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.

Generalized Predictive and Neural Generalized Predictive Control of Aerospace Systems

NASA Technical Reports Server (NTRS)

Kelkar, Atul G.

2000-01-01

The research work presented in this thesis addresses the problem of robust control of uncertain linear and nonlinear systems using Neural network-based Generalized Predictive Control (NGPC) methodology. A brief overview of predictive control and its comparison with Linear Quadratic (LQ) control is given to emphasize advantages and drawbacks of predictive control methods. It is shown that the Generalized Predictive Control (GPC) methodology overcomes the drawbacks associated with traditional LQ control as well as conventional predictive control methods. It is shown that in spite of the model-based nature of GPC it has good robustness properties being special case of receding horizon control. The conditions for choosing tuning parameters for GPC to ensure closed-loop stability are derived. A neural network-based GPC architecture is proposed for the control of linear and nonlinear uncertain systems. A methodology to account for parametric uncertainty in the system is proposed using on-line training capability of multi-layer neural network. Several simulation examples and results from real-time experiments are given to demonstrate the effectiveness of the proposed methodology.

Derivation of the linear-logistic model and Cox's proportional hazard model from a canonical system description.

PubMed

Voit, E O; Knapp, R G

1997-08-15

The linear-logistic regression model and Cox's proportional hazard model are widely used in epidemiology. Their successful application leaves no doubt that they are accurate reflections of observed disease processes and their associated risks or incidence rates. In spite of their prominence, it is not a priori evident why these models work. This article presents a derivation of the two models from the framework of canonical modeling. It begins with a general description of the dynamics between risk sources and disease development, formulates this description in the canonical representation of an S-system, and shows how the linear-logistic model and Cox's proportional hazard model follow naturally from this representation. The article interprets the model parameters in terms of epidemiological concepts as well as in terms of general systems theory and explains the assumptions and limitations generally accepted in the application of these epidemiological models.

Control of Distributed Parameter Systems

DTIC Science & Technology

1990-08-01

vari- ant of the general Lotka - Volterra model for interspecific competition. The variant described the emergence of one subpopulation from another as a...distribut ion unlimited. I&. ARSTRACT (MAUMUnw2O1 A unified arioroximation framework for Parameter estimation In general linear POE models has been completed...unified approximation framework for parameter estimation in general linear PDE models. This framework has provided the theoretical basis for a number of

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

DOE PAGES

Dodin, I. Y.; Zhmoginov, A. I.; Ruiz, D. E.

2017-02-24

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. We propose a different approach. Here, we show that for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. Particularly, we present a variational formulation for linear geometrical optics inmore » a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.« less

Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

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

Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D., E-mail: sergei.ivanov@uni-rostock.de

2015-06-28

Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied,more » usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.« less

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

NASA Technical Reports Server (NTRS)

Michalopoulos, C. D.

1974-01-01

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Zha, Hongyuan

1992-01-01

Systems of linear equations with Toeplitz coefficient matrices arise in many important applications. The classical Levinson algorithm computes solutions of Toeplitz systems with only O(n(sub 2)) arithmetic operations, as compared to O(n(sub 3)) operations that are needed for solving general linear systems. However, the Levinson algorithm in its original form requires that all leading principal submatrices are nonsingular. An extension of the Levinson algorithm to general Toeplitz systems is presented. The algorithm uses look-ahead to skip over exactly singular, as well as ill-conditioned leading submatrices, and, at the same time, it still fully exploits the Toeplitz structure. In our derivation of this algorithm, we make use of the intimate connection of Toeplitz matrices with formally biorthogonal polynomials.

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

A canonical form of the equation of motion of linear dynamical systems

NASA Astrophysics Data System (ADS)

Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

2018-03-01

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

Research in Applied Mathematics Related to Mathematical System Theory.

DTIC Science & Technology

1977-06-01

This report deals with research results obtained in the field of mathematical system theory . Special emphasis was given to the following areas: (1...Linear system theory over a field: parametrization of multi-input, multi-output systems and the geometric structure of classes of systems of...constant dimension. (2) Linear systems over a ring: development of the theory for very general classes of rings. (3) Nonlinear system theory : basic

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

ERIC Educational Resources Information Center

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

Linear relations in microbial reaction systems: a general overview of their origin, form, and use.

PubMed

Noorman, H J; Heijnen, J J; Ch A M Luyben, K

1991-09-01

In microbial reaction systems, there are a number of linear relations among net conversion rates. These can be very useful in the analysis of experimental data. This article provides a general approach for the formation and application of the linear relations. Two type of system descriptions, one considering the biomass as a black box and the other based on metabolic pathways, are encountered. These are defined in a linear vector and matrix algebra framework. A correct a priori description can be obtained by three useful tests: the independency, consistency, and observability tests. The independency are different. The black box approach provides only conservations relations. They are derived from element, electrical charge, energy, and Gibbs energy balances. The metabolic approach provides, in addition to the conservation relations, metabolic and reaction relations. These result from component, energy, and Gibbs energy balances. Thus it is more attractive to use the metabolic description than the black box approach. A number of different types of linear relations given in the literature are reviewed. They are classified according to the different categories that result from the black box or the metabolic system description. Validation of hypotheses related to metabolic pathways can be supported by experimental validation of the linear metabolic relations. However, definite proof from biochemical evidence remains indispensable.

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Linear Actuator System for the NASA Docking System

NASA Technical Reports Server (NTRS)

Dick, Brandon N.; Oesch, Christopher; Rupp, Timothy W.

2017-01-01

The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS. This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.

Artificial Intelligence Methodologies in Flight Related Differential Game, Control and Optimization Problems

DTIC Science & Technology

1993-01-31

28 Controllability and Observability ............................. .32 ’ Separation of Learning and Control ... ... 37 Linearization via... Linearization via Transformation of Coordinates and Nonlinear Fedlback . .1 Main Result ......... .............................. 13 Discussion...9 2.1 Basic Structure of a NLM........................ .󈧟 2.2 General Structure of NNLM .......................... .28 2.3 Linear System

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

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

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

Kalligiannaki, Evangelia, E-mail: ekalligian@tem.uoc.gr; Harmandaris, Vagelis, E-mail: harman@uoc.gr; Institute of Applied and Computational Mathematics

Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse grainingmore » mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.« less

Almost output regulation of LFT systems via gain-scheduling control

NASA Astrophysics Data System (ADS)

Yuan, Chengzhi; Duan, Chang; Wu, Fen

2018-05-01

Output regulation of general uncertain systems is a meaningful yet challenging problem. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective design mechanism. In this paper, we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation (LFT) with time-varying parametric uncertainties and unknown external perturbations. A novel semi-LFT gain-scheduling output regulator structure is proposed, such that the associated control synthesis conditions guaranteeing both output regulation and ? disturbance attenuation performance are formulated as a set of linear matrix inequalities (LMIs) plus parameter-dependent linear matrix equations, which can be solved separately. A numerical example has been used to demonstrate the effectiveness of the proposed approach.

Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: IV. Generalized matrix analysis of linear compartment systems.

PubMed

Langenbucher, Frieder

2005-01-01

A linear system comprising n compartments is completely defined by the rate constants between any of the compartments and the initial condition in which compartment(s) the drug is present at the beginning. The generalized solution is the time profiles of drug amount in each compartment, described by polyexponential equations. Based on standard matrix operations, an Excel worksheet computes the rate constants and the coefficients, finally the full time profiles for a specified range of time values.

System theory as applied differential geometry. [linear system

NASA Technical Reports Server (NTRS)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1992-01-01

The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

Derivation and definition of a linear aircraft model

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1988-01-01

A linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth is derived and defined. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.

Stability margin of linear systems with parameters described by fuzzy numbers.

PubMed

Husek, Petr

2011-10-01

This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.

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

Suhara, Tadahiro; Kanada-En'yo, Yoshiko

We investigate the linear-chain structures in highly excited states of {sup 14}C using a generalized molecular-orbital model, by which we incorporate an asymmetric configuration of three {alpha} clusters in the linear-chain states. By applying this model to the {sup 14}C system, we study the {sup 10}Be+{alpha} correlation in the linear-chain state of {sup 14}C. To clarify the origin of the {sup 10}Be+{alpha} correlation in the {sup 14}C linear-chain state, we analyze linear 3 {alpha} and 3{alpha} + n systems in a similar way. We find that a linear 3{alpha} system prefers the asymmetric 2{alpha} + {alpha} configuration, whose origin ismore » the many-body correlation incorporated by the parity projection. This configuration causes an asymmetric mean field for two valence neutrons, which induces the concentration of valence neutron wave functions around the correlating 2{alpha}. A linear-chain structure of {sup 16}C is also discussed.« less

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic circuit.

PubMed

Taghizadeh, Mostafa; Ghaffari, Ali; Najafi, Farid

2009-10-01

In this paper, the effect of pneumatic circuit design on the input-output behavior of PWM-driven servo-pneumatic systems is investigated and their control performances are improved using linear controllers instead of complex and costly nonlinear ones. Generally, servo-pneumatic systems are well known for their nonlinear behavior. However, PWM-driven servo-pneumatic systems have the advantage of flexibility in the design of pneumatic circuits which affects the input-output linearity of the whole system. A simple pneumatic circuit with only one fast switching valve is designed which leads to a quasi-linear input-output relation. The quasi-linear behavior of the proposed circuit is verified both experimentally and by simulations. Closed loop position control experiments are then carried out using linear P- and PD-controllers. Since the output position is noisy and cannot be directly differentiated, a Kalman filter is designed to estimate the velocity of the cylinder. Highly improved tracking performances are obtained using these linear controllers, compared to previous works with nonlinear controllers.

Thermospheric dynamics - A system theory approach

NASA Technical Reports Server (NTRS)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

NASA Astrophysics Data System (ADS)

Bičák, Jiří; Schmidt, Josef

2016-01-01

The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor (for example, that it is a linear combination of the terms quadratic in the first derivatives), and require it to be conserved as a consequence of field equations. In the case of the linear gravity in a general gauge we find a four-parametric system of conserved second-rank tensors which contains a unique symmetric tensor. This turns out to be the linearized Landau-Lifshitz pseudotensor employed often in full general relativity. We elucidate the relation of the four-parametric system to the expression proposed recently by Butcher et al. "on physical grounds" in harmonic gauge, and we show that the results coincide in the case of high-frequency waves in vacuum after a suitable averaging. In the massive gravity we show how one can arrive at the expression which coincides with the "generalized linear symmetric Landau-Lifshitz" tensor. However, there exists another uniquely given simpler symmetric tensor which can be obtained by adding the divergence of a suitable superpotential to the canonical energy-momentum tensor following from the Fierz-Pauli action. In contrast to the symmetric tensor derived by the Belinfante procedure which involves the second derivatives of the field variables, this expression contains only the field and its first derivatives. It is simpler than the generalized Landau-Lifshitz tensor but both yield the same total quantities since they differ by the divergence of a superpotential. We also discuss the role of the gauge conditions in the proofs of the uniqueness. In the Appendix, the symbolic tensor manipulation software cadabra is briefly described. It is very effective in obtaining various results which would otherwise require lengthy calculations.

Study report on guidelines and test procedures for investigating stability of nonlinear cardiovascular control system models

NASA Technical Reports Server (NTRS)

Fitzjerrell, D. G.

1974-01-01

A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.

Predicting the Underwater Sound of Moderate and Heavy Rainfall from Laboratory Measurements of Radiation from Single Large Raindrops

DTIC Science & Technology

1992-03-01

Elementary Linear Algebra with Applications, pp. 301- 323, John Wiley and Sons Inc., 1987. Atlas, D., and Ulbrich, C. E. W., "The Physical Basis for...vector drd In this case, the linear system is said to be inconsistent ( Anton and Rorres, 1987). In contrast, for an underdetermined system (where the...ocean acoustical tomography and seismology. In simplest terms, the general linear inverse problem consists of fimding the desired solution to a set of m

Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Powers, Robert K.

1987-01-01

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

Improvement of the linear polarization resistance method for testing steel corrosion inhibitors

NASA Astrophysics Data System (ADS)

Faritov, A. T.; Rozhdestvenskii, Yu. G.; Yamshchikova, S. A.; Minnikhanova, E. R.; Tyusenkov, A. S.

2016-11-01

The linear polarization resistance method is used to improve the technique of corrosion control in liquid conducting according to GOST 9.514-99 (General Corrosion and Aging Protection System. Corrosion Inhibitors for Metals in Water Systems. Electrochemical Method of Determining the Protective Ability). Corrosion monitoring is shown to be performed by electronic devices with real-time data transfer to industrial controllers and SCADA systems.

Linear Actuator System for the NASA Docking System

NASA Technical Reports Server (NTRS)

Dick, Brandon; Oesch, Chris

2017-01-01

The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS, which implements the Soft Impact Mating and Attenuation Concept (SIMAC). This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.

Response of discrete linear systems to forcing functions with inequality constraints.

NASA Technical Reports Server (NTRS)

Michalopoulos, C. D.; Riley, T. A.

1972-01-01

An analysis is made of the maximum response of discrete, linear mechanical systems to arbitrary forcing functions which lie within specified bounds. Primary attention is focused on the complete determination of the forcing function which will engender maximum displacement to any particular mass element of a multi-degree-of-freedom system. In general, the desired forcing function is found to be a bang-bang type function, i.e., a function which switches from the maximum to the minimum bound and vice-versa at certain instants of time. Examples of two-degree-of-freedom systems, with and without damping, are presented in detail. Conclusions are drawn concerning the effect of damping on the switching times and the general procedure for finding these times is discussed.

Application of a local linearization technique for the solution of a system of stiff differential equations associated with the simulation of a magnetic bearing assembly

NASA Technical Reports Server (NTRS)

Kibler, K. S.; Mcdaniel, G. A.

1981-01-01

A digital local linearization technique was used to solve a system of stiff differential equations which simulate a magnetic bearing assembly. The results prove the technique to be accurate, stable, and efficient when compared to a general purpose variable order Adams method with a stiff option.

Multishaker modal testing

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1987-01-01

The major accomplishments of this research are: (1) the refinement and documentation of a multi-input, multi-output modal parameter estimation algorithm which is applicable to general linear, time-invariant dynamic systems; (2) the development and testing of an unsymmetric block-Lanzcos algorithm for reduced-order modeling of linear systems with arbitrary damping; and (3) the development of a control-structure-interaction (CSI) test facility.

Second-order discrete Kalman filtering equations for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.

1991-01-01

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.

Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

NASA Technical Reports Server (NTRS)

Downie, John D.; Goodman, Joseph W.

1989-01-01

The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.

LDRD final report on massively-parallel linear programming : the parPCx system.

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

Parekh, Ojas; Phillips, Cynthia Ann; Boman, Erik Gunnar

2005-02-01

This report summarizes the research and development performed from October 2002 to September 2004 at Sandia National Laboratories under the Laboratory-Directed Research and Development (LDRD) project ''Massively-Parallel Linear Programming''. We developed a linear programming (LP) solver designed to use a large number of processors. LP is the optimization of a linear objective function subject to linear constraints. Companies and universities have expended huge efforts over decades to produce fast, stable serial LP solvers. Previous parallel codes run on shared-memory systems and have little or no distribution of the constraint matrix. We have seen no reports of general LP solver runsmore » on large numbers of processors. Our parallel LP code is based on an efficient serial implementation of Mehrotra's interior-point predictor-corrector algorithm (PCx). The computational core of this algorithm is the assembly and solution of a sparse linear system. We have substantially rewritten the PCx code and based it on Trilinos, the parallel linear algebra library developed at Sandia. Our interior-point method can use either direct or iterative solvers for the linear system. To achieve a good parallel data distribution of the constraint matrix, we use a (pre-release) version of a hypergraph partitioner from the Zoltan partitioning library. We describe the design and implementation of our new LP solver called parPCx and give preliminary computational results. We summarize a number of issues related to efficient parallel solution of LPs with interior-point methods including data distribution, numerical stability, and solving the core linear system using both direct and iterative methods. We describe a number of applications of LP specific to US Department of Energy mission areas and we summarize our efforts to integrate parPCx (and parallel LP solvers in general) into Sandia's massively-parallel integer programming solver PICO (Parallel Interger and Combinatorial Optimizer). We conclude with directions for long-term future algorithmic research and for near-term development that could improve the performance of parPCx.« less

Systems of Inhomogeneous Linear Equations

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

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.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

GMX approximation for the linear E ⊗ ɛ Jahn-Teller effect

NASA Astrophysics Data System (ADS)

Mancini, Jay D.; Fessatidis, Vassilios; Bowen, Samuel P.

2006-02-01

A newly developed generalized moments expansion (GMX) based on the t-expansion of Horn and Weinstein is applied to a linear E ⊗ ɛ Jahn-Teller system. Comparisons are made with other moments schemes as well a coupled cluster approximation.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

A computational system for aerodynamic design and analysis of supersonic aircraft. Part 1: General description and theoretical development

NASA Technical Reports Server (NTRS)

Middleton, W. D.; Lundry, J. L.

1976-01-01

An integrated system of computer programs was developed for the design and analysis of supersonic configurations. The system uses linearized theory methods for the calculation of surface pressures and supersonic area rule concepts in combination with linearized theory for calculation of aerodynamic force coefficients. Interactive graphics are optional at the user's request. Schematics of the program structure and the individual overlays and subroutines are described.

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

The generalized pole assignment problem. [dynamic output feedback problems

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Two dynamic output feedback problems for a linear, strictly proper system are considered, along with their interrelationships. The problems are formulated in the frequency domain and investigated in terms of linear equations over rings of polynomials. Necessary and sufficient conditions are expressed using genericity.

A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Walton, W. C., Jr.

1982-01-01

A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

An algorithm for control system design via parameter optimization. M.S. Thesis

NASA Technical Reports Server (NTRS)

Sinha, P. K.

1972-01-01

An algorithm for design via parameter optimization has been developed for linear-time-invariant control systems based on the model reference adaptive control concept. A cost functional is defined to evaluate the system response relative to nominal, which involves in general the error between the system and nominal response, its derivatives and the control signals. A program for the practical implementation of this algorithm has been developed, with the computational scheme for the evaluation of the performance index based on Lyapunov's theorem for stability of linear invariant systems.

On Markov parameters in system identification

NASA Technical Reports Server (NTRS)

Phan, Minh; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.

Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl (M | N)

NASA Astrophysics Data System (ADS)

Tsuboi, Zengo

2013-05-01

In [1] (Z. Tsuboi, Nucl. Phys. B 826 (2010) 399, arxiv:arXiv:0906.2039), we proposed Wronskian-like solutions of the T-system for [ M , N ]-hook of the general linear superalgebra gl (M | N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1 ,N1 ]-hook and [M2 ,N2 ]-hook (M =M1 +M2, N =N1 +N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl (M | N). Our solutions also include a Wronskian-like solution discussed in [2] (N. Gromov, V. Kazakov, S. Leurent, Z. Tsuboi, JHEP 1101 (2011) 155, arxiv:arXiv:1010.2720) in relation to the AdS5 /CFT4 spectral problem.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

NASA Astrophysics Data System (ADS)

Ampilogov, Dmitrii; Leble, Sergey

2016-07-01

We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

SCI Identification (SCIDNT) program user's guide. [maximum likelihood method for linear rotorcraft models

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

Information Fusion from the Point of View of Communication Theory; Fusing Information to Trade-Off the Resolution of Assessments Against the Probability of Mis-Assessment

DTIC Science & Technology

2013-08-19

excellence in linear models , 2010. She successfully defended her dissertation, Linear System Design for Fusion and Compression, on Aug 13, 2013. Her work was...measurements into canonical coordinates, scaling, and rotation; there is a water-filling interpretation; (3) the optimum design of a linear secondary channel of...measurements to fuse with a primary linear channel of measurements maximizes a generalized Rayleigh quotient; (4) the asymptotically optimum

SYSTEM THEORY: INTER-UNIVERSITY ELECTRONICS SERIES, VOLUME VIII,

DTIC Science & Technology

The book contains contributions in the area of general system theory , linear systems, nonlinear systems, stochastic and learning systems by...nationally and internationally known experts. It presents the most basic and important areas of system theory for the use and familiarization of mathematically-oriented nonspecialists. (Author)

Lessons from Jurassic Park: patients as complex adaptive systems.

PubMed

Katerndahl, David A

2009-08-01

With realization that non-linearity is generally the rule rather than the exception in nature, viewing patients and families as complex adaptive systems may lead to a better understanding of health and illness. Doctors who successfully practise the 'art' of medicine may recognize non-linear principles at work without having the jargon needed to label them. Complex adaptive systems are systems composed of multiple components that display complexity and adaptation to input. These systems consist of self-organized components, which display complex dynamics, ranging from simple periodicity to chaotic and random patterns showing trends over time. Understanding the non-linear dynamics of phenomena both internal and external to our patients can (1) improve our definition of 'health'; (2) improve our understanding of patients, disease and the systems in which they converge; (3) be applied to future monitoring systems; and (4) be used to possibly engineer change. Such a non-linear view of the world is quite congruent with the generalist perspective.

Optical linear algebra processors: noise and error-source modeling.

PubMed

Casasent, D; Ghosh, A

1985-06-01

The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

Optical linear algebra processors - Noise and error-source modeling

NASA Technical Reports Server (NTRS)

Casasent, D.; Ghosh, A.

1985-01-01

The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation

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

Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co

2015-05-15

In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.

Computer programs for the solution of systems of linear algebraic equations

NASA Technical Reports Server (NTRS)

Sequi, W. T.

1973-01-01

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Limit cycles in planar piecewise linear differential systems with nonregular separation line

NASA Astrophysics Data System (ADS)

Cardin, Pedro Toniol; Torregrosa, Joan

2016-12-01

In this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2 π - α, respectively, for α ∈(0 , π) . We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α, we prove the existence of systems with four limit cycles up to fifth order and, for α = π / 2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

Fuzzy branching temporal logic.

PubMed

Moon, Seong-ick; Lee, Kwang H; Lee, Doheon

2004-04-01

Intelligent systems require a systematic way to represent and handle temporal information containing uncertainty. In particular, a logical framework is needed that can represent uncertain temporal information and its relationships with logical formulae. Fuzzy linear temporal logic (FLTL), a generalization of propositional linear temporal logic (PLTL) with fuzzy temporal events and fuzzy temporal states defined on a linear time model, was previously proposed for this purpose. However, many systems are best represented by branching time models in which each state can have more than one possible future path. In this paper, fuzzy branching temporal logic (FBTL) is proposed to address this problem. FBTL adopts and generalizes concurrent tree logic (CTL*), which is a classical branching temporal logic. The temporal model of FBTL is capable of representing fuzzy temporal events and fuzzy temporal states, and the order relation among them is represented as a directed graph. The utility of FBTL is demonstrated using a fuzzy job shop scheduling problem as an example.

Improved importance sampling technique for efficient simulation of digital communication systems

NASA Technical Reports Server (NTRS)

Lu, Dingqing; Yao, Kung

1988-01-01

A new, improved importance sampling (IIS) approach to simulation is considered. Some basic concepts of IS are introduced, and detailed evolutions of simulation estimation variances for Monte Carlo (MC) and IS simulations are given. The general results obtained from these evolutions are applied to the specific previously known conventional importance sampling (CIS) technique and the new IIS technique. The derivation for a linear system with no signal random memory is considered in some detail. For the CIS technique, the optimum input scaling parameter is found, while for the IIS technique, the optimum translation parameter is found. The results are generalized to a linear system with memory and signals. Specific numerical and simulation results are given which show the advantages of CIS over MC and IIS over CIS for simulations of digital communications systems.

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 numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy.

PubMed

Huppert, Theodore J

2016-01-01

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

Machine Learning-based discovery of closures for reduced models of dynamical systems

NASA Astrophysics Data System (ADS)

Pan, Shaowu; Duraisamy, Karthik

2017-11-01

Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system.

PubMed

Hang, Chao; Huang, Guoxiang; Deng, L

2006-03-01

We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.

Whitham modulation theory for the Kadomtsev- Petviashvili equation.

PubMed

Ablowitz, Mark J; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

Whitham modulation theory for the Kadomtsev- Petviashvili equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

A linear shift-invariant image preprocessing technique for multispectral scanner systems

NASA Technical Reports Server (NTRS)

Mcgillem, C. D.; Riemer, T. E.

1973-01-01

A linear shift-invariant image preprocessing technique is examined which requires no specific knowledge of any parameter of the original image and which is sufficiently general to allow the effective radius of the composite imaging system to be arbitrarily shaped and reduced, subject primarily to the noise power constraint. In addition, the size of the point-spread function of the preprocessing filter can be arbitrarily controlled, thus minimizing truncation errors.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

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.

Linear frictional forces cause orbits to neither circularize nor precess

NASA Astrophysics Data System (ADS)

Hamilton, B.; Crescimanno, M.

2008-06-01

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov (2005 J. Phys. A: Math. Gen. 38 2145). In this generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coefficient. Beyond Kepler, we prove that, for any potential proportional to a power of the radius, the orbit shape and precession angle remain constant to leading order in the linear friction coefficient.

