food - part of a pattern in which environmentally induced effects were expressed inshore, genetic influences offshore. In each habitat species diversity was inversely related to the community's stability of fatty acid composition. These estimates revealed greatest dynamical robustness in the prolific yet simple riverine zooplankton, suggesting that the stable domain of parameter space was likewise greater here than offshore. Despite its diversity, microzooplankton was more dynamically fragile than the macrozooplankton, in agreement with current theory on the stability of communities. We conclude that monomeric composition offers a basic rationale for characterizing the sensitivities of natural communities to environmental change.« less

Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected into a High-Density Gas

NASA Technical Reports Server (NTRS)

Lawson, Anthony L.; Parthasarathy, Ramkumar N.

2002-01-01

It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity.

Structural and spectroscopic study of Al(III)-3-hydroxyflavone complex: determination of the stability constants in water-methanol mixtures.

PubMed

Davila, Y A; Sancho, M I; Almandoz, M C; Blanco, S E

2012-09-01

Stoichiometry and apparent stability constant (K(C)) of the complex formed between Al(III) and 3-hydroxyflavone were determined in methanol and water-methanol mixtures (% water w/w: 3.11; 6.15; 10.4; 15.2; 19.9 and 25.3) by UV-vis spectroscopy at 25.0°C and constant ionic strength (0.05 M, sodium chloride). Stoichiometry of the complex (1:2, metal:ligand) is not modified with an increase in water percentage in the analyzed interval. The value of K(C) in methanol is greater than in the binary solutions. The effects of changing solvent composition on K(C) data were explained by linear solvation free energy relationships using the solvatochromic parameter of Kamlet and Taft (α, β and π(*)). Multiple linear regression analysis indicates that the hydrogen bond donating ability (α) of the solvent and non-specific interactions (π(*)) play an important role in the degree of occurrence of the reaction. The effect of temperature on K(C) was also analyzed by assessing standard entropy and enthalpy variations of the reaction in methanol. Finally, the structure of the complex was investigated using FTIR spectroscopy and DFT calculations. The ligand exhibits small structural changes upon complexation, localized on the chelating site. The calculated vibrational frequencies of the complex were successfully compared against the experimental values. Copyright © 2012 Elsevier B.V. All rights reserved.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

Nonparallel linear stability analysis of unconfined vortices

NASA Astrophysics Data System (ADS)

Herrada, M. A.; Barrero, A.

2004-10-01

Parabolized stability equations [F. P. Bertolotti, Th. Herbert, and P. R. Spalart, J. Fluid. Mech. 242, 441 (1992)] have been used to study the stability of a family of swirling jets at high Reynolds numbers whose velocity and pressure fields decay far from the axis as rm-2 and r2(m-2), respectively [M. Pérez-Saborid, M. A. Herrada, A. Gómez-Barea, and A. Barrero, J. Fluid. Mech. 471, 51 (2002)]; r is the radial distance and m is a real number in the interval 0

Stabilizing effect of resistivity towards ELM-free H-mode discharge in lithium-conditioned NSTX

NASA Astrophysics Data System (ADS)

Banerjee, Debabrata; Zhu, Ping; Maingi, Rajesh

2017-07-01

Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned ELM-free H-mode equilibria is carried out in the context of the extended magneto-hydrodynamic (MHD) model in NIMROD. The purpose is to investigate the physical cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions, a non-ideal resistivity model is employed, taking into account the increase of Z eff after Li-conditioning in ELM-free H-mode. Unlike an earlier conclusion from an eigenvalue code analysis of these equilibria, NIMROD results find that after reduced recycling from divertor plates, profile modification is necessary but insufficient to explain the mechanism behind complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma resistivity due to higher Z eff, the complete stabilization could be explained. A thorough analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and non-ideal MHD models is presented, after accurately including a vacuum-like cold halo region in NIMROD to investigate ELMs.

Thrusting maneuver control of a small spacecraft via only gimbaled-thruster scheme

NASA Astrophysics Data System (ADS)

Kabganian, Mansour; Kouhi, Hamed; Shahravi, Morteza; Fani Saberi, Farhad

2018-05-01

The thrust vector control (TVC) scheme is a powerful method in spacecraft attitude control. Since the control of a small spacecraft is being studied here, a solid rocket motor (SRM) should be used instead of a liquid propellant motor. Among the TVC methods, gimbaled-TVC as an efficient method is employed in this paper. The spacecraft structure is composed of a body and a gimbaled-SRM where common attitude control systems such as reaction control system (RCS) and spin-stabilization are not presented. A nonlinear two-body model is considered for the characterization of the gimbaled-thruster spacecraft where, the only control input is provided by a gimbal actuator. The attitude of the spacecraft is affected by a large exogenous disturbance torque which is generated by a thrust vector misalignment from the center of mass (C.M). A linear control law is designed to stabilize the spacecraft attitude while rejecting the mentioned disturbance torque. A semi-analytical formulation of the region of attraction (RoA) is developed to ensure the local stability and fast convergence of the nonlinear closed-loop system. Simulation results of the 3D maneuvers are included to show the applicability of this method for use in a small spacecraft.

See Also:Mechanics of Cohesive-frictional MaterialsCopyright © 2004 John Wiley & Sons, Ltd.Get Sample Copy