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Sample records for gain-scheduled linear quadratic

  1. Worst-case analysis and linear parameter-varying gain-scheduled control of aerospace systems

    NASA Astrophysics Data System (ADS)

    Shin, Jong-Yeob

    In this thesis, two main subjects are discussed. The first is a worst-case performance analysis, the second is a linear parameter varying (LPV) synthesis using a blending approach. On the first subject, a linear fractional transformation (LFT) model of the linearized X-38 Crew Return Vehicle (CRV) has been developed to facilitate the analysis of its flight control system. The LFT model represents uncertainty in nine aerodynamic stability derivatives at a given flight condition. The X-38 LFT model, combined with a controller at specific flight conditions, is used to determine the aerodynamic coefficients within a predefined set that result in the worst-case performance and worst-case gain/phase margins of the closed-loop system. LPV and mu controllers are synthesized for the X-38 CRV lateral-directional axes over the candidate flight envelope and compared with the baseline gain-scheduled classical control design. Worst-case analysis of the LPV and mu controllers are compared with the baseline gain-scheduled classical control design. Analysis and time simulations show that the LPV controller achieves significant performance and robustness improvements when compared to a linear mu controller and the baseline gain-scheduled controller. On the second subject, a quasi-LPV model of the F-16 longitudinal axes was developed using three methods: Jacobian linearization, state transformation and function substitution. Time simulations of quasi-LPV models show that the quasi-LPV models developed using state transformation and function substitution accurately represent the nonlinear dynamics of the F-16 longitudinal axes. In designing an LPV controller for the F-16 longitudinal axes, the function substitution quasi-LPV models are used since these quasi-LPV models can represent the nonlinear dynamics at non-trim points. Two LPV controllers are synthesized for the F-16 longitudinal axes for two separated flight envelopes: low and high altitude regions. Blending these controllers

  2. Gain Scheduling for the Orion Launch Abort Vehicle Controller

    NASA Technical Reports Server (NTRS)

    McNamara, Sara J.; Restrepo, Carolina I.; Madsen, Jennifer M.; Medina, Edgar A.; Proud, Ryan W.; Whitley, Ryan J.

    2011-01-01

    One of NASAs challenges for the Orion vehicle is the control system design for the Launch Abort Vehicle (LAV), which is required to abort safely at any time during the atmospheric ascent portion of ight. The focus of this paper is the gain design and scheduling process for a controller that covers the wide range of vehicle configurations and flight conditions experienced during the full envelope of potential abort trajectories from the pad to exo-atmospheric flight. Several factors are taken into account in the automation process for tuning the gains including the abort effectors, the environmental changes and the autopilot modes. Gain scheduling is accomplished using a linear quadratic regulator (LQR) approach for the decoupled, simplified linear model throughout the operational envelope in time, altitude and Mach number. The derived gains are then implemented into the full linear model for controller requirement validation. Finally, the gains are tested and evaluated in a non-linear simulation using the vehicles ight software to ensure performance requirements are met. An overview of the LAV controller design and a description of the linear plant models are presented. Examples of the most significant challenges with the automation of the gain tuning process are then discussed. In conclusion, the paper will consider the lessons learned through out the process, especially in regards to automation, and examine the usefulness of the gain scheduling tool and process developed as applicable to non-Orion vehicles.

  3. Prompt critical control of the ACRR using a linear quadratic regulator design

    NASA Astrophysics Data System (ADS)

    Gilkey, Jeffrey C.

    1993-01-01

    This paper describes the application of ``Modern Control'' design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 mW on Sandia's Annular Core Research Reactor (ACRR). Prompt critical control at 1.02 net reactivity and at start-up rates over 350 decades per minute (DPM) has also been demonstrated using this controller.

  4. Communications circuit including a linear quadratic estimator

    DOEpatents

    Ferguson, Dennis D.

    2015-07-07

    A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

  5. Extended Decentralized Linear-Quadratic-Gaussian Control

    NASA Technical Reports Server (NTRS)

    Carpenter, J. Russell

    2000-01-01

    A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

  6. LPV Controller Interpolation for Improved Gain-Scheduling Control Performance

    NASA Technical Reports Server (NTRS)

    Wu, Fen; Kim, SungWan

    2002-01-01

    In this paper, a new gain-scheduling control design approach is proposed by combining LPV (linear parameter-varying) control theory with interpolation techniques. The improvement of gain-scheduled controllers can be achieved from local synthesis of Lyapunov functions and continuous construction of a global Lyapunov function by interpolation. It has been shown that this combined LPV control design scheme is capable of improving closed-loop performance derived from local performance improvement. The gain of the LPV controller will also change continuously across parameter space. The advantages of the newly proposed LPV control is demonstrated through a detailed AMB controller design example.

  7. A Note on the Linearly and Quadratically Weighted Kappa Coefficients.

    PubMed

    Li, Pingke

    2016-09-01

    The linearly and quadratically weighted kappa coefficients are popular statistics in measuring inter-rater agreement on an ordinal scale. It has been recently demonstrated that the linearly weighted kappa is a weighted average of the kappa coefficients of the embedded 2 by 2 agreement matrices, while the quadratically weighted kappa is insensitive to the agreement matrices that are row or column reflection symmetric. A rank-one matrix decomposition approach to the weighting schemes is presented in this note such that these phenomena can be demonstrated in a concise manner. PMID:27246436

  8. Design of Linear Quadratic Regulators and Kalman Filters

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Geyser, L.

    1986-01-01

    AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

  9. Finding Optimal Gains In Linear-Quadratic Control Problems

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.; Scheid, Robert E., Jr.

    1990-01-01

    Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

  10. Analysis of integral controls in linear quadratic regulator design

    NASA Technical Reports Server (NTRS)

    Slater, G. L.

    1979-01-01

    The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

  11. Reaction Wheel Control Design Using Linear Quadratic Controller

    NASA Astrophysics Data System (ADS)

    Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.

    2016-01-01

    This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.

  12. Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

    NASA Technical Reports Server (NTRS)

    Choi, Benjamin B.

    2002-01-01

    Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

  13. Robust linear quadratic designs with respect to parameter uncertainty

    NASA Technical Reports Server (NTRS)

    Douglas, Joel; Athans, Michael

    1992-01-01

    The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

  14. Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling

    SciTech Connect

    Fowler, Jack F.

    2009-04-01

    Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.

  15. AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.

    1994-01-01

    AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user

  16. A Novel Approach to Noise-Filtering Based on a Gain-Scheduling Neural Network Architecture

    NASA Technical Reports Server (NTRS)

    Troudet, T.; Merrill, W.

    1994-01-01

    A gain-scheduling neural network architecture is proposed to enhance the noise-filtering efficiency of feedforward neural networks, in terms of both nominal performance and robustness. The synergistic benefits of the proposed architecture are demonstrated and discussed in the context of the noise-filtering of signals that are typically encountered in aerospace control systems. The synthesis of such a gain-scheduled neurofiltering provides the robustness of linear filtering, while preserving the nominal performance advantage of conventional nonlinear neurofiltering. Quantitative performance and robustness evaluations are provided for the signal processing of pitch rate responses to typical pilot command inputs for a modern fighter aircraft model.

  17. Linear versus quadratic portfolio optimization model with transaction cost

    NASA Astrophysics Data System (ADS)

    Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

    2014-06-01

    Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

  18. Linear quadratic optimal controller for cable-driven parallel robots

    NASA Astrophysics Data System (ADS)

    Abdolshah, Saeed; Shojaei Barjuei, Erfan

    2015-12-01

    In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

  19. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1979-01-01

    Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

  20. A decentralized linear quadratic control design method for flexible structures

    NASA Technical Reports Server (NTRS)

    Su, Tzu-Jeng; Craig, Roy R., Jr.

    1990-01-01

    A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass

  1. Singular linear-quadratic control problem for systems with linear delay

    SciTech Connect

    Sesekin, A. N.

    2013-12-18

    A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.

  2. Self-consistent linearization of non-linear BEM formulations with quadratic convergence

    NASA Astrophysics Data System (ADS)

    Fernandes, G. R.; de Souza Neto, E. A.

    2013-11-01

    In this work, a general technique to obtain the self-consistent linearization of non-linear formulations of the boundary element method (BEM) is presented. In the incremental-iterative procedure required to solve the non-linear problem the convergence is quadratic, being the solution obtained from the consistent tangent operator. This technique is applied to non-linear BEM formulations for plates where two independent problems are discussed: the plate bending and the stretching problem. For both problems an equilibrium equation is written in terms of strains and internal forces and then the consistent tangent operator is derived by applying the Newton-Raphson’s scheme. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness, although the presented formulations can be used with any non-linear model. Numerical examples are presented showing the accuracy of the results as well as the high convergence rate of the iterative procedure.

  3. Closed-loop structural stability for linear-quadratic optimal systems

    NASA Technical Reports Server (NTRS)

    Wong, P. K.; Athans, M.

    1975-01-01

    This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

  4. Propagator for the time-dependent charged oscillator via linear and quadratic invariants

    SciTech Connect

    Abdalla, M. Sebawe Choi, Jeong-Ryeol

    2007-12-15

    The problem of a charged particle in the presence of a variable magnetic field is considered. Using the linear and the quadratic invariants as a tool, the wave functions in Fock state as well as in coherent state are obtained. The corresponding propagators which propagate the wave functions in the space-time are derived. Using numerical computations we have managed to draw some plots for the real, imaginary, and absolute values of the propagators. This has been used to analyze the properties of the propagators associated with both of the linear and the quadratic invariants. It has been shown that there is no essential difference between the behavior of the absolute value of the propagators in both of the linear and the quadratic invariants.

  5. Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

    PubMed

    McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

    2013-12-13

    Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model. PMID:24483652

  6. Nonadiabatic Effects in Ultracold Molecules via Anomalous Linear and Quadratic Zeeman Shifts

    NASA Astrophysics Data System (ADS)

    McGuyer, B. H.; Osborn, C. B.; McDonald, M.; Reinaudi, G.; Skomorowski, W.; Moszynski, R.; Zelevinsky, T.

    2013-12-01

    Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold $^{88}$Sr$_2$ molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite $f$-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art \\textit{ab initio} model.

  7. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1985-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

  8. A path-following interior-point algorithm for linear and quadratic problems

    SciTech Connect

    Wright, S.J.

    1993-12-01

    We describe an algorithm for the monotone linear complementarity problem that converges for many positive, not necessarily feasible, starting point and exhibits polynomial complexity if some additional assumptions are made on the starting point. If the problem has a strictly complementary solution, the method converges subquadratically. We show that the algorithm and its convergence extend readily to the mixed monotone linear complementarity problem and, hence, to all the usual formulations of the linear programming and convex quadratic programming problems.

  9. Linear quadratic servo control of a reusable rocket engine

    NASA Technical Reports Server (NTRS)

    Musgrave, Jeffrey L.

    1991-01-01

    A design method for a servo compensator is developed in the frequency domain using singular values. The method is applied to a reusable rocket engine. An intelligent control system for reusable rocket engines was proposed which includes a diagnostic system, a control system, and an intelligent coordinator which determines engine control strategies based on the identified failure modes. The method provides a means of generating various linear multivariable controllers capable of meeting performance and robustness specifications and accommodating failure modes identified by the diagnostic system. Command following with set point control is necessary for engine operation. A Kalman filter reconstructs the state while loop transfer recovery recovers the required degree of robustness while maintaining satisfactory rejection of sensor noise from the command error. The approach is applied to the design of a controller for a rocket engine satisfying performance constraints in the frequency domain. Simulation results demonstrate the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation.

  10. Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.

    ERIC Educational Resources Information Center

    Schafer, William D.; Wang, Yuh-Yin

    A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

  11. Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

    NASA Astrophysics Data System (ADS)

    Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

    2015-10-01

    In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

  12. Gain-scheduled controller synthesis for a nonlinear PDE

    NASA Astrophysics Data System (ADS)

    Mahdi Hashemi, Seyed; Werner, Herbert

    2012-01-01

    Linear parameter-varying (LPV) modelling and control of a nonlinear partial differential equation (PDE) is considered in this article. The one-dimensional viscous Burgers' equation is discretised using a finite difference scheme; the boundary conditions are taken as control inputs and the velocities at two grid points are assumed to be measurable. A nonlinear high-order state space model is generated and proper orthogonal decomposition is used for model order reduction. After assessing the accuracy of the reduced model, a low-order functional observer is designed to estimate the reduced states which are linear combinations of the velocities at all grid points. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model. A polytopic LPV controller is synthesised based on a generalised plant containing the LPV model and the functional observer. More generally, the proposed method can be used to design an LPV controller for a quasi-LPV system with non-measurable scheduling parameters. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller compared with a linear quadratic Gaussian (LQG) controller based on a linearised model.

  13. Gain-Scheduled Complementary Filter Design for a MEMS Based Attitude and Heading Reference System

    PubMed Central

    Yoo, Tae Suk; Hong, Sung Kyung; Yoon, Hyok Min; Park, Sungsu

    2011-01-01

    This paper describes a robust and simple algorithm for an attitude and heading reference system (AHRS) based on low-cost MEMS inertial and magnetic sensors. The proposed approach relies on a gain-scheduled complementary filter, augmented by an acceleration-based switching architecture to yield robust performance, even when the vehicle is subject to strong accelerations. Experimental results are provided for a road captive test during which the vehicle dynamics are in high-acceleration mode and the performance of the proposed filter is evaluated against the output from a conventional linear complementary filter. PMID:22163824

  14. Clifford group, stabilizer states, and linear and quadratic operations over GF(2)

    SciTech Connect

    Dehaene, Jeroen; Moor, Bart de

    2003-10-01

    We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.

  15. Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output

    NASA Astrophysics Data System (ADS)

    Van Beeumen, Roel; Meerbergen, Karl

    2010-09-01

    Balanced truncation is a widely used and appreciated projection-based model reduction technique for linear systems. This technique has the following two important properties: approximations by balanced truncation preserve the stability and the H∞-norm (the maximum of the frequency response) of the error system is bounded above by twice the sum of the neglected singular values. This paper tries to extend the framework of linear balanced truncation to systems with a quadratic output. For such systems, the controllability Gramian remains the same. The observability Gramian is computed from a linear system with multiple outputs that is derived from the quadratic output of the original system. We give a numerical example for a large-scale system arising from structural analysis.

  16. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1980-01-01

    Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

  17. Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

    1989-01-01

    A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

  18. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  19. Application of gain scheduling to the control of batch bioreactors

    NASA Technical Reports Server (NTRS)

    Cardello, Ralph; San, Ka-Yiu

    1987-01-01

    The implementation of control algorithms to batch bioreactors is often complicated by the inherent variations in process dynamics during the course of fermentation. Such a wide operating range may render the performance of fixed gain PID controllers unsatisfactory. In this work, a detailed study on the control of batch fermentation is performed. Furthermore, a simple batch controller design is proposed which incorporates the concept of gain-scheduling, a subclass of adaptive control, with oxygen uptake rate as an auxiliary variable. The control of oxygen tension in the biorector is used as a vehicle to convey the proposed idea, analysis and results. Simulation experiments indicate significant improvement in controller performance can be achieved by the proposed approach even in the presence of measurement noise.

  20. A linear-quadratic-Gaussian control problem with innovations-feedthrough solution

    NASA Technical Reports Server (NTRS)

    Platzman, L. K.; Johnson, T. L.

    1976-01-01

    The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback or, equivalently, innovations feedthrough (IF). Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.

  1. Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1984-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  2. Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  3. A linear quadratic tracker for Control Moment Gyro based attitude control of the Space Station

    NASA Technical Reports Server (NTRS)

    Kaidy, J. T.

    1986-01-01

    The paper discusses a design for an attitude control system for the Space Station which produces fast response, with minimal overshoot and cross-coupling with the use of Control Moment Gyros (CMG). The rigid body equations of motion are linearized and discretized and a Linear Quadratic Regulator (LQR) design and analysis study is performed. The resulting design is then modified such that integral and differential terms are added to the state equations to enhance response characteristics. Methods for reduction of computation time through channelization are discussed as well as the reduction of initial torque requirements.

  4. ORACLS - A linear-quadratic-Gaussian computer-aided design package

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1982-01-01

    ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.

  5. Anisotropic models with two fluids in linear and quadratic forms of f( T) gravitational theories

    NASA Astrophysics Data System (ADS)

    Nashed, Gamal G. L.

    2015-06-01

    Recent astronomical observations show that the universe may be anisotropic on large scales. The Union2 SnIa data hint that the universe has a preferred direction. If such a cosmological privileged axis indeed exists, one has to consider an anisotropic expanding universe, instead of the isotropic cosmological model. In this study, we apply the field equations of quadratic form of the modified teleparallel gravitational theories, f( T)= T+ ɛT 2, to anisotropic model. We assume two fluid components, the matter components have two equation of states (EoS). We study different equation of states for the linear case and show that there is no recombination era between the two fluids. For the quadratic one, we assume two equations of state corresponding to dark matter. In this model we obtain an inflation model and show that the values of the parameter, in the early universe, ɛ are depend on the sign of the cosmological constant.

  6. Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

    NASA Technical Reports Server (NTRS)

    Koppang, Paul; Leland, Robert

    1996-01-01

    Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

  7. Quadratic Herman-Wallis factors in the fundamental bands of linear molecules

    NASA Astrophysics Data System (ADS)

    Watson, James K. G.

    1987-10-01

    General theoretical formulas are derived for the coefficients in the terms M˜12 and M˜13 of the effective molecular dipole moment operator, and applied to the parallel and perpendicular fundamentals of linear molecules. The Herman-Wallis factors for P- and R-branch lines are F PR = [1 + A 1m + A 2PRm 2] 2, m = δ J( J' + J″ + 1)/2 and for Q-branch lines F Q = [1 + A 2QJ ( J + 1)] 2 The quadratic coefficients A2PR and A2Q depend on up to cubic potential derivatives and quadratic dipole derivatives. Calculated A2PR and A2Q values for the fundamentals of CO 2 do not agree well with recent measurements of Johns, and possible reasons for the discrepancies are discussed.

  8. Mechanistic model of radiation-induced cancer after fractionated radiotherapy using the linear-quadratic formula

    SciTech Connect

    Schneider, Uwe

    2009-04-15

    A simple mechanistic model for predicting cancer induction after fractionated radiotherapy is developed. The model is based upon the linear-quadratic model. The inductions of carcinomas and sarcomas are modeled separately. The linear-quadratic model of cell kill is applied to normal tissues which are unintentionally irradiated during a cancer treatment with radiotherapy. Tumor induction is modeled such that each transformation process results in a tumor cell. The microscopic transformation parameter was chosen such that in the limit of low dose and acute exposure, the parameters of the linear-no-threshold model for tumor induction were approached. The differential equations describing carcinoma and sarcoma inductions can be solved analytically. Cancer induction in this model is a function of treatment dose, the cell kill parameters ({alpha},{beta}), the tumor induction variable ({mu}), and the repopulation parameter ({xi}). Carcinoma induction shows a bell shaped behavior as long as cell repopulation is small. Assuming large cell repopulation rates, a plateaulike function is approached. In contrast, sarcoma induction is negligible for low doses and increases with increasing dose up to a constant value. The proposed model describes carcinoma and sarcoma inductions after fractionated radiotherapy as an analytical function of four parameters. In the limit of low dose and for an instant irradiation it reproduces the results of the linear-no-threshold model. The obtained dose-response curves for cancer induction can be implemented with other models such as the organ-equivalent dose model to predict second cancers after radiotherapy.

  9. Gantry cranes gain scheduling feedback control with friction compensation

    NASA Astrophysics Data System (ADS)

    Omar, Hanafy M.; Nayfeh, Ali H.

    2005-03-01

    We designed a controller based on gain-scheduling feedback to move a load on a gantry crane from point to point within one oscillation cycle and without inducing large swings. The settling time of the system is taken to be equal to the period of oscillation of the load. This criterion enables calculation of the controller feedback gains for varying load weight and cable length. Numerical simulations show that the controller is effective in reducing load oscillations and transferring the load in a reasonable time compared with that of optimal control. To experimentally validate the theory, we had to compensate for friction. To this end, we estimated the friction, and then applied an opposite control action to cancel it. To estimate the friction force, we assumed a mathematical model, and then we estimated the model coefficients using an off-line identification technique, such as the method of least squares (LS). First, the process of identification is applied to a theoretical model of a DC motor with known friction coefficients. From this example, some guidelines and rules are deduced for the choice of the LS parameters. Then, the friction coefficients of the gantry crane model are estimated and validated.

  10. Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

    PubMed

    Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

    2016-02-01

    Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467

  11. Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

    PubMed Central

    Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

    2016-01-01

    Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467

  12. Simultaneous structural and control optimization via linear quadratic regulator eigenstructure assignment

    NASA Technical Reports Server (NTRS)

    Becus, G. A.; Lui, C. Y.; Venkayya, V. B.; Tischler, V. A.

    1987-01-01

    A method for simultaneous structural and control design of large flexible space structures (LFSS) to reduce vibration generated by disturbances is presented. Desired natural frequencies and damping ratios for the closed loop system are achieved by using a combination of linear quadratic regulator (LQR) synthesis and numerical optimization techniques. The state and control weighing matrices (Q and R) are expressed in terms of structural parameters such as mass and stiffness. The design parameters are selected by numerical optimization so as to minimize the weight of the structure and to achieve the desired closed-loop eigenvalues. An illustrative example of the design of a two bar truss is presented.

  13. A new linear quadratic optimal controller for the 34-meter high efficiency antenna position loop

    NASA Technical Reports Server (NTRS)

    Nickerson, J. A.

    1987-01-01

    The design of a new position loop controller for the 34-meter High Efficiency Deep Space antennas using linear quadratic (LQ) optimal control techniques is discussed. The LQ optimal control theory is reviewed, and model development and verification are discussed. Families of optimal gain vectors are generated by varying weight parameters. Performance specifications were used to select a final gain vector. Estimator dynamics were selected and the corresponding gain vectors were computed. Final estimator selection was based on position, commanded rate, and estimator error responses.

  14. Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

  15. A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

    NASA Technical Reports Server (NTRS)

    Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.

    1979-01-01

    The paper describes a laboratory design facility for digital microprocessor implementation of Linear-Quadratic-Gaussian feedback compensators. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems are conditioned for implementation on a laboratory microcomputer system. The software consists of two parts: (1) an off-line high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains, and (2) a cross compiler/macro assembler which generates object code for the target microprocessor system. Application to the control of a two dimensional inverted pendulum and expanding the design/prototyping system to other target machine architectures are discussed.

  16. Gain-scheduling multivariable LPV control of an irrigation canal system.

    PubMed

    Bolea, Yolanda; Puig, Vicenç

    2016-07-01

    The purpose of this paper is to present a multivariable linear parameter varying (LPV) controller with a gain scheduling Smith Predictor (SP) scheme applicable to open-flow canal systems. This LPV controller based on SP is designed taking into account the uncertainty in the estimation of delay and the variation of plant parameters according to the operating point. This new methodology can be applied to a class of delay systems that can be represented by a set of models that can be factorized into a rational multivariable model in series with left/right diagonal (multiple) delays, such as, the case of irrigation canals. A multiple pool canal system is used to test and validate the proposed control approach. PMID:27184416

  17. Robust Gain-Scheduled Fault Tolerant Control for a Transport Aircraft

    NASA Technical Reports Server (NTRS)

    Shin, Jong-Yeob; Gregory, Irene

    2007-01-01

    This paper presents an application of robust gain-scheduled control concepts using a linear parameter-varying (LPV) control synthesis method to design fault tolerant controllers for a civil transport aircraft. To apply the robust LPV control synthesis method, the nonlinear dynamics must be represented by an LPV model, which is developed using the function substitution method over the entire flight envelope. The developed LPV model associated with the aerodynamic coefficient uncertainties represents nonlinear dynamics including those outside the equilibrium manifold. Passive and active fault tolerant controllers (FTC) are designed for the longitudinal dynamics of the Boeing 747-100/200 aircraft in the presence of elevator failure. Both FTC laws are evaluated in the full nonlinear aircraft simulation in the presence of the elevator fault and the results are compared to show pros and cons of each control law.

  18. ORACLS: A system for linear-quadratic-Gaussian control law design

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1978-01-01

    A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

  19. Isoeffect calculations with the linear quadratic and its extensions: An examination of model-dependent estimates at doses relevant to hypofractionation

    PubMed Central

    McKenna, Frederick W.; Ahmad, Salahuddin

    2011-01-01

    The linear quadratic is the standard model for calculating isoeffects in the range of conventional dose per fraction. However, the use of hypofractionation and stereotactic body radiation therapy can call for isoeffect calculations for large doses per fraction. The purpose of this work is to investigate the linear quadratic at large doses per fraction. The linear quadratic is compared to models that incorporate effects such as dose protraction, whose purpose is to extend the useful range of the linear quadratic to larger doses. The linear quadratic and extended linear quadratic models are fit to 4 data sets. The model-predicted isoeffects for these data sets are calculated. It is found that the linear quadratic and extended linear quadratic predict different isoeffect curves for certain data sets. However, for these data sets, by appropriate selection of a α/β ratio, the linear quadratic can well approximate the extended linear quadratic models. In particular, it is found that a α/β ratio of 0.5 well approximates the extended linear quadratic isoeffect curve for 2 prostate cell lines for conventional and moderate doses per fraction. PMID:21731226

  20. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

    An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

  1. Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

    NASA Technical Reports Server (NTRS)

    Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

    2009-01-01

    The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

  2. Modelling Ocean Dissipation in Icy Satellites: A Comparison of Linear and Quadratic Friction

    NASA Astrophysics Data System (ADS)

    Hay, H.; Matsuyama, I.

    2015-12-01

    Although subsurface oceans are confirmed in Europa, Ganymede, Callisto, and strongly suspected in Enceladus and Titan, the exact mechanism required to heat and maintain these liquid reservoirs over Solar System history remains a mystery. Radiogenic heating can supply enough energy for large satellites whereas tidal dissipation provides the best explanation for the presence of oceans in small icy satellites. The amount of thermal energy actually contributed to the interiors of these icy satellites through oceanic tidal dissipation is largely unquantified. Presented here is a numerical model that builds upon previous work for quantifying tidally dissipated energy in the subsurface oceans of the icy satellites. Recent semi-analytical models (Tyler, 2008 and Matsuyama, 2014) have solved the Laplace Tidal Equations to estimate the time averaged energy flux over an orbital period in icy satellite oceans, neglecting the presence of a solid icy shell. These models are only able to consider linear Rayleigh friction. The numerical model presented here is compared to one of these semi-analytical models, finding excellent agreement between velocity and displacement solutions for all three terms to the tidal potential. Time averaged energy flux is within 2-6% of the analytical values. Quadratic (bottom) friction is then incorporated into the model, replacing linear friction. This approach is commonly applied to terrestrial ocean dissipation studies where dissipation scales nonlinearly with velocity. A suite of simulations are also run for the quadratic friction case which are then compared to and analysed against recent scaling laws developed by Chen and Nimmo (2013).

  3. Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

    NASA Technical Reports Server (NTRS)

    Turso, James A.; Litt, Jonathan S.

    2004-01-01

    A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

  4. Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

    NASA Technical Reports Server (NTRS)

    Joshi, S. M.

    1984-01-01

    The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

  5. Infinite horizon linear quadratic stochastic Nash differential games of Markov jump linear systems with its application

    NASA Astrophysics Data System (ADS)

    Zhu, Huai-nian; Zhang, Cheng-ke; Bin, Ning

    2014-05-01

    In this paper, we deal with the problem of stochastic Nash differential games of Markov jump linear systems governed by Itô-type equation. Combining the stochastic stabilizability with the stochastic systems, a necessary and sufficient condition for the existence of the Nash strategy is presented by means of a set of cross-coupled stochastic algebraic Riccati equations. Moreover, the stochastic H2/H∞ control for stochastic Markov jump linear systems is discussed as an immediate application and an illustrative example is presented.

  6. A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations.

    PubMed

    Xia, Youshen; Feng, Gang; Wang, Jun

    2004-09-01

    This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications. PMID:15312842

  7. 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.