Explicit criteria for prioritization of cataract surgery

PubMed Central

Ma Quintana, José; Escobar, Antonio; Bilbao, Amaia

2006-01-01

Background Consensus techniques have been used previously to create explicit criteria to prioritize cataract extraction; however, the appropriateness of the intervention was not included explicitly in previous studies. We developed a prioritization tool for cataract extraction according to the RAND method. Methods Criteria were developed using a modified Delphi panel judgment process. A panel of 11 ophthalmologists was assembled. Ratings were analyzed regarding the level of agreement among panelists. We studied the effect of all variables on the final panel score using general linear and logistic regression models. Priority scoring systems were developed by means of optimal scaling and general linear models. The explicit criteria developed were summarized by means of regression tree analysis. Results Eight variables were considered to create the indications. Of the 310 indications that the panel evaluated, 22.6% were considered high priority, 52.3% intermediate priority, and 25.2% low priority. Agreement was reached for 31.9% of the indications and disagreement for 0.3%. Logistic regression and general linear models showed that the preoperative visual acuity of the cataractous eye, visual function, and anticipated visual acuity postoperatively were the most influential variables. Alternative and simple scoring systems were obtained by optimal scaling and general linear models where the previous variables were also the most important. The decision tree also shows the importance of the previous variables and the appropriateness of the intervention. Conclusion Our results showed acceptable validity as an evaluation and management tool for prioritizing cataract extraction. It also provides easy algorithms for use in clinical practice. PMID:16512893

Corrigendum to ;Lotka-Volterra systems satisfying a strong Painlevé property; [Phys. Lett. A 380 (47) (2016) 3977-3982

NASA Astrophysics Data System (ADS)

Bountis, Tassos; Vanhaecke, Pol

2017-12-01

The comment made after the proof of Proposition 3.3, in our paper [T. Bountis, P. Vanhaecke, Lotka-Volterra systems satisfying a strong Pailevé property, Phys. Lett. A 380 (47) (2016) 3977-3982], saying that the proposition can be generalized when linear terms are added to the Lotka-Volterra systems considered in the paper, is wrong. In general such deformed systems are not even Hamiltonian.

Linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2011-06-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Control Strategies for Guided Collective Motion

DTIC Science & Technology

2015-02-27

Rorres and H. Anton , “ Elementary linear algebra applications version,” 9th Edition, Wiley India Pvt. Ltd., 2011. [20] S.H. Strogatz, “From Kuramoto to... linear cyclic pursuit in which an agent pursues its leader with an angle of deviation. The sufficient conditions for the stability of such systems are...Generalized Hierarchical Cyclic Pursuit 6. D. Mukherjee and D. Ghose: Deviated Linear Cyclic Pursuit 7. D. Mukherjee and D. Ghose; On Synchronous and

General stability of memory-type thermoelastic Timoshenko beam acting on shear force

NASA Astrophysics Data System (ADS)

Apalara, Tijani A.

2018-03-01

In this paper, we consider a linear thermoelastic Timoshenko system with memory effects where the thermoelastic coupling is acting on shear force under Neumann-Dirichlet-Dirichlet boundary conditions. The same system with fully Dirichlet boundary conditions was considered by Messaoudi and Fareh (Nonlinear Anal TMA 74(18):6895-6906, 2011, Acta Math Sci 33(1):23-40, 2013), but they obtained a general stability result which depends on the speeds of wave propagation. In our case, we obtained a general stability result irrespective of the wave speeds of the system.

A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Guo, Ping

2017-10-01

The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.

Optimal generalized multistep integration formulae for real-time digital simulation

NASA Technical Reports Server (NTRS)

Moerder, D. D.; Halyo, N.

1985-01-01

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

Linear, multivariable robust control with a mu perspective

NASA Technical Reports Server (NTRS)

Packard, Andy; Doyle, John; Balas, Gary

1993-01-01

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Dual-systems and the development of reasoning: competence-procedural systems.

PubMed

Overton, Willis F; Ricco, Robert B

2011-03-01

Dual-system, dual-process, accounts of adult cognitive processing are examined in the context of a self-organizing relational developmental systems approaches to cognitive growth. Contemporary adult dual-process accounts describe a linear architecture of mind entailing two split-off, but interacting systems; a domain general, content-free 'analytic' system (system 2) and a domain specific highly contextualized 'heuristic' system (system 1). In the developmental literature on deductive reasoning, a similar distinction has been made between a domain general competence (reflective, algorithmic) system and a domain specific procedural system. In contrast to the linear accounts offered by empiricist, nativist, and/or evolutionary explanations, the dual competence-procedural developmental perspective argues that the mature systems emerge through developmental transformations as differentiations and intercoordinations of an early relatively undifferentiated action matrix. This development, whose microscopic mechanism is action-in-the-world, is characterized as being embodied, nonlinear, and epigenetic. WIREs Cogni Sci 2011 2 231-237 DOI: 10.1002/wcs.120 For further resources related to this article, please visit the WIREs website. © 2010 John Wiley & Sons, Ltd.

A FORTRAN program for the analysis of linear continuous and sample-data systems

NASA Technical Reports Server (NTRS)

Edwards, J. W.

1976-01-01

A FORTRAN digital computer program which performs the general analysis of linearized control systems is described. State variable techniques are used to analyze continuous, discrete, and sampled data systems. Analysis options include the calculation of system eigenvalues, transfer functions, root loci, root contours, frequency responses, power spectra, and transient responses for open- and closed-loop systems. A flexible data input format allows the user to define systems in a variety of representations. Data may be entered by inputing explicit data matrices or matrices constructed in user written subroutines, by specifying transfer function block diagrams, or by using a combination of these methods.

A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System

NASA Technical Reports Server (NTRS)

Torres-Pomales, Wilfredo

2015-01-01

This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.

Graph-based linear scaling electronic structure theory.

PubMed

Niklasson, Anders M N; Mniszewski, Susan M; Negre, Christian F A; Cawkwell, Marc J; Swart, Pieter J; Mohd-Yusof, Jamal; Germann, Timothy C; Wall, Michael E; Bock, Nicolas; Rubensson, Emanuel H; Djidjev, Hristo

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Graph-based linear scaling electronic structure theory

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

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Optimal Artificial Boundary Condition Configurations for Sensitivity-Based Model Updating and Damage Detection

DTIC Science & Technology

2010-09-01

matrix is used in many methods, like Jacobi or Gauss Seidel , for solving linear systems. Also, no partial pivoting is necessary for a strictly column...problems that arise during the procedure, which in general, converges to the solving of a linear system. The most common issue with the solution is the... iterative procedure to find an appropriate subset of parameters that produce an optimal solution commonly known as forward selection. Then, the

Robust root clustering for linear uncertain systems using generalized Lyapunov theory

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1993-01-01

Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

Phase space flows for non-Hamiltonian systems with constraints

NASA Astrophysics Data System (ADS)

Sergi, Alessandro

2005-09-01

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac’s formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one, Dirac’s recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac’s formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.

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.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems.

PubMed

Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai

2014-10-20

We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Linear solver performance in elastoplastic problem solution on GPU cluster

NASA Astrophysics Data System (ADS)

Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.

2017-12-01

Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Fibonacci Identities, Matrices, and Graphs

ERIC Educational Resources Information Center

Huang, Danrun

2005-01-01

General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…

A straightforward characterization of non-modal effects from the evolution of linear dynamical systems

NASA Astrophysics Data System (ADS)

Arratia, Cristobal

2014-11-01

A simple construction will be shown, which reveals a general property satisfied by the evolution in time of a state vector composed by a superposition of orthogonal eigenmodes of a linear dynamical system. This property results from the conservation of the inner product between such state vectors evolving forward and backwards in time, and it can be simply evaluated from the state vector and its first and second time derivatives. This provides an efficient way to characterize, instantaneously along any specific phase-space trajectory of the linear system, the relevance of the non-normality of the linearized Navier-Stokes operator on the energy (or any other norm) gain or decay of small perturbations. Examples of this characterization applied to stationary or time dependent base flows will be shown. CONICYT, Concurso de Apoyo al Retorno de Investigadores del Extranjero, folio 821320055.

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

PubMed

Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong

2017-03-01

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States.

PubMed

Chen, Zehua; Zhang, Du; Jin, Ye; Yang, Yang; Su, Neil Qiang; Yang, Weitao

2017-09-21

To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn-Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle-particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

NASA Astrophysics Data System (ADS)

Özer, Hatice; Delice, Özgür

2018-03-01

Two different ways of generalizing Einstein’s general theory of relativity with a cosmological constant to Brans–Dicke type scalar–tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity a cosmological constant has no role in these phenomena. We see that for the Brans–Dicke theory, the cosmological constant also has no effect on these phenomena. This is because solar system observations require very large values of the Brans–Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.

Multidimensional FEM-FCT schemes for arbitrary time stepping

NASA Astrophysics Data System (ADS)

Kuzmin, D.; Möller, M.; Turek, S.

2003-05-01

The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions.

Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices

ERIC Educational Resources Information Center

Glaister, P.

2008-01-01

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

Generalized Heisenberg algebra and (non linear) pseudo-bosons

NASA Astrophysics Data System (ADS)

Bagarello, F.; Curado, E. M. F.; Gazeau, J. P.

2018-04-01

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given physical system. We also discuss relations with nonlinear pseudo-bosons. Several examples are discussed.

Born approximation in linear-time invariant system

NASA Astrophysics Data System (ADS)

Gumjudpai, Burin

2017-09-01

An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.

Query construction, entropy, and generalization in neural-network models

NASA Astrophysics Data System (ADS)

Sollich, Peter

1994-05-01

We study query construction algorithms, which aim at improving the generalization ability of systems that learn from examples by choosing optimal, nonredundant training sets. We set up a general probabilistic framework for deriving such algorithms from the requirement of optimizing a suitable objective function; specifically, we consider the objective functions entropy (or information gain) and generalization error. For two learning scenarios, the high-low game and the linear perceptron, we evaluate the generalization performance obtained by applying the corresponding query construction algorithms and compare it to training on random examples. We find qualitative differences between the two scenarios due to the different structure of the underlying rules (nonlinear and ``noninvertible'' versus linear); in particular, for the linear perceptron, random examples lead to the same generalization ability as a sequence of queries in the limit of an infinite number of examples. We also investigate learning algorithms which are ill matched to the learning environment and find that, in this case, minimum entropy queries can in fact yield a lower generalization ability than random examples. Finally, we study the efficiency of single queries and its dependence on the learning history, i.e., on whether the previous training examples were generated randomly or by querying, and the difference between globally and locally optimal query construction.

Linear parameter varying representations for nonlinear control design

NASA Astrophysics Data System (ADS)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that neglects a subset of possible parameter trajectories. A computational algorithm is constructed for this suboptimal solution applied to a class of linear non-quadratic cost functions.

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

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.

Why Representations?

ERIC Educational Resources Information Center

Schultz, James E.; Waters, Michael S.

2000-01-01

Discusses representations in the context of solving a system of linear equations. Views representations (concrete, tables, graphs, algebraic, matrices) from perspectives of understanding, technology, generalization, exact versus approximate solution, and learning style. (KHR)

A new approach for the calculation of response spectral density of a linear stationary random multidegree of freedom system

NASA Astrophysics Data System (ADS)

Sharan, A. M.; Sankar, S.; Sankar, T. S.

1982-08-01

A new approach for the calculation of response spectral density for a linear stationary random multidegree of freedom system is presented. The method is based on modifying the stochastic dynamic equations of the system by using a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the system generalized displacements and velocities. The new method requires significantly less computation time as compared to the conventional method for calculating response spectral densities. Two numerical examples are presented to compare quantitatively the computation time.

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.

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

Mendelsohn, M.; Lowder, T.; Canavan, B.

Over the last several years, solar energy technologies have been, or are in the process of being, deployed at unprecedented levels. A critical recent development, resulting from the massive scale of projects in progress or recently completed, is having the power sold directly to electric utilities. Such 'utility-scale' systems offer the opportunity to deploy solar technologies far faster than the traditional 'behind-the-meter' projects designed to offset retail load. Moreover, these systems have employed significant economies of scale during construction and operation, attracting financial capital, which in turn can reduce the delivered cost of power. This report is a summary ofmore » the current U.S. utility-scale solar state-of-the-market and development pipeline. Utility-scale solar energy systems are generally categorized as one of two basic designs: concentrating solar power (CSP) and photovoltaic (PV). CSP systems can be further delineated into four commercially available technologies: parabolic trough, central receiver (CR), parabolic dish, and linear Fresnel reflector. CSP systems can also be categorized as hybrid, which combine a solar-based system (generally parabolic trough, CR, or linear Fresnel) and a fossil fuel energy system to produce electric power or steam.« less

Constrained optimization of image restoration filters

NASA Technical Reports Server (NTRS)

Riemer, T. E.; Mcgillem, C. D.

1973-01-01

A linear shift-invariant preprocessing technique is described which requires no specific knowledge of the image parameters and which is sufficiently general to allow the effective radius of the composite imaging system to be minimized while constraining other system parameters to remain within specified limits.

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

NASA Astrophysics Data System (ADS)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

Nonlinear ideal magnetohydrodynamics instabilities

NASA Astrophysics Data System (ADS)

Pfirsch, D.; Sudan, R. N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlüter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass, magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and nth order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, m=0 perturbations of a Bennet Z-pinch and z-independent perturbations of a θ pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

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

Chung, Moses; Qin, Hong; Davidson, Ronald C.

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Themore » new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.« less

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

DOE PAGES

Chung, Moses; Qin, Hong; Davidson, Ronald C.; ...

2016-11-23

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Themore » new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.« less

Center for Parallel Optimization.

DTIC Science & Technology

1996-03-19

A NEW OPTIMIZATION BASED APPROACH TO IMPROVING GENERALIZATION IN MACHINE LEARNING HAS BEEN PROPOSED AND COMPUTATIONALLY VALIDATED ON SIMPLE LINEAR MODELS AS WELL AS ON HIGHLY NONLINEAR SYSTEMS SUCH AS NEURAL NETWORKS.

Generalized concurrence in boson sampling.

PubMed

Chin, Seungbeom; Huh, Joonsuk

2018-04-17

A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the permanents of transition operator matrices, which is a hard problem for classical simulations (boson sampling problem). We can understand this problem by considering a quantum measure that directly determines the runtime for computing the transition amplitudes. In this paper, we suggest a quantum measure named "Fock state concurrence sum" C S , which is the summation over all the members of "the generalized Fock state concurrence" (a measure analogous to the generalized concurrences of entanglement and coherence). By introducing generalized algorithms for computing the transition amplitudes of the Fock state boson sampling with an arbitrary number of photons per mode, we show that the minimal classical runtime for all the known algorithms directly depends on C S . Therefore, we can state that the Fock state concurrence sum C S behaves as a collective measure that controls the computational complexity of Fock state BS. We expect that our observation on the role of the Fock state concurrence in the generalized algorithm for permanents would provide a unified viewpoint to interpret the quantum computing power of linear optics.

On the Axiomatization of Mathematical Understanding: Continuous Functions in the Transition to Topology

ERIC Educational Resources Information Center

Cheshire, Daniel C.

2017-01-01

The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…

Practical robustness measures in multivariable control system analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lehtomaki, N. A.

1981-01-01

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Some Properties and Stability Results for Sector-Bounded LTI Systems

NASA Technical Reports Server (NTRS)

Gupta, Sandeep; Joshi, Suresh M.

1994-01-01

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.

Tori and chaos in a simple C1-system

NASA Astrophysics Data System (ADS)

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

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

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to extend these ideas to situations where fixed points may not exist — either due to "monotone" flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.

A synthesis theory for the externally excited adaptive system /EEAS/

NASA Technical Reports Server (NTRS)

Horowitz, I. M.; Smay, J. W.; Shapiro, A.

1974-01-01

The externally excited adaptive system (EEAS) is a two-degree-of-freedom feedback system with a nonlinearity which is saturated hard by an external periodic signal. Under certain conditions, the EEAS responds quasi-linearly to command and plant disturbance signals, permitting the development of a quantitative synthesis theory for satisfying system tolerances despite large plant uncertainty. The great advantage of the EEAS is its zero sensitivity to plant gain variations, a property it shares with the self-oscillating adaptive system (SOAS). The EEAS is, however, more flexible than the SOAS in satisfying the quasi-linearity constraints. The essential difference is that in the EEAS the loop transmission bandwidth is not rigorously tied to the 'carrier' signal, as it is in the SOAS. There is a class of problems for which the EEAS is superior to the purely linear system, which in turn is superior to the SOAS. The superiority of the EEAS over the SOAS is especially marked in the case of significant plant disturbances, which generally vitiate a SOAS design.

Advances in diagnostic ultrasonography.

PubMed

Reef, V B

1991-08-01

A wide variety of ultrasonographic equipment currently is available for use in equine practice, but no one machine is optimal for every type of imaging. Image quality is the most important factor in equipment selection once the needs of the practitioner are ascertained. The transducer frequencies available, transducer footprints, depth of field displayed, frame rate, gray scale, simultaneous electrocardiography, Doppler, and functions to modify the image are all important considerations. The ability to make measurements off of videocassette recorder playback and future upgradability should be evaluated. Linear array and sector technology are the backbone of equine ultrasonography today. Linear array technology is most useful for a high-volume broodmare practice, whereas sector technology is ideal for a more general equine practice. The curved or convex linear scanner has more applications than the standard linear array and is equipped with the linear array rectal probe, which provides the equine practitioner with a more versatile unit for equine ultrasonographic evaluations. The annular array and phased array systems have improved image quality, but each has its own limitations. The new sector scanners still provide the most versatile affordable equipment for equine general practice.

Solution of underdetermined systems of equations with gridded a priori constraints.

PubMed

Stiros, Stathis C; Saltogianni, Vasso

2014-01-01

The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy. The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an R(n) grid containing an approximation of the real solution. The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the R(n) containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.

Single-phase power distribution system power flow and fault analysis

NASA Technical Reports Server (NTRS)

Halpin, S. M.; Grigsby, L. L.

1992-01-01

Alternative methods for power flow and fault analysis of single-phase distribution systems are presented. The algorithms for both power flow and fault analysis utilize a generalized approach to network modeling. The generalized admittance matrix, formed using elements of linear graph theory, is an accurate network model for all possible single-phase network configurations. Unlike the standard nodal admittance matrix formulation algorithms, the generalized approach uses generalized component models for the transmission line and transformer. The standard assumption of a common node voltage reference point is not required to construct the generalized admittance matrix. Therefore, truly accurate simulation results can be obtained for networks that cannot be modeled using traditional techniques.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

A Dynamic Model for Modern Military Conflict.

DTIC Science & Technology

1982-10-01

within the generalized form of the Lotka - Volterra equations, that can account for the important interactions of modern military conflicts described in...Mx + These equations are seen to be of the generalized Lotka - Volterra form; however, only 20 of the 32 parameters that might possibly be included...determine one equilibrium as the solution of a system of linear equations. The method is derived for the general nth order Lotka - Volterra model in

Predictive IP controller for robust position control of linear servo system.

PubMed

Lu, Shaowu; Zhou, Fengxing; Ma, Yajie; Tang, Xiaoqi

2016-07-01

Position control is a typical application of linear servo system. In this paper, to reduce the system overshoot, an integral plus proportional (IP) controller is used in the position control implementation. To further improve the control performance, a gain-tuning IP controller based on a generalized predictive control (GPC) law is proposed. Firstly, to represent the dynamics of the position loop, a second-order linear model is used and its model parameters are estimated on-line by using a recursive least squares method. Secondly, based on the GPC law, an optimal control sequence is obtained by using receding horizon, then directly supplies the IP controller with the corresponding control parameters in the real operations. Finally, simulation and experimental results are presented to show the efficiency of proposed scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Analytic wave solution with helicon and Trivelpiece-Gould modes in an annular plasma

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

Carlsson, Johan; Pavarin, Daniele; Walker, Mitchell

2009-11-26

Helicon sources in an annular configuration have applications for plasma thrusters. The theory of Klozenberg et al.[J. P. Klozenberg B. McNamara and P. C. Thonemann, J. Fluid Mech. 21(1965) 545-563] for the propagation and absorption of helicon and Trivelpiece-Gould modes in a cylindrical plasma has been generalized for annular plasmas. Analytic solutions are found also in the annular case, but in the presence of both helicon and Trivelpiece-Gould modes, a heterogeneous linear system of equations must be solved to match the plasma and inner and outer vacuum solutions. The linear system can be ill-conditioned or even exactly singular, leading tomore » a dispersion relation with a discrete set of discontinuities. The coefficients for the analytic solution are calculated by solving the linear system with singular-value decomposition.« less

On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

2017-04-01

We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program. [subroutines and flow charts

NASA Technical Reports Server (NTRS)

Utku, S.

1969-01-01

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

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

Asplund, Curtis T., E-mail: ca2621@columbia.edu; Berenstein, David, E-mail: dberens@physics.ucsb.edu

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate themore » dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.« less

hi-class: Horndeski in the Cosmic Linear Anisotropy Solving System

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

Zumalacárregui, Miguel; Bellini, Emilio; Sawicki, Ignacy

We present the public version of hi-class (www.hiclass-code.net), an extension of the Boltzmann code CLASS to a broad ensemble of modifications to general relativity. In particular, hi-class can calculate predictions for models based on Horndeski's theory, which is the most general scalar-tensor theory described by second-order equations of motion and encompasses any perfect-fluid dark energy, quintessence, Brans-Dicke, f ( R ) and covariant Galileon models. hi-class has been thoroughly tested and can be readily used to understand the impact of alternative theories of gravity on linear structure formation as well as for cosmological parameter extraction.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

NASA Astrophysics Data System (ADS)

Khusainov, T. A.; Shalashov, A. G.; Gospodchikov, E. D.

2018-05-01

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Using parallel banded linear system solvers in generalized eigenvalue problems

NASA Technical Reports Server (NTRS)

Zhang, Hong; Moss, William F.

1993-01-01

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

Nonlinear ideal magnetohydrodynamics instabilities

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

Pfirsch, D.; Sudan, R.N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlueter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass,more » magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and [ital n]th order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, [ital m]=0 perturbations of a Bennet Z-pinch and [ital z]-independent perturbations of a [theta] pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).« less

Strategic Decision Making in Higher Education: An Analysis of the New Planning System in Dutch Higher Education.

ERIC Educational Resources Information Center

Maassen, Peter, A. M.; Potman, Henry P.

1990-01-01

The new strategic planning system in Dutch higher education is described and the usefulness of strategic planning in higher education institutions in general is discussed. Three models are distinguished: linear, adaptive, and interpretive. Evidence suggesting the system has resulted in more homogenization than diversification is presented.…

A review on prognostic techniques for non-stationary and non-linear rotating systems

NASA Astrophysics Data System (ADS)

Kan, Man Shan; Tan, Andy C. C.; Mathew, Joseph

2015-10-01

The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

NASA Astrophysics Data System (ADS)

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

Optimisation of the vibrational response of ultrasonic cutting systems

NASA Astrophysics Data System (ADS)

Cartmell, M. P.; Lim, F. C. N.; Cardoni, A.; Lucas, M.

2005-10-01

This paper provides an account of an investigation into possible dynamic interactions between two coupled non-linear sub-systems, each possessing opposing non-linear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two-degree-of-freedom Duffing oscillator in which certain non-linear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently non-linear, and which is coupled to a bar- or block-horn, and to one or more material cutting blades, for example. The horn/blade configurations are also non-linear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two-degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall non-linear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also been shown experimentally that coupling of ultrasonic components with different non-linear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice. Further experiments have shown that a multiple horn/blade configuration can, under certain circumstances, display autoparametric responses based on the forced response of the desired longitudinal mode parametrically exciting an undesired lateral mode. Typical autoparametric response phenomena have been observed and are presented at the end of the paper.

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-01

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

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

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Algebraic solutions of shape-invariant position-dependent effective mass systems

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

Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@seecs.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk

2016-06-15

Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with position-dependent effective mass is discussed. We quantize the Hamiltonian of the pertaining system by using symmetric ordering of the operators concerning momentum and the spatially varying mass, initially proposed by von Roos and Lévy-Leblond. The algebraic method, used to obtain the solutions, is based on the concepts of supersymmetric quantum mechanics and shape invariance. In order to exemplify the general formalism a class ofmore » non-linear oscillators has been considered. This class includes the particular example of a one-dimensional oscillator with different position-dependent effective mass profiles. Explicit expressions for the eigenenergies and eigenfunctions in terms of generalized Hermite polynomials are presented. Moreover, properties of these modified Hermite polynomials, like existence of generating function and recurrence relations among the polynomials have also been studied. Furthermore, it has been shown that in the harmonic limit, all the results for the linear harmonic oscillator are recovered.« less

Computing Generalized Matrix Inverse on Spiking Neural Substrate.

PubMed

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines.