  8. Decoupled control analysis of a large flexible space antenna with linear quadratic regulator comparisons

    NASA Technical Reports Server (NTRS)

    Young, J. W.; Hamer, H. A.; Johnson, K. G.

    1984-01-01

    A decoupled-control analysis was performed for a large flexible space antenna. Control involved commanding changes in the rigid-body modes or nulling disturbances in the flexible modes. The study provides parametric-type data which could be useful in the final design of a large space antenna control system. Results are presented to illustrate the effect on control requirements of (1) the number of modes controlled; (2) the number, type, and location of control actuators; and (3) variations in the closed-loop dynamics of the control system. Comparisons are given between the decoupled-control results and those obtained by using a linear quadratic regulator approach. Time history responses are presented to illustrate the effects of the control procedures.

  9. A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

    NASA Technical Reports Server (NTRS)

    Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.

    1978-01-01

    A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.

  10. Frequency locking of an optical cavity using linear-quadratic Gaussian integral control

    NASA Astrophysics Data System (ADS)

    Sayed Hassen, S. Z.; Heurs, M.; Huntington, E. H.; Petersen, I. R.; James, M. R.

    2009-09-01

    We show that a systematic modern control technique such as linear-quadratic Gaussian (LQG) control can be applied to a problem in experimental quantum optics which has previously been addressed using traditional approaches to controller design. An LQG controller which includes integral action is synthesized to stabilize the frequency of the cavity to the laser frequency and to reject low frequency noise. The controller is successfully implemented in the laboratory using a dSpace digital signal processing board. One important advantage of the LQG technique is that it can be extended in a straightforward way to control systems with multiple measurements and multiple feedback loops. This work is expected to pave the way for extremely stable lasers with fluctuations approaching the quantum noise limit and which could be potentially used in a wide range of applications.

  11. Observer based output feedback tuning for underwater remotely operated vehicle based on linear quadratic performance

    NASA Astrophysics Data System (ADS)

    Aras, Mohd Shahrieel Mohd; Abdullah, Shahrum Shah; Kamarudin, Muhammad Nizam; Rahman, Ahmad Fadzli Nizam Abdul; Azis, Fadilah Abd; Jaafar, Hazriq Izzuan

    2015-05-01

    This paper describes the effectiveness of observer-based output feedback for Unmanned Underwater Vehicle (UUV) with Linear Quadratic Regulation (LQR) performance. Tuning of observer parameters is crucial for tracking purpose. Prior to tuning facility, the ranges of observer and LQR parameters are obtained via system output cum error. The validation of this technique using unmanned underwater vehicles called Remotely Operated Vehicle (ROV) modelling helps to improve steady state performance of system response. The ROV modeling is focused for depth control using ROV 1 developed by the Underwater Technology Research Group (UTeRG). The results are showing that this technique improves steady state performances in term of overshoot and settling time of the system response.

  12. Linear and quadratic dispersion characterization of millimeter-length fibers and waveguides using common-path interferometry.

    PubMed

    Mohammed, W; Meier, J; Galle, M; Qian, L; Aitchison, J S; Smith, P W E

    2007-11-15

    We measured linear and quadratic dispersion on millimeter-length fibers, waveguides, and nanowires based on common-path spectral interferometry. We obtained the linear dispersion parameter, beta', with a relative precision of 1.45 x 10(-4), and extracted the quadratic dispersion parameter, beta'', from the Taylor expansion of beta' x beta'' values show a discrepancy of < 1% when compared with simulation as well as with measurement results obtained by a conventional Michelson interferometer. Using this method, we experimentally confirmed the sign inversion of the group velocity dispersion of AlGaAs nanowires for what is believed to be the first time. PMID:18026291

  13. Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna

    NASA Technical Reports Server (NTRS)

    Gawronski, W. K.; Racho, C. S.; Mellstrom, J. A.

    1994-01-01

    The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller.

  14. 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.

  15. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1985-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  16. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1987-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  17. Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

    USGS Publications Warehouse

    Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

    1997-01-01

    One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

  18. Robust gain-scheduling for smart-structures in parallel robots

    NASA Astrophysics Data System (ADS)

    Algermissen, Stephan; Rose, Michael; Keimer, Ralf; Sinapius, Michael

    2009-03-01

    In the past years parallel robots demonstrated their capability in applications with high-dynamic trajectories. Smart-structures offer the potential to further increase the productivity of parallel robots by reducing disturbing vibrations caused by high dynamic loads effectively. To investigate parallel robots and their applications, including suitable control concepts for smart-structures, the Collaborative Research Center 562 was founded by the German Research Council (DFG). The latest prototype within this research center is called Triglide. It is a four degree of freedom (DOF) robot with three translational and one rotational DOF. It realizes an acceleration of 10 g* at the effector. In the structure of the robot six active rods and a tri-axial accelerometer are integrated to control effector vibrations in three translational DOF. The main challenge of this control application is the position dependent vibration behavior. A single robust controller is not able to gain satisfying performance within the entire workspace. Therefore a strategy for describing the vibration behavior by linearization at several operating points is developed. Behavior in-between is approximated by a linear approach. On a trajectory robust controllers in all operating points are smoothly switched by robust gain-scheduling. The scheduling parameters are fast varying and though a suitable stability proof is defined, based on Small-Gain approach. Several transformations enhance the results from Small-Gain Theorem and reduce the usual conservatism. Experimental data is used to show the improvements made.

  19. Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Chumalee, Sunan; Whidborne, James F.

    2015-01-01

    Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques.

  20. High School Teachers' Use of Graphing Calculators When Teaching Linear and Quadratic Functions: Professed Beliefs and Observed Practice

    ERIC Educational Resources Information Center

    Molenje, Levi

    2012-01-01

    This study was designed to explore secondary mathematics teachers' beliefs about graphing calculators, their practices with the graphing calculators when teaching linear and quadratic functions, and the relationship between the teachers' beliefs and their practices. The study was conducted in two phases. In the first phase, 81 teachers…

  1. Linear quadratic modeling of increased late normal-tissue effects in special clinical situations

    SciTech Connect

    Jones, Bleddyn . E-mail: b.jones.1@bham.ac.uk; Dale, Roger G.; Gaya, Andrew M.

    2006-03-01

    Purpose: To extend linear quadratic theory to allow changes in normal-tissue radiation tolerance after exposure to cytotoxic chemotherapy, after surgery, and in elderly patients. Methods: Examples of these situations are analyzed by use of the biologic effective dose (BED) concept. Changes in tolerance can be allowed for by: estimation of either the contribution of the additional factor as an equivalent BED or the equivalent dose in 2-Gy fractions or by the degree of radiosensitization by a mean dose-modifying factor (x). Results: The estimated x value is 1.063 (95% confidence limits for the mean, 1.056 to 1.070) for subcutaneous fibrosis after cyclophosphamide, methotrexate, and fluorouracil (CMF) chemotherapy and radiotherapy in breast cancer. The point estimate of x is 1.18 for the additional risk of gastrointestinal late-radiation effects after abdominal surgery in lymphoma patients (or 10.62 Gy at 2 Gy per fraction). For shoulder fibrosis in patients older than 60 years after breast and nodal irradiation, x is estimated to be 1.033 (95% confidence limits for the mean, 1.028 to 1.0385). The equivalent BED values were CMF chemotherapy (6.48 Gy{sub 3}), surgery (17.73 Gy{sub 3}), and age (3.61 Gy{sub 3}). Conclusions: The LQ model can, in principle, be extended to quantify reduced normal-tissue tolerance in special clinical situations.

  2. Antenna Linear-Quadratic-Gaussian (LQG) Controllers: Properties, Limits of Performance, and Tuning Procedure

    NASA Technical Reports Server (NTRS)

    Gawronski, W.

    2004-01-01

    Wind gusts are the main disturbances that depreciate tracking precision of microwave antennas and radiotelescopes. The linear-quadratic-Gaussian (LQG) controllers - as compared with the proportional-and-integral (PI) controllers significantly improve the tracking precision in wind disturbances. However, their properties have not been satisfactorily understood; consequently, their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller model and the selection of weights of the LQG performance index. This article analyzes properties of an open- and closed-loop antenna. It shows that the proper choice of coordinates of the open-loop model simplifies the shaping of the closed-loop performance. The closed-loop properties are influenced by the LQG weights. The article shows the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. The bandwidth and the disturbance rejection characterize the antenna performance, while the acceleration represents the performance limit set by the antenna hardware (motors). The article presents the controller tuning procedure, based on the coordinate selection and the weight properties. The procedure rationally shapes the closed-loop performance, as an alternative to the trial-and-error approach.

  3. Linear Quadratic Tracking Design for a Generic Transport Aircraft with Structural Load Constraints

    NASA Technical Reports Server (NTRS)

    Burken, John J.; Frost, Susan A.; Taylor, Brian R.

    2011-01-01

    When designing control laws for systems with constraints added to the tracking performance, control allocation methods can be utilized. Control allocations methods are used when there are more command inputs than controlled variables. Constraints that require allocators are such task as; surface saturation limits, structural load limits, drag reduction constraints or actuator failures. Most transport aircraft have many actuated surfaces compared to the three controlled variables (such as angle of attack, roll rate & angle of side slip). To distribute the control effort among the redundant set of actuators a fixed mixer approach can be utilized or online control allocation techniques. The benefit of an online allocator is that constraints can be considered in the design whereas the fixed mixer cannot. However, an online control allocator mixer has a disadvantage of not guaranteeing a surface schedule, which can then produce ill defined loads on the aircraft. The load uncertainty and complexity has prevented some controller designs from using advanced allocation techniques. This paper considers actuator redundancy management for a class of over actuated systems with real-time structural load limits using linear quadratic tracking applied to the generic transport model. A roll maneuver example of an artificial load limit constraint is shown and compared to the same no load limitation maneuver.

  4. A nanodosimetry-based linear-quadratic model of cell survival for mixed-LET radiations.

    PubMed

    Chris Wang, C-K; Zhang, Xin

    2006-12-01

    A new nanodosimetry-based linear-quadratic (LQ) model of cell survival for mixed-LET radiations has been developed. The new model employs three physical quantities and three biological quantities. The three physical quantities are related to energy depositions at two nanometre scales, 5 nm and 25 nm. The three biological quantities are related to the lesion production and interaction probabilities and the lesion repair rate. The coefficients alpha and beta of the LQ formula (alpha D + beta D(2)) are explicitly expressed in terms of the three physical quantities and the three biological quantities. The new model is shown to be consistent with the previously published cell survival curves of V-79 cells. The advantage of this new model is that it can be conveniently adopted to estimate the iso-effect for radiotherapies that involve ionizing radiation of mixed LET. An example is given to estimate the cell survival fractions for a high-dose-rate mixed neutron and gamma-ray field from a (252)Cf source. PMID:17110772

  5. A nanodosimetry-based linear-quadratic model of cell survival for mixed-LET radiations

    NASA Astrophysics Data System (ADS)

    Wang, C.-K. Chris; Zhang, Xin

    2006-12-01

    A new nanodosimetry-based linear-quadratic (LQ) model of cell survival for mixed-LET radiations has been developed. The new model employs three physical quantities and three biological quantities. The three physical quantities are related to energy depositions at two nanometre scales, 5 nm and 25 nm. The three biological quantities are related to the lesion production and interaction probabilities and the lesion repair rate. The coefficients α and β of the LQ formula (αD + βD2) are explicitly expressed in terms of the three physical quantities and the three biological quantities. The new model is shown to be consistent with the previously published cell survival curves of V-79 cells. The advantage of this new model is that it can be conveniently adopted to estimate the iso-effect for radiotherapies that involve ionizing radiation of mixed LET. An example is given to estimate the cell survival fractions for a high-dose-rate mixed neutron and gamma-ray field from a 252Cf source.

  6. Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs

    NASA Technical Reports Server (NTRS)

    Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

    2001-01-01

    Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

  7. Stability and monotone convergence of generalised policy iteration for discrete-time linear quadratic regulations

    NASA Astrophysics Data System (ADS)

    Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

    2016-03-01

    In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.

  8. Irrigation Control in the Presence of Salinity: Extended Linear Quadratic Approach

    NASA Astrophysics Data System (ADS)

    Bras, Rafael L.; Seo, Dong-Jun

    1987-07-01

    An intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic (ELQ) control. The ELQ control is well-suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon. A conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop. Moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration. For the intraseasonal model to be effective against perennial salt accumulation in the root zone, it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season, thus avoiding any significant leaching prior to the next growing season. This long-term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level. The ELQ control is employed in a case study of expected net benefit maximization over an irrigation season of corn in Fort Morgan, Colorado. The results, in general, correspond well with expected irrigation schedules under different conditions and provide valuable information on both short- and long-term aspects of irrigation control under saline conditions. The ELQ control, being an analytic iterative solution scheme with theoretically guaranteed fast convergence, has a distinct computational advantage over state-of-the-art procedures.

  9. Fitting the linear quadratic model to detailed data sets for different dose ranges

    NASA Astrophysics Data System (ADS)

    Garcia, L. M.; Leblanc, J.; Wilkins, D.; Raaphorst, G. P.

    2006-06-01

    Survival curve behaviour and degree of correspondence between the linear-quadratic (LQ) model and experimental data in an extensive dose range for high dose rates were analysed. Detailed clonogenic assays with irradiation given in 0.5 Gy increments and a total dose range varying from 10.5 to 16 Gy were performed. The cell lines investigated were: CHOAA8 (Chinese hamster fibroblast cells), U373MG (human glioblastoma cells), CP3 and DU145 (human prostate carcinoma cell lines). The analyses were based on χ2-statistics and Monte Carlo simulation of the experiments. A decline of LQ fit quality at very low doses (<2 Gy) is observed. This result can be explained by the hypersensitive effect observed in CHOAA8, U373MG and DU145 data and an adaptive-type response in the CP3 cell line. A clear improvement of the fit is discerned by removing the low dose data points. The fit worsening at high doses also shows that LQ cannot explain this region. This shows that the LQ model fits better the middle dose region of the survival curve. The analysis conducted in our study reveals a dose dependency of the LQ fit in different cell lines.

  10. Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs

    NASA Technical Reports Server (NTRS)

    Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

    2001-01-01

    Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.

  11. A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

    NASA Astrophysics Data System (ADS)

    Xu, Jiuping; Li, Jun

    2002-09-01

    In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

  12. LPV gain-scheduled control of SCR aftertreatment systems

    NASA Astrophysics Data System (ADS)

    Meisami-Azad, Mona; Mohammadpour, Javad; Grigoriadis, Karolos M.; Harold, Michael P.; Franchek, Matthew A.

    2012-01-01

    Hydrocarbons, carbon monoxide and some of other polluting emissions produced by diesel engines are usually lower than those produced by gasoline engines. While great strides have been made in the exhaust aftertreatment of vehicular pollutants, the elimination of nitrogen oxide (NO x ) from diesel vehicles is still a challenge. The primary reason is that diesel combustion is a fuel-lean process, and hence there is significant unreacted oxygen in the exhaust. Selective catalytic reduction (SCR) is a well-developed technology for power plants and has been recently employed for reducing NO x emissions from automotive sources and in particular, heavy-duty diesel engines. In this article, we develop a linear parameter-varying (LPV) feedforward/feedback control design method for the SCR aftertreatment system to decrease NO x emissions while keeping ammonia slippage to a desired low level downstream the catalyst. The performance of the closed-loop system obtained from the interconnection of the SCR system and the output feedback LPV control strategy is then compared with other control design methods including sliding mode, and observer-based static state-feedback parameter-varying control. To reduce the computational complexity involved in the control design process, the number of LPV parameters in the developed quasi-LPV (qLPV) model is reduced by applying the principal component analysis technique. An LPV feedback/feedforward controller is then designed for the qLPV model with reduced number of scheduling parameters. The designed full-order controller is further simplified to a first-order transfer function with a parameter-varying gain and pole. Finally, simulation results using both a low-order model and a high-fidelity and high-order model of SCR reactions in GT-POWER interfaced with MATLAB/SIMULINK illustrate the high NO x conversion efficiency of the closed-loop SCR system using the proposed parameter-varying control law.

  13. Revealing a quantum feature of dimensionless uncertainty in linear and quadratic potentials by changing potential intervals

    NASA Astrophysics Data System (ADS)

    Kheiri, R.

    2016-09-01

    As an undergraduate exercise, in an article (2012 Am. J. Phys. 80 780–14), quantum and classical uncertainties for dimensionless variables of position and momentum were evaluated in three potentials: infinite well, bouncing ball, and harmonic oscillator. While original quantum uncertainty products depend on {{\\hslash }} and the number of states (n), a dimensionless approach makes the comparison between quantum uncertainty and classical dispersion possible by excluding {{\\hslash }}. But the question is whether the uncertainty still remains dependent on quantum number n. In the above-mentioned article, there lies this contrast; on the one hand, the dimensionless quantum uncertainty of the potential box approaches classical dispersion only in the limit of large quantum numbers (n\\to ∞ )—consistent with the correspondence principle. On the other hand, similar evaluations for bouncing ball and harmonic oscillator potentials are equal to their classical counterparts independent of n. This equality may hide the quantum feature of low energy levels. In the current study, we change the potential intervals in order to make them symmetric for the linear potential and non-symmetric for the quadratic potential. As a result, it is shown in this paper that the dimensionless quantum uncertainty of these potentials in the new potential intervals is expressed in terms of quantum number n. In other words, the uncertainty requires the correspondence principle in order to approach the classical limit. Therefore, it can be concluded that the dimensionless analysis, as a useful pedagogical method, does not take away the quantum feature of the n-dependence of quantum uncertainty in general. Moreover, our numerical calculations include the higher powers of the position for the potentials.

  14. Robust gain-scheduling energy-to-peak control of vehicle lateral dynamics stabilisation

    NASA Astrophysics Data System (ADS)

    Zhang, Hui; Zhang, Xinjie; Wang, Junmin

    2014-03-01

    In this paper, we investigate the vehicle lateral dynamics stabilisation problem to enhance vehicle handling by considering time-varying longitudinal velocity. The longitudinal velocity is described by a polytope with finite vertices and a novel technique is proposed to reduce the number of vertices. Since the tyre dynamics is nonlinear, the cornering stiffness is represented via the norm-bounded uncertainty. Concerning the time-varying velocity and the nonlinear tyre model, a linear parameter-varying vehicle model is obtained. As the velocity and the states are measurable, a gain-scheduling state-feedback controller is introduced. In the lateral control, the sideslip angle is required to be as small as possible and the yaw rate is constrained to a certain level. Thus, the control objective is to minimise the sideslip angle while the yaw rate is under a prescribed level or constrain both the sideslip angle and the yaw rate to prescribed levels. To consider the transient response of the closed-loop system, the ?-stability is also employed in the energy-to-peak control. The optimal controller can be obtained by solving a set of linear matrix inequalities. A nonlinear vehicle model is utilised to illustrate the design procedure and the effectiveness of the proposed design method. Finally, simulations and comparisons are carried out to show the significant advantage of the designed controller. Compared to the open-loop system, the closed-loop system with the designed controller can achieve much smaller sideslip angle and the yaw rate is closer to the desired yaw rate from a reference model. Therefore, the vehicle safety and the handling are both improved in our simulation cases.

  15. Multivariable control for the F-100 engine using the LQG/LTR methodology. [Linear-Quadratic-Gaussian/Loop Transfer Recovery

    NASA Technical Reports Server (NTRS)

    Athans, M.; Kapasouris, P.; Kappos, E.; Spang, H. A., III

    1984-01-01

    The design of a multivariable feedback control system for the Pratt and Whitney F-100 turbofan jet engine is a challenging task for control engineers. This paper employs a linearized model of the F-100 engine to demonstrate the use of the newly developed Linear Quadratic Gaussian/Loop Transfer Recovery (LQG/LTR) design methodology, which adopts an integrated frequency-domain and time-domain approach to multivariable feedback control synthesis so as to meet stability-robustness, command-following, and disturbance-rejection specifications.

  16. The variability of extreme temperatures and their relationship with atmospheric circulation: the contribution of applying linear and quadratic models

    NASA Astrophysics Data System (ADS)

    Savić, Stevan; Milovanović, Boško; Lužanin, Zorana; Lazić, Lazar; Dolinaj, Dragan

    2015-08-01

    This paper presents an analysis of the homogenised mean maximum ( T max) and minimum ( T min) temperatures. The data used in the analysis were collected at eight stations in the Autonomous Province of Vojvodina (Serbia) during the 1949-2008 period. The trends obtained from the slopes of the regression lines using the least square method show 0.9 °C/60 years for T max and 1.1 °C/60 years for T min; the non-parametric Mann-Kendall test was used to determine the statistically significant increasing trends of these two extreme parameters. In this paper, we analyse the influence of the Vangengeim-Girs classification of atmospheric circulation on the T max and T min trends in the Autonomous Province of Vojvodina (Serbia) using linear and quadratic models based on the least square method. Linear stepwise regression and the forward method reveal the highest dependence of T max and T min when the W or E circulation types are included in the model. Non-linear models show a greater contribution of T max and T min at W, E and C circulation types, respectively. The correction of the variance contribution of quadratic models ranges from approximately 16 to 44 % for T max and 32 to 38 % for T min.

  17. The Increase in Animal Mortality Risk following Exposure to Sparsely Ionizing Radiation Is Not Linear Quadratic with Dose

    PubMed Central

    Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.

    2015-01-01

    Introduction The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). It was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies. Methods and Results We argue that the linear-quadratic model does not provide appropriate support to estimate the risk of contemporary exposures. In this work, we re-estimated DDREFLSS using 15 animal studies that were not included in BEIR VII’s original analysis. Acute exposure data led to a DDREFLSS estimate from 0.9 to 3.0. By contrast, data that included both acute and protracted exposures led to a DDREFLSS estimate from 4.8 to infinity. These two estimates are significantly different, violating the assumptions of the linear-quadratic model, which predicts that DDREFLSS values calculated in either way should be the same. Conclusions Therefore, we propose that future estimates of the risk of protracted exposures should be based on direct comparisons of data from acute and protracted exposures, rather than from extrapolations from a linear-quadratic model. The risk of low dose exposures may be extrapolated from these protracted estimates, though we encourage ongoing debate as to whether this is the most valid approach. We also encourage efforts to enlarge the datasets used to estimate the risk of protracted exposures by including both human and animal data, carcinogenesis outcomes, a wider range of exposures, and by making more radiobiology data publicly accessible. We believe that these steps will

  18. Practical gust load alleviation and flutter suppression control laws based on a LQG methodology. [Linear Quadratic Gaussian

    NASA Technical Reports Server (NTRS)

    Gangsaas, D.; Ly, U.; Norman, D. C.

    1981-01-01

    A modified linear quadratic Gaussian (LQG) synthesis procedure has been used to design low-order robust multiloop controllers for a flexible airplane. The introduction of properly constructed fictitious Gauss-Markov processes in the control loops allowed meeting classical frequency-domain stability criteria using the direct synthesis procedures of modern time-domain control theory. Model reduction was used to simplify the control laws to the point where they could be easily implemented on onboard flight computers. These control laws provided excellent gust load and flutter mode control with good stability margins and compared very favorably to other control laws synthesized by the classical root-locus technique.

  19. CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1983-01-01

    The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

  20. Gain scheduling adaptive control strategies for HVDC systems to accommodate large disturbances

    SciTech Connect

    Reeve, J.; Sultan, M. )

    1994-02-01

    Techniques have been developed to permit the response of the controls for dc transmission systems to adapt to large system changes. A gain scheduling approach tunes the control as an on-line function of the effective short-circuit ratio and contingency indicators. The method has been tested by digital simulation, based on EMTP, of a back-to-back dc system. It has been found to be robust and control performance has been enhanced.

  1. Gain-scheduling Control of Rotary Inverted Pendulum by Weight Optimization and H∞ Loop Shaping Procedure

    NASA Astrophysics Data System (ADS)

    Yubai, Kazuhiro; Okuhara, Kazunori; Hirai, Junji

    Gain-scheduling control is one of effective methods for plants whose dynamics changes significantly according to its operating point. A frozen parameter method is known to be a practical gain-scheduling controller synthesis, which interpolates the controllers designed at the prespecified (frozen) operating points according to the current operation point. Hyde et al. proposed a gain-scheduling control that H∞ loop shaping procedure is adopted as a controller synthesis at each operating point. H∞ loop shaping procedure is based on loop shaping of an open loop characteristic by frequency weights and is known to be effective for plants with bad condition number. However, weight selection satisfying control specifications is hard job for a designer. This paper describes the design of a suboptimal weight and a controller by means of algorithm that maximizes the robust stability margin and shapes the open loop characteristic into the desired shape at each operating point. Moreover, we formulate a weight optimization problem as a generalized eigenvalue minimization problem, which reduces the designer's burden of weight selection. Finally, we realize robust and high performance control system by scheduling both weights and controllers. The effectiveness of the proposed control system is verified in terms of the achieved robust stability margin and experimental time responses of a rotary inverted pendulum which involves strong nonlinear dynamics.

  2. Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources

    SciTech Connect

    Guerrero, Mariana; Carlone, Marco

    2010-08-15

    Purpose: In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. Methods: The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. Results: In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter {beta}. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusions: The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

  3. A Mathematical Study to Select Fractionation Regimen Based on Physical Dose Distribution and the Linear-Quadratic Model

    SciTech Connect

    Mizuta, Masahiro; Takao, Seishin; Date, Hiroyuki; Kishimoto, Naoki; Sutherland, Kenneth L.; Onimaru, Rikiya; Shirato, Hiroki

    2012-11-01

    Purpose: Hypofractionated irradiation is often used in precise radiotherapy instead of conventional multifractionated irradiation. We propose a novel mathematical method for selecting a hypofractionated or multifractionated irradiation regimen based on physical dose distribution adding to biologic consideration. Methods and Materials: The linear-quadratic model was used for the radiation effects on tumor and normal tissues, especially organs at risk (OARs). On the basis of the assumption that the OAR receives a fraction of the dose intended for the tumor, the minimization problem for the damage effect on the OAR was treated under the constraint that the radiation effect on the tumor is fixed. Results: For an N-time fractionated irradiation regimen, the constraint of tumor lethality was described by an N-dimensional hypersphere. The total dose of the fractionated irradiations was considered for minimizing the damage effect on the OAR under the hypersphere condition. It was found that the advantage of hypofractionated or multifractionated irradiation therapies depends on the magnitude of the ratio of {alpha}/{beta} parameters for the OAR and tumor in the linear-quadratic model and the ratio of the dose for the OAR and tumor. Conclusions: Our mathematical method shows that multifractionated irradiation with a constant dose is better if the ratio of {alpha}/{beta} for the OAR and tumor is less than the ratio of the dose for the OAR and tumor, whereas hypofractionated irradiation is better otherwise.

  4. The increase in animal mortality risk following exposure to sparsely ionizing radiation is not linear quadratic with dose

    DOE PAGESBeta

    Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.; Aravindan, Natarajan

    2015-12-09

    The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). As a result, it was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limitedmore » number of animal studies.« less

  5. The increase in animal mortality risk following exposure to sparsely ionizing radiation is not linear quadratic with dose

    SciTech Connect

    Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.; Aravindan, Natarajan

    2015-12-09

    The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). As a result, it was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.

  6. On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.; Wang, C.

    1990-01-01

    The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

  7. On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.; Wang, C.

    1992-01-01

    The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

  8. Using Linear versus Quadratic Rules in Predictive and Descriptive Discriminant Analysis.

    ERIC Educational Resources Information Center

    McGee, Jennifer

    Both predictive discriminant analysis (PDA) and descriptive discriminant analysis (DDA) require a decision to pool group covariance matrices, or alternatively, to retain separate group covariance matrices when the group covariance matrices are too dissimilar to pool. Pooling the group covariance matrices involves the so-called "linear" rule,…

  9. AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

    USGS Publications Warehouse

    Lefkoff, L.J.; Gorelick, S.M.

    1987-01-01

    A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

  10. Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

    SciTech Connect

    Ayvaz, Muzaffer; Demiralp, Metin

    2011-09-14

    In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

  11. Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

    PubMed

    Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

    2015-04-01

    Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. PMID:25746821

  12. Post-Stall Aerodynamic Modeling and Gain-Scheduled Control Design

    NASA Technical Reports Server (NTRS)

    Wu, Fen; Gopalarathnam, Ashok; Kim, Sungwan

    2005-01-01

    A multidisciplinary research e.ort that combines aerodynamic modeling and gain-scheduled control design for aircraft flight at post-stall conditions is described. The aerodynamic modeling uses a decambering approach for rapid prediction of post-stall aerodynamic characteristics of multiple-wing con.gurations using known section data. The approach is successful in bringing to light multiple solutions at post-stall angles of attack right during the iteration process. The predictions agree fairly well with experimental results from wind tunnel tests. The control research was focused on actuator saturation and .ight transition between low and high angles of attack regions for near- and post-stall aircraft using advanced LPV control techniques. The new control approaches maintain adequate control capability to handle high angle of attack aircraft control with stability and performance guarantee.

  13. Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

    NASA Astrophysics Data System (ADS)

    Na, Xiaoxiang; Cole, David J.

    2013-02-01

    This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy.

  14. Predicting the clonogenic survival of A549 cells after modulated x-ray irradiation using the linear quadratic model

    NASA Astrophysics Data System (ADS)

    Bromley, Regina; Oliver, Lyn; Davey, Ross; Harvie, Rozelle; Baldock, Clive

    2009-01-01

    In this study we present two prediction methods, mean dose and summed dose, for predicting the number of A549 cells that will survive after modulated x-ray irradiation. The prediction methods incorporate the dose profile from the modulated x-ray fluence map applied across the cell sample and the linear quadratic (LQ) model. We investigated the clonogenic survival of A549 cells when irradiated using two different modulated x-ray fluence maps. Differences between the measured and predicted surviving fraction were observed for modulated x-ray irradiation. When the x-ray fluence map produced a steep dose gradient across the sample, fewer cells survived in the unirradiated region than expected. When the x-ray fluence map produced a less steep dose gradient across the sample, more cells survived in the unirradiated region than expected. Regardless of the steepness of the dose gradient, more cells survived in the irradiated region than expected for the reference dose range of 1-10 Gy. The change in the cell survival for the unirradiated regions of the two different dose gradients may be an important factor to consider when predicting the number of cells that will survive at the edge of modulated x-ray fields. This investigation provides an improved method of predicting cell survival for modulated x-ray radiation treatment. It highlights the limitations of the LQ model, particularly in its ability to describe the biological response of cells irradiated under these conditions.

  15. Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

    NASA Astrophysics Data System (ADS)

    McAneney, H.; O'Rourke, S. F. C.

    2007-02-01

    The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

  16. High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller

    SciTech Connect

    Habibullah, H. Pota, H. R. Petersen, I. R.

    2014-03-15

    This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM’s piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.

  17. Feedback shape control for deployable mesh reflectors using gain scheduling method

    NASA Astrophysics Data System (ADS)

    Xie, Yangmin; Shi, Hang; Alleyne, Andrew; Yang, Bingen

    2016-04-01

    This paper presents a theoretical study on the dynamic shape control problem of deployable mesh reflectors (DMRs) via feedback approaches. The reflector structure is simplified from a nonlinear model to be quasi-static with respect to temperature variations but dynamic with respect to mechanical vibrations. The orbital cycle is segmented into multiple temperature zones, and an H∞ robust state feedback controller is designed for each zone to guarantee the local stability of the system under the model uncertainty caused by thermal effects and to reject external force disturbances. At the same time, gain scheduling control method is adopted to compensate thermal distortions and to ensure smooth transition response when switching among the local robust controllers. A DMR model is considered in the case study to show the effectiveness of the control approach. The structural vibrations caused by external force disturbances can be sufficiently suppressed in a much shorter time. The closed loop response of the DMR structure shows that much higher surface accuracy is obtained during the orbiting mission compared to the open-loop configuration, and transient focal length and transient de-focus of the reflector are well controlled within the satisfactory bounds, demonstrating the numerical feasibility of the proposed method to solve the dynamic shape control problem of DMRs.

  18. Control of microbial fuel cell voltage using a gain scheduling control strategy

    NASA Astrophysics Data System (ADS)

    Boghani, Hitesh C.; Michie, Iain; Dinsdale, Richard M.; Guwy, Alan J.; Premier, Giuliano C.

    2016-08-01

    Recent microbial fuel cell (MFC) research frequently addresses matters associated with scale and deployability. Modularisation is often needed to reduce ohmic losses with increasing volume. Series/parallel is then often an obvious strategy to enhance power quality during operation, to make best use of generated electricity. Hence, voltage reversal resulting from power and voltage mismatch between cells become virtually unavoidable. Control MFC voltages could be used to stabilise MFC stacks. Here, nonlinear MFCs are controlled using simple gain scheduled Proportional + Integral actions. Parsimonious control may be necessary for implementation in MFC arrays, so minimising costs. Controller parameterisation used several linearised models over the dynamic operating range of the MFCs. Controller gains were then scheduled according to the operating conditions. A digital potentiometer was used to actuate the control, varying the current sourced from the MFC. The results show that the controller was able to control MFC voltages, rejecting the disturbances. It was shown that the controller was transferable between MFCs with different power performances. This study demonstrates that the control of MFCs can be achieved with relatively simple digital approaches, plausibly implementable using low cost microcontrollers, and likely to be useful in the effective deployment of MFCs in large scale arrays.

  19. Quadratic Damping

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  20. Temperature effects on (1+1)-dimensional steady-state bright spatial solitons in biased photorefractive crystals with both the linear and quadratic effects

    NASA Astrophysics Data System (ADS)

    Hao, Lili; Wang, Qiang; Hou, Chunfeng

    2016-05-01

    The temperature effects on the intensity profile, self-deflection process, and stability of (1 + 1)-dimensional steady-state bright solitons resulting from both the linear and quadratic electro-optic effects are comprehensively analyzed. Moreover, three physical factors, i.e. diffusion effect, dark irradiance, and the dielectric constant, have been investigated through the theoretical analysis to determine which one dominates the temperature dependence of intensity profile and self-deflection of bright solitons. It is also found that the incident beam evolves into stable bright solitons in the vicinity of initial temperature, but oscillates or even collapses when the crystal temperature deviates significantly from the initial temperature.

  1. Modeling and distributed gain scheduling strategy for load frequency control in smart grids with communication topology changes.

    PubMed

    Liu, Shichao; Liu, Xiaoping P; El Saddik, Abdulmotaleb

    2014-03-01

    In this paper, we investigate the modeling and distributed control problems for the load frequency control (LFC) in a smart grid. In contrast with existing works, we consider more practical and real scenarios, where the communication topology of the smart grid changes because of either link failures or packet losses. These topology changes are modeled as a time-varying communication topology matrix. By using this matrix, a new closed-loop power system model is proposed to integrate the communication topology changes into the dynamics of a physical power system. The globally asymptotical stability of this closed-loop power system is analyzed. A distributed gain scheduling LFC strategy is proposed to compensate for the potential degradation of dynamic performance (mean square errors of state vectors) of the power system under communication topology changes. In comparison to conventional centralized control approaches, the proposed method can improve the robustness of the smart grid to the variation of the communication network as well as to reduce computation load. Simulation results show that the proposed distributed gain scheduling approach is capable to improve the robustness of the smart grid to communication topology changes. PMID:24200162

  2. Vehicle rollover avoidance by application of gain-scheduled LQR controllers using state observers

    NASA Astrophysics Data System (ADS)

    Dal Poggetto, Vinicius F.; Serpa, Alberto L.

    2016-02-01

    Many researches have been conducted in the area of control applied to vehicle dynamics, aiming at reducing the possibility of the occurrence of the type of accident known as rollover. In this research, based on a common nonlinear model and its linearisation, a method for properly selecting matrices for solving the Riccati equation considering different speeds was proposed. The method showed in which ways speed really influences the choice of controller gains. By developing the dynamic equations for the yaw- and roll-coupled motions and modelling of controllers and state observers, it is possible to compare the efficacy of this control strategy using both linear and nonlinear simulations using Matlab. Significant results were obtained regarding the reduction of the rollover coefficient for a double-lane change manoeuvre at different speeds, thus indicating advantages of using this controller in practical cases.

  3. Effects of model error on control of large flexible space antenna with comparisons of decoupled and linear quadratic regulator control procedures

    NASA Technical Reports Server (NTRS)

    Hamer, H. A.; Johnson, K. G.

    1986-01-01

    An analysis was performed to determine the effects of model error on the control of a large flexible space antenna. Control was achieved by employing two three-axis control-moment gyros (CMG's) located on the antenna column. State variables were estimated by including an observer in the control loop that used attitude and attitude-rate sensors on the column. Errors were assumed to exist in the individual model parameters: modal frequency, modal damping, mode slope (control-influence coefficients), and moment of inertia. Their effects on control-system performance were analyzed either for (1) nulling initial disturbances in the rigid-body modes, or (2) nulling initial disturbances in the first three flexible modes. The study includes the effects on stability, time to null, and control requirements (defined as maximum torque and total momentum), as well as on the accuracy of obtaining initial estimates of the disturbances. The effects on the transients of the undisturbed modes are also included. The results, which are compared for decoupled and linear quadratic regulator (LQR) control procedures, are shown in tabular form, parametric plots, and as sample time histories of modal-amplitude and control responses. Results of the analysis showed that the effects of model errors on the control-system performance were generally comparable for both control procedures. The effect of mode-slope error was the most serious of all model errors.

  4. Dosimetric characteristics of a newly designed grid block for megavoltage photon radiation and its therapeutic advantage using a linear quadratic model.

    PubMed

    Meigooni, Ali S; Dou, Kai; Meigooni, Navid J; Gnaster, Michael; Awan, Shahid; Dini, Sharifeh; Johnson, Ellis L

    2006-09-01

    Grid radiation therapy with megavoltage x-ray beam has been proven to be an effective technique for management of large, bulky malignant tumors. The clinical advantage of GRID therapy, combined with conventional radiation therapy, has been demonstrated using a prototype GRID block [Mohiuddin, Curtis, Grizos, and Komarnicky, Cancer 66, 114-118 (1990)]. Recently, a new GRID block design with improved dosimetric properties has become commercially available from Radiation Product Design, Inc. (Albertive, MN). This GRID collimator consists of an array of focused apertures in a cerrobend block arranged in a hexagonal pattern having a circular cross-section with a diameter and center-to-center spacing of 14.3 and 21.1 mm, respectively, in the plane of isocenter. In this project, dosimetric characteristics of the newly redesigned GRID block have been investigated for a Varian 21EX linear accelerator (Varian Associates, Palo Alto, CA). These determinations were performed using radiographic films, thermoluminescent dosimeters in Solid Water phantom materials, and an ionization chamber in water. The output factor, percentage depth dose, beam profiles, and isodose distributions of the GRID radiation as a function of field size and beam energy have been measured using both 6 and 18 MV x-ray beams. In addition, the therapeutic advantage obtained from this treatment modality with the new GRID block design for a high, single fraction of dose has been calculated using the linear quadratic model with alpha/beta ratios for typical tumor and normal cells. These biological characteristics of the new GRID block design will also be presented. PMID:17022209

  5. Dosimetric characteristics of a newly designed grid block for megavoltage photon radiation and its therapeutic advantage using a linear quadratic model

    SciTech Connect

    Meigooni, Ali S.; Dou Kai; Meigooni, Navid J.; Gnaster, Michael; Awan, Shahid; Dini, Sharifeh; Johnson, Ellis L.

    2006-09-15

    Grid radiation therapy with megavoltage x-ray beam has been proven to be an effective technique for management of large, bulky malignant tumors. The clinical advantage of GRID therapy, combined with conventional radiation therapy, has been demonstrated using a prototype GRID block [Mohiuddin, Curtis, Grizos, and Komarnicky, Cancer 66, 114-118 (1990)]. Recently, a new GRID block design with improved dosimetric properties has become commercially available from Radiation Product Design, Inc. (Albertive, MN). This GRID collimator consists of an array of focused apertures in a cerrobend block arranged in a hexagonal pattern having a circular cross-section with a diameter and center-to-center spacing of 14.3 and 21.1 mm, respectively, in the plane of isocenter. In this project, dosimetric characteristics of the newly redesigned GRID block have been investigated for a Varian 21EX linear accelerator (Varian Associates, Palo Alto, CA). These determinations were performed using radiographic films, thermoluminescent dosimeters in Solid Water trade mark sign phantom materials, and an ionization chamber in water. The output factor, percentage depth dose, beam profiles, and isodose distributions of the GRID radiation as a function of field size and beam energy have been measured using both 6 and 18 MV x-ray beams. In addition, the therapeutic advantage obtained from this treatment modality with the new GRID block design for a high, single fraction of dose has been calculated using the linear quadratic model with {alpha}/{beta} ratios for typical tumor and normal cells. These biological characteristics of the new GRID block design will also be presented.

  6. A model-based gain scheduling approach for controlling the common-rail system for GDI engines

    NASA Astrophysics Data System (ADS)

    di Gaeta, Alessandro; Montanaro, Umberto; Fiengo, Giovanni; Palladino, Angelo; Giglio, Veniero

    2012-04-01

    The progressive reduction in vehicle emission requirements have forced the automotive industry to invest in research for developing alternative and more efficient control strategies. All control features and resources are permanently active in an electronic control unit (ECU), ensuring the best performance with respect to emissions, fuel economy, driveability and diagnostics, independently from engine working point. In this article, a considerable step forward has been achieved by the common-rail technology which has made possible to vary the injection pressure over the entire engine speed range. As a consequence, the injection of a fixed amount of fuel is more precise and multiple injections in a combustion cycle can be made. In this article, a novel gain scheduling pressure controller for gasoline direct injection (GDI) engine is designed to stabilise the mean fuel pressure into the rail and to track demanded pressure trajectories. By exploiting a simple control-oriented model describing the mean pressure dynamics in the rail, the control structure turns to be simple enough to be effectively implemented in commercial ECUs. Experimental results in a wide range of operating points confirm the effectiveness of the proposed control method to tame efficiently the mean value pressure dynamics of the plant showing a good accuracy and robustness with respect to unavoidable parameters uncertainties, unmodelled dynamics, and hidden coupling terms.

  7. The application of the linear quadratic model to compensate the effects of prolonged fraction delivery time on a Balb/C breast adenocarcinoma tumor: An in vivo study.

    PubMed

    Nikzad, Safoora; Hashemi, Bijan; Hasan, Zuhair Saraf; Mozdarani, Hossein; Baradaran-Ghahfarokhi, Milad; Amini, Payam

    2016-01-01

    Purpose To investigate the effect of increasing the overall treatment time as well as delivering the compensating doses on the Balb/c breast adenocarcinoma (4T1) tumor. Materials and methods A total of 72 mice were divided into two aliquots (classes A and B) based on the initial size of their induced tumor. Each class was divided into a control and several treatment groups. Among the treatment groups, group 1 was continuously exposed to 2 Gy irradiation, and groups 2 and 3 received two subfractions of 1 Gy over the total treatment times of 30 and 60 min, respectively. To investigate the effect of compensating doses, calculated based on the developed linear quadratic model (LQ) model, the remaining two groups (groups 4 and 5) received two subfractions of 1.16 and 1.24 Gy over the total treatment times of 30 and 60 min, respectively. The growing curves, Tumor Growth Time (TGT), Tumor Growth Delay Time (TGDT) and the survival of the animals were studied. Results For class A (tumor size ≤ 30 mm(3)), the average tumor size in the irradiated groups 1-5 was considerably different compared to the control group as one unit (day) change in time, by amount of -160.8, -158.9, +39.4 and +44.0, respectively. While these amounts were +22.0, +17.9, -21.7 and -0.1 for class B (tumor size ≥ 400 mm(3)). For the class A of animals, the TGT and TGDT parameters were significantly lower (0 ≤ 0.05) for the groups 2 and 3, compared to group 1. There was no significant difference (p > 0.05) between groups 1, 4 and 5 in this class. There was no significant difference (p > 0.05) between all the treated groups in class B. Conclusions Increasing total treatment time affects the radiobiological efficiency of treatment especially in small-sized tumor. The compensating doses derived from the LQ model can be used to compensate the effects of prolonged treatment times at in vivo condition. PMID:26630280

  8. Self-Replicating Quadratics

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  9. A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

    NASA Astrophysics Data System (ADS)

    Sandhu, Amit

    A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

  10. Identification and robust control of linear parameter-varying systems

    NASA Astrophysics Data System (ADS)

    Lee, Lawton Hubert

    This dissertation deals with linear parameter-varying (LPV) systems: linear dynamic systems that depend on time-varying parameters. These systems appear in gain scheduling problems, and much recent research has been devoted to their prospective usefulness for systematic gain scheduling. We primarily focus on robust control of uncertain LPV systems and identification of LPV systems that are modelable as linear-fractional transformations (LFTs). Using parameter-dependent quadratic Lyapunov functions, linear matrix inequalities (LMIs), and scaled small-gain arguments, we define notions of stability and induced-{cal L}sb2 performance for uncertain LPV systems whose parameters and rates of parameter variation satisfy given bounds. The performance criterion involves integral quadratic constraints and implies naturally parameter-dependent induced-{cal L}sb2 norm bounds. We formulate and solve an {cal H}sb{infty}-like control problem for an LPV plant with measurable parameters and an "Output/State Feedback" structure: the feedback outputs include some noiselessly measured states. Necessary and sufficient solvability conditions reduce to LMIs that can be solved approximately using finite-dimensional convex programming. Reduced-order LPV controllers are constructed from the LMI solutions. A D-K iteration-like procedure provides robustness to structured, time-varying, parametric uncertainty. The design method is applied to a motivating example: flight control for the F-16 VISTA throughout its subsonic flight envelope. Parameter-dependent weights and {cal H}sb{infty} design principles describe the performance objectives. Closed-loop responses exhibited by nonlinear simulations indicate satisfactory flying qualities. Identification of linear-fractional LPV systems is treated using maximum-likelihood parameter estimation. Computing the gradient and Hessian of a maximum-likelihood cost function reduces to simulating one LPV filter per identified parameter. We use nonlinear

  11. Quadratic boundedness of uncertain nonlinear dynamic systems

    NASA Astrophysics Data System (ADS)

    Brockman, Mark Lawrence

    Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.

  12. Quadratic eigenvalue problems.

    SciTech Connect

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  13. Self-replicating quadratics

    NASA Astrophysics Data System (ADS)

    Withers, Christopher S.; Nadarajah, Saralees

    2012-06-01

    We show that there are exactly four quadratic polynomials, Q(x) = x 2 + ax + b, such that For n = 1, 2, … , these quadratic polynomials can be written as the product of N = 2 n quadratic polynomials in x 1/N , namely, ? , where w N is the Nth root of 1.

  14. 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.

  15. The Mystical "Quadratic Formula."

    ERIC Educational Resources Information Center

    March, Robert H.

    1993-01-01

    Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

  16. A Quadratic Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  17. Quadratic elongation: A quantitative measure of distortion in coordination polyhedra

    USGS Publications Warehouse

    Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.

    1971-01-01

    Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.

  18. Galactic chemical evolution and nucleocosmochronology - Analytic quadratic models

    NASA Technical Reports Server (NTRS)

    Clayton, D. D.

    1985-01-01

    Quadratic models of the chemical evolution of the Galaxy for a star formation rate proportional to the square of the gas mass are studied. The search for analytic solutions to the gas mass and star mass for time-dependent rates of gaseous infall onto the disk is examined. The quadratic models are compared to models having linear star formation rates. The mass, metallicity, number of stars, and U-235/U-238 isotopic ratio for the models which are subjected to the same infall rate, the same initial disk mass, and the same final gas fraction are compared. The results of the comparison indicate that: (1) the average dwarf age is greater in the quadratic model, (2) the metallicity grows initially faster in the quadratic model, (3) the quadratic model has a smaller percentage of low-Z dwarfs, and (4) the U-235/U-238 isotopic ratio indicates a younger quadratic model.

  19. Fourier analysis of quadratic phase interferograms

    NASA Astrophysics Data System (ADS)

    Muñoz-Maciel, Jesús; Mora-González, Miguel; Casillas-Rodríguez, Francisco J.; Peña-Lecona, Francisco G.

    2015-06-01

    A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.

  20. Single-photon quadratic optomechanics

    PubMed Central

    Liao, Jie-Qiao; Nori, Franco

    2014-01-01

    We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128

  1. AdS waves as exact solutions to quadratic gravity

    SciTech Connect

    Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin

    2011-04-15

    We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.

  2. Optimal Approximation of Quadratic Interval Functions

    NASA Technical Reports Server (NTRS)

    Koshelev, Misha; Taillibert, Patrick

    1997-01-01

    Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

  3. Solitons in quadratic media

    NASA Astrophysics Data System (ADS)

    Colin, M.; Di Menza, L.; Saut, J. C.

    2016-03-01

    In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.

  4. Quadratic algebras for three-dimensional superintegrable systems

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2010-02-15

    The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

  5. Quadratic spatial soliton interactions

    NASA Astrophysics Data System (ADS)

    Jankovic, Ladislav

    Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

  6. Quadratic soliton self-reflection at a quadratically nonlinear interface

    NASA Astrophysics Data System (ADS)

    Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

    2003-11-01

    The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

  7. Degenerate nonlinear programming with a quadratic growth condition.

    SciTech Connect

    Anitescu, M.; Mathematics and Computer Science

    2000-01-01

    We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.

  8. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  9. Quadratic Programming for Allocating Control Effort

    NASA Technical Reports Server (NTRS)

    Singh, Gurkirpal

    2005-01-01

    A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

  10. Holographic entropy increases in quadratic curvature gravity

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.

    2015-09-01

    Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.

  11. On the connection of the quadratic Lienard equation with an equation for the elliptic functions

    NASA Astrophysics Data System (ADS)

    Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.

    2015-07-01

    The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.

  12. Students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  13. A quadratic weight selection algorithm. [for optimal flight control

    NASA Technical Reports Server (NTRS)

    Broussard, J. R.

    1981-01-01

    A new numerical algorithm is presented which determines a positive semi-definite state weighting matrix in the linear-quadratic optimal control design problem. The algorithm chooses the weighting matrix by placing closed-loop eigenvalues and eigenvectors near desired locations using optimal feedback gains. A simplified flight control design example is used to illustrate the algorithms capabilities.

  14. Quadratic invariants for discrete clusters of weakly interacting waves

    NASA Astrophysics Data System (ADS)

    Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.

    2013-06-01

    We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.

  15. A transient, quadratic nodal method for triangular-Z geometry

    SciTech Connect

    DeLorey, T.F.

    1993-06-01

    Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

  16. Quadratic expressions by means of `summing all the matchsticks'

    NASA Astrophysics Data System (ADS)

    Faaiz Gierdien, M.

    2012-09-01

    This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such 'matchstick' problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are linear and not quadratic. It will be shown that a pedagogy of 'summing all the matchsticks' is central to the emergence of quadratic expressions. This pedagogy involves generational and transformational activities which are considered as some of the main activities of algebra. Key elements to these activities are processes such as recognizing and extending patterns, and specializing and generalizing particular functional relationships. Implications of these processes in terms of algebraic thinking are considered.

  17. Orthogonality preserving infinite dimensional quadratic stochastic operators

    SciTech Connect

    Akın, Hasan; Mukhamedov, Farrukh

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  18. Compact stars with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi

    2015-05-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  19. Feedback linearization application for LLRF control system

    SciTech Connect

    Kwon, S.; Regan, A.; Wang, Y.M.; Rohlev, T.

    1999-06-01

    The Low Energy Demonstration Accelerator (LEDA) being constructed at Los Alamos National Laboratory will serve as the prototype for the low energy section of Acceleration Production of Tritium (APT) accelerator. This paper addresses the problem of the LLRF control system for LEDA. The authors propose a control law which is based on exact feedback linearization coupled with gain scheduling which reduces the effect of the deterministic klystron cathode voltage ripple that is due to harmonics of the high voltage power supply and achieves tracking of desired set points. Also, they propose an estimator of the ripple and its time derivative and the estimates based feedback linearization controller.

  20. Feedback linearization application for LLRF control system

    SciTech Connect

    Kwon, S.; Regan, A.; Wang, Y.M.; Rohlev, T.

    1998-12-31

    The Low Energy Demonstration Accelerator (LEDA) being constructed at Los Alamos National Laboratory will serve as the prototype for the low energy section of Acceleration Production of Tritium (APT) accelerator. This paper addresses the problem of the LLRF control system for LEDA. The authors propose a control law which is based on exact feedback linearization coupled with gain scheduling which reduces the effect of the deterministic klystron cathode voltage ripple that is due to harmonics of the high voltage power supply and achieves tracking of desired set points. Also, they propose an estimator of the ripple and its time derivative and the estimates based feedback linearization controller.

  1. Coherent states for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Contreras-Astorga, Alonso; Fernández C, David J.; Velázquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  2. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  3. Geometrical and Graphical Solutions of Quadratic Equations.

    ERIC Educational Resources Information Center

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  4. Multivariable quadratic synthesis of an advanced turbofan engine controller

    NASA Technical Reports Server (NTRS)

    Dehoff, R. L.; Hall, W. E., Jr.

    1978-01-01

    A digital controller for an advanced turbofan engine utilizing multivariate feedback is described. The theoretical background of locally linearized control synthesis is reviewed briefly. The application of linear quadratic regulator techniques to the practical control problem is presented. The design procedure has been applied to the F100 turbofan engine, and details of the structure of this system are explained. Selected results from simulations of the engine and controller are utilized to illustrate the operation of the system. It is shown that the general multivariable design procedure will produce practical and implementable controllers for modern, high-performance turbine engines.

  5. Binary Quadratic Forms: A Historical View

    ERIC Educational Resources Information Center

    Khosravani, Azar N.; Beintema, Mark B.

    2006-01-01

    We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

  6. An Unexpected Influence on a Quadratic

    ERIC Educational Resources Information Center

    Davis, Jon D.

    2013-01-01

    Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

  7. Factorising a Quadratic Expression with Geometric Insights

    ERIC Educational Resources Information Center

    Joarder, Anwar H.

    2015-01-01

    An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

  8. A Quadratic Closure for Compressible Turbulence

    SciTech Connect

    Futterman, J A

    2008-09-16

    We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

  9. L -functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field

    NASA Astrophysics Data System (ADS)

    Louboutin, Stephane

    1992-07-01

    Starting from the analytic class number formula involving its L-function, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class number tables. Then, using class field theory, we will construct a periodic character &chi , defined on the ring of integers of a field K that is a quadratic extension of a principal imaginary quadratic field k, such that the zeta function of K is the product of the zeta function of k and of the L-function L(s,χ) . We will then determine an integral representation of this L-function that enables us to calculate the class number of K numerically, as soon as its regulator is known. It will also provide us with an upper bound for these class numbers, showing that Hua's bound for the class numbers of imaginary and real quadratic fields is not the best that one could expect. We give statistical results concerning the class numbers of the first 50000 quadratic extensions of {Q}(i) with prime relative discriminant (and with K/Q a non-Galois quartic extension). Our analytic calculation improves the algebraic calculation used by Lakein in the same way as the analytic calculation of the class numbers of real quadratic fields made by Williams and Broere improved the algebraic calculation consisting in counting the number of cycles of reduced ideals. Finally, we give upper bounds for class numbers of K that is a quadratic extension of an imaginary quadratic field k which is no longer assumed to be of class number one.

  10. Automated calculation of anharmonic vibrational contributions to first hyperpolarizabilities: Quadratic response functions from vibrational configuration interaction wave functions

    NASA Astrophysics Data System (ADS)

    Hansen, Mikkel Bo; Christiansen, Ove; Hättig, Christof

    2009-10-01

    Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.