Attitude Determination Error Analysis System (ADEAS) mathematical specifications document

NASA Technical Reports Server (NTRS)

Nicholson, Mark; Markley, F.; Seidewitz, E.

1988-01-01

The mathematical specifications of Release 4.0 of the Attitude Determination Error Analysis System (ADEAS), which provides a general-purpose linear error analysis capability for various spacecraft attitude geometries and determination processes, are presented. The analytical basis of the system is presented. The analytical basis of the system is presented, and detailed equations are provided for both three-axis-stabilized and spin-stabilized attitude sensor models.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Robust consensus control with guaranteed rate of convergence using second-order Hurwitz polynomials

NASA Astrophysics Data System (ADS)

Fruhnert, Michael; Corless, Martin

2017-10-01

This paper considers homogeneous networks of general, linear time-invariant, second-order systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilisable. We show that consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. To achieve this, we provide a new and simple derivation of the conditions for a second-order polynomial with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback.

Some New Properties of Quantum Correlations

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Fei; Wei, Yunxia

2017-02-01

Quantum coherence measures the correlation between different measurement results in a single-system, while entanglement and quantum discord measure the correlation among different subsystems in a multipartite system. In this paper, we focus on the relative entropy form of them, and obtain three new properties of them as follows: 1) General forms of maximally coherent states for the relative entropy coherence, 2) Linear monogamy of the relative entropy entanglement, and 3) Subadditivity of quantum discord. Here, the linear monogamy is defined as there is a small constant as the upper bound on the sum of the relative entropy entanglement in subsystems.

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

NASA Astrophysics Data System (ADS)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J.

2017-09-01

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Some Applications Of Semigroups And Computer Algebra In Discrete Structures

NASA Astrophysics Data System (ADS)

Bijev, G.

2009-11-01

An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. A map (p) is defined, which is similar to an orthogonal projection in linear vector spaces. Some other important maps with properties similar to those of the generalized inverses (pseudoinverses) of linear transformations and matrices corresponding to them are also defined and investigated. Let Ax = b be an equation with matrix A and vectors x and b Boolean. Stochastic experiments for solving the equation, which involves the maps defined and use computer algebra methods, have been made. As a result, the Hamming distance between vectors Ax = p(b) and b is equal or close to the least possible. We also share our experience in using computer algebra systems for teaching discrete mathematics and linear algebra and research. Some examples for computations with binary relations using Maple are given.

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application

PubMed Central

Karnatak, Rajat

2015-01-01

Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the main highlight of this scheme but questions related to its general applicability still need to be addressed. Focusing on the issue of targeting stationary solutions, this work demonstrates instances where the scheme fails to stabilize the required solutions and leads to other complicated dynamical scenarios. Examples from conservative as well as dissipative systems are presented in this regard and important applications in dissipative predator—prey systems are discussed, which include preventative measures to avoid potentially catastrophic dynamical transitions in these systems. PMID:26544879

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.

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.

PubMed

Mazandarani, Mehran; Pariz, Naser

2018-05-01

This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning

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

Ponce, Colin; Vassilevski, Panayot S.

2016-02-18

We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. Wemore » present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.« less

Theory of unidirectional magnetoresistance in magnetic heterostructures

NASA Astrophysics Data System (ADS)

Zhang, Steven S.-L.; Vignale, Giovanni

2017-09-01

We present a general drift-diffusion theory beyond linear response to explain the unidirectional magnetoresistance (UMR) observed in recent experiments in various magnetic heterostructures. In general, such nonlinear magnetoresistance may originate from the concerted action of current-induced spin accumulation and spin asymmetry in electron mobility. As a case study, we calculate the UMR in a bilayer system consisting of a heavy-metal (HM) and a ferromagnetic metal (FM), where the spin accumulation is induced via the spin Hall effect in the bulk of the HM layer. Our previous formulation [cf. PRB 94, 140411(R) (2016)] is generalized to include the interface resistance and spin memory loss, which allows us to analyze in details their effects on the UMR. We found that the UMR turns out to be independent of the spin asymmetry of the interfacial resistance, at variance with the linear giant-magnetoresistance (GMR) effect. A linear relation between the UMR and the conductivity-spin asymmetry is revealed, which provides an alternative way to control the sign and magnitude of the UMR and hence may serve as an experimental signature of our proposed mechanism.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Correlating non-linear properties with spectral states of RXTE data: possible observational evidences for four different accretion modes around compact objects

NASA Astrophysics Data System (ADS)

Adegoke, Oluwashina; Dhang, Prasun; Mukhopadhyay, Banibrata; Ramadevi, M. C.; Bhattacharya, Debbijoy

2018-05-01

By analysing the time series of RXTE/PCA data, the non-linear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different non-linear features. Sometimes they show low correlation/fractal dimension, but in other classes or intervals of time they exhibit stochastic nature. This could be because the accretion flow around a compact object is a non-linear general relativistic system involving magnetohydrodynamics. However, the more conventional way of addressing a compact source is the analysis of its spectral state. Therefore, the question arises: What is the connection of non-linearity to the underlying spectral properties of the flow when the non-linear properties are related to the associated transport mechanisms describing the geometry of the flow? This work is aimed at addressing this question. Based on the connection between observed spectral and non-linear (time series) properties of two X-ray binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying accretion modes of the sources in terms of known accretion classes, namely, Keplerian disc, slim disc, advection dominated accretion flow and general advective accretion flow. We explore the possible transition of the sources from one accretion mode to others with time. We further argue that the accretion rate must play an important role in transition between these modes.

A mathematical theory of learning control for linear discrete multivariable systems

NASA Technical Reports Server (NTRS)

Phan, Minh; Longman, Richard W.

1988-01-01

When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.

General linear codes for fault-tolerant matrix operations on processor arrays

NASA Technical Reports Server (NTRS)

Nair, V. S. S.; Abraham, J. A.

1988-01-01

Various checksum codes have been suggested for fault-tolerant matrix computations on processor arrays. Use of these codes is limited due to potential roundoff and overflow errors. Numerical errors may also be misconstrued as errors due to physical faults in the system. In this a set of linear codes is identified which can be used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU-decomposition, with minimum numerical error. Encoding schemes are given for some of the example codes which fall under the general set of codes. With the help of experiments, a rule of thumb for the selection of a particular code for a given application is derived.

Distributed Leader-Following Finite-Time Consensus Control for Linear Multiagent Systems under Switching Topology

PubMed Central

Xu, Xiaole; Chen, Shengyong

2014-01-01

This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach. PMID:24883367

Measurement system analysis of viscometers used for drilling mud characterization

NASA Astrophysics Data System (ADS)

Mat-Shayuti, M. S.; Adzhar, S. N.

2017-07-01

Viscometers in the Faculty of Chemical Engineering, University Teknologi MARA, are subject to heavy utilization from the members of the faculty. Due to doubts surrounding their result integrity and maintenance management, Measurement System Analysis was executed. 5 samples of drilling muds with varied barite content from 5 - 25 weight% were prepared and their rheological properties determined in 3 trials by 3 operators using the viscometers. Gage Linearity and Bias Study were performed using Minitab software and the result shows high biases in the range of 19.2% to 38.7%, with non-linear trend along the span of measurements. Gage Repeatability & Reproducibility (Nested) analysis later produces Percent Repeatability & Reproducibility more than 7.7% and Percent Tolerance above 30%. Lastly, good and marginal Distinct Categories output are seen among the results. Despite acceptable performance of the measurement system in Distinct Categories, the poor results in accuracy, linearity, and Percent Repeatability & Reproducibility render the gage generally not capable. Improvement to the measurement system is imminent.

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

Design of an optimal preview controller for linear discrete-time descriptor systems with state delay

NASA Astrophysics Data System (ADS)

Cao, Mengjuan; Liao, Fucheng

2015-04-01

In this paper, the linear discrete-time descriptor system with state delay is studied, and a design method for an optimal preview controller is proposed. First, by using the discrete lifting technique, the original system is transformed into a general descriptor system without state delay in form. Then, taking advantage of the first-order forward difference operator, we construct a descriptor augmented error system, including the state vectors of the lifted system, error vectors, and desired target signals. Rigorous mathematical proofs are given for the regularity, stabilisability, causal controllability, and causal observability of the descriptor augmented error system. Based on these, the optimal preview controller with preview feedforward compensation for the original system is obtained by using the standard optimal regulator theory of the descriptor system. The effectiveness of the proposed method is shown by numerical simulation.

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems. Ph.D. Thesis - Massachusetts Inst. of Technology, Aug. 1991

NASA Technical Reports Server (NTRS)

Nachtigal, Noel M.

1991-01-01

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Giesy, Daniel P.

1998-01-01

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.

Attitude dynamics simulation subroutines for systems of hinge-connected rigid bodies

NASA Technical Reports Server (NTRS)

Fleischer, G. E.; Likins, P. W.

1974-01-01

Several computer subroutines are designed to provide the solution to minimum-dimension sets of discrete-coordinate equations of motion for systems consisting of an arbitrary number of hinge-connected rigid bodies assembled in a tree topology. In particular, these routines may be applied to: (1) the case of completely unrestricted hinge rotations, (2) the totally linearized case (all system rotations are small), and (3) the mixed, or partially linearized, case. The use of the programs in each case is demonstrated using a five-body spacecraft and attitude control system configuration. The ability of the subroutines to accommodate prescribed motions of system bodies is also demonstrated. Complete listings and user instructions are included for these routines (written in FORTRAN V) which are intended as multi- and general-purpose tools in the simulation of spacecraft and other complex electromechanical systems.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

On the characterization of dynamic supramolecular systems: a general mathematical association model for linear supramolecular copolymers and application on a complex two-component hydrogen-bonding system.

PubMed

Odille, Fabrice G J; Jónsson, Stefán; Stjernqvist, Susann; Rydén, Tobias; Wärnmark, Kenneth

2007-01-01

A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab, and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4n5m as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the DeltaH degrees and DeltaS degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters.

The Vertical Linear Fractional Initialization Problem

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

Linear hypergeneralization of learned dynamics across movement speeds reveals anisotropic, gain-encoding primitives for motor adaptation.

PubMed

Joiner, Wilsaan M; Ajayi, Obafunso; Sing, Gary C; Smith, Maurice A

2011-01-01

The ability to generalize learned motor actions to new contexts is a key feature of the motor system. For example, the ability to ride a bicycle or swing a racket is often first developed at lower speeds and later applied to faster velocities. A number of previous studies have examined the generalization of motor adaptation across movement directions and found that the learned adaptation decays in a pattern consistent with the existence of motor primitives that display narrow Gaussian tuning. However, few studies have examined the generalization of motor adaptation across movement speeds. Following adaptation to linear velocity-dependent dynamics during point-to-point reaching arm movements at one speed, we tested the ability of subjects to transfer this adaptation to short-duration higher-speed movements aimed at the same target. We found near-perfect linear extrapolation of the trained adaptation with respect to both the magnitude and the time course of the velocity profiles associated with the high-speed movements: a 69% increase in movement speed corresponded to a 74% extrapolation of the trained adaptation. The close match between the increase in movement speed and the corresponding increase in adaptation beyond what was trained indicates linear hypergeneralization. Computational modeling shows that this pattern of linear hypergeneralization across movement speeds is not compatible with previous models of adaptation in which motor primitives display isotropic Gaussian tuning of motor output around their preferred velocities. Instead, we show that this generalization pattern indicates that the primitives involved in the adaptation to viscous dynamics display anisotropic tuning in velocity space and encode the gain between motor output and motion state rather than motor output itself.

General technique for discrete retardation-modulation polarimetry

NASA Technical Reports Server (NTRS)

Saxena, Indu

1993-01-01

The general theory and rigorous solutions of the Stokes parameters of light of a new technique in time-resolved ellipsometry are outlined. In this technique the phase of the linear retarder is stepped over three discrete values over a time interval for which the Stokes vector is determined. The technique has an advantage over synchronous detection techniques, as it can be implemented as a digitizable system.

Gas-Solid Dynamics at Disordered and Adsorbate Covered Surfaces

DTIC Science & Technology

1992-09-02

interesting physical problems in which non-linear reactions occur at localized defects. The Lotka - Volterra system is considered, in which the source, sink...designing external optical fields for manipulating molecular scale events. A general formulation of the theory was developed, for treating rotational...interrelated avenues of study were pursued. The goals of the research were achieved, thereby producing a general theoretical framework for both optimal

Young children make their gestural communication systems more language-like: segmentation and linearization of semantic elements in motion events.

PubMed

Clay, Zanna; Pople, Sally; Hood, Bruce; Kita, Sotaro

2014-08-01

Research on Nicaraguan Sign Language, created by deaf children, has suggested that young children use gestures to segment the semantic elements of events and linearize them in ways similar to those used in signed and spoken languages. However, it is unclear whether this is due to children's learning processes or to a more general effect of iterative learning. We investigated whether typically developing children, without iterative learning, segment and linearize information. Gestures produced in the absence of speech to express a motion event were examined in 4-year-olds, 12-year-olds, and adults (all native English speakers). We compared the proportions of gestural expressions that segmented semantic elements into linear sequences and that encoded them simultaneously. Compared with adolescents and adults, children reshaped the holistic stimuli by segmenting and recombining their semantic features into linearized sequences. A control task on recognition memory ruled out the possibility that this was due to different event perception or memory. Young children spontaneously bring fundamental properties of language into their communication system. © The Author(s) 2014.

Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, Rutwig

2017-03-01

Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

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

Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es

Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.

1999-01-01

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

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.

Predicting oropharyngeal tumor volume throughout the course of radiation therapy from pretreatment computed tomography data using general linear models.

PubMed

Yock, Adam D; Rao, Arvind; Dong, Lei; Beadle, Beth M; Garden, Adam S; Kudchadker, Rajat J; Court, Laurence E

2014-05-01

The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: -11.6%-23.8%) and 14.6% (range: -7.3%-27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: -6.8%-40.3%) and 13.1% (range: -1.5%-52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: -11.1%-20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography images and facilitate improved treatment management.

An iterative technique to stabilize a linear time invariant multivariable system with output feedback

NASA Technical Reports Server (NTRS)

Sankaran, V.

1974-01-01

An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.

Dynamic analysis of a flexible spacecraft with rotating components. Volume 1: Analytical developments

NASA Technical Reports Server (NTRS)

Bodley, C. S.; Devers, A. D.; Park, A. C.

1975-01-01

Analytical procedures and digital computer code are presented for the dynamic analysis of a flexible spacecraft with rotating components. Topics, considered include: (1) nonlinear response in the time domain, and (2) linear response in the frequency domain. The spacecraft is assumed to consist of an assembly of connected rigid or flexible subassemblies. The total system is not restricted to a topological connection arrangement and may be acting under the influence of passive or active control systems and external environments. The analytics and associated digital code provide the user with the capability to establish spacecraft system nonlinear total response for specified initial conditions, linear perturbation response about a calculated or specified nominal motion, general frequency response and graphical display, and spacecraft system stability analysis.

Dynamical localization of coupled relativistic kicked rotors

NASA Astrophysics Data System (ADS)

Rozenbaum, Efim B.; Galitski, Victor

2017-02-01

A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work [Phys. Rev. B 94, 085120 (2016), 10.1103/PhysRevB.94.085120], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.

An exact noniterative linear method for locating sources based on measuring receiver arrival times.

PubMed

Militello, C; Buenafuente, S R

2007-06-01

In this paper an exact, linear solution to the source localization problem based on the time of arrival at the receivers is presented. The method is unique in that the source's position can be obtained by solving a system of linear equations, three for a plane and four for a volume. This simplification means adding an additional receiver to the minimum mathematically required (3+1 in two dimensions and 4+1 in three dimensions). The equations are easily worked out for any receiver configuration and their geometrical interpretation is straightforward. Unlike other methods, the system of reference used to describe the receivers' positions is completely arbitrary. The relationship between this method and previously published ones is discussed, showing how the present, more general, method overcomes nonlinearity and unknown dependency issues.

Identification of single-input-single-output quantum linear systems

NASA Astrophysics Data System (ADS)

Levitt, Matthew; GuÅ£ǎ, Mǎdǎlin

2017-03-01

The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realization from sufficient input-output data? We show that for time-dependent inputs, the systems which cannot be distinguished are related by symplectic transformations acting on the space of system modes. This complements a previous result of Guţă and Yamamoto [IEEE Trans. Autom. Control 61, 921 (2016), 10.1109/TAC.2015.2448491] for passive linear systems. In the regime of stationary quantum noise input, the output is completely determined by the power spectrum. We define the notion of global minimality for a given power spectrum, and characterize globally minimal systems as those with a fully mixed stationary state. We show that in the case of systems with a cascade realization, the power spectrum completely fixes the transfer function, so the system can be identified up to a symplectic transformation. We give a method for constructing a globally minimal subsystem direct from the power spectrum. Restricting to passive systems the analysis simplifies so that identifiability may be completely understood from the eigenvalues of a particular system matrix.

Item Purification in Differential Item Functioning Using Generalized Linear Mixed Models

ERIC Educational Resources Information Center

Liu, Qian

2011-01-01

For this dissertation, four item purification procedures were implemented onto the generalized linear mixed model for differential item functioning (DIF) analysis, and the performance of these item purification procedures was investigated through a series of simulations. Among the four procedures, forward and generalized linear mixed model (GLMM)…

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

A high performance linear equation solver on the VPP500 parallel supercomputer

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

Nakanishi, Makoto; Ina, Hiroshi; Miura, Kenichi

1994-12-31

This paper describes the implementation of two high performance linear equation solvers developed for the Fujitsu VPP500, a distributed memory parallel supercomputer system. The solvers take advantage of the key architectural features of VPP500--(1) scalability for an arbitrary number of processors up to 222 processors, (2) flexible data transfer among processors provided by a crossbar interconnection network, (3) vector processing capability on each processor, and (4) overlapped computation and transfer. The general linear equation solver based on the blocked LU decomposition method achieves 120.0 GFLOPS performance with 100 processors in the LIN-PACK Highly Parallel Computing benchmark.

Design of linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang-San; Zhen, Liu; Coleman, Norman P.

1990-01-01

Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

Multilayer neural networks for reduced-rank approximation.

PubMed

Diamantaras, K I; Kung, S Y

1994-01-01

This paper is developed in two parts. First, the authors formulate the solution to the general reduced-rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors. The authors' treatment unifies linear regression, Wiener filtering, full rank approximation, auto-association networks, SVD and principal component analysis (PCA) as special cases. The authors' analysis also shows that two-layer linear neural networks with reduced number of hidden units, trained with the least-squares error criterion, produce weights that correspond to the generalized singular value decomposition of the input-teacher cross-correlation matrix and the input data matrix. As a corollary the linear two-layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components. Second, the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem. By introducing and utilizing the extended concept of deflation (originally proposed for the standard eigenvalue problem) the authors are able to find that a sequential version of linear BP can extract the exact generalized eigenvector components. The advantage of this approach is that it's easier to update the model structure by adding one more unit or pruning one or more units when the application requires it. An alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper- and lower-layer weights. The authors call this the lateral orthogonalization network (LON) and show via theoretical analysis-and verify via simulation-that the network extracts the desired components. The advantage of the LON-based model is that it can be applied in a parallel fashion so that the components are extracted concurrently. Finally, the authors show the application of their results to the solution of the identification problem of systems whose excitation has a non-invertible autocorrelation matrix. Previous identification methods usually rely on the invertibility assumption of the input autocorrelation, therefore they can not be applied to this case.

Treatment of systematic errors in land data assimilation systems

NASA Astrophysics Data System (ADS)

Crow, W. T.; Yilmaz, M.

2012-12-01

Data assimilation systems are generally designed to minimize the influence of random error on the estimation of system states. Yet, experience with land data assimilation systems has also revealed the presence of large systematic differences between model-derived and remotely-sensed estimates of land surface states. Such differences are commonly resolved prior to data assimilation through implementation of a pre-processing rescaling step whereby observations are scaled (or non-linearly transformed) to somehow "match" comparable predictions made by an assimilation model. While the rationale for removing systematic differences in means (i.e., bias) between models and observations is well-established, relatively little theoretical guidance is currently available to determine the appropriate treatment of higher-order moments during rescaling. This talk presents a simple analytical argument to define an optimal linear-rescaling strategy for observations prior to their assimilation into a land surface model. While a technique based on triple collocation theory is shown to replicate this optimal strategy, commonly-applied rescaling techniques (e.g., so called "least-squares regression" and "variance matching" approaches) are shown to represent only sub-optimal approximations to it. Since the triple collocation approach is likely infeasible in many real-world circumstances, general advice for deciding between various feasible (yet sub-optimal) rescaling approaches will be presented with an emphasis of the implications of this work for the case of directly assimilating satellite radiances. While the bulk of the analysis will deal with linear rescaling techniques, its extension to nonlinear cases will also be discussed.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Hydrogen storage and generation system

DOEpatents

Dentinger, Paul M.; Crowell, Jeffrey A. W.

2010-08-24

A system for storing and generating hydrogen generally and, in particular, a system for storing and generating hydrogen for use in an H.sub.2/O.sub.2 fuel cell. The hydrogen storage system uses the beta particles from a beta particle emitting material to degrade an organic polymer material to release substantially pure hydrogen. In a preferred embodiment of the invention, beta particles from .sup.63Ni are used to release hydrogen from linear polyethylene.

Implementation of Rosenbrock methods

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

Shampine, L. F.

1980-11-01

Rosenbrock formulas have shown promise in research codes for the solution of initial-value problems for stiff systems of ordinary differential equations (ODEs). To help assess their practical value, the author wrote an item of mathematical software based on such a formula. This required a variety of algorithmic and software developments. Those of general interest are reported in this paper. Among them is a way to select automatically, at every step, an explicit Runge-Kutta formula or a Rosenbrock formula according to the stiffness of the problem. Solving linear systems is important to methods for stiff ODEs, and is rather special formore » Rosenbrock methods. A cheap, effective estimate of the condition of the linear systems is derived. Some numerical results are presented to illustrate the developments.« less

Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Rapid solution of large-scale systems of equations

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.

Block Gauss elimination followed by a classical iterative method for the solution of linear systems

NASA Astrophysics Data System (ADS)

Alanelli, Maria; Hadjidimos, Apostolos

2004-02-01

In the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the Gauss elimination process in the hope that this will increase the rates of convergence of the iterative method. This combination of methods has been proven successful especially when the matrix A of the system is an M-matrix. The purpose of this paper is to extend the idea of one to more Gauss elimination steps, consider other classes of matrices A, e.g., p-cyclic consistently ordered, and generalize and improve the asymptotic convergence rates of some of the methods known so far.

Self-error-rejecting photonic qubit transmission in polarization-spatial modes with linear optical elements

NASA Astrophysics Data System (ADS)

Jiang, YuXiao; Guo, PengLiang; Gao, ChengYan; Wang, HaiBo; Alzahrani, Faris; Hobiny, Aatef; Deng, FuGuo

2017-12-01

We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channels. Our self-error-rejecting transmission scheme can be generalized to hyperentangled n-photon systems and is useful in practical high-capacity quantum communications with photon systems in two degrees of freedom.

Thermoelectric efficiency of nanoscale devices in the linear regime

NASA Astrophysics Data System (ADS)

Bevilacqua, G.; Grosso, G.; Menichetti, G.; Pastori Parravicini, G.

2016-12-01

We study quantum transport through two-terminal nanoscale devices in contact with two particle reservoirs at different temperatures and chemical potentials. We discuss the general expressions controlling the electric charge current, heat currents, and the efficiency of energy transmutation in steady conditions in the linear regime. With focus in the parameter domain where the electron system acts as a power generator, we elaborate workable expressions for optimal efficiency and thermoelectric parameters of nanoscale devices. The general concepts are set at work in the paradigmatic cases of Lorentzian resonances and antiresonances, and the encompassing Fano transmission function: the treatments are fully analytic, in terms of the trigamma functions and Bernoulli numbers. From the general curves here reported describing transport through the above model transmission functions, useful guidelines for optimal efficiency and thermopower can be inferred for engineering nanoscale devices in energy regions where they show similar transmission functions.

Computing Generalized Matrix Inverse on Spiking Neural Substrate

PubMed Central

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines. PMID:29593483

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Efficient hybrid-symbolic methods for quantum mechanical calculations

NASA Astrophysics Data System (ADS)

Scott, T. C.; Zhang, Wenxing

2015-06-01

We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantum mechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Design of general apochromatic drift-quadrupole beam lines

NASA Astrophysics Data System (ADS)

Lindstrøm, C. A.; Adli, E.

2016-07-01

Chromatic errors are normally corrected using sextupoles in regions of large dispersion. In low emittance linear accelerators, use of sextupoles can be challenging. Apochromatic focusing is a lesser-known alternative approach, whereby chromatic errors of Twiss parameters are corrected without the use of sextupoles, and has consequently been subject to renewed interest in advanced linear accelerator research. Proof of principle designs were first established by Montague and Ruggiero and developed more recently by Balandin et al. We describe a general method for designing drift-quadrupole beam lines of arbitrary order in apochromatic correction, including analytic expressions for emittance growth and other merit functions. Worked examples are shown for plasma wakefield accelerator staging optics and for a simple final focus system.

Real-time imaging of human brain function by near-infrared spectroscopy using an adaptive general linear model

PubMed Central

Abdelnour, A. Farras; Huppert, Theodore

2009-01-01

Near-infrared spectroscopy is a non-invasive neuroimaging method which uses light to measure changes in cerebral blood oxygenation associated with brain activity. In this work, we demonstrate the ability to record and analyze images of brain activity in real-time using a 16-channel continuous wave optical NIRS system. We propose a novel real-time analysis framework using an adaptive Kalman filter and a state–space model based on a canonical general linear model of brain activity. We show that our adaptive model has the ability to estimate single-trial brain activity events as we apply this method to track and classify experimental data acquired during an alternating bilateral self-paced finger tapping task. PMID:19457389

Gravity Waves and Linear Inflation From Axion Monodromy

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

McAllister, Liam; /Cornell U., LEPP /Cornell U., Phys. Dept.; Silverstein, Eva

2010-08-26

Wrapped branes in string compactifications introduce a monodromy that extends the field range of individual closed-string axions to beyond the Planck scale. Furthermore, approximate shift symmetries of the system naturally control corrections to the axion potential. This suggests a general mechanism for chaotic inflation driven by monodromy-extended closed-string axions. We systematically analyze this possibility and show that the mechanism is compatible with moduli stabilization and can be realized in many types of compactifications, including warped Calabi-Yau manifolds and more general Ricci-curved spaces. In this broad class of models, the potential is linear in the canonical inflaton field, predicting a tensormore » to scalar ratio r {approx} 0.07 accessible to upcoming cosmic microwave background (CMB) observations.« less

Application of Mathematical Signal Processing Techniques to Mission Systems. (l’Application des techniques mathematiques du traitement du signal aux systemes de conduite des missions)

DTIC Science & Technology

1999-11-01

represents the linear time invariant (LTI) response of the combined analysis /synthesis system while the second repre- sents the aliasing introduced into...effectively to implement voice scrambling systems based on time - frequency permutation . The most general form of such a system is shown in Fig. 22 where...92201 NEUILLY-SUR-SEINE CEDEX, FRANCE RTO LECTURE SERIES 216 Application of Mathematical Signal Processing Techniques to Mission Systems (1

Smoothed Residual Plots for Generalized Linear Models. Technical Report #450.

ERIC Educational Resources Information Center

Brant, Rollin

Methods for examining the viability of assumptions underlying generalized linear models are considered. By appealing to the likelihood, a natural generalization of the raw residual plot for normal theory models is derived and is applied to investigating potential misspecification of the linear predictor. A smooth version of the plot is also…

Non-linear vibrating systems excited by a nonideal energy source with a large slope characteristic

NASA Astrophysics Data System (ADS)

González-Carbajal, Javier; Domínguez, Jaime

2017-11-01

This paper revisits the problem of an unbalanced motor attached to a fixed frame by means of a nonlinear spring and a linear damper. The excitation provided by the motor is, in general, nonideal, which means it is affected by the vibratory response. Since the system behaviour is highly dependent on the order of magnitude of the motor characteristic slope, the case of large slope is considered herein. Some Perturbation Methods are applied to the system of equations, which allows transforming the original 4D system into a much simpler 2D system. The fixed points of this reduced system and their stability are carefully studied. We find the existence of a Hopf bifurcation which, to the authors' knowledge, has not been addressed before in the literature. These analytical results are supported by numerical simulations. We also compare our approach and results with those published by other authors.

Modeling demand for public transit services in rural areas

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

Attaluri, P.; Seneviratne, P.N.; Javid, M.

1997-05-01

Accurate estimates of demand are critical for planning, designing, and operating public transit systems. Previous research has demonstrated that the expected demand in rural areas is a function of both demographic and transit system variables. Numerous models have been proposed to describe the relationship between the aforementioned variables. However, most of them are site specific and their validity over time and space is not reported or perhaps has not been tested. Moreover, input variables in some cases are extremely difficult to quantify. In this article, the estimation of demand using the generalized linear modeling technique is discussed. Two separate models,more » one for fixed-route and another for demand-responsive services, are presented. These models, calibrated with data from systems in nine different states, are used to demonstrate the appropriateness and validity of generalized linear models compared to the regression models. They explain over 70% of the variation in expected demand for fixed-route services and 60% of the variation in expected demand for demand-responsive services. It was found that the models are spatially transferable and that data for calibration are easily obtainable.« less

Theoretical foundations of spatially-variant mathematical morphology part ii: gray-level images.

PubMed

Bouaynaya, Nidhal; Schonfeld, Dan

2008-05-01

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

PubMed

Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao

2014-10-06

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

Fit Point-Wise AB Initio Calculation Potential Energies to a Multi-Dimension Long-Range Model

NASA Astrophysics Data System (ADS)

Zhai, Yu; Li, Hui; Le Roy, Robert J.

2016-06-01

A potential energy surface (PES) is a fundamental tool and source of understanding for theoretical spectroscopy and for dynamical simulations. Making correct assignments for high-resolution rovibrational spectra of floppy polyatomic and van der Waals molecules often relies heavily on predictions generated from a high quality ab initio potential energy surface. Moreover, having an effective analytic model to represent such surfaces can be as important as the ab initio results themselves. For the one-dimensional potentials of diatomic molecules, the most successful such model to date is arguably the ``Morse/Long-Range'' (MLR) function developed by R. J. Le Roy and coworkers. It is very flexible, is everywhere differentiable to all orders. It incorporates correct predicted long-range behaviour, extrapolates sensibly at both large and small distances, and two of its defining parameters are always the physically meaningful well depth {D}_e and equilibrium distance r_e. Extensions of this model, called the Multi-Dimension Morse/Long-Range (MD-MLR) function, linear molecule-linear molecule systems and atom-non-linear molecule system. have been applied successfully to atom-plus-linear molecule, linear molecule-linear molecule and atom-non-linear molecule systems. However, there are several technical challenges faced in modelling the interactions of general molecule-molecule systems, such as the absence of radial minima for some relative alignments, difficulties in fitting short-range potential energies, and challenges in determining relative-orientation dependent long-range coefficients. This talk will illustrate some of these challenges and describe our ongoing work in addressing them. Mol. Phys. 105, 663 (2007); J. Chem. Phys. 131, 204309 (2009); Mol. Phys. 109, 435 (2011). Phys. Chem. Chem. Phys. 10, 4128 (2008); J. Chem. Phys. 130, 144305 (2009) J. Chem. Phys. 132, 214309 (2010) J. Chem. Phys. 140, 214309 (2010)

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Follow the line: Mysterious bright streaks on Dione and Rhea

NASA Astrophysics Data System (ADS)

Martin, E. S.; Patthoff, D. A.

2017-12-01

Our recent mapping of the wispy terrains of Saturn's moons Dione and Rhea has revealed unique linear features that are generally long (10s-100s km), narrow (1-10 km), brighter than the surrounding terrains, and their detection may be sensitive to lighting geometries. We refer to these features as `linear virgae.' Wherever linear virgae are observed, they appear to crosscut all other structures, suggesting that they are the youngest features on these satellites. Despite their young age and wide distribution, linear virgae on Rhea and Dione have largely been overlooked in the literature. Linear virgae on Dione have previously been identified in Voyager and Cassini Data, but their formation remains an open question. If linear virgae are found to be endogenic, it would suggest that the surfaces of Dione and Rhea have been active recently. Alternatively, if linear virgae are exogenic it would suggest that the surfaces have been modified by a possibly common mechanism. Further work would be necessary to determine both a source of material and the dynamical environment that could produce these features. Here we present detailed morphometric measurements to further constrain whether linear virgae on Rhea and Dione share common origins. We complete an in-depth assessment of the lighting geometries where these features are visible. If linear virgae in the Saturnian system show common morphologies and distributions, a new, recently active, possibly system-wide mechanism may be revealed, thereby improving our understanding of the recent dynamical environment around Saturn.

Variational Iterative Methods for Nonsymmetric Systems of Linear Equations.

DTIC Science & Technology

1981-08-01

With a third matrix-vector product, b(i) can be computed as i j ( ATAr i+l’pj)/ApjpApj), and the previous (Apj) need not be saved. Page 8 I OCR I Orthomin... Economics and Mathematical Systems, Volume 134, Springer-Verlag, Berlin, 1976. [51 Paul Concus, Gene H. Golub, and Dianne P. O’Leary. A generalized

Hyperbolic conservation laws and numerical methods

NASA Technical Reports Server (NTRS)

Leveque, Randall J.

1990-01-01

The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

Endoreversible quantum heat engines in the linear response regime.

PubMed

Wang, Honghui; He, Jizhou; Wang, Jianhui

2017-07-01

We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.

A generalized fuzzy linear programming approach for environmental management problem under uncertainty.

PubMed

Fan, Yurui; Huang, Guohe; Veawab, Amornvadee

2012-01-01

In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO2) control planning model to identify effective SO2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP and then identify desired policies for SO2-emission control under uncertainty.

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

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

Hager, Robert, E-mail: rhager@pppl.gov; Yoon, E.S., E-mail: yoone@rpi.edu; Ku, S., E-mail: sku@pppl.gov

2016-06-15

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable onmore » high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.« less

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

DOE PAGES

Hager, Robert; Yoon, E. S.; Ku, S.; ...

2016-04-04

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less

Analysis of linear and cyclic oligomers in polyamide-6 without sample preparation by liquid chromatography using the sandwich injection method. II. Methods of detection and quantification and overall long-term performance.

PubMed

Mengerink, Y; Peters, R; Kerkhoff, M; Hellenbrand, J; Omloo, H; Andrien, J; Vestjens, M; van der Wal, S

2000-05-05

By separating the first six linear and cyclic oligomers of polyamide-6 on a reversed-phase high-performance liquid chromatographic system after sandwich injection, quantitative determination of these oligomers becomes feasible. Low-wavelength UV detection of the different oligomers and selective post-column reaction detection of the linear oligomers with o-phthalic dicarboxaldehyde (OPA) and 3-mercaptopropionic acid (3-MPA) are discussed. A general methodology for quantification of oligomers in polymers was developed. It is demonstrated that the empirically determined group-equivalent absorption coefficients and quench factors are a convenient way of quantifying linear and cyclic oligomers of nylon-6. The overall long-term performance of the method was studied by monitoring a reference sample and the calibration factors of the linear and cyclic oligomers.

Imparting Motion to a Test Object Such as a Motor Vehicle in a Controlled Fashion

NASA Technical Reports Server (NTRS)

Southward, Stephen C. (Inventor); Reubush, Chandler (Inventor); Pittman, Bryan (Inventor); Roehrig, Kurt (Inventor); Gerard, Doug (Inventor)

2014-01-01

An apparatus imparts motion to a test object such as a motor vehicle in a controlled fashion. A base has mounted on it a linear electromagnetic motor having a first end and a second end, the first end being connected to the base. A pneumatic cylinder and piston combination have a first end and a second end, the first end connected to the base so that the pneumatic cylinder and piston combination is generally parallel with the linear electromagnetic motor. The second ends of the linear electromagnetic motor and pneumatic cylinder and piston combination being commonly linked to a mount for the test object. A control system for the linear electromagnetic motor and pneumatic cylinder and piston combination drives the pneumatic cylinder and piston combination to support a substantial static load of the test object and the linear electromagnetic motor to impart controlled motion to the test object.

Protein fiber linear dichroism for structure determination and kinetics in a low-volume, low-wavelength couette flow cell.

PubMed

Dafforn, Timothy R; Rajendra, Jacindra; Halsall, David J; Serpell, Louise C; Rodger, Alison

2004-01-01

High-resolution structure determination of soluble globular proteins relies heavily on x-ray crystallography techniques. Such an approach is often ineffective for investigations into the structure of fibrous proteins as these proteins generally do not crystallize. Thus investigations into fibrous protein structure have relied on less direct methods such as x-ray fiber diffraction and circular dichroism. Ultraviolet linear dichroism has the potential to provide additional information on the structure of such biomolecular systems. However, existing systems are not optimized for the requirements of fibrous proteins. We have designed and built a low-volume (200 microL), low-wavelength (down to 180 nm), low-pathlength (100 microm), high-alignment flow-alignment system (couette) to perform ultraviolet linear dichroism studies on the fibers formed by a range of biomolecules. The apparatus has been tested using a number of proteins for which longer wavelength linear dichroism spectra had already been measured. The new couette cell has also been used to obtain data on two medically important protein fibers, the all-beta-sheet amyloid fibers of the Alzheimer's derived protein Abeta and the long-chain assemblies of alpha1-antitrypsin polymers.

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

NASA Astrophysics Data System (ADS)

Hagemann, Alexander; Rohr, Karl; Stiehl, H. Siegfried

2000-06-01

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

On-line pulse control for structural and mechanical systems

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.; Tabaie, S.

1981-01-01

This paper studies the feasibility of using open-loop adaptive on-line pulse control for limiting the response of large linear multidegree of freedom systems subjected to general dynamic loading environments. Pulses of short durations are used to control the system when the system response exceeds a given threshold level. The pulse magnitudes are obtained in closed form, leading to large computational efficiencies when compared with optimal control theoretic methods. The technique is illustrated for a structural system subjected to earthquake-like base excitations.

The Impact of New Technology on Accounting Education.

ERIC Educational Resources Information Center

Shaoul, Jean

The introduction of computers in the Department of Accounting and Finance at Manchester University is described. General background outlining the increasing need for microcomputers in the accounting curriculum (including financial modelling tools and decision support systems such as linear programming, statistical packages, and simulation) is…

Foundations for a Post-Modern Curriculum.

ERIC Educational Resources Information Center

Doll, William E., Jr.

This paper suggests that present-day curriculum, based on Newtonian thought, has been rendered obsolete by the holistic and interactive "post-modern" world view based on quantum physics, nonlinear mathematics, general systems theory, and Ilya Prigogine's nonequilibrium thermodynamics. The Newtonian world view, which is linear and…

State variable modeling of the integrated engine and aircraft dynamics

NASA Astrophysics Data System (ADS)

Rotaru, Constantin; Sprinţu, Iuliana

2014-12-01

This study explores the dynamic characteristics of the combined aircraft-engine system, based on the general theory of the state variables for linear and nonlinear systems, with details leading first to the separate formulation of the longitudinal and the lateral directional state variable models, followed by the merging of the aircraft and engine models into a single state variable model. The linearized equations were expressed in a matrix form and the engine dynamics was included in terms of variation of thrust following a deflection of the throttle. The linear model of the shaft dynamics for a two-spool jet engine was derived by extending the one-spool model. The results include the discussion of the thrust effect upon the aircraft response when the thrust force associated with the engine has a sizable moment arm with respect to the aircraft center of gravity for creating a compensating moment.

Incremental harmonic balance method for predicting amplitudes of a multi-d.o.f. non-linear wheel shimmy system with combined Coulomb and quadratic damping

NASA Astrophysics Data System (ADS)

Zhou, J. X.; Zhang, L.

2005-01-01

Incremental harmonic balance (IHB) formulations are derived for general multiple degrees of freedom (d.o.f.) non-linear autonomous systems. These formulations are developed for a concerned four-d.o.f. aircraft wheel shimmy system with combined Coulomb and velocity-squared damping. A multi-harmonic analysis is performed and amplitudes of limit cycles are predicted. Within a large range of parametric variations with respect to aircraft taxi velocity, the IHB method can, at a much cheaper cost, give results with high accuracy as compared with numerical results given by a parametric continuation method. In particular, the IHB method avoids the stiff problems emanating from numerical treatment of aircraft wheel shimmy system equations. The development is applicable to other vibration control systems that include commonly used dry friction devices or velocity-squared hydraulic dampers.

General algebraic method applied to control analysis of complex engine types

NASA Technical Reports Server (NTRS)

Boksenbom, Aaron S; Hood, Richard

1950-01-01

A general algebraic method of attack on the problem of controlling gas-turbine engines having any number of independent variables was utilized employing operational functions to describe the assumed linear characteristics for the engine, the control, and the other units in the system. Matrices were used to describe the various units of the system, to form a combined system showing all effects, and to form a single condensed matrix showing the principal effects. This method directly led to the conditions on the control system for noninteraction so that any setting disturbance would affect only its corresponding controlled variable. The response-action characteristics were expressed in terms of the control system and the engine characteristics. The ideal control-system characteristics were explicitly determined in terms of any desired response action.

Characterizing entanglement with global and marginal entropic measures

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

Adesso, Gerardo; Illuminati, Fabrizio; De Siena, Silvio

2003-12-01

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entanglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such statesmore » cannot be discriminated by the majorization criterion.« less

Universal linear and nonlinear electrodynamics of a Dirac fluid

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, Dmitry N.; Fogler, Michael M.

2018-03-01

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential, or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

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.

Asymptotic Representations of Quantum Affine Superalgebras

NASA Astrophysics Data System (ADS)

Zhang, Huafeng

2017-08-01

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.

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.

AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

NASA Technical Reports Server (NTRS)

Klumpp, A. R.

1994-01-01

This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

Design, construction, and evaluation of new high resolution medical imaging detector/systems

NASA Astrophysics Data System (ADS)

Jain, Amit

Increasing need of minimally invasive endovascular image guided interventional procedures (EIGI) for accurate and successful treatment of vascular disease has set a quest for better image quality. Current state of the art detectors are not up to the mark for these complex procedures due to their inherent limitations. Our group has been actively working on the design and construction of a high resolution, region of interest CCD-based X-ray imager for some time. As a part of that endeavor, a Micro-angiographic fluoroscope (MAF) was developed to serve as a high resolution, ROI X-ray imaging detector in conjunction with large lower resolution full field of view (FOV) state-of-the-art x-ray detectors. The newly developed MAF is an indirect x-ray imaging detector capable of providing real-time images with high resolution, high sensitivity, no lag and low instrumentation noise. It consists of a CCD camera coupled to a light image intensifier (LII) through a fiber optic taper. The CsI(Tl) phosphor serving as the front end is coupled to the LII. For this work, the MAF was designed and constructed. The linear system cascade theory was used to evaluate the performance theoretically. Linear system metrics such as MTF and DQE were used to gauge the detector performance experimentally. The capabilities of the MAF as a complete system were tested using generalized linear system metrics. With generalized linear system metrics the effects of finite size focal spot, geometric magnification and the presence of scatter are included in the analysis and study. To minimize the effect of scatter, an anti-scatter grid specially designed for the MAF was also studied. The MAF was compared with the flat panel detector using signal-to-noise ratio and the two dimensional linear system metrics. The signal-to-noise comparison was carried out to point out the effect of pixel size and Point Spread Function of the detector. The two dimensional linear system metrics were used to investigate the comparative performance of both the detectors in similar simulated clinical neuro-vascular conditions. The last part of this work presents a unique quality of the MAF: operation in single photon mode. The successful operation of the MAF was demonstrated with considerable improvement in spatial and contrast resolution over conventional energy integrating mode. The work presented shows the evolution of a high resolution, high sensitivity, and region of interest x-ray imaging detector as an attractive and capable x-ray imager for the betterment of complex EIGI procedures. The capability of single photon counting mode imaging provides the potential for additional uses of the MAF including the possibility of use in dual modality imaging with radionuclide sources as well as x-rays.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Yu; Cao, Jianshu

2018-01-01

We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ˜1 /√{NB } where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1 /√{NB } scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

A survey of the state of the art and focused research in range systems, task 2

NASA Technical Reports Server (NTRS)

Yao, K.

1986-01-01

Many communication, control, and information processing subsystems are modeled by linear systems incorporating tapped delay lines (TDL). Such optimized subsystems result in full precision multiplications in the TDL. In order to reduce complexity and cost in a microprocessor implementation, these multiplications can be replaced by single-shift instructions which are equivalent to powers of two multiplications. Since, in general, the obvious operation of rounding the infinite precision TDL coefficients to the nearest powers of two usually yield quite poor system performance, the optimum powers of two coefficient solution was considered. Detailed explanations on the use of branch-and-bound algorithms for finding the optimum powers of two solutions are given. Specific demonstration of this methodology to the design of a linear data equalizer and its implementation in assembly language on a 8080 microprocessor with a 12 bit A/D converter are reported. This simple microprocessor implementation with optimized TDL coefficients achieves a system performance comparable to the optimum linear equalization with full precision multiplications for an input data rate of 300 baud. The philosophy demonstrated in this implementation is dully applicable to many other microprocessor controlled information processing systems.

Transient times in linear metabolic pathways under constant affinity constraints.

PubMed

Lloréns, M; Nuño, J C; Montero, F

1997-10-15

In the early seventies, Easterby began the analytical study of transition times for linear reaction schemes [Easterby (1973) Biochim. Biophys. Acta 293, 552-558]. In this pioneer work and in subsequent papers, a state function (the transient time) was used to measure the period before the stationary state, for systems constrained to work under both constant and variable input flux, was reached. Despite the undoubted usefulness of this quantity to describe the time-dependent features of these kinds of systems, its application to the study of chemical reactions under other constraints is questionable. In the present work, a generalization of these magnitudes to linear metabolic pathways functioning under a constant-affinity constraint is carried out. It is proved that classical definitions of transient times do not reflect the actual properties of the transition to the steady state in systems evolving under this restriction. Alternatively, a more adequate framework for interpretation of the transient times for systems with both constant and variable input flux is suggested. Within this context, new definitions that reflect more accurately the transient characteristics of constant affinity systems are stated. Finally, the meaning of these transient times is discussed.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Functional aging in pilots : an examination of a mathematical model based on medical data on general aviation pilots.

DOT National Transportation Integrated Search

1982-06-01

The purpose of this study was to apply mathematical procedures to the Federal Aviation Administration (FAA) pilot medical data to examine the feasibility of devising a linear numbering system such that (1) the cumulative probability distribution func...

Watt steam governor stability

NASA Astrophysics Data System (ADS)

Denny, Mark

2002-05-01

The physics of the fly-ball governor, introduced to regulate the speed of steam engines, is here analysed anew. The original analysis is generalized to arbitrary governor geometry. The well-known stability criterion for the linearized system breaks down for large excursions from equilibrium; we show approximately how this criterion changes.

Entropy production and nonlinear Fokker-Planck equations.

PubMed

Casas, G A; Nobre, F D; Curado, E M F

2012-12-01

The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

On the classical and quantum integrability of systems of resonant oscillators

NASA Astrophysics Data System (ADS)

Marino, Massimo

2017-01-01

We study in this paper systems of harmonic oscillators with resonant frequencies. For these systems we present general procedures for the construction of sets of functionally independent constants of motion, which can be used for the definition of generalized actionangle variables, in accordance with the general description of degenerate integrable systems which was presented by Nekhoroshev in a seminal paper in 1972. We then apply to these classical integrable systems the procedure of quantization which has been proposed to the author by Nekhoroshev during his last years of activity at Milan University. This procedure is based on the construction of linear operators by means of the symmetrization of the classical constants of motion mentioned above. For 3 oscillators with resonance 1: 1: 2, by using a computer program we have discovered an exceptional integrable system, which cannot be obtained with the standard methods based on the obvious symmetries of the Hamiltonian function. In this exceptional case, quantum integrability can be realized only by means of a modification of the symmetrization procedure.

Modeling meniscus rise in capillary tubes using fluid in rigid-body motion approach

NASA Astrophysics Data System (ADS)

Hamdan, Mohammad O.; Abu-Nabah, Bassam A.

2018-04-01

In this study, a new term representing net flux rate of linear momentum is introduced to Lucas-Washburn equation. Following a fluid in rigid-body motion in modeling the meniscus rise in vertical capillary tubes transforms the nonlinear Lucas-Washburn equation to a linear mass-spring-damper system. The linear nature of mass-spring-damper system with constant coefficients offers a nondimensional analytical solution where meniscus dynamics are dictated by two parameters, namely the system damping ratio and its natural frequency. This connects the numerous fluid-surface interaction physical and geometrical properties to rather two nondimensional parameters, which capture the underlying physics of meniscus dynamics in three distinct cases, namely overdamped, critically damped, and underdamped systems. Based on experimental data available in the literature and the understanding meniscus dynamics, the proposed model brings a new approach of understanding the system initial conditions. Accordingly, a closed form relation is produced for the imbibition velocity, which equals half of the Bosanquet velocity divided by the damping ratio. The proposed general analytical model is ideal for overdamped and critically damped systems. While for underdamped systems, the solution shows fair agreement with experimental measurements once the effective viscosity is determined. Moreover, the presented model shows meniscus oscillations around equilibrium height occur if the damping ratio is less than one.

General, database-driven fast-feedback system for the Stanford Linear Collider

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

Rouse, F.; Allison, S.; Castillo, S.