  11. Seven Wonders of the Ancient and Modern Quadratic World.

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2001-01-01

    Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

  12. Quadratic Stochastic Operators with Countable State Space

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir

    2016-03-01

    In this paper, we provide the classes of Poisson and Geometric quadratic stochastic operators with countable state space, study the dynamics of these operators and discuss their application to economics.

  13. Schur Stability Regions for Complex Quadratic Polynomials

    ERIC Educational Resources Information Center

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  14. Quantum integrability of quadratic Killing tensors

    SciTech Connect

    Duval, C.; Valent, G.

    2005-05-01

    Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.

  15. Measurement of quadratic electrogyration effect in castor oil

    NASA Astrophysics Data System (ADS)

    Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

    2015-07-01

    This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

  16. Weight of quadratic forms and graph states

    NASA Astrophysics Data System (ADS)

    Cosentino, Alessandro; Severini, Simone

    2009-11-01

    We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.

  17. Phase recovery based on quadratic programming

    NASA Astrophysics Data System (ADS)

    Zhang, Quan Bing; Ge, Xiao Juan; Cheng, Ya Dong; Ni, Na

    2014-11-01

    Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years, the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR) algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not recover the sparse signal effectively.

  18. The Factorability of Quadratics: Motivation for More Techniques

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2005-01-01

    Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

  19. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  20. Limit cycles near hyperbolas in quadratic systems

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume

    In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.

  1. Fast approximate quadratic programming for graph matching.

    PubMed

    Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  2. Quadratic forms of projective spaces over rings

    NASA Astrophysics Data System (ADS)

    Levchuk, V. M.; Starikova, O. A.

    2006-06-01

    In the passage from fields to rings of coefficients quadratic forms with invertible matrices lose their decisive role. It turns out that if all quadratic forms over a ring are diagonalizable, then in effect this is always a local principal ideal ring R with 2\\in R^*. The problem of the construction of a `normal' diagonal form of a quadratic form over a ring R faces obstacles in the case of indices \\vert R^*:R^{*2}\\vert greater than 1. In the case of index 2 this problem has a solution given in Theorem 2.1 for 1+R^{*2}\\subseteq R^{*2} (an extension of the law of inertia for real quadratic forms) and in Theorem 2.2 for 1+R^2 containing an invertible non-square. Under the same conditions on a ring R with nilpotent maximal ideal the number of classes of projectively congruent quadratic forms of the projective space associated with a free R-module of rank n is explicitly calculated (Proposition 3.2). Up to projectivities, the list of forms is presented for the projective plane over R and also (Theorem 3.3) over the local ring F\\lbrack\\lbrack x,y\\rbrack\\rbrack/\\langle x^{2},xy,y^{2}\\rangle with non-principal maximal ideal, where F=2F is a field with an invertible non-square in 1+F^{2} and \\vert F^{*}:F^{*2}\\vert=2. In the latter case the number of classes of non-diagonalizable quadratic forms of rank 0 depends on one's choice of the field F and is not even always finite; all the other forms make up 21 classes.

  3. Quintessence with quadratic coupling to dark matter

    SciTech Connect

    Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy

    2010-04-15

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  4. Heredity in one-dimensional quadratic maps

    NASA Astrophysics Data System (ADS)

    Romera, M.; Pastor, G.; Alvarez, G.; Montoya, F.

    1998-12-01

    In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found, and the ancestral path that joins all its ancestors. The ancestral path holds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the pattern constitute the family tree of the pattern, which is important to study and understand the orbit's ordering.

  5. Quadratic-Like Dynamics of Cubic Polynomials

    NASA Astrophysics Data System (ADS)

    Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen

    2016-02-01

    A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.

  6. Guises and disguises of quadratic divergences

    SciTech Connect

    Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  7. On orthogonality preserving quadratic stochastic operators

    SciTech Connect

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  8. Integration of the Quadratic Function and Generalization

    ERIC Educational Resources Information Center

    Mitsuma, Kunio

    2011-01-01

    We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

  9. Curious Consequences of a Miscopied Quadratic

    ERIC Educational Resources Information Center

    Poet, Jeffrey L.; Vestal, Donald L., Jr.

    2005-01-01

    The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

  10. Quadratic minima and modular forms II

    NASA Astrophysics Data System (ADS)

    Brent, Barry

    We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two even positive-definite quadratic form. These bounds extend partial results in part I.

  11. Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

    SciTech Connect

    Campoamor-Stursberg, R.

    2008-05-15

    By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.

  12. Haar wavelet operational matrix method for solving constrained nonlinear quadratic optimal control problem

    NASA Astrophysics Data System (ADS)

    Swaidan, Waleeda; Hussin, Amran

    2015-10-01

    Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.

  13. User's guide for SOL/QPSOL: a Fortran package for quadratic programming

    SciTech Connect

    Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.

    1983-07-01

    This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.

  14. An Instability Index Theory for Quadratic Pencils and Applications

    NASA Astrophysics Data System (ADS)

    Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

    2014-04-01

    Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

  15. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

  16. Factorization using the quadratic sieve algorithm

    SciTech Connect

    Davis, J.A.; Holdridge, D.B.

    1983-12-01

    Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

  17. Factorization using the quadratic sieve algorithm

    SciTech Connect

    Davis, J.A.; Holdridge, D.B.

    1983-01-01

    Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

  18. Characterization of a Quadratic Function in Rn

    ERIC Educational Resources Information Center

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  19. An alternative method on quadratic programming problems

    NASA Astrophysics Data System (ADS)

    Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.

    2015-05-01

    In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.

  20. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    ERIC Educational Resources Information Center

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  1. THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

    EPA Science Inventory

    Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

  2. Cosmology for quadratic gravity in generalized Weyl geometry

    NASA Astrophysics Data System (ADS)

    Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.

    2016-04-01

    A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.

  3. Wind turbine power tracking using an improved multimodel quadratic approach.

    PubMed

    Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

    2010-07-01

    In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. PMID:20434153

  4. Developed Adomian method for quadratic Kaluza-Klein relativity

    NASA Astrophysics Data System (ADS)

    Azreg-Aïnou, Mustapha

    2010-01-01

    We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4 × 4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic five-dimensional GR, derive some of their properties using ADecM and construct the most general unique power series solutions. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.

  5. Schwarz and multilevel methods for quadratic spline collocation

    SciTech Connect

    Christara, C.C.; Smith, B.

    1994-12-31

    Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

  6. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

    SciTech Connect

    Golubkov, A A; Makarov, Vladimir A

    2011-11-30

    We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

  7. A nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term

    NASA Astrophysics Data System (ADS)

    Wang, Xiao-Lu; Fan, Xiang-Yu; He, Yong-Ming; Nie, Ren-Shi; Huang, Quan-Hua

    2013-08-01

    Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log-log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately.

  8. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

    PubMed Central

    Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

    2015-01-01

    It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

  9. Modelling non-normal data: The relationship between the skew-normal factor model and the quadratic factor model.

    PubMed

    Smits, Iris A M; Timmerman, Marieke E; Stegeman, Alwin

    2016-05-01

    Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew-normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew-normal factor are equivalent to those under a quadratic model up to third-order moments. The reverse only holds if the quadratic loadings are equal to each other and within certain bounds. We illustrate that observed data which follow any skew-normal factor model can be so well approximated with the quadratic factor model that the models are empirically indistinguishable, and that the reverse does not hold in general. The choice between the two models to account for deviations of normality is illustrated by an empirical example from clinical psychology. PMID:26566696

  10. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method

    NASA Astrophysics Data System (ADS)

    Bizyaev, I. A.; Kozlov, V. V.

    2015-12-01

    We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.

  11. Linear collider: a preview

    SciTech Connect

    Wiedemann, H.

    1981-11-01

    Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.

  12. Inter-annual precipitation changes as quadratic signals in the GRACE time-variable gravity

    NASA Astrophysics Data System (ADS)

    Ogawa, R.; Chao, B. F.; Heki, K.

    2009-04-01

    The Gravity Recovery and Climate Experiment (GRACE) satellite mission has been producing scientific results on mass variations on inter-annual timescales, e.g. melting of ice sheet in Greenland and mountain glaciers in Alaska, Eastern Africa drought, water level increase in Caspian Sea, etc. In these discussions only linear trends and the seasonal components have been analyzed in the monthly GRACE time series, whereas little attention has been paid so far to the existence of the quadratic changes which signify the temporal accelerations. With over 6 years of GRACE data and revisiting the time-variable gravity field of various regions, we find that such acceleration/deceleration terms are quite often significantly different from zero. They include East Africa, near Obi River, Caspian Sea, Black Sea, Central Asia, and southern South America, whereof discussions of linear trends without specifying the epochs are inadequate. Here we investigate geophysical implication of these quadratic terms; in particular gravity changes in land areas reflect, to a large extent, soil moisture variations. Soil moisture is the time integration of water fluxes, i.e. precipitation, evapotranspiration and runoff. Here we consider that the linear trend in precipitation is responsible for the quadratic change in gravity, and examine trends of observed precipitation in various regions from CMAP (Climate Prediction Center Merged Analysis of Precipitation). Thus, in order to compare linear trend in CMAP and acceleration in GRACE, we calculate month-to-month difference of equivalent water depth at GRACE grid points, and modeled them with seasonal variations and linear trends. We found good agreement between their geographical distributions although amplitudes are smaller in GRACE, meaning the quadratic gravity changes in the GRACE data do reflect inter-annual changes of precipitation fairly faithfully.

  13. Reduced order parameter estimation using quasilinearization and quadratic programming

    NASA Astrophysics Data System (ADS)

    Siade, Adam J.; Putti, Mario; Yeh, William W.-G.

    2012-06-01

    The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

  14. A quadratic analog-to-digital converter

    NASA Technical Reports Server (NTRS)

    Harrison, D. C.; Staples, M. H.

    1980-01-01

    An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.

  15. Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.

    PubMed

    Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A

    2016-03-21

    Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037

  16. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

  17. Blind deconvolution estimation of fluorescence measurements through quadratic programming

    NASA Astrophysics Data System (ADS)

    Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.

    2015-07-01

    Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.

  18. Quadratic spline collocation and parareal deferred correction method for parabolic PDEs

    NASA Astrophysics Data System (ADS)

    Liu, Jun; Wang, Yan; Li, Rongjian

    2016-06-01

    In this paper, we consider a linear parabolic PDE, and use optimal quadratic spline collocation (QSC) methods for the space discretization, proceed the parareal technique on the time domain. Meanwhile, deferred correction technique is used to improve the accuracy during the iterations. The error estimation is presented and the stability is analyzed. Numerical experiments, which is carried out on a parallel computer with 40 CPUs, are attached to exhibit the effectiveness of the hybrid algorithm.

  19. A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model

    SciTech Connect

    Endicott, Julia S.; Joubert-Doriol, Loïc; Izmaylov, Artur F.

    2014-07-21

    We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.

  20. When does brain aging accelerate? Dangers of quadratic fits in cross-sectional studies.

    PubMed

    Fjell, Anders M; Walhovd, Kristine B; Westlye, Lars T; Østby, Ylva; Tamnes, Christian K; Jernigan, Terry L; Gamst, Anthony; Dale, Anders M

    2010-05-01

    Many brain structures show a complex, non-linear pattern of maturation and age-related change. Often, quadratic models (beta(0) + beta(1)age + beta(2)age(2) + epsilon) are used to describe such relationships. Here, we demonstrate that the fitting of quadratic models is substantially affected by seemingly irrelevant factors, such as the age-range sampled. Hippocampal volume was measured in 434 healthy participants between 8 and 85 years of age, and quadratic models were fit to subsets of the sample with different age-ranges. It was found that as the bottom of the age-range increased, the age at which volumes appeared to peak was moved upwards and the estimated decline in the last part of the age-span became larger. Thus, whether children were included or not affected the estimated decline between 60 and 85 years. We conclude that caution should be exerted in inferring age-trajectories from global fit models, e.g. the quadratic model. A nonparametric local smoothing technique (the smoothing spline) was found to be more robust to the effects of different starting ages. The results were replicated in an independent sample of 309 participants. PMID:20109562

  1. Quadratic relations in continuous and discrete Painlevé equations

    NASA Astrophysics Data System (ADS)

    Ramani, A.; Grammaticos, B.; Tamizhmani, T.

    2000-04-01

    The quadratic relations between the solutions of a Painlevé equation and that of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the quadratic relations existing for the continuous PII , PIII , PV and PVI have analogues as well as consequences in the discrete case. Moreover, the discrete Painlevé equations have quadratic relations of their own without any reference to the continuous case.

  2. Quadratic dynamical decoupling with nonuniform error suppression

    SciTech Connect

    Quiroz, Gregory; Lidar, Daniel A.

    2011-10-15

    We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.

  3. Large-scale sequential quadratic programming algorithms

    SciTech Connect

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  4. Conditions for the non-negativity of integral quadratic forms with constant coefficients on a half-axis

    SciTech Connect

    Milyutin, A A

    2002-04-30

    An integral quadratic functional with constant coefficients on a half-axis is considered. A necessary and sufficient condition for its non-negativity at all square integrable pairs of functions related by a linear ODE is proposed, which is based on the Hamilton-Jacobi inequality. A connection between this condition and the well-known frequency criterion is established.

  5. Gain-Scheduled Fault Tolerance Control Under False Identification

    NASA Technical Reports Server (NTRS)

    Shin, Jong-Yeob; Belcastro, Christine (Technical Monitor)

    2006-01-01

    An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

  6. A gain-scheduled observer under transmissions without delivery acknowledgment

    NASA Astrophysics Data System (ADS)

    Dolz, Daniel; Peñarrocha, Ignacio; Sanchis, Roberto

    2015-11-01

    This paper addresses the estimation problem for discrete-time systems where both measurements and control commands are sent to a central station through a lossy network without delivery acknowledgment. The central unit implements the estimation and control algorithms. We propose a jump observer that uses the expected value of the unknown control input at the actuator to run an open loop estimation. Then, the absence of acknowledgment in the control input transmission is dealt with through the introduction of an unknown disturbance. The observer update is performed by means of jumping gains when there are available measurements. We employ an statistic of the control error (new disturbance), i.e., the difference between the control inputs at the plant and at the observer, to schedule the observer gains in real time. The observer is designed to minimize the H∞ norm from disturbances, measurement noises and control input errors, to estimation error. The infinite-dimensional design problem is turn into an optimization problem over polynomials using sum-of-squares decomposition techniques. Benefits of the proposal are shown in a simulation example.

  7. Analysis of Students' Error in Learning of Quadratic Equations

    ERIC Educational Resources Information Center

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  8. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    ERIC Educational Resources Information Center

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  9. Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    Vaiyavutjamai, Pongchawee; Clements, M. A.

    2006-01-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

  10. Geometric quadratic stochastic operator on countable infinite set

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-02-03

    In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

  11. Visualising the Roots of Quadratic Equations with Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  12. An Authentic Task That Models Quadratics

    ERIC Educational Resources Information Center

    Baron, Lorraine M.

    2015-01-01

    As students develop algebraic reasoning in grades 5 to 9, they learn to recognize patterns and understand expressions, equations, and variables. Linear functions are a focus in eighth-grade mathematics, and by algebra 1, students must make sense of functions that are not linear. This article describes how students worked through a classroom task…

  13. Quadratic divergences and quantum gravitational contributions to gauge coupling constants

    NASA Astrophysics Data System (ADS)

    Toms, David J.

    2011-10-01

    The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.

  14. Quadratic Measurement and Conditional State Preparation in an Optomechanical System

    NASA Astrophysics Data System (ADS)

    Brawley, George; Vanner, Michael; Bowen, Warwick; Schmid, Silvan; Boisen, Anja

    2014-03-01

    An important requirement in the study of quantum systems is the ability to measure non-linear observables at the level of quantum fluctuations. Such measurements enable the conditional preparation of highly non-classical states. Nonlinear measurement, although achieved in a variety of quantum systems including microwave cavity modes and optical fields, remains an outstanding problem in both electromechanical and optomechanical systems. To the best of our knowledge, previous experimental efforts to achieve nonlinear measurement of mechanical motion have not yielded strong coupling, nor the observation of quadratic mechanical motion. Here using a new technique reliant on the intrinsic nonlinearity of the optomechanical interaction, we experimentally observe for the first time a position squared (x2) measurement of the room-temperature Brownian motion of a nanomechanical oscillator. We utilize this measurement to conditionally prepare non-Gaussian bimodal states, which are the high temperature classical analogue of quantum macroscopic superposition states, or cat states. In the future with the aid of cryogenics and state-of-the-art optical cavities, our approach will provide a viable method of generating quantum superposition states of mechanical oscillators. This research was funded by the ARC Center of Excellence for Engineered Quantum Systems.

  15. Phase Transitions in the Quadratic Contact Process on Complex Networks

    NASA Astrophysics Data System (ADS)

    Varghese, Chris; Durrett, Rick

    2013-03-01

    The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where a single infected (1) individual can infect a susceptible (0) neighbor and infected individuals are allowed to recover (1 --> 0). In the QCP, a combination of two 1's is required to effect a 0 --> 1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks as a model for the change in a population via sexual reproduction and death. We define two versions of the QCP - vertex centered (VQCP) and edge centered (EQCP) with birth events 1 - 0 - 1 --> 1 - 1 - 1 and 1 - 1 - 0 --> 1 - 1 - 1 respectively, where ` -' represents an edge. We investigate the effects of network topology by considering the QCP on regular, Erdős-Rényi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the homogeneous graphs (regular and Erdős-Rényi) there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.

  16. Impact of a global quadratic potential on galactic rotation curves.

    PubMed

    Mannheim, Philip D; O'Brien, James G

    2011-03-25

    We present a conformal gravity fit to the 20 largest of a sample of 110 spiral galaxies. We identify the presence of a universal quadratic potential V(κ)(r)=-κc²r²/2 with κ=9.54×10⁻⁵⁴ cm⁻² induced by cosmic inhomogeneities. When V(κ)(r) is taken in conjunction with both a universal linear potential V(γ₀)(r)=γ₀c²r/2 with γ₀=3.06×10⁻³⁰ cm⁻¹ generated by the homogeneous cosmic background and the contribution generated by the local luminous matter in galaxies, the theory then accounts for the rotation curve systematics observed in the entire 110 galaxies, without the need for any dark matter whatsoever. Our study suggests that using dark matter may be nothing more than an attempt to describe global effects in purely local galactic terms. With V(κ)(r) being negative, galaxies can only support bound orbits up to distances of order γ₀/κ=100kpc, with global physics imposing a limit on the size of galaxies. PMID:21517292

  17. Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

    NASA Astrophysics Data System (ADS)

    Shao, J. M.; Yang, G. W.

    2016-02-01

    Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger) term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy) just correspond to the absorptions of left-handed (σ-) and right-handed (σ+) polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ- are decided by the magnitude of the quadratic term and the magnetic field.

  18. The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

    NASA Technical Reports Server (NTRS)

    Townsend, Barbara K.

    1987-01-01

    A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

  19. Polychromatic solitons in a quadratic medium.

    PubMed

    Towers, I N; Malomed, B A

    2002-10-01

    We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate. PMID:12443362

  20. Optimal channels for channelized quadratic estimators.

    PubMed

    Kupinski, Meredith K; Clarkson, Eric

    2016-06-01

    We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem. PMID:27409452

  1. Direct Orthogonal Distance to Quadratic Surfaces in 3D.

    PubMed

    Lott, Gus K

    2014-09-01

    Discovering the orthogonal distance to a quadratic surface is a classic geometric task in vision, modeling, and robotics. I describe a simple, efficient, and stable direct solution for the orthogonal distance (foot-point) to an arbitrary quadratic surface from a general finite 3D point. The problem is expressed as the intersection of three quadratic surfaces, two of which are derived from the requirement of orthogonality of two non-coincident planes with the tangent plane to the quadric. A sixth order single-variable polynomial is directly generated in one coordinate of the surface point. The method detects intersection points at infinity and operates smoothly across all real quadratic surface classes. The method also geometrically detects continuums of orthogonal points (i.e., from the exact center of a sphere). I discuss algorithm performance, compare it to a state-of-the-art estimator, demonstrate the algorithm on synthetic data, and describe extension to arbitrary dimension. PMID:26352239

  2. On a 'Mysterious' Case of a Quadratic Hamiltonian

    NASA Astrophysics Data System (ADS)

    Sakovich, Sergei

    2006-07-01

    We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painlevé test for integrability.

  3. Adiabatic femtosecond pulse compression and control by using quadratic cascading nonlinearity

    NASA Astrophysics Data System (ADS)

    Zeng, Xianglong; Ashihara, Satoshi; Shimura, Tsutomu; Kuroda, Kazuo

    2008-01-01

    We experimentally demonstrate that adiabatic compression of femtosecond pulse can be achieved by employing the management of quadratic cascading nonlinearity in quasi-phase-matching gratings. Cascading nonlinearity is not a simple analogy with third-order optical nonlinearity in term of the engineering properties of the magnitude and focusing (or defocusing) nonlinearity. Femtosecond pulse compression is investigated based on type-I (e: o + o) collinear QPM geometry of aperiodically poled MgO-doped LiNbO 3 (MgO: LN). Group-velocity-matching condition is chosen to generate quadratic femtosecond soliton consisting of fundamental (FF) and second harmonic (SH) pulses. Adiabatic-like compression process is observed in the length of 50 mm linearly chirped QPM. Cascading nonlinearity is local managed, instead of dispersion management used in fiber adiabatic soliton compression. Quadratic soliton including FF and SH pulses are obtained from the compression of 95 fs FF pulse in the initial experiments. Dependence on the phase mismatch and group velocity mismatch, cascading nonlinearity has a flexible property and presents a new challenge for exploring femtosecond pulse shaping and control. The demonstrated pulse compression and control based on cascading nonlinearity is useful for generation of shorter pulses with clean temporal profiles, efficient femtosecond second harmonic generation and group-velocity control.

  4. Finite-element analysis of earing using non-quadratic yield surfaces

    SciTech Connect

    Logan, R.W.

    1995-06-18

    During deep draw cupping, the phenomenon known as earing may occur as the cup wall is formed, resulting in a periodic variation of cup wall height around the perimeter of the finished cup. This is generally due to planar anisotropy of flow in rolled sheet product. It is generally observed that the anisotropy parameter R will vary in the plane of the sheet when ears are observed in cupping, with a parameter {Delta}R describing the variation of R in the plane of the sheet. For many common textures in face-centered and body-centered materials, the ears form relative to the sheet rolling direction at 0{degrees} and 90{degrees} around the perimeter if {Delta}R>0, and at -45{degrees} and +45{degrees} if {Delta}R<0. There is extensive experimental evidence that ear height shows a linear correlation with {Delta}R/R, but attempts to duplicate this using the finite-element method are highly dependent on both the methodology and yield surface used. It was shown previously that using a coarse mesh and the quadratic Hill yield surface tends to greatly under predict earing. In this study, we have used two different finite-element codes developed at LLNL to examine the predicted earing using both quadratic Hill and alternative non-quadratic yield surfaces. These results are compared to experimental data and conclusions drawn about the most desirable closed-form yield surfaces to duplicate the observed earing phenomena.

  5. Use of non-quadratic yield surfaces in design of optimal deep-draw blank geometry

    SciTech Connect

    Logan, R.W.

    1995-12-01

    Planar anisotropy in the deep-drawing of sheet can lead to the formation of ears in cylindrical cups and to undesirable metal flow in the blankholder in the general case. For design analysis purposes in non-linear finite-element codes, this anisotropy is characterized by the use of an appropriate yield surface which is then implemented into codes such as DYNA3D . The quadratic Hill yield surface offers a relatively straightforward implementation and can be formulated to be invariant to the coordinate system. Non-quadratic yield surfaces can provide more realistic strength or strain increment ratios, but they may not provide invariance and thus demand certain approximations. Forms due to Hosford and Badat et al. have been shown to more accurately address the earning phenomenon. in this work, use is made of these non-quadratic yield surfaces in order to determine the optimal blank shape for cups and other shapes using ferrous and other metal blank materials with planar anisotropy. The analyses are compared to previous experimental studies on non-uniform blank motion due to anisotropy and asymmetric geometry.

  6. An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

    PubMed

    Culpepper, Steven Andrew

    2016-06-01

    Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity. The results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity. This paper offers at least three significant contributions to the existing literature. First, a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations. Second, derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements. New results are presented on the bias associated with using the standard range restriction correction formula, and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0.2 for high to moderate selectivity. Third, Monte Carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships. PMID:25953477

  7. Quadratic function approaching method for magnetotelluric soundingdata inversion

    SciTech Connect

    Liangjun, Yan; Wenbao, Hu; Zhang, Keni

    2004-04-05

    The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.

  8. Gravity waves from non-minimal quadratic inflation

    SciTech Connect

    Pallis, Constantinos; Shafi, Qaisar

    2015-03-12

    We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.

  9. Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

    NASA Astrophysics Data System (ADS)

    Hong, Xiaochun; Xie, Shaolong; Chen, Longwei

    In this study, we determine the associated number of zeros for Abelian integrals in four classes of quadratic reversible centers of genus one. Based on the results of [Li et al., 2002b],, we prove that the upper bounds of the associated number of zeros for Abelian integrals with orbits formed by conics, cubics, quartics, and sextics, under polynomial perturbations of arbitrary degree n, depend linearly on n.

  10. Design of a candidate flutter suppression control law for DAST ARW-2

    NASA Technical Reports Server (NTRS)

    Adams, W. M., Jr.; Tiffany, S. H.

    1984-01-01

    A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQC (Linear Quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

  11. Design of a candidate flutter suppression control law for DAST ARW-2. [Drones for Aerodynamic and Structural Testing Aeroelastic Research Wing

    NASA Technical Reports Server (NTRS)

    Adams, W. M., Jr.; Tiffany, S. H.

    1983-01-01

    A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (linear quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

  12. Linear stochastic optimal control and estimation

    NASA Technical Reports Server (NTRS)

    Geyser, L. C.; Lehtinen, F. K. B.

    1976-01-01

    Digital program has been written to solve the LSOCE problem by using a time-domain formulation. LSOCE problem is defined as that of designing controls for linear time-invariant system which is disturbed by white noise in such a way as to minimize quadratic performance index.

  13. A reduced successive quadratic programming strategy for errors-in-variables estimation.

    SciTech Connect

    Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

    1992-01-01

    Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases at least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.

  14. Formalism for the solution of quadratic Hamiltonians with large cosine terms

    NASA Astrophysics Data System (ADS)

    Ganeshan, Sriram; Levin, Michael

    2016-02-01

    We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

  15. Airborne gravimetry data sparse reconstruction via L1-norm convex quadratic programming

    NASA Astrophysics Data System (ADS)

    Yang, Ya-Peng; Wu, Mei-Ping; Tang, Gang

    2015-06-01

    In practice, airborne gravimetry is a sub-Nyquist sampling method because of the restrictions imposed by national boundaries, financial cost, and database size. In this study, we analyze the sparsity of airborne gravimetry data by using the discrete Fourier transform and propose a reconstruction method based on the theory of compressed sensing for large-scale gravity anomaly data. Consequently, the reconstruction of the gravity anomaly data is transformed to a L1-norm convex quadratic programming problem. We combine the preconditioned conjugate gradient algorithm (PCG) and the improved interior-point method (IPM) to solve the convex quadratic programming problem. Furthermore, a flight test was carried out with the homegrown strapdown airborne gravimeter SGA-WZ. Subsequently, we reconstructed the gravity anomaly data of the flight test, and then, we compared the proposed method with the linear interpolation method, which is commonly used in airborne gravimetry. The test results show that the PCG-IPM algorithm can be used to reconstruct large-scale gravity anomaly data with higher accuracy and more effectiveness than the linear interpolation method.

  16. Tandem time-of-flight mass spectrometer (TOF-TOF) with a quadratic-field ion mirror

    NASA Astrophysics Data System (ADS)

    Giannakopulos, Anastassios E.; Thomas, Benjamin; Colburn, Alex W.; Reynolds, David J.; Raptakis, Emmanuel N.; Makarov, Alexander A.; Derrick, Peter J.