A new feedback system has been developed for stabilizing the SLC beams at many locations. The feedback loops are designed to sample and correct at the 60 Hz repetition rate of the accelerator. Each loop can be distributed across several of the standard 80386 microprocessors which control the SLC hardware. A new communications system, KISNet, has been implemented to pass signals between the microprocessors at this rate. The software is written in a general fashion using the state space formalism of digital control theory. This allows a new loop to be implemented by just setting up the online database andmore » perhaps installing a communications link. 3 refs., 4 figs.« less

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

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

Graber, P. Jameson, E-mail: jameson-graber@baylor.edu

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

Optimal design of neural stimulation current waveforms.

PubMed

Halpern, Mark

2009-01-01

This paper contains results on the design of electrical signals for delivering charge through electrodes to achieve neural stimulation. A generalization of the usual constant current stimulation phase to a stepped current waveform is presented. The electrode current design is then formulated as the calculation of the current step sizes to minimize the peak electrode voltage while delivering a specified charge in a given number of time steps. This design problem can be formulated as a finite linear program, or alternatively by using techniques for discrete-time linear system design.

Supertrace formulae for nonlinearly realized supersymmetry

NASA Astrophysics Data System (ADS)

Murli, Divyanshu; Yamada, Yusuke

2018-04-01

We derive the general supertrace formula for a system with N chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral superfield breaking supersymmetry spontaneously. As we show, however, the modified formula is not simply related to the scalar-decoupling limit of the supertrace in linearly-realized supersymmetry. We also show that the supertrace formula reduces to that of a linearly realized supersymmetric theory with a decoupled sGoldstino if the Goldstino is the fermion in the nilpotent multiplet.

MUSTA fluxes for systems of conservation laws

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2006-08-01

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporate GFORCE in the framework of the MUSTA approach [E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003], resulting in a version that we call GMUSTA. For non-linear systems this gives results that are comparable to those of the Godunov method in conjunction with the exact Riemann solver or complete approximate Riemann solvers, noting however that in our approach, the solution of the Riemann problem in the conventional sense is avoided. Both the GFORCE and GMUSTA fluxes are extended to multi-dimensional non-linear systems in a straightforward unsplit manner, resulting in linearly stable schemes that have the same stability regions as the straightforward multi-dimensional extension of Godunov's method. The methods are applicable to general meshes. The schemes of this paper share with the family of centred methods the common properties of being simple and applicable to a large class of hyperbolic systems, but the schemes of this paper are distinctly more accurate. Finally, we proceed to the practical implementation of our numerical fluxes in the framework of high-order finite volume WENO methods for multi-dimensional non-linear hyperbolic systems. Numerical results are presented for the Euler equations and for the equations of magnetohydrodynamics.

A multiloop generalization of the circle criterion for stability margin analysis

NASA Technical Reports Server (NTRS)

Safonov, M. G.; Athans, M.

1979-01-01

In order to provide a theoretical tool suited for characterizing the stability margins of multiloop feedback systems, multiloop input-output stability results generalizing the circle stability criterion are considered. Generalized conic sectors with 'centers' and 'radii' determined by linear dynamical operators are employed to specify the stability margins as a frequency dependent convex set of modeling errors (including nonlinearities, gain variations and phase variations) which the system must be able to tolerate in each feedback loop without instability. The resulting stability criterion gives sufficient conditions for closed loop stability in the presence of frequency dependent modeling errors, even when the modeling errors occur simultaneously in all loops. The stability conditions yield an easily interpreted scalar measure of the amount by which a multiloop system exceeds, or falls short of, its stability margin specifications.

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Geurdes, Han; Batle, Josep; Abdalla, Soliman; Farouk, Ahmed; Diep, Do Ngoc

2018-04-01

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f( x) := s. x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = ( x 1, … , x N ), x j ∈ R and the coefficients s = ( s 1, … , s N ), s j ∈ N. Given the interpolation values (f(1), f(2),...,f(N))=ěc {y}, the unknown coefficients s = (s1(ěc {y}),\\dots , sN(ěc {y})) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Geurdes, Han; Batle, Josep; Abdalla, Soliman; Farouk, Ahmed; Diep, Do Ngoc

2017-12-01

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = (x 1, … , x N ), x j ∈ R and the coefficients s = (s 1, … , s N ), s j ∈ N. Given the interpolation values (f(1), f(2),...,f(N))=ěc {y}, the unknown coefficients s = (s1(ěc {y}),\\dots , sN(ěc {y})) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Machine learning-based methods for prediction of linear B-cell epitopes.

PubMed

Wang, Hsin-Wei; Pai, Tun-Wen

2014-01-01

B-cell epitope prediction facilitates immunologists in designing peptide-based vaccine, diagnostic test, disease prevention, treatment, and antibody production. In comparison with T-cell epitope prediction, the performance of variable length B-cell epitope prediction is still yet to be satisfied. Fortunately, due to increasingly available verified epitope databases, bioinformaticians could adopt machine learning-based algorithms on all curated data to design an improved prediction tool for biomedical researchers. Here, we have reviewed related epitope prediction papers, especially those for linear B-cell epitope prediction. It should be noticed that a combination of selected propensity scales and statistics of epitope residues with machine learning-based tools formulated a general way for constructing linear B-cell epitope prediction systems. It is also observed from most of the comparison results that the kernel method of support vector machine (SVM) classifier outperformed other machine learning-based approaches. Hence, in this chapter, except reviewing recently published papers, we have introduced the fundamentals of B-cell epitope and SVM techniques. In addition, an example of linear B-cell prediction system based on physicochemical features and amino acid combinations is illustrated in details.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

DOE PAGES

Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

2015-09-08

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

System and method for generating 3D images of non-linear properties of rock formation using surface seismic or surface to borehole seismic or both

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

Vu, Cung Khac; Nihei, Kurt Toshimi; Johnson, Paul A.

A system and method of characterizing properties of a medium from a non-linear interaction are include generating, by first and second acoustic sources disposed on a surface of the medium on a first line, first and second acoustic waves. The first and second acoustic sources are controllable such that trajectories of the first and second acoustic waves intersect in a mixing zone within the medium. The method further includes receiving, by a receiver positioned in a plane containing the first and second acoustic sources, a third acoustic wave generated by a non-linear mixing process from the first and second acousticmore » waves in the mixing zone; and creating a first two-dimensional image of non-linear properties or a first ratio of compressional velocity and shear velocity, or both, of the medium in a first plane generally perpendicular to the surface and containing the first line, based on the received third acoustic wave.« less

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation

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

Simakov, Andrei N., E-mail: simakov@lanl.gov; Molvig, Kim

2016-03-15

A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. - JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to closemore » the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produce two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in Paper II [A. N. Simakov and K. Molvig, Phys. Plasmas 23, 032116 (2016)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas.« less

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Generalized Multilevel Structural Equation Modeling

ERIC Educational Resources Information Center

Rabe-Hesketh, Sophia; Skrondal, Anders; Pickles, Andrew

2004-01-01

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…

Effects of biomotor structures on performance of competitive gymnastics elements in elementary school male sixth-graders.

PubMed

Delas, Suncica; Zagorac, Nebojsa; Katić, Ratko

2008-06-01

In order to identify the biomotor systems that determine performance of competitive gymnastics elements in elementary school male sixth-graders, factor structures of morphological characteristics and basic motor abilities were determined first, followed by relations of the morphological-motor system factors obtained with a set of criterion variables evaluating specific motor skills in competitive gymnastics in 110 male children aged 12 years +/- 3 months. Factor analysis of 17 morphological measures produced three morphological factors: factor of mesoectoendomorphy (general morphological factor) and factor of pronounced endomorphy, i.e. excessive adipose tissue, along with low skeleton longitudinality. Factor analysis of 16 motor variables yielded four motor factors: factor of general motoricity; factor integrating leg flexibility and arm explosiveness; factor juxtaposing body flexibility and repetitive leg strength; and factor predominantly defining leg movement frequency. Three significant canonical correlations, i.e. linear combinations, explained the association between the set of six latent variables of the morphological and basic motor system, and five variables assessing the knowledge in competitive gymnastics. The first canonical linear combination was based on the favorable and predominant impact of the general motor factor (a system integrating leg explosiveness, whole body coordination, relative arm and trunk strength, and arm movement frequency), along with unfavorable effect of morphological factors on the gymnastics elements performance, squat vault and handstand in particular The relation of the second pair of canonical factors pointed to the effects of leg flexibility and arm explosiveness on the cartwheel and backward pullover mount performance, whereas the relation of the third pair of canonical factors showed a favorable impact of the general morphological factor and leg movement frequency regulator on the forward shoulderkip from increase, cartwheel and handstand performance.

Development of a technique for estimating noise covariances using multiple observers

NASA Technical Reports Server (NTRS)

Bundick, W. Thomas

1988-01-01

Friedland's technique for estimating the unknown noise variances of a linear system using multiple observers has been extended by developing a general solution for the estimates of the variances, developing the statistics (mean and standard deviation) of these estimates, and demonstrating the solution on two examples.

Compressed Scaling of Abstract Numerosity Representations in Adult Humans and Monkeys

ERIC Educational Resources Information Center

Merten, Katharina; Nieder, Andreas

2009-01-01

There is general agreement that nonverbal animals and humans endowed with language possess an evolutionary precursor system for representing and comparing numerical values. However, whether nonverbal numerical representations in human and nonhuman primates are quantitatively similar and whether linear or logarithmic coding underlies such magnitude…

Rotating metric in nonsingular infinite derivative theories of gravity

NASA Astrophysics Data System (ADS)

Cornell, Alan S.; Harmsen, Gerhard; Lambiase, Gaetano; Mazumdar, Anupam

2018-05-01

In this paper, we will provide a nonsingular rotating spacetime metric for a ghost-free infinite derivative theory of gravity in a linearized limit. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that from general relativity.

Analysis techniques for multivariate root loci. [a tool in linear control systems

NASA Technical Reports Server (NTRS)

Thompson, P. M.; Stein, G.; Laub, A. J.

1980-01-01

Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus.

Computer Series, 65. Bits and Pieces, 26.

ERIC Educational Resources Information Center

Moore, John W., Ed.

1985-01-01

Describes: (l) a microcomputer-based system for filing test questions and assembling examinations; (2) microcomputer use in practical and simulated experiments of gamma rays scattering by outer shell electrons; (3) an interactive, screen-oriented, general linear regression program; and (4) graphics drill and game programs for benzene synthesis.…

The existence of solutions of q-difference-differential equations.

PubMed

Wang, Xin-Li; Wang, Hua; Xu, Hong-Yan

2016-01-01

By using the Nevanlinna theory of value distribution, we investigate the existence of solutions of some types of non-linear q-difference differential equations. In particular, we generalize the Rellich-Wittich-type theorem and Malmquist-type theorem about differential equations to the case of q-difference differential equations (system).

Evaluation: Boundary Identification in the Non-Linear Special Education System.

ERIC Educational Resources Information Center

Yacobacci, Patricia M.

The evaluation process within special education, as in general education, most often becomes one of data collection consisting of formal and informal tests given by the school psychologist and the classroom instructor. Influences of the complex environment on the educational process are often ignored. Evaluation factors include mainstreaming,…

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

Inverse scattering method and soliton double solution family for the general symplectic gravity model

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

Gao Yajun

A previously established Hauser-Ernst-type extended double-complex linear system is slightly modified and used to develop an inverse scattering method for the stationary axisymmetric general symplectic gravity model. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method applied fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.

Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

NASA Astrophysics Data System (ADS)

Inoue, Rei; Lam, Thomas; Pylyavskyy, Pavlo

2016-11-01

We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.

Unobtrusive Detection of Mild Cognitive Impairment in Older Adults Through Home Monitoring.

PubMed

Akl, Ahmad; Snoek, Jasper; Mihailidis, Alex

2017-03-01

The early detection of dementias such as Alzheimer's disease can in some cases reverse, stop, or slow cognitive decline and in general greatly reduce the burden of care. This is of increasing significance as demographic studies are warning of an aging population in North America and worldwide. Various smart homes and systems have been developed to detect cognitive decline through continuous monitoring of high risk individuals. However, the majority of these smart homes and systems use a number of predefined heuristics to detect changes in cognition, which has been demonstrated to focus on the idiosyncratic nuances of the individual subjects, and thus, does not generalize. In this paper, we address this problem by building generalized linear models of home activity of older adults monitored using unobtrusive sensing technologies. We use inhomogenous Poisson processes to model the presence of the recruited older adults within different rooms throughout the day. We employ an information theoretic approach to compare the generalized linear models learned, and we observe significant statistical differences between the cognitively intact and impaired older adults. Using a simple thresholding approach, we were able to detect mild cognitive impairment in older adults with an average area under the ROC curve of 0.716 and an average area under the precision-recall curve of 0.706 using activity models estimated over a time window of 12 weeks.

A substructure coupling procedure applicable to general linear time-invariant dynamic systems

NASA Technical Reports Server (NTRS)

Howsman, T. G.; Craig, R. R., Jr.

1984-01-01

A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.

Module theoretic zero structures for system matrices

NASA Technical Reports Server (NTRS)

Wyman, Bostwick F.; Sain, Michael K.

1987-01-01

The coordinate-free module-theoretic treatment of transmission zeros for MIMO transfer functions developed by Wyman and Sain (1981) is generalized to include noncontrollable and nonobservable linear dynamical systems. Rational, finitely-generated-modular, and torsion-divisible interpretations of the Rosenbrock system matrix are presented; Gamma-zero and Omega-zero modules are defined and shown to contain the output-decoupling and input-decoupling zero modules, respectively, as submodules; and the cases of left and right invertible transfer functions are considered.

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

PubMed

Lin, Huiming; Fu, Bo; Qin, Guoyou; Zhu, Zhongyi

2017-12-01

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study. © 2017, The International Biometric Society.

Analysis of Operating Principles with S-system Models

PubMed Central

Lee, Yun; Chen, Po-Wei; Voit, Eberhard O.

2011-01-01

Operating principles address general questions regarding the response dynamics of biological systems as we observe or hypothesize them, in comparison to a priori equally valid alternatives. In analogy to design principles, the question arises: Why are some operating strategies encountered more frequently than others and in what sense might they be superior? It is at this point impossible to study operation principles in complete generality, but the work here discusses the important situation where a biological system must shift operation from its normal steady state to a new steady state. This situation is quite common and includes many stress responses. We present two distinct methods for determining different solutions to this task of achieving a new target steady state. Both methods utilize the property of S-system models within Biochemical Systems Theory (BST) that steady-states can be explicitly represented as systems of linear algebraic equations. The first method uses matrix inversion, a pseudo-inverse, or regression to characterize the entire admissible solution space. Operations on the basis of the solution space permit modest alterations of the transients toward the target steady state. The second method uses standard or mixed integer linear programming to determine admissible solutions that satisfy criteria of functional effectiveness, which are specified beforehand. As an illustration, we use both methods to characterize alternative response patterns of yeast subjected to heat stress, and compare them with observations from the literature. PMID:21377479

Application of Design Methodologies for Feedback Compensation Associated with Linear Systems

NASA Technical Reports Server (NTRS)

Smith, Monty J.

1996-01-01

The work that follows is concerned with the application of design methodologies for feedback compensation associated with linear systems. In general, the intent is to provide a well behaved closed loop system in terms of stability and robustness (internal signals remain bounded with a certain amount of uncertainty) and simultaneously achieve an acceptable level of performance. The approach here has been to convert the closed loop system and control synthesis problem into the interpolation setting. The interpolation formulation then serves as our mathematical representation of the design process. Lifting techniques have been used to solve the corresponding interpolation and control synthesis problems. Several applications using this multiobjective design methodology have been included to show the effectiveness of these techniques. In particular, the mixed H 2-H performance criteria with algorithm has been used on several examples including an F-18 HARV (High Angle of Attack Research Vehicle) for sensitivity performance.

Correlations in the degeneracy of structurally controllable topologies for networks

NASA Astrophysics Data System (ADS)

Campbell, Colin; Aucott, Steven; Ruths, Justin; Ruths, Derek; Shea, Katriona; Albert, Réka

2017-04-01

Many dynamic systems display complex emergent phenomena. By directly controlling a subset of system components (nodes) via external intervention it is possible to indirectly control every other component in the system. When the system is linear or can be approximated sufficiently well by a linear model, methods exist to identify the number and connectivity of a minimum set of external inputs (constituting a so-called minimal control topology, or MCT). In general, many MCTs exist for a given network; here we characterize a broad ensemble of empirical networks in terms of the fraction of nodes and edges that are always, sometimes, or never a part of an MCT. We study the relationships between the measures, and apply the methodology to the T-LGL leukemia signaling network as a case study. We show that the properties introduced in this report can be used to predict key components of biological networks, with potentially broad applications to network medicine.

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

The development of optimal control laws for orbiting tethered platform systems

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Woodard, S.; Juang, J.-N.

1986-01-01

A mathematical model of the open and closed loop in-orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Lagrangian formulation yields equations describing platform pitch, subsatellite tether-line swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

The development of optimal control laws for orbiting tethered platform systems

NASA Technical Reports Server (NTRS)

Bainum, P. M.

1986-01-01

A mathematical model of the open and closed loop in orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Langrangian formulation yields equations describing platform pitch, subsatellite tetherline swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

Supervised Learning for Dynamical System Learning.

PubMed

Hefny, Ahmed; Downey, Carlton; Gordon, Geoffrey J

2015-01-01

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L 1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

Optimal control theory (OWEM) applied to a helicopter in the hover and approach phase

NASA Technical Reports Server (NTRS)

Born, G. J.; Kai, T.

1975-01-01

A major difficulty in the practical application of linear-quadratic regulator theory is how to choose the weighting matrices in quadratic cost functions. The control system design with optimal weighting matrices was applied to a helicopter in the hover and approach phase. The weighting matrices were calculated to extremize the closed loop total system damping subject to constraints on the determinants. The extremization is really a minimization of the effects of disturbances, and interpreted as a compromise between the generalized system accuracy and the generalized system response speed. The trade-off between the accuracy and the response speed is adjusted by a single parameter, the ratio of determinants. By this approach an objective measure can be obtained for the design of a control system. The measure is to be determined by the system requirements.

Computing anticipatory systems with incursion and hyperincursion

NASA Astrophysics Data System (ADS)

Dubois, Daniel M.

1998-07-01

An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1)=F[…,x(t-1),x(t),x(t+1),…] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the Pearl-Verhulst map model: x(t+1)=a.x(t).[1-x(t)] is controlled by the following anticipatory incursive model: x(t+1)=a.x(t).[1-x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt=a.x(t).[1-x(t+1)]-x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and non-linear oscillators. The non-linear oscillator is based on the Lotka-Volterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability condition than the original differential equations without numerical instabilities. The linearisation of the incursive discrete non-linear Lotka-Volterra equation system gives rise to the classical harmonic oscillator. The incursive discretisation of the linear oscillator is similar to define backward and forward discrete derivatives. A generalized complex derivative is then considered and applied to the harmonic oscillator. Non-locality seems to be a property of anticipatory systems. With some mathematical assumption, the Schrödinger quantum equation is derived for a particle in a uniform potential. Finally an hyperincursive system is given in the case of a neural stack memory.

Characterizing driver-response relationships in marine pelagic ecosystems for improved ocean management.

PubMed

Hunsicker, Mary E; Kappel, Carrie V; Selkoe, Kimberly A; Halpern, Benjamin S; Scarborough, Courtney; Mease, Lindley; Amrhein, Alisan

2016-04-01

Scientists and resource managers often use methods and tools that assume ecosystem components respond linearly to environmental drivers and human stressors. However, a growing body of literature demonstrates that many relationships are-non-linear, where small changes in a driver prompt a disproportionately large ecological response. We aim to provide a comprehensive assessment of the relationships between drivers and ecosystem components to identify where and when non-linearities are likely to occur. We focused our analyses on one of the best-studied marine systems, pelagic ecosystems, which allowed us to apply robust statistical techniques on a large pool of previously published studies. In this synthesis, we (1) conduct a wide literature review on single driver-response relationships in pelagic systems, (2) use statistical models to identify the degree of non-linearity in these relationships, and (3) assess whether general patterns exist in the strengths and shapes of non-linear relationships across drivers. Overall we found that non-linearities are common in pelagic ecosystems, comprising at least 52% of all driver-response relation- ships. This is likely an underestimate, as papers with higher quality data and analytical approaches reported non-linear relationships at a higher frequency (on average 11% more). Consequently, in the absence of evidence for a linear relationship, it is safer to assume a relationship is non-linear. Strong non-linearities can lead to greater ecological and socioeconomic consequences if they are unknown (and/or unanticipated), but if known they may provide clear thresholds to inform management targets. In pelagic systems, strongly non-linear relationships are often driven by climate and trophodynamic variables but are also associated with local stressors, such as overfishing and pollution, that can be more easily controlled by managers. Even when marine resource managers cannot influence ecosystem change, they can use information about threshold responses to guide how other stressors are managed and to adapt to new ocean conditions. As methods to detect and reduce uncertainty around threshold values improve, managers will be able to better understand and account for ubiquitous non-linear relationships.

Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials

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

Gottwald, Fabian; Ivanov, Sergei D., E-mail: sergei.ivanov@uni-rostock.de; Kühn, Oliver

2016-04-28

The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy owing to its utmost simplicity. However, the applicability of the model to cases with anharmonic system potentials, as it is required for the description of realistic systems in solution, is questionable due to the presence of the invertibility problem [F. Gottwald et al., J. Phys. Chem. Lett. 6, 2722 (2015)] unless the system itself resembles the CL model form. This might well be the case at surfaces or in the solid regime, which we here confirm for a particularmore » example of an iodine molecule in the atomic argon environment under high pressure. For this purpose we extend the recently proposed Fourier method for parameterizing linear generalized Langevin dynamics [F. Gottwald et al., J. Chem. Phys. 142, 244110 (2015)] to the non-linear case based on the CL model and perform an extensive error analysis. In order to judge on the applicability of this model in advance, we give practical empirical criteria and discuss the effect of the potential renormalization term. The obtained results provide evidence that the CL model can be used for describing a potentially broad class of systems.« less

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

PubMed Central

Neri, Peter

2015-01-01

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components. PMID:26556758

Decentralised fixed modes of networked MIMO systems

NASA Astrophysics Data System (ADS)

Hao, Yuqing; Duan, Zhisheng; Chen, Guanrong

2018-04-01

In this paper, decentralised fixed modes (DFMs) of a networked system are studied. The network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. The effects of the network topology, the node-system dynamics, the external control inputs, and the inner interactions on the existence of DFMs for the whole networked system are investigated. A necessary and sufficient condition for networked multi-input/multi-output (MIMO) systems in a general topology to possess no DFMs is derived. For networked single-input/single-output (SISO) LTI systems in general as well as some typical topologies, some specific conditions for having no DFMs are established. It is shown that the existence of DFMs is an integrated result of the aforementioned relevant factors which cannot be decoupled into individual DFMs of the node-systems and the properties solely determined by the network topology.

The linear stability of the post-Newtonian triangular equilibrium in the three-body problem

NASA Astrophysics Data System (ADS)

Yamada, Kei; Tsuchiya, Takuya

2017-12-01

Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein-Infeld-Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations.

Building generalized inverses of matrices using only row and column operations

NASA Astrophysics Data System (ADS)

Stuart, Jeffrey

2010-12-01

Most students complete their first and only course in linear algebra with the understanding that a real, square matrix A has an inverse if and only if rref(A), the reduced row echelon form of A, is the identity matrix I n . That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix [A | I n ] to obtain [rref(A) | P], then the matrix A is invertible exactly when rref(A) = I n , in which case, P = A -1. Many students must wonder what happens when A is not invertible, and what information P conveys in that case. That question is, however, seldom answered in a first course. We show that investigating that question emphasizes the close relationships between matrix multiplication, elementary row operations, linear systems, and the four fundamental spaces associated with a matrix. More important, answering that question provides an opportunity to show students how mathematicians extend results by relaxing hypotheses and then exploring the strengths and limitations of the resulting generalization, and how the first relaxation found is often not the best relaxation to be found. Along the way, we introduce students to the basic properties of generalized inverses. Finally, our approach should fit within the time and topic constraints of a first course in linear algebra.

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control.

PubMed

Molnár, S; Gámez, M; López, I; Cabello, T

2013-08-01

Linear verticum-type control and observation systems have been introduced for modelling certain industrial systems, consisting of subsystems, vertically connected by certain state variables. Recently the concept of verticum-type observation systems and the corresponding observability condition have been extended by the authors to the nonlinear case. In the present paper the general concept of a nonlinear verticum-type control system is introduced, and a sufficient condition for local controllability to equilibrium is obtained. In addition to a usual linearization, the basic idea is a decomposition of the control of the whole system into the control of the subsystems. Starting from the integrated pest control model of Rafikov and Limeira (2012) and Rafikov et al. (2012), a nonlinear verticum-type model has been set up an equilibrium control is obtained. Furthermore, a corresponding bioeconomical problem is solved minimizing the total cost of integrated pest control (combining chemical control with a biological one). Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Linear and Non-Linear Dielectric Response of Periodic Systems from Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Umari, Paolo

2006-03-01

We present a novel approach that allows to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wavefunction, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence. The polarization is sampled through forward-walking. This approach has been validated for the case of the polarizability of an isolated hydrogen atom, and then applied to a periodic system. We then calculate the linear susceptibility and second-order hyper-susceptibility of molecular-hydrogen chains whith different bond-length alternations, and assess the quality of nodal surfaces derived from density-functional theory or from Hartree-Fock. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.P. Umari, A.J. Williamson, G. Galli, and N. MarzariPhys. Rev. Lett. 95, 207602 (2005).