    2002-05-01

    A tandem time-of-flight (TOF-TOF) mass spectrometer comprised of two ion mirrors is described. The first ion mirror, which is a linear-field, single-stage mirror (MS1) with an intermediate collision cell, has been designed to provide the temporal focus necessary for the second, quadratic-field ion mirror (MS2) to function effectively. Due to the wide energy-range focusing capabilities of the quadratic field employed in the second ion mirror all the fragment ions can be collected in one spectrum without the need to step the reflecting working voltage of the MS2. The size of the active area of the microchannel plate detector used in the preliminary experiments was the limiting factor governing the collection efficiently of fragment ions. The use of the first ion mirror to provide temporal focusing of the precursor ion packet at the first focal point of the quadratic mirror used as the MS2 requires no alteration of the focusing conditions for different masses, in contrast to delayed extraction or postsource pulsed focusing. Precursor ions formed by matrix-assisted laser desorption/ionization were mass-selected with an ion gate located before the collision cell and the fragment ions were mass analyzed using the quadratic-field ion mirror. Experimental results demonstrating effective high-energy collision-induced dissociation of polymer and fullerene molecule-ions are presented.

  17. On Volterra quadratic stochastic operators with continual state space

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-15

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  18. On Volterra quadratic stochastic operators with continual state space

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-01

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (V λ )(A ) = ∫X ∫X P (x ,y ,A )d λ (x )d λ (y ), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim n →∞ Vn(λ ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  19. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.

    2016-06-01

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.

  20. Radar Rainfall Estimation using a Quadratic Z-R equation

    NASA Astrophysics Data System (ADS)

    Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan

    2016-04-01

    The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.

  1. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

    ERIC Educational Resources Information Center

    Leyendekkers, J. V.; Shannon, A. G.

    2004-01-01

    An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

  2. Tuning a fuzzy controller using quadratic response surfaces

    NASA Technical Reports Server (NTRS)

    Schott, Brian; Whalen, Thomas

    1992-01-01

    Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

  3. A Version of Quadratic Regression with Interpretable Parameters.

    ERIC Educational Resources Information Center

    Cudeck, Robert; du Toit, Stephen H. C.

    2002-01-01

    Suggests an alternative form of the quadratic model that has the same expectation function of the original model but has the useful feature that its parameters are interpretable. Provides examples of a simple regression problem and a nonlinear mixed-effects model. (SLD)

  4. Solving the Quadratic Capacitated Facilities Location Problem by Computer.

    ERIC Educational Resources Information Center

    Cote, Leon C.; Smith, Wayland P.

    Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

  5. Confidence set interference with a prior quadratic bound. [in geophysics

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

  6. Quadratic Expressions by Means of "Summing All the Matchsticks"

    ERIC Educational Resources Information Center

    Gierdien, M. Faaiz

    2012-01-01

    This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

  7. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  8. Selfsimilarity in a Class of Quadratic-Quasiperiodic Chains

    NASA Astrophysics Data System (ADS)

    Kaneko, Masanobu; Odagaki, Takashi

    1993-04-01

    We prove that quasiperiodic chains associated with a class of quadratic irrational numbers have an inflation symmetry and can be generated from a regular chain by a hyperinflation. We devise the explicit method to find the hyperinflation symmetry and discuss the properties of such a class of quasiperiodic sequences.

  9. Unravelling Student Challenges with Quadratics: A Cognitive Approach

    ERIC Educational Resources Information Center

    Kotsopoulos, Donna

    2007-01-01

    The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

  10. A Unified Approach to Teaching Quadratic and Cubic Equations.

    ERIC Educational Resources Information Center

    Ward, A. J. B.

    2003-01-01

    Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

  11. The linear separability problem: some testing methods.

    PubMed

    Elizondo, D

    2006-03-01

    The notion of linear separability is used widely in machine learning research. Learning algorithms that use this concept to learn include neural networks (single layer perceptron and recursive deterministic perceptron), and kernel machines (support vector machines). This paper presents an overview of several of the methods for testing linear separability between two classes. The methods are divided into four groups: Those based on linear programming, those based on computational geometry, one based on neural networks, and one based on quadratic programming. The Fisher linear discriminant method is also presented. A section on the quantification of the complexity of classification problems is included. PMID:16566462

  12. A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

    NASA Astrophysics Data System (ADS)

    Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.

    2009-12-01

    A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.

  13. Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

    NASA Astrophysics Data System (ADS)

    Landsman, Zinoviy

    2008-10-01

    We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

  14. Linear Approximation SAR Azimuth Processing Study

    NASA Technical Reports Server (NTRS)

    Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.

    1979-01-01

    A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

  15. Quadratic programming-based approach for autonomous vehicle path planning in space

    NASA Astrophysics Data System (ADS)

    Chen, Yang; Han, Jianda; Wu, Huaiyu

    2012-07-01

    Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades. The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one, and also can not solve the inherent constraints arising from the robot body and the exterior environment. To address these difficulties, this research aims to provide a feasible trajectory based on quadratic programming(QP) for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles. First, the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target, as well as the angle between the velocity and the position in the relative velocity coordinates(RVCs). The optimization is in quadratic polynomial form according to QP formulation. Then, the avoidance task is modeled with linear constraints in RVCs. Some other constraints, such as kinematics, dynamics, and sensor range, are included. Last, simulations with typical multiple obstacles are carried out, including in static and dynamic environments and one of human-in-the-loop. The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances. Therefore, the QP model proposed in this paper not only adapts to dynamic environment with uncertainty, but also can satisfy all kinds of constraints, and it provides an efficient approach to solve the problems of path planning in three-dimensional space.

  16. Quadratic Herman-Wallis contributions associated with vibration-rotation resonances

    NASA Astrophysics Data System (ADS)

    Watson, James K. G.

    1988-12-01

    The quadratic terms A2PRm2 and A2QJ( J + 1) in the Herman-Wallis correction factors for infrared line intensities in linear molecules are normally small for transitions between nonresonant states, but significant values are obtained for transitions involving states perturbed by Fermi or l-type resonance. Detailed equations are given for these quadratic Herman-Wallis terms in transitions from a nonresonant state to the Fermi dyad [(1, 0 0, V' 3), (0, 2 0, V' 3)] together with its l-resonance partner (0, 2 2 e, V' 3). Applications to the parallel bands [(1, 0 0, 1), (0, 2 0, 1)] ← (0, 0 0, 0) and the perpendicular bands [(1, 0 0, 0), (0, 2 0, 0), (0, 2 2, 0)] ← (0, 1 1, 0) of CO 2 and to the parallel bands [(1, 0 0, 0), (0, 2 0, 0)] ← (0, 0 0, 0) of N 2O give good agreement with recent measurements. In particular, the pattern of A2 coefficients in the three perpendicular bands of CO 2, in which the A2 coefficients have been found by Johns to be small for all three pairs of P and R branches and for the Q branch to the l = 2 component, but not for the Q branches to the l = 0 components, is shown to be due to cancellations between contributions in all branches except these two Q branches.

  17. Placement of cells: Theory and solution of a quadratic 0/1 optimization problem

    NASA Astrophysics Data System (ADS)

    Weismantel, Robert

    1992-01-01

    The placement problem by design of electronic chips is studied in the framework of very large scale integration. Methods for modeling placement are presented, such as min-cut heuristics, simulated annealing, and a continuous quadratic optimization method based on relaxation. The 'sea of cells' concept was chosen and a quadratic 0/1 optimization problem was described with a graph theory formulation. Variations of the problem and existence of polynomial, epsilon approximative algorithms were discussed. The problem was solved with heuristic decomposition method, with 16 locations for each cell and with 9 locations for each cell. A dynamic decomposition process was also described and a linear Lagrange relaxation solution was proposed. The clustering problem was introduced to reduce magnitude order of placement problem. The r-clustering polytope was presented from a polyhedral point of view. Several classes of facets were described by inequalities, which combine nodes and branches in the following cases: roof dual and disjuncted stars, roof dual and a tree, roof dual and a star, and roof dual and a branch.

  18. Linear-quadratic dose kinetics or dose-dependent repair/misrepair

    SciTech Connect

    Braby, L.A.; Nelson, J.M.

    1991-09-01

    Models for the response of cells exposed to low LET radiation can be grouped into three general types on the basis of assumptions about the nature of the interaction which results in the shoulder of the survival curve. The three forms of interaction are (1) sublethal damage becoming lethal, (2) potentially lethal damage becoming irreparable, and (3) potentially lethal damage saturating'' a repair system. The effects that these three forms of interaction would have on the results of specific types of experiments are investigated. Comparisons with experimental results indicate that only the second type is significant in determining the response of typical cultured mammalian cells. 5 refs., 2 figs.

  19. Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Jeon, G. J.

    1983-01-01

    Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

  20. Controller design approaches for large space structures using LQG control theory. [Linear Quadratic Gaussian

    NASA Technical Reports Server (NTRS)

    Joshi, S. M.; Groom, N. J.

    1979-01-01

    The paper presents several approaches for the design of reduced order controllers for large space structures. These approaches are shown to be based on LQG control theory and include truncation, modified truncation regulators and estimators, use of higher order estimators, selective modal suppression, and use of polynomial estimators. Further, the use of direct sensor feedback, as opposed to a state estimator, is investigated for some of these approaches. Finally, numerical results are given for a long free beam.

  1. Pre-Service Teachers' Linear and Quadratic Inequalities Understandings

    ERIC Educational Resources Information Center

    Bicer, Ali; Capraro, Robert M.; Capraro, Mary M.

    2014-01-01

    The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

  2. Antenna Linear-Quadratic-Gaussian (LQG) Ccontrollers: Properties, Limits of Performance, and Tuning

    NASA Technical Reports Server (NTRS)

    Gawronski, Wodek K.

    2004-01-01

    The LQG controllers significantly improve antenna tracking precision, but their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller, and the selection of weights of the LQG performance index. The paper selects the coordinates of the open-loop model that simplify the shaping of the closed-loop performance. and analyzes the impact of thc weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. Finally, it presents the LQG controller tuning procedure that rationally shapes the closed-loop performance.

  3. Close proximity formation flying via linear quadratic tracking controller and artificial potential function

    NASA Astrophysics Data System (ADS)

    Palacios, Leonel; Ceriotti, Matteo; Radice, Gianmarco

    2015-11-01

    A Riccati-based tracking controller with collision avoidance capabilities is presented for proximity operations of spacecraft formation flying near elliptic reference orbits. The proposed dynamical model incorporates nonlinear accelerations from an artificial potential field, in order to perform evasive maneuvers during proximity operations. In order to validate the design of the controller, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) will be implemented, extending it to scenarios with multiple spacecraft performing reconfigurations and on-orbit position switching. The results show that the tracking controller is effective, even when nonlinear repelling accelerations are present in the dynamics to avoid collisions, and that the potential-based collision avoidance scheme is convenient for reducing collision threat.

  4. Large radius of curvature measurement based on virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer.

    PubMed

    Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun

    2016-06-10

    We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm. PMID:27409038

  5. On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane. [central processing units

    NASA Technical Reports Server (NTRS)

    Cooper, D. B.; Yalabik, N.

    1975-01-01

    Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.

  6. FIBER OPTIC POINT QUADRAT SYSTEM FOR IMPROVED ACCURACY IN VEGETATION SAMPLING

    EPA Science Inventory

    An automated, fiber optic point quadrat system for vegetation sampling is described. Because the effective point diameter of the system never exceeds 25um it minimizes the substantial errors which can arise with conventional point quadrats. Automatic contact detection eliminates ...

  7. Quadratic nonlinear Klein-Gordon equation in one dimension

    NASA Astrophysics Data System (ADS)

    Hayashi, Nakao; Naumkin, Pavel I.

    2012-10-01

    We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = λv2, t ∈ R, x ∈ R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ∈ R, where v0 and v1 are real-valued functions, λ ∈ R. Using the method of normal forms of Shatah ["Normal forms and quadratic nonlinear Klein-Gordon equations," Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort ["Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1," Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

  8. Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators

    NASA Astrophysics Data System (ADS)

    Marquette, Ian

    2011-06-01

    We present a generalized Kaluza-Klein monopole system. We solve this quantum superintegrable system on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schrödinger equation in spherical and parabolic coordinates. We present the integrals of motion of this system, the quadratic algebra generated by these integrals, the realization in terms of a deformed oscillator algebra using the Daskaloyannis construction and the energy spectrum. The structure constants and the Casimir operator are functions not only of the Hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an Abelian subalgebra. We present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators.

  9. Exploring {{W}}_{∞ } in the quadratic basis

    NASA Astrophysics Data System (ADS)

    Procházka, Tomáš

    2015-09-01

    We study the operator product expansions in the chiral algebra {W}_{∞ } , first using the associativity conditions in the basis of primary generating fields and then using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form. The results in the quadratic basis can be compactly written using certain bilocal combinations of the generating fields and we conjecture a closed-form expression for the complete OPE in this basis. Next we show that the commutation relations as well as correlation functions can be easily computed using properties of these bilocal fields. In the last part we verify the consistency with results derived previously by studying minimal models of {W}_{∞ } and comparing them to known reductions of {W}_{∞ } to {W}_N . The results we obtain illustrate nicely the role of triality symmetry in the representation theory of {W}_{∞ }.

  10. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

    Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

    2010-09-15

    We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

  11. Discrete quadratic solitons with competing second-harmonic components

    SciTech Connect

    Setzpfandt, Frank; Pertsch, Thomas; Sukhorukov, Andrey A.

    2011-11-15

    We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.

  12. Construction of Lagrangian Local Symmetries for General Quadratic Theory

    NASA Astrophysics Data System (ADS)

    Deriglazov, A. A.

    We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of the so-called structure matrices of the Dirac formalism are obtained. The procedure fulfill in terms of initial variables of the theory, and does not imply either separation of constraints on first and second class subsets or any other choice of basis for constraints.

  13. Quadratic mutual information for dimensionality reduction and classification

    NASA Astrophysics Data System (ADS)

    Gray, David M.; Principe, José C.

    2010-04-01

    A research area based on the application of information theory to machine learning has attracted considerable interest in the last few years. This research area has been coined information-theoretic learning within the community. In this paper we apply elements of information-theoretic learning to the problem of automatic target recognition (ATR). A number of researchers have previously shown the benefits of designing classifiers based on maximizing the mutual information between the class data and the class labels. Following prior research in information-theoretic learning, in the current results we show that quadratic mutual information, derived using a special case of the more general Renyi's entropy, can be used for classifier design. In this implementation, a simple subspace projection classifier is formulated to find the optimal projection weights such that the quadratic mutual information between the class data and the class labels is maximized. This subspace projection accomplishes a dimensionality reduction of the raw data set wherein information about the class membership is retained while irrelevant information is discarded. A subspace projection based on this criterion preserves as much class discriminability as possible within the subspace. For this paper, laser radar images are used to demonstrate the results. Classification performance against this data set is compared for a gradient descent MLP classifier and a quadratic mutual information MLP classifier.

  14. Design and cost analysis of rapid aquifer restoration systems using flow simulation and quadratic programming.

    USGS Publications Warehouse

    Lefkoff, L.J.; Gorelick, S.M.

    1986-01-01

    Detailed two-dimensional flow simulation of a complex ground-water system is combined with quadratic and linear programming to evaluate design alternatives for rapid aquifer restoration. Results show how treatment and pumping costs depend dynamically on the type of treatment process, and capacity of pumping and injection wells, and the number of wells. The design for an inexpensive treatment process minimizes pumping costs, while an expensive process results in the minimization of treatment costs. Substantial reductions in pumping costs occur with increases in injection capacity or in the number of wells. Treatment costs are reduced by expansions in pumping capacity or injecion capacity. The analysis identifies maximum pumping and injection capacities.-from Authors

  15. Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

    NASA Technical Reports Server (NTRS)

    Badavi, F. F.; Everhart, Joel L.

    1987-01-01

    This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

  16. Diffusion of a particle quadratically coupled to a thermally fluctuating field

    NASA Astrophysics Data System (ADS)

    Démery, Vincent

    2013-05-01

    We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak-coupling limit, a path-integral formulation allows us to compute the effective diffusion coefficient in the cases of an active particle, which tends to suppress field fluctuations, and of a passive particle, which only undergoes field fluctuations. We show that the behavior is similar to what was previously found for a linear coupling: an active particle is always slowed down, whereas a passive particle is slowed down in a slow field and accelerated in a fast field. Numerical simulations show a good agreement with the analytical calculations. The examples of a membrane protein coupled to the curvature or composition of the membrane are discussed, with a focus on the room for anomalous diffusion.

  17. Suppressing the primordial tensor amplitude without changing the scalar sector in quadratic curvature gravity

    NASA Astrophysics Data System (ADS)

    Yajima, Kohji; Kobayashi, Tsutomu

    2015-11-01

    We address the question of how one can modify the inflationary tensor spectrum without changing at all the successful predictions on the curvature perturbation. We show that this is indeed possible, and determine the two quadratic curvature corrections that are free from instabilities and affect only the tensor sector at the level of linear cosmological perturbations. Both of the two corrections can reduce the tensor amplitude, though one of them generates large non-Gaussianity of the curvature perturbation. It turns out that the other one corresponds to so-called Lorentz-violating Weyl gravity. In this latter case one can obtain as small as 65% of the standard tensor amplitude. Utilizing this effect we demonstrate that even power-law inflation can be within the 2 σ contour of the Planck results.

  18. An Improved Linear Tetrahedral Element for Plasticity

    SciTech Connect

    Puso, M

    2005-04-25

    A stabilized, nodally integrated linear tetrahedral is formulated and analyzed. It is well known that linear tetrahedral elements perform poorly in problems with plasticity, nearly incompressible materials, and acute bending. For a variety of reasons, linear tetrahedral elements are preferable to quadratic tetrahedral elements in most nonlinear problems. Whereas, mixed methods work well for linear hexahedral elements, they don't for linear tetrahedrals. On the other hand, automatic mesh generation is typically not feasible for building many 3D hexahedral meshes. A stabilized, nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity, nearly incompressible materials and acute bending. Furthermore, the formulation is analytically and numerically shown to be stable and optimally convergent. The element is demonstrated to perform well in several standard linear and nonlinear benchmarks.

  19. Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

    NASA Astrophysics Data System (ADS)

    Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

    2016-03-01

    To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

  20. Piecewise linear approximation for hereditary control problems

    NASA Technical Reports Server (NTRS)

    Propst, Georg

    1990-01-01

    This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.

  1. Linear Accelerators

    NASA Astrophysics Data System (ADS)

    Sidorin, Anatoly

    2010-01-01

    In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.

  2. Linear Accelerators

    SciTech Connect

    Sidorin, Anatoly

    2010-01-05

    In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.

  3. Analysis of electroperforated materials using the quadrat counts method

    NASA Astrophysics Data System (ADS)

    Miranda, E.; Garzón, C.; Martínez-Cisneros, C.; Alonso, J.; García-García, J.

    2011-06-01

    The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.

  4. Rigorous performance bounds for quadratic and nested dynamical decoupling

    SciTech Connect

    Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.

    2011-12-15

    We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

  5. Frontogenesis driven by horizontally quadratic distributions of density

    NASA Technical Reports Server (NTRS)

    Jacqmin, David

    1991-01-01

    Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.

  6. Nios II hardware acceleration of the epsilon quadratic sieve algorithm

    NASA Astrophysics Data System (ADS)

    Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio

    2010-04-01

    The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ɛ-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.

  7. Cyclicity of a fake saddle inside the quadratic vector fields

    NASA Astrophysics Data System (ADS)

    De Maesschalck, P.; Rebollo-Perdomo, S.; Torregrosa, J.

    2015-01-01

    This paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as an impassable grain. The canonical form of the unperturbed vector field is like a degenerate flow box. Near the singularity, the phase portrait consists of parallel fibers, all but one of which have no singular points, and at the singular fiber, there is one node. We demonstrate different techniques in order to show that the cyclicity is bigger than or equal to two when the canonical form is quadratic.

  8. Quadratic integrand double-hybrid made spin-component-scaled

    NASA Astrophysics Data System (ADS)

    Brémond, Éric; Savarese, Marika; Sancho-García, Juan C.; Pérez-Jiménez, Ángel J.; Adamo, Carlo

    2016-03-01

    We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

  9. On a quadratic transformation due to Kummer and its generalizations

    NASA Astrophysics Data System (ADS)

    Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om

    2016-05-01

    The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.

  10. Quadratic Interaction Functional for General Systems of Conservation Laws

    NASA Astrophysics Data System (ADS)

    Bianchini, Stefano; Modena, Stefano

    2015-09-01

    For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

  11. On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

    NASA Technical Reports Server (NTRS)

    Belcastro, Christine M.

    1998-01-01

    Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

  12. Quadratic Reciprocity and the Group Orders of Particle States

    SciTech Connect

    DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.

    2001-06-01

    The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.

  13. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    PubMed

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

  14. Sequential quadratic programming method for determining the minimum energy path.

    PubMed

    Burger, Steven K; Yang, Weitao

    2007-10-28

    A new method, referred to as the sequential quadratic programming method, is presented for determining minimum energy paths. The method is based on minimizing the points representing the path in the subspace perpendicular to the tangent of the path while using a penalty term to prevent kinks from forming. Rather than taking one full step, the minimization is divided into a number of sequential steps on an approximate quadratic surface. The resulting method can efficiently determine the reaction mechanism, from which transition state can be easily identified and refined with other methods. To improve the resolution of the path close to the transition state, points are clustered close to this region with a reparametrization scheme. The usefulness of the algorithm is demonstrated for the Muller-Brown potential, amide hydrolysis, and an 89 atom cluster taken from the active site of 4-oxalocrotonate tautomerase for the reaction which catalyzes 2-oxo-4-hexenedioate to the intermediate 2-hydroxy-2,4-hexadienedioate. PMID:17979319

  15. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

    PubMed Central

    RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

    2013-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

  16. Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System

    NASA Astrophysics Data System (ADS)

    Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. Hernández

    Alternate quadratic systems A : xn+1 = 1 - axn2,if n is even 1 - a∗xn2,if n is odd andB : xn+1 = 1 - a∗xn2,if n is even 1 - axn2, if n is odd, where a and a∗ are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (“hidden” because it is not visible at normal resolution and “nonstandard” because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.

  17. Application of quadratic regression model for Fenton treatment of municipal landfill leachate.

    PubMed

    Ghanbarzadeh Lak, Mehdi; Sabour, Mohammad Reza; Amiri, Allahyar; Rabbani, Omid

    2012-10-01

    The effectiveness of Fenton process in municipal landfill leachate treatment, as a pre- or post-treatment approach, has been demonstrated. However, no general recommendations of universal validity could be made in the term of optimized conditions affecting Fenton process. At the first stage of this study, collected leachate samples from Aradkooh site, Tehran, Iran, were investigated using one-factor-at-a-time method to find out optimum coagulation pH and flocculation time values. Subsequently, the obtained results in addition to data issued previously by the authors were employed to develop a predictive model of the true response surface, namely chemical oxygen demand (COD) removal efficiency. Finally, the main parameters of Fenton procedure, i.e. initial pH, [H(2)O(2)]/[Fe(2+)] molar ratio, Fe(2+) dosage, and coagulation pH were optimized taking advantage of the above-mentioned quadratic model. The derived second-order model included both significant linear and quadratic terms and seemed to be adequate in predicting responses (R(2)=0.9896 and prediction R(2)=0.6954). It was found that the interaction between initial pH and Fe(2+) dosage has a significant effect on COD removal. While, the optimal [H(2)O(2)]/[Fe(2+)] molar ratio was independent of ferrous ion dosage. The optimum conditions for the maximum COD removal of 50.76% for the parameters of initial pH, [H(2)O(2)]/[Fe(2+)] molar ratio, Fe(2+) dosage, and coagulation pH were found to be 5.8, 8.0, 22,500 mg/L, and 8.7 respectively. PMID:22717412

  18. Quadratic coupling between a classical nanomechanical oscillator and a single spin

    NASA Astrophysics Data System (ADS)

    Dhingra, Shonali

    Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellen theta2 sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NVcontaining diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices.

  19. Rear-heavy car control by adaptive linear optimal preview

    NASA Astrophysics Data System (ADS)

    Thommyppillai, M.; Evangelou, S.; Sharp, R. S.

    2010-05-01

    Adaptive linear optimal preview control theory is applied to a simple but non-linear car model, with parameters chosen to make the rear axle saturate first in any quasi-steady manoeuvre. The tendency of such a car to spin above a critical speed, which is a function of its running state, causes control to be especially difficult when operating near to the limit of the rear-axle force system. As in previous work, trim states and optimal gains are computed off-line for a given speed and a full range of lateral accelerations. Gain-scheduling with interpolation over trims and gain sets is used to keep the control appropriate to the running conditions, as they change. Simulations of manoeuvres are used to test and demonstrate the system capability. It is shown that utilising the rear-axle lateral-slip ratio as the scheduling variable, in the case of this rear-heavy car, gives excellent tracking, even when the tyres are run close to full saturation. It is implied by this and previous work that the general case can be treated effectively by monitoring both front- and rear-axle slips and scheduling on a worst-case basis.

  20. Linear Collisions

    ERIC Educational Resources Information Center

    Walkiewicz, T. A.; Newby, N. D., Jr.

    1972-01-01

    A discussion of linear collisions between two or three objects is related to a junior-level course in analytical mechanics. The theoretical discussion uses a geometrical approach that treats elastic and inelastic collisions from a unified point of view. Experiments with a linear air track are described. (Author/TS)

  1. Optimal Regulator Algorithms For The Control Of Linear Systems (ORACLS)

    NASA Technical Reports Server (NTRS)

    Frisch, Harold P.

    1990-01-01

    Control theory design package offers engineer full range of subroutines to manipulate and solve Linear-Quadratic-Gaussian types of problems. ORACLS is rigorous tool, intended for multi-input and multi-output dynamic systems in both continuous and discrete form. Written in FORTRAN.

  2. Rays of Small Integer Solutions of Homogeneous Ternary Quadratic Equations

    NASA Astrophysics Data System (ADS)

    Mishra, Sudhakara

    1991-02-01

    We have dealt with the general ternary quadratic equation: ax2 + by^ {2} + cz2 + dxy + exz + fyz = 0 with integer coefficients. After giving a matrix-reduction formula for a quadratic equation in any number of variables, of which the reduction of the above ternary equation is an easy consequence, we have devoted our attention to the reduced equation: ax^ {2} + by2 + cz^{2 } = 0. We have devised an algorithm for reducing Dirichlet's possibly larger solutions to this prescribed range of Holzer's. Then we have generalized Holzer's theorem to the case of the ternary equation: ax^{2 } + by2 + cz2 + dxy + exz + fyz = 0, giving in this context a new range called the CM-range, of which the Holzer's range is a particular case when d = e = f = 0. We have described an algorithm for getting a solution of the general ternary within this CM-range. After that we have devised an algorithm for getting all the solutions of the Legendre's equation ax 2 + by2 + cz^ {2} = 0 within the Holzer's range--and have shown that if we regard this Legendre's equation as a double cone, these solutions within the Holzer's range lie along some definite rays, here called the CM-rays, which are completely determined by the prime factors of the coefficients a, b and c. After giving an algorithm for detecting these CM-rays of the reduced equation: ax^2 + by^2 + cz^2 = 0, we have shown how one can produce some similar rays of solutions of the above general ternary quadratic equation: ax2 + by2 + cz2 + dxy + exz + fyz = 0. Note that apart from the method of exhausting all the possibilities, so far there has been no precisely stated algorithm to find the minimum solutions of the above ternary equations. Towards the end, observing in the context of our main result an inequality involving two functions, namely C and PCM from doubz_sp{*} {3} to doubz_+, and simultaneously presenting some tables of these positive CM-rays or PCM-rays lying in the positive octant, we have concluded this work with a number of

  3. Absence of the Gribov ambiguity in a quadratic gauge

    NASA Astrophysics Data System (ADS)

    Raval, Haresh

    2016-05-01

    The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S^3, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.

  4. Quadratic Forms for the Fermionic Unitary Gas Model

    NASA Astrophysics Data System (ADS)

    Finco, Domenico; Teta, Alessandro

    2012-04-01

    We consider a quantum system in dimension three composed by a group of N identical fermions, with mass 1/2, interacting via zero-range interaction with a group of M identical fermions of a different type, with mass m/2. Exploiting a renormalization procedure, we construct the corresponding quadratic form and define the so-called Skornyakov-Ter-Martirosyan extension Hα, which is the natural candidate as a possible Hamiltonian of the system. It is shown that if the form is unbounded from below then Hα is not a self-adjoint and bounded from below operator, and this in particular suggests that the so-called Thomas effect could occur. In the special case N = 2, M = 1 we prove that this is in fact the case when a suitable condition on the parameter m is satisfied.

  5. Quadratic Finite Element Method for 1D Deterministic Transport

    SciTech Connect

    Tolar, Jr., D R; Ferguson, J M

    2004-01-06

    In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

  6. A Fixed-Point Iteration Method with Quadratic Convergence

    SciTech Connect

    Walker, Kevin P.; Sham, Sam

    2012-01-01

    The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.

  7. Recognition of Graphs with Convex Quadratic Stability Number

    NASA Astrophysics Data System (ADS)

    Pacheco, Maria F.; Cardoso, Domingos M.

    2009-09-01

    A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.

  8. Motion corrected intracranial MRA using PROPELLER with RF quadratic encoding.

    PubMed

    Zwart, Nicholas R; Pipe, James G

    2009-06-01

    A new motion corrected Time-of-Flight MRA technique named Variable Pitch PROPELLER is presented. This technique employs the PROPELLER acquisition and reconstruction scheme for in-plane bulk motion correction. A non- Fourier through-plane encoding mechanism called quadratic encoding boosts SNR, relative to conventional 2D MRA, in lieu of traditional 3D encoding. Partial Fourier encoding is applied in the slice direction for a further reduction in scan time. This work details the construction and optimization of this technique. VPPROP MRAs are compared with a clinical MOTSA protocol. Initial results show promising robustness to bulk motion effects. The comparisons with MOTSA provide insight as to the additions required to create a comparable scan. PMID:19353668

  9. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.

    PubMed

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-12

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986

  10. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-01

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.

  11. Dark state in a nonlinear optomechanical system with quadratic coupling

    NASA Astrophysics Data System (ADS)

    Huang, Yue-Xin; Zhou, Xiang-Fa; Guo, Guang-Can; Zhang, Yong-Sheng

    We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed. Supported by the National Fundamental Research Program of China (Grants No. 2011CB921200 and No. 2011CBA00200), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB01030200), and NSFC (Grants No. 61275122 and 11474266).

  12. Linear Time Vertex Partitioning on Massive Graphs

    PubMed Central

    Mell, Peter; Harang, Richard; Gueye, Assane

    2016-01-01

    The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity. PMID:27336059

  13. LINEAR ACCELERATOR

    DOEpatents

    Christofilos, N.C.; Polk, I.J.

    1959-02-17

    Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.

  14. SUBOPT: A CAD program for suboptimal linear regulators

    NASA Technical Reports Server (NTRS)

    Fleming, P. J.

    1985-01-01

    An interactive software package which provides design solutions for both standard linear quadratic regulator (LQR) and suboptimal linear regulator problems is described. Intended for time-invariant continuous systems, the package is easily modified to include sampled-data systems. LQR designs are obtained by established techniques while the large class of suboptimal problems containing controller and/or performance index options is solved using a robust gradient minimization technique. Numerical examples demonstrate features of the package and recent developments are described.

  15. Minimum-variance fixed-form compensation of linear systems

    NASA Technical Reports Server (NTRS)

    Johnson, T. L.

    1979-01-01

    The problem of determining the linear time-invariant compensator of a specified dimension which minimizes the asymptotic expected value of a quadratic form in the state variables of a linear stochastic system of arbitrary order, is considered. It is shown that under appropriate assumptions, the solution of this problem can be interpreted as a minimum-order observer-based or dual observer-based compensator for an optimally aggregated model of the plant.

  16. Ensemble control of linear systems with parameter uncertainties

    NASA Astrophysics Data System (ADS)

    Kou, Kit Ian; Liu, Yang; Zhang, Dandan; Tu, Yanshuai

    2016-07-01

    In this paper, we study the optimal control problem for a class of four-dimensional linear systems based on quaternionic and Fourier analysis. When the control is unconstrained, the optimal ensemble controller for this linear ensemble control systems is given in terms of prolate spheroidal wave functions. For the constrained convex optimisation problem of such systems, the quadratic programming is presented to obtain the optimal control laws. Simulations are given to verity the effectiveness of the proposed theory.

  17. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    SciTech Connect

    Ita, B. I.

    2014-11-12

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

  18. Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2012-01-01

    In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

  19. PPN Metric and PPN torsion in the quadratic poincaré gauge theory of gravity

    NASA Astrophysics Data System (ADS)

    Gladchenko, M. S.; Ponomariov, V. N.; Zhytnikov, V. V.

    1990-05-01

    The post-newtonian approximation of the quadratic Poincaré gauge theory of gravity is studied. As a result of this investigation the modified PPN metric and PPN torsion is obtained. Post-newtonian equations of motion for different test bodies are analyzed and some restrictions on the parameters of the quadratic lagrangian are found.

  20. The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system

    NASA Astrophysics Data System (ADS)

    Li, Chengzhi; Llibre, Jaume

    2009-12-01

    We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.

  1. Fast and accurate computation of two-dimensional non-separable quadratic-phase integrals.

    PubMed

    Koç, Aykut; Ozaktas, Haldun M; Hesselink, Lambertus

    2010-06-01

    We report a fast and accurate algorithm for numerical computation of two-dimensional non-separable linear canonical transforms (2D-NS-LCTs). Also known as quadratic-phase integrals, this class of integral transforms represents a broad class of optical systems including Fresnel propagation in free space, propagation in graded-index media, passage through thin lenses, and arbitrary concatenations of any number of these, including anamorphic/astigmatic/non-orthogonal cases. The general two-dimensional non-separable case poses several challenges which do not exist in the one-dimensional case and the separable two-dimensional case. The algorithm takes approximately N log N time, where N is the two-dimensional space-bandwidth product of the signal. Our method properly tracks and controls the space-bandwidth products in two dimensions, in order to achieve information theoretically sufficient, but not wastefully redundant, sampling required for the reconstruction of the underlying continuous functions at any stage of the algorithm. Additionally, we provide an alternative definition of general 2D-NS-LCTs that shows its kernel explicitly in terms of its ten parameters, and relate these parameters bidirectionally to conventional ABCD matrix parameters. PMID:20508697

  2. The use of quadratic forms in the calculation of ground state electronic structures

    SciTech Connect

    Keller, Jaime; Weinberger, Peter

    2006-08-15

    There are many examples in theoretical physics where a fundamental quantity can be considered a quadratic form {rho}={sigma}{sub i}{rho}{sub i}=vertical bar {psi} vertical bar{sup 2} and the corresponding linear form {psi}={sigma}{sub i}{psi}{sub i} is highly relevant for the physical problem under study. This, in particular, is the case of the density and the wave function in quantum mechanics. In the study of N-identical-fermion systems we have the additional feature that {psi} is a function of the 3N configuration space coordinates and {rho} is defined in three-dimensional real space. For many-electron systems in the ground state the wave function and the Hamiltonian are to be expressed in terms of the configuration space (CS), a replica of real space for each electron. Here we present a geometric formulation of the CS, of the wave function, of the density, and of the Hamiltonian to compute the electronic structure of the system. Then, using the new geometric notation and the indistinguishability and equivalence of the electrons, we obtain an alternative computational method for the ground state of the system. We present the method and discuss its usefulness and relation to other approaches.

  3. Degradation reliability modeling based on an independent increment process with quadratic variance

    NASA Astrophysics Data System (ADS)

    Wang, Zhihua; Zhang, Yongbo; Wu, Qiong; Fu, Huimin; Liu, Chengrui; Krishnaswamy, Sridhar

    2016-03-01

    Degradation testing is an important technique for assessing life time information of complex systems and highly reliable products. Motivated by fatigue crack growth (FCG) data and our previous study, this paper develops a novel degradation modeling approach, in which degradation is represented by an independent increment process with linear mean and general quadratic variance functions of test time or transformed test time if necessary. Based on the constructed degradation model, closed-form expressions of failure time distribution (FTD) and its percentiles can be straightforwardly derived and calculated. A one-stage method is developed to estimate model parameters and FTD. Simulation studies are conducted to validate the proposed approach, and the results illustrate that the approach can provide reasonable estimates even for small sample size situations. Finally, the method is verified by the FCG data set given as the motivating example, and the results show that it can be considered as an effective degradation modeling approach compared with the multivariate normal model and graphic approach.

  4. Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

    NASA Technical Reports Server (NTRS)

    Kottapalli, Sesi; Leyland, Jane

    2014-01-01

    In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

  5. Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene.

    PubMed

    Pujari, Sumiran; Lang, Thomas C; Murthy, Ganpathy; Kaul, Ribhu K

    2016-08-19

    We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state. PMID:27588872

  6. Phosphorescence lifetime analysis with a quadratic programming algorithm for determining quencher distributions in heterogeneous systems.

    PubMed Central

    Vinogradov, S A; Wilson, D F

    1994-01-01

    A new method for analysis of phosphorescence lifetime distributions in heterogeneous systems has been developed. This method is based on decomposition of the data vector to a linearly independent set of exponentials and uses quadratic programming principles for x2 minimization. Solution of the resulting algorithm requires a finite number of calculations (it is not iterative) and is computationally fast and robust. The algorithm has been tested on various simulated decays and for analysis of phosphorescence measurements of experimental systems with descrete distributions of lifetimes. Critical analysis of the effect of signal-to-noise on the resolving capability of the algorithm is presented. This technique is recommended for resolution of the distributions of quencher concentration in heterogeneous samples, of which oxygen distributions in tissue is an important example. Phosphors of practical importance for biological oxygen measurements: Pd-meso-tetra (4-carboxyphenyl) porphyrin (PdTCPP) and Pd-meso-porphyrin (PdMP) have been used to provide experimental test of the algorithm. PMID:7858142

  7. Bogoliubov theory and Lee-Huang-Yang corrections in spin-1 and spin-2 Bose-Einstein condensates in the presence of the quadratic Zeeman effect

    SciTech Connect

    Uchino, Shun; Kobayashi, Michikazu; Ueda, Masahito

    2010-06-15

    We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, pressure, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.

  8. Quadratic Fermi node in a 3D strongly correlated semimetal

    SciTech Connect

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

  9. Quadratic Fermi node in a 3D strongly correlated semimetal

    PubMed Central

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-01-01

    Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

  10. Hydroxyl functionalized thermosensitive microgels with quadratic crosslinking density distribution.

    PubMed

    Elmas, Begum; Tuncel, Murvet; Senel, Serap; Patir, S; Tuncel, Ali

    2007-09-01

    N-isopropylacrylamide (NIPA) based uniform thermosensitive microgels were synthesized by dispersion polymerization by using relatively hydrophilic crosslinking agents with hydroxyl functionality. Glycerol dimethacrylate (GDMA), pentaerythritol triacrylate (PETA) and pentaerythritol propoxylate triacrylate (PEPTA) were used as crosslinking agents with different hydrophilicities. A protocol was first proposed to determine the crosslinking density distribution in the thermosensitive microgel particles by confocal laser scanning microscopy (CLSM). The microgels were fluorescently labeled by using hydroxyl group of the crosslinking agent. The CLSM observations performed with the microgels synthesized by three different crosslinking agents showed that the crosslinking density exhibited a quadratic decrease with the increasing radial distance in the spherical microgel particles. This structure led to the formation of more loose gel structure on the particle surface with respect to the center. Then the use of hydrophilic crosslinking agents in the dispersion polymerization of NIPA made possible the synthesis of thermosensitive microgels carrying long, flexible and chemically derivatizable (i.e., hydroxyl functionalized) fringes on the surface by a single-stage dispersion polymerization. The microgels with all crosslinking agents exhibited volume phase transition with the increasing temperature. The microgel obtained by the most hydrophilic crosslinking agent, GDMA exhibited higher hydrodynamic diameters in the fully swollen form at low temperatures than those obtained by PETA and PEPTA. Higher hydrodynamic size decrease from fully swollen form to the fully shrunken form was also observed with the same microgel. PMID:17532327

  11. Gap solitons in a nonlinear quadratic negative-index cavity.

    PubMed

    Scalora, Michael; de Ceglia, Domenico; D'Aguanno, Giuseppe; Mattiucci, Nadia; Akozbek, Neset; Centini, Marco; Bloemer, Mark J

    2007-06-01

    We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton. PMID:17677375

  12. Quadratic Fermi node in a 3D strongly correlated semimetal

    NASA Astrophysics Data System (ADS)

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-12-01

    Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

  13. GR angular momentum in the quadratic spinor Lagrangian formulation

    NASA Astrophysics Data System (ADS)

    Li, Siao-Jing

    2016-08-01

    We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.

  14. Quadratic Fermi node in a 3D strongly correlated semimetal

    DOE PAGESBeta

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; et al

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less

  15. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  16. Inverse problem of quadratic time-dependent Hamiltonians

    NASA Astrophysics Data System (ADS)

    Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing

    2015-08-01

    Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).

  17. Junction conditions in quadratic gravity: thin shells and double layers

    NASA Astrophysics Data System (ADS)

    Reina, Borja; Senovilla, José M. M.; Vera, Raül

    2016-05-01

    The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.

  18. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.

    2012-01-01

    A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

  19. Quadratic Fermi node in a 3D strongly correlated semimetal.

    PubMed

    Kondo, Takeshi; Nakayama, M; Chen, R; Ishikawa, J J; Moon, E-G; Yamamoto, T; Ota, Y; Malaeb, W; Kanai, H; Nakashima, Y; Ishida, Y; Yoshida, R; Yamamoto, H; Matsunami, M; Kimura, S; Inami, N; Ono, K; Kumigashira, H; Nakatsuji, S; Balents, L; Shin, S

    2015-01-01

    Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

  20. Quadratic isothermal amplification for the detection of microRNA.

    PubMed

    Duan, Ruixue; Zuo, Xiaolei; Wang, Shutao; Quan, Xiyun; Chen, Dongliang; Chen, Zhifei; Jiang, Lei; Fan, Chunhai; Xia, Fan

    2014-03-01

    This protocol describes an isothermal amplification approach for ultrasensitive detection of specific microRNAs (miRNAs). It achieves this level of sensitivity through quadratic amplification of the target oligonucleotide by using a Bst DNA polymerase-induced strand-displacement reaction and a lambda exonuclease-aided recycling reaction. First, the target miRNA binds to a specifically designed molecular beacon, causing it to become a fluorescence emitter. A primer then binds to the activated beacon, and Bst polymerase initiates the synthesis of a double-stranded DNA segment templated on the molecular beacon. This causes the concomitant release of the target miRNA from the beacon--the first round of 'recycling'. Second, the duplex beacon thus produced is a suitable substrate for a nicking enzyme present in solution. After the duplex beacon is nicked, the lambda exonuclease digests the beacon and releases the DNA single strand just synthesized, which is complementary to the molecular beacon, inducing the second round of recycling. The miRNA detection limit of this protocol is 10 fmol at 37 °C and 1 amol at 4 °C. This approach also affords high selectivity when applied to miRNA extracted from MCF-7 and PC3 cell lines and even from breast cancer tissue samples. Upon isolation of miRNA, the detection process can be completed in ∼2 h. PMID:24525753

  1. Optimized Large-scale CMB Likelihood and Quadratic Maximum Likelihood Power Spectrum Estimation

    NASA Astrophysics Data System (ADS)

    Gjerløw, E.; Colombo, L. P. L.; Eriksen, H. K.; Górski, K. M.; Gruppuso, A.; Jewell, J. B.; Plaszczynski, S.; Wehus, I. K.

    2015-11-01

    We revisit the problem of exact cosmic microwave background (CMB) likelihood and power spectrum estimation with the goal of minimizing computational costs through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al., and here we develop it into a fully functioning computational framework for large-scale polarization analysis, adopting WMAP as a working example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors, and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at ℓ ≤ 32 and a maximum shift in the mean values of a joint distribution of an amplitude-tilt model of 0.006σ. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation, which requires less than 3 GB of memory and 2 CPU minutes per iteration for ℓ ≤ 32, rendering low-ℓ QML CMB power spectrum analysis fully tractable on a standard laptop.

  2. On the Impact of a Quadratic Acceleration Term in the Analysis of Position Time Series

    NASA Astrophysics Data System (ADS)

    Bogusz, Janusz; Klos, Anna; Bos, Machiel Simon; Hunegnaw, Addisu; Teferle, Felix Norman

    2016-04-01

    The analysis of Global Navigation Satellite System (GNSS) position time series generally assumes that each of the coordinate component series is described by the sum of a linear rate (velocity) and various periodic terms. The residuals, the deviations between the fitted model and the observations, are then a measure of the epoch-to-epoch scatter and have been used for the analysis of the stochastic character (noise) of the time series. Often the parameters of interest in GNSS position time series are the velocities and their associated uncertainties, which have to be determined with the highest reliability. It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series. This non-linear motion could be a response to purely geophysical processes, for example, elastic rebound of the Earth's crust due to ice mass loss in Greenland, artefacts due to deficiencies in bias mitigation models, for example, of the GNSS satellite and receiver antenna phase centres, or any combination thereof. In this study we have simulated 20 time series with different stochastic characteristics such as white, flicker or random walk noise of length of 23 years. The noise amplitude was assumed at 1 mm/y-/4. Then, we added the deterministic part consisting of a linear trend of 20 mm/y (that represents the averaged horizontal velocity) and accelerations ranging from minus 0.6 to plus 0.6 mm/y2. For all these data we estimated the noise parameters with Maximum Likelihood Estimation (MLE) using the Hector software package without taken into account the non-linear term. In this way we set the benchmark to then investigate how the noise properties and velocity uncertainty may be affected by any un-modelled, non-linear term. The velocities and their uncertainties versus the accelerations for

  3. Universality of Effective Medium and Random Resistor Network models for disorder-induced linear unsaturating magnetoresistance

    NASA Astrophysics Data System (ADS)

    Lara, Silvia; Lai, Ying Tong; Love, Cameron; Ramakrishnan, Navneeth; Adam, Shaffique

    In recent years, the Effective Medium Theory (EMT) and the Random Resistor Network (RRN) have been separately used to explain disorder induced magnetoresistance that is quadratic at low fields and linear at high fields. We demonstrate that the quadratic and linear coefficients of the magnetoresistance and the transition point from the quadratic to the linear regime depend only on the inhomogeneous carrier density profile. We use this to find a mapping between the two models using dimensionless parameters that determine the magnetoresistance and show numerically that they belong to the same universality class. This work is supported by the Singapore National Research Foundation (NRF-NRFF2012-01) and the Singapore Ministry of Education and Yale-NUS College through Grant Number R-607-265-01312.

  4. New type of Weyl semimetal with quadratic double Weyl fermions.

    PubMed

    Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid

    2016-02-01

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914

  5. Moments for general quadratic densities in n dimensions

    SciTech Connect

    Furman, Miguel A.

    2002-03-20

    We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.

  6. New type of Weyl semimetal with quadratic double Weyl fermions

    PubMed Central

    Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid

    2016-01-01

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914

  7. Post-Newtonian, quasicircular binary inspirals in quadratic modified gravity

    NASA Astrophysics Data System (ADS)

    Yagi, Kent; Stein, Leo C.; Yunes, Nicolás; Tanaka, Takahiro

    2012-03-01

    We consider a general class of quantum gravity-inspired, modified gravity theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to scalar fields with standard kinetic energy. This class of theories includes Einstein-Dilaton-Gauss-Bonnet and Chern-Simons modified gravity as special cases. We analytically derive and solve the coupled field equations in the post-Newtonian approximation, assuming a comparable-mass, spinning black hole binary source in a quasicircular, weak-field/slow-motion orbit. We find that a naive subtraction of divergent piece associated with the point-particle approximation is ill-suited to represent compact objects in these theories. Instead, we model them by appropriate effective sources built so that known strong-field solutions are reproduced in the far-field limit. In doing so, we prove that black holes in Einstein-Dilaton-Gauss-Bonnet and Chern-Simons theory can have hair, while neutron stars have no scalar monopole charge, in diametrical opposition to results in scalar-tensor theories. We then employ techniques similar to the direct integration of the relaxed Einstein equations to obtain analytic expressions for the scalar field, metric perturbation, and the associated gravitational wave luminosity measured at infinity. We find that scalar field emission mainly dominates the energy flux budget, sourcing electric-type (even-parity) dipole scalar radiation and magnetic-type (odd-parity) quadrupole scalar radiation, correcting the General Relativistic prediction at relative -1PN and 2PN orders. Such modifications lead to corrections in the emitted gravitational waves that can be mapped to the parameterized post-Einsteinian framework. Such modifications could be strongly constrained with gravitational wave observations.

  8. LINEAR ACCELERATOR

    DOEpatents

    Colgate, S.A.

    1958-05-27

    An improvement is presented in linear accelerators for charged particles with respect to the stable focusing of the particle beam. The improvement consists of providing a radial electric field transverse to the accelerating electric fields and angularly introducing the beam of particles in the field. The results of the foregoing is to achieve a beam which spirals about the axis of the acceleration path. The combination of the electric fields and angular motion of the particles cooperate to provide a stable and focused particle beam.

  9. Linear Clouds

    NASA Technical Reports Server (NTRS)

    2006-01-01

    [figure removed for brevity, see original site] Context image for PIA03667 Linear Clouds

    These clouds are located near the edge of the south polar region. The cloud tops are the puffy white features in the bottom half of the image.

    Image information: VIS instrument. Latitude -80.1N, Longitude 52.1E. 17 meter/pixel resolution.

    Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

    NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

  10. Stability of the equilibrium positions of an engine with nonlinear quadratic springs

    NASA Astrophysics Data System (ADS)

    Stănescu, Nicolae-Doru; Popa, Dinel

    2014-06-01

    Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.

  11. The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems

    PubMed Central

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980

  12. On ideal structure in quadratic DDS in R{sup 2}

    SciTech Connect

    Kutnjak, Milan

    2008-11-13

    We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.

  13. The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.

    PubMed

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3). PMID:24982980

  14. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  15. Line integral formulation of energy and QUadratic invariants preserving (EQUIP) methods for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice

    2016-06-01

    The family of EQUIP (Energy and QUadratic Invariants Preserving) methods for Hamiltonian systems is here recasted in the framework of Line Integral Methods, in order to provide a more efficient discrete problem.

  16. Maximization of Sums of Quotients of Quadratic Forms and Some Generalizations.

    ERIC Educational Resources Information Center

    Kiers, Henk A. L.

    1995-01-01

    Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)

  17. PHYSICAL FOUNDATIONS OF QUANTUM ELECTRONICS: A study of radiation propagation in a medium with quadratic inhomogeneity

    NASA Astrophysics Data System (ADS)

    Pikulev, A. A.

    2001-09-01

    The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed.

  18. Bianchi type-I cosmological model with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Reddy, D. R. K.; Adhav, K. S.; Purandare, M. A.

    2015-05-01

    Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been studied in general theory of relativity. The general solutions of the Einstein's field equations for Bianchi type-I space-time have been obtained under the assumption of quadratic equation of state (EoS) p= αρ 2- ρ, where α is constant and strictly α≠0. The physical and geometrical aspects of the model are discussed.

  19. Solution of the Dirac equation with some superintegrable potentials by the quadratic algebra approach

    NASA Astrophysics Data System (ADS)

    Aghaei, S.; Chenaghlou, A.

    2014-02-01

    The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

  20. Instrument Induced Linear Flow Resistance In Öresund

    NASA Astrophysics Data System (ADS)

    Green, M.; Stigebrandt, A.

    Previous studies of the flow resistance in Öresund indicate the presence of a linear rela- tionship between sea-level and flow rate. The linear term is superposed on the common quadratic relationship from bottom friction and form drag. In previous works, cross- stream geostrophy or generation of internal waves have explained the linear term. The present analysis is based on two different flow-rate data sets. The first set was the same data set used in earlier studies showing the linear term. It consists of data from RCM7 and S4. The second set was taken with ADCP. The observations were fitted to two different strait flow models. The first model had a quadratic flow resistance term only, whereas the second had both a quadratic and a linear term. In addition to the current data, sea-level observations from both ends of the strait were used. The analyses showed that the linear term is significant in the first data set but not in the second. This result holds regardless of season and part of data set and current meter and sea-level gauge combination. The only explanation is that it is an artefact caused by non-linear current meter response by the RCM7 and S4 instruments. These meters underestimate the velocity if it is higher than approximately 50 cm/s, which often is the case in Öresund. Published papers support this statement. The linear term is thus an artefact generated by the instruments, and unfortunately not a feature of the physics of the strait flow.

  1. Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

    SciTech Connect

    Soudackov, Alexander; Hammes-Schiffer, Sharon

    2015-11-17

    Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency regimes for the proton donor-acceptor vibrational mode. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term does not significantly impact the rate constants derived using the cumulant expansion approach in any of the regimes studied. The effects of the quadratic term may become significant when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant, however, particularly at high temperatures and for proton transfer interfaces with extremely soft proton donor-acceptor modes that are associated with extraordinarily weak hydrogen bonds. Even with the thermal averaging procedure, the effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances, and the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes. We are grateful for support from National Institutes of Health Grant GM056207 (applications to enzymes) and the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy

  2. Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

    SciTech Connect

    Soudackov, Alexander V.; Hammes-Schiffer, Sharon

    2015-11-21

    Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton

  3. Late-time quadratic growth in single-mode Rayleigh-Taylor instability.

    PubMed

    Wei, Tie; Livescu, Daniel

    2012-10-01

    The growth of the two-dimensional single-mode Rayleigh-Taylor instability (RTI) at low Atwood number (A=0.04) is investigated using Direct Numerical Simulations. The main result of the paper is that, at long times and sufficiently high Reynolds numbers, the bubble acceleration becomes stationary, indicating mean quadratic growth. This is contrary to the general belief that single-mode Rayleigh-Taylor instability reaches a constant bubble velocity at long times. At unity Schmidt number, the development of the instability is strongly influenced by the perturbation Reynolds number, defined as Rep≡λsqrt[Agλ/(1+A)]/ν. Thus, the instability undergoes different growth stages at low and high Rep. A new stage, chaotic development, was found at sufficiently high Rep values, after the reacceleration stage. During the chaotic stage, the instability experiences seemingly random acceleration and deceleration phases, as a result of complex vortical motions, with strong dependence on the initial perturbation shape (i.e., wavelength, amplitude, and diffusion thickness). Nevertheless, our results show that the mean acceleration of the bubble front becomes constant at late times, with little influence from the initial shape of the interface. As Rep is lowered to small values, the later instability stages, chaotic development, reacceleration, potential flow growth, and even the exponential growth described by linear stability theory, are subsequently no longer reached. Therefore, the results suggest a minimum Reynolds number and a minimum development time necessary to achieve all stages of single-mode RTI development, requirements which were not satisfied in the previous studies of single-mode RTI. PMID:23214698

  4. 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.

  5. Quadratic optimal cooperative control synthesis with flight control application

    NASA Technical Reports Server (NTRS)

    Schmidt, D. K.; Innocenti, M.

    1984-01-01

    An optimal control-law synthesis approach is presented that involves simultaneous solution for two cooperating controllers operating in parallel. One controller's structure includes stochastic state estimation and linear feedback of the state estimates, while the other controller involves direct linear feedback of selected system output measurements. This structure is shown to be optimal under the constraint of linear feedback of system outputs in one controller. Furthermore, it is appropriate for flight control synthesis where the full-state optimal stochastic controller can be adjusted to be representative of an optimal control model of the human pilot in a stochastic regulation task. The method is experimentally verified in the case of the selection of pitch-damper gain for optimum pitch tracking, where optimum implies the best subjective pilot rating in the task. Finally, results from application of the method to synthesize a controller for a multivariable fighter aircraft are presented, and implications of the results of this method regarding the optimal plant dynamics for tracking are discussed.