Event-triggered fault detection for a class of discrete-time linear systems using interval observers.

PubMed

Zhang, Zhi-Hui; Yang, Guang-Hong

2017-05-01

This paper provides a novel event-triggered fault detection (FD) scheme for discrete-time linear systems. First, an event-triggered interval observer is proposed to generate the upper and lower residuals by taking into account the influence of the disturbances and the event error. Second, the robustness of the residual interval against the disturbances and the fault sensitivity are improved by introducing l 1 and H ∞ performances. Third, dilated linear matrix inequalities are used to decouple the Lyapunov matrices from the system matrices. The nonnegative conditions for the estimation error variables are presented with the aid of the slack matrix variables. This technique allows considering a more general Lyapunov function. Furthermore, the FD decision scheme is proposed by monitoring whether the zero value belongs to the residual interval. It is shown that the information communication burden is reduced by designing the event-triggering mechanism, while the FD performance can still be guaranteed. Finally, simulation results demonstrate the effectiveness of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Linear maps preserving maximal deviation and the Jordan structure of quantum systems

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

Hamhalter, Jan

2012-12-15

In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only onemore » numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Molnar.« less

Visual Tracking Using 3D Data and Region-Based Active Contours

DTIC Science & Technology

2016-09-28

adaptive control strategies which explicitly take uncertainty into account. Filtering methods ranging from the classical Kalman filters valid for...linear systems to the much more general particle filters also fit into this framework in a very natural manner. In particular, the particle filtering ...the number of samples required for accurate filtering increases with the dimension of the system noise. In our approach, we approximate curve

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Linear analysis of a force reflective teleoperator

NASA Technical Reports Server (NTRS)

Biggers, Klaus B.; Jacobsen, Stephen C.; Davis, Clark C.

1989-01-01

Complex force reflective teleoperation systems are often very difficult to analyze due to the large number of components and control loops involved. One mode of a force reflective teleoperator is described. An analysis of the performance of the system based on a linear analysis of the general full order model is presented. Reduced order models are derived and correlated with the full order models. Basic effects of force feedback and position feedback are examined and the effects of time delays between the master and slave are studied. The results show that with symmetrical position-position control of teleoperators, a basic trade off must be made between the intersystem stiffness of the teleoperator, and the impedance felt by the operator in free space.

1985 Particle Accelerator Conference: Accelerator Engineering and Technology, 11th, Vancouver, Canada, May 13-16, 1985, Proceedings

NASA Astrophysics Data System (ADS)

Strathdee, A.

1985-10-01

The topics discussed are related to high-energy accelerators and colliders, particle sources and electrostatic accelerators, controls, instrumentation and feedback, beam dynamics, low- and intermediate-energy circular accelerators and rings, RF and other acceleration systems, beam injection, extraction and transport, operations and safety, linear accelerators, applications of accelerators, radiation sources, superconducting supercolliders, new acceleration techniques, superconducting components, cryogenics, and vacuum. Accelerator and storage ring control systems are considered along with linear and nonlinear orbit theory, transverse and longitudinal instabilities and cures, beam cooling, injection and extraction orbit theory, high current dynamics, general beam dynamics, and medical and radioisotope applications. Attention is given to superconducting RF structures, magnet technology, superconducting magnets, and physics opportunities with relativistic heavy ion accelerators.

Estimation of group means when adjusting for covariates in generalized linear models.

PubMed

Qu, Yongming; Luo, Junxiang

2015-01-01

Generalized linear models are commonly used to analyze categorical data such as binary, count, and ordinal outcomes. Adjusting for important prognostic factors or baseline covariates in generalized linear models may improve the estimation efficiency. The model-based mean for a treatment group produced by most software packages estimates the response at the mean covariate, not the mean response for this treatment group for the studied population. Although this is not an issue for linear models, the model-based group mean estimates in generalized linear models could be seriously biased for the true group means. We propose a new method to estimate the group mean consistently with the corresponding variance estimation. Simulation showed the proposed method produces an unbiased estimator for the group means and provided the correct coverage probability. The proposed method was applied to analyze hypoglycemia data from clinical trials in diabetes. Copyright © 2014 John Wiley & Sons, Ltd.

Structure of 1-alkyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide ionic liquids with linear, branched, and cyclic alkyl groups.

PubMed

Kashyap, Hemant K; Santos, Cherry S; Murthy, N Sanjeeva; Hettige, Jeevapani J; Kerr, Kijana; Ramati, Sharon; Gwon, JinHee; Gohdo, Masao; Lall-Ramnarine, Sharon I; Wishart, James F; Margulis, Claudio J; Castner, Edward W

2013-12-12

X-ray scattering and molecular dynamics simulations have been carried out to investigate structural differences and similarities in the condensed phase between pyrrolidinium-based ionic liquids paired with the bis(trifluoromethylsulfonyl)amide (NTf2(-)) anion where the cationic tail is linear, branched, or cyclic. This is important in light of the charge and polarity type alternations that have recently been shown to be present in the case of liquids with cations of moderately long linear tails. For this study, we have chosen to use the 1-alkyl-1-methylpyrrolidinium, Pyrr(1,n(+)) with n = 5 or 7, as systems with linear tails, 1-(2-ethylhexyl)-1-methylpyrrolidinium, Pyrr(1,EtHx(+)), as a system with a branched tail, and 1-(cyclohexylmethyl)-1-methylpyrrolidinium, Pyrr(1,ChxMe(+)), as a system with a cyclic tail. We put these results into context by comparing these data with recently published results for the Pyrr(1,n(+))/NTf2(-) ionic liquids with n = 4, 6, 8, and 10.1,2 General methods for interpreting the structure function S(q) in terms of q-dependent natural partitionings are described. This allows for an in-depth analysis of the scattering data based on molecular dynamics (MD) trajectories that highlight the effect of modifying the cationic tail.

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L. C.

1984-01-01

AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

Baryonic Force for Accelerated Cosmic Expansion and Generalized U1b Gauge Symmetry in Particle-Cosmology

NASA Astrophysics Data System (ADS)

Khan, Mehbub; Hao, Yun; Hsu, Jong-Ping

2018-01-01

Based on baryon charge conservation and a generalized Yang-Mills symmetry for Abelian (and non-Abelian) groups, we discuss a new baryonic gauge field and its linear potential for two point-like baryon charges. The force between two point-like baryons is repulsive, extremely weak and independent of distance. However, for two extended baryonic systems, we have a dominant linear force α r. Thus, only in the later stage of the cosmic evolution, when two baryonic galaxies are separated by an extremely large distance, the new repulsive baryonic force can overcome the gravitational attractive force. Such a model provides a gauge-field-theoretic understanding of the late-time accelerated cosmic expansion. The baryonic force can be tested by measuring the accelerated Wu-Doppler frequency shifts of supernovae at different distances.

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

A new statistical method for transfer coefficient calculations in the framework of the general multiple-compartment model of transport for radionuclides in biological systems.

PubMed

Garcia, F; Arruda-Neto, J D; Manso, M V; Helene, O M; Vanin, V R; Rodriguez, O; Mesa, J; Likhachev, V P; Filho, J W; Deppman, A; Perez, G; Guzman, F; de Camargo, S P

1999-10-01

A new and simple statistical procedure (STATFLUX) for the calculation of transfer coefficients of radionuclide transport to animals and plants is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. By using experimentally available curves of radionuclide concentrations versus time, for each animal compartment (organs), flow parameters were estimated by employing a least-squares procedure, whose consistency is tested. Some numerical results are presented in order to compare the STATFLUX transfer coefficients with those from other works and experimental data.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Digital receiver study and implementation

NASA Technical Reports Server (NTRS)

Fogle, D. A.; Lee, G. M.; Massey, J. C.

1972-01-01

Computer software was developed which makes it possible to use any general purpose computer with A/D conversion capability as a PSK receiver for low data rate telemetry processing. Carrier tracking, bit synchronization, and matched filter detection are all performed digitally. To aid in the implementation of optimum computer processors, a study of general digital processing techniques was performed which emphasized various techniques for digitizing general analog systems. In particular, the phase-locked loop was extensively analyzed as a typical non-linear communication element. Bayesian estimation techniques for PSK demodulation were studied. A hardware implementation of the digital Costas loop was developed.

LIGO GW150914 and GW151226 gravitational wave detection and generalized gravitation theory (MOG)

NASA Astrophysics Data System (ADS)

Moffat, J. W.

2016-12-01

The nature of gravitational waves in a generalized gravitation theory is investigated. The linearized field equations and the metric tensor quadrupole moment power and the decrease in radius of an inspiralling binary system of two compact objects are derived. The generalized Kerr metric describing a spinning black hole is determined by its mass M and the spin parameter a = cS / GM2. The LIGO-Virgo collaboration data is fitted with smaller binary black hole masses in agreement with the current electromagnetic, observed X-ray binary upper bound for a black hole mass, M ≲ 10M⊙.

Generalizations of Tikhonov's regularized method of least squares to non-Euclidean vector norms

NASA Astrophysics Data System (ADS)

Volkov, V. V.; Erokhin, V. I.; Kakaev, V. V.; Onufrei, A. Yu.

2017-09-01

Tikhonov's regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by "instrumental" generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study.

PubMed

Nimmegeers, Philippe; Lauwers, Joost; Telen, Dries; Logist, Filip; Impe, Jan Van

2017-06-01

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a 'non-informative' and 'informative' experiment, which are heuristically designed. The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult. Copyright © 2017. Published by Elsevier Inc.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

PubMed Central

Bajaj, Chandrajit; Ihm, Insung; Min, Jungki; Oh, Jinsang

2009-01-01

The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of ȳ = Ax̄ + b̄, where A is a matrix, and x̄, ȳ and b̄ are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. PMID:19946569

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism

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

Yavari, M., E-mail: yavari@iaukashan.ac.ir

2016-06-15

We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.

Statistical methods for launch vehicle guidance, navigation, and control (GN&C) system design and analysis

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

[Subclinical hypothyroidism in obese children].

PubMed

Januszek-Trzciąkowska, Aleksandra; Małecka-Tendera, Ewa

2013-08-05

Subclinical hypothyroidism (SH) is defined as an elevated thyroid stimulating hormone (TSH) associated with normal levels of free thyroxine. In obese persons prevalence of SH is significantly higher than in general population. SH is of particular interest in children with respect to the crucial role of thyroid hormones in the development of central nervous system and linear growth. Currently there is no general consensus on the treatment of SH with L-tyroxine. It is suggested that this hormonal state is rather a consequence that the cause of the overweight status.

Neutron star dynamics under time-dependent external torques

NASA Astrophysics Data System (ADS)

Gügercinoǧlu, Erbil; Alpar, M. Ali

2017-11-01

The two-component model describes neutron star dynamics incorporating the response of the superfluid interior. Conventional solutions and applications involve constant external torques, as appropriate for radio pulsars on dynamical time-scales. We present the general solution of two-component dynamics under arbitrary time-dependent external torques, with internal torques that are linear in the rotation rates, or with the extremely non-linear internal torques due to vortex creep. The two-component model incorporating the response of linear or non-linear internal torques can now be applied not only to radio pulsars but also to magnetars and to neutron stars in binary systems, with strong observed variability and noise in the spin-down or spin-up rates. Our results allow the extraction of the time-dependent external torques from the observed spin-down (or spin-up) time series, \\dot{Ω }(t). Applications are discussed.

A motion-constraint logic for moving-base simulators based on variable filter parameters

NASA Technical Reports Server (NTRS)

Miller, G. K., Jr.

1974-01-01

A motion-constraint logic for moving-base simulators has been developed that is a modification to the linear second-order filters generally employed in conventional constraints. In the modified constraint logic, the filter parameters are not constant but vary with the instantaneous motion-base position to increase the constraint as the system approaches the positional limits. With the modified constraint logic, accelerations larger than originally expected are limited while conventional linear filters would result in automatic shutdown of the motion base. In addition, the modified washout logic has frequency-response characteristics that are an improvement over conventional linear filters with braking for low-frequency pilot inputs. During simulated landing approaches of an externally blown flap short take-off and landing (STOL) transport using decoupled longitudinal controls, the pilots were unable to detect much difference between the modified constraint logic and the logic based on linear filters with braking.

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1991-01-01

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Tunnel magnetoresistance and linear conductance of double quantum dots strongly coupled to ferromagnetic leads

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

Weymann, Ireneusz, E-mail: weymann@amu.edu.pl

2015-05-07

We analyze the spin-dependent linear-response transport properties of double quantum dots strongly coupled to external ferromagnetic leads. By using the numerical renormalization group method, we determine the dependence of the linear conductance and tunnel magnetoresistance on the degree of spin polarization of the leads and the position of the double dot levels. We focus on the transport regime where the system exhibits the SU(4) Kondo effect. It is shown that the presence of ferromagnets generally leads the suppression of the linear conductance due to the presence of an exchange field. Moreover, the exchange field gives rise to a transition frommore » the SU(4) to the orbital SU(2) Kondo effect. We also analyze the dependence of the tunnel magnetoresistance on the double dot levels' positions and show that it exhibits a very nontrivial behavior.« less

Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions

NASA Astrophysics Data System (ADS)

Stagner, L.; Heidbrink, W. W.

2017-09-01

Due to the usually complicated and anisotropic nature of the fast-ion distribution function, diagnostic velocity-space weight functions, which indicate the sensitivity of a diagnostic to different fast-ion velocities, are used to facilitate the analysis of experimental data. Additionally, when velocity-space weight functions are discretized, a linear equation relating the fast-ion density and the expected diagnostic signal is formed. In a technique known as velocity-space tomography, many measurements can be combined to create an ill-conditioned system of linear equations that can be solved using various computational methods. However, when velocity-space weight functions (which by definition ignore spatial dependencies) are used, velocity-space tomography is restricted, both by the accuracy of its forward model and also by the availability of spatially overlapping diagnostic measurements. In this work, we extend velocity-space weight functions to a full 6D generalized coordinate system and then show how to reduce them to a 3D orbit-space without loss of generality using an action-angle formulation. Furthermore, we show how diagnostic orbit-weight functions can be used to infer the full fast-ion distribution function, i.e., orbit tomography. In depth derivations of orbit weight functions for the neutron, neutral particle analyzer, and fast-ion D-α diagnostics are also shown.

Reformulating the Schrödinger equation as a Shabat-Zakharov system

NASA Astrophysics Data System (ADS)

Boonserm, Petarpa; Visser, Matt

2010-02-01

We reformulate the second-order Schrödinger equation as a set of two coupled first-order differential equations, a so-called "Shabat-Zakharov system" (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasize the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrödinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ordinary differential equation.

Aztec user`s guide. Version 1

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

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1995-10-01

Aztec is an iterative library that greatly simplifies the parallelization process when solving the linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. Aztec is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparsemore » unstructured matrices for parallel solution. Once the distributed matrix is created, computation can be performed on any of the parallel machines running Aztec: nCUBE 2, IBM SP2 and Intel Paragon, MPI platforms as well as standard serial and vector platforms. Aztec includes a number of Krylov iterative methods such as conjugate gradient (CG), generalized minimum residual (GMRES) and stabilized biconjugate gradient (BICGSTAB) to solve systems of equations. These Krylov methods are used in conjunction with various preconditioners such as polynomial or domain decomposition methods using LU or incomplete LU factorizations within subdomains. Although the matrix A can be general, the package has been designed for matrices arising from the approximation of partial differential equations (PDEs). In particular, the Aztec package is oriented toward systems arising from PDE applications.« less

A rigorous computational approach to linear response

NASA Astrophysics Data System (ADS)

Bahsoun, Wael; Galatolo, Stefano; Nisoli, Isaia; Niu, Xiaolong

2018-03-01

We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We apply our results to expanding circle maps. In particular, we present examples where we compute, up to a pre-specified error in the L∞ -norm, the response of expanding circle maps under stochastic and deterministic perturbations. Moreover, we present an example where we compute, up to a pre-specified error in the L 1-norm, the response of the intermittent family at the boundary; i.e. when the unperturbed system is the doubling map. This work was mainly conducted during a visit of SG to Loughborough University. WB and SG would like to thank The Leverhulme Trust for supporting mutual research visits through the Network Grant IN-2014-021. SG thanks the Department of Mathematical Sciences at Loughborough University for hospitality. WB thanks Dipartimento di Matematica, Universita di Pisa. The research of SG and IN is partially supported by EU Marie-Curie IRSES ‘Brazilian-European partnership in Dynamical Systems’ (FP7-PEOPLE-2012-IRSES 318999 BREUDS). IN was partially supported by CNPq and FAPERJ. IN would like to thank the Department of Mathematics at Uppsala University and the support of the KAW grant 2013.0315.

Application of a Non-linear Program to the Establishment of a Hub and Spoke System in Africa

DTIC Science & Technology

2010-06-01

barriers, religious fanaticism, and hostage taking (King, 1994). Perhaps the greatest impact on the history of Africa and its relations with the United......areas of commerce, light manufacturing, and the tourism industry (United States Department of State, 2009). Generally speaking, Kenya maintains a

Answer Markup Algorithms for Southeast Asian Languages.

ERIC Educational Resources Information Center

Henry, George M.

1991-01-01

Typical markup methods for providing feedback to foreign language learners are not applicable to languages not written in a strictly linear fashion. A modification of Hart's edit markup software is described, along with a second variation based on a simple edit distance algorithm adapted to a general Southeast Asian font system. (10 references)…

Symmetry Analysis of Gauge-Invariant Field Equations via a Generalized Harrison-Estabrook Formalism.

NASA Astrophysics Data System (ADS)

Papachristou, Costas J.

The Harrison-Estabrook formalism for the study of invariance groups of partial differential equations is generalized and extended to equations that define, through their solutions, sections on vector bundles of various kinds. Applications include the Dirac, Yang-Mills, and self-dual Yang-Mills (SDYM) equations. The latter case exhibits interesting connections between the internal symmetries of SDYM and the existence of integrability characteristics such as a linear ("inverse scattering") system and Backlund transformations (BT's). By "verticalizing" the generators of coordinate point transformations of SDYM, nine nonlocal, generalized (as opposed to local, point) symmetries are constructed. The observation is made that the prolongations of these symmetries are parametric BT's for SDYM. It is thus concluded that the entire point group of SDYM contributes, upon verticalization, BT's to the system.

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

A geometric approach to failure detection and identification in linear systems

NASA Technical Reports Server (NTRS)

Massoumnia, M. A.

1986-01-01

Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

NASA Astrophysics Data System (ADS)

Abramov, R. V.

2011-12-01

Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger chaotic system would result in general increase of chaos at the slow variables.

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains.

PubMed

Dudowicz, Jacek; Freed, Karl F

2012-02-14

The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations. © 2012 American Institute of Physics

Equicontrollability and the model following problem

NASA Technical Reports Server (NTRS)

Curran, R. T.

1971-01-01

Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.

Parallel dynamics between non-Hermitian and Hermitian systems

NASA Astrophysics Data System (ADS)

Wang, P.; Lin, S.; Jin, L.; Song, Z.

2018-06-01

We reveals a connection between non-Hermitian and Hermitian systems by studying the connection between a family of non-Hermitian and Hermitian Hamiltonians based on exact solutions. In general, for a dynamic process in a non-Hermitian system H , there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate system H†. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H , and we present the relations between {H ,H ,H†} .

Venus Chasmata: A Lithospheric Stretching Model

NASA Technical Reports Server (NTRS)

Solomon, S. C.; Head, J. W.

1985-01-01

An outstanding problem for Venus is the characterization of its style of global tectonics, an issue intimately related to the dominant mechanism of lithospheric heat loss. Among the most spectacular and extensive of the major tectonic features on Venus are the chasmata, deep linear valleys generally interpreted to be the products of lithospheric extension and rifting. Systems of chasmata and related features can be traced along several tectonic zones up to 20,000 km in linear extent. A lithospheric stretching model was developed to explain the topographic characteristics of Venus chasmata and to constrain the physical properties of the Venus crust and lithosphere.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, A. E.; Epton, M. A.

1981-01-01

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

An Ada Linear-Algebra Software Package Modeled After HAL/S

NASA Technical Reports Server (NTRS)

Klumpp, Allan R.; Lawson, Charles L.

1990-01-01

New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

Negative base encoding in optical linear algebra processors

NASA Technical Reports Server (NTRS)

Perlee, C.; Casasent, D.

1986-01-01

In the digital multiplication by analog convolution algorithm, the bits of two encoded numbers are convolved to form the product of the two numbers in mixed binary representation; this output can be easily converted to binary. Attention is presently given to negative base encoding, treating base -2 initially, and then showing that the negative base system can be readily extended to any radix. In general, negative base encoding in optical linear algebra processors represents a more efficient technique than either sign magnitude or 2's complement encoding, when the additions of digitally encoded products are performed in parallel.

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System: Algebraic Structures, Bäcklund Transformation and Hidden Structural Symmetries

NASA Astrophysics Data System (ADS)

Souleymanou, Abbagari; Thomas, B. Bouetou; Timoleon, C. Kofane

2013-08-01

The prolongation structure methodologies of Wahlquist—Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.

Classification and Evaluation of Coherent Synchronous Sampled-Data Telemetry Systems

NASA Technical Reports Server (NTRS)

Viterbi, Andrew

1961-01-01

This paper analyzes the various types of continuous wave and pulse modulation for the transmission of sampled data over channels perturbed by white gaussian noise. Optimal coherent synchronous detection schemes for all the different modulation methods are shown to belong to one of two general classes: linear synchronous detection and correlation detection. The figures of merit, mean-square signal-to-error ratio and bandwidth occupancy, are determined for each system and compared.

Dynamic System Coupler Program (DYSCO 4.1). Volume 1. Theoretical Manual

DTIC Science & Technology

1989-01-01

present analysis is as follows: 1. Triplet X, Y, Z represents an inertia frame, R. The R system coordinates are the rotor shaft axes when there is...small perturbation analysis . 2.5 3-D MODAL STRUCTURE - CFM3 A three-dimensional structure is represented as a linear combination of orth­ ogonal modes...Include rotor blade damage modeling, Elgen analysis development, general time history solution development, frequency domain solution development

Decision Support Systems: Theory.

DTIC Science & Technology

1976-01-01

Ko tt r, 1.. "Toward an Explicit Model for Media Selection," ,J. Advertising Res. 4, 14-41 , Mar. 1964. Kriebel, C. tt., "MIS Technology - A View of...Research Study of Sales Re- sponse to Advertising ," Opns. Res. 5, 370-381 ,1957. Von Bertalanffy, Ludwig , General Systems Theory. New York: George...Zangwill, W. I., " Media Slection by Decision Programming," J. Advertising Res. 5.30-36 , Sept. 1964. Zeleny, M., Linear Multiobjective Programming

Three-dimensional repositioning accuracy of semiadjustable articulator cast mounting systems.

PubMed

Tan, Ming Yi; Ung, Justina Youlin; Low, Ada Hui Yin; Tan, En En; Tan, Keson Beng Choon

2014-10-01

In spite of its importance in prosthesis precision and quality, the 3-dimensional repositioning accuracy of cast mounting systems has not been reported in detail. The purpose of this study was to quantify the 3-dimensional repositioning accuracy of 6 selected cast mounting systems. Five magnetic mounting systems were compared with a conventional screw-on system. Six systems on 3 semiadjustable articulators were evaluated: Denar Mark II with conventional screw-on mounting plates (DENSCR) and magnetic mounting system with converter plates (DENCON); Denar Mark 330 with in-built magnetic mounting system (DENMAG) and disposable mounting plates; and Artex CP with blue (ARTBLU), white (ARTWHI), and black (ARTBLA) magnetic mounting plates. Test casts with 3 high-precision ceramic ball bearings at the mandibular central incisor (Point I) and the right and left second molar (Point R; Point L) positions were mounted on 5 mounting plates (n=5) for all 6 systems. Each cast was repositioned 10 times by 4 operators in random order. Nine linear (Ix, Iy, Iz; Rx, Ry, Rz; Lx, Ly, Lz) and 3 angular (anteroposterior, mediolateral, twisting) displacements were measured with a coordinate measuring machine. The mean standard deviations of the linear and angular displacements defined repositioning accuracy. Anteroposterior linear repositioning accuracy ranged from 23.8 ±3.7 μm (DENCON) to 4.9 ±3.2 μm (DENSCR). Mediolateral linear repositioning accuracy ranged from 46.0 ±8.0 μm (DENCON) to 3.7 ±1.5 μm (ARTBLU), and vertical linear repositioning accuracy ranged from 7.2 ±9.6 μm (DENMAG) to 1.5 ±0.9 μm (ARTBLU). Anteroposterior angular repositioning accuracy ranged from 0.0084 ±0.0080 degrees (DENCON) to 0.0020 ±0.0006 degrees (ARTBLU), and mediolateral angular repositioning accuracy ranged from 0.0120 ±0.0111 degrees (ARTWHI) to 0.0027 ±0.0008 degrees (ARTBLU). Twisting angular repositioning accuracy ranged from 0.0419 ±0.0176 degrees (DENCON) to 0.0042 ±0.0038 degrees (ARTBLA). One-way ANOVA found significant differences (P<.05) among all systems for Iy, Ry, Lx, Ly, and twisting. Generally, vertical linear displacements were less likely to reach the threshold of clinical detectability compared with anteroposterior or mediolateral linear displacements. The overall repositioning accuracy of DENSCR was comparable with 4 magnetic mounting systems (DENMAG, ARTBLU, ARTWHI, ARTBLA). DENCON exhibited the worst repositioning accuracy for Iy, Ry, Lx, Ly, and twisting. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

Effects of biomotor structures on performance of competitive gymnastics elements in elementary school female sixth-graders.

PubMed

Delas, Suncica; Babin, Josip; Katić, Ratko

2007-12-01

In order to identify biomotor systems that determine performance of competitive gymnastics elements in elementary school female sixth-graders, factor structures of morphological characteristics and basic motor abilities were determined first, followed by relations of the morphological-motor system factors obtained with a set of criterion variables evaluating specific motor skills in competitive gymnastics in 126 female children aged 12 years +/- 3 months. Factor analysis of 17 morphological measures yielded three morphological factors: factor of mesoendomorphy and/or adipose body voluminosity; factor of longitudinal body dimensionality; and factor of transverse arm dimensionality. Factor analysis of 16 motor variables produced four motor factors: general motoricity factor (motor system); general speed factor; factor of explosive strength of throwing type (arm explosiveness); and factor of arm and leg flexibility. Three significant canonical correlations, i.e. linear combinations, explained the association between the set of seven latent variables of the morphological and basic motor system, and five variables evaluating the knowledge in competitive gymnastics. The first canonical linear combination was based on a favorable and predominant impact of the general motor factor (a system integrating whole body coordination, leg explosiveness, relative arm strength, arm movement frequency and body flexibility) on performance of gymnastics elements, cartwheel, handstand and backward pullover mount in particular, and to a lesser extent front scale and double leg pirouette for 180 degrees. The relation of the second pair of canonical factors additionally explained the role of transverse dimensionality of arm skeleton, arm flexibility and explosiveness in performing cartwheel and squat vault, whereas the relation of the third pair of canonical factors explained the unfavorable impact of adipose voluminosity on the performance of squat vault and backward pullover mount.

Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming

PubMed Central

Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian

2017-01-01

Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex systems. PMID:28072870

Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-06-01

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail since the operators cannot be diagonalized. The curse of nondiagonalizability also plays an important role even in finite-dimensional linear operators, leading to analytical impediments that occur across many scientific domains. We show how to circumvent it via two tracks. First, using the well-known holomorphic functional calculus, we develop new practical results about spectral projection operators and the relationship between left and right generalized eigenvectors. Second, we generalize the holomorphic calculus to a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. This simultaneously simplifies and generalizes functional calculus so that it is readily applicable to analyzing complex physical systems. Together, these results extend the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics arise, including memoryful stochastic processes, open nonunitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator, highlighting the special role of the zero eigenvalue. Furthermore, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a new general method to construct it. We provide new formulae for constructing spectral projection operators and delineate the relations among projection operators, eigenvectors, and left and right generalized eigenvectors. By way of illustrating its application, we explore several, rather distinct examples. First, we analyze stochastic transition operators in discrete and continuous time. Second, we show that nondiagonalizability can be a robust feature of a stochastic process, induced even by simple counting. As a result, we directly derive distributions of the time-dependent Poisson process and point out that nondiagonalizability is intrinsic to it and the broad class of hidden semi-Markov processes. Third, we show that the Drazin inverse arises naturally in stochastic thermodynamics and that applying the meromorphic functional calculus provides closed-form solutions for the dynamics of key thermodynamic observables. Finally, we draw connections to the Ruelle-Frobenius-Perron and Koopman operators for chaotic dynamical systems and propose how to extract eigenvalues from a time-series.

An Explicit Linear Filtering Solution for the Optimization of Guidance Systems with Statistical Inputs

NASA Technical Reports Server (NTRS)

Stewart, Elwood C.

1961-01-01

The determination of optimum filtering characteristics for guidance system design is generally a tedious process which cannot usually be carried out in general terms. In this report a simple explicit solution is given which is applicable to many different types of problems. It is shown to be applicable to problems which involve optimization of constant-coefficient guidance systems and time-varying homing type systems for several stationary and nonstationary inputs. The solution is also applicable to off-design performance, that is, the evaluation of system performance for inputs for which the system was not specifically optimized. The solution is given in generalized form in terms of the minimum theoretical error, the optimum transfer functions, and the optimum transient response. The effects of input signal, contaminating noise, and limitations on the response are included. From the results given, it is possible in an interception problem, for example, to rapidly assess the effects on minimum theoretical error of such factors as target noise and missile acceleration. It is also possible to answer important questions regarding the effect of type of target maneuver on optimum performance.

A case of "order insensitivity"? Natural and artificial language processing in a man with primary progressive aphasia.

PubMed

Zimmerer, Vitor C; Varley, Rosemary A

2015-08-01

Processing of linear word order (linear configuration) is important for virtually all languages and essential to languages such as English which have little functional morphology. Damage to systems underpinning configurational processing may specifically affect word-order reliant sentence structures. We explore order processing in WR, a man with primary progressive aphasia (PPA). In a previous report, we showed how WR showed impaired processing of actives, which rely strongly on word order, but not passives where functional morphology signals thematic roles. Using the artificial grammar learning (AGL) paradigm, we examined WR's ability to process order in non-verbal, visual sequences and compared his profile to that of healthy controls, and aphasic participants with and without severe syntactic disorder. Results suggested that WR, like some other patients with severe syntactic impairment, was unable to detect linear configurational structure. The data are consistent with the notion that disruption of possibly domain-general linearization systems differentially affects processing of active and passive sentence structures. Further research is needed to test this account, and we suggest hypotheses for future studies. Copyright © 2015 Elsevier Ltd. All rights reserved.

Metric versus observable operator representation, higher spin models

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-02-01

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

DOE PAGES

Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; ...

2016-01-06

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

NASA Technical Reports Server (NTRS)

Guo, Tong-Yi; Hwang, Chyi; Shieh, Leang-San

1994-01-01

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

An Approach to Stable Gradient-Descent Adaptation of Higher Order Neural Units.

PubMed

Bukovsky, Ivo; Homma, Noriyasu

2017-09-01

Stability evaluation of a weight-update system of higher order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on the spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring the stability of the weight-update system (at every single adaptation step) naturally results in the adaptation stability of the whole neural architecture that adapts to the target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.

Fast secant methods for the iterative solution of large nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Deuflhard, Peter; Freund, Roland; Walter, Artur

1990-01-01

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times.

PubMed

Molenaar, Dylan; Tuerlinckx, Francis; van der Maas, Han L J

2015-01-01

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.

Evaluation of a Nonlinear Finite Element Program - ABAQUS.

DTIC Science & Technology

1983-03-15

anisotropic properties. * MATEXP - Linearly elastic thermal expansions with isotropic, orthotropic and anisotropic properties. * MATELG - Linearly...elastic materials for general sections (options available for beam and shell elements). • MATEXG - Linearly elastic thermal expansions for general...decomposition of a matrix. * Q-R algorithm • Vector normalization, etc. Obviously, by consolidating all the utility subroutines in a library, ABAQUS has

Linear quadratic servo control of a reusable rocket engine

NASA Technical Reports Server (NTRS)

Musgrave, Jeffrey L.

1991-01-01

The paper deals with the development of a design method for a servo component in the frequency domain using singular values and its application to a reusable rocket engine. A general methodology used to design a class of linear multivariable controllers for intelligent control systems is presented. Focus is placed on performance and robustness characteristics, and an estimator design performed in the framework of the Kalman-filter formalism with emphasis on using a sensor set different from the commanded values is discussed. It is noted that loop transfer recovery modifies the nominal plant noise intensities in order to obtain the desired degree of robustness to uncertainty reflected at the plant input. Simulation results demonstrating the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation are discussed.

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

2012-10-01

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.

On the stabilization of decentralized control systems.

NASA Technical Reports Server (NTRS)

Wang, S.-H.; Davison, E. J.

1973-01-01

This paper considers the problem of stabilizing a linear time-variant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called fixed modes, which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given.

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

Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

NASA Astrophysics Data System (ADS)

Zhao, Liang; Healy, John J.; Muniraj, Inbarasan; Cui, Xiao-Guang; Malallah, Ra'ed; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

Massive parallelization of serial inference algorithms for a complex generalized linear model

PubMed Central

Suchard, Marc A.; Simpson, Shawn E.; Zorych, Ivan; Ryan, Patrick; Madigan, David

2014-01-01

Following a series of high-profile drug safety disasters in recent years, many countries are redoubling their efforts to ensure the safety of licensed medical products. Large-scale observational databases such as claims databases or electronic health record systems are attracting particular attention in this regard, but present significant methodological and computational concerns. In this paper we show how high-performance statistical computation, including graphics processing units, relatively inexpensive highly parallel computing devices, can enable complex methods in large databases. We focus on optimization and massive parallelization of cyclic coordinate descent approaches to fit a conditioned generalized linear model involving tens of millions of observations and thousands of predictors in a Bayesian context. We find orders-of-magnitude improvement in overall run-time. Coordinate descent approaches are ubiquitous in high-dimensional statistics and the algorithms we propose open up exciting new methodological possibilities with the potential to significantly improve drug safety. PMID:25328363

An approximate generalized linear model with random effects for informative missing data.

PubMed

Follmann, D; Wu, M

1995-03-01

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

High-Dimensional Quantum Information Processing with Linear Optics

NASA Astrophysics Data System (ADS)

Fitzpatrick, Casey A.

Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for carrying out quantum walks on arbitrary graph structures, a powerful tool for any quantum computer. It is shown that the novel architecture provides new, efficient capabilities for the optical quantum simulation of Hamiltonians and topologically protected states. Further, these simulations use exponentially fewer resources than feedforward techniques, scale linearly to higher-dimensional systems, and use only linear optics, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

The standard calibration instrument automation system for the atomic absorption spectrophotometer. Part 3: Program documentation

NASA Astrophysics Data System (ADS)

Ryan, D. P.; Roth, G. S.

1982-04-01

Complete documentation of the 15 programs and 11 data files of the EPA Atomic Absorption Instrument Automation System is presented. The system incorporates the following major features: (1) multipoint calibration using first, second, or third degree regression or linear interpolation, (2) timely quality control assessments for spiked samples, duplicates, laboratory control standards, reagent blanks, and instrument check standards, (3) reagent blank subtraction, and (4) plotting of calibration curves and raw data peaks. The programs of this system are written in Data General Extended BASIC, Revision 4.3, as enhanced for multi-user, real-time data acquisition. They run in a Data General Nova 840 minicomputer under the operating system RDOS, Revision 6.2. There is a functional description, a symbol definitions table, a functional flowchart, a program listing, and a symbol cross reference table for each program. The structure of every data file is also detailed.

Drainage-system development in consecutive melt seasons at a polythermal, Arctic glacier, evaluated by flow-recession analysis and linear-reservoir simulation.

PubMed

Hodgkins, Richard; Cooper, Richard; Tranter, Martyn; Wadham, Jemma

2013-07-26

[1] The drainage systems of polythermal glaciers play an important role in high-latitude hydrology, and are determinants of ice flow rate. Flow-recession analysis and linear-reservoir simulation of runoff time series are here used to evaluate seasonal and inter-annual variability in the drainage system of the polythermal Finsterwalderbreen, Svalbard, in 1999 and 2000. Linear-flow recessions are pervasive, with mean coefficients of a fast reservoir varying from 16 (1999) to 41 h (2000), and mean coefficients of an intermittent, slow reservoir varying from 54 (1999) to 114 h (2000). Drainage-system efficiency is greater overall in the first of the two seasons, the simplest explanation of which is more rapid depletion of the snow cover. Reservoir coefficients generally decline during each season (at 0.22 h d -1 in 1999 and 0.52 h d -1 in 2000), denoting an increase in drainage efficiency. However, coefficients do not exhibit a consistent relationship with discharge. Finsterwalderbreen therefore appears to behave as an intermediate case between temperate glaciers and other polythermal glaciers with smaller proportions of temperate ice. Linear-reservoir runoff simulations exhibit limited sensitivity to a relatively wide range of reservoir coefficients, although the use of fixed coefficients in a spatially lumped model can generate significant subseasonal error. At Finsterwalderbreen, an ice-marginal channel with the characteristics of a fast reservoir, and a subglacial upwelling with the characteristics of a slow reservoir, both route meltwater to the terminus. This suggests that drainage-system components of significantly contrasting efficiencies can coexist spatially and temporally at polythermal glaciers.

White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

PubMed Central

Lipson, E D

1975-01-01

The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model. PMID:1203444

Resultant as the determinant of a Koszul complex

NASA Astrophysics Data System (ADS)

Anokhina, A. S.; Morozov, A. Yu.; Shakirov, Sh. R.

2009-09-01

The determinant is a very important characteristic of a linear map between vector spaces. Two generalizations of linear maps are intensively used in modern theory: linear complexes (nilpotent chains of linear maps) and nonlinear maps. The determinant of a complex and the resultant are then the corresponding generalizations of the determinant of a linear map. It turns out that these two quantities are related: the resultant of a nonlinear map is the determinant of the corresponding Koszul complex. We give an elementary introduction into these notions and relations, which will definitely play a role in the future development of theoretical physics.

FAST TRACK COMMUNICATION: Quantization over boson operator spaces

NASA Astrophysics Data System (ADS)

Prosen, Tomaž; Seligman, Thomas H.

2010-10-01

The framework of third quantization—canonical quantization in the Liouville space—is developed for open many-body bosonic systems. We show how to diagonalize the quantum Liouvillean for an arbitrary quadratic n-boson Hamiltonian with arbitrary linear Lindblad couplings to the baths and, as an example, explicitly work out a general case of a single boson.

Applications of Random Differential Equations to Engineering Science. Wave Propagation in Turbulent Media and Random Linear Hyperbolic Systems.

DTIC Science & Technology

1981-11-10

1976), 745-754. 4. (with W. C. Tam) Periodic and traveling wave solutions to Volterra - Lotka equation with diffusion. Bull. Math. Biol. 38 (1976), 643...with applications [17,19,20). (5) A general method for reconstructing the mutual coherent function of a static or moving source from the random

Dynamical Analysis in the Mathematical Modelling of Human Blood Glucose

ERIC Educational Resources Information Center

Bae, Saebyok; Kang, Byungmin

2012-01-01

We want to apply the geometrical method to a dynamical system of human blood glucose. Due to the educational importance of model building, we show a relatively general modelling process using observational facts. Next, two models of some concrete forms are analysed in the phase plane by means of linear stability, phase portrait and vector…

Mathematics. Unit 6: A Core Curriculum of Related Instruction for Apprentices.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Occupational and Career Curriculum Development.

The mathematics unit is presented to assist apprentices to acquire a general knowledge of mathematic skills. The unit consists of nine modules: (1) basic addition, subtraction, multiplication, and division; (2) conventional linear measure; (3) using the metric system, (4) steps to take in solving problems, (5) how to calculate areas and volumes,…

Spinning particle and gauge theories as integrability conditions

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

Starting from a new four dimensional spinning point particle we obtain new representations of the standard four dimensional gauge field equations in terms of a generalized space (Minkowski + light cone). In terms of this new formulation we define linear systems whose integrability conditions imply the massive Dirac-Maxwell and the Yang-Mills equations. Research supported by the Rothschild Fellowship.

General magnetic transition dipole moments for electron paramagnetic resonance.

PubMed

Nehrkorn, Joscha; Schnegg, Alexander; Holldack, Karsten; Stoll, Stefan

2015-01-09

We present general expressions for the magnetic transition rates in electron paramagnetic resonance (EPR) experiments of anisotropic spin systems in the solid state. The expressions apply to general spin centers and arbitrary excitation geometry (Voigt, Faraday, and intermediate). They work for linear and circular polarized as well as unpolarized excitation, and for crystals and powders. The expressions are based on the concept of the (complex) magnetic transition dipole moment vector. Using the new theory, we determine the parities of ground and excited spin states of high-spin (S=5/2) Fe(III) in hemin from the polarization dependence of experimental EPR line intensities.

Verifying Stability of Dynamic Soft-Computing Systems

NASA Technical Reports Server (NTRS)

Wen, Wu; Napolitano, Marcello; Callahan, John

1997-01-01

Soft computing is a general term for algorithms that learn from human knowledge and mimic human skills. Example of such algorithms are fuzzy inference systems and neural networks. Many applications, especially in control engineering, have demonstrated their appropriateness in building intelligent systems that are flexible and robust. Although recent research have shown that certain class of neuro-fuzzy controllers can be proven bounded and stable, they are implementation dependent and difficult to apply to the design and validation process. Many practitioners adopt the trial and error approach for system validation or resort to exhaustive testing using prototypes. In this paper, we describe our on-going research towards establishing necessary theoretic foundation as well as building practical tools for the verification and validation of soft-computing systems. A unified model for general neuro-fuzzy system is adopted. Classic non-linear system control theory and recent results of its applications to neuro-fuzzy systems are incorporated and applied to the unified model. It is hoped that general tools can be developed to help the designer to visualize and manipulate the regions of stability and boundedness, much the same way Bode plots and Root locus plots have helped conventional control design and validation.

Using Linear and Quadratic Functions to Teach Number Patterns in Secondary School

ERIC Educational Resources Information Center

Kenan, Kok Xiao-Feng

2017-01-01

This paper outlines an approach to definitively find the general term in a number pattern, of either a linear or quadratic form, by using the general equation of a linear or quadratic function. This approach is governed by four principles: (1) identifying the position of the term (input) and the term itself (output); (2) recognising that each…

Microprocessor based implementation of attitude and shape control of large space structures

NASA Technical Reports Server (NTRS)

Reddy, A. S. S. R.

1984-01-01

The feasibility of off the shelf eight bit and 16 bit microprocessors to implement linear state variable feedback control laws and assessing the real time response to spacecraft dynamics is studied. The complexity of the dynamic model is described along with the appropriate software. An experimental setup of a beam, microprocessor system for implementing the control laws and the needed generalized software to implement any state variable feedback control system is included.

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

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

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

Rise time analysis of pulsed klystron-modulator for efficiency improvement of linear colliders

NASA Astrophysics Data System (ADS)

Oh, J. S.; Cho, M. H.; Namkung, W.; Chung, K. H.; Shintake, T.; Matsumoto, H.

2000-04-01

In linear accelerators, the periods during the rise and fall of a klystron-modulator pulse cannot be used to generate RF power. Thus, these periods need to be minimized to get high efficiency, especially in large-scale machines. In this paper, we present a simplified and generalized voltage rise time function of a pulsed modulator with a high-power klystron load using the equivalent circuit analysis method. The optimum pulse waveform is generated when this pulsed power system is tuned with a damping factor of ˜0.85. The normalized rise time chart presented in this paper allows one to predict the rise time and pulse shape of the pulsed power system in general. The results can be summarized as follows: The large distributed capacitance in the pulse tank and operating parameters, Vs× Tp , where Vs is load voltage and Tp is the pulse width, are the main factors determining the pulse rise time in the high-power RF system. With an RF pulse compression scheme, up to ±3% ripple of the modulator voltage is allowed without serious loss of compressor efficiency, which allows the modulator efficiency to be improved as well. The wiring inductance should be minimized to get the fastest rise time.

Explicitly-correlated Gaussian geminals in electronic structure calculations

NASA Astrophysics Data System (ADS)

Szalewicz, Krzysztof; Jeziorski, Bogumił

2010-11-01

Explicitly correlated functions have been used since 1929, but initially only for two-electron systems. In 1960, Boys and Singer showed that if the correlating factor is of Gaussian form, many-electron integrals can be computed for general molecules. The capability of explicitly correlated Gaussian (ECG) functions to accurately describe many-electron atoms and molecules was demonstrated only in the early 1980s when Monkhorst, Zabolitzky and the present authors cast the many-body perturbation theory (MBPT) and coupled cluster (CC) equations as a system of integro-differential equations and developed techniques of solving these equations with two-electron ECG functions (Gaussian-type geminals, GTG). This work brought a new accuracy standard to MBPT/CC calculations. In 1985, Kutzelnigg suggested that the linear r 12 correlating factor can also be employed if n-electron integrals, n > 2, are factorised with the resolution of identity. Later, this factor was replaced by more general functions f (r 12), most often by ? , usually represented as linear combinations of Gaussian functions which makes the resulting approach (called F12) a special case of the original GTG expansion. The current state-of-art is that, for few-electron molecules, ECGs provide more accurate results than any other basis available, but for larger systems the F12 approach is the method of choice, giving significant improvements over orbital calculations.

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

NASA Astrophysics Data System (ADS)

Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.

2012-08-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

Continuum analogues of contragredient Lie algebras (Lie algebras with a Cartan operator and nonlinear dynamical systems)

NASA Astrophysics Data System (ADS)

Saveliev, M. V.; Vershik, A. M.

1989-12-01

We present an axiomatic formulation of a new class of infinitedimensional Lie algebras-the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras “continuum Lie algebras.” The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered.

Component-Level Tuning of Kinematic Features from Composite Therapist Impressions of Movement Quality

PubMed Central

Venkataraman, Vinay; Turaga, Pavan; Baran, Michael; Lehrer, Nicole; Du, Tingfang; Cheng, Long; Rikakis, Thanassis; Wolf, Steven L.

2016-01-01

In this paper, we propose a general framework for tuning component-level kinematic features using therapists’ overall impressions of movement quality, in the context of a Home-based Adaptive Mixed Reality Rehabilitation (HAMRR) system. We propose a linear combination of non-linear kinematic features to model wrist movement, and propose an approach to learn feature thresholds and weights using high-level labels of overall movement quality provided by a therapist. The kinematic features are chosen such that they correlate with the quality of wrist movements to clinical assessment scores. Further, the proposed features are designed to be reliably extracted from an inexpensive and portable motion capture system using a single reflective marker on the wrist. Using a dataset collected from ten stroke survivors, we demonstrate that the framework can be reliably used for movement quality assessment in HAMRR systems. The system is currently being deployed for large-scale evaluations, and will represent an increasingly important application area of motion capture and activity analysis. PMID:25438331

GPU computing with Kaczmarz’s and other iterative algorithms for linear systems

PubMed Central

Elble, Joseph M.; Sahinidis, Nikolaos V.; Vouzis, Panagiotis

2009-01-01

The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradient-accelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out of favor for solving such problems, for the problems studied in this paper, the CGNR method implemented on the GPU performed better than the other methods, including a cluster implementation of the CARP-CG method. PMID:20526446

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 2, Part 2: Appendixes B, C, D and E

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

The derivation of the equations is presented, the rate control algorithm described, and simulation methodologies summarized. A set of dynamics equations that can be used recursively to calculate forces and torques acting at the joints of an n link manipulator given the manipulator joint rates are derived. The equations are valid for any n link manipulator system with any kind of joints connected in any sequence. The equations of motion for the class of manipulators consisting of n rigid links interconnected by rotary joints are derived. A technique is outlined for reducing the system of equations to eliminate contraint torques. The linearized dynamics equations for an n link manipulator system are derived. The general n link linearized equations are then applied to a two link configuration. The coordinated rate control algorithm used to compute individual joint rates when given end effector rates is described. A short discussion of simulation methodologies is presented.