  6. Age-related rarefaction in retinal vasculature is not linear.

    PubMed

    Azemin, M Z Che; Ab Hamid, F; Aminuddin, A; Wang, J J; Kawasaki, R; Kumar, D K

    2013-10-24

    The fractal dimension is a global measure of complexity and is useful for quantifying anatomical structures, including the retinal vascular network. A previous study found a linear declining trend with aging on the retinal vascular fractal dimension (DF); however, it was limited to the older population (49 years and older). This study aimed to investigate the possible models of the fractal dimension changes from young to old subjects (10 to 73 years). A total of 215 right-eye retinal samples, including those of 119 (55%) women and 96 (45%) men, were selected. The retinal vessels were segmented using computer-assisted software, and non-vessel fragments were deleted. The fractal dimension was measured based on the log-log plot of the number of grids versus the size. The retinal vascular Df was analyzed to determine changes with increasing age. Finally, the data were fitted to three polynomial models. All three models are statistically significant (Linear: R(2) = 0.1270, 213 d.f., p<0.001, Quadratic: R(2) = 0.1536, 212 d.f., p<0.001, Cubic: R(2) = 0.1529, 211 d.f., p<0.001). The quadratic regression is significantly better than the linear regression (p<0.001); however, the increase in R(2) from the quadratic model to the cubic model is not significant (p=0.97). These results suggest that the decreasing trend of the fractal dimension associated with aging is better explained by the quadratic model than by the linear and cubic models in a sample with a broader age spectrum. PMID:24512773

  7. Method of Conjugate Radii for Solving Linear and Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Nachtsheim, Philip R.

    1999-01-01

    This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

  8. On linear area embedding of planar graphs

    NASA Astrophysics Data System (ADS)

    Dolev, D.; Trickey, H.

    1981-09-01

    Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. An algorithm to embed outerplanar graphs in linear area is given. This algorithm is extended to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs.

  9. Controller design approach based on linear programming.

    PubMed

    Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

    2013-11-01

    This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. PMID:23910155

  10. Invertible linear transformations and the Lie algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Yufeng; Tam, Honwah; Guo, Fukui

    2008-07-01

    With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.

  11. The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples

    NASA Technical Reports Server (NTRS)

    Bensoussan, A.; Delfour, M. C.; Mitter, S. K.

    1976-01-01

    Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

  12. A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

    PubMed Central

    Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

    2014-01-01

    The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

  13. Classification of the quantum two-dimensional superintegrable systems with quadratic integrals and the Staeckel transforms

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2008-05-15

    The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient -{h_bar}{sup 2} plus a quantum deformation of order {h_bar}{sup 4} and {h_bar}{sup 6}. The systems inside the classes are transformed using Staeckel transforms in the quantum case as in the classical case. The general form of the Staeckel transform between superintegrable systems is discussed.

  14. A wavelet bicoherence-based quadratic nonlinearity feature for translational axis condition monitoring.

    PubMed

    Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

    2014-01-01

    The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

  15. Quantum stochastic calculus associated with quadratic quantum noises

    NASA Astrophysics Data System (ADS)

    Ji, Un Cig; Sinha, Kalyan B.

    2016-02-01

    We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

  16. Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2

    SciTech Connect

    Ellis, John; García, Marcos A.G.; Olive, Keith A.; Nanopoulos, Dimitri V. E-mail: garciagarcia@physics.umn.edu E-mail: olive@physics.umn.edu

    2014-05-01

    The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential ∝ φ{sup n} : n ≅ 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R+R{sup 2} model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N = 1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focusing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

  17. Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros

    NASA Astrophysics Data System (ADS)

    Yamada, Katsuhiko; Jikuya, Ichiro

    2014-09-01

    Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

  18. Detection of code spread OFDM based on 0-1 integer quadratic programming

    NASA Astrophysics Data System (ADS)

    Elghariani, Ali; Zoltowski, Michael D.

    2012-05-01

    In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.

  19. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    SciTech Connect

    Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  20. On the chaotic behavior of the primal–dual affine–scaling algorithm for linear optimization

    SciTech Connect

    Bruin, H.; Fokkink, R. Roos, C.; Gu, G.

    2014-12-15

    We study a one-parameter family of quadratic maps, which serves as a template for interior point methods. It is known that such methods can exhibit chaotic behavior, but this has been verified only for particular linear optimization problems. Our results indicate that this chaotic behavior is generic.

  1. Fixed order dynamic compensation for multivariable linear systems

    NASA Technical Reports Server (NTRS)

    Kramer, F. S.; Calise, A. J.

    1986-01-01

    This paper considers the design of fixed order dynamic compensators for multivariable time invariant linear systems, minimizing a linear quadratic performance cost functional. Attention is given to robustness issues in terms of multivariable frequency domain specifications. An output feedback formulation is adopted by suitably augmenting the system description to include the compensator states. Either a controller or observer canonical form is imposed on the compensator description to reduce the number of free parameters to its minimal number. The internal structure of the compensator is prespecified by assigning a set of ascending feedback invariant indices, thus forming a Brunovsky structure for the nominal compensator.

  2. The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function.

    PubMed

    Hendrickx, Christophe; Araújo, Ricardo; Mateus, Octávio

    2015-01-01

    The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber-invaded by the quadrate diverticulum of the mandibular arch pneumatic system-was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

  3. The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

    PubMed Central

    Araújo, Ricardo; Mateus, Octávio

    2015-01-01

    The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

  4. An efficient algorithm for computing the roots of general quadratic, cubic and quartic equations

    NASA Astrophysics Data System (ADS)

    Mahmood, Munir; Hammad, Sali; Mahmood, Ibtihal

    2014-10-01

    While the solution to deriving the roots of the general quadratic equation is adequately covered in a typical classroom environment, the same is not true for the general cubic and quartic equations. To the best of our knowledge, we do not see the roots of the general cubic or quartic equation discussed in any typical algebra textbook at the undergraduate level. In this paper, we propose an efficient algorithm in order to calculate the roots of the general quadratic, cubic and quartic equations. Examples are given to demonstrate the usefulness of this proposed algorithm.

  5. OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE

    PubMed Central

    Xie, Xianchao; Kou, S. C.; Brown, Lawrence

    2015-01-01

    This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results. PMID:27041778

  6. Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

    NASA Astrophysics Data System (ADS)

    Lee, T.-W.; An, Keju

    2016-06-01

    We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

  7. Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential

    NASA Astrophysics Data System (ADS)

    Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei

    2016-07-01

    In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.

  8. A study of radiation propagation in a medium with quadratic inhomogeneity

    SciTech Connect

    Pikulev, A A

    2001-09-30

    The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed. (physical foundations of quantum electronics)

  9. Multi-isotopic transuranic waste interrogation using delayed neutron nondestructive assay and iterative quadratic programming techniques

    NASA Astrophysics Data System (ADS)

    Wu, Cheng-Wei

    1997-11-01

    Nuclear safeguards for Special Nuclear Materials is to protect the nuclear materials against malevolent use and to insure their peaceful usage. The nondestructive assay technique (NDA) offers an efficient and proliferation resistance method for nuclear safeguards technology. NDA techniques were investigated for multi-isotopic transuranic waste interrogation. This work was originally intended for the Integral Fast Reactor (IFR) under development at Argonne National Laboratory. One major feature of the IFR is its integral fuel cycle based on a pyrometallurgical process. More than 99% of transuranics produced in the fuel are returned to the makeup fuel and burned in the reactor. With the long-lived actinides removed from the waste stream, the waste produced will decay sufficiently in 300 years dropping below the cancer risk level of natural uranium ore and easing the perceived waste management problem. The feasibility of using nondestructive assay techniques for the IFR fuel cycle waste interrogation were studied. A special DNNDA experimental device was designed and analysis techniques were developed. The DNNDA technique uses the delayed neutrons emitted after the activation of a 14 MeV neutron source as the characteristic signature for each fissionable isotope. A tantalum/polyethylene filter was employed to enhance the discrimination between the fissile and the fissionable isotopes. Spontaneous fissions from 240Pu were also measured to assist the mass assay. A nonlinear overdetermined system was established based on the DNNDA measurements. An Iterative Quadratic Programming (IQP) method was applied to perform the estimates. The IQP method has several advantages over the linear least squares and Kalman filter methods, it has the flexibility of adding additional constraints, it has superlinear global convergence and it can be utilized for nonlinear problems. The results show that using the IQP method with the DNNDA technique is quite promising for multi-isotopic assay

  10. Localization of the SFT inspired nonlocal linear models and exact solutions

    NASA Astrophysics Data System (ADS)

    Vernov, S. Yu.

    2011-05-01

    A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function ℱ(□ g ), which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.

  11. Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation

    NASA Astrophysics Data System (ADS)

    Rousseau, Christiane

    We give here a planar quadratic differential system depending on two parameters, λ, δ. There is a curve in the λ-δ space corresponding to a homoclinic loop bifurcation (HLB). The bifurcation is degenerate at one point of the curve and we get a narrow tongue in which we have two limit cycles. This is the first example of such a bifurcation in planar quadratic differential systems. We propose also a model for the bifurcation diagram of a system with two limit cycles appearing at a singular point from a degenerate Hopf bifurcation, and dying in a degenerate HLB. This model shows a deep duality between degenerate Hopf bifurcations and degenerate HLBs. We give a bound for the maximal number of cycles that can appear in certain simultaneous Hopf and homoclinic loop bifurcations. We also give an example of quadratic system depending on three parameters which has at one place a degenerate Hopf bifurcation of order 3, and at another place a Hopf bifurcation of order 2 together with a HLB. We characterize the planar quadratic systems which are integrable in the neighbourhood of a homoclinic loop.

  12. Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

    ERIC Educational Resources Information Center

    Didis, Makbule Gozde; Erbas, Ayhan Kursat

    2015-01-01

    This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…

  13. Horizontal Distance Travelled by a Mobile Experiencing a Quadratic Drag Force: Normalized Distance and Parametrization

    ERIC Educational Resources Information Center

    Vial, Alexandre

    2007-01-01

    We investigate the problem of the horizontal distance travelled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial…

  14. Changes in methodology for monitoring long-term vegetation quadrats on the Jornada Experimental Range

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Nearly 150 sq. mi. quadrats were established for long-term monitoring of vegetation dynamics on the Jornada Experimental Range in south central New Mexico in the early 1900s. Today, approximately 120 of those sites are revisited on a five year sampling rotation. Although some of the methods for data...

  15. Optical synthetic-aperture radar processor archietecture with quadratic phase-error correction

    SciTech Connect

    Dickey, F.M.; Mason, J.J. )

    1990-10-15

    Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.

  16. Failures and Inabilities of High School Students about Quadratic Equations and Functions

    ERIC Educational Resources Information Center

    Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma

    2015-01-01

    In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…

  17. A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

    ERIC Educational Resources Information Center

    Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

    2012-01-01

    Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

  18. Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane

    ERIC Educational Resources Information Center

    McDonald, Todd

    2006-01-01

    This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

  19. The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

    1994-01-01

    The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

  20. Inflation driven by scalar field with non-minimal kinetic coupling with Higgs and quadratic potentials

    SciTech Connect

    Granda, L.N.

    2011-04-01

    We study a scalar field with non-minimal kinetic coupling to itself and to the curvature. The slow rolling conditions allowing an inflationary background have been found. The quadratic and Higgs type potentials have been considered, and the corresponding values for the scalar fields at the end of inflation allows to recover the connection with particle physics.

  1. Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP). GMAC® Research Report RR-14-01

    ERIC Educational Resources Information Center

    Han, Kyung T.; Rudner, Lawrence M.

    2014-01-01

    This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…

  2. Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets

    ERIC Educational Resources Information Center

    Benacka, Jan

    2010-01-01

    This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…

  3. Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

    ERIC Educational Resources Information Center

    Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

    2015-01-01

    The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

  4. Landau-Zener transition in quadratic nonlinear two-state systems

    SciTech Connect

    Ishkhanyan, A. M.

    2010-05-15

    A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula provides a highly accurate approximation for the whole rage of the variation of the Landau-Zener parameter.

  5. Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry

    ERIC Educational Resources Information Center

    Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo

    2014-01-01

    The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…

  6. Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

    ERIC Educational Resources Information Center

    Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.

    2011-01-01

    Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

  7. Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

    PubMed

    Kiselev, Aleksei P; Plachenov, Alexandr B

    2016-04-01

    The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given. PMID:27140777

  8. An alternative proof of Lie's linearization theorem using a new λ -symmetry criterion

    NASA Astrophysics Data System (ADS)

    Al-Dweik, Ahmad Y.; Mustafa, M. T.; Mara'Beh, Raed A.; Mahomed, F. M.

    2015-09-01

    An alternative proof of Lie's approach for the linearization of scalar second-order ordinary differential equations is derived by using the relationship between λ -symmetries and first integrals. This relation further leads to a new λ -symmetry linearization criterion for second-order ordinary differential equations which provides a new approach for constructing the linearization transformations with lower complexity. The effectiveness of the approach is illustrated by obtaining the local linearization transformations for the linearizable nonlinear ordinary differential equations of the form y″ +F1 (x, y)y‧ + F (x, y) = 0 . Examples of linearizable nonlinear ordinary differential equations which are quadratic or cubic in the first derivative are also presented.

  9. Field testing of linear individual pitch control on the two-bladed controls advanced research turbine

    SciTech Connect

    van Solingen, Edwin; Fleming, Paul A.; Scholbrock, Andrew; van Wingerden, Jan-Willem

    2015-04-17

    This paper presents the results of field tests using linear individual pitch control (LIPC) on the two-bladed Controls Advanced Research Turbine 2 (CART2) at the National Renewable Energy Laboratory (NREL). LIPC has recently been introduced as an alternative to the conventional individual pitch control (IPC) strategy for two-bladed wind turbines. The main advantage of LIPC over conventional IPC is that it requires, at most, only two feedback loops to potentially reduce the periodic blade loads. In previous work, LIPC was designed to implement blade pitch angles at a fixed frequency (e.g., the once-per-revolution (1P) frequency), which made it only applicable in above-rated wind turbine operating conditions. In this study, LIPC is extended to below-rated operating conditions by gain scheduling the controller on the rotor speed. With this extension, LIPC and conventional IPC are successfully applied to the NREL CART2 wind turbine. Lastly, the field-test results obtained during the measurement campaign indicate that LIPC significantly reduces the wind turbine loads for both below-rated and above-rated operation.

  10. Field testing of linear individual pitch control on the two-bladed controls advanced research turbine

    DOE PAGESBeta

    van Solingen, Edwin; Fleming, Paul A.; Scholbrock, Andrew; van Wingerden, Jan-Willem

    2015-04-17

    This paper presents the results of field tests using linear individual pitch control (LIPC) on the two-bladed Controls Advanced Research Turbine 2 (CART2) at the National Renewable Energy Laboratory (NREL). LIPC has recently been introduced as an alternative to the conventional individual pitch control (IPC) strategy for two-bladed wind turbines. The main advantage of LIPC over conventional IPC is that it requires, at most, only two feedback loops to potentially reduce the periodic blade loads. In previous work, LIPC was designed to implement blade pitch angles at a fixed frequency (e.g., the once-per-revolution (1P) frequency), which made it only applicablemore » in above-rated wind turbine operating conditions. In this study, LIPC is extended to below-rated operating conditions by gain scheduling the controller on the rotor speed. With this extension, LIPC and conventional IPC are successfully applied to the NREL CART2 wind turbine. Lastly, the field-test results obtained during the measurement campaign indicate that LIPC significantly reduces the wind turbine loads for both below-rated and above-rated operation.« less

  11. Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

    NASA Astrophysics Data System (ADS)

    Recchioni, Maria Cristina

    2001-12-01

    This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

  12. Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

    NASA Technical Reports Server (NTRS)

    Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.

    2014-01-01

    A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

  13. Trellis Decoding Complexity of Linear Block Codes

    NASA Technical Reports Server (NTRS)

    Kiely, A. B.; McEliece, R. J.; Lin, W.; Ekroot, L.; Dolinar, S.

    1995-01-01

    We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code, or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: if a trellis is optimum with respect to this partial ordering, it has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.

  14. Organometallic complexes for nonlinear optics. 43. Quadratic optical nonlinearities of dipolar alkynylruthenium complexes with phenyleneethynylene/phenylenevinylene bridges.

    PubMed

    Rigamonti, Luca; Babgi, Bandar; Cifuentes, Marie P; Roberts, Rachel L; Petrie, Simon; Stranger, Robert; Righetto, Stefania; Teshome, Ayele; Asselberghs, Inge; Clays, Koen; Humphrey, Mark G

    2009-04-20

    The syntheses of trans-[Ru(4,4'-C[triple bond]CC(6)H(4)C[triple bond]CC(6)H(4)NO(2))Cl(dppe)(2)] (19) and the systematically varied complexes trans-[Ru(4,4',4''-C[triple bond]CC(6)H(4)X(2)C(6)H(4)Y(2)C(6)H(4)NO(2))Cl(L(2))(2)] [L(2) = dppe, X(2) = C[triple bond]C, Y(2) = (E)-CH=CH (12), C[triple bond]C (18); L(2) = dppe, X(2) = (E)-CH=CH, Y(2) = C[triple bond]C (14), (E)-CH=CH (16); L(2) = dppm, X(2) = C[triple bond]C, Y(2) = (E)-CH=CH (13); L(2) = dppm, X(2) = (E)-CH=CH, Y(2) = C[triple bond]C (15), (E)-CH=CH (17)] are reported, the latter being donor-bridge-acceptor complexes varying in bridge composition by replacement of yne with E-ene linkages, together with their cyclic voltammetric data, linear optical, and quadratic nonlinear optical response data. Ru(II/III) oxidation potentials increase on replacing yne linkage by E-ene linkage at the phenylene adjacent to the metal center, and on replacing dppe by dppm co-ligands. The low-energy optical absorption maxima occur in the region 20,400-23,300 cm(-1) and are metal-to-ligand charge-transfer (MLCT) in origin; these bands undergo a blue-shift upon pi-bridge lengthening by addition of phenyleneethynylene units, and on replacing E-ene linkages by yne linkages. Time-dependent density functional theory calculations on model complexes have suggested assignments for the low-energy bands. The optical spectra of selected oxidized species contain low-energy ligand-to-metal charge transfer (LMCT) bands centered in the region 9760-11,800 cm(-1). Quadratic molecular nonlinearities from hyper-Rayleigh scattering (HRS) studies at 1064 nm reveal an increase in the two-level-corrected beta(0) value on pi-bridge lengthening, a trend that is not seen with beta values because of the blue-shift in lambda(max) for this structural modification. Replacing yne linkages by E-ene linkage at the phenylene adjacent to the metal center or dppm co-ligand by dppe results in an increase in beta and beta(0) values. In contrast, quadratic

  15. Linear and nonlinear associations between general intelligence and personality in Project TALENT.

    PubMed

    Major, Jason T; Johnson, Wendy; Deary, Ian J

    2014-04-01

    Research on the relations of personality traits to intelligence has primarily been concerned with linear associations. Yet, there are no a priori reasons why linear relations should be expected over nonlinear ones, which represent a much larger set of all possible associations. Using 2 techniques, quadratic and generalized additive models, we tested for linear and nonlinear associations of general intelligence (g) with 10 personality scales from Project TALENT (PT), a nationally representative sample of approximately 400,000 American high school students from 1960, divided into 4 grade samples (Flanagan et al., 1962). We departed from previous studies, including one with PT (Reeve, Meyer, & Bonaccio, 2006), by modeling latent quadratic effects directly, controlling the influence of the common factor in the personality scales, and assuming a direction of effect from g to personality. On the basis of the literature, we made 17 directional hypotheses for the linear and quadratic associations. Of these, 53% were supported in all 4 male grades and 58% in all 4 female grades. Quadratic associations explained substantive variance above and beyond linear effects (mean R² between 1.8% and 3.6%) for Sociability, Maturity, Vigor, and Leadership in males and Sociability, Maturity, and Tidiness in females; linear associations were predominant for other traits. We discuss how suited current theories of the personality-intelligence interface are to explain these associations, and how research on intellectually gifted samples may provide a unique way of understanding them. We conclude that nonlinear models can provide incremental detail regarding personality and intelligence associations. PMID:24660993

  16. Obstacle avoidance for autonomous land vehicle navigation in indoor environments by quadratic classifier.

    PubMed

    Ku, C H; Tsai, W H

    1999-01-01

    A vision-based approach to obstacle avoidance for autonomous land vehicle (ALV) navigation in indoor environments is proposed. The approach is based on the use of a pattern recognition scheme, the quadratic classifier, to find collision-free paths in unknown indoor corridor environments. Obstacles treated in this study include the walls of the corridor and the objects that appear in the way of ALV navigation in the corridor. Detected obstacles as well as the two sides of the ALV body are considered as patterns. A systematic method for separating these patterns into two classes is proposed. The two pattern classes are used as the input data to design a quadratic classifier. Finally, the two-dimensional decision boundary of the classifier, which goes through the middle point between the two front vehicle wheels, is taken as a local collision-free path. This approach is implemented on a real ALV and successful navigations confirm the feasibility of the approach. PMID:18252315

  17. Equation for disentangling time-ordered exponentials with arbitrary quadratic generators

    SciTech Connect

    Budanov, V.G.

    1987-12-01

    In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function.

  18. The algebraic decoding of the (41, 21, 9) quadratic residue code

    NASA Technical Reports Server (NTRS)

    Reed, Irving S.; Truong, T. K.; Chen, Xuemin; Yin, Xiaowei

    1992-01-01

    A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

  19. Error analysis of the quadratic nodal expansion method in slab geometry

    SciTech Connect

    Penland, R.C.; Turinsky, P.J.; Azmy, Y.Y.

    1994-10-01

    As part of an effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal diffusion codes, the authors derive error bounds on the solution variables of the quadratic Nodal Expansion Method (NEM) in slab geometry. Closure of the system is obtained through flux discontinuity relationships and boundary conditions. In order to verify the analysis presented, the authors compare the quadratic NEM to the analytic solution of a test problem. The test problem for this investigation is a one-dimensional slab [0,20cm] with L{sup 2} = 6.495cm{sup 2} and D = 0.1429cm. The slab has a unit neutron source distributed uniformly throughout and zero flux boundary conditions. The analytic solution to this problem is used to compute the node-average fluxes over a variety of meshes, and these are used to compute the NEM maximum error on each mesh.

  20. Superintegrable deformations of superintegrable systems: Quadratic superintegrability and higher-order superintegrability

    NASA Astrophysics Data System (ADS)

    Rañada, Manuel F.

    2015-04-01

    The superintegrability of four Hamiltonians H r ˜ = λ H r , r = a, b, c, d, where Hr are known Hamiltonians and λ is a certain function defined on the configuration space and depended on a parameter κ, is studied. The new Hamiltonians, and the associated constants of motion Jri, i = 1, 2, 3, are continous functions of the parameter κ. The first part is concerned with separability and quadratic superintegrability (the integrals of motion are quadratic in the momenta) and the second part is devoted to the existence of higher-order superintegrability. The results obtained in the second part are related with the Tremblay-Turbiner-Winternitz and the Post-Winternitz systems.

  1. Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions

    NASA Astrophysics Data System (ADS)

    Li, Run-Bing; Zhou, Lin; Wang, Jin; Zhan, Ming-Sheng

    2009-04-01

    We demonstrate a technique for directly measuring the quadratic Zeeman shift using stimulated Raman transitions. The quadratic Zeeman shift has been measured yielding Δν=1296.8±3.3 Hz/G 2 for magnetically insensitive sublevels ( 5S,F=2,mF=0→5S,F=3,mF=0) of 85Rb by compensating the magnetic field and cancelling the ac Stark shift. We also measured the cancellation ratio of the differential ac Stark shift due to the imbalanced Raman beams by using two pairs of Raman beams ( σ+, σ+) and it is 1:3.67 when the one-photon detuning is 1.5 GHz in the experiment.

  2. Photonic EPR State from Quadratic Waveguide Array with Alternating Positive and Negative Couplings

    NASA Astrophysics Data System (ADS)

    Ying, Yang; Ping, Xu; Liang-Liang, Lu; Shi-Ning, Zhu

    2016-02-01

    We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction. This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space. Supported by the State Key Program for Basic Research in China under Grant No. 2012CB921802, the National Natural Science Foundations of China under Grant Nos. 91321312, 11321063 and 11422438

  3. Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Sharov, G. S.

    2016-06-01

    Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H(z) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale rs(zd). Among the considered models the best value of χ2 is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.

  4. Numerical solution of quadratic matrix equations for free vibration analysis of structures

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1975-01-01

    This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

  5. A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

    PubMed Central

    Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

    2012-01-01

    Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data. PMID:22429193

  6. A 3D Frictional Segment-to-Segment Contact Method for Large Deformations and Quadratic Elements

    SciTech Connect

    Puso, M; Laursen, T; Solberg, J

    2004-04-01

    Node-on-segment contact is the most common form of contact used today but has many deficiencies ranging from potential locking to non-smooth behavior with large sliding. Furthermore, node-on-segment approaches are not at all applicable to higher order discretizations (e.g. quadratic elements). In a previous work, [3, 4] we developed a segment-to-segment contact approach for eight node hexahedral elements based on the mortar method that was applicable to large deformation mechanics. The approach proved extremely robust since it eliminated the over-constraint that caused 'locking' and provided smooth force variations in large sliding. Here, we extend this previous approach to treat frictional contact problems. In addition, the method is extended to 3D quadratic tetrahedrals and hexahedrals. The proposed approach is then applied to several challenging frictional contact problems that demonstrate its effectiveness.

  7. Learning control for minimizing a quadratic cost during repetitions of a task

    NASA Technical Reports Server (NTRS)

    Longman, Richard W.; Chang, Chi-Kuang

    1990-01-01

    In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.

  8. Identify Secretory Protein of Malaria Parasite with Modified Quadratic Discriminant Algorithm and Amino Acid Composition.

    PubMed

    Feng, Yong-E

    2016-06-01

    Malaria parasite secretes various proteins in infected red blood cell for its growth and survival. Thus identification of these secretory proteins is important for developing vaccine or drug against malaria. In this study, the modified method of quadratic discriminant analysis is presented for predicting the secretory proteins. Firstly, 20 amino acids are divided into five types according to the physical and chemical characteristics of amino acids. Then, we used five types of amino acids compositions as inputs of the modified quadratic discriminant algorithm. Finally, the best prediction performance is obtained by using 20 amino acid compositions, the sensitivity of 96 %, the specificity of 92 % with 0.88 of Mathew's correlation coefficient in fivefold cross-validation test. The results are also compared with those of existing prediction methods. The compared results shown our method are prominent in the prediction of secretory proteins. PMID:26286010

  9. Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching

    NASA Astrophysics Data System (ADS)

    Janssen, Lukas; Herbut, Igor F.

    2015-07-01

    We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions. Within a properly formulated epsilon-expansion this theory is found to have a quantum critical point, which describes the (presumably continuous) transition from the semimetal into a (nematic) Mott insulator. The latter phase breaks the rotational, but not the time-reversal, symmetry and may be relevant to materials such as gray tin or mercury telluride at low temperatures. The critical point represents a simple quantum analog of the familiar classical isotropic-to-nematic transition in liquid crystals. The properties and the consequences of this quantum critical point are discussed. Its existence supports the scenario of the "fixed-point collision," according to which three-dimensional Fermi systems with quadratic band touching and long-range Coulomb interactions are unstable towards the gapped nematic ground state at low temperatures.