On the validity of Zeeman's classification for three dimensional competitive differential equations with linearly determined nullclines

NASA Astrophysics Data System (ADS)

Jiang, Jifa; Niu, Lei

2017-12-01

We study three dimensional competitive differential equations with linearly determined nullclines and prove that they always have 33 stable nullcline classes in total. Each class is given in terms of inequalities on the intrinsic growth rates and competitive coefficients and is independent of generating functions. The common characteristics are that every trajectory converges to an equilibrium in classes 1-25, that Hopf bifurcations do not occur within class 32, and that there is always a heteroclinic cycle in class 27. Nontrivial dynamical behaviors, such as the existence and multiplicity of limit cycles, only may occur in classes 26-33, but these nontrivial dynamical behaviors depend on generating functions. We show that Hopf bifurcation can occur within each of classes 26-31 for continuous-time Leslie/Gower system and Ricker system, the same as Lotka-Volterra system; but it only occurs in classes 26 and 27 for continuous-time Atkinson/Allen system and Gompertz system. There is an apparent distinction between Lotka-Volterra system and Leslie/Gower system, Ricker system, Atkinson/Allen system, and Gompertz system with the identical growth rate. Lotka-Volterra system with the identical growth rate has no limit cycle, but admits a center on the carrying simplex in classes 26 and 27. But Leslie/Gower system, Ricker system, Atkinson/Allen system, and Gompertz system with the identical growth rate do possess limit cycles. At last, we provide examples to show that Leslie/Gower system and Ricker system can also admit two limit cycles. This general classification greatly widens applications of Zeeman's method and makes it possible to investigate the existence and multiplicity of limit cycles, centers and stability of heteroclinic cycles for three dimensional competitive systems with linearly determined nullclines, as done in planar systems.

A survey of packages for large linear systems

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

Wu, Kesheng; Milne, Brent

2000-02-11

This paper evaluates portable software packages for the iterative solution of very large sparse linear systems on parallel architectures. While we cannot hope to tell individual users which package will best suit their needs, we do hope that our systematic evaluation provides essential unbiased information about the packages and the evaluation process may serve as an example on how to evaluate these packages. The information contained here include feature comparisons, usability evaluations and performance characterizations. This review is primarily focused on self-contained packages that can be easily integrated into an existing program and are capable of computing solutions to verymore » large sparse linear systems of equations. More specifically, it concentrates on portable parallel linear system solution packages that provide iterative solution schemes and related preconditioning schemes because iterative methods are more frequently used than competing schemes such as direct methods. The eight packages evaluated are: Aztec, BlockSolve,ISIS++, LINSOL, P-SPARSLIB, PARASOL, PETSc, and PINEAPL. Among the eight portable parallel iterative linear system solvers reviewed, we recommend PETSc and Aztec for most application programmers because they have well designed user interface, extensive documentation and very responsive user support. Both PETSc and Aztec are written in the C language and are callable from Fortran. For those users interested in using Fortran 90, PARASOL is a good alternative. ISIS++is a good alternative for those who prefer the C++ language. Both PARASOL and ISIS++ are relatively new and are continuously evolving. Thus their user interface may change. In general, those packages written in Fortran 77 are more cumbersome to use because the user may need to directly deal with a number of arrays of varying sizes. Languages like C++ and Fortran 90 offer more convenient data encapsulation mechanisms which make it easier to implement a clean and intuitive user interface. In addition to reviewing these portable parallel iterative solver packages, we also provide a more cursory assessment of a range of related packages, from specialized parallel preconditioners to direct methods for sparse linear systems.« less

Unification of the general non-linear sigma model and the Virasoro master equation

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

Boer, J. de; Halpern, M.B.

1997-06-01

The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfymore » the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.« less

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

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.

Linear response theory for a pseudo-Hermitian system-reservoir interaction

NASA Astrophysics Data System (ADS)

Duarte, O. S.; Luiz, F. S.; Moussa, M. H. Y.

2018-03-01

We present here an extension of the Caldeira-Leggett linear response model considering a pseudo-Hermitian PT} -symmetric system-reservoir interaction. Our generalized Feynman-Vernon functional, derived from the PT} -symmetric coupling, accounts for two influence channels: a velocity-dependent one, which can act in reverse, providing energy to the system instead of draining it as usual, and an acceleration-dependent drain, analogue to the radiation-emission process. Therefore, an adequate choice of the Hamiltonian's parameters may allow the system to extract energy from the reservoir even at absolute zero for a period that may be much longer than the characteristic relaxation time. After this energy supply, the system is driven to a steady state whose energy is necessarily higher than the thermodynamic equilibrium energy due to the velocity-dependent pump. This heating mechanism of the system is more pronounced the more distant from the hermiticity is its coupling with the reservoir. An analytical derivation of the high-temperature master equation is provided helping us to better understand the whole scenario and to compute the associated relaxation and decoherence rates.

A General Accelerated Degradation Model Based on the Wiener Process.

PubMed

Liu, Le; Li, Xiaoyang; Sun, Fuqiang; Wang, Ning

2016-12-06

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

A General Accelerated Degradation Model Based on the Wiener Process

PubMed Central

Liu, Le; Li, Xiaoyang; Sun, Fuqiang; Wang, Ning

2016-01-01

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses. PMID:28774107

Clusters in nonsmooth oscillator networks

NASA Astrophysics Data System (ADS)

Nicks, Rachel; Chambon, Lucie; Coombes, Stephen

2018-03-01

For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory, this approach has recently been extended to treat more general cluster states. However, the MSF and its generalizations require the determination of a set of Floquet multipliers from variational equations obtained by linearization around a periodic orbit. Since closed form solutions for periodic orbits are invariably hard to come by, the framework is often explored using numerical techniques. Here, we show that further insight into network dynamics can be obtained by focusing on piecewise linear (PWL) oscillator models. Not only do these allow for the explicit construction of periodic orbits, their variational analysis can also be explicitly performed. The price for adopting such nonsmooth systems is that many of the notions from smooth dynamical systems, and in particular linear stability, need to be modified to take into account possible jumps in the components of Jacobians. This is naturally accommodated with the use of saltation matrices. By augmenting the variational approach for studying smooth dynamical systems with such matrices we show that, for a wide variety of networks that have been used as models of biological systems, cluster states can be explicitly investigated. By way of illustration, we analyze an integrate-and-fire network model with event-driven synaptic coupling as well as a diffusively coupled network built from planar PWL nodes, including a reduction of the popular Morris-Lecar neuron model. We use these examples to emphasize that the stability of network cluster states can depend as much on the choice of single node dynamics as it does on the form of network structural connectivity. Importantly, the procedure that we present here, for understanding cluster synchronization in networks, is valid for a wide variety of systems in biology, physics, and engineering that can be described by PWL oscillators.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

A tensor approach to modeling of nonhomogeneous nonlinear systems

NASA Technical Reports Server (NTRS)

Yurkovich, S.; Sain, M.

1980-01-01

Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.

General Results in Optimal Control of Discrete-Time Nonlinear Stochastic Systems

DTIC Science & Technology

1988-01-01

P. J. McLane, "Optimal Stochastic Control of Linear System. with State- and Control-Dependent Distur- bances," ZEEE Trans. 4uto. Contr., Vol. 16, No...Vol. 45, No. 1, pp. 359-362, 1987 (9] R. R. Mohler and W. J. Kolodziej, "An Overview of Stochastic Bilinear Control Processes," ZEEE Trans. Syst...34 J. of Math. anal. App.:, Vol. 47, pp. 156-161, 1974 [14) E. Yaz, "A Control Scheme for a Class of Discrete Nonlinear Stochastic Systems," ZEEE Trans

Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

DOE PAGES

Hatch, D. R.; Jenko, F.; Navarro, A. Banon; ...

2016-07-26

A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest inmore » the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.« less

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

Optical Manipulation with Plasmonic Beam Shaping Antenna Structures

DOE PAGES

Jun, Young Chul; Brener, Igal

2012-01-01

Near-field optical trapping of objects using plasmonic antenna structures has recently attracted great attention. However, metal nanostructures also provide a compact platform for general wavefront engineering of intermediate and far-field beams. Here, we analyze optical forces generated by plasmonic beam shaping antenna structures and show that they can be used for general optical manipulation such as guiding of a dielectric particle along a linear or curved trajectory. This removes the need for bulky diffractive optical components and facilitates the integration of optical force manipulation into a highly functional, compact system.

Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

NASA Astrophysics Data System (ADS)

Rossani, A.; Scarfone, A. M.

2009-06-01

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.

Fiber optic sensors and systems at the Federal University of Rio de Janeiro

NASA Astrophysics Data System (ADS)

Werneck, Marcelo M.; dos Santos, Paulo A. M.; Ferreira, Aldo P.; Maggi, Luis E.; de Carvalho, Carlos R., Jr.; Ribeiro, R. M.

1998-08-01

As widely known, fiberoptics (FO) are being used in a large variety of sensors and systems particularly for their small dimensions and low cost, large bandwidth and favorable dielectric properties. These properties have allowed us to develop sensors and systems for general applications and, particularly, for biomedical engineering. The intravascular pressure sensor was designed for small dimensions and high bandwidth. The system is based on light-intensity modulation technique and uses a 2 mm-diameter elastomer membrane as the sensor element and a pigtailed laser as a light source. The optical power output curve was linear for pressures within the range of 0 to 300 mmHg. The real time optical biosensor uses the evanescent field technique for monitoring Escherichia coli growth in culture media. The optical biosensor monitors interactions between the analytic (bacteria) and the evanescent field of an optical fiber passing through it. The FO based high voltage and current sensor is a measuring system designed for monitoring voltage and current in high voltage transmission lines. The linearity of the system is better than 2% in both ranges of 0 to 25 kV and 0 to 1000 A. The optical flowmeter uses a cross-correlation technique that analyses two light beams crossing the flow separated by a fixed distance. The x-ray image sensor uses a scintillating FO array, one FO for each image pixel to form an image of the x-ray field. The systems described in these paper use general-purpose components including optical fibers and optoelectronic devices, which are readily available, and of low cost.

Research progress in fiber optic sensors and systems at the Federal University of Rio de Janeiro

NASA Astrophysics Data System (ADS)

Werneck, Marcelo M.; Ferreira, Aldo P.; Maggi, Luis E.; De Carvalho, C. C.; Ribeiro, R. M.

1999-02-01

As widely known, fiberoptics (FO) are being used in a large variety of sensor an systems particularly for their small dimensions and low cost, large bandwidth and favorable dielectric properties. These properties have allowed us to develop sensor and systems for general applications and, particularly, for biomedical engineering. The intravasculator pressure sensor was designed for small dimensions and high bandwidth. The system is based on light- intensity modulation technique and use a 2 mm-diameter elastomer membrane as the sensor element and a pigtailed laser as a light source. The optical power out put curve was linear for pressures within the range of 0 to 300 mmHg. The real time optical biosensor uses the evanescent field technique for monitoring Escherichia coli growth in culture media. The optical biosensor monitors interactions between the analytic and the evanescent field of an optical fiber passing through it. The FO based high voltage and current sensor is a measuring system designed for monitoring voltage and current in high voltage transmission lines. The linearity of the system is better than 2 percent in both ranges of 0 to 25 kV and 0 to 1000 A. The optical flowmeter uses a cross-correlation technique that analyzes two light beams crossing the flow separated by a fixed distance. The x-ray image sensor uses a scintillating FO array, one FO for each image pixel to form an image of the x-ray field. The systems described in this paper use general-purpose components including optical fibers and optoelectronic devices, which are readily available, and of low cost.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Generalized topology for resonators having N commensurate harmonics

NASA Astrophysics Data System (ADS)

Danzi, Francesco; Gibert, James M.; Frulla, Giacomo; Cestino, Enrico

2018-04-01

Despite the ubiquity of both linear and nonlinear multimember resonators in MEMS and kinetic energy harvesting devices very few research efforts examine the orientation of members in the resonator on its dynamic behavior. Previous efforts to design this type of resonator constrains the members to have relative orientations that are 0○ or 90○ to each other, i.e., the elements are connected inline with adjoining members or are perpendicular to adjoining members. The work expands upon the existing body of research by considering the effect of the relative orientation between members on the dynamic behavior of the system. In this manuscript, we derive a generalized reduced-order model for the design of a multi-member planar resonator that has integer multiple modal frequencies. The model is based on a Rayleigh Ritz approximation where the number of degrees of freedom equals the number of structural members in the resonator. The analysis allows the generation of design curves, representing all the possible solutions for modal frequencies that are commensurate. The generalized model, valid for an N-DOF structure, is then restricted for a 2- and 3-DOF system/member resonator, where the linear dynamic behavior of the resonator is investigated in depth. Furthermore, this analysis demonstrates a rule of thumb; relaxing restrictions on the relative orientation of members in a planar structure, allows the structure to exhibit exactly N commensurable frequencies if it contains N members.

Comparing Multiple-Group Multinomial Log-Linear Models for Multidimensional Skill Distributions in the General Diagnostic Model. Research Report. ETS RR-08-35

ERIC Educational Resources Information Center

Xu, Xueli; von Davier, Matthias

2008-01-01

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…

A complete and partial integrability technique of the Lorenz system

NASA Astrophysics Data System (ADS)

Bougoffa, Lazhar; Al-Awfi, Saud; Bougouffa, Smail

2018-06-01

In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage to the Lorenz system. Furthermore, we show that the reduction to the third order non linear equation can be performed. Therefore, the obtained differential equation can be analytically solved in some special cases and transformed to Abel, Dufing, Painlevé and generalized Emden-Fowler equations. So, a motivating technique that permitted a complete and partial integrability of the Lorenz system is presented.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Toward intelligent information sysytem

NASA Astrophysics Data System (ADS)

Onodera, Natsuo

"Hypertext" means a concept of a novel computer-assisted tool for storage and retrieval of text information based on human association. Structure of knowledge in our idea processing is generally complicated and networked, but traditional paper documents merely express it in essentially linear and sequential forms. However, recent advances in work-station technology have allowed us to process easily electronic documents containing non-linear structure such as references or hierarchies. This paper describes concept, history and basic organization of hypertext, and shows the outline and features of existing main hypertext systems. Particularly, use of the hypertext database is illustrated by an example of Intermedia developed by Brown University.

Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy

NASA Astrophysics Data System (ADS)

van der Heyden, M. J.; Diks, C.; Pijn, J. P. M.; Velis, D. N.

1996-02-01

Intracranial electroencephalograms from patients suffering from mesial temporal lobe epilepsy were tested for time reversibility. If the recorded time series is irreversible, the input of the recording system cannot be a realisation of a linear Gaussian random process. We confirmed experimentally that the measurement equipment did not introduce irreversibility in the recorded output when the input was a realisation of a linear Gaussian random process. In general, the non-seizure recordings are reversible, whereas the seizure recordings are irreversible. These results suggest that time reversibility is a useful property for the characterisation of human intracranial EEG recordings in mesial temporal lobe epilepsy.

Young—Capelli symmetrizers in superalgebras†

PubMed Central

Brini, Andrea; Teolis, Antonio G. B.

1989-01-01

Let Supern[U [unk] V] be the nth homogeneous subspace of the supersymmetric algebra of U [unk] V, where U and V are Z2-graded vector spaces over a field K of characteristic zero. The actions of the general linear Lie superalgebras pl(U) and pl(V) span two finite-dimensional K-subalgebras B and [unk] of EndK(Supern[U [unk] V]) that are the centralizers of each other. Young—Capelli symmetrizers and Young—Capelli *-symmetrizers give rise to K-linear bases of B and [unk] containing orthogonal systems of idempotents; thus they yield complete decompositions of B and [unk] into minimal left and right ideals, respectively. PMID:16594014

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

The Use of Efficient Broadcast Protocols in Asynchronous Distributed Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Schmuck, Frank Bernhard

1988-01-01

Reliable broadcast protocols are important tools in distributed and fault-tolerant programming. They are useful for sharing information and for maintaining replicated data in a distributed system. However, a wide range of such protocols has been proposed. These protocols differ in their fault tolerance and delivery ordering characteristics. There is a tradeoff between the cost of a broadcast protocol and how much ordering it provides. It is, therefore, desirable to employ protocols that support only a low degree of ordering whenever possible. This dissertation presents techniques for deciding how strongly ordered a protocol is necessary to solve a given application problem. It is shown that there are two distinct classes of application problems: problems that can be solved with efficient, asynchronous protocols, and problems that require global ordering. The concept of a linearization function that maps partially ordered sets of events to totally ordered histories is introduced. How to construct an asynchronous implementation that solves a given problem if a linearization function for it can be found is shown. It is proved that in general the question of whether a problem has an asynchronous solution is undecidable. Hence there exists no general algorithm that would automatically construct a suitable linearization function for a given problem. Therefore, an important subclass of problems that have certain commutativity properties are considered. Techniques for constructing asynchronous implementations for this class are presented. These techniques are useful for constructing efficient asynchronous implementations for a broad range of practical problems.

Advanced stitching technology

NASA Technical Reports Server (NTRS)

Scardino, Frank L.

1992-01-01

In the design of textile composites, the selection of materials and constructional techniques must be matched with product performance, productivity, and cost requirements. Constructional techniques vary. A classification of various textile composite systems is given. In general, the chopped fiber system is not suitable for structural composite applications because of fiber discontinuity, uncontrolled fiber orientation and a lack of fiber integration or entanglement. Linear filament yarn systems are acceptable for structural components which are exposed to simple tension in their applications. To qualify for more general use as structural components, filament yarn systems must be multi-directionally positioned. With the most sophisticated filament winding and laying techniques, however, the Type 2 systems have limited potential for general load-bearing applications because of a lack of filament integration or entanglement, which means vulnerability to splitting and delamination among filament layers. The laminar systems (Type 3) represented by a variety of simple fabrics (woven, knitted, braided and nonwoven) are especially suitable for load-bearing panels in flat form and for beams in a roled up to wound form. The totally integrated, advanced fabric system (Type 4) are thought to be the most reliable for general load-bearing applications because of fiber continuity and because of controlled multiaxial fiber orientation and entanglement. Consequently, the risk of splitting and delamination is minimized and practically omitted. Type 4 systems can be woven, knitted, braided or stitched through with very special equipment. Multiaxial fabric technologies are discussed.

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

NASA Astrophysics Data System (ADS)

Shao, Zhiqiang

2018-04-01

The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

Multi-Maneuver Clohessy-Wiltshire Targeting

NASA Technical Reports Server (NTRS)

Dannemiller, David P.

2011-01-01

Orbital rendezvous involves execution of a sequence of maneuvers by a chaser vehicle to bring the chaser to a desired state relative to a target vehicle while meeting intermediate and final relative constraints. Intermediate and final relative constraints are necessary to meet a multitude of requirements such as to control approach direction, ensure relative position is adequate for operation of space-to-space communication systems and relative sensors, provide fail-safe trajectory features, and provide contingency hold points. The effect of maneuvers on constraints is often coupled, so the maneuvers must be solved for as a set. For example, maneuvers that affect orbital energy change both the chaser's height and downrange position relative to the target vehicle. Rendezvous designers use experience and rules-of-thumb to design a sequence of maneuvers and constraints. A non-iterative method is presented for targeting a rendezvous scenario that includes a sequence of maneuvers and relative constraints. This method is referred to as Multi-Maneuver Clohessy-Wiltshire Targeting (MM_CW_TGT). When a single maneuver is targeted to a single relative position, the classic CW targeting solution is obtained. The MM_CW_TGT method involves manipulation of the CW state transition matrix to form a linear system. As a starting point for forming the algorithm, the effects of a series of impulsive maneuvers on the state are derived. Simple and moderately complex examples are used to demonstrate the pattern of the resulting linear system. The general form of the pattern results in an algorithm for formation of the linear system. The resulting linear system relates the effect of maneuver components and initial conditions on relative constraints specified by the rendezvous designer. Solution of the linear system includes the straight-forward inverse of a square matrix. Inversion of the square matrix is assured if the designer poses a controllable scenario - a scenario where the the constraints can be met by the sequence of maneuvers. Matrices in the linear system are dependent on selection of maneuvers and constraints by the designer, but the matrices are independent of the chaser's initial conditions. For scenarios where the sequence of maneuvers and constraints are fixed, the linear system can be formed and the square matrix inverted prior to real-time operations. Example solutions are presented for several rendezvous scenarios to illustrate the utility of the method. The MM_CW_TGT method has been used during the preliminary design of rendezvous scenarios and is expected to be useful for iterative methods in the generation of an initial guess and corrections.

Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation

DOE PAGES

Simakov, Andrei Nikolaevich; Molvig, Kim

2016-03-17

A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close themore » fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produces two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in the companion paper [A. N. Simakov and K. Molvig, Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas, submitted to Phys. Plasmas (2015)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas.« less

A higher order panel method for linearized supersonic flow

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Epton, M. A.; Johnson, F. T.; Magnus, A. E.; Rubbert, P. E.

1979-01-01

The basic integral equations of linearized supersonic theory for an advanced supersonic panel method are derived. Methods using only linear varying source strength over each panel or only quadratic doublet strength over each panel gave good agreement with analytic solutions over cones and zero thickness cambered wings. For three dimensional bodies and wings of general shape, combined source and doublet panels with interior boundary conditions to eliminate the internal perturbations lead to a stable method providing good agreement experiment. A panel system with all edges contiguous resulted from dividing the basic four point non-planar panel into eight triangular subpanels, and the doublet strength was made continuous at all edges by a quadratic distribution over each subpanel. Superinclined panels were developed and tested on s simple nacelle and on an airplane model having engine inlets, with excellent results.

Implications of discontinuous elevation gradients on fragmentation and restoration in patterned wetlands

USGS Publications Warehouse

Zweig, Christa L.; Reichert, Brian E.; Kitchens, Wiley M.

2011-01-01

Large wetlands around the world face the possibility of degradation, not only from complete conversion, but also from subtle changes in their structure and function. While fragmentation and isolation of wetlands within heterogeneous landscapes has received much attention, the disruption of spatial patterns/processes within large wetland systems and the resulting fragmentation of community components are less well documented. A greater understanding of pattern/process relationships and landscape gradients, and what occurs when they are altered, could help avoid undesirable consequences of restoration actions. The objective of this study is to determine the amount of fragmentation of sawgrass ridges due to artificial impoundment of water and how that may be differentially affected by spatial position relative to north and south levees. We also introduce groundbreaking evidence of landscape-level discontinuous elevation gradients within WCA3AS by comparing generalized linear and generalized additive models. These relatively abrupt breaks in elevation may have non-linear effects on hydrology and vegetation communities and would be crucial in restoration considerations. Modeling suggests there are abrupt breaks in elevation as a function of northing (Y-coordinate). Fragmentation indices indicate that fragmentation is a function of elevation and easting (X-coordinate), and that fragmentation has increased from 1988-2002. When landscapes change and the changes are compounded by non-linear landscape variables that are described herein, the maintenance processes change with them, creating a degraded feedback loop that alters the system's response to structuring variables and diminishes our ability to predict the effects of restoration projects or climate change. Only when these landscape variables and linkages are clearly defined can we predict the response to potential perturbations and apply the knowledge to other landscape-level wetland systems in need of future restoration.

Inference of directed climate networks: role of instability of causality estimation methods

NASA Astrophysics Data System (ADS)

Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Paluš, Milan

2013-04-01

Climate data are increasingly analyzed by complex network analysis methods, including graph-theoretical approaches [1]. For such analysis, links between localized nodes of climate network are typically quantified by some statistical measures of dependence (connectivity) between measured variables of interest. To obtain information on the directionality of the interactions in the networks, a wide range of methods exists. These can be broadly divided into linear and nonlinear methods, with some of the latter having the theoretical advantage of being model-free, and principally a generalization of the former [2]. However, as a trade-off, this generality comes together with lower accuracy - in particular if the system was close to linear. In an overall stationary system, this may potentially lead to higher variability in the nonlinear network estimates. Therefore, with the same control of false alarms, this may lead to lower sensitivity for detection of real changes in the network structure. These problems are discussed on the example of daily SAT and SLP data from the NCEP/NCAR reanalysis dataset. We first reduce the dimensionality of data using PCA with VARIMAX rotation to detect several dozens of components that together explain most of the data variability. We further construct directed climate networks applying a selection of most widely used methods - variants of linear Granger causality and conditional mutual information. Finally, we assess the stability of the detected directed climate networks by computing them in sliding time windows. To understand the origin of the observed instabilities and their range, we also apply the same procedure to two types of surrogate data: either with non-stationarity in network structure removed, or imposed in a controlled way. In general, the linear methods show stable results in terms of overall similarity of directed climate networks inferred. For instance, for different decades of SAT data, the Spearman correlation of edge weights in the networks is ~ 0.6. The networks constructed using nonlinear measures were in general less stable both in real data and stationarized surrogates. Interestingly, when the nonlinear method parameters are optimized with respect to temporal stability of the networks, the networks seem to converge close to those detected by linear Granger causality. This provides further evidence for the hypothesis of overall sparsity and weakness of nonlinear coupling in climate networks on this spatial and temporal scale [3] and sufficient support for the use of linear methods in this context, unless specific clearly detectable nonlinear phenomena are targeted. Acknowledgement: This study is supported by the Czech Science Foundation, Project No. P103/11/J068. [1] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M. & Hwang, D. U.: Complex networks: Structure and dynamics, Physics Reports, 2006, 424, 175-308 [2] Barnett, L.; Barrett, A. B. & Seth, A. K.: Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables, Physical Review Letters, 2009, 103, 238701 [3] Hlinka, J.; Hartman, D.; Vejmelka, M.; Novotná, D.; Paluš, M.: Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity, submitted preprint (http://arxiv.org/abs/1211.6688)

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

PubMed

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

PubMed

Zhao, Yingfeng; Liu, Sanyang

2016-01-01

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.