  10. Remark on the subtractive renormalization of the quadratically divergent scalar mass

    SciTech Connect

    Fujikawa, Kazuo

    2011-05-15

    The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We reexamine some technical aspects of the subtractive renormalization, in particular, the mass-independent renormalization of massive {lambda}{phi}{sup 4} theory with higher derivative regularization. We then discuss an unconventional scheme to introduce the notion of renormalization point {mu} to the subtractive renormalization in a theory defined by a large fixed cutoff M. The resulting renormalization group equation generally becomes inhomogeneous, but it is transformed to be homogeneous. The renormalized scalar mass consists of two components in this scheme, one with the ordinary anomalous dimension and the other which is proportional to the renormalization scale {mu}. This scheme interpolates between the theory defined by dimensional regularization and the theory with unsubtracted quadratic divergences.

  11. Reconstruction of quadratic curves in 3D using two or more perspective views: simulation studies

    NASA Astrophysics Data System (ADS)

    Kumar, Sanjeev; Sukavanam, N.; Balasubramanian, R.

    2006-01-01

    The shapes of many natural and man-made objects have planar and curvilinear surfaces. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method of reconstruction of a quadratic curve in 3-D space as an intersection of two cones containing the respective projected curve images. The correspondence between this pair of projections of the curve is assumed to be established in this work. Using least-square curve fitting, the parameters of a curve in 2-D space are found. From this we are reconstructing the 3-D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of reconstructed curve are given. The result of the described reconstruction methodology are studied by simulation studies. This reconstruction methodology is applicable to LBW decision in cricket, path of the missile, Robotic Vision, path lanning etc.

  12. KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry

    SciTech Connect

    Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.

    1993-07-01

    This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code`s flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array.

  13. Random vibrations of quadratic damping systems. [optimum damping analysis for automobile suspension system

    NASA Technical Reports Server (NTRS)

    Sireteanu, T.

    1974-01-01

    An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.

  14. A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

    NASA Astrophysics Data System (ADS)

    Mestel, B. D.; Osbaldestin, A. H.

    2004-10-01

    We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

  15. Classification of constraints and degrees of freedom for quadratic discrete actions

    SciTech Connect

    Höhn, Philipp A.

    2014-11-15

    We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph

  16. On the time evolution operator for time-dependent quadratic Hamiltonians

    SciTech Connect

    Fernandez, F. M.

    1989-07-01

    The Schr/umlt o/dinger equation with a time-dependent quadratic Hamiltonian isinvestigated. The time-evolution operator is written as a product of exponentialoperators determined by the Heisenberg equations of motion. This productoperator is shown to be global in the occupation number representation when theHamiltonian is Hermitian. The success of some physical applications of theproduct-form representation is explained.

  17. Interpretation of the power response of a fuel cell with a quadratic logistic differential equation

    SciTech Connect

    Gonzalez, E.R.

    1996-06-01

    The interpretation of the behavior of a fuel cell may be done on the basis of models that require specific assumptions on both the description of the system and the mathematical treatment. This work shows that the power response of a fuel cell can be described by a quadratic logistic differential equation. In this way the interpretation of the dynamical behavior of the system can be done with the general concepts of dissipation, nonlinearity, and feedback.

  18. Tilt measurement and compensation algorithm for holographic data storage with optimized quadratic windows

    NASA Astrophysics Data System (ADS)

    Son, Kyungchan; Lim, Sung-Yong; Lee, Jae-seong; Jeong, Wooyoung; Yang, Hyunseok

    2016-09-01

    In holographic data storage, tilt is one of the critical disturbances. There are two types of tilt: tangential and radial. In real systems, tangential and radial tilt occur simultaneously. Thus, it is difficult to measure and compensate for tilt. In this study, using a quadratic window, which compares the intensity of a certain area, a tilt error signal was generated and compensated for with the proposed algorithm. The compensated image obtained satisfied a 0.3 dB tolerance.

  19. Regularized adelic formulas for string and superstring amplitudes in one-class quadratic fields

    NASA Astrophysics Data System (ADS)

    Vladimirov, V. S.

    2010-09-01

    We obtain regularized adelic formulas for gamma and beta functions for fields of rational numbers and the one-class quadratic fields and arbitrary quasicharacters (ramified or not). We consider applications to four-tachyon tree string amplitudes, generalized Veneziano amplitudes (open string), perturbed Virasoro amplitudes (closed string), massless four-particle tree open and closed superstring amplitudes, Ramond-Neveu-Schwarz superstring amplitudes, and charged heterotic superstring amplitudes. We establish certain relations between different string and superstring amplitudes.

  20. Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

    NASA Technical Reports Server (NTRS)

    Juang, J.-N.; Turner, J. D.; Chun, H. M.

    1984-01-01

    Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

  1. Interval-parameter robust quadratic programming for water quality management under uncertainty

    NASA Astrophysics Data System (ADS)

    Li, Y. P.; Huang, G. H.; Nie, S. L.; Mo, D. W.

    2008-07-01

    Effective planning of water quality management is important for facilitating sustainable socio-economic development in watershed systems. An interval-parameter robust quadratic programming (IRQP) method is developed by incorporating techniques of robust programming and interval quadratic programming within a general optimization framework. The IRQP improves upon existing quadratic programming methods, and can tackle uncertainties presented as interval numbers and fuzzy sets as well as their combinations. Moreover, it can deal with nonlinearities in the objective function such that economies-of-scale effects can be reflected. The developed method is applied to a case study of a water quality management under uncertainty. A number of decision alternatives are generated based on the interval solutions as well as the projected applicable conditions. They represent multiple decision options with various environmental and economic considerations. Willingness to accept a low economic revenue will guarantee satisfying the water quality requirements. A strong desire to acquire a high benefit will run the risk of violating environmental criteria.

  2. Entanglement in a model for Hawking radiation: An application of quadratic algebras

    SciTech Connect

    Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

    2013-03-15

    Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

  3. On Pure Quasi-Quantum Quadratic Operators of 𝕄2(ℂ) II

    NASA Astrophysics Data System (ADS)

    Mukhamedov, Farrukh

    2015-11-01

    In this paper we study quasi quantum quadratic operators (QQO) acting on the algebra of 2×2 matrices 𝕄2(ℂ). We consider two kinds of quasi QQO the corresponding quadratic operator maps from the unit circle into the sphere and from the sphere into the unit circle, respectively. In our early paper we have defined a q-purity of quasi QQO. This notion is equivalent to the invariance of the unit sphere in ℝ3. But to check this condition, in general, is tricky. Therefore, it would be better to find weaker conditions to check the q-purity. One of the main results of this paper is to provide a criterion of q-purity of quasi QQO in terms of the unit circles. Moreover, we are able to classify all possible kinds of quadratic operators which can produce q-pure quasi QQO. We think that such result will allow one to check whether a given mapping is a pure channel or not. This finding suggests us to study such a class of nonpositive mappings. Correspondingly, the complement of this class will be of potential interest for physicist since this set contains all completely positive mappings.

  4. Vagal activity is quadratically related to prosocial traits, prosocial emotions, and observer perceptions of prosociality.

    PubMed

    Kogan, Aleksandr; Oveis, Christopher; Carr, Evan W; Gruber, June; Mauss, Iris B; Shallcross, Amanda; Impett, Emily A; van der Lowe, Ilmo; Hui, Bryant; Cheng, Cecilia; Keltner, Dacher

    2014-12-01

    In the present article, we introduce the quadratic vagal activity-prosociality hypothesis, a theoretical framework for understanding the vagus nerve's involvement in prosociality. We argue that vagus nerve activity supports prosocial behavior by regulating physiological systems that enable emotional expression, empathy for others' mental and emotional states, the regulation of one's own distress, and the experience of positive emotions. However, we contend that extremely high levels of vagal activity can be detrimental to prosociality. We present 3 studies providing support for our model, finding consistent evidence of a quadratic relationship between respiratory sinus arrhythmia--the degree to which the vagus nerve modulates the heart rate--and prosociality. Individual differences in vagal activity were quadratically related to prosocial traits (Study 1), prosocial emotions (Study 2), and outside ratings of prosociality by complete strangers (Study 3). Thus, too much or too little vagal activity appears to be detrimental to prosociality. The present article provides the 1st theoretical and empirical account of the nonlinear relationship between vagal activity and prosociality. PMID:25243414

  5. The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2

    NASA Astrophysics Data System (ADS)

    Yan, Litan; Liu, Junfeng; Chen, Chao

    2014-11-01

    In this paper, we study the generalized quadratic covariation of f(BH) and BH defined by $ [f(BH),BH](H)t:=\\lim_\\varepsilon\\downarrow 0}(1)/(\\varepsilon2H)\\int 0t{f(BHs+\\varepsilon) -f(BHs)}(BHs+\\varepsilon-BH_s)ds2H in probability, where f is a Borel function and BH is a fractional Brownian motion with Hurst index 0 < H < 1/2. We construct a Banach space {H} of measurable functions such that the generalized quadratic covariation exists in L2(Ω) and the Bouleau-Yor identity takes the form [f(BH),BH]t(H)=-\\int_ {R}}f(x){L}H(dx,t) provided f\\in {H}, where {L}^{H}(x, t) is the weighted local time of BH. These are also extended to the time-dependent case, and as an application we give the identity between the generalized quadratic covariation and the 4-covariation [g(BH), BH, BH, BH] when H = 1/4.

  6. Emotion suppression moderates the quadratic association between RSA and executive function

    PubMed Central

    Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby

    2016-01-01

    There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941

  7. An algorithm for the solution of dynamic linear programs

    NASA Technical Reports Server (NTRS)

    Psiaki, Mark L.

    1989-01-01

    The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation

  8. A General Method for Solving Systems of Non-Linear Equations

    NASA Technical Reports Server (NTRS)

    Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)

    1995-01-01

    The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

  9. Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

    PubMed

    Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

    2013-01-01

    Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning. PMID:23576983

  10. Statistical Performance of Cascaded Linear Shift-Invariant Processing

    NASA Astrophysics Data System (ADS)

    Reed, Stuart; Coupland, Jeremy

    2000-11-01

    The cascaded correlator architecture comprises a series of traditional linear correlators separated by nonlinear threshold functions, trained with neural-network techniques. We investigate the shift-invariant classification performance of cascaded correlators in comparison with optimum Bayes classifiers. Inputs are formulated as randomly generated sample members of known statistical class distributions. It is shown that when the separability of true and false classes is varied in both the first and the second orders, the two-stage cascaded correlator shows performance similar to that of the optimum quadratic Bayes classifier throughout the studied range. It is shown that this is due to the similar decision boundaries implemented by the two nonlinear classifiers.

  11. Two linear time, low overhead algorithms for graph layout

    Energy Science and Technology Software Center (ESTSC)

    2008-01-10

    The software comprises two algorithms designed to perform a 2D layout of a graph structure in time linear with respect to the vertices and edges in the graph, whereas most other layout algorithms have a running time that is quadratic with respect to the number of vertices or greater. Although these layout algorithms run in a fraction of the time as their competitors, they provide competitive results when applied to most real-world graphs. These algorithmsmore » also have a low constant running time and small memory footprint, making them useful for small to large graphs.« less

  12. Algebraic methods for the solution of some linear matrix equations

    NASA Technical Reports Server (NTRS)

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

    1979-01-01

    The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

  13. Orthogonal linear group-subgroup pairs with the same invariants

    NASA Astrophysics Data System (ADS)

    Solomon, S.

    2005-03-01

    The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no longer true: There exist counterexample group-subgroup pairs with the same invariants. However, it's possible to classify all these counterexamples for certain types of groups. In [16], we provided the classification for connected complex irreducible groups, and, in this paper, for connected complex orthogonal groups, i.e., groups that preserve some non-degenerate quadratic form.

  14. Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling

    SciTech Connect

    Rodriguez, K.; Argueelles, A.; Colome-Tatche, M.; Vekua, T.; Santos, L.

    2010-07-30

    We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2) x SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Neel order in spin-1/2 gases.

  15. Orbital instability of standing waves for the quadratic-cubic Klein-Gordon-Schrödinger system

    NASA Astrophysics Data System (ADS)

    Natali, Fábio; Pastor, Ademir

    2015-08-01

    We consider the Klein-Gordon-Schrödinger system with quadratic and cubic interactions. Smooth curves of periodic- and solitary-wave solutions are obtained via the implicit function theorem. Orbital instability of such waves is then established.

  16. Quadratic energy-loss straggling and energy widths of the states of slow ions in an electron gas

    SciTech Connect

    Wang, N.

    1997-10-01

    The energy-loss straggling and energy width of states of slow ions interacting with a homogeneous electron gas are evaluated within a quadratic response theory and the random-phase approximation. These results are compared with corresponding results determined from a fully nonlinear scattering theory approach. The quadratic response theory is shown to be a good approximation for high electron densities and small ion charges. {copyright} {ital 1997} {ital The American Physical Society}

  17. A linear programming manual

    NASA Technical Reports Server (NTRS)

    Tuey, R. C.

    1972-01-01

    Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

  18. Linear integrated circuits

    NASA Astrophysics Data System (ADS)

    Young, T.

    This book is intended to be used as a textbook in a one-semester course at a variety of levels. Because of self-study features incorporated, it may also be used by practicing electronic engineers as a formal and thorough introduction to the subject. The distinction between linear and digital integrated circuits is discussed, taking into account digital and linear signal characteristics, linear and digital integrated circuit characteristics, the definitions for linear and digital circuits, applications of digital and linear integrated circuits, aspects of fabrication, packaging, and classification and numbering. Operational amplifiers are considered along with linear integrated circuit (LIC) power requirements and power supplies, voltage and current regulators, linear amplifiers, linear integrated circuit oscillators, wave-shaping circuits, active filters, DA and AD converters, demodulators, comparators, instrument amplifiers, current difference amplifiers, analog circuits and devices, and aspects of troubleshooting.

  19. Eulerian action principles for linearized reduced dynamical equations

    NASA Astrophysics Data System (ADS)

    Brizard, Alain

    1994-08-01

    New Eulerian action principles for the linearized gyrokinetic Maxwell-Vlasov equations and the linearized kinetic-magnetohydrodynamic (kinetic-MHD) equations are presented. The variational fields for the linearized gyrokinetic Vlasov-Maxwell equations are the perturbed electromagnetic potentials (φ1,A1) and the gyroangle-independent gyrocenter (gy) function Sgy, while the variational fields for the linearized kinetic-MHD equations are the ideal MHD fluid displacement ξ and the gyroangle-independent drift-kinetic (dk) function Sdk (defined as the drift-kinetic limit of Sgy). According to the Lie-transform approach to Vlasov perturbation theory, Sgy generates first-order perturbations in the gyrocenter distribution F1≡{Sgy, F0}gc, where F1 satisfies the linearized gyrokinetic Vlasov equation and {, }gc denotes the unperturbed guiding-center (gc) Poisson bracket. Previous quadratic variational forms were constructed ad hoc from the linearized equations, and required the linearized gyrokinetic (or drift-kinetic) Vlasov equation to be solved a priori (e.g., by integration along an unperturbed guiding-center orbit) through the use of the normal-mode and ballooning-mode representations. The presented action principles ignore these requirements and, thus, apply to more general perturbations.

  20. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  1. Thermodynamical first laws of black holes in quadratically-extended gravities

    NASA Astrophysics Data System (ADS)

    Fan, Zhong-Ying; Lü, H.

    2015-03-01

    Einstein gravities in general dimensions coupled to a cosmological constant and extended with quadratic curvature invariants admit a variety of black holes that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We adopt the Wald formalism to derive an explicit formula for calculating the thermodynamical first law for the static black holes with spherical, toric, or hyperbolic isometries in these theories. This allows us to derive or rederive the first laws for a wide range of black holes in the literature. Furthermore, we construct many new exact solutions and obtain their first laws.

  2. Traversable wormholes and non-singular black holes from the vacuum of quadratic gravity

    NASA Astrophysics Data System (ADS)

    Duplessis, Francis; Easson, Damien A.

    2015-08-01

    We present new traversable wormhole and nonsingular black hole solutions in pure, scale-free R2 gravity. These exotic solutions require no null energy condition violating or "exotic" matter and are supported only by the vacuum of the theory. It is well known that f (R ) theories of gravity may be recast as dual theories in the Einstein frame. The solutions we present are found when the conformal transformation required to move to the dual frame is singular. For quadratic R2 gravity, the required conformal factor is identically zero for spacetimes with R =0 . Solutions in this case are argued to arise in the strong coupling limit of general relativity.

  3. Thin-shell wormholes with a double layer in quadratic F (R ) gravity

    NASA Astrophysics Data System (ADS)

    Eiroa, Ernesto F.; Figueroa Aguirre, Griselda

    2016-08-01

    We present a family of spherically symmetric Lorentzian wormholes in quadratic F (R ) gravity, with a thin shell of matter corresponding to the throat. At each side of the shell, the geometry has a different constant value of the curvature scalar R . The junction conditions determine the equation of state between the pressure and energy density at the throat, where a double layer is also located. We analyze the stability of the configurations under perturbations preserving the spherical symmetry. In particular, we study thin-shell wormholes with mass and charge. We find that there exist values of the parameters for which stable static solutions are possible.

  4. Effect of the domain shape on noncollinear second-harmonic emission in disordered quadratic media.

    PubMed

    Ayoub, Mousa; Passlick, Markus; Koynov, Kaloian; Imbrock, Jörg; Denz, Cornelia

    2013-12-16

    We study the role of the individual ferroelectric domain shape on the second-harmonic emission in strontium barium niobate featuring a random quadratic nonlinearity. The noncollinearly emitted second-harmonic signal is scanned in the far-field at different incident angles for different domain size distributions. This offers the possibility to retrieve the Fourier spectrum, corresponding to the spatial domain distribution and domain shape. Based on images of the domain structures retrieved by Čerenkov-type second-harmonic microscopy, domain patterns are simulated, the second-harmonic intensities are calculated, and finally compared with the measurements. PMID:24514720

  5. On the use of the OCM's quadratic objective function as a pilot rating metric

    NASA Technical Reports Server (NTRS)

    Schmidt, D. K.

    1981-01-01

    A correlation between the magnitude of the quadratic objective function from an optimal control pilot model and the subjective rating of the vehicle and task provides a valuable tool for handling qualities research and flight control synthesis. An analysis of simulation results for fourteen aircraft configurations flight tested earlier was conducted. A fixed set of pilot model parameters, are found for all cases in modeling the simulated regulation task. The agreement obtained between performance statistics is shown and a strong correlation was obtained between the cost function and rating.

  6. Computation of p -units in ray class fields of real quadratic number fields

    NASA Astrophysics Data System (ADS)

    Chapdelaine, Hugo

    2009-12-01

    Let K be a real quadratic field, let p be a prime number which is inert in K and let K_p be the completion of K at p . As part of a Ph.D. thesis, we constructed a certain p -adic invariant uin K_p^{times} , and conjectured that u is, in fact, a p -unit in a suitable narrow ray class field of K . In this paper we give numerical evidence in support of that conjecture. Our method of computation is similar to the one developed by Dasgupta and relies on partial modular symbols attached to Eisenstein series.

  7. Quadratic and rate-independent limits for a large-deviations functional

    NASA Astrophysics Data System (ADS)

    Bonaschi, Giovanni A.; Peletier, Mark A.

    2016-07-01

    We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers' law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ` L log L' gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.

  8. Adaptive Doppler separation by quadratic detection of distance-confused radar signals

    NASA Astrophysics Data System (ADS)

    de Reffye, Jerome

    1988-02-01

    Possible improvements in the Doppler radar processing necessary to separate two targets whose distance ranges are confused are considered, with special attention given to the case of the detection of a missile in the presence of an aircraft. Real-time adaptive filtering methods are developed which permit the rejection of harmonics in nonwhite noise. Procedures for the quadratic integration of frequency-modulated signals representing the missile in the acceleration phase are then studied. Finally, the developed techniques are applied to a nonlinear problem.

  9. Coherent anti-Stokes Raman spectroscopy utilizing phase mismatched cascaded quadratic optical interactions in nonlinear crystals

    PubMed Central

    Petrov, Georgi I.; Zhi, Miaochan; Yakovlev, Vladislav V.

    2013-01-01

    We experimentally investigated the nonlinear optical interaction between the instantaneous four-wave mixing and the cascaded quadratic frequency conversion in commonly used nonlinear optical KTP and LiNbO3 with the aim of a possible background suppression of the non-resonant background in coherent anti-Stokes Raman scattering. The possibility of background-free heterodyne coherent anti-Stokes Raman scattering microspectroscopy is investigated at the interface formed by a liquid (isopropyl alcohol) and a nonlinear crystal (LiNbO3). PMID:24514791

  10. Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras

    NASA Technical Reports Server (NTRS)

    Byrnes, C. I.

    1980-01-01

    It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

  11. Two-photon Anderson localization in a disordered quadratic waveguide array

    NASA Astrophysics Data System (ADS)

    Bai, Y. F.; Xu, P.; Lu, L. L.; Zhong, M. L.; Zhu, S. N.

    2016-05-01

    We theoretically investigate two-photon Anderson localization in a χ (2) waveguide array with off-diagonal disorder. The nonlinear parametric down-conversion process would enhance both the single-photon and the two-photon Anderson localization. In the strong disorder regime, the two-photon position correlation exhibits a bunching distribution around the pumped waveguides, which is independent of pumping conditions and geometrical structures of waveguide arrays. Quadratic nonlinearity can be supplied as a new ingredient for Anderson localization. Also, our results pave the way for engineering quantum states through nonlinear quantum walks.

  12. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  13. Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence

    NASA Astrophysics Data System (ADS)

    Fortunati, Alessandro; Wiggins, Stephen

    2014-09-01

    The aim of this paper is to prove a Kolmogorov type result for a nearly integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists in the possibility to choose an arbitrarily small decaying coefficient consistently with the perturbation size. The proof, based on the Lie series formalism, is a generalization of a work by A. Giorgilli.

  14. Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions

    PubMed Central

    Li, Chunhua; Hayashi, Nakao

    2014-01-01

    The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2-dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in n-dimensional space, where n ≥ 2. The existence of scattering operators and finite time blow-up of the solutions for the systems in higher space dimensions is also shown. PMID:25143965

  15. Persistence, Turing Instability and Hopf Bifurcation in a Diffusive Plankton System with Delay and Quadratic Closure

    NASA Astrophysics Data System (ADS)

    Zhao, Jiantao; Wei, Junjie

    A reaction-diffusion plankton system with delay and quadratic closure term is investigated to study the interactions between phytoplankton and zooplankton. Sufficient conditions independent of diffusion and delay are obtained for the persistence of the system. Our conclusions show that diffusion can induce Turing instability, delay can influence the stability of the positive equilibrium and induce Hopf bifurcations to occur. The computational formulas which determine the properties of bifurcating periodic solutions are given by calculating the normal form on the center manifold, and some numerical simulations are carried out for illustrating the theoretical results.

  16. Linear unsaturating magnetoresistance in disordered systems

    NASA Astrophysics Data System (ADS)

    Lai, Ying Tong; Lara, Silvia; Love, Cameron; Ramakrishnan, Navneeth; Adam, Shaffique

    Theoretical works have shown that disordered systems exhibit classical magnetoresistance (MR). In this talk, we examine a variety of experimental systems that observe linear MR at high magnetic fields, including silver chalcogenides, graphene, graphite and Weyl semimetals. We show that a careful analysis of the magnitude of the MR, as well as the field strength at which the MR changes from quadratic to linear, reveal important properties of the system, such as the ratio of the root-mean-square fluctuations in the carrier density and the average carrier density. By looking at other properties such as the zero-field mobility, we show that this carrier density inhomogeneity is consistent with what is known about the microscopic impurities in these experiments. The application of this disorder-induced MR to a variety of different experimental scenarios underline the universality of these theoretical models. This work is supported by the Singapore National Research Foundation (NRF-NRFF2012-01) and the Singapore Ministry of Education and Yale-NUS College through Grant Number R-607-265-01312.

  17. Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents.

    PubMed

    Rotstein, Horacio G

    2015-04-01

    We investigate the biophysical and dynamic mechanisms of generation of subthreshold amplitude and phase resonance in response to sinusoidal input currents in two-dimensional models of quadratic type. These models feature a parabolic voltage nullcline and a linear nullcline for the recovery gating variable, capturing the interplay of the so-called resonant currents (e.g., hyperpolarization-activated mixed-cation inward and slow potassium) and amplifying currents (e.g., persistent sodium) in biophysically realistic parameter regimes. These currents underlie the generation of resonance in medial entorhinal cortex layer II stellate cells and CA1 pyramidal cells. We show that quadratic models exhibit nonlinear amplifications of the voltage response to sinusoidal inputs in the resonant frequency band. These are expressed as an increase in the impedance profile as the input amplitude increases. They are stronger for values positive than negative to resting potential and are accompanied by a shift in the phase profile, a decrease in the resonant and phase-resonant frequencies, and an increase in the sharpness of the voltage response. These effects are more prominent for smaller values of ∊ (larger levels of the time scale separation between the voltage and the resonant gating variable) and for values of the resting potential closer to threshold for spike generation. All other parameter fixed, as ∊ increases the voltage response becomes "more linear"; i.e., the nonlinearities are present, but "ignored". In addition, the nonlinear effects are strongly modulated by the curvature of the parabolic voltage nullcline (partially reflecting the effects of the amplifying current) and the slope of the resonant current activation curve. Following the effects of changes in the biophysical conductances of realistic conductance-based models through the parameters of the quadratic model, we characterize the qualitatively different effects that resonant and amplifying currents have on

  18. Decoding coalescent hidden Markov models in linear time

    PubMed Central

    Harris, Kelley; Sheehan, Sara; Kamm, John A.; Song, Yun S.

    2014-01-01

    In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population. PMID:25340178

  19. Linear and nonlinear optomechanics in a cryogenic membrane-in-the-middle system

    NASA Astrophysics Data System (ADS)

    Lee, Donghun; Underwood, Mitchell; Mason, David; Shkarin, Alexey; Hoch, Scott; Harris, Jack

    2014-03-01

    In cavity optomechanics, linear optomechanical interactions have been used to readout and cool the motion of mechanical oscillators, while nonlinear interactions have been proposed to study quantum non-demolition measurements of mechanical oscillators and the production of non-Gaussian mechanical states. A membrane-in-the-middle system can provide both types of interactions. In this talk, we will present recent results measured in both linear and nonlinear interaction regimes with a membrane-in-the-middle system operating at 500 mK. Linear coupling in this device enables us to cool the mechanical mode of a SiN membrane at 705 kHz to roughly one phonon. During the cooling measurement, we also observed strong asymmetry between the mechanical sidebands, in agreement with the phonon number inferred from other measurements. We also measured nonlinear optomechanics, in particular the quadratic interaction. With a simple theoretical model, we systematically characterized the classical dynamics arising from this quadratic optomechanical interaction. We expect that by combining quadratic coupling with resolved-sideband laser cooling, this device will be able to explore the aforementioned quantum phenomena. We gracefully acknowledge financial support from AFOSR (No. FA9550-90-1-0484).

  20. Characterization of the excited states of a squaraine molecule with quadratic electroabsorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Poga, C.; Brown, T. M.; Kuzyk, M. G.; Dirk, Carl W.

    1995-04-01

    We apply quadratic electroabsorption spectroscopy (QES) to thin-film solid solutions of squarylium dye molecules in poly(methyl methacrylate) polymer to study the dye's electronic excited states and to investigate the importance of these states with regard to their contribution to the third-order nonlinear-optical susceptibility. We first show that the room-temperature tensor ratio a= chi (3)3333/ chi (3)1133 \\approximately 3 throughout most of the visible region to establish that the electronic mechanism dominates. Because QES is a third-order nonlinear-optical susceptibility measurement, it can be used to identify two photon states. By obtaining good agreement between the quadratic electroabsorption spectrum and a three level model, we conclude that there are two dominant states that contribute to the near-resonant and a two-photon state that are separated by less than 0.2 eV in energy. QES is thus shown to be a versatile tool for measuring the nature of excited states in a molecule. Furthermore, by applying a Kramers-Kronig transformation to determine the real part of the response, we are able to assess the two-photon all-optical device figure of merit of these materials. Such an